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Map identifier: Mp00078

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Map name: Schuetzenberger involution

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Domain: Gelfand-Tsetlin patterns

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Codomain: Gelfand-Tsetlin patterns

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Description: Applies the Schuetzenberger involution to a Gelfand-Tsetlin pattern.

The Schuetzenberger involution is usually regarded as an involution on semistandard Young tableaux with a fixed bound on the size of the entries.  It is also known as evacuation, and in the context of crystal graphs of type $A$ it realizes Lusztig's involution.

In the language of tableaux it is defined as follows.  Consider a semistandard tableau with no entry larger than $n$.  Use Schuetzenberger's jeu de taquin to slide all entries equal to $1$ to the outer border of the tableau.  Do the same for all entries equal to $2$, restricting the tableau to the entries larger than $2$, and so on, until the tableau is a reverse semistandard tableau.  Finally, replace each entry with its complement with respect to $n$, that is, replace $e$ with $n+1-e$.

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References: 

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Code:

def mapping(P):
    return GelfandTsetlinPatterns(n=len(P[0]))(P.to_tableau().schuetzenberger_involution(len(P[0])))

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Map images:

[[1,0],[0]]                                                             => [[1,0],[1]]
[[1,0],[1]]                                                             => [[1,0],[0]]
[[2,0],[0]]                                                             => [[2,0],[2]]
[[2,0],[1]]                                                             => [[2,0],[1]]
[[2,0],[2]]                                                             => [[2,0],[0]]
[[1,1],[1]]                                                             => [[1,1],[1]]
[[3,0],[0]]                                                             => [[3,0],[3]]
[[3,0],[1]]                                                             => [[3,0],[2]]
[[3,0],[2]]                                                             => [[3,0],[1]]
[[3,0],[3]]                                                             => [[3,0],[0]]
[[2,1],[1]]                                                             => [[2,1],[2]]
[[2,1],[2]]                                                             => [[2,1],[1]]
[[4,0],[0]]                                                             => [[4,0],[4]]
[[4,0],[1]]                                                             => [[4,0],[3]]
[[4,0],[2]]                                                             => [[4,0],[2]]
[[4,0],[3]]                                                             => [[4,0],[1]]
[[4,0],[4]]                                                             => [[4,0],[0]]
[[3,1],[1]]                                                             => [[3,1],[3]]
[[3,1],[2]]                                                             => [[3,1],[2]]
[[3,1],[3]]                                                             => [[3,1],[1]]
[[2,2],[2]]                                                             => [[2,2],[2]]
[[5,0],[0]]                                                             => [[5,0],[5]]
[[5,0],[1]]                                                             => [[5,0],[4]]
[[5,0],[2]]                                                             => [[5,0],[3]]
[[5,0],[3]]                                                             => [[5,0],[2]]
[[5,0],[4]]                                                             => [[5,0],[1]]
[[5,0],[5]]                                                             => [[5,0],[0]]
[[4,1],[1]]                                                             => [[4,1],[4]]
[[4,1],[2]]                                                             => [[4,1],[3]]
[[4,1],[3]]                                                             => [[4,1],[2]]
[[4,1],[4]]                                                             => [[4,1],[1]]
[[3,2],[2]]                                                             => [[3,2],[3]]
[[3,2],[3]]                                                             => [[3,2],[2]]
[[6,0],[0]]                                                             => [[6,0],[6]]
[[6,0],[1]]                                                             => [[6,0],[5]]
[[6,0],[2]]                                                             => [[6,0],[4]]
[[6,0],[3]]                                                             => [[6,0],[3]]
[[6,0],[4]]                                                             => [[6,0],[2]]
[[6,0],[5]]                                                             => [[6,0],[1]]
[[6,0],[6]]                                                             => [[6,0],[0]]
[[5,1],[1]]                                                             => [[5,1],[5]]
[[5,1],[2]]                                                             => [[5,1],[4]]
[[5,1],[3]]                                                             => [[5,1],[3]]
[[5,1],[4]]                                                             => [[5,1],[2]]
[[5,1],[5]]                                                             => [[5,1],[1]]
[[4,2],[2]]                                                             => [[4,2],[4]]
[[4,2],[3]]                                                             => [[4,2],[3]]
[[4,2],[4]]                                                             => [[4,2],[2]]
[[3,3],[3]]                                                             => [[3,3],[3]]
[[7,0],[0]]                                                             => [[7,0],[7]]
[[7,0],[1]]                                                             => [[7,0],[6]]
[[7,0],[2]]                                                             => [[7,0],[5]]
[[7,0],[3]]                                                             => [[7,0],[4]]
[[7,0],[4]]                                                             => [[7,0],[3]]
[[7,0],[5]]                                                             => [[7,0],[2]]
[[7,0],[6]]                                                             => [[7,0],[1]]
[[7,0],[7]]                                                             => [[7,0],[0]]
[[6,1],[1]]                                                             => [[6,1],[6]]
[[6,1],[2]]                                                             => [[6,1],[5]]
[[6,1],[3]]                                                             => [[6,1],[4]]
[[6,1],[4]]                                                             => [[6,1],[3]]
[[6,1],[5]]                                                             => [[6,1],[2]]
[[6,1],[6]]                                                             => [[6,1],[1]]
[[5,2],[2]]                                                             => [[5,2],[5]]
[[5,2],[3]]                                                             => [[5,2],[4]]
[[5,2],[4]]                                                             => [[5,2],[3]]
[[5,2],[5]]                                                             => [[5,2],[2]]
[[4,3],[3]]                                                             => [[4,3],[4]]
[[4,3],[4]]                                                             => [[4,3],[3]]
[[1,0,0],[0,0],[0]]                                                     => [[1,0,0],[1,0],[1]]
[[1,0,0],[1,0],[0]]                                                     => [[1,0,0],[1,0],[0]]
[[1,0,0],[1,0],[1]]                                                     => [[1,0,0],[0,0],[0]]
[[2,0,0],[0,0],[0]]                                                     => [[2,0,0],[2,0],[2]]
[[2,0,0],[1,0],[0]]                                                     => [[2,0,0],[2,0],[1]]
[[2,0,0],[1,0],[1]]                                                     => [[2,0,0],[1,0],[1]]
[[2,0,0],[2,0],[0]]                                                     => [[2,0,0],[2,0],[0]]
[[2,0,0],[2,0],[1]]                                                     => [[2,0,0],[1,0],[0]]
[[2,0,0],[2,0],[2]]                                                     => [[2,0,0],[0,0],[0]]
[[1,1,0],[1,0],[0]]                                                     => [[1,1,0],[1,1],[1]]
[[1,1,0],[1,0],[1]]                                                     => [[1,1,0],[1,0],[1]]
[[1,1,0],[1,1],[1]]                                                     => [[1,1,0],[1,0],[0]]
[[3,0,0],[0,0],[0]]                                                     => [[3,0,0],[3,0],[3]]
[[3,0,0],[1,0],[0]]                                                     => [[3,0,0],[3,0],[2]]
[[3,0,0],[1,0],[1]]                                                     => [[3,0,0],[2,0],[2]]
[[3,0,0],[2,0],[0]]                                                     => [[3,0,0],[3,0],[1]]
[[3,0,0],[2,0],[1]]                                                     => [[3,0,0],[2,0],[1]]
[[3,0,0],[2,0],[2]]                                                     => [[3,0,0],[1,0],[1]]
[[3,0,0],[3,0],[0]]                                                     => [[3,0,0],[3,0],[0]]
[[3,0,0],[3,0],[1]]                                                     => [[3,0,0],[2,0],[0]]
[[3,0,0],[3,0],[2]]                                                     => [[3,0,0],[1,0],[0]]
[[3,0,0],[3,0],[3]]                                                     => [[3,0,0],[0,0],[0]]
[[2,1,0],[1,0],[0]]                                                     => [[2,1,0],[2,1],[2]]
[[2,1,0],[1,0],[1]]                                                     => [[2,1,0],[2,0],[2]]
[[2,1,0],[1,1],[1]]                                                     => [[2,1,0],[2,0],[1]]
[[2,1,0],[2,0],[0]]                                                     => [[2,1,0],[2,1],[1]]
[[2,1,0],[2,0],[1]]                                                     => [[2,1,0],[1,1],[1]]
[[2,1,0],[2,0],[2]]                                                     => [[2,1,0],[1,0],[1]]
[[2,1,0],[2,1],[1]]                                                     => [[2,1,0],[2,0],[0]]
