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*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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*    This information is distributed in the hope that it will be useful,    *
*    but WITHOUT ANY WARRANTY; without even the implied warranty of         *
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*****************************************************************************

-----------------------------------------------------------------------------
Statistic identifier: St001921

-----------------------------------------------------------------------------
Collection: Plane partitions

-----------------------------------------------------------------------------
Description: The number of boxes that can be added such that the result is a plane partition.

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

-----------------------------------------------------------------------------
Code:
def statistic(p):
    c = 0
    for i, row in enumerate(list(p) + [(0,)]):
        for j, entry in enumerate(row + (0,)):
            h = None if not j else row[j-1]
            v = None if not i or len(p[i-1]) == j else p[i-1][j]
            if (h is None or entry < h) and (v is None or entry < v):
                c += 1
    return c


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

[[1]]                                     => 3
[[1],[1]]                                 => 4
[[2]]                                     => 3
[[1,1]]                                   => 3
[[1],[1],[1]]                             => 5
[[2],[1]]                                 => 5
[[1,1],[1]]                               => 4
[[3]]                                     => 3
[[2,1]]                                   => 4
[[1,1,1]]                                 => 3
[[1],[1],[1],[1]]                         => 6
[[2],[1],[1]]                             => 6
[[2],[2]]                                 => 4
[[1,1],[1],[1]]                           => 5
[[1,1],[1,1]]                             => 4
[[3],[1]]                                 => 5
[[2,1],[1]]                               => 6
[[1,1,1],[1]]                             => 4
[[4]]                                     => 3
[[3,1]]                                   => 4
[[2,2]]                                   => 3
[[2,1,1]]                                 => 4
[[1,1,1,1]]                               => 3
[[1],[1],[1],[1],[1]]                     => 7
[[2],[1],[1],[1]]                         => 7
[[2],[2],[1]]                             => 6
[[1,1],[1],[1],[1]]                       => 6
[[1,1],[1,1],[1]]                         => 5
[[3],[1],[1]]                             => 6
[[3],[2]]                                 => 5
[[2,1],[1],[1]]                           => 7
[[2,1],[2]]                               => 5
[[2,1],[1,1]]                             => 6
[[1,1,1],[1],[1]]                         => 5
[[1,1,1],[1,1]]                           => 4
[[4],[1]]                                 => 5
[[3,1],[1]]                               => 6
[[2,2],[1]]                               => 5
[[2,1,1],[1]]                             => 6
[[1,1,1,1],[1]]                           => 4
[[5]]                                     => 3
[[4,1]]                                   => 4
[[3,2]]                                   => 4
[[3,1,1]]                                 => 4
[[2,2,1]]                                 => 4
[[2,1,1,1]]                               => 4
[[1,1,1,1,1]]                             => 3
[[1],[1],[1],[1],[1],[1]]                 => 8
[[2],[1],[1],[1],[1]]                     => 8
[[2],[2],[1],[1]]                         => 7
[[2],[2],[2]]                             => 5
[[1,1],[1],[1],[1],[1]]                   => 7
[[1,1],[1,1],[1],[1]]                     => 6
[[1,1],[1,1],[1,1]]                       => 5
[[3],[1],[1],[1]]                         => 7
[[3],[2],[1]]                             => 7
[[3],[3]]                                 => 4
[[2,1],[1],[1],[1]]                       => 8
[[2,1],[2],[1]]                           => 7
[[2,1],[1,1],[1]]                         => 7
[[2,1],[2,1]]                             => 5
[[1,1,1],[1],[1],[1]]                     => 6
[[1,1,1],[1,1],[1]]                       => 5
[[1,1,1],[1,1,1]]                         => 4
[[4],[1],[1]]                             => 6
[[4],[2]]                                 => 5
[[3,1],[1],[1]]                           => 7
[[3,1],[2]]                               => 6
[[3,1],[1,1]]                             => 6
[[2,2],[1],[1]]                           => 6
[[2,2],[2]]                               => 4
[[2,2],[1,1]]                             => 5
[[2,1,1],[1],[1]]                         => 7
[[2,1,1],[2]]                             => 5
[[2,1,1],[1,1]]                           => 6
[[1,1,1,1],[1],[1]]                       => 5
[[1,1,1,1],[1,1]]                         => 4
[[5],[1]]                                 => 5
[[4,1],[1]]                               => 6
[[3,2],[1]]                               => 6
