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Map identifier: Mp00212

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Map name: inverse cycle

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Domain: Gelfand-Tsetlin patterns

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Codomain: Gelfand-Tsetlin patterns

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Description: The inverse cycle action on a Gelfand-Tsetlin pattern.

Regard a Gelfand-Tsetlin pattern $p$ as an element of the $A_{m-1}$ crystal of shape $\lambda$, where $\lambda$ is the partition given by the first row of $p$ and $m$ is the width of $p$. Let $s_i(p)$ be the reflection of $p$ along its $i$-string, for $i\in\{1,\dots,m-1\}$. Then this map returns $c^{-1}(p)=s_{m-1}\dots s_2 s_1 (p)$.

The order of this action is the width of the pattern. As a map on semistandard tableaux, it preserves the shape. Moreover, the weight of $c^{-1}(p)$ is the same as the weight of the inverse promotion of $p$.

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References: [1]   Oh, Y.-T., Park, E. Crystals, semistandard tableaux and cyclic sieving phenomenon [[MathSciNet:4039345]] [[arXiv:1906.07420]]

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Code:

def mapping(G):
    m = len(G)
    T = G.to_tableau()
    la = T.shape()
    C = crystals.Tableaux(CartanType("A", m-1), shape=la)
    x = C(rows=T)
    for i in range(1, m):
        x = x.s(i)
    return GelfandTsetlinPatterns(m)(x.to_tableau())


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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],[0]]
[[1,0,0],[1,0],[0]]                                                     => [[1,0,0],[1,0],[1]]
[[1,0,0],[1,0],[1]]                                                     => [[1,0,0],[0,0],[0]]
[[2,0,0],[0,0],[0]]                                                     => [[2,0,0],[2,0],[0]]
[[2,0,0],[1,0],[0]]                                                     => [[2,0,0],[2,0],[1]]
[[2,0,0],[1,0],[1]]                                                     => [[2,0,0],[1,0],[0]]
[[2,0,0],[2,0],[0]]                                                     => [[2,0,0],[2,0],[2]]
[[2,0,0],[2,0],[1]]                                                     => [[2,0,0],[1,0],[1]]
[[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],[0]]
[[1,1,0],[1,1],[1]]                                                     => [[1,1,0],[1,0],[1]]
[[3,0,0],[0,0],[0]]                                                     => [[3,0,0],[3,0],[0]]
[[3,0,0],[1,0],[0]]                                                     => [[3,0,0],[3,0],[1]]
[[3,0,0],[1,0],[1]]                                                     => [[3,0,0],[2,0],[0]]
[[3,0,0],[2,0],[0]]                                                     => [[3,0,0],[3,0],[2]]
[[3,0,0],[2,0],[1]]                                                     => [[3,0,0],[2,0],[1]]
[[3,0,0],[2,0],[2]]                                                     => [[3,0,0],[1,0],[0]]
[[3,0,0],[3,0],[0]]                                                     => [[3,0,0],[3,0],[3]]
[[3,0,0],[3,0],[1]]                                                     => [[3,0,0],[2,0],[2]]
[[3,0,0],[3,0],[2]]                                                     => [[3,0,0],[1,0],[1]]
[[3,0,0],[3,0],[3]]                                                     => [[3,0,0],[0,0],[0]]
[[2,1,0],[1,0],[0]]                                                     => [[2,1,0],[2,1],[1]]
[[2,1,0],[1,0],[1]]                                                     => [[2,1,0],[2,0],[0]]
[[2,1,0],[1,1],[1]]                                                     => [[2,1,0],[1,1],[1]]
[[2,1,0],[2,0],[0]]                                                     => [[2,1,0],[2,1],[2]]
[[2,1,0],[2,0],[1]]                                                     => [[2,1,0],[2,0],[1]]
[[2,1,0],[2,0],[2]]                                                     => [[2,1,0],[1,0],[0]]
[[2,1,0],[2,1],[1]]                                                     => [[2,1,0],[2,0],[2]]
[[2,1,0],[2,1],[2]]                                                     => [[2,1,0],[1,0],[1]]
[[1,1,1],[1,1],[1]]                                                     => [[1,1,1],[1,1],[1]]
[[4,0,0],[0,0],[0]]                                                     => [[4,0,0],[4,0],[0]]
[[4,0,0],[1,0],[0]]                                                     => [[4,0,0],[4,0],[1]]
[[4,0,0],[1,0],[1]]                                                     => [[4,0,0],[3,0],[0]]
[[4,0,0],[2,0],[0]]                                                     => [[4,0,0],[4,0],[2]]
[[4,0,0],[2,0],[1]]                                                     => [[4,0,0],[3,0],[1]]
[[4,0,0],[2,0],[2]]                                                     => [[4,0,0],[2,0],[0]]
[[4,0,0],[3,0],[0]]                                                     => [[4,0,0],[4,0],[3]]
[[4,0,0],[3,0],[1]]                                                     => [[4,0,0],[3,0],[2]]
[[4,0,0],[3,0],[2]]                                                     => [[4,0,0],[2,0],[1]]
[[4,0,0],[3,0],[3]]                                                     => [[4,0,0],[1,0],[0]]
[[4,0,0],[4,0],[0]]                                                     => [[4,0,0],[4,0],[4]]
[[4,0,0],[4,0],[1]]                                                     => [[4,0,0],[3,0],[3]]
[[4,0,0],[4,0],[2]]                                                     => [[4,0,0],[2,0],[2]]
[[4,0,0],[4,0],[3]]                                                     => [[4,0,0],[1,0],[1]]
[[4,0,0],[4,0],[4]]                                                     => [[4,0,0],[0,0],[0]]
[[3,1,0],[1,0],[0]]                                                     => [[3,1,0],[3,1],[1]]
[[3,1,0],[1,0],[1]]                                                     => [[3,1,0],[3,0],[0]]
[[3,1,0],[1,1],[1]]                                                     => [[3,1,0],[2,1],[1]]
[[3,1,0],[2,0],[0]]                                                     => [[3,1,0],[3,1],[2]]
[[3,1,0],[2,0],[1]]                                                     => [[3,1,0],[3,0],[1]]
[[3,1,0],[2,0],[2]]                                                     => [[3,1,0],[2,0],[0]]
[[3,1,0],[2,1],[1]]                                                     => [[3,1,0],[2,1],[2]]
[[3,1,0],[2,1],[2]]                                                     => [[3,1,0],[1,1],[1]]
[[3,1,0],[3,0],[0]]                                                     => [[3,1,0],[3,1],[3]]
[[3,1,0],[3,0],[1]]                                                     => [[3,1,0],[3,0],[2]]
[[3,1,0],[3,0],[2]]                                                     => [[3,1,0],[2,0],[1]]
[[3,1,0],[3,0],[3]]                                                     => [[3,1,0],[1,0],[0]]
[[3,1,0],[3,1],[1]]                                                     => [[3,1,0],[3,0],[3]]
[[3,1,0],[3,1],[2]]                                                     => [[3,1,0],[2,0],[2]]
[[3,1,0],[3,1],[3]]                                                     => [[3,1,0],[1,0],[1]]
[[2,2,0],[2,0],[0]]                                                     => [[2,2,0],[2,2],[2]]
[[2,2,0],[2,0],[1]]                                                     => [[2,2,0],[2,1],[1]]
[[2,2,0],[2,0],[2]]                                                     => [[2,2,0],[2,0],[0]]
[[2,2,0],[2,1],[1]]                                                     => [[2,2,0],[2,1],[2]]
[[2,2,0],[2,1],[2]]                                                     => [[2,2,0],[2,0],[1]]
[[2,2,0],[2,2],[2]]                                                     => [[2,2,0],[2,0],[2]]
[[2,1,1],[1,1],[1]]                                                     => [[2,1,1],[2,1],[1]]
[[2,1,1],[2,1],[1]]                                                     => [[2,1,1],[2,1],[2]]
[[2,1,1],[2,1],[2]]                                                     => [[2,1,1],[1,1],[1]]
[[5,0,0],[0,0],[0]]                                                     => [[5,0,0],[5,0],[0]]
[[5,0,0],[1,0],[0]]                                                     => [[5,0,0],[5,0],[1]]
[[5,0,0],[1,0],[1]]                                                     => [[5,0,0],[4,0],[0]]
[[5,0,0],[2,0],[0]]                                                     => [[5,0,0],[5,0],[2]]
[[5,0,0],[2,0],[1]]                                                     => [[5,0,0],[4,0],[1]]
[[5,0,0],[2,0],[2]]                                                     => [[5,0,0],[3,0],[0]]
[[5,0,0],[3,0],[0]]                                                     => [[5,0,0],[5,0],[3]]
[[5,0,0],[3,0],[1]]                                                     => [[5,0,0],[4,0],[2]]
[[5,0,0],[3,0],[2]]                                                     => [[5,0,0],[3,0],[1]]
[[5,0,0],[3,0],[3]]                                                     => [[5,0,0],[2,0],[0]]
[[5,0,0],[4,0],[0]]                                                     => [[5,0,0],[5,0],[4]]
[[5,0,0],[4,0],[1]]                                                     => [[5,0,0],[4,0],[3]]
[[5,0,0],[4,0],[2]]                                                     => [[5,0,0],[3,0],[2]]
[[5,0,0],[4,0],[3]]                                                     => [[5,0,0],[2,0],[1]]
[[5,0,0],[4,0],[4]]                                                     => [[5,0,0],[1,0],[0]]
[[5,0,0],[5,0],[0]]                                                     => [[5,0,0],[5,0],[5]]
[[5,0,0],[5,0],[1]]                                                     => [[5,0,0],[4,0],[4]]
[[5,0,0],[5,0],[2]]                                                     => [[5,0,0],[3,0],[3]]
[[5,0,0],[5,0],[3]]                                                     => [[5,0,0],[2,0],[2]]
[[5,0,0],[5,0],[4]]                                                     => [[5,0,0],[1,0],[1]]
[[5,0,0],[5,0],[5]]                                                     => [[5,0,0],[0,0],[0]]
[[4,1,0],[1,0],[0]]                                                     => [[4,1,0],[4,1],[1]]
[[4,1,0],[1,0],[1]]                                                     => [[4,1,0],[4,0],[0]]
