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------------------------------------------------------------------------
Map identifier: Mp00186
------------------------------------------------------------------------
Map name: dominating partition
------------------------------------------------------------------------
Domain: Skew partitions
------------------------------------------------------------------------
Codomain: Integer partitions
------------------------------------------------------------------------
Description: The dominating partition in the Schur expansion.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a sublattice of the dominance order and that its top element is the conjugate of the partition formed by sorting the column lengths of $\lambda / \mu$ into decreasing order.
This map returns the largest partition $\nu$ in dominance order for which $c^\lambda_{\mu, \nu}$ is positive.
For example,
$$
s_{331/2} = s_{311} + s_{32},
$$
and the partition $32$ dominates $311$.
------------------------------------------------------------------------
References: [1] Azenhas, O. The admissible interval for the invariant factors of a product of matrices [[MathSciNet:1712853]]
------------------------------------------------------------------------
Code:
def mapping(la):
return Partition(sorted(la.column_lengths(), reverse=True)).conjugate()
------------------------------------------------------------------------
Map images:
[[1],[]] => [1]
[[2],[]] => [2]
[[1,1],[]] => [1,1]
[[2,1],[1]] => [2]
[[3],[]] => [3]
[[2,1],[]] => [2,1]
[[3,1],[1]] => [3]
[[2,2],[1]] => [2,1]
[[3,2],[2]] => [3]
[[1,1,1],[]] => [1,1,1]
[[2,2,1],[1,1]] => [2,1]
[[2,1,1],[1]] => [2,1]
[[3,2,1],[2,1]] => [3]
[[4],[]] => [4]
[[3,1],[]] => [3,1]
[[4,1],[1]] => [4]
[[2,2],[]] => [2,2]
[[3,2],[1]] => [3,1]
[[4,2],[2]] => [4]
[[2,1,1],[]] => [2,1,1]
[[3,2,1],[1,1]] => [3,1]
[[3,1,1],[1]] => [3,1]
[[4,2,1],[2,1]] => [4]
[[3,3],[2]] => [3,1]
[[4,3],[3]] => [4]
[[2,2,1],[1]] => [2,2]
[[3,3,1],[2,1]] => [3,1]
[[3,2,1],[2]] => [3,1]
[[4,3,1],[3,1]] => [4]
[[2,2,2],[1,1]] => [2,1,1]
[[3,3,2],[2,2]] => [3,1]
[[3,2,2],[2,1]] => [3,1]
[[4,3,2],[3,2]] => [4]
[[1,1,1,1],[]] => [1,1,1,1]
[[2,2,2,1],[1,1,1]] => [2,1,1]
[[2,2,1,1],[1,1]] => [2,2]
[[3,3,2,1],[2,2,1]] => [3,1]
[[2,1,1,1],[1]] => [2,1,1]
[[3,2,2,1],[2,1,1]] => [3,1]
[[3,2,1,1],[2,1]] => [3,1]
[[4,3,2,1],[3,2,1]] => [4]
[[5],[]] => [5]
[[4,1],[]] => [4,1]
[[5,1],[1]] => [5]
[[3,2],[]] => [3,2]
[[4,2],[1]] => [4,1]
[[5,2],[2]] => [5]
[[3,1,1],[]] => [3,1,1]
[[4,2,1],[1,1]] => [4,1]
[[4,1,1],[1]] => [4,1]
[[5,2,1],[2,1]] => [5]
[[3,3],[1]] => [3,2]
[[4,3],[2]] => [4,1]
[[5,3],[3]] => [5]
[[2,2,1],[]] => [2,2,1]
[[3,3,1],[1,1]] => [3,2]
[[3,2,1],[1]] => [3,2]
[[4,3,1],[2,1]] => [4,1]
[[4,2,1],[2]] => [4,1]
[[5,3,1],[3,1]] => [5]
[[3,2,2],[1,1]] => [3,1,1]
[[4,3,2],[2,2]] => [4,1]
[[4,2,2],[2,1]] => [4,1]
[[5,3,2],[3,2]] => [5]
[[2,1,1,1],[]] => [2,1,1,1]
[[3,2,2,1],[1,1,1]] => [3,1,1]
[[3,2,1,1],[1,1]] => [3,2]
[[4,3,2,1],[2,2,1]] => [4,1]
[[3,1,1,1],[1]] => [3,1,1]
[[4,2,2,1],[2,1,1]] => [4,1]
[[4,2,1,1],[2,1]] => [4,1]
[[5,3,2,1],[3,2,1]] => [5]
[[4,4],[3]] => [4,1]
[[5,4],[4]] => [5]
[[3,3,1],[2]] => [3,2]
[[4,4,1],[3,1]] => [4,1]
[[4,3,1],[3]] => [4,1]
[[5,4,1],[4,1]] => [5]
[[2,2,2],[1]] => [2,2,1]
[[3,3,2],[2,1]] => [3,2]
[[4,4,2],[3,2]] => [4,1]
[[3,2,2],[2]] => [3,2]
[[4,3,2],[3,1]] => [4,1]
[[5,4,2],[4,2]] => [5]
[[2,2,1,1],[1]] => [2,2,1]
[[3,3,2,1],[2,1,1]] => [3,2]
[[3,3,1,1],[2,1]] => [3,2]
[[4,4,2,1],[3,2,1]] => [4,1]
[[3,2,1,1],[2]] => [3,1,1]
[[4,3,2,1],[3,1,1]] => [4,1]
[[4,3,1,1],[3,1]] => [4,1]
[[5,4,2,1],[4,2,1]] => [5]
[[3,3,3],[2,2]] => [3,1,1]
[[4,4,3],[3,3]] => [4,1]
[[4,3,3],[3,2]] => [4,1]
[[5,4,3],[4,3]] => [5]
[[2,2,2,1],[1,1]] => [2,2,1]
[[3,3,3,1],[2,2,1]] => [3,1,1]
[[3,3,2,1],[2,2]] => [3,2]
[[4,4,3,1],[3,3,1]] => [4,1]
[[3,2,2,1],[2,1]] => [3,2]
[[4,3,3,1],[3,2,1]] => [4,1]
[[4,3,2,1],[3,2]] => [4,1]
[[5,4,3,1],[4,3,1]] => [5]
[[2,2,2,2],[1,1,1]] => [2,1,1,1]
[[3,3,3,2],[2,2,2]] => [3,1,1]
[[3,3,2,2],[2,2,1]] => [3,2]
[[4,4,3,2],[3,3,2]] => [4,1]
[[3,2,2,2],[2,1,1]] => [3,1,1]
[[4,3,3,2],[3,2,2]] => [4,1]
[[4,3,2,2],[3,2,1]] => [4,1]
[[5,4,3,2],[4,3,2]] => [5]
[[1,1,1,1,1],[]] => [1,1,1,1,1]
[[2,2,2,2,1],[1,1,1,1]] => [2,1,1,1]
[[2,2,2,1,1],[1,1,1]] => [2,2,1]
[[3,3,3,2,1],[2,2,2,1]] => [3,1,1]
[[2,2,1,1,1],[1,1]] => [2,2,1]
[[3,3,2,2,1],[2,2,1,1]] => [3,2]
[[3,3,2,1,1],[2,2,1]] => [3,2]
[[4,4,3,2,1],[3,3,2,1]] => [4,1]
[[2,1,1,1,1],[1]] => [2,1,1,1]
[[3,2,2,2,1],[2,1,1,1]] => [3,1,1]
[[3,2,2,1,1],[2,1,1]] => [3,2]
[[4,3,3,2,1],[3,2,2,1]] => [4,1]
[[3,2,1,1,1],[2,1]] => [3,1,1]
[[4,3,2,2,1],[3,2,1,1]] => [4,1]
[[4,3,2,1,1],[3,2,1]] => [4,1]
[[5,4,3,2,1],[4,3,2,1]] => [5]
[[6],[]] => [6]
[[5,1],[]] => [5,1]
[[6,1],[1]] => [6]
[[4,2],[]] => [4,2]