[[2,1,0],[2,1],[2]]                                                     => [[2,1,0],[1,0],[0]]
[[1,1,1],[1,1],[1]]                                                     => [[1,1,1],[1,1],[1]]
[[4,0,0],[0,0],[0]]                                                     => [[4,0,0],[4,0],[4]]
[[4,0,0],[1,0],[0]]                                                     => [[4,0,0],[4,0],[3]]
[[4,0,0],[1,0],[1]]                                                     => [[4,0,0],[3,0],[3]]
[[4,0,0],[2,0],[0]]                                                     => [[4,0,0],[4,0],[2]]
[[4,0,0],[2,0],[1]]                                                     => [[4,0,0],[3,0],[2]]
[[4,0,0],[2,0],[2]]                                                     => [[4,0,0],[2,0],[2]]
[[4,0,0],[3,0],[0]]                                                     => [[4,0,0],[4,0],[1]]
[[4,0,0],[3,0],[1]]                                                     => [[4,0,0],[3,0],[1]]
[[4,0,0],[3,0],[2]]                                                     => [[4,0,0],[2,0],[1]]
[[4,0,0],[3,0],[3]]                                                     => [[4,0,0],[1,0],[1]]
[[4,0,0],[4,0],[0]]                                                     => [[4,0,0],[4,0],[0]]
[[4,0,0],[4,0],[1]]                                                     => [[4,0,0],[3,0],[0]]
[[4,0,0],[4,0],[2]]                                                     => [[4,0,0],[2,0],[0]]
[[4,0,0],[4,0],[3]]                                                     => [[4,0,0],[1,0],[0]]
[[4,0,0],[4,0],[4]]                                                     => [[4,0,0],[0,0],[0]]
[[3,1,0],[1,0],[0]]                                                     => [[3,1,0],[3,1],[3]]
[[3,1,0],[1,0],[1]]                                                     => [[3,1,0],[3,0],[3]]
[[3,1,0],[1,1],[1]]                                                     => [[3,1,0],[3,0],[2]]
[[3,1,0],[2,0],[0]]                                                     => [[3,1,0],[3,1],[2]]
[[3,1,0],[2,0],[1]]                                                     => [[3,1,0],[2,1],[2]]
[[3,1,0],[2,0],[2]]                                                     => [[3,1,0],[2,0],[2]]
[[3,1,0],[2,1],[1]]                                                     => [[3,1,0],[3,0],[1]]
[[3,1,0],[2,1],[2]]                                                     => [[3,1,0],[2,0],[1]]
[[3,1,0],[3,0],[0]]                                                     => [[3,1,0],[3,1],[1]]
[[3,1,0],[3,0],[1]]                                                     => [[3,1,0],[2,1],[1]]
[[3,1,0],[3,0],[2]]                                                     => [[3,1,0],[1,1],[1]]
[[3,1,0],[3,0],[3]]                                                     => [[3,1,0],[1,0],[1]]
[[3,1,0],[3,1],[1]]                                                     => [[3,1,0],[3,0],[0]]
[[3,1,0],[3,1],[2]]                                                     => [[3,1,0],[2,0],[0]]
[[3,1,0],[3,1],[3]]                                                     => [[3,1,0],[1,0],[0]]
[[2,2,0],[2,0],[0]]                                                     => [[2,2,0],[2,2],[2]]
[[2,2,0],[2,0],[1]]                                                     => [[2,2,0],[2,1],[2]]
[[2,2,0],[2,0],[2]]                                                     => [[2,2,0],[2,0],[2]]
[[2,2,0],[2,1],[1]]                                                     => [[2,2,0],[2,1],[1]]
[[2,2,0],[2,1],[2]]                                                     => [[2,2,0],[2,0],[1]]
[[2,2,0],[2,2],[2]]                                                     => [[2,2,0],[2,0],[0]]
[[2,1,1],[1,1],[1]]                                                     => [[2,1,1],[2,1],[2]]
[[2,1,1],[2,1],[1]]                                                     => [[2,1,1],[2,1],[1]]
[[2,1,1],[2,1],[2]]                                                     => [[2,1,1],[1,1],[1]]
[[5,0,0],[0,0],[0]]                                                     => [[5,0,0],[5,0],[5]]
[[5,0,0],[1,0],[0]]                                                     => [[5,0,0],[5,0],[4]]
[[5,0,0],[1,0],[1]]                                                     => [[5,0,0],[4,0],[4]]
[[5,0,0],[2,0],[0]]                                                     => [[5,0,0],[5,0],[3]]
[[5,0,0],[2,0],[1]]                                                     => [[5,0,0],[4,0],[3]]
[[5,0,0],[2,0],[2]]                                                     => [[5,0,0],[3,0],[3]]
[[5,0,0],[3,0],[0]]                                                     => [[5,0,0],[5,0],[2]]
[[5,0,0],[3,0],[1]]                                                     => [[5,0,0],[4,0],[2]]
[[5,0,0],[3,0],[2]]                                                     => [[5,0,0],[3,0],[2]]
[[5,0,0],[3,0],[3]]                                                     => [[5,0,0],[2,0],[2]]
[[5,0,0],[4,0],[0]]                                                     => [[5,0,0],[5,0],[1]]
[[5,0,0],[4,0],[1]]                                                     => [[5,0,0],[4,0],[1]]
[[5,0,0],[4,0],[2]]                                                     => [[5,0,0],[3,0],[1]]
[[5,0,0],[4,0],[3]]                                                     => [[5,0,0],[2,0],[1]]
[[5,0,0],[4,0],[4]]                                                     => [[5,0,0],[1,0],[1]]
[[5,0,0],[5,0],[0]]                                                     => [[5,0,0],[5,0],[0]]
[[5,0,0],[5,0],[1]]                                                     => [[5,0,0],[4,0],[0]]
[[5,0,0],[5,0],[2]]                                                     => [[5,0,0],[3,0],[0]]
[[5,0,0],[5,0],[3]]                                                     => [[5,0,0],[2,0],[0]]
[[5,0,0],[5,0],[4]]                                                     => [[5,0,0],[1,0],[0]]
[[5,0,0],[5,0],[5]]                                                     => [[5,0,0],[0,0],[0]]
[[4,1,0],[1,0],[0]]                                                     => [[4,1,0],[4,1],[4]]
[[4,1,0],[1,0],[1]]                                                     => [[4,1,0],[4,0],[4]]
[[4,1,0],[1,1],[1]]                                                     => [[4,1,0],[4,0],[3]]
[[4,1,0],[2,0],[0]]                                                     => [[4,1,0],[4,1],[3]]
[[4,1,0],[2,0],[1]]                                                     => [[4,1,0],[3,1],[3]]
[[4,1,0],[2,0],[2]]                                                     => [[4,1,0],[3,0],[3]]
[[4,1,0],[2,1],[1]]                                                     => [[4,1,0],[4,0],[2]]
[[4,1,0],[2,1],[2]]                                                     => [[4,1,0],[3,0],[2]]
[[4,1,0],[3,0],[0]]                                                     => [[4,1,0],[4,1],[2]]
[[4,1,0],[3,0],[1]]                                                     => [[4,1,0],[3,1],[2]]
[[4,1,0],[3,0],[2]]                                                     => [[4,1,0],[2,1],[2]]
[[4,1,0],[3,0],[3]]                                                     => [[4,1,0],[2,0],[2]]
[[4,1,0],[3,1],[1]]                                                     => [[4,1,0],[4,0],[1]]
[[4,1,0],[3,1],[2]]                                                     => [[4,1,0],[3,0],[1]]
[[4,1,0],[3,1],[3]]                                                     => [[4,1,0],[2,0],[1]]
[[4,1,0],[4,0],[0]]                                                     => [[4,1,0],[4,1],[1]]
[[4,1,0],[4,0],[1]]                                                     => [[4,1,0],[3,1],[1]]
[[4,1,0],[4,0],[2]]                                                     => [[4,1,0],[2,1],[1]]
[[4,1,0],[4,0],[3]]                                                     => [[4,1,0],[1,1],[1]]
[[4,1,0],[4,0],[4]]                                                     => [[4,1,0],[1,0],[1]]
[[4,1,0],[4,1],[1]]                                                     => [[4,1,0],[4,0],[0]]
[[4,1,0],[4,1],[2]]                                                     => [[4,1,0],[3,0],[0]]
[[4,1,0],[4,1],[3]]                                                     => [[4,1,0],[2,0],[0]]
[[4,1,0],[4,1],[4]]                                                     => [[4,1,0],[1,0],[0]]
[[3,2,0],[2,0],[0]]                                                     => [[3,2,0],[3,2],[3]]
[[3,2,0],[2,0],[1]]                                                     => [[3,2,0],[3,1],[3]]
[[3,2,0],[2,0],[2]]                                                     => [[3,2,0],[3,0],[3]]
[[3,2,0],[2,1],[1]]                                                     => [[3,2,0],[3,1],[2]]
[[3,2,0],[2,1],[2]]                                                     => [[3,2,0],[3,0],[2]]
[[3,2,0],[2,2],[2]]                                                     => [[3,2,0],[3,0],[1]]
[[3,2,0],[3,0],[0]]                                                     => [[3,2,0],[3,2],[2]]
[[3,2,0],[3,0],[1]]                                                     => [[3,2,0],[2,2],[2]]
[[3,2,0],[3,0],[2]]                                                     => [[3,2,0],[2,1],[2]]
[[3,2,0],[3,0],[3]]                                                     => [[3,2,0],[2,0],[2]]
[[3,2,0],[3,1],[1]]                                                     => [[3,2,0],[3,1],[1]]
[[3,2,0],[3,1],[2]]                                                     => [[3,2,0],[2,1],[1]]
[[3,2,0],[3,1],[3]]                                                     => [[3,2,0],[2,0],[1]]
[[3,2,0],[3,2],[2]]                                                     => [[3,2,0],[3,0],[0]]
[[3,2,0],[3,2],[3]]                                                     => [[3,2,0],[2,0],[0]]
[[3,1,1],[1,1],[1]]                                                     => [[3,1,1],[3,1],[3]]
[[3,1,1],[2,1],[1]]                                                     => [[3,1,1],[3,1],[2]]
[[3,1,1],[2,1],[2]]                                                     => [[3,1,1],[2,1],[2]]
[[3,1,1],[3,1],[1]]                                                     => [[3,1,1],[3,1],[1]]
[[3,1,1],[3,1],[2]]                                                     => [[3,1,1],[2,1],[1]]
[[3,1,1],[3,1],[3]]                                                     => [[3,1,1],[1,1],[1]]
[[2,2,1],[2,1],[1]]                                                     => [[2,2,1],[2,2],[2]]
