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*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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-----------------------------------------------------------------------------
Statistic identifier: St000115

-----------------------------------------------------------------------------
Collection: Gelfand-Tsetlin patterns

-----------------------------------------------------------------------------
Description: The single entry in the last row.

-----------------------------------------------------------------------------
References: 

-----------------------------------------------------------------------------
Code:
def statistic(g):
    return g[-1][0]

-----------------------------------------------------------------------------
Statistic values:

[[1]]                                                                                                                                                                                 => 1
[[2]]                                                                                                                                                                                 => 2
[[3]]                                                                                                                                                                                 => 3
[[4]]                                                                                                                                                                                 => 4
[[5]]                                                                                                                                                                                 => 5
[[1,0],[0]]                                                                                                                                                                           => 0
[[1,0],[1]]                                                                                                                                                                           => 1
[[2,0],[0]]                                                                                                                                                                           => 0
[[2,0],[1]]                                                                                                                                                                           => 1
[[2,0],[2]]                                                                                                                                                                           => 2
[[1,1],[1]]                                                                                                                                                                           => 1
[[3,0],[0]]                                                                                                                                                                           => 0
[[3,0],[1]]                                                                                                                                                                           => 1
[[3,0],[2]]                                                                                                                                                                           => 2
[[3,0],[3]]                                                                                                                                                                           => 3
[[2,1],[1]]                                                                                                                                                                           => 1
[[2,1],[2]]                                                                                                                                                                           => 2
[[4,0],[0]]                                                                                                                                                                           => 0
[[4,0],[1]]                                                                                                                                                                           => 1
[[4,0],[2]]                                                                                                                                                                           => 2
[[4,0],[3]]                                                                                                                                                                           => 3
[[4,0],[4]]                                                                                                                                                                           => 4
[[3,1],[1]]                                                                                                                                                                           => 1
[[3,1],[2]]                                                                                                                                                                           => 2
[[3,1],[3]]                                                                                                                                                                           => 3
[[2,2],[2]]                                                                                                                                                                           => 2
[[5,0],[0]]                                                                                                                                                                           => 0
[[5,0],[1]]                                                                                                                                                                           => 1
[[5,0],[2]]                                                                                                                                                                           => 2
[[5,0],[3]]                                                                                                                                                                           => 3
[[5,0],[4]]                                                                                                                                                                           => 4
[[5,0],[5]]                                                                                                                                                                           => 5
[[4,1],[1]]                                                                                                                                                                           => 1
[[4,1],[2]]                                                                                                                                                                           => 2
[[4,1],[3]]                                                                                                                                                                           => 3
[[4,1],[4]]                                                                                                                                                                           => 4
[[3,2],[2]]                                                                                                                                                                           => 2
[[3,2],[3]]                                                                                                                                                                           => 3
[[6,0],[0]]                                                                                                                                                                           => 0
[[6,0],[1]]                                                                                                                                                                           => 1
[[6,0],[2]]                                                                                                                                                                           => 2
[[6,0],[3]]                                                                                                                                                                           => 3
[[6,0],[4]]                                                                                                                                                                           => 4
[[6,0],[5]]                                                                                                                                                                           => 5
[[6,0],[6]]                                                                                                                                                                           => 6
[[5,1],[1]]                                                                                                                                                                           => 1
[[5,1],[2]]                                                                                                                                                                           => 2
[[5,1],[3]]                                                                                                                                                                           => 3
[[5,1],[4]]                                                                                                                                                                           => 4
[[5,1],[5]]                                                                                                                                                                           => 5
[[4,2],[2]]                                                                                                                                                                           => 2
[[4,2],[3]]                                                                                                                                                                           => 3
[[4,2],[4]]                                                                                                                                                                           => 4
[[3,3],[3]]                                                                                                                                                                           => 3
[[1,0,0],[0,0],[0]]                                                                                                                                                                   => 0
[[1,0,0],[1,0],[0]]                                                                                                                                                                   => 0
[[1,0,0],[1,0],[1]]                                                                                                                                                                   => 1
[[2,0,0],[0,0],[0]]                                                                                                                                                                   => 0
[[2,0,0],[1,0],[0]]                                                                                                                                                                   => 0
[[2,0,0],[1,0],[1]]                                                                                                                                                                   => 1
[[2,0,0],[2,0],[0]]                                                                                                                                                                   => 0
[[2,0,0],[2,0],[1]]                                                                                                                                                                   => 1
[[2,0,0],[2,0],[2]]                                                                                                                                                                   => 2
[[1,1,0],[1,0],[0]]                                                                                                                                                                   => 0
[[1,1,0],[1,0],[1]]                                                                                                                                                                   => 1
[[1,1,0],[1,1],[1]]                                                                                                                                                                   => 1