[[5,2],[1]] => [5,1]
[[6,2],[2]] => [6]
[[4,1,1],[]] => [4,1,1]
[[5,2,1],[1,1]] => [5,1]
[[5,1,1],[1]] => [5,1]
[[6,2,1],[2,1]] => [6]
[[3,3],[]] => [3,3]
[[4,3],[1]] => [4,2]
[[5,3],[2]] => [5,1]
[[6,3],[3]] => [6]
[[3,2,1],[]] => [3,2,1]
[[4,3,1],[1,1]] => [4,2]
[[4,2,1],[1]] => [4,2]
[[5,3,1],[2,1]] => [5,1]
[[5,2,1],[2]] => [5,1]
[[6,3,1],[3,1]] => [6]
[[4,2,2],[1,1]] => [4,1,1]
[[5,3,2],[2,2]] => [5,1]
[[5,2,2],[2,1]] => [5,1]
[[6,3,2],[3,2]] => [6]
[[3,1,1,1],[]] => [3,1,1,1]
[[4,2,2,1],[1,1,1]] => [4,1,1]
[[4,2,1,1],[1,1]] => [4,2]
[[5,3,2,1],[2,2,1]] => [5,1]
[[4,1,1,1],[1]] => [4,1,1]
[[5,2,2,1],[2,1,1]] => [5,1]
[[5,2,1,1],[2,1]] => [5,1]
[[6,3,2,1],[3,2,1]] => [6]
[[4,4],[2]] => [4,2]
[[5,4],[3]] => [5,1]
[[6,4],[4]] => [6]
[[3,3,1],[1]] => [3,3]
[[4,4,1],[2,1]] => [4,2]
[[4,3,1],[2]] => [4,2]
[[5,4,1],[3,1]] => [5,1]
[[5,3,1],[3]] => [5,1]
[[6,4,1],[4,1]] => [6]
[[2,2,2],[]] => [2,2,2]
[[3,3,2],[1,1]] => [3,2,1]
[[4,4,2],[2,2]] => [4,2]
[[3,2,2],[1]] => [3,2,1]
[[4,3,2],[2,1]] => [4,2]
[[5,4,2],[3,2]] => [5,1]
[[4,2,2],[2]] => [4,2]
[[5,3,2],[3,1]] => [5,1]
[[6,4,2],[4,2]] => [6]
[[2,2,1,1],[]] => [2,2,1,1]
[[3,3,2,1],[1,1,1]] => [3,2,1]
[[3,3,1,1],[1,1]] => [3,3]
[[4,4,2,1],[2,2,1]] => [4,2]
[[3,2,1,1],[1]] => [3,2,1]
[[4,3,2,1],[2,1,1]] => [4,2]
[[4,3,1,1],[2,1]] => [4,2]
[[5,4,2,1],[3,2,1]] => [5,1]
[[4,2,1,1],[2]] => [4,1,1]
[[5,3,2,1],[3,1,1]] => [5,1]
[[5,3,1,1],[3,1]] => [5,1]
[[6,4,2,1],[4,2,1]] => [6]
[[4,3,3],[2,2]] => [4,1,1]
[[5,4,3],[3,3]] => [5,1]
[[5,3,3],[3,2]] => [5,1]
[[6,4,3],[4,3]] => [6]
[[3,2,2,1],[1,1]] => [3,2,1]
[[4,3,3,1],[2,2,1]] => [4,1,1]
[[4,3,2,1],[2,2]] => [4,2]
[[5,4,3,1],[3,3,1]] => [5,1]
[[4,2,2,1],[2,1]] => [4,2]
[[5,3,3,1],[3,2,1]] => [5,1]
[[5,3,2,1],[3,2]] => [5,1]
[[6,4,3,1],[4,3,1]] => [6]
[[3,2,2,2],[1,1,1]] => [3,1,1,1]
[[4,3,3,2],[2,2,2]] => [4,1,1]
[[4,3,2,2],[2,2,1]] => [4,2]
[[5,4,3,2],[3,3,2]] => [5,1]
[[4,2,2,2],[2,1,1]] => [4,1,1]
[[5,3,3,2],[3,2,2]] => [5,1]
[[5,3,2,2],[3,2,1]] => [5,1]
[[6,4,3,2],[4,3,2]] => [6]
[[2,1,1,1,1],[]] => [2,1,1,1,1]
[[3,2,2,2,1],[1,1,1,1]] => [3,1,1,1]
[[3,2,2,1,1],[1,1,1]] => [3,2,1]
[[4,3,3,2,1],[2,2,2,1]] => [4,1,1]
[[3,2,1,1,1],[1,1]] => [3,2,1]
[[4,3,2,2,1],[2,2,1,1]] => [4,2]
[[4,3,2,1,1],[2,2,1]] => [4,2]
[[5,4,3,2,1],[3,3,2,1]] => [5,1]
[[3,1,1,1,1],[1]] => [3,1,1,1]
[[4,2,2,2,1],[2,1,1,1]] => [4,1,1]
[[4,2,2,1,1],[2,1,1]] => [4,2]
[[5,3,3,2,1],[3,2,2,1]] => [5,1]
[[4,2,1,1,1],[2,1]] => [4,1,1]
[[5,3,2,2,1],[3,2,1,1]] => [5,1]
[[5,3,2,1,1],[3,2,1]] => [5,1]
[[6,4,3,2,1],[4,3,2,1]] => [6]
[[5,5],[4]] => [5,1]
[[6,5],[5]] => [6]
[[4,4,1],[3]] => [4,2]
[[5,5,1],[4,1]] => [5,1]
[[5,4,1],[4]] => [5,1]
[[6,5,1],[5,1]] => [6]
[[3,3,2],[2]] => [3,3]
[[4,4,2],[3,1]] => [4,2]
[[5,5,2],[4,2]] => [5,1]
[[4,3,2],[3]] => [4,2]
[[5,4,2],[4,1]] => [5,1]
[[6,5,2],[5,2]] => [6]
[[3,3,1,1],[2]] => [3,2,1]
[[4,4,2,1],[3,1,1]] => [4,2]
[[4,4,1,1],[3,1]] => [4,2]
[[5,5,2,1],[4,2,1]] => [5,1]
[[4,3,1,1],[3]] => [4,1,1]
[[5,4,2,1],[4,1,1]] => [5,1]
[[5,4,1,1],[4,1]] => [5,1]
[[6,5,2,1],[5,2,1]] => [6]
[[3,3,3],[2,1]] => [3,2,1]
[[4,4,3],[3,2]] => [4,2]
[[5,5,3],[4,3]] => [5,1]
[[4,3,3],[3,1]] => [4,2]
[[5,4,3],[4,2]] => [5,1]
[[6,5,3],[5,3]] => [6]
[[2,2,2,1],[1]] => [2,2,2]
[[3,3,3,1],[2,1,1]] => [3,2,1]
[[3,3,2,1],[2,1]] => [3,3]
[[4,4,3,1],[3,2,1]] => [4,2]
[[4,4,2,1],[3,2]] => [4,2]
[[5,5,3,1],[4,3,1]] => [5,1]
[[3,2,2,1],[2]] => [3,2,1]
[[4,3,3,1],[3,1,1]] => [4,2]
[[4,3,2,1],[3,1]] => [4,2]
[[5,4,3,1],[4,2,1]] => [5,1]
[[5,4,2,1],[4,2]] => [5,1]
[[6,5,3,1],[5,3,1]] => [6]
[[3,3,2,2],[2,1,1]] => [3,2,1]
[[4,4,3,2],[3,2,2]] => [4,2]
[[4,4,2,2],[3,2,1]] => [4,2]
[[5,5,3,2],[4,3,2]] => [5,1]
[[4,3,2,2],[3,1,1]] => [4,1,1]
[[5,4,3,2],[4,2,2]] => [5,1]
[[5,4,2,2],[4,2,1]] => [5,1]
[[6,5,3,2],[5,3,2]] => [6]
[[2,2,1,1,1],[1]] => [2,2,1,1]
[[3,3,2,2,1],[2,1,1,1]] => [3,2,1]
[[3,3,2,1,1],[2,1,1]] => [3,3]
[[4,4,3,2,1],[3,2,2,1]] => [4,2]
[[3,3,1,1,1],[2,1]] => [3,2,1]
[[4,4,2,2,1],[3,2,1,1]] => [4,2]
[[4,4,2,1,1],[3,2,1]] => [4,2]
[[5,5,3,2,1],[4,3,2,1]] => [5,1]
[[3,2,1,1,1],[2]] => [3,1,1,1]
[[4,3,2,2,1],[3,1,1,1]] => [4,1,1]
[[4,3,2,1,1],[3,1,1]] => [4,2]
[[5,4,3,2,1],[4,2,2,1]] => [5,1]
[[4,3,1,1,1],[3,1]] => [4,1,1]
[[5,4,2,2,1],[4,2,1,1]] => [5,1]
[[5,4,2,1,1],[4,2,1]] => [5,1]
[[6,5,3,2,1],[5,3,2,1]] => [6]
[[4,4,4],[3,3]] => [4,1,1]
[[5,5,4],[4,4]] => [5,1]
[[5,4,4],[4,3]] => [5,1]
[[6,5,4],[5,4]] => [6]
[[3,3,3,1],[2,2]] => [3,2,1]
[[4,4,4,1],[3,3,1]] => [4,1,1]
[[4,4,3,1],[3,3]] => [4,2]
[[5,5,4,1],[4,4,1]] => [5,1]
[[4,3,3,1],[3,2]] => [4,2]
[[5,4,4,1],[4,3,1]] => [5,1]
[[5,4,3,1],[4,3]] => [5,1]
[[6,5,4,1],[5,4,1]] => [6]
[[2,2,2,2],[1,1]] => [2,2,1,1]
[[3,3,3,2],[2,2,1]] => [3,2,1]
[[4,4,4,2],[3,3,2]] => [4,1,1]
[[3,3,2,2],[2,2]] => [3,3]
[[4,4,3,2],[3,3,1]] => [4,2]
[[5,5,4,2],[4,4,2]] => [5,1]
[[3,2,2,2],[2,1]] => [3,2,1]