[[4,1,0],[1,1],[1]]                                                     => [[4,1,0],[3,1],[1]]
[[4,1,0],[2,0],[0]]                                                     => [[4,1,0],[4,1],[2]]
[[4,1,0],[2,0],[1]]                                                     => [[4,1,0],[4,0],[1]]
[[4,1,0],[2,0],[2]]                                                     => [[4,1,0],[3,0],[0]]
[[4,1,0],[2,1],[1]]                                                     => [[4,1,0],[3,1],[2]]
[[4,1,0],[2,1],[2]]                                                     => [[4,1,0],[2,1],[1]]
[[4,1,0],[3,0],[0]]                                                     => [[4,1,0],[4,1],[3]]
[[4,1,0],[3,0],[1]]                                                     => [[4,1,0],[4,0],[2]]
[[4,1,0],[3,0],[2]]                                                     => [[4,1,0],[3,0],[1]]
[[4,1,0],[3,0],[3]]                                                     => [[4,1,0],[2,0],[0]]
[[4,1,0],[3,1],[1]]                                                     => [[4,1,0],[3,1],[3]]
[[4,1,0],[3,1],[2]]                                                     => [[4,1,0],[2,1],[2]]
[[4,1,0],[3,1],[3]]                                                     => [[4,1,0],[1,1],[1]]
[[4,1,0],[4,0],[0]]                                                     => [[4,1,0],[4,1],[4]]
[[4,1,0],[4,0],[1]]                                                     => [[4,1,0],[4,0],[3]]
[[4,1,0],[4,0],[2]]                                                     => [[4,1,0],[3,0],[2]]
[[4,1,0],[4,0],[3]]                                                     => [[4,1,0],[2,0],[1]]
[[4,1,0],[4,0],[4]]                                                     => [[4,1,0],[1,0],[0]]
[[4,1,0],[4,1],[1]]                                                     => [[4,1,0],[4,0],[4]]
[[4,1,0],[4,1],[2]]                                                     => [[4,1,0],[3,0],[3]]
[[4,1,0],[4,1],[3]]                                                     => [[4,1,0],[2,0],[2]]
[[4,1,0],[4,1],[4]]                                                     => [[4,1,0],[1,0],[1]]
[[3,2,0],[2,0],[0]]                                                     => [[3,2,0],[3,2],[2]]
[[3,2,0],[2,0],[1]]                                                     => [[3,2,0],[3,1],[1]]
[[3,2,0],[2,0],[2]]                                                     => [[3,2,0],[3,0],[0]]
[[3,2,0],[2,1],[1]]                                                     => [[3,2,0],[2,2],[2]]
[[3,2,0],[2,1],[2]]                                                     => [[3,2,0],[2,1],[1]]
[[3,2,0],[2,2],[2]]                                                     => [[3,2,0],[2,1],[2]]
[[3,2,0],[3,0],[0]]                                                     => [[3,2,0],[3,2],[3]]
[[3,2,0],[3,0],[1]]                                                     => [[3,2,0],[3,1],[2]]
[[3,2,0],[3,0],[2]]                                                     => [[3,2,0],[3,0],[1]]
[[3,2,0],[3,0],[3]]                                                     => [[3,2,0],[2,0],[0]]
[[3,2,0],[3,1],[1]]                                                     => [[3,2,0],[3,1],[3]]
[[3,2,0],[3,1],[2]]                                                     => [[3,2,0],[3,0],[2]]
[[3,2,0],[3,1],[3]]                                                     => [[3,2,0],[2,0],[1]]
[[3,2,0],[3,2],[2]]                                                     => [[3,2,0],[3,0],[3]]
[[3,2,0],[3,2],[3]]                                                     => [[3,2,0],[2,0],[2]]
[[3,1,1],[1,1],[1]]                                                     => [[3,1,1],[3,1],[1]]
[[3,1,1],[2,1],[1]]                                                     => [[3,1,1],[3,1],[2]]
[[3,1,1],[2,1],[2]]                                                     => [[3,1,1],[2,1],[1]]
[[3,1,1],[3,1],[1]]                                                     => [[3,1,1],[3,1],[3]]
[[3,1,1],[3,1],[2]]                                                     => [[3,1,1],[2,1],[2]]
[[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],[1]]
[[2,2,1],[2,2],[2]]                                                     => [[2,2,1],[2,1],[2]]
[[6,0,0],[0,0],[0]]                                                     => [[6,0,0],[6,0],[0]]
[[6,0,0],[1,0],[0]]                                                     => [[6,0,0],[6,0],[1]]
[[6,0,0],[1,0],[1]]                                                     => [[6,0,0],[5,0],[0]]
[[6,0,0],[2,0],[0]]                                                     => [[6,0,0],[6,0],[2]]
[[6,0,0],[2,0],[1]]                                                     => [[6,0,0],[5,0],[1]]
[[6,0,0],[2,0],[2]]                                                     => [[6,0,0],[4,0],[0]]
[[6,0,0],[3,0],[0]]                                                     => [[6,0,0],[6,0],[3]]
[[6,0,0],[3,0],[1]]                                                     => [[6,0,0],[5,0],[2]]
[[6,0,0],[3,0],[2]]                                                     => [[6,0,0],[4,0],[1]]
[[6,0,0],[3,0],[3]]                                                     => [[6,0,0],[3,0],[0]]
[[6,0,0],[4,0],[0]]                                                     => [[6,0,0],[6,0],[4]]
[[6,0,0],[4,0],[1]]                                                     => [[6,0,0],[5,0],[3]]
[[6,0,0],[4,0],[2]]                                                     => [[6,0,0],[4,0],[2]]
[[6,0,0],[4,0],[3]]                                                     => [[6,0,0],[3,0],[1]]
[[6,0,0],[4,0],[4]]                                                     => [[6,0,0],[2,0],[0]]
[[6,0,0],[5,0],[0]]                                                     => [[6,0,0],[6,0],[5]]
[[6,0,0],[5,0],[1]]                                                     => [[6,0,0],[5,0],[4]]
[[6,0,0],[5,0],[2]]                                                     => [[6,0,0],[4,0],[3]]
[[6,0,0],[5,0],[3]]                                                     => [[6,0,0],[3,0],[2]]
[[6,0,0],[5,0],[4]]                                                     => [[6,0,0],[2,0],[1]]
[[6,0,0],[5,0],[5]]                                                     => [[6,0,0],[1,0],[0]]
[[6,0,0],[6,0],[0]]                                                     => [[6,0,0],[6,0],[6]]
[[6,0,0],[6,0],[1]]                                                     => [[6,0,0],[5,0],[5]]
[[6,0,0],[6,0],[2]]                                                     => [[6,0,0],[4,0],[4]]
[[6,0,0],[6,0],[3]]                                                     => [[6,0,0],[3,0],[3]]
[[6,0,0],[6,0],[4]]                                                     => [[6,0,0],[2,0],[2]]
[[6,0,0],[6,0],[5]]                                                     => [[6,0,0],[1,0],[1]]
[[6,0,0],[6,0],[6]]                                                     => [[6,0,0],[0,0],[0]]
[[5,1,0],[1,0],[0]]                                                     => [[5,1,0],[5,1],[1]]
[[5,1,0],[1,0],[1]]                                                     => [[5,1,0],[5,0],[0]]
[[5,1,0],[1,1],[1]]                                                     => [[5,1,0],[4,1],[1]]
[[5,1,0],[2,0],[0]]                                                     => [[5,1,0],[5,1],[2]]
[[5,1,0],[2,0],[1]]                                                     => [[5,1,0],[5,0],[1]]
[[5,1,0],[2,0],[2]]                                                     => [[5,1,0],[4,0],[0]]
[[5,1,0],[2,1],[1]]                                                     => [[5,1,0],[4,1],[2]]
[[5,1,0],[2,1],[2]]                                                     => [[5,1,0],[3,1],[1]]
[[5,1,0],[3,0],[0]]                                                     => [[5,1,0],[5,1],[3]]
[[5,1,0],[3,0],[1]]                                                     => [[5,1,0],[5,0],[2]]
[[5,1,0],[3,0],[2]]                                                     => [[5,1,0],[4,0],[1]]
[[5,1,0],[3,0],[3]]                                                     => [[5,1,0],[3,0],[0]]
[[5,1,0],[3,1],[1]]                                                     => [[5,1,0],[4,1],[3]]
[[5,1,0],[3,1],[2]]                                                     => [[5,1,0],[3,1],[2]]
[[5,1,0],[3,1],[3]]                                                     => [[5,1,0],[2,1],[1]]
[[5,1,0],[4,0],[0]]                                                     => [[5,1,0],[5,1],[4]]
[[5,1,0],[4,0],[1]]                                                     => [[5,1,0],[5,0],[3]]
[[5,1,0],[4,0],[2]]                                                     => [[5,1,0],[4,0],[2]]
[[5,1,0],[4,0],[3]]                                                     => [[5,1,0],[3,0],[1]]
[[5,1,0],[4,0],[4]]                                                     => [[5,1,0],[2,0],[0]]
[[5,1,0],[4,1],[1]]                                                     => [[5,1,0],[4,1],[4]]
[[5,1,0],[4,1],[2]]                                                     => [[5,1,0],[3,1],[3]]
[[5,1,0],[4,1],[3]]                                                     => [[5,1,0],[2,1],[2]]
[[5,1,0],[4,1],[4]]                                                     => [[5,1,0],[1,1],[1]]
[[5,1,0],[5,0],[0]]                                                     => [[5,1,0],[5,1],[5]]
[[5,1,0],[5,0],[1]]                                                     => [[5,1,0],[5,0],[4]]
[[5,1,0],[5,0],[2]]                                                     => [[5,1,0],[4,0],[3]]
[[5,1,0],[5,0],[3]]                                                     => [[5,1,0],[3,0],[2]]
[[5,1,0],[5,0],[4]]                                                     => [[5,1,0],[2,0],[1]]
[[5,1,0],[5,0],[5]]                                                     => [[5,1,0],[1,0],[0]]
[[5,1,0],[5,1],[1]]                                                     => [[5,1,0],[5,0],[5]]
[[5,1,0],[5,1],[2]]                                                     => [[5,1,0],[4,0],[4]]
[[5,1,0],[5,1],[3]]                                                     => [[5,1,0],[3,0],[3]]
[[5,1,0],[5,1],[4]]                                                     => [[5,1,0],[2,0],[2]]
[[5,1,0],[5,1],[5]]                                                     => [[5,1,0],[1,0],[1]]