[[3,0,0],[0,0],[0]]                                                                                                                                                                   => 0
[[3,0,0],[1,0],[0]]                                                                                                                                                                   => 0
[[3,0,0],[1,0],[1]]                                                                                                                                                                   => 1
[[3,0,0],[2,0],[0]]                                                                                                                                                                   => 0
[[3,0,0],[2,0],[1]]                                                                                                                                                                   => 1
[[3,0,0],[2,0],[2]]                                                                                                                                                                   => 2
[[3,0,0],[3,0],[0]]                                                                                                                                                                   => 0
[[3,0,0],[3,0],[1]]                                                                                                                                                                   => 1
[[3,0,0],[3,0],[2]]                                                                                                                                                                   => 2
[[3,0,0],[3,0],[3]]                                                                                                                                                                   => 3
[[2,1,0],[1,0],[0]]                                                                                                                                                                   => 0
[[2,1,0],[1,0],[1]]                                                                                                                                                                   => 1
[[2,1,0],[1,1],[1]]                                                                                                                                                                   => 1
[[2,1,0],[2,0],[0]]                                                                                                                                                                   => 0
[[2,1,0],[2,0],[1]]                                                                                                                                                                   => 1
[[2,1,0],[2,0],[2]]                                                                                                                                                                   => 2
[[2,1,0],[2,1],[1]]                                                                                                                                                                   => 1
[[2,1,0],[2,1],[2]]                                                                                                                                                                   => 2
[[1,1,1],[1,1],[1]]                                                                                                                                                                   => 1
[[4,0,0],[0,0],[0]]                                                                                                                                                                   => 0
[[4,0,0],[1,0],[0]]                                                                                                                                                                   => 0
[[4,0,0],[1,0],[1]]                                                                                                                                                                   => 1
[[4,0,0],[2,0],[0]]                                                                                                                                                                   => 0
[[4,0,0],[2,0],[1]]                                                                                                                                                                   => 1
[[4,0,0],[2,0],[2]]                                                                                                                                                                   => 2
[[4,0,0],[3,0],[0]]                                                                                                                                                                   => 0
[[4,0,0],[3,0],[1]]                                                                                                                                                                   => 1
[[4,0,0],[3,0],[2]]                                                                                                                                                                   => 2
[[4,0,0],[3,0],[3]]                                                                                                                                                                   => 3
[[4,0,0],[4,0],[0]]                                                                                                                                                                   => 0
[[4,0,0],[4,0],[1]]                                                                                                                                                                   => 1
[[4,0,0],[4,0],[2]]                                                                                                                                                                   => 2
[[4,0,0],[4,0],[3]]                                                                                                                                                                   => 3
[[4,0,0],[4,0],[4]]                                                                                                                                                                   => 4
[[3,1,0],[1,0],[0]]                                                                                                                                                                   => 0
[[3,1,0],[1,0],[1]]                                                                                                                                                                   => 1
[[3,1,0],[1,1],[1]]                                                                                                                                                                   => 1
[[3,1,0],[2,0],[0]]                                                                                                                                                                   => 0
[[3,1,0],[2,0],[1]]                                                                                                                                                                   => 1
[[3,1,0],[2,0],[2]]                                                                                                                                                                   => 2
[[3,1,0],[2,1],[1]]                                                                                                                                                                   => 1
[[3,1,0],[2,1],[2]]                                                                                                                                                                   => 2
[[3,1,0],[3,0],[0]]                                                                                                                                                                   => 0
[[3,1,0],[3,0],[1]]                                                                                                                                                                   => 1
[[3,1,0],[3,0],[2]]                                                                                                                                                                   => 2
[[3,1,0],[3,0],[3]]                                                                                                                                                                   => 3
[[3,1,0],[3,1],[1]]                                                                                                                                                                   => 1
[[3,1,0],[3,1],[2]]                                                                                                                                                                   => 2
[[3,1,0],[3,1],[3]]                                                                                                                                                                   => 3
[[2,2,0],[2,0],[0]]                                                                                                                                                                   => 0
[[2,2,0],[2,0],[1]]                                                                                                                                                                   => 1
[[2,2,0],[2,0],[2]]                                                                                                                                                                   => 2
[[2,2,0],[2,1],[1]]                                                                                                                                                                   => 1
[[2,2,0],[2,1],[2]]                                                                                                                                                                   => 2
[[2,2,0],[2,2],[2]]                                                                                                                                                                   => 2
[[2,1,1],[1,1],[1]]                                                                                                                                                                   => 1
[[2,1,1],[2,1],[1]]                                                                                                                                                                   => 1
[[2,1,1],[2,1],[2]]                                                                                                                                                                   => 2
[[5,0,0],[0,0],[0]]                                                                                                                                                                   => 0
[[5,0,0],[1,0],[0]]                                                                                                                                                                   => 0
[[5,0,0],[1,0],[1]]                                                                                                                                                                   => 1
[[5,0,0],[2,0],[0]]                                                                                                                                                                   => 0
[[5,0,0],[2,0],[1]]                                                                                                                                                                   => 1
[[5,0,0],[2,0],[2]]                                                                                                                                                                   => 2
[[5,0,0],[3,0],[0]]                                                                                                                                                                   => 0
[[5,0,0],[3,0],[1]]                                                                                                                                                                   => 1
[[5,0,0],[3,0],[2]]                                                                                                                                                                   => 2
[[5,0,0],[3,0],[3]]                                                                                                                                                                   => 3
[[5,0,0],[4,0],[0]]                                                                                                                                                                   => 0