[[4,3,3,2],[3,2,1]] => [4,2]
[[5,4,4,2],[4,3,2]] => [5,1]
[[4,3,2,2],[3,2]] => [4,2]
[[5,4,3,2],[4,3,1]] => [5,1]
[[6,5,4,2],[5,4,2]] => [6]
[[2,2,2,1,1],[1,1]] => [2,2,2]
[[3,3,3,2,1],[2,2,1,1]] => [3,2,1]
[[3,3,3,1,1],[2,2,1]] => [3,2,1]
[[4,4,4,2,1],[3,3,2,1]] => [4,1,1]
[[3,3,2,1,1],[2,2]] => [3,2,1]
[[4,4,3,2,1],[3,3,1,1]] => [4,2]
[[4,4,3,1,1],[3,3,1]] => [4,2]
[[5,5,4,2,1],[4,4,2,1]] => [5,1]
[[3,2,2,1,1],[2,1]] => [3,2,1]
[[4,3,3,2,1],[3,2,1,1]] => [4,2]
[[4,3,3,1,1],[3,2,1]] => [4,2]
[[5,4,4,2,1],[4,3,2,1]] => [5,1]
[[4,3,2,1,1],[3,2]] => [4,1,1]
[[5,4,3,2,1],[4,3,1,1]] => [5,1]
[[5,4,3,1,1],[4,3,1]] => [5,1]
[[6,5,4,2,1],[5,4,2,1]] => [6]
[[3,3,3,3],[2,2,2]] => [3,1,1,1]
[[4,4,4,3],[3,3,3]] => [4,1,1]
[[4,4,3,3],[3,3,2]] => [4,2]
[[5,5,4,3],[4,4,3]] => [5,1]
[[4,3,3,3],[3,2,2]] => [4,1,1]
[[5,4,4,3],[4,3,3]] => [5,1]
[[5,4,3,3],[4,3,2]] => [5,1]
[[6,5,4,3],[5,4,3]] => [6]
[[2,2,2,2,1],[1,1,1]] => [2,2,1,1]
[[3,3,3,3,1],[2,2,2,1]] => [3,1,1,1]
[[3,3,3,2,1],[2,2,2]] => [3,2,1]
[[4,4,4,3,1],[3,3,3,1]] => [4,1,1]
[[3,3,2,2,1],[2,2,1]] => [3,3]
[[4,4,3,3,1],[3,3,2,1]] => [4,2]
[[4,4,3,2,1],[3,3,2]] => [4,2]
[[5,5,4,3,1],[4,4,3,1]] => [5,1]
[[3,2,2,2,1],[2,1,1]] => [3,2,1]
[[4,3,3,3,1],[3,2,2,1]] => [4,1,1]
[[4,3,3,2,1],[3,2,2]] => [4,2]
[[5,4,4,3,1],[4,3,3,1]] => [5,1]
[[4,3,2,2,1],[3,2,1]] => [4,2]
[[5,4,3,3,1],[4,3,2,1]] => [5,1]
[[5,4,3,2,1],[4,3,2]] => [5,1]
[[6,5,4,3,1],[5,4,3,1]] => [6]
[[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]
[[3,3,3,2,2],[2,2,2,1]] => [3,2,1]
[[4,4,4,3,2],[3,3,3,2]] => [4,1,1]
[[3,3,2,2,2],[2,2,1,1]] => [3,2,1]
[[4,4,3,3,2],[3,3,2,2]] => [4,2]
[[4,4,3,2,2],[3,3,2,1]] => [4,2]
[[5,5,4,3,2],[4,4,3,2]] => [5,1]
[[3,2,2,2,2],[2,1,1,1]] => [3,1,1,1]
[[4,3,3,3,2],[3,2,2,2]] => [4,1,1]
[[4,3,3,2,2],[3,2,2,1]] => [4,2]
[[5,4,4,3,2],[4,3,3,2]] => [5,1]
[[4,3,2,2,2],[3,2,1,1]] => [4,1,1]
[[5,4,3,3,2],[4,3,2,2]] => [5,1]
[[5,4,3,2,2],[4,3,2,1]] => [5,1]
[[6,5,4,3,2],[5,4,3,2]] => [6]
[[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]
[[2,2,2,2,1,1],[1,1,1,1]] => [2,2,1,1]
[[3,3,3,3,2,1],[2,2,2,2,1]] => [3,1,1,1]
[[2,2,2,1,1,1],[1,1,1]] => [2,2,2]
[[3,3,3,2,2,1],[2,2,2,1,1]] => [3,2,1]
[[3,3,3,2,1,1],[2,2,2,1]] => [3,2,1]
[[4,4,4,3,2,1],[3,3,3,2,1]] => [4,1,1]
[[2,2,1,1,1,1],[1,1]] => [2,2,1,1]
[[3,3,2,2,2,1],[2,2,1,1,1]] => [3,2,1]
[[3,3,2,2,1,1],[2,2,1,1]] => [3,3]
[[4,4,3,3,2,1],[3,3,2,2,1]] => [4,2]
[[3,3,2,1,1,1],[2,2,1]] => [3,2,1]
[[4,4,3,2,2,1],[3,3,2,1,1]] => [4,2]
[[4,4,3,2,1,1],[3,3,2,1]] => [4,2]
[[5,5,4,3,2,1],[4,4,3,2,1]] => [5,1]
[[2,1,1,1,1,1],[1]] => [2,1,1,1,1]
[[3,2,2,2,2,1],[2,1,1,1,1]] => [3,1,1,1]
[[3,2,2,2,1,1],[2,1,1,1]] => [3,2,1]
[[4,3,3,3,2,1],[3,2,2,2,1]] => [4,1,1]
[[3,2,2,1,1,1],[2,1,1]] => [3,2,1]
[[4,3,3,2,2,1],[3,2,2,1,1]] => [4,2]
[[4,3,3,2,1,1],[3,2,2,1]] => [4,2]
[[5,4,4,3,2,1],[4,3,3,2,1]] => [5,1]
[[3,2,1,1,1,1],[2,1]] => [3,1,1,1]
[[4,3,2,2,2,1],[3,2,1,1,1]] => [4,1,1]
[[4,3,2,2,1,1],[3,2,1,1]] => [4,2]
[[5,4,3,3,2,1],[4,3,2,2,1]] => [5,1]
[[4,3,2,1,1,1],[3,2,1]] => [4,1,1]
[[5,4,3,2,2,1],[4,3,2,1,1]] => [5,1]
[[5,4,3,2,1,1],[4,3,2,1]] => [5,1]
[[6,5,4,3,2,1],[5,4,3,2,1]] => [6]
[[7],[]] => [7]
[[6,1],[]] => [6,1]
[[7,1],[1]] => [7]
[[5,2],[]] => [5,2]
[[6,2],[1]] => [6,1]
[[7,2],[2]] => [7]
[[5,1,1],[]] => [5,1,1]
[[6,2,1],[1,1]] => [6,1]
[[6,1,1],[1]] => [6,1]
[[7,2,1],[2,1]] => [7]
[[4,3],[]] => [4,3]
[[5,3],[1]] => [5,2]
[[6,3],[2]] => [6,1]
[[7,3],[3]] => [7]
[[4,2,1],[]] => [4,2,1]
[[5,3,1],[1,1]] => [5,2]
[[5,2,1],[1]] => [5,2]
[[6,3,1],[2,1]] => [6,1]
[[6,2,1],[2]] => [6,1]
[[7,3,1],[3,1]] => [7]
[[5,2,2],[1,1]] => [5,1,1]
[[6,3,2],[2,2]] => [6,1]
[[6,2,2],[2,1]] => [6,1]
[[7,3,2],[3,2]] => [7]
[[4,1,1,1],[]] => [4,1,1,1]
[[5,2,2,1],[1,1,1]] => [5,1,1]
[[5,2,1,1],[1,1]] => [5,2]
[[6,3,2,1],[2,2,1]] => [6,1]
[[5,1,1,1],[1]] => [5,1,1]
[[6,2,2,1],[2,1,1]] => [6,1]
[[6,2,1,1],[2,1]] => [6,1]
[[7,3,2,1],[3,2,1]] => [7]
[[4,4],[1]] => [4,3]
[[5,4],[2]] => [5,2]
[[6,4],[3]] => [6,1]
[[7,4],[4]] => [7]
[[3,3,1],[]] => [3,3,1]
[[4,4,1],[1,1]] => [4,3]
[[4,3,1],[1]] => [4,3]
[[5,4,1],[2,1]] => [5,2]
[[5,3,1],[2]] => [5,2]
[[6,4,1],[3,1]] => [6,1]
[[6,3,1],[3]] => [6,1]
[[7,4,1],[4,1]] => [7]
[[3,2,2],[]] => [3,2,2]
[[4,3,2],[1,1]] => [4,2,1]
[[5,4,2],[2,2]] => [5,2]
[[4,2,2],[1]] => [4,2,1]
[[5,3,2],[2,1]] => [5,2]
[[6,4,2],[3,2]] => [6,1]
[[5,2,2],[2]] => [5,2]
[[6,3,2],[3,1]] => [6,1]
[[7,4,2],[4,2]] => [7]
[[3,2,1,1],[]] => [3,2,1,1]
[[4,3,2,1],[1,1,1]] => [4,2,1]
[[4,3,1,1],[1,1]] => [4,3]
[[5,4,2,1],[2,2,1]] => [5,2]
[[4,2,1,1],[1]] => [4,2,1]
[[5,3,2,1],[2,1,1]] => [5,2]
[[5,3,1,1],[2,1]] => [5,2]
[[6,4,2,1],[3,2,1]] => [6,1]
[[5,2,1,1],[2]] => [5,1,1]
[[6,3,2,1],[3,1,1]] => [6,1]
[[6,3,1,1],[3,1]] => [6,1]
[[7,4,2,1],[4,2,1]] => [7]
[[5,3,3],[2,2]] => [5,1,1]
[[6,4,3],[3,3]] => [6,1]
[[6,3,3],[3,2]] => [6,1]
[[7,4,3],[4,3]] => [7]