[[2,2,1],[2,1],[2]]                                                     => [[2,2,1],[2,1],[2]]
[[2,2,1],[2,2],[2]]                                                     => [[2,2,1],[2,1],[1]]
[[6,0,0],[0,0],[0]]                                                     => [[6,0,0],[6,0],[6]]
[[6,0,0],[1,0],[0]]                                                     => [[6,0,0],[6,0],[5]]
[[6,0,0],[1,0],[1]]                                                     => [[6,0,0],[5,0],[5]]
[[6,0,0],[2,0],[0]]                                                     => [[6,0,0],[6,0],[4]]
[[6,0,0],[2,0],[1]]                                                     => [[6,0,0],[5,0],[4]]
[[6,0,0],[2,0],[2]]                                                     => [[6,0,0],[4,0],[4]]
[[6,0,0],[3,0],[0]]                                                     => [[6,0,0],[6,0],[3]]
[[6,0,0],[3,0],[1]]                                                     => [[6,0,0],[5,0],[3]]
[[6,0,0],[3,0],[2]]                                                     => [[6,0,0],[4,0],[3]]
[[6,0,0],[3,0],[3]]                                                     => [[6,0,0],[3,0],[3]]
[[6,0,0],[4,0],[0]]                                                     => [[6,0,0],[6,0],[2]]
[[6,0,0],[4,0],[1]]                                                     => [[6,0,0],[5,0],[2]]
[[6,0,0],[4,0],[2]]                                                     => [[6,0,0],[4,0],[2]]
[[6,0,0],[4,0],[3]]                                                     => [[6,0,0],[3,0],[2]]
[[6,0,0],[4,0],[4]]                                                     => [[6,0,0],[2,0],[2]]
[[6,0,0],[5,0],[0]]                                                     => [[6,0,0],[6,0],[1]]
[[6,0,0],[5,0],[1]]                                                     => [[6,0,0],[5,0],[1]]
[[6,0,0],[5,0],[2]]                                                     => [[6,0,0],[4,0],[1]]
[[6,0,0],[5,0],[3]]                                                     => [[6,0,0],[3,0],[1]]
[[6,0,0],[5,0],[4]]                                                     => [[6,0,0],[2,0],[1]]
[[6,0,0],[5,0],[5]]                                                     => [[6,0,0],[1,0],[1]]
[[6,0,0],[6,0],[0]]                                                     => [[6,0,0],[6,0],[0]]
[[6,0,0],[6,0],[1]]                                                     => [[6,0,0],[5,0],[0]]
[[6,0,0],[6,0],[2]]                                                     => [[6,0,0],[4,0],[0]]
[[6,0,0],[6,0],[3]]                                                     => [[6,0,0],[3,0],[0]]
[[6,0,0],[6,0],[4]]                                                     => [[6,0,0],[2,0],[0]]
[[6,0,0],[6,0],[5]]                                                     => [[6,0,0],[1,0],[0]]
[[6,0,0],[6,0],[6]]                                                     => [[6,0,0],[0,0],[0]]
[[5,1,0],[1,0],[0]]                                                     => [[5,1,0],[5,1],[5]]
[[5,1,0],[1,0],[1]]                                                     => [[5,1,0],[5,0],[5]]
[[5,1,0],[1,1],[1]]                                                     => [[5,1,0],[5,0],[4]]
[[5,1,0],[2,0],[0]]                                                     => [[5,1,0],[5,1],[4]]
[[5,1,0],[2,0],[1]]                                                     => [[5,1,0],[4,1],[4]]
[[5,1,0],[2,0],[2]]                                                     => [[5,1,0],[4,0],[4]]
[[5,1,0],[2,1],[1]]                                                     => [[5,1,0],[5,0],[3]]
[[5,1,0],[2,1],[2]]                                                     => [[5,1,0],[4,0],[3]]
[[5,1,0],[3,0],[0]]                                                     => [[5,1,0],[5,1],[3]]
[[5,1,0],[3,0],[1]]                                                     => [[5,1,0],[4,1],[3]]
[[5,1,0],[3,0],[2]]                                                     => [[5,1,0],[3,1],[3]]
[[5,1,0],[3,0],[3]]                                                     => [[5,1,0],[3,0],[3]]
[[5,1,0],[3,1],[1]]                                                     => [[5,1,0],[5,0],[2]]
[[5,1,0],[3,1],[2]]                                                     => [[5,1,0],[4,0],[2]]
[[5,1,0],[3,1],[3]]                                                     => [[5,1,0],[3,0],[2]]
[[5,1,0],[4,0],[0]]                                                     => [[5,1,0],[5,1],[2]]
[[5,1,0],[4,0],[1]]                                                     => [[5,1,0],[4,1],[2]]
[[5,1,0],[4,0],[2]]                                                     => [[5,1,0],[3,1],[2]]
[[5,1,0],[4,0],[3]]                                                     => [[5,1,0],[2,1],[2]]
[[5,1,0],[4,0],[4]]                                                     => [[5,1,0],[2,0],[2]]
[[5,1,0],[4,1],[1]]                                                     => [[5,1,0],[5,0],[1]]
[[5,1,0],[4,1],[2]]                                                     => [[5,1,0],[4,0],[1]]
[[5,1,0],[4,1],[3]]                                                     => [[5,1,0],[3,0],[1]]
[[5,1,0],[4,1],[4]]                                                     => [[5,1,0],[2,0],[1]]
[[5,1,0],[5,0],[0]]                                                     => [[5,1,0],[5,1],[1]]
[[5,1,0],[5,0],[1]]                                                     => [[5,1,0],[4,1],[1]]
[[5,1,0],[5,0],[2]]                                                     => [[5,1,0],[3,1],[1]]
[[5,1,0],[5,0],[3]]                                                     => [[5,1,0],[2,1],[1]]
[[5,1,0],[5,0],[4]]                                                     => [[5,1,0],[1,1],[1]]
[[5,1,0],[5,0],[5]]                                                     => [[5,1,0],[1,0],[1]]
[[5,1,0],[5,1],[1]]                                                     => [[5,1,0],[5,0],[0]]
[[5,1,0],[5,1],[2]]                                                     => [[5,1,0],[4,0],[0]]
[[5,1,0],[5,1],[3]]                                                     => [[5,1,0],[3,0],[0]]
[[5,1,0],[5,1],[4]]                                                     => [[5,1,0],[2,0],[0]]
[[5,1,0],[5,1],[5]]                                                     => [[5,1,0],[1,0],[0]]
[[4,2,0],[2,0],[0]]                                                     => [[4,2,0],[4,2],[4]]
[[4,2,0],[2,0],[1]]                                                     => [[4,2,0],[4,1],[4]]
[[4,2,0],[2,0],[2]]                                                     => [[4,2,0],[4,0],[4]]
[[4,2,0],[2,1],[1]]                                                     => [[4,2,0],[4,1],[3]]
[[4,2,0],[2,1],[2]]                                                     => [[4,2,0],[4,0],[3]]
[[4,2,0],[2,2],[2]]                                                     => [[4,2,0],[4,0],[2]]
[[4,2,0],[3,0],[0]]                                                     => [[4,2,0],[4,2],[3]]
[[4,2,0],[3,0],[1]]                                                     => [[4,2,0],[3,2],[3]]
[[4,2,0],[3,0],[2]]                                                     => [[4,2,0],[3,1],[3]]
[[4,2,0],[3,0],[3]]                                                     => [[4,2,0],[3,0],[3]]
[[4,2,0],[3,1],[1]]                                                     => [[4,2,0],[4,1],[2]]
[[4,2,0],[3,1],[2]]                                                     => [[4,2,0],[3,1],[2]]
[[4,2,0],[3,1],[3]]                                                     => [[4,2,0],[3,0],[2]]
[[4,2,0],[3,2],[2]]                                                     => [[4,2,0],[4,0],[1]]
[[4,2,0],[3,2],[3]]                                                     => [[4,2,0],[3,0],[1]]
[[4,2,0],[4,0],[0]]                                                     => [[4,2,0],[4,2],[2]]
[[4,2,0],[4,0],[1]]                                                     => [[4,2,0],[3,2],[2]]
[[4,2,0],[4,0],[2]]                                                     => [[4,2,0],[2,2],[2]]
[[4,2,0],[4,0],[3]]                                                     => [[4,2,0],[2,1],[2]]
[[4,2,0],[4,0],[4]]                                                     => [[4,2,0],[2,0],[2]]
[[4,2,0],[4,1],[1]]                                                     => [[4,2,0],[4,1],[1]]
[[4,2,0],[4,1],[2]]                                                     => [[4,2,0],[3,1],[1]]
[[4,2,0],[4,1],[3]]                                                     => [[4,2,0],[2,1],[1]]
[[4,2,0],[4,1],[4]]                                                     => [[4,2,0],[2,0],[1]]
[[4,2,0],[4,2],[2]]                                                     => [[4,2,0],[4,0],[0]]
[[4,2,0],[4,2],[3]]                                                     => [[4,2,0],[3,0],[0]]
[[4,2,0],[4,2],[4]]                                                     => [[4,2,0],[2,0],[0]]
[[4,1,1],[1,1],[1]]                                                     => [[4,1,1],[4,1],[4]]
[[4,1,1],[2,1],[1]]                                                     => [[4,1,1],[4,1],[3]]
[[4,1,1],[2,1],[2]]                                                     => [[4,1,1],[3,1],[3]]
[[4,1,1],[3,1],[1]]                                                     => [[4,1,1],[4,1],[2]]
[[4,1,1],[3,1],[2]]                                                     => [[4,1,1],[3,1],[2]]
[[4,1,1],[3,1],[3]]                                                     => [[4,1,1],[2,1],[2]]
[[4,1,1],[4,1],[1]]                                                     => [[4,1,1],[4,1],[1]]
[[4,1,1],[4,1],[2]]                                                     => [[4,1,1],[3,1],[1]]
[[4,1,1],[4,1],[3]]                                                     => [[4,1,1],[2,1],[1]]
[[4,1,1],[4,1],[4]]                                                     => [[4,1,1],[1,1],[1]]
[[3,3,0],[3,0],[0]]                                                     => [[3,3,0],[3,3],[3]]
[[3,3,0],[3,0],[1]]                                                     => [[3,3,0],[3,2],[3]]
[[3,3,0],[3,0],[2]]                                                     => [[3,3,0],[3,1],[3]]
[[3,3,0],[3,0],[3]]                                                     => [[3,3,0],[3,0],[3]]
[[3,3,0],[3,1],[1]]                                                     => [[3,3,0],[3,2],[2]]
[[3,3,0],[3,1],[2]]                                                     => [[3,3,0],[3,1],[2]]