[[4,2,0],[2,0],[0]]                                                     => [[4,2,0],[4,2],[2]]
[[4,2,0],[2,0],[1]]                                                     => [[4,2,0],[4,1],[1]]
[[4,2,0],[2,0],[2]]                                                     => [[4,2,0],[4,0],[0]]
[[4,2,0],[2,1],[1]]                                                     => [[4,2,0],[3,2],[2]]
[[4,2,0],[2,1],[2]]                                                     => [[4,2,0],[3,1],[1]]
[[4,2,0],[2,2],[2]]                                                     => [[4,2,0],[2,2],[2]]
[[4,2,0],[3,0],[0]]                                                     => [[4,2,0],[4,2],[3]]
[[4,2,0],[3,0],[1]]                                                     => [[4,2,0],[4,1],[2]]
[[4,2,0],[3,0],[2]]                                                     => [[4,2,0],[4,0],[1]]
[[4,2,0],[3,0],[3]]                                                     => [[4,2,0],[3,0],[0]]
[[4,2,0],[3,1],[1]]                                                     => [[4,2,0],[3,2],[3]]
[[4,2,0],[3,1],[2]]                                                     => [[4,2,0],[3,1],[2]]
[[4,2,0],[3,1],[3]]                                                     => [[4,2,0],[2,1],[1]]
[[4,2,0],[3,2],[2]]                                                     => [[4,2,0],[3,1],[3]]
[[4,2,0],[3,2],[3]]                                                     => [[4,2,0],[2,1],[2]]
[[4,2,0],[4,0],[0]]                                                     => [[4,2,0],[4,2],[4]]
[[4,2,0],[4,0],[1]]                                                     => [[4,2,0],[4,1],[3]]
[[4,2,0],[4,0],[2]]                                                     => [[4,2,0],[4,0],[2]]
[[4,2,0],[4,0],[3]]                                                     => [[4,2,0],[3,0],[1]]
[[4,2,0],[4,0],[4]]                                                     => [[4,2,0],[2,0],[0]]
[[4,2,0],[4,1],[1]]                                                     => [[4,2,0],[4,1],[4]]
[[4,2,0],[4,1],[2]]                                                     => [[4,2,0],[4,0],[3]]
[[4,2,0],[4,1],[3]]                                                     => [[4,2,0],[3,0],[2]]
[[4,2,0],[4,1],[4]]                                                     => [[4,2,0],[2,0],[1]]
[[4,2,0],[4,2],[2]]                                                     => [[4,2,0],[4,0],[4]]
[[4,2,0],[4,2],[3]]                                                     => [[4,2,0],[3,0],[3]]
[[4,2,0],[4,2],[4]]                                                     => [[4,2,0],[2,0],[2]]
[[4,1,1],[1,1],[1]]                                                     => [[4,1,1],[4,1],[1]]
[[4,1,1],[2,1],[1]]                                                     => [[4,1,1],[4,1],[2]]
[[4,1,1],[2,1],[2]]                                                     => [[4,1,1],[3,1],[1]]
[[4,1,1],[3,1],[1]]                                                     => [[4,1,1],[4,1],[3]]
[[4,1,1],[3,1],[2]]                                                     => [[4,1,1],[3,1],[2]]
[[4,1,1],[3,1],[3]]                                                     => [[4,1,1],[2,1],[1]]
[[4,1,1],[4,1],[1]]                                                     => [[4,1,1],[4,1],[4]]
[[4,1,1],[4,1],[2]]                                                     => [[4,1,1],[3,1],[3]]
[[4,1,1],[4,1],[3]]                                                     => [[4,1,1],[2,1],[2]]
[[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],[2]]
[[3,3,0],[3,0],[2]]                                                     => [[3,3,0],[3,1],[1]]
[[3,3,0],[3,0],[3]]                                                     => [[3,3,0],[3,0],[0]]
[[3,3,0],[3,1],[1]]                                                     => [[3,3,0],[3,2],[3]]
[[3,3,0],[3,1],[2]]                                                     => [[3,3,0],[3,1],[2]]
[[3,3,0],[3,1],[3]]                                                     => [[3,3,0],[3,0],[1]]
[[3,3,0],[3,2],[2]]                                                     => [[3,3,0],[3,1],[3]]
[[3,3,0],[3,2],[3]]                                                     => [[3,3,0],[3,0],[2]]
[[3,3,0],[3,3],[3]]                                                     => [[3,3,0],[3,0],[3]]
[[3,2,1],[2,1],[1]]                                                     => [[3,2,1],[3,2],[2]]
[[3,2,1],[2,1],[2]]                                                     => [[3,2,1],[3,1],[1]]
[[3,2,1],[2,2],[2]]                                                     => [[3,2,1],[2,2],[2]]
[[3,2,1],[3,1],[1]]                                                     => [[3,2,1],[3,2],[3]]
[[3,2,1],[3,1],[2]]                                                     => [[3,2,1],[3,1],[2]]
[[3,2,1],[3,1],[3]]                                                     => [[3,2,1],[2,1],[1]]
[[3,2,1],[3,2],[2]]                                                     => [[3,2,1],[3,1],[3]]
[[3,2,1],[3,2],[3]]                                                     => [[3,2,1],[2,1],[2]]
[[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],[0,0],[0]]
[[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],[1,0],[1]]
[[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],[0,0],[0]]
[[2,0,0,0],[1,0,0],[0,0],[0]]                                           => [[2,0,0,0],[2,0,0],[1,0],[0]]
[[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],[0,0],[0]]
[[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],[2,0],[1]]
[[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],[2,0],[2]]
[[2,0,0,0],[2,0,0],[2,0],[1]]                                           => [[2,0,0,0],[1,0,0],[1,0],[1]]
[[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],[1,0],[0]]
[[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],[0,0],[0]]
[[1,1,0,0],[1,1,0],[1,0],[0]]                                           => [[1,1,0,0],[1,1,0],[1,1],[1]]
[[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],[1,0],[1]]
[[3,0,0,0],[0,0,0],[0,0],[0]]                                           => [[3,0,0,0],[3,0,0],[0,0],[0]]
[[3,0,0,0],[1,0,0],[0,0],[0]]                                           => [[3,0,0,0],[3,0,0],[1,0],[0]]
[[3,0,0,0],[1,0,0],[1,0],[0]]                                           => [[3,0,0,0],[3,0,0],[1,0],[1]]
[[3,0,0,0],[1,0,0],[1,0],[1]]                                           => [[3,0,0,0],[2,0,0],[0,0],[0]]
[[3,0,0,0],[2,0,0],[0,0],[0]]                                           => [[3,0,0,0],[3,0,0],[2,0],[0]]
[[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],[1,0],[0]]
[[3,0,0,0],[2,0,0],[2,0],[0]]                                           => [[3,0,0,0],[3,0,0],[2,0],[2]]
[[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],[0,0],[0]]
[[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],[3,0],[1]]
[[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],[3,0],[2]]
[[3,0,0,0],[3,0,0],[2,0],[1]]                                           => [[3,0,0,0],[2,0,0],[2,0],[1]]
[[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],[3,0],[3]]
[[3,0,0,0],[3,0,0],[3,0],[1]]                                           => [[3,0,0,0],[2,0,0],[2,0],[2]]
[[3,0,0,0],[3,0,0],[3,0],[2]]                                           => [[3,0,0,0],[1,0,0],[1,0],[1]]
[[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],[1,0],[0]]
[[2,1,0,0],[1,0,0],[1,0],[0]]                                           => [[2,1,0,0],[2,1,0],[1,0],[1]]
[[2,1,0,0],[1,0,0],[1,0],[1]]                                           => [[2,1,0,0],[2,0,0],[0,0],[0]]
[[2,1,0,0],[1,1,0],[1,0],[0]]                                           => [[2,1,0,0],[2,1,0],[1,1],[1]]
[[2,1,0,0],[1,1,0],[1,0],[1]]                                           => [[2,1,0,0],[1,1,0],[1,0],[0]]
[[2,1,0,0],[1,1,0],[1,1],[1]]                                           => [[2,1,0,0],[1,1,0],[1,0],[1]]
[[2,1,0,0],[2,0,0],[0,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,0],[0]]
[[2,1,0,0],[2,0,0],[1,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,0],[1]]
[[2,1,0,0],[2,0,0],[1,0],[1]]                                           => [[2,1,0,0],[2,0,0],[1,0],[0]]
[[2,1,0,0],[2,0,0],[2,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,0],[2]]
[[2,1,0,0],[2,0,0],[2,0],[1]]                                           => [[2,1,0,0],[2,0,0],[1,0],[1]]
[[2,1,0,0],[2,0,0],[2,0],[2]]                                           => [[2,1,0,0],[1,0,0],[0,0],[0]]
[[2,1,0,0],[2,1,0],[1,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,1],[1]]
[[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],[1,1,0],[1,1],[1]]
[[2,1,0,0],[2,1,0],[2,0],[0]]                                           => [[2,1,0,0],[2,1,0],[2,1],[2]]
[[2,1,0,0],[2,1,0],[2,0],[1]]                                           => [[2,1,0,0],[2,0,0],[2,0],[1]]
[[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],[2,0],[2]]
[[2,1,0,0],[2,1,0],[2,1],[2]]                                           => [[2,1,0,0],[1,0,0],[1,0],[1]]
[[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],[1,0],[0]]
[[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],[1,1],[1]]
[[4,0,0,0],[0,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[0,0],[0]]
[[4,0,0,0],[1,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[1,0],[0]]
[[4,0,0,0],[1,0,0],[1,0],[0]]                                           => [[4,0,0,0],[4,0,0],[1,0],[1]]
[[4,0,0,0],[1,0,0],[1,0],[1]]                                           => [[4,0,0,0],[3,0,0],[0,0],[0]]
[[4,0,0,0],[2,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[2,0],[0]]
[[4,0,0,0],[2,0,0],[1,0],[0]]                                           => [[4,0,0,0],[4,0,0],[2,0],[1]]
[[4,0,0,0],[2,0,0],[1,0],[1]]                                           => [[4,0,0,0],[3,0,0],[1,0],[0]]
[[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],[1,0],[1]]
[[4,0,0,0],[2,0,0],[2,0],[2]]                                           => [[4,0,0,0],[2,0,0],[0,0],[0]]
[[4,0,0,0],[3,0,0],[0,0],[0]]                                           => [[4,0,0,0],[4,0,0],[3,0],[0]]
[[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],[2,0],[0]]