[[4,2,2,1],[1,1]] => [4,2,1]
[[5,3,3,1],[2,2,1]] => [5,1,1]
[[5,3,2,1],[2,2]] => [5,2]
[[6,4,3,1],[3,3,1]] => [6,1]
[[5,2,2,1],[2,1]] => [5,2]
[[6,3,3,1],[3,2,1]] => [6,1]
[[6,3,2,1],[3,2]] => [6,1]
[[7,4,3,1],[4,3,1]] => [7]
[[4,2,2,2],[1,1,1]] => [4,1,1,1]
[[5,3,3,2],[2,2,2]] => [5,1,1]
[[5,3,2,2],[2,2,1]] => [5,2]
[[6,4,3,2],[3,3,2]] => [6,1]
[[5,2,2,2],[2,1,1]] => [5,1,1]
[[6,3,3,2],[3,2,2]] => [6,1]
[[6,3,2,2],[3,2,1]] => [6,1]
[[7,4,3,2],[4,3,2]] => [7]
[[3,1,1,1,1],[]] => [3,1,1,1,1]
[[4,2,2,2,1],[1,1,1,1]] => [4,1,1,1]
[[4,2,2,1,1],[1,1,1]] => [4,2,1]
[[5,3,3,2,1],[2,2,2,1]] => [5,1,1]
[[4,2,1,1,1],[1,1]] => [4,2,1]
[[5,3,2,2,1],[2,2,1,1]] => [5,2]
[[5,3,2,1,1],[2,2,1]] => [5,2]
[[6,4,3,2,1],[3,3,2,1]] => [6,1]
[[4,1,1,1,1],[1]] => [4,1,1,1]
[[5,2,2,2,1],[2,1,1,1]] => [5,1,1]
[[5,2,2,1,1],[2,1,1]] => [5,2]
[[6,3,3,2,1],[3,2,2,1]] => [6,1]
[[5,2,1,1,1],[2,1]] => [5,1,1]
[[6,3,2,2,1],[3,2,1,1]] => [6,1]
[[6,3,2,1,1],[3,2,1]] => [6,1]
[[7,4,3,2,1],[4,3,2,1]] => [7]
[[5,5],[3]] => [5,2]
[[6,5],[4]] => [6,1]
[[7,5],[5]] => [7]
[[4,4,1],[2]] => [4,3]
[[5,5,1],[3,1]] => [5,2]
[[5,4,1],[3]] => [5,2]
[[6,5,1],[4,1]] => [6,1]
[[6,4,1],[4]] => [6,1]
[[7,5,1],[5,1]] => [7]
[[3,3,2],[1]] => [3,3,1]
[[4,4,2],[2,1]] => [4,3]
[[5,5,2],[3,2]] => [5,2]
[[4,3,2],[2]] => [4,3]
[[5,4,2],[3,1]] => [5,2]
[[6,5,2],[4,2]] => [6,1]
[[5,3,2],[3]] => [5,2]
[[6,4,2],[4,1]] => [6,1]
[[7,5,2],[5,2]] => [7]
[[3,3,1,1],[1]] => [3,3,1]
[[4,4,2,1],[2,1,1]] => [4,3]
[[4,4,1,1],[2,1]] => [4,3]
[[5,5,2,1],[3,2,1]] => [5,2]
[[4,3,1,1],[2]] => [4,2,1]
[[5,4,2,1],[3,1,1]] => [5,2]
[[5,4,1,1],[3,1]] => [5,2]
[[6,5,2,1],[4,2,1]] => [6,1]
[[5,3,1,1],[3]] => [5,1,1]
[[6,4,2,1],[4,1,1]] => [6,1]
[[6,4,1,1],[4,1]] => [6,1]
[[7,5,2,1],[5,2,1]] => [7]
[[3,3,3],[1,1]] => [3,2,2]
[[4,4,3],[2,2]] => [4,2,1]
[[5,5,3],[3,3]] => [5,2]
[[4,3,3],[2,1]] => [4,2,1]
[[5,4,3],[3,2]] => [5,2]
[[6,5,3],[4,3]] => [6,1]
[[5,3,3],[3,1]] => [5,2]
[[6,4,3],[4,2]] => [6,1]
[[7,5,3],[5,3]] => [7]
[[2,2,2,1],[]] => [2,2,2,1]
[[3,3,3,1],[1,1,1]] => [3,2,2]
[[3,3,2,1],[1,1]] => [3,3,1]
[[4,4,3,1],[2,2,1]] => [4,2,1]
[[4,4,2,1],[2,2]] => [4,3]
[[5,5,3,1],[3,3,1]] => [5,2]
[[3,2,2,1],[1]] => [3,2,2]
[[4,3,3,1],[2,1,1]] => [4,2,1]
[[4,3,2,1],[2,1]] => [4,3]
[[5,4,3,1],[3,2,1]] => [5,2]
[[5,4,2,1],[3,2]] => [5,2]
[[6,5,3,1],[4,3,1]] => [6,1]
[[4,2,2,1],[2]] => [4,2,1]
[[5,3,3,1],[3,1,1]] => [5,2]
[[5,3,2,1],[3,1]] => [5,2]
[[6,4,3,1],[4,2,1]] => [6,1]
[[6,4,2,1],[4,2]] => [6,1]
[[7,5,3,1],[5,3,1]] => [7]
[[3,3,2,2],[1,1,1]] => [3,2,1,1]
[[4,4,3,2],[2,2,2]] => [4,2,1]
[[4,4,2,2],[2,2,1]] => [4,3]
[[5,5,3,2],[3,3,2]] => [5,2]
[[4,3,2,2],[2,1,1]] => [4,2,1]
[[5,4,3,2],[3,2,2]] => [5,2]
[[5,4,2,2],[3,2,1]] => [5,2]
[[6,5,3,2],[4,3,2]] => [6,1]
[[5,3,2,2],[3,1,1]] => [5,1,1]
[[6,4,3,2],[4,2,2]] => [6,1]
[[6,4,2,2],[4,2,1]] => [6,1]
[[7,5,3,2],[5,3,2]] => [7]
[[2,2,1,1,1],[]] => [2,2,1,1,1]
[[3,3,2,2,1],[1,1,1,1]] => [3,2,1,1]
[[3,3,2,1,1],[1,1,1]] => [3,3,1]
[[4,4,3,2,1],[2,2,2,1]] => [4,2,1]
[[3,3,1,1,1],[1,1]] => [3,3,1]
[[4,4,2,2,1],[2,2,1,1]] => [4,3]
[[4,4,2,1,1],[2,2,1]] => [4,3]
[[5,5,3,2,1],[3,3,2,1]] => [5,2]
[[3,2,1,1,1],[1]] => [3,2,1,1]
[[4,3,2,2,1],[2,1,1,1]] => [4,2,1]
[[4,3,2,1,1],[2,1,1]] => [4,3]
[[5,4,3,2,1],[3,2,2,1]] => [5,2]
[[4,3,1,1,1],[2,1]] => [4,2,1]
[[5,4,2,2,1],[3,2,1,1]] => [5,2]
[[5,4,2,1,1],[3,2,1]] => [5,2]
[[6,5,3,2,1],[4,3,2,1]] => [6,1]
[[4,2,1,1,1],[2]] => [4,1,1,1]
[[5,3,2,2,1],[3,1,1,1]] => [5,1,1]
[[5,3,2,1,1],[3,1,1]] => [5,2]
[[6,4,3,2,1],[4,2,2,1]] => [6,1]
[[5,3,1,1,1],[3,1]] => [5,1,1]
[[6,4,2,2,1],[4,2,1,1]] => [6,1]
[[6,4,2,1,1],[4,2,1]] => [6,1]
[[7,5,3,2,1],[5,3,2,1]] => [7]
[[5,4,4],[3,3]] => [5,1,1]
[[6,5,4],[4,4]] => [6,1]
[[6,4,4],[4,3]] => [6,1]
[[7,5,4],[5,4]] => [7]
[[4,3,3,1],[2,2]] => [4,2,1]
[[5,4,4,1],[3,3,1]] => [5,1,1]
[[5,4,3,1],[3,3]] => [5,2]
[[6,5,4,1],[4,4,1]] => [6,1]
[[5,3,3,1],[3,2]] => [5,2]
[[6,4,4,1],[4,3,1]] => [6,1]
[[6,4,3,1],[4,3]] => [6,1]
[[7,5,4,1],[5,4,1]] => [7]
[[3,2,2,2],[1,1]] => [3,2,1,1]
[[4,3,3,2],[2,2,1]] => [4,2,1]
[[5,4,4,2],[3,3,2]] => [5,1,1]
[[4,3,2,2],[2,2]] => [4,3]
[[5,4,3,2],[3,3,1]] => [5,2]
[[6,5,4,2],[4,4,2]] => [6,1]
[[4,2,2,2],[2,1]] => [4,2,1]
[[5,3,3,2],[3,2,1]] => [5,2]
[[6,4,4,2],[4,3,2]] => [6,1]
[[5,3,2,2],[3,2]] => [5,2]
[[6,4,3,2],[4,3,1]] => [6,1]
[[7,5,4,2],[5,4,2]] => [7]
[[3,2,2,1,1],[1,1]] => [3,2,2]
[[4,3,3,2,1],[2,2,1,1]] => [4,2,1]
[[4,3,3,1,1],[2,2,1]] => [4,2,1]
[[5,4,4,2,1],[3,3,2,1]] => [5,1,1]
[[4,3,2,1,1],[2,2]] => [4,2,1]
[[5,4,3,2,1],[3,3,1,1]] => [5,2]
[[5,4,3,1,1],[3,3,1]] => [5,2]
[[6,5,4,2,1],[4,4,2,1]] => [6,1]
[[4,2,2,1,1],[2,1]] => [4,2,1]
[[5,3,3,2,1],[3,2,1,1]] => [5,2]
[[5,3,3,1,1],[3,2,1]] => [5,2]
[[6,4,4,2,1],[4,3,2,1]] => [6,1]
[[5,3,2,1,1],[3,2]] => [5,1,1]
[[6,4,3,2,1],[4,3,1,1]] => [6,1]
[[6,4,3,1,1],[4,3,1]] => [6,1]