[[3,3,0],[3,1],[3]]                                                     => [[3,3,0],[3,0],[2]]
[[3,3,0],[3,2],[2]]                                                     => [[3,3,0],[3,1],[1]]
[[3,3,0],[3,2],[3]]                                                     => [[3,3,0],[3,0],[1]]
[[3,3,0],[3,3],[3]]                                                     => [[3,3,0],[3,0],[0]]
[[3,2,1],[2,1],[1]]                                                     => [[3,2,1],[3,2],[3]]
[[3,2,1],[2,1],[2]]                                                     => [[3,2,1],[3,1],[3]]
[[3,2,1],[2,2],[2]]                                                     => [[3,2,1],[3,1],[2]]
[[3,2,1],[3,1],[1]]                                                     => [[3,2,1],[3,2],[2]]
[[3,2,1],[3,1],[2]]                                                     => [[3,2,1],[2,2],[2]]
[[3,2,1],[3,1],[3]]                                                     => [[3,2,1],[2,1],[2]]
[[3,2,1],[3,2],[2]]                                                     => [[3,2,1],[3,1],[1]]
[[3,2,1],[3,2],[3]]                                                     => [[3,2,1],[2,1],[1]]
[[2,2,2],[2,2],[2]]                                                     => [[2,2,2],[2,2],[2]]
[[1,0,0,0],[0,0,0],[0,0],[0]]                                           => [[1,0,0,0],[1,0,0],[1,0],[1]]
[[1,0,0,0],[1,0,0],[0,0],[0]]                                           => [[1,0,0,0],[1,0,0],[1,0],[0]]
[[1,0,0,0],[1,0,0],[1,0],[0]]                                           => [[1,0,0,0],[1,0,0],[0,0],[0]]
[[1,0,0,0],[1,0,0],[1,0],[1]]                                           => [[1,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0],[0,0,0],[0,0],[0]]                                           => [[2,0,0,0],[2,0,0],[2,0],[2]]
[[2,0,0,0],[1,0,0],[0,0],[0]]                                           => [[2,0,0,0],[2,0,0],[2,0],[1]]
[[2,0,0,0],[1,0,0],[1,0],[0]]                                           => [[2,0,0,0],[2,0,0],[1,0],[1]]
[[2,0,0,0],[1,0,0],[1,0],[1]]                                           => [[2,0,0,0],[1,0,0],[1,0],[1]]
[[2,0,0,0],[2,0,0],[0,0],[0]]                                           => [[2,0,0,0],[2,0,0],[2,0],[0]]
[[2,0,0,0],[2,0,0],[1,0],[0]]                                           => [[2,0,0,0],[2,0,0],[1,0],[0]]
[[2,0,0,0],[2,0,0],[1,0],[1]]                                           => [[2,0,0,0],[1,0,0],[1,0],[0]]
[[2,0,0,0],[2,0,0],[2,0],[0]]                                           => [[2,0,0,0],[2,0,0],[0,0],[0]]
[[2,0,0,0],[2,0,0],[2,0],[1]]                                           => [[2,0,0,0],[1,0,0],[0,0],[0]]
[[2,0,0,0],[2,0,0],[2,0],[2]]                                           => [[2,0,0,0],[0,0,0],[0,0],[0]]
[[1,1,0,0],[1,0,0],[0,0],[0]]                                           => [[1,1,0,0],[1,1,0],[1,1],[1]]
[[1,1,0,0],[1,0,0],[1,0],[0]]                                           => [[1,1,0,0],[1,1,0],[1,0],[1]]
[[1,1,0,0],[1,0,0],[1,0],[1]]                                           => [[1,1,0,0],[1,0,0],[1,0],[1]]
[[1,1,0,0],[1,1,0],[1,0],[0]]                                           => [[1,1,0,0],[1,1,0],[1,0],[0]]
[[1,1,0,0],[1,1,0],[1,0],[1]]                                           => [[1,1,0,0],[1,0,0],[1,0],[0]]
[[1,1,0,0],[1,1,0],[1,1],[1]]                                           => [[1,1,0,0],[1,0,0],[0,0],[0]]
[[3,0,0,0],[0,0,0],[0,0],[0]]                                           => [[3,0,0,0],[3,0,0],[3,0],[3]]
[[3,0,0,0],[1,0,0],[0,0],[0]]                                           => [[3,0,0,0],[3,0,0],[3,0],[2]]
[[3,0,0,0],[1,0,0],[1,0],[0]]                                           => [[3,0,0,0],[3,0,0],[2,0],[2]]
[[3,0,0,0],[1,0,0],[1,0],[1]]                                           => [[3,0,0,0],[2,0,0],[2,0],[2]]
[[3,0,0,0],[2,0,0],[0,0],[0]]                                           => [[3,0,0,0],[3,0,0],[3,0],[1]]
[[3,0,0,0],[2,0,0],[1,0],[0]]                                           => [[3,0,0,0],[3,0,0],[2,0],[1]]
[[3,0,0,0],[2,0,0],[1,0],[1]]                                           => [[3,0,0,0],[2,0,0],[2,0],[1]]
[[3,0,0,0],[2,0,0],[2,0],[0]]                                           => [[3,0,0,0],[3,0,0],[1,0],[1]]
[[3,0,0,0],[2,0,0],[2,0],[1]]                                           => [[3,0,0,0],[2,0,0],[1,0],[1]]
[[3,0,0,0],[2,0,0],[2,0],[2]]                                           => [[3,0,0,0],[1,0,0],[1,0],[1]]
[[3,0,0,0],[3,0,0],[0,0],[0]]                                           => [[3,0,0,0],[3,0,0],[3,0],[0]]
[[3,0,0,0],[3,0,0],[1,0],[0]]                                           => [[3,0,0,0],[3,0,0],[2,0],[0]]
[[3,0,0,0],[3,0,0],[1,0],[1]]                                           => [[3,0,0,0],[2,0,0],[2,0],[0]]
[[3,0,0,0],[3,0,0],[2,0],[0]]                                           => [[3,0,0,0],[3,0,0],[1,0],[0]]
[[3,0,0,0],[3,0,0],[2,0],[1]]                                           => [[3,0,0,0],[2,0,0],[1,0],[0]]
[[3,0,0,0],[3,0,0],[2,0],[2]]                                           => [[3,0,0,0],[1,0,0],[1,0],[0]]
[[3,0,0,0],[3,0,0],[3,0],[0]]                                           => [[3,0,0,0],[3,0,0],[0,0],[0]]
[[3,0,0,0],[3,0,0],[3,0],[1]]                                           => [[3,0,0,0],[2,0,0],[0,0],[0]]
[[3,0,0,0],[3,0,0],[3,0],[2]]                                           => [[3,0,0,0],[1,0,0],[0,0],[0]]
[[3,0,0,0],[3,0,0],[3,0],[3]]                                           => [[3,0,0,0],[0,0,0],[0,0],[0]]
[[2,1,0,0],[1,0,0],[0,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,1],[2]]
[[2,1,0,0],[1,0,0],[1,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,0],[2]]
[[2,1,0,0],[1,0,0],[1,0],[1]]                                           => [[2,1,0,0],[2,0,0],[2,0],[2]]
[[2,1,0,0],[1,1,0],[1,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,0],[1]]
[[2,1,0,0],[1,1,0],[1,0],[1]]                                           => [[2,1,0,0],[2,0,0],[2,0],[1]]
[[2,1,0,0],[1,1,0],[1,1],[1]]                                           => [[2,1,0,0],[2,0,0],[1,0],[1]]
[[2,1,0,0],[2,0,0],[0,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,1],[1]]
[[2,1,0,0],[2,0,0],[1,0],[0]]                                           => [[2,1,0,0],[2,1,0],[1,1],[1]]
[[2,1,0,0],[2,0,0],[1,0],[1]]                                           => [[2,1,0,0],[1,1,0],[1,1],[1]]
[[2,1,0,0],[2,0,0],[2,0],[0]]                                           => [[2,1,0,0],[2,1,0],[1,0],[1]]
[[2,1,0,0],[2,0,0],[2,0],[1]]                                           => [[2,1,0,0],[1,1,0],[1,0],[1]]
[[2,1,0,0],[2,0,0],[2,0],[2]]                                           => [[2,1,0,0],[1,0,0],[1,0],[1]]
[[2,1,0,0],[2,1,0],[1,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,0],[0]]
[[2,1,0,0],[2,1,0],[1,0],[1]]                                           => [[2,1,0,0],[2,0,0],[2,0],[0]]
[[2,1,0,0],[2,1,0],[1,1],[1]]                                           => [[2,1,0,0],[2,0,0],[1,0],[0]]
[[2,1,0,0],[2,1,0],[2,0],[0]]                                           => [[2,1,0,0],[2,1,0],[1,0],[0]]
[[2,1,0,0],[2,1,0],[2,0],[1]]                                           => [[2,1,0,0],[1,1,0],[1,0],[0]]
[[2,1,0,0],[2,1,0],[2,0],[2]]                                           => [[2,1,0,0],[1,0,0],[1,0],[0]]
[[2,1,0,0],[2,1,0],[2,1],[1]]                                           => [[2,1,0,0],[2,0,0],[0,0],[0]]
[[2,1,0,0],[2,1,0],[2,1],[2]]                                           => [[2,1,0,0],[1,0,0],[0,0],[0]]
[[1,1,1,0],[1,1,0],[1,0],[0]]                                           => [[1,1,1,0],[1,1,1],[1,1],[1]]
[[1,1,1,0],[1,1,0],[1,0],[1]]                                           => [[1,1,1,0],[1,1,0],[1,1],[1]]
[[1,1,1,0],[1,1,0],[1,1],[1]]                                           => [[1,1,1,0],[1,1,0],[1,0],[1]]
[[1,1,1,0],[1,1,1],[1,1],[1]]                                           => [[1,1,1,0],[1,1,0],[1,0],[0]]
[[4,0,0,0],[0,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[4,0],[4]]
[[4,0,0,0],[1,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[4,0],[3]]
[[4,0,0,0],[1,0,0],[1,0],[0]]                                           => [[4,0,0,0],[4,0,0],[3,0],[3]]
[[4,0,0,0],[1,0,0],[1,0],[1]]                                           => [[4,0,0,0],[3,0,0],[3,0],[3]]
[[4,0,0,0],[2,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[4,0],[2]]
[[4,0,0,0],[2,0,0],[1,0],[0]]                                           => [[4,0,0,0],[4,0,0],[3,0],[2]]
[[4,0,0,0],[2,0,0],[1,0],[1]]                                           => [[4,0,0,0],[3,0,0],[3,0],[2]]
[[4,0,0,0],[2,0,0],[2,0],[0]]                                           => [[4,0,0,0],[4,0,0],[2,0],[2]]
[[4,0,0,0],[2,0,0],[2,0],[1]]                                           => [[4,0,0,0],[3,0,0],[2,0],[2]]
[[4,0,0,0],[2,0,0],[2,0],[2]]                                           => [[4,0,0,0],[2,0,0],[2,0],[2]]
[[4,0,0,0],[3,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[4,0],[1]]
[[4,0,0,0],[3,0,0],[1,0],[0]]                                           => [[4,0,0,0],[4,0,0],[3,0],[1]]
[[4,0,0,0],[3,0,0],[1,0],[1]]                                           => [[4,0,0,0],[3,0,0],[3,0],[1]]
[[4,0,0,0],[3,0,0],[2,0],[0]]                                           => [[4,0,0,0],[4,0,0],[2,0],[1]]
[[4,0,0,0],[3,0,0],[2,0],[1]]                                           => [[4,0,0,0],[3,0,0],[2,0],[1]]
[[4,0,0,0],[3,0,0],[2,0],[2]]                                           => [[4,0,0,0],[2,0,0],[2,0],[1]]
[[4,0,0,0],[3,0,0],[3,0],[0]]                                           => [[4,0,0,0],[4,0,0],[1,0],[1]]
[[4,0,0,0],[3,0,0],[3,0],[1]]                                           => [[4,0,0,0],[3,0,0],[1,0],[1]]
[[4,0,0,0],[3,0,0],[3,0],[2]]                                           => [[4,0,0,0],[2,0,0],[1,0],[1]]
[[4,0,0,0],[3,0,0],[3,0],[3]]                                           => [[4,0,0,0],[1,0,0],[1,0],[1]]
[[4,0,0,0],[4,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[4,0],[0]]
[[4,0,0,0],[4,0,0],[1,0],[0]]                                           => [[4,0,0,0],[4,0,0],[3,0],[0]]
[[4,0,0,0],[4,0,0],[1,0],[1]]                                           => [[4,0,0,0],[3,0,0],[3,0],[0]]
[[4,0,0,0],[4,0,0],[2,0],[0]]                                           => [[4,0,0,0],[4,0,0],[2,0],[0]]
[[4,0,0,0],[4,0,0],[2,0],[1]]                                           => [[4,0,0,0],[3,0,0],[2,0],[0]]