[[4,0,0,0],[3,0,0],[2,0],[0]]                                           => [[4,0,0,0],[4,0,0],[3,0],[2]]
[[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],[1,0],[0]]
[[4,0,0,0],[3,0,0],[3,0],[0]]                                           => [[4,0,0,0],[4,0,0],[3,0],[3]]
[[4,0,0,0],[3,0,0],[3,0],[1]]                                           => [[4,0,0,0],[3,0,0],[2,0],[2]]
[[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],[0,0],[0]]
[[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],[4,0],[1]]
[[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],[4,0],[2]]
[[4,0,0,0],[4,0,0],[2,0],[1]]                                           => [[4,0,0,0],[3,0,0],[3,0],[1]]
[[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],[4,0],[3]]
[[4,0,0,0],[4,0,0],[3,0],[1]]                                           => [[4,0,0,0],[3,0,0],[3,0],[2]]
[[4,0,0,0],[4,0,0],[3,0],[2]]                                           => [[4,0,0,0],[2,0,0],[2,0],[1]]
[[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],[4,0],[4]]
[[4,0,0,0],[4,0,0],[4,0],[1]]                                           => [[4,0,0,0],[3,0,0],[3,0],[3]]
[[4,0,0,0],[4,0,0],[4,0],[2]]                                           => [[4,0,0,0],[2,0,0],[2,0],[2]]
[[4,0,0,0],[4,0,0],[4,0],[3]]                                           => [[4,0,0,0],[1,0,0],[1,0],[1]]
[[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],[1,0],[0]]
[[3,1,0,0],[1,0,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[1,0],[1]]
[[3,1,0,0],[1,0,0],[1,0],[1]]                                           => [[3,1,0,0],[3,0,0],[0,0],[0]]
[[3,1,0,0],[1,1,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[1,1],[1]]
[[3,1,0,0],[1,1,0],[1,0],[1]]                                           => [[3,1,0,0],[2,1,0],[1,0],[0]]
[[3,1,0,0],[1,1,0],[1,1],[1]]                                           => [[3,1,0,0],[2,1,0],[1,0],[1]]
[[3,1,0,0],[2,0,0],[0,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,0],[0]]
[[3,1,0,0],[2,0,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,0],[1]]
[[3,1,0,0],[2,0,0],[1,0],[1]]                                           => [[3,1,0,0],[3,0,0],[1,0],[0]]
[[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],[3,0,0],[1,0],[1]]
[[3,1,0,0],[2,0,0],[2,0],[2]]                                           => [[3,1,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0],[2,1,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,1],[1]]
[[3,1,0,0],[2,1,0],[1,0],[1]]                                           => [[3,1,0,0],[2,1,0],[2,0],[0]]
[[3,1,0,0],[2,1,0],[1,1],[1]]                                           => [[3,1,0,0],[2,1,0],[1,1],[1]]
[[3,1,0,0],[2,1,0],[2,0],[0]]                                           => [[3,1,0,0],[3,1,0],[2,1],[2]]
[[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],[1,1,0],[1,0],[0]]
[[3,1,0,0],[2,1,0],[2,1],[1]]                                           => [[3,1,0,0],[2,1,0],[2,0],[2]]
[[3,1,0,0],[2,1,0],[2,1],[2]]                                           => [[3,1,0,0],[1,1,0],[1,0],[1]]
[[3,1,0,0],[3,0,0],[0,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,0],[0]]
[[3,1,0,0],[3,0,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,0],[1]]
[[3,1,0,0],[3,0,0],[1,0],[1]]                                           => [[3,1,0,0],[3,0,0],[2,0],[0]]
[[3,1,0,0],[3,0,0],[2,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,0],[2]]
[[3,1,0,0],[3,0,0],[2,0],[1]]                                           => [[3,1,0,0],[3,0,0],[2,0],[1]]
[[3,1,0,0],[3,0,0],[2,0],[2]]                                           => [[3,1,0,0],[2,0,0],[1,0],[0]]
[[3,1,0,0],[3,0,0],[3,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,0],[3]]
[[3,1,0,0],[3,0,0],[3,0],[1]]                                           => [[3,1,0,0],[3,0,0],[2,0],[2]]
[[3,1,0,0],[3,0,0],[3,0],[2]]                                           => [[3,1,0,0],[2,0,0],[1,0],[1]]
[[3,1,0,0],[3,0,0],[3,0],[3]]                                           => [[3,1,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0],[3,1,0],[1,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,1],[1]]
[[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],[2,1,0],[2,1],[1]]
[[3,1,0,0],[3,1,0],[2,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,1],[2]]
[[3,1,0,0],[3,1,0],[2,0],[1]]                                           => [[3,1,0,0],[3,0,0],[3,0],[1]]
[[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],[2,1,0],[2,1],[2]]
[[3,1,0,0],[3,1,0],[2,1],[2]]                                           => [[3,1,0,0],[1,1,0],[1,1],[1]]
[[3,1,0,0],[3,1,0],[3,0],[0]]                                           => [[3,1,0,0],[3,1,0],[3,1],[3]]
[[3,1,0,0],[3,1,0],[3,0],[1]]                                           => [[3,1,0,0],[3,0,0],[3,0],[2]]
[[3,1,0,0],[3,1,0],[3,0],[2]]                                           => [[3,1,0,0],[2,0,0],[2,0],[1]]
[[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],[3,0],[3]]
[[3,1,0,0],[3,1,0],[3,1],[2]]                                           => [[3,1,0,0],[2,0,0],[2,0],[2]]
[[3,1,0,0],[3,1,0],[3,1],[3]]                                           => [[3,1,0,0],[1,0,0],[1,0],[1]]
[[2,2,0,0],[2,0,0],[0,0],[0]]                                           => [[2,2,0,0],[2,2,0],[2,0],[0]]
[[2,2,0,0],[2,0,0],[1,0],[0]]                                           => [[2,2,0,0],[2,2,0],[2,0],[1]]
[[2,2,0,0],[2,0,0],[1,0],[1]]                                           => [[2,2,0,0],[2,1,0],[1,0],[0]]
[[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],[1,0],[1]]
[[2,2,0,0],[2,0,0],[2,0],[2]]                                           => [[2,2,0,0],[2,0,0],[0,0],[0]]
[[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],[2,0],[0]]
[[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],[2,1],[2]]
[[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],[1,0],[0]]
[[2,2,0,0],[2,1,0],[2,1],[1]]                                           => [[2,2,0,0],[2,1,0],[2,0],[2]]
[[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],[2,2],[2]]
[[2,2,0,0],[2,2,0],[2,0],[1]]                                           => [[2,2,0,0],[2,1,0],[2,1],[1]]
[[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],[2,1],[2]]
[[2,2,0,0],[2,2,0],[2,1],[2]]                                           => [[2,2,0,0],[2,0,0],[2,0],[1]]
[[2,2,0,0],[2,2,0],[2,2],[2]]                                           => [[2,2,0,0],[2,0,0],[2,0],[2]]
[[2,1,1,0],[1,1,0],[1,0],[0]]                                           => [[2,1,1,0],[2,1,1],[1,1],[1]]
[[2,1,1,0],[1,1,0],[1,0],[1]]                                           => [[2,1,1,0],[2,1,0],[1,0],[0]]
[[2,1,1,0],[1,1,0],[1,1],[1]]                                           => [[2,1,1,0],[2,1,0],[1,0],[1]]
[[2,1,1,0],[1,1,1],[1,1],[1]]                                           => [[2,1,1,0],[1,1,1],[1,1],[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],[2,0],[0]]
[[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],[2,1],[2]]
[[2,1,1,0],[2,1,0],[2,0],[1]]                                           => [[2,1,1,0],[2,1,0],[2,0],[1]]
[[2,1,1,0],[2,1,0],[2,0],[2]]                                           => [[2,1,1,0],[1,1,0],[1,0],[0]]
[[2,1,1,0],[2,1,0],[2,1],[1]]                                           => [[2,1,1,0],[2,1,0],[2,0],[2]]
[[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],[2,1],[1]]
[[2,1,1,0],[2,1,1],[2,1],[1]]                                           => [[2,1,1,0],[2,1,0],[2,1],[2]]
[[2,1,1,0],[2,1,1],[2,1],[2]]                                           => [[2,1,1,0],[1,1,0],[1,1],[1]]
[[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],[0,0],[0]]
[[5,0,0,0],[1,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[1,0],[0]]
[[5,0,0,0],[1,0,0],[1,0],[0]]                                           => [[5,0,0,0],[5,0,0],[1,0],[1]]
[[5,0,0,0],[1,0,0],[1,0],[1]]                                           => [[5,0,0,0],[4,0,0],[0,0],[0]]
[[5,0,0,0],[2,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[2,0],[0]]
[[5,0,0,0],[2,0,0],[1,0],[0]]                                           => [[5,0,0,0],[5,0,0],[2,0],[1]]
[[5,0,0,0],[2,0,0],[1,0],[1]]                                           => [[5,0,0,0],[4,0,0],[1,0],[0]]
[[5,0,0,0],[2,0,0],[2,0],[0]]                                           => [[5,0,0,0],[5,0,0],[2,0],[2]]
[[5,0,0,0],[2,0,0],[2,0],[1]]                                           => [[5,0,0,0],[4,0,0],[1,0],[1]]
[[5,0,0,0],[2,0,0],[2,0],[2]]                                           => [[5,0,0,0],[3,0,0],[0,0],[0]]
[[5,0,0,0],[3,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[3,0],[0]]
[[5,0,0,0],[3,0,0],[1,0],[0]]                                           => [[5,0,0,0],[5,0,0],[3,0],[1]]
[[5,0,0,0],[3,0,0],[1,0],[1]]                                           => [[5,0,0,0],[4,0,0],[2,0],[0]]
[[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],[2,0],[1]]
[[5,0,0,0],[3,0,0],[2,0],[2]]                                           => [[5,0,0,0],[3,0,0],[1,0],[0]]
[[5,0,0,0],[3,0,0],[3,0],[0]]                                           => [[5,0,0,0],[5,0,0],[3,0],[3]]
[[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],[1,0],[1]]
[[5,0,0,0],[3,0,0],[3,0],[3]]                                           => [[5,0,0,0],[2,0,0],[0,0],[0]]
[[5,0,0,0],[4,0,0],[0,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[0]]
[[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],[3,0],[0]]
[[5,0,0,0],[4,0,0],[2,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[2]]
[[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],[2,0],[0]]
[[5,0,0,0],[4,0,0],[3,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[3]]
[[5,0,0,0],[4,0,0],[3,0],[1]]                                           => [[5,0,0,0],[4,0,0],[3,0],[2]]
[[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],[1,0],[0]]
[[5,0,0,0],[4,0,0],[4,0],[0]]                                           => [[5,0,0,0],[5,0,0],[4,0],[4]]
[[5,0,0,0],[4,0,0],[4,0],[1]]                                           => [[5,0,0,0],[4,0,0],[3,0],[3]]
[[5,0,0,0],[4,0,0],[4,0],[2]]                                           => [[5,0,0,0],[3,0,0],[2,0],[2]]