[[7,5,4,2,1],[5,4,2,1]] => [7]
[[4,3,3,3],[2,2,2]] => [4,1,1,1]
[[5,4,4,3],[3,3,3]] => [5,1,1]
[[5,4,3,3],[3,3,2]] => [5,2]
[[6,5,4,3],[4,4,3]] => [6,1]
[[5,3,3,3],[3,2,2]] => [5,1,1]
[[6,4,4,3],[4,3,3]] => [6,1]
[[6,4,3,3],[4,3,2]] => [6,1]
[[7,5,4,3],[5,4,3]] => [7]
[[3,2,2,2,1],[1,1,1]] => [3,2,1,1]
[[4,3,3,3,1],[2,2,2,1]] => [4,1,1,1]
[[4,3,3,2,1],[2,2,2]] => [4,2,1]
[[5,4,4,3,1],[3,3,3,1]] => [5,1,1]
[[4,3,2,2,1],[2,2,1]] => [4,3]
[[5,4,3,3,1],[3,3,2,1]] => [5,2]
[[5,4,3,2,1],[3,3,2]] => [5,2]
[[6,5,4,3,1],[4,4,3,1]] => [6,1]
[[4,2,2,2,1],[2,1,1]] => [4,2,1]
[[5,3,3,3,1],[3,2,2,1]] => [5,1,1]
[[5,3,3,2,1],[3,2,2]] => [5,2]
[[6,4,4,3,1],[4,3,3,1]] => [6,1]
[[5,3,2,2,1],[3,2,1]] => [5,2]
[[6,4,3,3,1],[4,3,2,1]] => [6,1]
[[6,4,3,2,1],[4,3,2]] => [6,1]
[[7,5,4,3,1],[5,4,3,1]] => [7]
[[3,2,2,2,2],[1,1,1,1]] => [3,1,1,1,1]
[[4,3,3,3,2],[2,2,2,2]] => [4,1,1,1]
[[4,3,3,2,2],[2,2,2,1]] => [4,2,1]
[[5,4,4,3,2],[3,3,3,2]] => [5,1,1]
[[4,3,2,2,2],[2,2,1,1]] => [4,2,1]
[[5,4,3,3,2],[3,3,2,2]] => [5,2]
[[5,4,3,2,2],[3,3,2,1]] => [5,2]
[[6,5,4,3,2],[4,4,3,2]] => [6,1]
[[4,2,2,2,2],[2,1,1,1]] => [4,1,1,1]
[[5,3,3,3,2],[3,2,2,2]] => [5,1,1]
[[5,3,3,2,2],[3,2,2,1]] => [5,2]
[[6,4,4,3,2],[4,3,3,2]] => [6,1]
[[5,3,2,2,2],[3,2,1,1]] => [5,1,1]
[[6,4,3,3,2],[4,3,2,2]] => [6,1]
[[6,4,3,2,2],[4,3,2,1]] => [6,1]
[[7,5,4,3,2],[5,4,3,2]] => [7]
[[2,1,1,1,1,1],[]] => [2,1,1,1,1,1]
[[3,2,2,2,2,1],[1,1,1,1,1]] => [3,1,1,1,1]
[[3,2,2,2,1,1],[1,1,1,1]] => [3,2,1,1]
[[4,3,3,3,2,1],[2,2,2,2,1]] => [4,1,1,1]
[[3,2,2,1,1,1],[1,1,1]] => [3,2,2]
[[4,3,3,2,2,1],[2,2,2,1,1]] => [4,2,1]
[[4,3,3,2,1,1],[2,2,2,1]] => [4,2,1]
[[5,4,4,3,2,1],[3,3,3,2,1]] => [5,1,1]
[[3,2,1,1,1,1],[1,1]] => [3,2,1,1]
[[4,3,2,2,2,1],[2,2,1,1,1]] => [4,2,1]
[[4,3,2,2,1,1],[2,2,1,1]] => [4,3]
[[5,4,3,3,2,1],[3,3,2,2,1]] => [5,2]
[[4,3,2,1,1,1],[2,2,1]] => [4,2,1]
[[5,4,3,2,2,1],[3,3,2,1,1]] => [5,2]
[[5,4,3,2,1,1],[3,3,2,1]] => [5,2]
[[6,5,4,3,2,1],[4,4,3,2,1]] => [6,1]
[[3,1,1,1,1,1],[1]] => [3,1,1,1,1]
[[4,2,2,2,2,1],[2,1,1,1,1]] => [4,1,1,1]
[[4,2,2,2,1,1],[2,1,1,1]] => [4,2,1]
[[5,3,3,3,2,1],[3,2,2,2,1]] => [5,1,1]
[[4,2,2,1,1,1],[2,1,1]] => [4,2,1]
[[5,3,3,2,2,1],[3,2,2,1,1]] => [5,2]
[[5,3,3,2,1,1],[3,2,2,1]] => [5,2]
[[6,4,4,3,2,1],[4,3,3,2,1]] => [6,1]
[[4,2,1,1,1,1],[2,1]] => [4,1,1,1]
[[5,3,2,2,2,1],[3,2,1,1,1]] => [5,1,1]
[[5,3,2,2,1,1],[3,2,1,1]] => [5,2]
[[6,4,3,3,2,1],[4,3,2,2,1]] => [6,1]
[[5,3,2,1,1,1],[3,2,1]] => [5,1,1]
[[6,4,3,2,2,1],[4,3,2,1,1]] => [6,1]
[[6,4,3,2,1,1],[4,3,2,1]] => [6,1]
[[7,5,4,3,2,1],[5,4,3,2,1]] => [7]
[[6,6],[5]] => [6,1]
[[7,6],[6]] => [7]
[[5,5,1],[4]] => [5,2]
[[6,6,1],[5,1]] => [6,1]
[[6,5,1],[5]] => [6,1]
[[7,6,1],[6,1]] => [7]
[[4,4,2],[3]] => [4,3]
[[5,5,2],[4,1]] => [5,2]
[[6,6,2],[5,2]] => [6,1]
[[5,4,2],[4]] => [5,2]
[[6,5,2],[5,1]] => [6,1]
[[7,6,2],[6,2]] => [7]
[[4,4,1,1],[3]] => [4,2,1]
[[5,5,2,1],[4,1,1]] => [5,2]
[[5,5,1,1],[4,1]] => [5,2]
[[6,6,2,1],[5,2,1]] => [6,1]
[[5,4,1,1],[4]] => [5,1,1]
[[6,5,2,1],[5,1,1]] => [6,1]
[[6,5,1,1],[5,1]] => [6,1]
[[7,6,2,1],[6,2,1]] => [7]
[[3,3,3],[2]] => [3,3,1]
[[4,4,3],[3,1]] => [4,3]
[[5,5,3],[4,2]] => [5,2]
[[6,6,3],[5,3]] => [6,1]
[[4,3,3],[3]] => [4,3]
[[5,4,3],[4,1]] => [5,2]
[[6,5,3],[5,2]] => [6,1]
[[7,6,3],[6,3]] => [7]
[[3,3,2,1],[2]] => [3,3,1]
[[4,4,3,1],[3,1,1]] => [4,3]
[[4,4,2,1],[3,1]] => [4,3]
[[5,5,3,1],[4,2,1]] => [5,2]
[[5,5,2,1],[4,2]] => [5,2]
[[6,6,3,1],[5,3,1]] => [6,1]
[[4,3,2,1],[3]] => [4,2,1]
[[5,4,3,1],[4,1,1]] => [5,2]
[[5,4,2,1],[4,1]] => [5,2]
[[6,5,3,1],[5,2,1]] => [6,1]
[[6,5,2,1],[5,2]] => [6,1]
[[7,6,3,1],[6,3,1]] => [7]
[[4,4,2,2],[3,1,1]] => [4,2,1]
[[5,5,3,2],[4,2,2]] => [5,2]
[[5,5,2,2],[4,2,1]] => [5,2]
[[6,6,3,2],[5,3,2]] => [6,1]
[[5,4,2,2],[4,1,1]] => [5,1,1]
[[6,5,3,2],[5,2,2]] => [6,1]
[[6,5,2,2],[5,2,1]] => [6,1]
[[7,6,3,2],[6,3,2]] => [7]
[[3,3,1,1,1],[2]] => [3,2,1,1]
[[4,4,2,2,1],[3,1,1,1]] => [4,2,1]
[[4,4,2,1,1],[3,1,1]] => [4,3]
[[5,5,3,2,1],[4,2,2,1]] => [5,2]
[[4,4,1,1,1],[3,1]] => [4,2,1]
[[5,5,2,2,1],[4,2,1,1]] => [5,2]
[[5,5,2,1,1],[4,2,1]] => [5,2]
[[6,6,3,2,1],[5,3,2,1]] => [6,1]
[[4,3,1,1,1],[3]] => [4,1,1,1]
[[5,4,2,2,1],[4,1,1,1]] => [5,1,1]
[[5,4,2,1,1],[4,1,1]] => [5,2]
[[6,5,3,2,1],[5,2,2,1]] => [6,1]
[[5,4,1,1,1],[4,1]] => [5,1,1]
[[6,5,2,2,1],[5,2,1,1]] => [6,1]
[[6,5,2,1,1],[5,2,1]] => [6,1]
[[7,6,3,2,1],[6,3,2,1]] => [7]
[[4,4,4],[3,2]] => [4,2,1]
[[5,5,4],[4,3]] => [5,2]
[[6,6,4],[5,4]] => [6,1]
[[5,4,4],[4,2]] => [5,2]
[[6,5,4],[5,3]] => [6,1]
[[7,6,4],[6,4]] => [7]
[[3,3,3,1],[2,1]] => [3,3,1]
[[4,4,4,1],[3,2,1]] => [4,2,1]
[[4,4,3,1],[3,2]] => [4,3]
[[5,5,4,1],[4,3,1]] => [5,2]
[[5,5,3,1],[4,3]] => [5,2]
[[6,6,4,1],[5,4,1]] => [6,1]
[[4,3,3,1],[3,1]] => [4,3]
[[5,4,4,1],[4,2,1]] => [5,2]
[[5,4,3,1],[4,2]] => [5,2]
[[6,5,4,1],[5,3,1]] => [6,1]
[[6,5,3,1],[5,3]] => [6,1]
[[7,6,4,1],[6,4,1]] => [7]