[[4,0,0,0],[4,0,0],[2,0],[2]]                                           => [[4,0,0,0],[2,0,0],[2,0],[0]]
[[4,0,0,0],[4,0,0],[3,0],[0]]                                           => [[4,0,0,0],[4,0,0],[1,0],[0]]
[[4,0,0,0],[4,0,0],[3,0],[1]]                                           => [[4,0,0,0],[3,0,0],[1,0],[0]]
[[4,0,0,0],[4,0,0],[3,0],[2]]                                           => [[4,0,0,0],[2,0,0],[1,0],[0]]
[[4,0,0,0],[4,0,0],[3,0],[3]]                                           => [[4,0,0,0],[1,0,0],[1,0],[0]]
[[4,0,0,0],[4,0,0],[4,0],[0]]                                           => [[4,0,0,0],[4,0,0],[0,0],[0]]
[[4,0,0,0],[4,0,0],[4,0],[1]]                                           => [[4,0,0,0],[3,0,0],[0,0],[0]]
[[4,0,0,0],[4,0,0],[4,0],[2]]                                           => [[4,0,0,0],[2,0,0],[0,0],[0]]
[[4,0,0,0],[4,0,0],[4,0],[3]]                                           => [[4,0,0,0],[1,0,0],[0,0],[0]]
[[4,0,0,0],[4,0,0],[4,0],[4]]                                           => [[4,0,0,0],[0,0,0],[0,0],[0]]
[[3,1,0,0],[1,0,0],[0,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,1],[3]]
[[3,1,0,0],[1,0,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,0],[3]]
[[3,1,0,0],[1,0,0],[1,0],[1]]                                           => [[3,1,0,0],[3,0,0],[3,0],[3]]
[[3,1,0,0],[1,1,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,0],[2]]
[[3,1,0,0],[1,1,0],[1,0],[1]]                                           => [[3,1,0,0],[3,0,0],[3,0],[2]]
[[3,1,0,0],[1,1,0],[1,1],[1]]                                           => [[3,1,0,0],[3,0,0],[2,0],[2]]
[[3,1,0,0],[2,0,0],[0,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,1],[2]]
[[3,1,0,0],[2,0,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,1],[2]]
[[3,1,0,0],[2,0,0],[1,0],[1]]                                           => [[3,1,0,0],[2,1,0],[2,1],[2]]
[[3,1,0,0],[2,0,0],[2,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,0],[2]]
[[3,1,0,0],[2,0,0],[2,0],[1]]                                           => [[3,1,0,0],[2,1,0],[2,0],[2]]
[[3,1,0,0],[2,0,0],[2,0],[2]]                                           => [[3,1,0,0],[2,0,0],[2,0],[2]]
[[3,1,0,0],[2,1,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,0],[1]]
[[3,1,0,0],[2,1,0],[1,0],[1]]                                           => [[3,1,0,0],[3,0,0],[3,0],[1]]
[[3,1,0,0],[2,1,0],[1,1],[1]]                                           => [[3,1,0,0],[3,0,0],[2,0],[1]]
[[3,1,0,0],[2,1,0],[2,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,0],[1]]
[[3,1,0,0],[2,1,0],[2,0],[1]]                                           => [[3,1,0,0],[2,1,0],[2,0],[1]]
[[3,1,0,0],[2,1,0],[2,0],[2]]                                           => [[3,1,0,0],[2,0,0],[2,0],[1]]
[[3,1,0,0],[2,1,0],[2,1],[1]]                                           => [[3,1,0,0],[3,0,0],[1,0],[1]]
[[3,1,0,0],[2,1,0],[2,1],[2]]                                           => [[3,1,0,0],[2,0,0],[1,0],[1]]
[[3,1,0,0],[3,0,0],[0,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,1],[1]]
[[3,1,0,0],[3,0,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,1],[1]]
[[3,1,0,0],[3,0,0],[1,0],[1]]                                           => [[3,1,0,0],[2,1,0],[2,1],[1]]
[[3,1,0,0],[3,0,0],[2,0],[0]]                                           => [[3,1,0,0],[3,1,0],[1,1],[1]]
[[3,1,0,0],[3,0,0],[2,0],[1]]                                           => [[3,1,0,0],[2,1,0],[1,1],[1]]
[[3,1,0,0],[3,0,0],[2,0],[2]]                                           => [[3,1,0,0],[1,1,0],[1,1],[1]]
[[3,1,0,0],[3,0,0],[3,0],[0]]                                           => [[3,1,0,0],[3,1,0],[1,0],[1]]
[[3,1,0,0],[3,0,0],[3,0],[1]]                                           => [[3,1,0,0],[2,1,0],[1,0],[1]]
[[3,1,0,0],[3,0,0],[3,0],[2]]                                           => [[3,1,0,0],[1,1,0],[1,0],[1]]
[[3,1,0,0],[3,0,0],[3,0],[3]]                                           => [[3,1,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0],[3,1,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,0],[0]]
[[3,1,0,0],[3,1,0],[1,0],[1]]                                           => [[3,1,0,0],[3,0,0],[3,0],[0]]
[[3,1,0,0],[3,1,0],[1,1],[1]]                                           => [[3,1,0,0],[3,0,0],[2,0],[0]]
[[3,1,0,0],[3,1,0],[2,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,0],[0]]
[[3,1,0,0],[3,1,0],[2,0],[1]]                                           => [[3,1,0,0],[2,1,0],[2,0],[0]]
[[3,1,0,0],[3,1,0],[2,0],[2]]                                           => [[3,1,0,0],[2,0,0],[2,0],[0]]
[[3,1,0,0],[3,1,0],[2,1],[1]]                                           => [[3,1,0,0],[3,0,0],[1,0],[0]]
[[3,1,0,0],[3,1,0],[2,1],[2]]                                           => [[3,1,0,0],[2,0,0],[1,0],[0]]
[[3,1,0,0],[3,1,0],[3,0],[0]]                                           => [[3,1,0,0],[3,1,0],[1,0],[0]]
[[3,1,0,0],[3,1,0],[3,0],[1]]                                           => [[3,1,0,0],[2,1,0],[1,0],[0]]
[[3,1,0,0],[3,1,0],[3,0],[2]]                                           => [[3,1,0,0],[1,1,0],[1,0],[0]]
[[3,1,0,0],[3,1,0],[3,0],[3]]                                           => [[3,1,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0],[3,1,0],[3,1],[1]]                                           => [[3,1,0,0],[3,0,0],[0,0],[0]]
[[3,1,0,0],[3,1,0],[3,1],[2]]                                           => [[3,1,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0],[3,1,0],[3,1],[3]]                                           => [[3,1,0,0],[1,0,0],[0,0],[0]]
[[2,2,0,0],[2,0,0],[0,0],[0]]                                           => [[2,2,0,0],[2,2,0],[2,2],[2]]
[[2,2,0,0],[2,0,0],[1,0],[0]]                                           => [[2,2,0,0],[2,2,0],[2,1],[2]]
[[2,2,0,0],[2,0,0],[1,0],[1]]                                           => [[2,2,0,0],[2,1,0],[2,1],[2]]
[[2,2,0,0],[2,0,0],[2,0],[0]]                                           => [[2,2,0,0],[2,2,0],[2,0],[2]]
[[2,2,0,0],[2,0,0],[2,0],[1]]                                           => [[2,2,0,0],[2,1,0],[2,0],[2]]
[[2,2,0,0],[2,0,0],[2,0],[2]]                                           => [[2,2,0,0],[2,0,0],[2,0],[2]]
[[2,2,0,0],[2,1,0],[1,0],[0]]                                           => [[2,2,0,0],[2,2,0],[2,1],[1]]
[[2,2,0,0],[2,1,0],[1,0],[1]]                                           => [[2,2,0,0],[2,1,0],[2,1],[1]]
[[2,2,0,0],[2,1,0],[1,1],[1]]                                           => [[2,2,0,0],[2,1,0],[1,1],[1]]
[[2,2,0,0],[2,1,0],[2,0],[0]]                                           => [[2,2,0,0],[2,2,0],[2,0],[1]]
[[2,2,0,0],[2,1,0],[2,0],[1]]                                           => [[2,2,0,0],[2,1,0],[2,0],[1]]
[[2,2,0,0],[2,1,0],[2,0],[2]]                                           => [[2,2,0,0],[2,0,0],[2,0],[1]]
[[2,2,0,0],[2,1,0],[2,1],[1]]                                           => [[2,2,0,0],[2,1,0],[1,0],[1]]
[[2,2,0,0],[2,1,0],[2,1],[2]]                                           => [[2,2,0,0],[2,0,0],[1,0],[1]]
[[2,2,0,0],[2,2,0],[2,0],[0]]                                           => [[2,2,0,0],[2,2,0],[2,0],[0]]
[[2,2,0,0],[2,2,0],[2,0],[1]]                                           => [[2,2,0,0],[2,1,0],[2,0],[0]]
[[2,2,0,0],[2,2,0],[2,0],[2]]                                           => [[2,2,0,0],[2,0,0],[2,0],[0]]
[[2,2,0,0],[2,2,0],[2,1],[1]]                                           => [[2,2,0,0],[2,1,0],[1,0],[0]]
[[2,2,0,0],[2,2,0],[2,1],[2]]                                           => [[2,2,0,0],[2,0,0],[1,0],[0]]
[[2,2,0,0],[2,2,0],[2,2],[2]]                                           => [[2,2,0,0],[2,0,0],[0,0],[0]]
[[2,1,1,0],[1,1,0],[1,0],[0]]                                           => [[2,1,1,0],[2,1,1],[2,1],[2]]
[[2,1,1,0],[1,1,0],[1,0],[1]]                                           => [[2,1,1,0],[2,1,0],[2,1],[2]]
[[2,1,1,0],[1,1,0],[1,1],[1]]                                           => [[2,1,1,0],[2,1,0],[2,0],[2]]
[[2,1,1,0],[1,1,1],[1,1],[1]]                                           => [[2,1,1,0],[2,1,0],[2,0],[1]]
[[2,1,1,0],[2,1,0],[1,0],[0]]                                           => [[2,1,1,0],[2,1,1],[2,1],[1]]
[[2,1,1,0],[2,1,0],[1,0],[1]]                                           => [[2,1,1,0],[2,1,0],[2,1],[1]]
[[2,1,1,0],[2,1,0],[1,1],[1]]                                           => [[2,1,1,0],[2,1,0],[1,1],[1]]
[[2,1,1,0],[2,1,0],[2,0],[0]]                                           => [[2,1,1,0],[2,1,1],[1,1],[1]]
[[2,1,1,0],[2,1,0],[2,0],[1]]                                           => [[2,1,1,0],[1,1,1],[1,1],[1]]
[[2,1,1,0],[2,1,0],[2,0],[2]]                                           => [[2,1,1,0],[1,1,0],[1,1],[1]]
[[2,1,1,0],[2,1,0],[2,1],[1]]                                           => [[2,1,1,0],[2,1,0],[1,0],[1]]
[[2,1,1,0],[2,1,0],[2,1],[2]]                                           => [[2,1,1,0],[1,1,0],[1,0],[1]]
[[2,1,1,0],[2,1,1],[1,1],[1]]                                           => [[2,1,1,0],[2,1,0],[2,0],[0]]
[[2,1,1,0],[2,1,1],[2,1],[1]]                                           => [[2,1,1,0],[2,1,0],[1,0],[0]]
[[2,1,1,0],[2,1,1],[2,1],[2]]                                           => [[2,1,1,0],[1,1,0],[1,0],[0]]
[[1,1,1,1],[1,1,1],[1,1],[1]]                                           => [[1,1,1,1],[1,1,1],[1,1],[1]]
[[5,0,0,0],[0,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[5,0],[5]]
[[5,0,0,0],[1,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[5,0],[4]]
[[5,0,0,0],[1,0,0],[1,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[4]]
[[5,0,0,0],[1,0,0],[1,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[4]]
[[5,0,0,0],[2,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[5,0],[3]]
[[5,0,0,0],[2,0,0],[1,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[3]]
[[5,0,0,0],[2,0,0],[1,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[3]]
[[5,0,0,0],[2,0,0],[2,0],[0]]                                           => [[5,0,0,0],[5,0,0],[3,0],[3]]
[[5,0,0,0],[2,0,0],[2,0],[1]]                                           => [[5,0,0,0],[4,0,0],[3,0],[3]]
[[5,0,0,0],[2,0,0],[2,0],[2]]                                           => [[5,0,0,0],[3,0,0],[3,0],[3]]
[[5,0,0,0],[3,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[5,0],[2]]