[[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],[0,0],[0]]
[[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],[5,0],[1]]
[[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],[5,0],[2]]
[[5,0,0,0],[5,0,0],[2,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[1]]
[[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],[5,0],[3]]
[[5,0,0,0],[5,0,0],[3,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[2]]
[[5,0,0,0],[5,0,0],[3,0],[2]]                                           => [[5,0,0,0],[3,0,0],[3,0],[1]]
[[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],[5,0],[4]]
[[5,0,0,0],[5,0,0],[4,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[3]]
[[5,0,0,0],[5,0,0],[4,0],[2]]                                           => [[5,0,0,0],[3,0,0],[3,0],[2]]
[[5,0,0,0],[5,0,0],[4,0],[3]]                                           => [[5,0,0,0],[2,0,0],[2,0],[1]]
[[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],[5,0],[5]]
[[5,0,0,0],[5,0,0],[5,0],[1]]                                           => [[5,0,0,0],[4,0,0],[4,0],[4]]
[[5,0,0,0],[5,0,0],[5,0],[2]]                                           => [[5,0,0,0],[3,0,0],[3,0],[3]]
[[5,0,0,0],[5,0,0],[5,0],[3]]                                           => [[5,0,0,0],[2,0,0],[2,0],[2]]
[[5,0,0,0],[5,0,0],[5,0],[4]]                                           => [[5,0,0,0],[1,0,0],[1,0],[1]]
[[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],[1,0],[0]]
[[4,1,0,0],[1,0,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[1,0],[1]]
[[4,1,0,0],[1,0,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[0,0],[0]]
[[4,1,0,0],[1,1,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[1,1],[1]]
[[4,1,0,0],[1,1,0],[1,0],[1]]                                           => [[4,1,0,0],[3,1,0],[1,0],[0]]
[[4,1,0,0],[1,1,0],[1,1],[1]]                                           => [[4,1,0,0],[3,1,0],[1,0],[1]]
[[4,1,0,0],[2,0,0],[0,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,0],[0]]
[[4,1,0,0],[2,0,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,0],[1]]
[[4,1,0,0],[2,0,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[1,0],[0]]
[[4,1,0,0],[2,0,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,0],[2]]
[[4,1,0,0],[2,0,0],[2,0],[1]]                                           => [[4,1,0,0],[4,0,0],[1,0],[1]]
[[4,1,0,0],[2,0,0],[2,0],[2]]                                           => [[4,1,0,0],[3,0,0],[0,0],[0]]
[[4,1,0,0],[2,1,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,1],[1]]
[[4,1,0,0],[2,1,0],[1,0],[1]]                                           => [[4,1,0,0],[3,1,0],[2,0],[0]]
[[4,1,0,0],[2,1,0],[1,1],[1]]                                           => [[4,1,0,0],[3,1,0],[1,1],[1]]
[[4,1,0,0],[2,1,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[2,1],[2]]
[[4,1,0,0],[2,1,0],[2,0],[1]]                                           => [[4,1,0,0],[3,1,0],[2,0],[1]]
[[4,1,0,0],[2,1,0],[2,0],[2]]                                           => [[4,1,0,0],[2,1,0],[1,0],[0]]
[[4,1,0,0],[2,1,0],[2,1],[1]]                                           => [[4,1,0,0],[3,1,0],[2,0],[2]]
[[4,1,0,0],[2,1,0],[2,1],[2]]                                           => [[4,1,0,0],[2,1,0],[1,0],[1]]
[[4,1,0,0],[3,0,0],[0,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,0],[0]]
[[4,1,0,0],[3,0,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,0],[1]]
[[4,1,0,0],[3,0,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[2,0],[0]]
[[4,1,0,0],[3,0,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,0],[2]]
[[4,1,0,0],[3,0,0],[2,0],[1]]                                           => [[4,1,0,0],[4,0,0],[2,0],[1]]
[[4,1,0,0],[3,0,0],[2,0],[2]]                                           => [[4,1,0,0],[3,0,0],[1,0],[0]]
[[4,1,0,0],[3,0,0],[3,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,0],[3]]
[[4,1,0,0],[3,0,0],[3,0],[1]]                                           => [[4,1,0,0],[4,0,0],[2,0],[2]]
[[4,1,0,0],[3,0,0],[3,0],[2]]                                           => [[4,1,0,0],[3,0,0],[1,0],[1]]
[[4,1,0,0],[3,0,0],[3,0],[3]]                                           => [[4,1,0,0],[2,0,0],[0,0],[0]]
[[4,1,0,0],[3,1,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,1],[1]]
[[4,1,0,0],[3,1,0],[1,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,0],[0]]
[[4,1,0,0],[3,1,0],[1,1],[1]]                                           => [[4,1,0,0],[3,1,0],[2,1],[1]]
[[4,1,0,0],[3,1,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,1],[2]]
[[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],[2,1,0],[2,0],[0]]
[[4,1,0,0],[3,1,0],[2,1],[1]]                                           => [[4,1,0,0],[3,1,0],[2,1],[2]]
[[4,1,0,0],[3,1,0],[2,1],[2]]                                           => [[4,1,0,0],[2,1,0],[1,1],[1]]
[[4,1,0,0],[3,1,0],[3,0],[0]]                                           => [[4,1,0,0],[4,1,0],[3,1],[3]]
[[4,1,0,0],[3,1,0],[3,0],[1]]                                           => [[4,1,0,0],[3,1,0],[3,0],[2]]
[[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],[1,1,0],[1,0],[0]]
[[4,1,0,0],[3,1,0],[3,1],[1]]                                           => [[4,1,0,0],[3,1,0],[3,0],[3]]
[[4,1,0,0],[3,1,0],[3,1],[2]]                                           => [[4,1,0,0],[2,1,0],[2,0],[2]]
[[4,1,0,0],[3,1,0],[3,1],[3]]                                           => [[4,1,0,0],[1,1,0],[1,0],[1]]
[[4,1,0,0],[4,0,0],[0,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[0]]
[[4,1,0,0],[4,0,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[1]]
[[4,1,0,0],[4,0,0],[1,0],[1]]                                           => [[4,1,0,0],[4,0,0],[3,0],[0]]
[[4,1,0,0],[4,0,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[2]]
[[4,1,0,0],[4,0,0],[2,0],[1]]                                           => [[4,1,0,0],[4,0,0],[3,0],[1]]
[[4,1,0,0],[4,0,0],[2,0],[2]]                                           => [[4,1,0,0],[3,0,0],[2,0],[0]]
[[4,1,0,0],[4,0,0],[3,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[3]]
[[4,1,0,0],[4,0,0],[3,0],[1]]                                           => [[4,1,0,0],[4,0,0],[3,0],[2]]
[[4,1,0,0],[4,0,0],[3,0],[2]]                                           => [[4,1,0,0],[3,0,0],[2,0],[1]]
[[4,1,0,0],[4,0,0],[3,0],[3]]                                           => [[4,1,0,0],[2,0,0],[1,0],[0]]
[[4,1,0,0],[4,0,0],[4,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,0],[4]]
[[4,1,0,0],[4,0,0],[4,0],[1]]                                           => [[4,1,0,0],[4,0,0],[3,0],[3]]
[[4,1,0,0],[4,0,0],[4,0],[2]]                                           => [[4,1,0,0],[3,0,0],[2,0],[2]]
[[4,1,0,0],[4,0,0],[4,0],[3]]                                           => [[4,1,0,0],[2,0,0],[1,0],[1]]
[[4,1,0,0],[4,0,0],[4,0],[4]]                                           => [[4,1,0,0],[1,0,0],[0,0],[0]]
[[4,1,0,0],[4,1,0],[1,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,1],[1]]
[[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],[3,1,0],[3,1],[1]]
[[4,1,0,0],[4,1,0],[2,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,1],[2]]
[[4,1,0,0],[4,1,0],[2,0],[1]]                                           => [[4,1,0,0],[4,0,0],[4,0],[1]]
[[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],[3,1,0],[3,1],[2]]
[[4,1,0,0],[4,1,0],[2,1],[2]]                                           => [[4,1,0,0],[2,1,0],[2,1],[1]]
[[4,1,0,0],[4,1,0],[3,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,1],[3]]
[[4,1,0,0],[4,1,0],[3,0],[1]]                                           => [[4,1,0,0],[4,0,0],[4,0],[2]]
[[4,1,0,0],[4,1,0],[3,0],[2]]                                           => [[4,1,0,0],[3,0,0],[3,0],[1]]
[[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],[3,1,0],[3,1],[3]]
[[4,1,0,0],[4,1,0],[3,1],[2]]                                           => [[4,1,0,0],[2,1,0],[2,1],[2]]
[[4,1,0,0],[4,1,0],[3,1],[3]]                                           => [[4,1,0,0],[1,1,0],[1,1],[1]]
[[4,1,0,0],[4,1,0],[4,0],[0]]                                           => [[4,1,0,0],[4,1,0],[4,1],[4]]
[[4,1,0,0],[4,1,0],[4,0],[1]]                                           => [[4,1,0,0],[4,0,0],[4,0],[3]]
[[4,1,0,0],[4,1,0],[4,0],[2]]                                           => [[4,1,0,0],[3,0,0],[3,0],[2]]
[[4,1,0,0],[4,1,0],[4,0],[3]]                                           => [[4,1,0,0],[2,0,0],[2,0],[1]]
[[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],[4,0],[4]]
[[4,1,0,0],[4,1,0],[4,1],[2]]                                           => [[4,1,0,0],[3,0,0],[3,0],[3]]
[[4,1,0,0],[4,1,0],[4,1],[3]]                                           => [[4,1,0,0],[2,0,0],[2,0],[2]]
[[4,1,0,0],[4,1,0],[4,1],[4]]                                           => [[4,1,0,0],[1,0,0],[1,0],[1]]
[[3,2,0,0],[2,0,0],[0,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,0],[0]]
[[3,2,0,0],[2,0,0],[1,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,0],[1]]
[[3,2,0,0],[2,0,0],[1,0],[1]]                                           => [[3,2,0,0],[3,1,0],[1,0],[0]]
[[3,2,0,0],[2,0,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,0],[2]]
[[3,2,0,0],[2,0,0],[2,0],[1]]                                           => [[3,2,0,0],[3,1,0],[1,0],[1]]
[[3,2,0,0],[2,0,0],[2,0],[2]]                                           => [[3,2,0,0],[3,0,0],[0,0],[0]]
[[3,2,0,0],[2,1,0],[1,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,1],[1]]
[[3,2,0,0],[2,1,0],[1,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,0],[0]]
[[3,2,0,0],[2,1,0],[1,1],[1]]                                           => [[3,2,0,0],[3,1,0],[1,1],[1]]
[[3,2,0,0],[2,1,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,1],[2]]
[[3,2,0,0],[2,1,0],[2,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,0],[1]]
[[3,2,0,0],[2,1,0],[2,0],[2]]                                           => [[3,2,0,0],[2,1,0],[1,0],[0]]
[[3,2,0,0],[2,1,0],[2,1],[1]]                                           => [[3,2,0,0],[2,2,0],[2,0],[2]]
[[3,2,0,0],[2,1,0],[2,1],[2]]                                           => [[3,2,0,0],[2,1,0],[1,0],[1]]
[[3,2,0,0],[2,2,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[2,2],[2]]