[[2,2,2,2],[1]] => [2,2,2,1]
[[3,3,3,2],[2,1,1]] => [3,2,2]
[[4,4,4,2],[3,2,2]] => [4,2,1]
[[3,3,2,2],[2,1]] => [3,3,1]
[[4,4,3,2],[3,2,1]] => [4,3]
[[5,5,4,2],[4,3,2]] => [5,2]
[[4,4,2,2],[3,2]] => [4,3]
[[5,5,3,2],[4,3,1]] => [5,2]
[[6,6,4,2],[5,4,2]] => [6,1]
[[3,2,2,2],[2]] => [3,2,2]
[[4,3,3,2],[3,1,1]] => [4,2,1]
[[5,4,4,2],[4,2,2]] => [5,2]
[[4,3,2,2],[3,1]] => [4,2,1]
[[5,4,3,2],[4,2,1]] => [5,2]
[[6,5,4,2],[5,3,2]] => [6,1]
[[5,4,2,2],[4,2]] => [5,2]
[[6,5,3,2],[5,3,1]] => [6,1]
[[7,6,4,2],[6,4,2]] => [7]
[[2,2,2,1,1],[1]] => [2,2,2,1]
[[3,3,3,2,1],[2,1,1,1]] => [3,2,2]
[[3,3,3,1,1],[2,1,1]] => [3,3,1]
[[4,4,4,2,1],[3,2,2,1]] => [4,2,1]
[[3,3,2,1,1],[2,1]] => [3,3,1]
[[4,4,3,2,1],[3,2,1,1]] => [4,3]
[[4,4,3,1,1],[3,2,1]] => [4,3]
[[5,5,4,2,1],[4,3,2,1]] => [5,2]
[[4,4,2,1,1],[3,2]] => [4,2,1]
[[5,5,3,2,1],[4,3,1,1]] => [5,2]
[[5,5,3,1,1],[4,3,1]] => [5,2]
[[6,6,4,2,1],[5,4,2,1]] => [6,1]
[[3,2,2,1,1],[2]] => [3,2,1,1]
[[4,3,3,2,1],[3,1,1,1]] => [4,2,1]
[[4,3,3,1,1],[3,1,1]] => [4,3]
[[5,4,4,2,1],[4,2,2,1]] => [5,2]
[[4,3,2,1,1],[3,1]] => [4,2,1]
[[5,4,3,2,1],[4,2,1,1]] => [5,2]
[[5,4,3,1,1],[4,2,1]] => [5,2]
[[6,5,4,2,1],[5,3,2,1]] => [6,1]
[[5,4,2,1,1],[4,2]] => [5,1,1]
[[6,5,3,2,1],[5,3,1,1]] => [6,1]
[[6,5,3,1,1],[5,3,1]] => [6,1]
[[7,6,4,2,1],[6,4,2,1]] => [7]
[[4,4,3,3],[3,2,2]] => [4,2,1]
[[5,5,4,3],[4,3,3]] => [5,2]
[[5,5,3,3],[4,3,2]] => [5,2]
[[6,6,4,3],[5,4,3]] => [6,1]
[[5,4,3,3],[4,2,2]] => [5,1,1]
[[6,5,4,3],[5,3,3]] => [6,1]
[[6,5,3,3],[5,3,2]] => [6,1]
[[7,6,4,3],[6,4,3]] => [7]
[[3,3,2,2,1],[2,1,1]] => [3,3,1]
[[4,4,3,3,1],[3,2,2,1]] => [4,2,1]
[[4,4,3,2,1],[3,2,2]] => [4,3]
[[5,5,4,3,1],[4,3,3,1]] => [5,2]
[[4,4,2,2,1],[3,2,1]] => [4,3]
[[5,5,3,3,1],[4,3,2,1]] => [5,2]
[[5,5,3,2,1],[4,3,2]] => [5,2]
[[6,6,4,3,1],[5,4,3,1]] => [6,1]
[[4,3,2,2,1],[3,1,1]] => [4,2,1]
[[5,4,3,3,1],[4,2,2,1]] => [5,1,1]
[[5,4,3,2,1],[4,2,2]] => [5,2]
[[6,5,4,3,1],[5,3,3,1]] => [6,1]
[[5,4,2,2,1],[4,2,1]] => [5,2]
[[6,5,3,3,1],[5,3,2,1]] => [6,1]
[[6,5,3,2,1],[5,3,2]] => [6,1]
[[7,6,4,3,1],[6,4,3,1]] => [7]
[[3,3,2,2,2],[2,1,1,1]] => [3,2,1,1]
[[4,4,3,3,2],[3,2,2,2]] => [4,2,1]
[[4,4,3,2,2],[3,2,2,1]] => [4,3]
[[5,5,4,3,2],[4,3,3,2]] => [5,2]
[[4,4,2,2,2],[3,2,1,1]] => [4,2,1]
[[5,5,3,3,2],[4,3,2,2]] => [5,2]
[[5,5,3,2,2],[4,3,2,1]] => [5,2]
[[6,6,4,3,2],[5,4,3,2]] => [6,1]
[[4,3,2,2,2],[3,1,1,1]] => [4,1,1,1]
[[5,4,3,3,2],[4,2,2,2]] => [5,1,1]
[[5,4,3,2,2],[4,2,2,1]] => [5,2]
[[6,5,4,3,2],[5,3,3,2]] => [6,1]
[[5,4,2,2,2],[4,2,1,1]] => [5,1,1]
[[6,5,3,3,2],[5,3,2,2]] => [6,1]
[[6,5,3,2,2],[5,3,2,1]] => [6,1]
[[7,6,4,3,2],[6,4,3,2]] => [7]
[[2,2,1,1,1,1],[1]] => [2,2,1,1,1]
[[3,3,2,2,2,1],[2,1,1,1,1]] => [3,2,1,1]
[[3,3,2,2,1,1],[2,1,1,1]] => [3,3,1]
[[4,4,3,3,2,1],[3,2,2,2,1]] => [4,2,1]
[[3,3,2,1,1,1],[2,1,1]] => [3,3,1]
[[4,4,3,2,2,1],[3,2,2,1,1]] => [4,3]
[[4,4,3,2,1,1],[3,2,2,1]] => [4,3]
[[5,5,4,3,2,1],[4,3,3,2,1]] => [5,2]
[[3,3,1,1,1,1],[2,1]] => [3,2,1,1]
[[4,4,2,2,2,1],[3,2,1,1,1]] => [4,2,1]
[[4,4,2,2,1,1],[3,2,1,1]] => [4,3]
[[5,5,3,3,2,1],[4,3,2,2,1]] => [5,2]
[[4,4,2,1,1,1],[3,2,1]] => [4,2,1]
[[5,5,3,2,2,1],[4,3,2,1,1]] => [5,2]
[[5,5,3,2,1,1],[4,3,2,1]] => [5,2]
[[6,6,4,3,2,1],[5,4,3,2,1]] => [6,1]
[[3,2,1,1,1,1],[2]] => [3,1,1,1,1]
[[4,3,2,2,2,1],[3,1,1,1,1]] => [4,1,1,1]
[[4,3,2,2,1,1],[3,1,1,1]] => [4,2,1]
[[5,4,3,3,2,1],[4,2,2,2,1]] => [5,1,1]
[[4,3,2,1,1,1],[3,1,1]] => [4,2,1]
[[5,4,3,2,2,1],[4,2,2,1,1]] => [5,2]
[[5,4,3,2,1,1],[4,2,2,1]] => [5,2]
[[6,5,4,3,2,1],[5,3,3,2,1]] => [6,1]
[[4,3,1,1,1,1],[3,1]] => [4,1,1,1]
[[5,4,2,2,2,1],[4,2,1,1,1]] => [5,1,1]
[[5,4,2,2,1,1],[4,2,1,1]] => [5,2]
[[6,5,3,3,2,1],[5,3,2,2,1]] => [6,1]
[[5,4,2,1,1,1],[4,2,1]] => [5,1,1]
[[6,5,3,2,2,1],[5,3,2,1,1]] => [6,1]
[[6,5,3,2,1,1],[5,3,2,1]] => [6,1]
[[7,6,4,3,2,1],[6,4,3,2,1]] => [7]
[[5,5,5],[4,4]] => [5,1,1]
[[6,6,5],[5,5]] => [6,1]
[[6,5,5],[5,4]] => [6,1]
[[7,6,5],[6,5]] => [7]
[[4,4,4,1],[3,3]] => [4,2,1]
[[5,5,5,1],[4,4,1]] => [5,1,1]
[[5,5,4,1],[4,4]] => [5,2]
[[6,6,5,1],[5,5,1]] => [6,1]
[[5,4,4,1],[4,3]] => [5,2]
[[6,5,5,1],[5,4,1]] => [6,1]
[[6,5,4,1],[5,4]] => [6,1]
[[7,6,5,1],[6,5,1]] => [7]
[[3,3,3,2],[2,2]] => [3,3,1]
[[4,4,4,2],[3,3,1]] => [4,2,1]
[[5,5,5,2],[4,4,2]] => [5,1,1]
[[4,4,3,2],[3,3]] => [4,3]
[[5,5,4,2],[4,4,1]] => [5,2]
[[6,6,5,2],[5,5,2]] => [6,1]
[[4,3,3,2],[3,2]] => [4,3]
[[5,4,4,2],[4,3,1]] => [5,2]
[[6,5,5,2],[5,4,2]] => [6,1]
[[5,4,3,2],[4,3]] => [5,2]
[[6,5,4,2],[5,4,1]] => [6,1]
[[7,6,5,2],[6,5,2]] => [7]
[[3,3,3,1,1],[2,2]] => [3,2,2]
[[4,4,4,2,1],[3,3,1,1]] => [4,2,1]
[[4,4,4,1,1],[3,3,1]] => [4,2,1]
[[5,5,5,2,1],[4,4,2,1]] => [5,1,1]
[[4,4,3,1,1],[3,3]] => [4,2,1]
[[5,5,4,2,1],[4,4,1,1]] => [5,2]
[[5,5,4,1,1],[4,4,1]] => [5,2]
[[6,6,5,2,1],[5,5,2,1]] => [6,1]
[[4,3,3,1,1],[3,2]] => [4,2,1]
[[5,4,4,2,1],[4,3,1,1]] => [5,2]
[[5,4,4,1,1],[4,3,1]] => [5,2]
[[6,5,5,2,1],[5,4,2,1]] => [6,1]