[[5,0,0,0],[3,0,0],[1,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[2]]
[[5,0,0,0],[3,0,0],[1,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[2]]
[[5,0,0,0],[3,0,0],[2,0],[0]]                                           => [[5,0,0,0],[5,0,0],[3,0],[2]]
[[5,0,0,0],[3,0,0],[2,0],[1]]                                           => [[5,0,0,0],[4,0,0],[3,0],[2]]
[[5,0,0,0],[3,0,0],[2,0],[2]]                                           => [[5,0,0,0],[3,0,0],[3,0],[2]]
[[5,0,0,0],[3,0,0],[3,0],[0]]                                           => [[5,0,0,0],[5,0,0],[2,0],[2]]
[[5,0,0,0],[3,0,0],[3,0],[1]]                                           => [[5,0,0,0],[4,0,0],[2,0],[2]]
[[5,0,0,0],[3,0,0],[3,0],[2]]                                           => [[5,0,0,0],[3,0,0],[2,0],[2]]
[[5,0,0,0],[3,0,0],[3,0],[3]]                                           => [[5,0,0,0],[2,0,0],[2,0],[2]]
[[5,0,0,0],[4,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[5,0],[1]]
[[5,0,0,0],[4,0,0],[1,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[1]]
[[5,0,0,0],[4,0,0],[1,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[1]]
[[5,0,0,0],[4,0,0],[2,0],[0]]                                           => [[5,0,0,0],[5,0,0],[3,0],[1]]
[[5,0,0,0],[4,0,0],[2,0],[1]]                                           => [[5,0,0,0],[4,0,0],[3,0],[1]]
[[5,0,0,0],[4,0,0],[2,0],[2]]                                           => [[5,0,0,0],[3,0,0],[3,0],[1]]
[[5,0,0,0],[4,0,0],[3,0],[0]]                                           => [[5,0,0,0],[5,0,0],[2,0],[1]]
[[5,0,0,0],[4,0,0],[3,0],[1]]                                           => [[5,0,0,0],[4,0,0],[2,0],[1]]
[[5,0,0,0],[4,0,0],[3,0],[2]]                                           => [[5,0,0,0],[3,0,0],[2,0],[1]]
[[5,0,0,0],[4,0,0],[3,0],[3]]                                           => [[5,0,0,0],[2,0,0],[2,0],[1]]
[[5,0,0,0],[4,0,0],[4,0],[0]]                                           => [[5,0,0,0],[5,0,0],[1,0],[1]]
[[5,0,0,0],[4,0,0],[4,0],[1]]                                           => [[5,0,0,0],[4,0,0],[1,0],[1]]
[[5,0,0,0],[4,0,0],[4,0],[2]]                                           => [[5,0,0,0],[3,0,0],[1,0],[1]]
[[5,0,0,0],[4,0,0],[4,0],[3]]                                           => [[5,0,0,0],[2,0,0],[1,0],[1]]
[[5,0,0,0],[4,0,0],[4,0],[4]]                                           => [[5,0,0,0],[1,0,0],[1,0],[1]]
[[5,0,0,0],[5,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[5,0],[0]]
[[5,0,0,0],[5,0,0],[1,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[0]]
[[5,0,0,0],[5,0,0],[1,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[0]]
[[5,0,0,0],[5,0,0],[2,0],[0]]                                           => [[5,0,0,0],[5,0,0],[3,0],[0]]
[[5,0,0,0],[5,0,0],[2,0],[1]]                                           => [[5,0,0,0],[4,0,0],[3,0],[0]]
[[5,0,0,0],[5,0,0],[2,0],[2]]                                           => [[5,0,0,0],[3,0,0],[3,0],[0]]
[[5,0,0,0],[5,0,0],[3,0],[0]]                                           => [[5,0,0,0],[5,0,0],[2,0],[0]]
[[5,0,0,0],[5,0,0],[3,0],[1]]                                           => [[5,0,0,0],[4,0,0],[2,0],[0]]
[[5,0,0,0],[5,0,0],[3,0],[2]]                                           => [[5,0,0,0],[3,0,0],[2,0],[0]]
[[5,0,0,0],[5,0,0],[3,0],[3]]                                           => [[5,0,0,0],[2,0,0],[2,0],[0]]
[[5,0,0,0],[5,0,0],[4,0],[0]]                                           => [[5,0,0,0],[5,0,0],[1,0],[0]]
[[5,0,0,0],[5,0,0],[4,0],[1]]                                           => [[5,0,0,0],[4,0,0],[1,0],[0]]
[[5,0,0,0],[5,0,0],[4,0],[2]]                                           => [[5,0,0,0],[3,0,0],[1,0],[0]]
[[5,0,0,0],[5,0,0],[4,0],[3]]                                           => [[5,0,0,0],[2,0,0],[1,0],[0]]
[[5,0,0,0],[5,0,0],[4,0],[4]]                                           => [[5,0,0,0],[1,0,0],[1,0],[0]]
[[5,0,0,0],[5,0,0],[5,0],[0]]                                           => [[5,0,0,0],[5,0,0],[0,0],[0]]
[[5,0,0,0],[5,0,0],[5,0],[1]]                                           => [[5,0,0,0],[4,0,0],[0,0],[0]]
[[5,0,0,0],[5,0,0],[5,0],[2]]                                           => [[5,0,0,0],[3,0,0],[0,0],[0]]
[[5,0,0,0],[5,0,0],[5,0],[3]]                                           => [[5,0,0,0],[2,0,0],[0,0],[0]]
[[5,0,0,0],[5,0,0],[5,0],[4]]                                           => [[5,0,0,0],[1,0,0],[0,0],[0]]
[[5,0,0,0],[5,0,0],[5,0],[5]]                                           => [[5,0,0,0],[0,0,0],[0,0],[0]]
[[4,1,0,0],[1,0,0],[0,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,1],[4]]
[[4,1,0,0],[1,0,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[4]]
[[4,1,0,0],[1,0,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[4,0],[4]]
[[4,1,0,0],[1,1,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[3]]
[[4,1,0,0],[1,1,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[4,0],[3]]
[[4,1,0,0],[1,1,0],[1,1],[1]]                                           => [[4,1,0,0],[4,0,0],[3,0],[3]]
[[4,1,0,0],[2,0,0],[0,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,1],[3]]
[[4,1,0,0],[2,0,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,1],[3]]
[[4,1,0,0],[2,0,0],[1,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,1],[3]]
[[4,1,0,0],[2,0,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,0],[3]]
[[4,1,0,0],[2,0,0],[2,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,0],[3]]
[[4,1,0,0],[2,0,0],[2,0],[2]]                                           => [[4,1,0,0],[3,0,0],[3,0],[3]]
[[4,1,0,0],[2,1,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[2]]
[[4,1,0,0],[2,1,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[4,0],[2]]
[[4,1,0,0],[2,1,0],[1,1],[1]]                                           => [[4,1,0,0],[4,0,0],[3,0],[2]]
[[4,1,0,0],[2,1,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,0],[2]]
[[4,1,0,0],[2,1,0],[2,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,0],[2]]
[[4,1,0,0],[2,1,0],[2,0],[2]]                                           => [[4,1,0,0],[3,0,0],[3,0],[2]]
[[4,1,0,0],[2,1,0],[2,1],[1]]                                           => [[4,1,0,0],[4,0,0],[2,0],[2]]
[[4,1,0,0],[2,1,0],[2,1],[2]]                                           => [[4,1,0,0],[3,0,0],[2,0],[2]]
[[4,1,0,0],[3,0,0],[0,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,1],[2]]
[[4,1,0,0],[3,0,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,1],[2]]
[[4,1,0,0],[3,0,0],[1,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,1],[2]]
[[4,1,0,0],[3,0,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,1],[2]]
[[4,1,0,0],[3,0,0],[2,0],[1]]                                           => [[4,1,0,0],[3,1,0],[2,1],[2]]
[[4,1,0,0],[3,0,0],[2,0],[2]]                                           => [[4,1,0,0],[2,1,0],[2,1],[2]]
[[4,1,0,0],[3,0,0],[3,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,0],[2]]
[[4,1,0,0],[3,0,0],[3,0],[1]]                                           => [[4,1,0,0],[3,1,0],[2,0],[2]]
[[4,1,0,0],[3,0,0],[3,0],[2]]                                           => [[4,1,0,0],[2,1,0],[2,0],[2]]
[[4,1,0,0],[3,0,0],[3,0],[3]]                                           => [[4,1,0,0],[2,0,0],[2,0],[2]]
[[4,1,0,0],[3,1,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[1]]
[[4,1,0,0],[3,1,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[4,0],[1]]
[[4,1,0,0],[3,1,0],[1,1],[1]]                                           => [[4,1,0,0],[4,0,0],[3,0],[1]]
[[4,1,0,0],[3,1,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,0],[1]]
[[4,1,0,0],[3,1,0],[2,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,0],[1]]
[[4,1,0,0],[3,1,0],[2,0],[2]]                                           => [[4,1,0,0],[3,0,0],[3,0],[1]]
[[4,1,0,0],[3,1,0],[2,1],[1]]                                           => [[4,1,0,0],[4,0,0],[2,0],[1]]
[[4,1,0,0],[3,1,0],[2,1],[2]]                                           => [[4,1,0,0],[3,0,0],[2,0],[1]]
[[4,1,0,0],[3,1,0],[3,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,0],[1]]
[[4,1,0,0],[3,1,0],[3,0],[1]]                                           => [[4,1,0,0],[3,1,0],[2,0],[1]]
[[4,1,0,0],[3,1,0],[3,0],[2]]                                           => [[4,1,0,0],[2,1,0],[2,0],[1]]
[[4,1,0,0],[3,1,0],[3,0],[3]]                                           => [[4,1,0,0],[2,0,0],[2,0],[1]]
[[4,1,0,0],[3,1,0],[3,1],[1]]                                           => [[4,1,0,0],[4,0,0],[1,0],[1]]
[[4,1,0,0],[3,1,0],[3,1],[2]]                                           => [[4,1,0,0],[3,0,0],[1,0],[1]]
[[4,1,0,0],[3,1,0],[3,1],[3]]                                           => [[4,1,0,0],[2,0,0],[1,0],[1]]
[[4,1,0,0],[4,0,0],[0,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,1],[1]]
[[4,1,0,0],[4,0,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,1],[1]]
[[4,1,0,0],[4,0,0],[1,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,1],[1]]
[[4,1,0,0],[4,0,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,1],[1]]
[[4,1,0,0],[4,0,0],[2,0],[1]]                                           => [[4,1,0,0],[3,1,0],[2,1],[1]]
[[4,1,0,0],[4,0,0],[2,0],[2]]                                           => [[4,1,0,0],[2,1,0],[2,1],[1]]
[[4,1,0,0],[4,0,0],[3,0],[0]]                                           => [[4,1,0,0],[4,1,0],[1,1],[1]]
[[4,1,0,0],[4,0,0],[3,0],[1]]                                           => [[4,1,0,0],[3,1,0],[1,1],[1]]
[[4,1,0,0],[4,0,0],[3,0],[2]]                                           => [[4,1,0,0],[2,1,0],[1,1],[1]]
[[4,1,0,0],[4,0,0],[3,0],[3]]                                           => [[4,1,0,0],[1,1,0],[1,1],[1]]
[[4,1,0,0],[4,0,0],[4,0],[0]]                                           => [[4,1,0,0],[4,1,0],[1,0],[1]]
[[4,1,0,0],[4,0,0],[4,0],[1]]                                           => [[4,1,0,0],[3,1,0],[1,0],[1]]
[[4,1,0,0],[4,0,0],[4,0],[2]]                                           => [[4,1,0,0],[2,1,0],[1,0],[1]]
[[4,1,0,0],[4,0,0],[4,0],[3]]                                           => [[4,1,0,0],[1,1,0],[1,0],[1]]
[[4,1,0,0],[4,0,0],[4,0],[4]]                                           => [[4,1,0,0],[1,0,0],[1,0],[1]]
[[4,1,0,0],[4,1,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[0]]
[[4,1,0,0],[4,1,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[4,0],[0]]