[[3,2,0,0],[2,2,0],[2,0],[1]]                                           => [[3,2,0,0],[2,2,0],[2,1],[1]]
[[3,2,0,0],[2,2,0],[2,0],[2]]                                           => [[3,2,0,0],[2,1,0],[2,0],[0]]
[[3,2,0,0],[2,2,0],[2,1],[1]]                                           => [[3,2,0,0],[2,2,0],[2,1],[2]]
[[3,2,0,0],[2,2,0],[2,1],[2]]                                           => [[3,2,0,0],[2,1,0],[2,0],[1]]
[[3,2,0,0],[2,2,0],[2,2],[2]]                                           => [[3,2,0,0],[2,1,0],[2,0],[2]]
[[3,2,0,0],[3,0,0],[0,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,0],[0]]
[[3,2,0,0],[3,0,0],[1,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,0],[1]]
[[3,2,0,0],[3,0,0],[1,0],[1]]                                           => [[3,2,0,0],[3,1,0],[2,0],[0]]
[[3,2,0,0],[3,0,0],[2,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,0],[2]]
[[3,2,0,0],[3,0,0],[2,0],[1]]                                           => [[3,2,0,0],[3,1,0],[2,0],[1]]
[[3,2,0,0],[3,0,0],[2,0],[2]]                                           => [[3,2,0,0],[3,0,0],[1,0],[0]]
[[3,2,0,0],[3,0,0],[3,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,0],[3]]
[[3,2,0,0],[3,0,0],[3,0],[1]]                                           => [[3,2,0,0],[3,1,0],[2,0],[2]]
[[3,2,0,0],[3,0,0],[3,0],[2]]                                           => [[3,2,0,0],[3,0,0],[1,0],[1]]
[[3,2,0,0],[3,0,0],[3,0],[3]]                                           => [[3,2,0,0],[2,0,0],[0,0],[0]]
[[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],[3,0],[0]]
[[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],[3,1],[2]]
[[3,2,0,0],[3,1,0],[2,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,0],[1]]
[[3,2,0,0],[3,1,0],[2,0],[2]]                                           => [[3,2,0,0],[3,0,0],[2,0],[0]]
[[3,2,0,0],[3,1,0],[2,1],[1]]                                           => [[3,2,0,0],[3,1,0],[2,1],[2]]
[[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],[3,1],[3]]
[[3,2,0,0],[3,1,0],[3,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,0],[2]]
[[3,2,0,0],[3,1,0],[3,0],[2]]                                           => [[3,2,0,0],[3,0,0],[2,0],[1]]
[[3,2,0,0],[3,1,0],[3,0],[3]]                                           => [[3,2,0,0],[2,0,0],[1,0],[0]]
[[3,2,0,0],[3,1,0],[3,1],[1]]                                           => [[3,2,0,0],[3,1,0],[3,0],[3]]
[[3,2,0,0],[3,1,0],[3,1],[2]]                                           => [[3,2,0,0],[3,0,0],[2,0],[2]]
[[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],[3,2],[2]]
[[3,2,0,0],[3,2,0],[2,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,1],[1]]
[[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],[2,2,0],[2,2],[2]]
[[3,2,0,0],[3,2,0],[2,1],[2]]                                           => [[3,2,0,0],[2,1,0],[2,1],[1]]
[[3,2,0,0],[3,2,0],[2,2],[2]]                                           => [[3,2,0,0],[2,1,0],[2,1],[2]]
[[3,2,0,0],[3,2,0],[3,0],[0]]                                           => [[3,2,0,0],[3,2,0],[3,2],[3]]
[[3,2,0,0],[3,2,0],[3,0],[1]]                                           => [[3,2,0,0],[3,1,0],[3,1],[2]]
[[3,2,0,0],[3,2,0],[3,0],[2]]                                           => [[3,2,0,0],[3,0,0],[3,0],[1]]
[[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],[3,1],[3]]
[[3,2,0,0],[3,2,0],[3,1],[2]]                                           => [[3,2,0,0],[3,0,0],[3,0],[2]]
[[3,2,0,0],[3,2,0],[3,1],[3]]                                           => [[3,2,0,0],[2,0,0],[2,0],[1]]
[[3,2,0,0],[3,2,0],[3,2],[2]]                                           => [[3,2,0,0],[3,0,0],[3,0],[3]]
[[3,2,0,0],[3,2,0],[3,2],[3]]                                           => [[3,2,0,0],[2,0,0],[2,0],[2]]
[[3,1,1,0],[1,1,0],[1,0],[0]]                                           => [[3,1,1,0],[3,1,1],[1,1],[1]]
[[3,1,1,0],[1,1,0],[1,0],[1]]                                           => [[3,1,1,0],[3,1,0],[1,0],[0]]
[[3,1,1,0],[1,1,0],[1,1],[1]]                                           => [[3,1,1,0],[3,1,0],[1,0],[1]]
[[3,1,1,0],[1,1,1],[1,1],[1]]                                           => [[3,1,1,0],[2,1,1],[1,1],[1]]
[[3,1,1,0],[2,1,0],[1,0],[0]]                                           => [[3,1,1,0],[3,1,1],[2,1],[1]]
[[3,1,1,0],[2,1,0],[1,0],[1]]                                           => [[3,1,1,0],[3,1,0],[2,0],[0]]
[[3,1,1,0],[2,1,0],[1,1],[1]]                                           => [[3,1,1,0],[3,1,0],[1,1],[1]]
[[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],[3,1,0],[2,0],[1]]
[[3,1,1,0],[2,1,0],[2,0],[2]]                                           => [[3,1,1,0],[2,1,0],[1,0],[0]]
[[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],[1,0],[1]]
[[3,1,1,0],[2,1,1],[1,1],[1]]                                           => [[3,1,1,0],[2,1,1],[2,1],[1]]
[[3,1,1,0],[2,1,1],[2,1],[1]]                                           => [[3,1,1,0],[2,1,1],[2,1],[2]]
[[3,1,1,0],[2,1,1],[2,1],[2]]                                           => [[3,1,1,0],[1,1,1],[1,1],[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],[3,0],[0]]
[[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],[3,1],[2]]
[[3,1,1,0],[3,1,0],[2,0],[1]]                                           => [[3,1,1,0],[3,1,0],[3,0],[1]]
[[3,1,1,0],[3,1,0],[2,0],[2]]                                           => [[3,1,1,0],[2,1,0],[2,0],[0]]
[[3,1,1,0],[3,1,0],[2,1],[1]]                                           => [[3,1,1,0],[3,1,0],[2,1],[2]]
[[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],[3,1],[3]]
[[3,1,1,0],[3,1,0],[3,0],[1]]                                           => [[3,1,1,0],[3,1,0],[3,0],[2]]
[[3,1,1,0],[3,1,0],[3,0],[2]]                                           => [[3,1,1,0],[2,1,0],[2,0],[1]]
[[3,1,1,0],[3,1,0],[3,0],[3]]                                           => [[3,1,1,0],[1,1,0],[1,0],[0]]
[[3,1,1,0],[3,1,0],[3,1],[1]]                                           => [[3,1,1,0],[3,1,0],[3,0],[3]]
[[3,1,1,0],[3,1,0],[3,1],[2]]                                           => [[3,1,1,0],[2,1,0],[2,0],[2]]
[[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],[3,1],[1]]
[[3,1,1,0],[3,1,1],[2,1],[1]]                                           => [[3,1,1,0],[3,1,0],[3,1],[2]]
[[3,1,1,0],[3,1,1],[2,1],[2]]                                           => [[3,1,1,0],[2,1,0],[2,1],[1]]
[[3,1,1,0],[3,1,1],[3,1],[1]]                                           => [[3,1,1,0],[3,1,0],[3,1],[3]]
[[3,1,1,0],[3,1,1],[3,1],[2]]                                           => [[3,1,1,0],[2,1,0],[2,1],[2]]
[[3,1,1,0],[3,1,1],[3,1],[3]]                                           => [[3,1,1,0],[1,1,0],[1,1],[1]]
[[2,2,1,0],[2,1,0],[1,0],[0]]                                           => [[2,2,1,0],[2,2,1],[2,1],[1]]
[[2,2,1,0],[2,1,0],[1,0],[1]]                                           => [[2,2,1,0],[2,2,0],[2,0],[0]]
[[2,2,1,0],[2,1,0],[1,1],[1]]                                           => [[2,2,1,0],[2,1,1],[1,1],[1]]
[[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],[2,2,0],[2,0],[1]]
[[2,2,1,0],[2,1,0],[2,0],[2]]                                           => [[2,2,1,0],[2,1,0],[1,0],[0]]
[[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],[1,0],[1]]
[[2,2,1,0],[2,1,1],[1,1],[1]]                                           => [[2,2,1,0],[2,1,1],[2,1],[1]]
[[2,2,1,0],[2,1,1],[2,1],[1]]                                           => [[2,2,1,0],[2,1,1],[2,1],[2]]
[[2,2,1,0],[2,1,1],[2,1],[2]]                                           => [[2,2,1,0],[2,1,0],[1,1],[1]]
[[2,2,1,0],[2,2,0],[2,0],[0]]                                           => [[2,2,1,0],[2,2,1],[2,2],[2]]
[[2,2,1,0],[2,2,0],[2,0],[1]]                                           => [[2,2,1,0],[2,2,0],[2,1],[1]]
[[2,2,1,0],[2,2,0],[2,0],[2]]                                           => [[2,2,1,0],[2,1,0],[2,0],[0]]
[[2,2,1,0],[2,2,0],[2,1],[1]]                                           => [[2,2,1,0],[2,2,0],[2,1],[2]]
[[2,2,1,0],[2,2,0],[2,1],[2]]                                           => [[2,2,1,0],[2,1,0],[2,0],[1]]
[[2,2,1,0],[2,2,0],[2,2],[2]]                                           => [[2,2,1,0],[2,1,0],[2,0],[2]]
[[2,2,1,0],[2,2,1],[2,1],[1]]                                           => [[2,2,1,0],[2,2,0],[2,2],[2]]
[[2,2,1,0],[2,2,1],[2,1],[2]]                                           => [[2,2,1,0],[2,1,0],[2,1],[1]]
[[2,2,1,0],[2,2,1],[2,2],[2]]                                           => [[2,2,1,0],[2,1,0],[2,1],[2]]
[[2,1,1,1],[1,1,1],[1,1],[1]]                                           => [[2,1,1,1],[2,1,1],[1,1],[1]]
[[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],[2,1],[2]]
[[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],[0,0,0],[0,0],[0]]
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[1,0,0,0,0],[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],[1,0,0],[1,0],[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],[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],[0,0,0],[0,0],[0]]
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[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],[0,0,0],[0,0],[0]]
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[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],[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],[2,0,0],[1,0],[1]]
[[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],[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],[2,0],[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],[2,0,0],[2,0],[1]]
[[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],[2,0,0],[2,0],[0]]                               => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[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],[1,0],[1]]
[[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],[1,0,0],[0,0],[0]]
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[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],[0,0,0],[0,0],[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],[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],[1,1,0],[1,0],[1]]