[[5,0,0],[4,0],[1]]                                                                                                                                                                   => 1
[[5,0,0],[4,0],[2]]                                                                                                                                                                   => 2
[[5,0,0],[4,0],[3]]                                                                                                                                                                   => 3
[[5,0,0],[4,0],[4]]                                                                                                                                                                   => 4
[[5,0,0],[5,0],[1]]                                                                                                                                                                   => 1
[[5,0,0],[5,0],[2]]                                                                                                                                                                   => 2
[[5,0,0],[5,0],[3]]                                                                                                                                                                   => 3
[[5,0,0],[5,0],[4]]                                                                                                                                                                   => 4
[[5,0,0],[5,0],[5]]                                                                                                                                                                   => 5
[[4,1,0],[1,0],[0]]                                                                                                                                                                   => 0
[[4,1,0],[1,0],[1]]                                                                                                                                                                   => 1
[[4,1,0],[1,1],[1]]                                                                                                                                                                   => 1
[[4,1,0],[2,0],[0]]                                                                                                                                                                   => 0
[[4,1,0],[2,0],[1]]                                                                                                                                                                   => 1
[[4,1,0],[2,0],[2]]                                                                                                                                                                   => 2
[[4,1,0],[2,1],[1]]                                                                                                                                                                   => 1
[[4,1,0],[2,1],[2]]                                                                                                                                                                   => 2
[[4,1,0],[3,0],[0]]                                                                                                                                                                   => 0
[[4,1,0],[3,0],[1]]                                                                                                                                                                   => 1
[[4,1,0],[3,0],[2]]                                                                                                                                                                   => 2
[[4,1,0],[3,0],[3]]                                                                                                                                                                   => 3
[[4,1,0],[3,1],[1]]                                                                                                                                                                   => 1
[[4,1,0],[3,1],[2]]                                                                                                                                                                   => 2
[[4,1,0],[3,1],[3]]                                                                                                                                                                   => 3
[[4,1,0],[4,0],[0]]                                                                                                                                                                   => 0
[[4,1,0],[4,0],[1]]                                                                                                                                                                   => 1
[[4,1,0],[4,0],[2]]                                                                                                                                                                   => 2
[[4,1,0],[4,0],[3]]                                                                                                                                                                   => 3
[[4,1,0],[4,0],[4]]                                                                                                                                                                   => 4
[[4,1,0],[4,1],[1]]                                                                                                                                                                   => 1
[[4,1,0],[4,1],[2]]                                                                                                                                                                   => 2
[[4,1,0],[4,1],[3]]                                                                                                                                                                   => 3
[[4,1,0],[4,1],[4]]                                                                                                                                                                   => 4
[[3,2,0],[2,0],[0]]                                                                                                                                                                   => 0
[[3,2,0],[2,0],[1]]                                                                                                                                                                   => 1
[[3,2,0],[2,0],[2]]                                                                                                                                                                   => 2
[[3,2,0],[2,1],[1]]                                                                                                                                                                   => 1
[[3,2,0],[2,1],[2]]                                                                                                                                                                   => 2
[[3,2,0],[2,2],[2]]                                                                                                                                                                   => 2
[[3,2,0],[3,0],[0]]                                                                                                                                                                   => 0
[[3,2,0],[3,0],[1]]                                                                                                                                                                   => 1
[[3,2,0],[3,0],[2]]                                                                                                                                                                   => 2
[[3,2,0],[3,0],[3]]                                                                                                                                                                   => 3
[[3,2,0],[3,1],[1]]                                                                                                                                                                   => 1
[[3,2,0],[3,1],[2]]                                                                                                                                                                   => 2
[[3,2,0],[3,1],[3]]                                                                                                                                                                   => 3
[[3,2,0],[3,2],[2]]                                                                                                                                                                   => 2
[[3,2,0],[3,2],[3]]                                                                                                                                                                   => 3
[[3,1,1],[1,1],[1]]                                                                                                                                                                   => 1
[[3,1,1],[2,1],[1]]                                                                                                                                                                   => 1
[[3,1,1],[2,1],[2]]                                                                                                                                                                   => 2
[[3,1,1],[3,1],[1]]                                                                                                                                                                   => 1
[[3,1,1],[3,1],[2]]                                                                                                                                                                   => 2
[[3,1,1],[3,1],[3]]                                                                                                                                                                   => 3
[[2,2,1],[2,1],[1]]                                                                                                                                                                   => 1
[[2,2,1],[2,1],[2]]                                                                                                                                                                   => 2
[[2,2,1],[2,2],[2]]                                                                                                                                                                   => 2
[[3,3,0],[3,0],[0]]                                                                                                                                                                   => 0
[[3,3,0],[3,0],[1]]                                                                                                                                                                   => 1
[[3,3,0],[3,0],[2]]                                                                                                                                                                   => 2
[[3,3,0],[3,0],[3]]                                                                                                                                                                   => 3
[[3,3,0],[3,1],[1]]                                                                                                                                                                   => 1
[[3,3,0],[3,1],[2]]                                                                                                                                                                   => 2
[[3,3,0],[3,1],[3]]                                                                                                                                                                   => 3
[[3,3,0],[3,2],[2]]                                                                                                                                                                   => 2
[[3,3,0],[3,2],[3]]                                                                                                                                                                   => 3
[[3,3,0],[3,3],[3]]                                                                                                                                                                   => 3
[[3,2,1],[2,1],[1]]                                                                                                                                                                   => 1
[[3,2,1],[2,1],[2]]                                                                                                                                                                   => 2
[[3,2,1],[2,2],[2]]                                                                                                                                                                   => 2