[[5,4,3,1,1],[4,3]] => [5,1,1]
[[6,5,4,2,1],[5,4,1,1]] => [6,1]
[[6,5,4,1,1],[5,4,1]] => [6,1]
[[7,6,5,2,1],[6,5,2,1]] => [7]
[[3,3,3,3],[2,2,1]] => [3,2,1,1]
[[4,4,4,3],[3,3,2]] => [4,2,1]
[[5,5,5,3],[4,4,3]] => [5,1,1]
[[4,4,3,3],[3,3,1]] => [4,3]
[[5,5,4,3],[4,4,2]] => [5,2]
[[6,6,5,3],[5,5,3]] => [6,1]
[[4,3,3,3],[3,2,1]] => [4,2,1]
[[5,4,4,3],[4,3,2]] => [5,2]
[[6,5,5,3],[5,4,3]] => [6,1]
[[5,4,3,3],[4,3,1]] => [5,2]
[[6,5,4,3],[5,4,2]] => [6,1]
[[7,6,5,3],[6,5,3]] => [7]
[[2,2,2,2,1],[1,1]] => [2,2,2,1]
[[3,3,3,3,1],[2,2,1,1]] => [3,2,1,1]
[[3,3,3,2,1],[2,2,1]] => [3,3,1]
[[4,4,4,3,1],[3,3,2,1]] => [4,2,1]
[[4,4,4,2,1],[3,3,2]] => [4,2,1]
[[5,5,5,3,1],[4,4,3,1]] => [5,1,1]
[[3,3,2,2,1],[2,2]] => [3,3,1]
[[4,4,3,3,1],[3,3,1,1]] => [4,3]
[[4,4,3,2,1],[3,3,1]] => [4,3]
[[5,5,4,3,1],[4,4,2,1]] => [5,2]
[[5,5,4,2,1],[4,4,2]] => [5,2]
[[6,6,5,3,1],[5,5,3,1]] => [6,1]
[[3,2,2,2,1],[2,1]] => [3,2,2]
[[4,3,3,3,1],[3,2,1,1]] => [4,2,1]
[[4,3,3,2,1],[3,2,1]] => [4,3]
[[5,4,4,3,1],[4,3,2,1]] => [5,2]
[[5,4,4,2,1],[4,3,2]] => [5,2]
[[6,5,5,3,1],[5,4,3,1]] => [6,1]
[[4,3,2,2,1],[3,2]] => [4,2,1]
[[5,4,3,3,1],[4,3,1,1]] => [5,2]
[[5,4,3,2,1],[4,3,1]] => [5,2]
[[6,5,4,3,1],[5,4,2,1]] => [6,1]
[[6,5,4,2,1],[5,4,2]] => [6,1]
[[7,6,5,3,1],[6,5,3,1]] => [7]
[[3,3,3,2,2],[2,2,1,1]] => [3,2,2]
[[4,4,4,3,2],[3,3,2,2]] => [4,2,1]
[[4,4,4,2,2],[3,3,2,1]] => [4,2,1]
[[5,5,5,3,2],[4,4,3,2]] => [5,1,1]
[[4,4,3,2,2],[3,3,1,1]] => [4,2,1]
[[5,5,4,3,2],[4,4,2,2]] => [5,2]
[[5,5,4,2,2],[4,4,2,1]] => [5,2]
[[6,6,5,3,2],[5,5,3,2]] => [6,1]
[[4,3,3,2,2],[3,2,1,1]] => [4,2,1]
[[5,4,4,3,2],[4,3,2,2]] => [5,2]
[[5,4,4,2,2],[4,3,2,1]] => [5,2]
[[6,5,5,3,2],[5,4,3,2]] => [6,1]
[[5,4,3,2,2],[4,3,1,1]] => [5,1,1]
[[6,5,4,3,2],[5,4,2,2]] => [6,1]
[[6,5,4,2,2],[5,4,2,1]] => [6,1]
[[7,6,5,3,2],[6,5,3,2]] => [7]
[[2,2,2,1,1,1],[1,1]] => [2,2,2,1]
[[3,3,3,2,2,1],[2,2,1,1,1]] => [3,2,2]
[[3,3,3,2,1,1],[2,2,1,1]] => [3,3,1]
[[4,4,4,3,2,1],[3,3,2,2,1]] => [4,2,1]
[[3,3,3,1,1,1],[2,2,1]] => [3,2,2]
[[4,4,4,2,2,1],[3,3,2,1,1]] => [4,2,1]
[[4,4,4,2,1,1],[3,3,2,1]] => [4,2,1]
[[5,5,5,3,2,1],[4,4,3,2,1]] => [5,1,1]
[[3,3,2,1,1,1],[2,2]] => [3,2,1,1]
[[4,4,3,2,2,1],[3,3,1,1,1]] => [4,2,1]
[[4,4,3,2,1,1],[3,3,1,1]] => [4,3]
[[5,5,4,3,2,1],[4,4,2,2,1]] => [5,2]
[[4,4,3,1,1,1],[3,3,1]] => [4,2,1]
[[5,5,4,2,2,1],[4,4,2,1,1]] => [5,2]
[[5,5,4,2,1,1],[4,4,2,1]] => [5,2]
[[6,6,5,3,2,1],[5,5,3,2,1]] => [6,1]
[[3,2,2,1,1,1],[2,1]] => [3,2,1,1]
[[4,3,3,2,2,1],[3,2,1,1,1]] => [4,2,1]
[[4,3,3,2,1,1],[3,2,1,1]] => [4,3]
[[5,4,4,3,2,1],[4,3,2,2,1]] => [5,2]
[[4,3,3,1,1,1],[3,2,1]] => [4,2,1]
[[5,4,4,2,2,1],[4,3,2,1,1]] => [5,2]
[[5,4,4,2,1,1],[4,3,2,1]] => [5,2]
[[6,5,5,3,2,1],[5,4,3,2,1]] => [6,1]
[[4,3,2,1,1,1],[3,2]] => [4,1,1,1]
[[5,4,3,2,2,1],[4,3,1,1,1]] => [5,1,1]
[[5,4,3,2,1,1],[4,3,1,1]] => [5,2]
[[6,5,4,3,2,1],[5,4,2,2,1]] => [6,1]
[[5,4,3,1,1,1],[4,3,1]] => [5,1,1]
[[6,5,4,2,2,1],[5,4,2,1,1]] => [6,1]
[[6,5,4,2,1,1],[5,4,2,1]] => [6,1]
[[7,6,5,3,2,1],[6,5,3,2,1]] => [7]
[[4,4,4,4],[3,3,3]] => [4,1,1,1]
[[5,5,5,4],[4,4,4]] => [5,1,1]
[[5,5,4,4],[4,4,3]] => [5,2]
[[6,6,5,4],[5,5,4]] => [6,1]
[[5,4,4,4],[4,3,3]] => [5,1,1]
[[6,5,5,4],[5,4,4]] => [6,1]
[[6,5,4,4],[5,4,3]] => [6,1]
[[7,6,5,4],[6,5,4]] => [7]
[[3,3,3,3,1],[2,2,2]] => [3,2,1,1]
[[4,4,4,4,1],[3,3,3,1]] => [4,1,1,1]
[[4,4,4,3,1],[3,3,3]] => [4,2,1]
[[5,5,5,4,1],[4,4,4,1]] => [5,1,1]
[[4,4,3,3,1],[3,3,2]] => [4,3]
[[5,5,4,4,1],[4,4,3,1]] => [5,2]
[[5,5,4,3,1],[4,4,3]] => [5,2]
[[6,6,5,4,1],[5,5,4,1]] => [6,1]
[[4,3,3,3,1],[3,2,2]] => [4,2,1]
[[5,4,4,4,1],[4,3,3,1]] => [5,1,1]
[[5,4,4,3,1],[4,3,3]] => [5,2]
[[6,5,5,4,1],[5,4,4,1]] => [6,1]
[[5,4,3,3,1],[4,3,2]] => [5,2]
[[6,5,4,4,1],[5,4,3,1]] => [6,1]
[[6,5,4,3,1],[5,4,3]] => [6,1]
[[7,6,5,4,1],[6,5,4,1]] => [7]
[[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]
[[4,4,4,4,2],[3,3,3,2]] => [4,1,1,1]
[[3,3,3,2,2],[2,2,2]] => [3,3,1]
[[4,4,4,3,2],[3,3,3,1]] => [4,2,1]
[[5,5,5,4,2],[4,4,4,2]] => [5,1,1]
[[3,3,2,2,2],[2,2,1]] => [3,3,1]
[[4,4,3,3,2],[3,3,2,1]] => [4,3]
[[5,5,4,4,2],[4,4,3,2]] => [5,2]
[[4,4,3,2,2],[3,3,2]] => [4,3]
[[5,5,4,3,2],[4,4,3,1]] => [5,2]
[[6,6,5,4,2],[5,5,4,2]] => [6,1]
[[3,2,2,2,2],[2,1,1]] => [3,2,1,1]
[[4,3,3,3,2],[3,2,2,1]] => [4,2,1]
[[5,4,4,4,2],[4,3,3,2]] => [5,1,1]
[[4,3,3,2,2],[3,2,2]] => [4,3]
[[5,4,4,3,2],[4,3,3,1]] => [5,2]
[[6,5,5,4,2],[5,4,4,2]] => [6,1]
[[4,3,2,2,2],[3,2,1]] => [4,2,1]
[[5,4,3,3,2],[4,3,2,1]] => [5,2]
[[6,5,4,4,2],[5,4,3,2]] => [6,1]
[[5,4,3,2,2],[4,3,2]] => [5,2]
[[6,5,4,3,2],[5,4,3,1]] => [6,1]
[[7,6,5,4,2],[6,5,4,2]] => [7]
[[2,2,2,2,1,1],[1,1,1]] => [2,2,2,1]
[[3,3,3,3,2,1],[2,2,2,1,1]] => [3,2,1,1]
[[3,3,3,3,1,1],[2,2,2,1]] => [3,2,1,1]
[[4,4,4,4,2,1],[3,3,3,2,1]] => [4,1,1,1]
[[3,3,3,2,1,1],[2,2,2]] => [3,2,2]
[[4,4,4,3,2,1],[3,3,3,1,1]] => [4,2,1]
[[4,4,4,3,1,1],[3,3,3,1]] => [4,2,1]