[[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],[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],[1,1,0],[1,1],[1]]
[[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],[1,1,0],[1,1],[1]]                               => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]
[[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],[1,0],[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],[1,0,0],[0,0],[0]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]
[[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],[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],[1,0,0],[1,0],[0]]
[[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],[2,0],[2]]
[[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],[0,0,0],[0,0],[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],[0,0],[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],[1,0],[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],[3,0,0],[1,0],[1]]
[[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],[0,0],[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],[2,0],[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],[3,0,0],[2,0],[1]]
[[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],[3,0,0],[2,0],[2]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[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],[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],[3,0],[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],[3,0,0],[3,0],[1]]
[[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],[2,0],[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],[3,0,0],[3,0],[2]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[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],[3,0,0],[3,0],[0]]                               => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]                               => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[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],[1,0],[1]]
[[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],[1,0,0],[0,0],[0]]
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]
[[2,1,0,0,0],[1,0,0,0],[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],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[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],[0,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]
[[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],[1,0],[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],[1,0,0],[0,0],[0]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[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],[2,0,0],[2,0],[2]]                               => [[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[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],[1,0],[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],[2,1,0],[1,0],[1]]
[[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],[0,0],[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],[2,1,0],[1,1],[1]]
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[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],[1,1,0],[1,1],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[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],[2,0],[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],[2,1,0],[2,0],[1]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[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],[2,0,0],[2,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[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],[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],[2,1,0],[2,1],[1]]
[[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],[2,0],[0]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]                               => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]                               => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[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],[2,1,0],[2,1],[1]]                               => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[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],[1,0],[1]]
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]]
[[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],[1,0],[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],[1,0,0],[0,0],[0]]
[[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],[1,1,0],[1,0],[1]]                               => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[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],[1,1,1],[1,1],[1]]
[[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],[1,1,0],[1,0],[1]]
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]                               => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]]
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]
[[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],[1,0,0],[1,0],[1]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]]
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]]
[[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],[1,0],[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],[2,0,0],[0,0],[0]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]]
[[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],[2,0,0],[1,0],[0]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]
[[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],[1,0],[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],[1,0,0],[0,0],[0]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]]
[[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],[3,0],[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],[2,0,0],[2,0],[0]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]
[[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],[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],[1,0,0],[1,0],[0]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]
[[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],[2,0],[2]]
[[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],[0,0,0],[0,0],[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],[0,0],[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],[1,0],[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],[4,0,0],[1,0],[1]]
[[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],[0,0],[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],[4,0,0],[2,0],[1]]
[[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],[1,0],[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],[4,0,0],[2,0],[2]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]
[[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],[0,0],[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],[3,0],[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],[4,0,0],[3,0],[1]]
[[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],[2,0],[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],[4,0,0],[3,0],[2]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]
[[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],[4,0,0],[3,0],[3]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[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],[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],[4,0],[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],[4,0,0],[4,0],[1]]
[[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],[3,0],[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],[4,0,0],[4,0],[2]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]
[[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],[2,0],[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],[4,0,0],[4,0],[3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[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],[4,0,0],[4,0],[0]]                               => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]]                               => [[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]]                               => [[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[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],[1,0],[1]]
[[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],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[1,0,0,0],[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],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]]
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]]
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]
[[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],[3,0,0,0],[1,0,0],[1,0],[1]]
[[3,1,0,0,0],[2,0,0,0],[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],[2,1,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]]
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[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],[2,1,0],[2,0],[0]]
[[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],[2,0,0],[1,0],[0]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]]
[[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],[1,0],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[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],[2,1,0],[2,1],[2]]
[[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],[1]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[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],[0,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[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],[1,0,0],[0,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[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],[3,0,0],[3,0],[3]]                               => [[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[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],[1,0],[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],[3,1,0],[1,0],[1]]
[[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],[0,0],[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],[3,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[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],[1,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]
[[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],[3,1,0],[2,0],[1]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[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],[2,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]