[[3,2,1],[3,1],[1]]                                                                                                                                                                   => 1
[[3,2,1],[3,1],[2]]                                                                                                                                                                   => 2
[[3,2,1],[3,1],[3]]                                                                                                                                                                   => 3
[[3,2,1],[3,2],[2]]                                                                                                                                                                   => 2
[[3,2,1],[3,2],[3]]                                                                                                                                                                   => 3
[[2,2,2],[2,2],[2]]                                                                                                                                                                   => 2
[[3,3,1],[3,3],[3]]                                                                                                                                                                   => 3
[[3,3,1],[3,2],[3]]                                                                                                                                                                   => 3
[[3,3,1],[3,1],[3]]                                                                                                                                                                   => 3
[[3,3,1],[3,2],[2]]                                                                                                                                                                   => 2
[[3,3,1],[3,1],[2]]                                                                                                                                                                   => 2
[[3,3,1],[3,1],[1]]                                                                                                                                                                   => 1
[[3,2,2],[3,2],[3]]                                                                                                                                                                   => 3
[[3,2,2],[3,2],[2]]                                                                                                                                                                   => 2
[[3,2,2],[2,2],[2]]                                                                                                                                                                   => 2
[[1,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[1,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[2,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[2,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,0,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[2,0,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,0,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,0,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,0,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,0,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[1,1,0,0],[1,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[1,1,0,0],[1,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[1,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[1,1,0,0],[1,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[1,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[1,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,0,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,0,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,0,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,0,0,0],[3,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[3,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[3,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,0,0,0],[3,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,0,0,0],[3,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,0,0,0],[3,0,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,0,0,0],[3,0,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,0,0,0],[3,0,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,0,0,0],[3,0,0],[3,0],[3]]                                                                                                                                                         => 3
[[2,1,0,0],[1,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[2,1,0,0],[1,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[1,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[2,1,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,1,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,1,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,1,0,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,1,0,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,1,0,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[2,1,0,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[1,1,1,0],[1,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[1,1,1,0],[1,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[1,1,1,0],[1,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[1,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,0,0,0],[3,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[3,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[3,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[3,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[3,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,0,0,0],[3,0,0],[3,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[3,0,0],[3,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[3,0,0],[3,0],[2]]                                                                                                                                                         => 2
[[4,0,0,0],[3,0,0],[3,0],[3]]                                                                                                                                                         => 3
[[4,0,0,0],[4,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[4,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[4,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[4,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[4,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[4,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,0,0,0],[4,0,0],[3,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[4,0,0],[3,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[4,0,0],[3,0],[2]]                                                                                                                                                         => 2
[[4,0,0,0],[4,0,0],[3,0],[3]]                                                                                                                                                         => 3
[[4,0,0,0],[4,0,0],[4,0],[0]]                                                                                                                                                         => 0
[[4,0,0,0],[4,0,0],[4,0],[1]]                                                                                                                                                         => 1
[[4,0,0,0],[4,0,0],[4,0],[2]]                                                                                                                                                         => 2
[[4,0,0,0],[4,0,0],[4,0],[3]]                                                                                                                                                         => 3
[[4,0,0,0],[4,0,0],[4,0],[4]]                                                                                                                                                         => 4
[[3,1,0,0],[1,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[1,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[1,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[3,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[3,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[3,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[3,0,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[3,0,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,0,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[3,0,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,1,0,0],[3,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[3,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[3,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[3,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[3,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,1,0,0],[3,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[3,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,1,0,0],[3,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,1,0,0],[3,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,1,0,0],[3,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[2,2,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[2,2,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,2,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,2,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,2,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,2,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,2,0,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,2,0,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[2,2,0,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,2,0,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,2,0,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,0,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,0,0],[2,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,2,0,0],[2,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,2,0,0],[2,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,2,0,0],[2,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,0,0],[2,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,0,0],[2,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[2,1,1,0],[1,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,1,1,0],[1,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[1,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,1,1,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,1,1,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[2,1,1,0],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[2,1,1,0],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[1,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[1,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[1,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[3,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[3,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[3,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[3,0,0],[3,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[3,0,0],[3,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,0,0],[3,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[3,0,0],[3,0],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[3,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[3,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[3,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[3,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[3,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[3,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[3,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[3,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[3,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[3,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[4,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,0,0],[3,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,0,0],[3,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,0,0],[3,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,0,0],[3,0],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[4,0,0],[4,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,0,0],[4,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,0,0],[4,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,0,0],[4,0],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[4,0,0],[4,0],[4]]                                                                                                                                                         => 4
[[4,1,0,0],[4,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[4,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[4,1,0],[4,0],[0]]                                                                                                                                                         => 0
[[4,1,0,0],[4,1,0],[4,0],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,1,0],[4,0],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,1,0],[4,0],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[4,1,0],[4,0],[4]]                                                                                                                                                         => 4