[[4,1,0,0],[4,1,0],[1,1],[1]]                                           => [[4,1,0,0],[4,0,0],[3,0],[0]]
[[4,1,0,0],[4,1,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,0],[0]]
[[4,1,0,0],[4,1,0],[2,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,0],[0]]
[[4,1,0,0],[4,1,0],[2,0],[2]]                                           => [[4,1,0,0],[3,0,0],[3,0],[0]]
[[4,1,0,0],[4,1,0],[2,1],[1]]                                           => [[4,1,0,0],[4,0,0],[2,0],[0]]
[[4,1,0,0],[4,1,0],[2,1],[2]]                                           => [[4,1,0,0],[3,0,0],[2,0],[0]]
[[4,1,0,0],[4,1,0],[3,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,0],[0]]
[[4,1,0,0],[4,1,0],[3,0],[1]]                                           => [[4,1,0,0],[3,1,0],[2,0],[0]]
[[4,1,0,0],[4,1,0],[3,0],[2]]                                           => [[4,1,0,0],[2,1,0],[2,0],[0]]
[[4,1,0,0],[4,1,0],[3,0],[3]]                                           => [[4,1,0,0],[2,0,0],[2,0],[0]]
[[4,1,0,0],[4,1,0],[3,1],[1]]                                           => [[4,1,0,0],[4,0,0],[1,0],[0]]
[[4,1,0,0],[4,1,0],[3,1],[2]]                                           => [[4,1,0,0],[3,0,0],[1,0],[0]]
[[4,1,0,0],[4,1,0],[3,1],[3]]                                           => [[4,1,0,0],[2,0,0],[1,0],[0]]
[[4,1,0,0],[4,1,0],[4,0],[0]]                                           => [[4,1,0,0],[4,1,0],[1,0],[0]]
[[4,1,0,0],[4,1,0],[4,0],[1]]                                           => [[4,1,0,0],[3,1,0],[1,0],[0]]
[[4,1,0,0],[4,1,0],[4,0],[2]]                                           => [[4,1,0,0],[2,1,0],[1,0],[0]]
[[4,1,0,0],[4,1,0],[4,0],[3]]                                           => [[4,1,0,0],[1,1,0],[1,0],[0]]
[[4,1,0,0],[4,1,0],[4,0],[4]]                                           => [[4,1,0,0],[1,0,0],[1,0],[0]]
[[4,1,0,0],[4,1,0],[4,1],[1]]                                           => [[4,1,0,0],[4,0,0],[0,0],[0]]
[[4,1,0,0],[4,1,0],[4,1],[2]]                                           => [[4,1,0,0],[3,0,0],[0,0],[0]]
[[4,1,0,0],[4,1,0],[4,1],[3]]                                           => [[4,1,0,0],[2,0,0],[0,0],[0]]
[[4,1,0,0],[4,1,0],[4,1],[4]]                                           => [[4,1,0,0],[1,0,0],[0,0],[0]]
[[3,2,0,0],[2,0,0],[0,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,2],[3]]
[[3,2,0,0],[2,0,0],[1,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,1],[3]]
[[3,2,0,0],[2,0,0],[1,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,1],[3]]
[[3,2,0,0],[2,0,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,0],[3]]
[[3,2,0,0],[2,0,0],[2,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,0],[3]]
[[3,2,0,0],[2,0,0],[2,0],[2]]                                           => [[3,2,0,0],[3,0,0],[3,0],[3]]
[[3,2,0,0],[2,1,0],[1,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,1],[2]]
[[3,2,0,0],[2,1,0],[1,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,1],[2]]
[[3,2,0,0],[2,1,0],[1,1],[1]]                                           => [[3,2,0,0],[3,1,0],[2,1],[2]]
[[3,2,0,0],[2,1,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,0],[2]]
[[3,2,0,0],[2,1,0],[2,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,0],[2]]
[[3,2,0,0],[2,1,0],[2,0],[2]]                                           => [[3,2,0,0],[3,0,0],[3,0],[2]]
[[3,2,0,0],[2,1,0],[2,1],[1]]                                           => [[3,2,0,0],[3,1,0],[2,0],[2]]
[[3,2,0,0],[2,1,0],[2,1],[2]]                                           => [[3,2,0,0],[3,0,0],[2,0],[2]]
[[3,2,0,0],[2,2,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,0],[1]]
[[3,2,0,0],[2,2,0],[2,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,0],[1]]
[[3,2,0,0],[2,2,0],[2,0],[2]]                                           => [[3,2,0,0],[3,0,0],[3,0],[1]]
[[3,2,0,0],[2,2,0],[2,1],[1]]                                           => [[3,2,0,0],[3,1,0],[2,0],[1]]
[[3,2,0,0],[2,2,0],[2,1],[2]]                                           => [[3,2,0,0],[3,0,0],[2,0],[1]]
[[3,2,0,0],[2,2,0],[2,2],[2]]                                           => [[3,2,0,0],[3,0,0],[1,0],[1]]
[[3,2,0,0],[3,0,0],[0,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,2],[2]]
[[3,2,0,0],[3,0,0],[1,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,2],[2]]
[[3,2,0,0],[3,0,0],[1,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,2],[2]]
[[3,2,0,0],[3,0,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,1],[2]]
[[3,2,0,0],[3,0,0],[2,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,1],[2]]
[[3,2,0,0],[3,0,0],[2,0],[2]]                                           => [[3,2,0,0],[2,1,0],[2,1],[2]]
[[3,2,0,0],[3,0,0],[3,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,0],[2]]
[[3,2,0,0],[3,0,0],[3,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,0],[2]]
[[3,2,0,0],[3,0,0],[3,0],[2]]                                           => [[3,2,0,0],[2,1,0],[2,0],[2]]
[[3,2,0,0],[3,0,0],[3,0],[3]]                                           => [[3,2,0,0],[2,0,0],[2,0],[2]]
[[3,2,0,0],[3,1,0],[1,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,1],[1]]
[[3,2,0,0],[3,1,0],[1,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,1],[1]]
[[3,2,0,0],[3,1,0],[1,1],[1]]                                           => [[3,2,0,0],[3,1,0],[2,1],[1]]
[[3,2,0,0],[3,1,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,1],[1]]
[[3,2,0,0],[3,1,0],[2,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,1],[1]]
[[3,2,0,0],[3,1,0],[2,0],[2]]                                           => [[3,2,0,0],[2,1,0],[2,1],[1]]
[[3,2,0,0],[3,1,0],[2,1],[1]]                                           => [[3,2,0,0],[3,1,0],[1,1],[1]]
[[3,2,0,0],[3,1,0],[2,1],[2]]                                           => [[3,2,0,0],[2,1,0],[1,1],[1]]
[[3,2,0,0],[3,1,0],[3,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,0],[1]]
[[3,2,0,0],[3,1,0],[3,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,0],[1]]
[[3,2,0,0],[3,1,0],[3,0],[2]]                                           => [[3,2,0,0],[2,1,0],[2,0],[1]]
[[3,2,0,0],[3,1,0],[3,0],[3]]                                           => [[3,2,0,0],[2,0,0],[2,0],[1]]
[[3,2,0,0],[3,1,0],[3,1],[1]]                                           => [[3,2,0,0],[3,1,0],[1,0],[1]]
[[3,2,0,0],[3,1,0],[3,1],[2]]                                           => [[3,2,0,0],[2,1,0],[1,0],[1]]
[[3,2,0,0],[3,1,0],[3,1],[3]]                                           => [[3,2,0,0],[2,0,0],[1,0],[1]]
[[3,2,0,0],[3,2,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,0],[0]]
[[3,2,0,0],[3,2,0],[2,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,0],[0]]
[[3,2,0,0],[3,2,0],[2,0],[2]]                                           => [[3,2,0,0],[3,0,0],[3,0],[0]]
[[3,2,0,0],[3,2,0],[2,1],[1]]                                           => [[3,2,0,0],[3,1,0],[2,0],[0]]
[[3,2,0,0],[3,2,0],[2,1],[2]]                                           => [[3,2,0,0],[3,0,0],[2,0],[0]]
[[3,2,0,0],[3,2,0],[2,2],[2]]                                           => [[3,2,0,0],[3,0,0],[1,0],[0]]
[[3,2,0,0],[3,2,0],[3,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,0],[0]]
[[3,2,0,0],[3,2,0],[3,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,0],[0]]
[[3,2,0,0],[3,2,0],[3,0],[2]]                                           => [[3,2,0,0],[2,1,0],[2,0],[0]]
[[3,2,0,0],[3,2,0],[3,0],[3]]                                           => [[3,2,0,0],[2,0,0],[2,0],[0]]
[[3,2,0,0],[3,2,0],[3,1],[1]]                                           => [[3,2,0,0],[3,1,0],[1,0],[0]]
[[3,2,0,0],[3,2,0],[3,1],[2]]                                           => [[3,2,0,0],[2,1,0],[1,0],[0]]
[[3,2,0,0],[3,2,0],[3,1],[3]]                                           => [[3,2,0,0],[2,0,0],[1,0],[0]]
[[3,2,0,0],[3,2,0],[3,2],[2]]                                           => [[3,2,0,0],[3,0,0],[0,0],[0]]
[[3,2,0,0],[3,2,0],[3,2],[3]]                                           => [[3,2,0,0],[2,0,0],[0,0],[0]]
[[3,1,1,0],[1,1,0],[1,0],[0]]                                           => [[3,1,1,0],[3,1,1],[3,1],[3]]
[[3,1,1,0],[1,1,0],[1,0],[1]]                                           => [[3,1,1,0],[3,1,0],[3,1],[3]]
[[3,1,1,0],[1,1,0],[1,1],[1]]                                           => [[3,1,1,0],[3,1,0],[3,0],[3]]
[[3,1,1,0],[1,1,1],[1,1],[1]]                                           => [[3,1,1,0],[3,1,0],[3,0],[2]]
[[3,1,1,0],[2,1,0],[1,0],[0]]                                           => [[3,1,1,0],[3,1,1],[3,1],[2]]
[[3,1,1,0],[2,1,0],[1,0],[1]]                                           => [[3,1,1,0],[3,1,0],[3,1],[2]]
[[3,1,1,0],[2,1,0],[1,1],[1]]                                           => [[3,1,1,0],[3,1,0],[2,1],[2]]
[[3,1,1,0],[2,1,0],[2,0],[0]]                                           => [[3,1,1,0],[3,1,1],[2,1],[2]]
[[3,1,1,0],[2,1,0],[2,0],[1]]                                           => [[3,1,1,0],[2,1,1],[2,1],[2]]
[[3,1,1,0],[2,1,0],[2,0],[2]]                                           => [[3,1,1,0],[2,1,0],[2,1],[2]]
[[3,1,1,0],[2,1,0],[2,1],[1]]                                           => [[3,1,1,0],[3,1,0],[2,0],[2]]
[[3,1,1,0],[2,1,0],[2,1],[2]]                                           => [[3,1,1,0],[2,1,0],[2,0],[2]]
[[3,1,1,0],[2,1,1],[1,1],[1]]                                           => [[3,1,1,0],[3,1,0],[3,0],[1]]
[[3,1,1,0],[2,1,1],[2,1],[1]]                                           => [[3,1,1,0],[3,1,0],[2,0],[1]]
[[3,1,1,0],[2,1,1],[2,1],[2]]                                           => [[3,1,1,0],[2,1,0],[2,0],[1]]
[[3,1,1,0],[3,1,0],[1,0],[0]]                                           => [[3,1,1,0],[3,1,1],[3,1],[1]]
[[3,1,1,0],[3,1,0],[1,0],[1]]                                           => [[3,1,1,0],[3,1,0],[3,1],[1]]
[[3,1,1,0],[3,1,0],[1,1],[1]]                                           => [[3,1,1,0],[3,1,0],[2,1],[1]]
[[3,1,1,0],[3,1,0],[2,0],[0]]                                           => [[3,1,1,0],[3,1,1],[2,1],[1]]
[[3,1,1,0],[3,1,0],[2,0],[1]]                                           => [[3,1,1,0],[2,1,1],[2,1],[1]]
[[3,1,1,0],[3,1,0],[2,0],[2]]                                           => [[3,1,1,0],[2,1,0],[2,1],[1]]
[[3,1,1,0],[3,1,0],[2,1],[1]]                                           => [[3,1,1,0],[3,1,0],[1,1],[1]]