[[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],[0,0],[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],[3,1,0],[2,1],[1]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[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],[2,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[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],[2,1,0],[2,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[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],[3,0],[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],[3,1,0],[3,0],[1]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[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],[3,0,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[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],[3,0,0],[3,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[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],[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],[3,1,0],[3,1],[1]]
[[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],[3,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]
[[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],[2,0],[0]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]]                               => [[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]]                               => [[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]]                               => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[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],[3,1,0],[3,1],[1]]                               => [[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]]                               => [[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[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],[1,0],[1]]
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]
[[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],[1,0,0],[1,0],[1]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]]
[[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],[1,0],[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],[2,0,0],[0,0],[0]]
[[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],[1,1,0],[1,0],[0]]
[[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],[1,0],[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],[2,1,0],[2,0],[0]]
[[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],[2,0,0],[1,0],[0]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]]
[[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],[1,0],[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],[1,0,0],[0,0],[0]]
[[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],[2,1],[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],[2,0,0],[2,0],[0]]
[[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],[2,1,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]]
[[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],[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],[1,0,0],[1,0],[0]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]
[[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],[2,2,0],[2,0],[1]]
[[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],[1,0],[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],[2,2,0],[2,0],[2]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]
[[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],[0,0],[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],[2,2,0],[2,1],[1]]
[[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],[2,0],[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],[2,1,0],[1,1],[1]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]
[[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],[2,1,0],[2,0],[2]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]]                               => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]]                               => [[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]
[[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],[2,0],[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],[2,1,0],[2,1],[2]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]]                               => [[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[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],[1,1,1],[1,1],[1]]
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]                               => [[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]]
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]]                               => [[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]
[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[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],[1,0,0],[0,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]]
[[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],[1,0],[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],[2,0,0],[0,0],[0]]
[[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],[1,1,0],[1,0],[0]]
[[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],[1,0],[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],[2,1,0],[2,0],[0]]
[[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],[2,0],[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],[2,0,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[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],[2,0,0],[2,0],[2]]                               => [[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]
[[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],[2,1],[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],[2,0,0],[2,0],[0]]
[[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],[2,1,0],[2,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[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],[1,0,0],[1,0],[0]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]
[[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],[2,1,1],[1,1],[1]]
[[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],[1,0],[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],[2,1,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                               => [[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]]
[[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],[2,0],[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],[2,1,0],[1,1],[1]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]]                               => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]
[[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],[2,1,0],[2,0],[2]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]]                               => [[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]]                               => [[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]
[[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],[0,0,0,0],[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],[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],[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],[1,0,0],[1,0],[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],[1,0,0],[1,0],[1]]
[[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],[0,0,0,0],[0,0,0],[0,0],[0]]
[[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],[1,0,0,0],[0,0,0],[0,0],[0]]
[[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],[1,0,0,0],[1,0,0],[0,0],[0]]
[[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],[1,0,0,0],[1,0,0],[1,0],[0]]
[[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],[0,0,0,0],[0,0,0],[0,0],[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],[0,0,0],[0,0],[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],[1,0,0],[0,0],[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],[2,0,0,0],[1,0,0],[1,0],[1]]
[[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],[0,0,0],[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],[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],[2,0,0],[1,0],[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],[2,0,0,0],[2,0,0],[1,0],[1]]
[[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],[2,0,0],[2,0],[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],[2,0,0,0],[2,0,0],[2,0],[1]]
[[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],[1,0],[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],[2,0,0,0],[2,0,0],[2,0],[2]]
[[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],[1,0,0],[1,0],[1]]
[[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],[1,0,0,0],[0,0,0],[0,0],[0]]
[[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],[1,0,0,0],[1,0,0],[0,0],[0]]
[[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],[1,0,0,0],[1,0,0],[1,0],[0]]
[[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],[0,0,0,0],[0,0,0],[0,0],[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],[1,0,0],[0,0],[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],[1,1,0,0],[1,0,0],[1,0],[1]]
[[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],[0,0,0],[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],[1,1,0],[1,0],[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],[1,1,0,0],[1,1,0],[1,0],[1]]
[[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],[1,1,0,0],[1,1,0],[1,1],[1]]
[[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],[1,0],[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],[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]] => [[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],[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],[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],[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],[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],[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],[1,0,0],[1,0],[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],[1,0,0,0],[1,0,0],[1,0],[1]]
[[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: Feb 23, 2021 at 18:56 by Martin Rubey

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Last Updated: Feb 23, 2021 at 18:56 by Martin Rubey