[[4,1,0,0],[4,1,0],[4,1],[1]]                                                                                                                                                         => 1
[[4,1,0,0],[4,1,0],[4,1],[2]]                                                                                                                                                         => 2
[[4,1,0,0],[4,1,0],[4,1],[3]]                                                                                                                                                         => 3
[[4,1,0,0],[4,1,0],[4,1],[4]]                                                                                                                                                         => 4
[[3,2,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[2,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[2,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[2,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[2,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[2,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[2,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,0,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,0,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,0,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,0,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,2,0,0],[3,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,2,0,0],[3,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,0,0],[3,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,2,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,2,0,0],[3,2,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,2,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,2,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,2,0,0],[3,2,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,0,0],[3,2,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,2,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,0,0],[3,2,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,0,0],[3,2,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,1,1,0],[1,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,1,0],[1,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[1,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,1,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[3,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,1,0],[3,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,1,1,0],[3,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[3,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[3,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,1,1,0],[3,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[3,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,1,1,0],[3,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[3,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,1,1,0],[3,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[3,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,1,1,0],[3,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,1,1,0],[3,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[2,2,1,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[2,2,1,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,2,1,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,2,1,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,1,0],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,1,0],[2,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,2,1,0],[2,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,2,1,0],[2,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,1,0],[2,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[2,2,1,0],[2,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,1,0],[2,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,1,0],[2,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[2,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[2,1,1,1],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[2,1,1,1],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[2,1,1,1],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,2,0,0],[2,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,2,0,0],[2,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,2,0,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,2,0,0],[2,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,2,0,0],[2,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,2,0,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,2,0,0],[2,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,2,0,0],[2,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[4,1,0],[4,1],[4]]                                                                                                                                                         => 4
[[4,1,1,0],[4,1,0],[4,0],[4]]                                                                                                                                                         => 4
[[4,1,1,0],[4,1,0],[4,1],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[4,1,0],[4,0],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[4,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[3,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[3,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[4,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[3,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[4,1,0],[4,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,0],[4,0],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[3,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[3,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[3,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[3,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[3,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[3,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,0],[4,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,0],[4,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[1,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[3,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[1,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,0],[4,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[4,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[3,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[4,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[3,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[4,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[3,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[4,1,1,0],[1,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,2,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,2,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,2,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,0,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,2,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,2,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,2,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,0,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,0,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,2,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,2,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,0,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,0,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,0,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,2,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,0,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,0,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,0,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[3,2,1,0],[3,2,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,2,1,0],[3,2,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,1,0],[3,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,1,0],[3,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,1,0],[3,2,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,2,1,0],[3,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,2,1,0],[3,2,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[2,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[2,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[2,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[2,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[2,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[2,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[2,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,2,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[2,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,2,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,2,1,0],[3,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,2,1,0],[3,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,1,0],[3,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,1,0],[2,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,1,0],[2,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,1,0],[3,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,2,1,0],[2,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,1,1,1],[3,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,1,1,1],[3,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,1,1,1],[3,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,1,1,1],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,1,1,1],[3,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,1,1,1],[3,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,1,1,1],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,1,1,1],[3,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,1,1],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[2,2,2,0],[2,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[2,2,2,0],[2,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[2,2,2,0],[2,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,2,0],[2,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,2,0],[2,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[2,2,2,0],[2,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,2,0],[2,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,2,0],[2,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[2,2,2,0],[2,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[2,2,1,1],[2,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[2,2,1,1],[2,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,1,1],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,1,1],[2,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,1,1],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,1,1],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,3,2,1],[4,3,2],[4,3],[4]]                                                                                                                                                         => 4
[[4,3,2,1],[4,3,2],[4,3],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,3,2],[4,2],[4]]                                                                                                                                                         => 4
[[4,3,2,1],[4,3,2],[4,2],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,3,2],[3,2],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,3,2],[4,2],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,3,2],[3,2],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,3,1],[4,3],[4]]                                                                                                                                                         => 4
[[4,3,2,1],[4,3,1],[4,3],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,3,1],[4,2],[4]]                                                                                                                                                         => 4
[[4,3,2,1],[4,3,1],[4,2],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,3,1],[3,2],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,3,1],[4,2],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,3,1],[3,2],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,2,1],[4,2],[4]]                                                                                                                                                         => 4
[[4,3,2,1],[4,2,1],[4,2],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,2,1],[4,2],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,3,1],[4,1],[4]]                                                                                                                                                         => 4
[[4,3,2,1],[4,3,1],[4,1],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,3,1],[3,1],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,3,1],[4,1],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,3,1],[3,1],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,2,1],[4,1],[4]]                                                                                                                                                         => 4