[[3,1,1,0],[3,1,0],[2,1],[2]]                                           => [[3,1,1,0],[2,1,0],[1,1],[1]]
[[3,1,1,0],[3,1,0],[3,0],[0]]                                           => [[3,1,1,0],[3,1,1],[1,1],[1]]
[[3,1,1,0],[3,1,0],[3,0],[1]]                                           => [[3,1,1,0],[2,1,1],[1,1],[1]]
[[3,1,1,0],[3,1,0],[3,0],[2]]                                           => [[3,1,1,0],[1,1,1],[1,1],[1]]
[[3,1,1,0],[3,1,0],[3,0],[3]]                                           => [[3,1,1,0],[1,1,0],[1,1],[1]]
[[3,1,1,0],[3,1,0],[3,1],[1]]                                           => [[3,1,1,0],[3,1,0],[1,0],[1]]
[[3,1,1,0],[3,1,0],[3,1],[2]]                                           => [[3,1,1,0],[2,1,0],[1,0],[1]]
[[3,1,1,0],[3,1,0],[3,1],[3]]                                           => [[3,1,1,0],[1,1,0],[1,0],[1]]
[[3,1,1,0],[3,1,1],[1,1],[1]]                                           => [[3,1,1,0],[3,1,0],[3,0],[0]]
[[3,1,1,0],[3,1,1],[2,1],[1]]                                           => [[3,1,1,0],[3,1,0],[2,0],[0]]
[[3,1,1,0],[3,1,1],[2,1],[2]]                                           => [[3,1,1,0],[2,1,0],[2,0],[0]]
[[3,1,1,0],[3,1,1],[3,1],[1]]                                           => [[3,1,1,0],[3,1,0],[1,0],[0]]
[[3,1,1,0],[3,1,1],[3,1],[2]]                                           => [[3,1,1,0],[2,1,0],[1,0],[0]]
[[3,1,1,0],[3,1,1],[3,1],[3]]                                           => [[3,1,1,0],[1,1,0],[1,0],[0]]
[[2,2,1,0],[2,1,0],[1,0],[0]]                                           => [[2,2,1,0],[2,2,1],[2,2],[2]]
[[2,2,1,0],[2,1,0],[1,0],[1]]                                           => [[2,2,1,0],[2,2,0],[2,2],[2]]
[[2,2,1,0],[2,1,0],[1,1],[1]]                                           => [[2,2,1,0],[2,2,0],[2,1],[2]]
[[2,2,1,0],[2,1,0],[2,0],[0]]                                           => [[2,2,1,0],[2,2,1],[2,1],[2]]
[[2,2,1,0],[2,1,0],[2,0],[1]]                                           => [[2,2,1,0],[2,1,1],[2,1],[2]]
[[2,2,1,0],[2,1,0],[2,0],[2]]                                           => [[2,2,1,0],[2,1,0],[2,1],[2]]
[[2,2,1,0],[2,1,0],[2,1],[1]]                                           => [[2,2,1,0],[2,2,0],[2,0],[2]]
[[2,2,1,0],[2,1,0],[2,1],[2]]                                           => [[2,2,1,0],[2,1,0],[2,0],[2]]
[[2,2,1,0],[2,1,1],[1,1],[1]]                                           => [[2,2,1,0],[2,2,0],[2,1],[1]]
[[2,2,1,0],[2,1,1],[2,1],[1]]                                           => [[2,2,1,0],[2,2,0],[2,0],[1]]
[[2,2,1,0],[2,1,1],[2,1],[2]]                                           => [[2,2,1,0],[2,1,0],[2,0],[1]]
[[2,2,1,0],[2,2,0],[2,0],[0]]                                           => [[2,2,1,0],[2,2,1],[2,1],[1]]
[[2,2,1,0],[2,2,0],[2,0],[1]]                                           => [[2,2,1,0],[2,1,1],[2,1],[1]]
[[2,2,1,0],[2,2,0],[2,0],[2]]                                           => [[2,2,1,0],[2,1,0],[2,1],[1]]
[[2,2,1,0],[2,2,0],[2,1],[1]]                                           => [[2,2,1,0],[2,1,1],[1,1],[1]]
[[2,2,1,0],[2,2,0],[2,1],[2]]                                           => [[2,2,1,0],[2,1,0],[1,1],[1]]
[[2,2,1,0],[2,2,0],[2,2],[2]]                                           => [[2,2,1,0],[2,1,0],[1,0],[1]]
[[2,2,1,0],[2,2,1],[2,1],[1]]                                           => [[2,2,1,0],[2,2,0],[2,0],[0]]
[[2,2,1,0],[2,2,1],[2,1],[2]]                                           => [[2,2,1,0],[2,1,0],[2,0],[0]]
[[2,2,1,0],[2,2,1],[2,2],[2]]                                           => [[2,2,1,0],[2,1,0],[1,0],[0]]
[[2,1,1,1],[1,1,1],[1,1],[1]]                                           => [[2,1,1,1],[2,1,1],[2,1],[2]]
[[2,1,1,1],[2,1,1],[1,1],[1]]                                           => [[2,1,1,1],[2,1,1],[2,1],[1]]
[[2,1,1,1],[2,1,1],[2,1],[1]]                                           => [[2,1,1,1],[2,1,1],[1,1],[1]]
[[2,1,1,1],[2,1,1],[2,1],[2]]                                           => [[2,1,1,1],[1,1,1],[1,1],[1]]
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                               => [[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                               => [[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                               => [[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                               => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                               => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                               => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                               => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                               => [[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                               => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]                               => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]                               => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]                               => [[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]                               => [[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                               => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]                               => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]                               => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]                               => [[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                               => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]]
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                               => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                               => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                               => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                               => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]]                               => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]]
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]                               => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]]                               => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]                               => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]]
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]                               => [[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]                               => [[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]]                               => [[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]]                               => [[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]]                               => [[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]]
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]]
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]]
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]]
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]]
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]
[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]                               => [[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]]                               => [[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]]                               => [[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]]                               => [[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]]
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]]
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]
[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]                               => [[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]                               => [[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]                               => [[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]                               => [[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]                               => [[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]                               => [[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                               => [[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]]                               => [[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]]                               => [[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]
[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                 => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                 => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                 => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                 => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                 => [[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                 => [[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                 => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                 => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                 => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                 => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                 => [[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                 => [[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                 => [[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                 => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                 => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                 => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                 => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                 => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                 => [[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[1,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]

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Created: Jan 26, 2020 at 12:32 by FindStatCrew

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Last Updated: Jan 26, 2020 at 12:32 by Martin Rubey