[[5,5,5,4,2,1],[4,4,4,2,1]] => [5,1,1]
[[3,3,2,2,1,1],[2,2,1]] => [3,3,1]
[[4,4,3,3,2,1],[3,3,2,1,1]] => [4,3]
[[4,4,3,3,1,1],[3,3,2,1]] => [4,3]
[[5,5,4,4,2,1],[4,4,3,2,1]] => [5,2]
[[4,4,3,2,1,1],[3,3,2]] => [4,2,1]
[[5,5,4,3,2,1],[4,4,3,1,1]] => [5,2]
[[5,5,4,3,1,1],[4,4,3,1]] => [5,2]
[[6,6,5,4,2,1],[5,5,4,2,1]] => [6,1]
[[3,2,2,2,1,1],[2,1,1]] => [3,2,2]
[[4,3,3,3,2,1],[3,2,2,1,1]] => [4,2,1]
[[4,3,3,3,1,1],[3,2,2,1]] => [4,2,1]
[[5,4,4,4,2,1],[4,3,3,2,1]] => [5,1,1]
[[4,3,3,2,1,1],[3,2,2]] => [4,2,1]
[[5,4,4,3,2,1],[4,3,3,1,1]] => [5,2]
[[5,4,4,3,1,1],[4,3,3,1]] => [5,2]
[[6,5,5,4,2,1],[5,4,4,2,1]] => [6,1]
[[4,3,2,2,1,1],[3,2,1]] => [4,2,1]
[[5,4,3,3,2,1],[4,3,2,1,1]] => [5,2]
[[5,4,3,3,1,1],[4,3,2,1]] => [5,2]
[[6,5,4,4,2,1],[5,4,3,2,1]] => [6,1]
[[5,4,3,2,1,1],[4,3,2]] => [5,1,1]
[[6,5,4,3,2,1],[5,4,3,1,1]] => [6,1]
[[6,5,4,3,1,1],[5,4,3,1]] => [6,1]
[[7,6,5,4,2,1],[6,5,4,2,1]] => [7]
[[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]
[[4,4,4,3,3],[3,3,3,2]] => [4,2,1]
[[5,5,5,4,3],[4,4,4,3]] => [5,1,1]
[[4,4,3,3,3],[3,3,2,2]] => [4,2,1]
[[5,5,4,4,3],[4,4,3,3]] => [5,2]
[[5,5,4,3,3],[4,4,3,2]] => [5,2]
[[6,6,5,4,3],[5,5,4,3]] => [6,1]
[[4,3,3,3,3],[3,2,2,2]] => [4,1,1,1]
[[5,4,4,4,3],[4,3,3,3]] => [5,1,1]
[[5,4,4,3,3],[4,3,3,2]] => [5,2]
[[6,5,5,4,3],[5,4,4,3]] => [6,1]
[[5,4,3,3,3],[4,3,2,2]] => [5,1,1]
[[6,5,4,4,3],[5,4,3,3]] => [6,1]
[[6,5,4,3,3],[5,4,3,2]] => [6,1]
[[7,6,5,4,3],[6,5,4,3]] => [7]
[[2,2,2,2,2,1],[1,1,1,1]] => [2,2,1,1,1]
[[3,3,3,3,3,1],[2,2,2,2,1]] => [3,1,1,1,1]
[[3,3,3,3,2,1],[2,2,2,2]] => [3,2,1,1]
[[4,4,4,4,3,1],[3,3,3,3,1]] => [4,1,1,1]
[[3,3,3,2,2,1],[2,2,2,1]] => [3,3,1]
[[4,4,4,3,3,1],[3,3,3,2,1]] => [4,2,1]
[[4,4,4,3,2,1],[3,3,3,2]] => [4,2,1]
[[5,5,5,4,3,1],[4,4,4,3,1]] => [5,1,1]
[[3,3,2,2,2,1],[2,2,1,1]] => [3,3,1]
[[4,4,3,3,3,1],[3,3,2,2,1]] => [4,2,1]
[[4,4,3,3,2,1],[3,3,2,2]] => [4,3]
[[5,5,4,4,3,1],[4,4,3,3,1]] => [5,2]
[[4,4,3,2,2,1],[3,3,2,1]] => [4,3]
[[5,5,4,3,3,1],[4,4,3,2,1]] => [5,2]
[[5,5,4,3,2,1],[4,4,3,2]] => [5,2]
[[6,6,5,4,3,1],[5,5,4,3,1]] => [6,1]
[[3,2,2,2,2,1],[2,1,1,1]] => [3,2,1,1]
[[4,3,3,3,3,1],[3,2,2,2,1]] => [4,1,1,1]
[[4,3,3,3,2,1],[3,2,2,2]] => [4,2,1]
[[5,4,4,4,3,1],[4,3,3,3,1]] => [5,1,1]
[[4,3,3,2,2,1],[3,2,2,1]] => [4,3]
[[5,4,4,3,3,1],[4,3,3,2,1]] => [5,2]
[[5,4,4,3,2,1],[4,3,3,2]] => [5,2]
[[6,5,5,4,3,1],[5,4,4,3,1]] => [6,1]
[[4,3,2,2,2,1],[3,2,1,1]] => [4,2,1]
[[5,4,3,3,3,1],[4,3,2,2,1]] => [5,1,1]
[[5,4,3,3,2,1],[4,3,2,2]] => [5,2]
[[6,5,4,4,3,1],[5,4,3,3,1]] => [6,1]
[[5,4,3,2,2,1],[4,3,2,1]] => [5,2]
[[6,5,4,3,3,1],[5,4,3,2,1]] => [6,1]
[[6,5,4,3,2,1],[5,4,3,2]] => [6,1]
[[7,6,5,4,3,1],[6,5,4,3,1]] => [7]
[[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]
[[3,3,3,3,2,2],[2,2,2,2,1]] => [3,2,1,1]
[[4,4,4,4,3,2],[3,3,3,3,2]] => [4,1,1,1]
[[3,3,3,2,2,2],[2,2,2,1,1]] => [3,2,2]
[[4,4,4,3,3,2],[3,3,3,2,2]] => [4,2,1]
[[4,4,4,3,2,2],[3,3,3,2,1]] => [4,2,1]
[[5,5,5,4,3,2],[4,4,4,3,2]] => [5,1,1]
[[3,3,2,2,2,2],[2,2,1,1,1]] => [3,2,1,1]
[[4,4,3,3,3,2],[3,3,2,2,2]] => [4,2,1]
[[4,4,3,3,2,2],[3,3,2,2,1]] => [4,3]
[[5,5,4,4,3,2],[4,4,3,3,2]] => [5,2]
[[4,4,3,2,2,2],[3,3,2,1,1]] => [4,2,1]
[[5,5,4,3,3,2],[4,4,3,2,2]] => [5,2]
[[5,5,4,3,2,2],[4,4,3,2,1]] => [5,2]
[[6,6,5,4,3,2],[5,5,4,3,2]] => [6,1]
[[3,2,2,2,2,2],[2,1,1,1,1]] => [3,1,1,1,1]
[[4,3,3,3,3,2],[3,2,2,2,2]] => [4,1,1,1]
[[4,3,3,3,2,2],[3,2,2,2,1]] => [4,2,1]
[[5,4,4,4,3,2],[4,3,3,3,2]] => [5,1,1]
[[4,3,3,2,2,2],[3,2,2,1,1]] => [4,2,1]
[[5,4,4,3,3,2],[4,3,3,2,2]] => [5,2]
[[5,4,4,3,2,2],[4,3,3,2,1]] => [5,2]
[[6,5,5,4,3,2],[5,4,4,3,2]] => [6,1]
[[4,3,2,2,2,2],[3,2,1,1,1]] => [4,1,1,1]
[[5,4,3,3,3,2],[4,3,2,2,2]] => [5,1,1]
[[5,4,3,3,2,2],[4,3,2,2,1]] => [5,2]
[[6,5,4,4,3,2],[5,4,3,3,2]] => [6,1]
[[5,4,3,2,2,2],[4,3,2,1,1]] => [5,1,1]
[[6,5,4,3,3,2],[5,4,3,2,2]] => [6,1]
[[6,5,4,3,2,2],[5,4,3,2,1]] => [6,1]
[[7,6,5,4,3,2],[6,5,4,3,2]] => [7]
[[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]
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [2,2,1,1,1]
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [3,1,1,1,1]
[[2,2,2,2,1,1,1],[1,1,1,1]] => [2,2,2,1]
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [3,2,1,1]
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [3,2,1,1]
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [4,1,1,1]
[[2,2,2,1,1,1,1],[1,1,1]] => [2,2,2,1]
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [3,2,2]
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [3,3,1]
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [4,2,1]
[[3,3,3,2,1,1,1],[2,2,2,1]] => [3,2,2]
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [4,2,1]
-----------------------------------------------------------------------------
Created: Sep 27, 2020 at 14:56 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Sep 08, 2023 at 21:38 by Martin Rubey