[[4,3,2,1],[4,2,1],[4,1],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[4,3,2,1],[4,2,1],[4,1],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,3,2,1],[4,3,1],[4,1],[1]]                                                                                                                                                         => 1
[[4,3,2,1],[4,3,1],[3,1],[1]]                                                                                                                                                         => 1
[[4,3,2,1],[4,2,1],[4,1],[1]]                                                                                                                                                         => 1
[[4,3,2,1],[4,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[4,3,2,1],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[4,3,2,1],[4,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[4,3,2,1],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[1,0,0,0,0],[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]]                                                                                                                                             => 0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                                                                                                                                             => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                                                                                                                                             => 1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                                                                                                                                             => 2
[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                                                                                                                                             => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                                             => 1
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                                                                                                                                             => 0
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                                                                                                                                             => 2
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]                                                                                                                                             => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]                                                                                                                                             => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]                                                                                                                                             => 1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]                                                                                                                                             => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]                                                                                                                                             => 3
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]                                                                                                                                             => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                                                                                                                                             => 2
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]                                                                                                                                             => 2
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]                                                                                                                                             => 2
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]                                                                                                                                             => 1
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]                                                                                                                                             => 2
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]                                                                                                                                             => 0
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]                                                                                                                                             => 0
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                                             => 1
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]                                                                                                                                             => 0
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                                             => 1
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                                             => 1
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]                                                                                                                                             => 1
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]]                                                                                                                                             => 1
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                                             => 1
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                                             => 1
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                                             => 1
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                                             => 1
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                                             => 1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                                             => 1
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                                             => 1
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                                             => 1
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                                             => 1
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                                             => 1
[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                                             => 1
[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                                             => 1
[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                                             => 1
[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                               => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                               => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[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]]                                                                                                                               => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                               => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                               => 1
[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                               => 0
[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                               => 0
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[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]]                                                                                                                               => 0
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                               => 0
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                               => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                               => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                               => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]                                                                                                                               => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]                                                                                                                               => 1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]                                                                                                                               => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                               => 0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[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]]                                                                                                                               => 0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]                                                                                                                               => 0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                               => 1
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]                                                                                                                               => 1
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]                                                                                                                               => 1
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]                                                                                                                               => 1
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]                                                                                                                               => 1
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                                               => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                                               => 1
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                                               => 1
[[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                               => 1
[[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                               => 1
[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                               => 1
[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                               => 1
[[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                               => 1
[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                               => 1
[[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                                               => 1
[[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                               => 1
[[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                                               => 1
[[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                               => 1
[[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                                               => 1
[[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                                               => 1
[[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                               => 1
[[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                               => 1
[[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                                               => 1
[[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                               => 1
[[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                                               => 1
[[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                                               => 1
[[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                             => 1
[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                             => 1
[[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                             => 1
[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                             => 1
[[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                             => 1
[[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                                             => 1
[[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                             => 1
[[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                             => 1
[[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                                             => 1
[[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                                             => 1
[[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                             => 1
[[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                             => 1
[[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                                             => 1
[[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                                             => 1
[[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                         => 1
[[2,2,2,1,1,1,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                         => 1
[[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                         => 1
[[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                                         => 1
[[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                         => 1
[[7,2,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                         => 1
[[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                         => 1
[[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[6,2,1,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                         => 1
[[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                                         => 1
[[5,3,1,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                         => 1
[[5,2,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                         => 1
[[5,2,1,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                         => 1
[[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[4,4,1,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                                         => 1
[[4,3,2,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                         => 1
[[4,3,1,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                         => 1
[[4,2,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                         => 1
[[4,2,1,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                         => 1
[[3,3,1,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[3,2,2,2,0,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                                         => 1
[[3,2,2,1,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                                         => 1
[[3,2,1,1,1,1,0,0,0],[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[2,2,2,2,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                                         => 1
[[2,2,2,1,1,1,0,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[2,2,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[2,1,1,1,1,1,1,1,0],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                                         => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                  => 1
[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[7,1,1,1,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[6,3,1,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[6,2,1,1,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,3,1,1,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,4,1,1,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,3,2,1,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[3,3,3,1,0,0,0,0,0,0],[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[3,3,2,2,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[3,3,1,1,1,1,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[3,2,1,1,1,1,1,0,0,0],[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[3,1,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[2,2,2,2,1,1,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[2,2,2,1,1,1,1,0,0,0],[2,2,2,1,1,1,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]                                                   => 1
[[1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[8,2,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[8,1,1,0,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                   => 1
[[7,3,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[7,2,1,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                   => 1
[[7,1,1,1,0,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[6,3,1,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[6,2,2,0,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[6,2,1,1,0,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                   => 1
[[6,1,1,1,1,0,0,0,0,0],[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[5,4,1,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,3,2,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[5,3,1,1,0,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                   => 1
[[5,2,2,1,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                   => 1
[[5,2,1,1,1,0,0,0,0,0],[4,2,1,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[5,1,1,1,1,1,0,0,0,0],[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[4,4,2,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[4,4,1,1,0,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                   => 1
[[4,3,3,0,0,0,0,0,0,0],[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]                                                   => 1
[[4,3,2,1,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                   => 1
[[4,3,1,1,1,0,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[4,2,2,2,0,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[4,2,2,1,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                   => 1
[[4,2,1,1,1,1,0,0,0,0],[3,2,1,1,1,1,0,0,0],[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[4,1,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[3,3,3,1,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]                                                   => 1
[[3,3,2,2,0,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]                                                   => 1
[[3,3,2,1,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                   => 1
[[3,3,1,1,1,1,0,0,0,0],[3,2,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[3,2,2,2,1,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]                                                   => 1
[[3,2,2,1,1,1,0,0,0,0],[2,2,2,1,1,1,0,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[3,2,1,1,1,1,1,0,0,0],[2,2,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[3,1,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,1,0],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[2,2,2,2,1,1,0,0,0,0],[2,2,2,1,1,1,0,0,0],[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]                                                   => 1
[[2,2,2,1,1,1,1,0,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[2,2,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[2,1,1,1,1,1,1,1,1,0],[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]                                                   => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 1
[[0,0],[0]]                                                                                                                                                                           => 0
[[0,0,0],[0,0],[0]]                                                                                                                                                                   => 0
[[3,3,2],[3,2],[2]]                                                                                                                                                                   => 2
[[3,3,2],[3,2],[3]]                                                                                                                                                                   => 3
[[3,3,2],[3,3],[3]]                                                                                                                                                                   => 3
[[3,3,3],[3,3],[3]]                                                                                                                                                                   => 3
[[0,0,0,0],[0,0,0],[0,0],[0]]                                                                                                                                                         => 0
[[2,2,2,0],[2,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[2,2,2,1],[2,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[2,2,2,1],[2,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[2,2,2,1],[2,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[2,2,2,1],[2,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[2,2,2,2],[2,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,1,0],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,1,0],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,1,0],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,2,1,1],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,2,1,1],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,1],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[2,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,1],[2,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[2,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[3,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,2,1,1],[3,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,1],[3,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[3,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,1,1],[3,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[3,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,1,1],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,1,1],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[3,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,1,1],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,1,1],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,1,1],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,2,2,0],[2,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,2,0],[2,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[2,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[2,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[2,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[2,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[2,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[2,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[2,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[2,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,2,2,0],[3,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[3,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[3,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,2,2,0],[3,2,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[3,2,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,2,2,0],[3,2,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[3,2,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,2,0],[3,2,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,2,2,0],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,2,0],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,2,0],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,2,2,0],[3,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,2,0],[3,2,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,2,2,1],[2,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,2,1],[2,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[2,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[2,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,2,2,1],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[3,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,2,2,1],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,2,2,1],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,2,2,1],[3,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[3,2,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,2,1],[3,2,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,2,2,2],[2,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,2],[3,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,2,2,2],[3,2,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,2,2,2],[3,2,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,3,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,0,0],[3,3,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,3,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,3,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,3,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,0,0],[3,3,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,3,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,3,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,0,0],[3,3,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,0,0],[3,3,0],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,1,0],[1,0],[0]]                                                                                                                                                         => 0
[[3,3,1,0],[3,1,0],[1,0],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,0],[1,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,3,1,0],[3,1,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,1,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,1,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,1,0],[3,1,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,1,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,1,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,1,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,3,1,0],[3,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,1,0],[3,2,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,2,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,2,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,2,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,2,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,3,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,1,0],[3,3,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,3,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,3,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,3,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,3,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,3,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,3,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,3,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,3,0],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,3,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,0],[3,3,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,3,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,3,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,1,0],[3,3,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,1,0],[3,3,1],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,1,1],[3,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[3,3,1,1],[3,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,1,1],[3,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,1,1],[3,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,1],[3,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,1],[3,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,1],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,1,1],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,1,1],[3,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,1,1],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,1],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,1],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,1],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,1,1],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,1,1],[3,3,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,1,1],[3,3,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,1,1],[3,3,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,1,1],[3,3,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,1,1],[3,3,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,1,1],[3,3,1],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,2,0],[2,0],[0]]                                                                                                                                                         => 0
[[3,3,2,0],[3,2,0],[2,0],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,2,0],[2,0],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,0],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,2,0],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,0],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,2,0],[3,2,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,2,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,2,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,2,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,2,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,2,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,2,0],[3,3,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,3,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,3,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,3,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,3,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,3,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,0],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,2,0],[3,3,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,3,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,3,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,1],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,0],[3,3,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,0],[3,3,2],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,2,1],[3,2,1],[2,1],[1]]                                                                                                                                                         => 1
[[3,3,2,1],[3,2,1],[2,1],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,2,1],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,2,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,2,1],[3,2,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,2,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,2,1],[3,2,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,2,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,1],[3,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,2,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,2,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,1],[3,3,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,2,1],[3,3,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,3,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,2,1],[3,3,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,3,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,1],[3,3,1],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,2,1],[3,3,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,1],[3,3,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,1],[3,3,2],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,2,2],[3,2,2],[2,2],[2]]                                                                                                                                                         => 2
[[3,3,2,2],[3,2,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,2],[3,2,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,2],[3,3,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,2,2],[3,3,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,2,2],[3,3,2],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,0],[3,0],[0]]                                                                                                                                                         => 0
[[3,3,3,0],[3,3,0],[3,0],[1]]                                                                                                                                                         => 1
[[3,3,3,0],[3,3,0],[3,0],[2]]                                                                                                                                                         => 2
[[3,3,3,0],[3,3,0],[3,0],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,0],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,3,0],[3,3,0],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,3,0],[3,3,0],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,0],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,3,0],[3,3,0],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,0],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,3,0],[3,3,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,3,0],[3,3,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,3,0],[3,3,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,1],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,3,0],[3,3,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,2],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,0],[3,3,3],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,1],[3,3,1],[3,1],[1]]                                                                                                                                                         => 1
[[3,3,3,1],[3,3,1],[3,1],[2]]                                                                                                                                                         => 2
[[3,3,3,1],[3,3,1],[3,1],[3]]                                                                                                                                                         => 3
[[3,3,3,1],[3,3,1],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,3,1],[3,3,1],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,3,1],[3,3,1],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,1],[3,3,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,3,1],[3,3,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,3,1],[3,3,2],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,1],[3,3,3],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,2],[3,3,2],[3,2],[2]]                                                                                                                                                         => 2
[[3,3,3,2],[3,3,2],[3,2],[3]]                                                                                                                                                         => 3
[[3,3,3,2],[3,3,2],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,2],[3,3,3],[3,3],[3]]                                                                                                                                                         => 3
[[3,3,3,3],[3,3,3],[3,3],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[4,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[4,1,1],[4,1],[1]]                                                                                                                                                         => 1
[[4,1,1,0],[4,1,1],[4,1],[2]]                                                                                                                                                         => 2
[[4,1,1,0],[4,1,1],[4,1],[3]]                                                                                                                                                         => 3
[[4,1,1,0],[4,1,1],[4,1],[4]]                                                                                                                                                         => 4
[[4,1,1,1],[1,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[2,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[2,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[2,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,1],[3,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[3,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[3,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,1],[3,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[3,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[4,1,1,1],[3,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[4,1,1,1],[4,1,1],[1,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[4,1,1],[2,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[4,1,1],[2,1],[2]]                                                                                                                                                         => 2
[[4,1,1,1],[4,1,1],[3,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[4,1,1],[3,1],[2]]                                                                                                                                                         => 2
[[4,1,1,1],[4,1,1],[3,1],[3]]                                                                                                                                                         => 3
[[4,1,1,1],[4,1,1],[4,1],[1]]                                                                                                                                                         => 1
[[4,1,1,1],[4,1,1],[4,1],[2]]                                                                                                                                                         => 2
[[4,1,1,1],[4,1,1],[4,1],[3]]                                                                                                                                                         => 3
[[4,1,1,1],[4,1,1],[4,1],[4]]                                                                                                                                                         => 4

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Created: Jun 17, 2013 at 11:21 by Jessica Striker

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Last Updated: Feb 23, 2021 at 08:39 by Martin Rubey