[[3,1,1],[1]]                             => 6
[[2,2,1],[1]]                             => 6
[[2,1,1,1],[1]]                           => 6
[[1,1,1,1,1],[1]]                         => 4
[[6]]                                     => 3
[[5,1]]                                   => 4
[[4,2]]                                   => 4
[[4,1,1]]                                 => 4
[[3,3]]                                   => 3
[[3,2,1]]                                 => 5
[[3,1,1,1]]                               => 4
[[2,2,2]]                                 => 3
[[2,2,1,1]]                               => 4
[[2,1,1,1,1]]                             => 4
[[1,1,1,1,1,1]]                           => 3
[[1],[1],[1],[1],[1],[1],[1]]             => 9
[[2],[1],[1],[1],[1],[1]]                 => 9
[[2],[2],[1],[1],[1]]                     => 8
[[2],[2],[2],[1]]                         => 7
[[1,1],[1],[1],[1],[1],[1]]               => 8
[[1,1],[1,1],[1],[1],[1]]                 => 7
[[1,1],[1,1],[1,1],[1]]                   => 6
[[3],[1],[1],[1],[1]]                     => 8
[[3],[2],[1],[1]]                         => 8
[[3],[2],[2]]                             => 6
[[3],[3],[1]]                             => 6
[[2,1],[1],[1],[1],[1]]                   => 9
[[2,1],[2],[1],[1]]                       => 8
[[2,1],[2],[2]]                           => 6
[[2,1],[1,1],[1],[1]]                     => 8
[[2,1],[1,1],[1,1]]                       => 7
[[2,1],[2,1],[1]]                         => 7
[[1,1,1],[1],[1],[1],[1]]                 => 7
[[1,1,1],[1,1],[1],[1]]                   => 6
[[1,1,1],[1,1],[1,1]]                     => 5
[[1,1,1],[1,1,1],[1]]                     => 5
[[4],[1],[1],[1]]                         => 7
[[4],[2],[1]]                             => 7
[[4],[3]]                                 => 5
[[3,1],[1],[1],[1]]                       => 8
[[3,1],[2],[1]]                           => 8
[[3,1],[1,1],[1]]                         => 7
[[3,1],[3]]                               => 5
[[3,1],[2,1]]                             => 6
[[2,2],[1],[1],[1]]                       => 7
[[2,2],[2],[1]]                           => 6
[[2,2],[1,1],[1]]                         => 6
[[2,2],[2,1]]                             => 5
[[2,1,1],[1],[1],[1]]                     => 8
[[2,1,1],[2],[1]]                         => 7
[[2,1,1],[1,1],[1]]                       => 7
[[2,1,1],[2,1]]                           => 5
[[2,1,1],[1,1,1]]                         => 6
[[1,1,1,1],[1],[1],[1]]                   => 6
[[1,1,1,1],[1,1],[1]]                     => 5
[[1,1,1,1],[1,1,1]]                       => 4
[[5],[1],[1]]                             => 6
[[5],[2]]                                 => 5
[[4,1],[1],[1]]                           => 7
[[4,1],[2]]                               => 6
[[4,1],[1,1]]                             => 6
[[3,2],[1],[1]]                           => 7
[[3,2],[2]]                               => 6
[[3,2],[1,1]]                             => 6
[[3,1,1],[1],[1]]                         => 7
[[3,1,1],[2]]                             => 6
[[3,1,1],[1,1]]                           => 6
[[2,2,1],[1],[1]]                         => 7
[[2,2,1],[2]]                             => 5
[[2,2,1],[1,1]]                           => 6
[[2,1,1,1],[1],[1]]                       => 7
[[2,1,1,1],[2]]                           => 5
[[2,1,1,1],[1,1]]                         => 6
[[1,1,1,1,1],[1],[1]]                     => 5
[[1,1,1,1,1],[1,1]]                       => 4
[[6],[1]]                                 => 5
[[5,1],[1]]                               => 6
[[4,2],[1]]                               => 6
[[4,1,1],[1]]                             => 6
[[3,3],[1]]                               => 5
[[3,2,1],[1]]                             => 7
[[3,1,1,1],[1]]                           => 6
[[2,2,2],[1]]                             => 5
[[2,2,1,1],[1]]                           => 6
[[2,1,1,1,1],[1]]                         => 6
[[1,1,1,1,1,1],[1]]                       => 4
[[7]]                                     => 3
[[6,1]]                                   => 4
[[5,2]]                                   => 4
[[5,1,1]]                                 => 4
[[4,3]]                                   => 4
[[4,2,1]]                                 => 5
[[4,1,1,1]]                               => 4
[[3,3,1]]                                 => 4
[[3,2,2]]                                 => 4
[[3,2,1,1]]                               => 5
[[3,1,1,1,1]]                             => 4
[[2,2,2,1]]                               => 4
[[2,2,1,1,1]]                             => 4
[[2,1,1,1,1,1]]                           => 4
[[1,1,1,1,1,1,1]]                         => 3
[[1],[1],[1],[1],[1],[1],[1],[1]]         => 10
[[2],[1],[1],[1],[1],[1],[1]]             => 10
[[2],[2],[1],[1],[1],[1]]                 => 9
[[2],[2],[2],[1],[1]]                     => 8
[[2],[2],[2],[2]]                         => 6
[[1,1],[1],[1],[1],[1],[1],[1]]           => 9
[[1,1],[1,1],[1],[1],[1],[1]]             => 8
[[1,1],[1,1],[1,1],[1],[1]]               => 7
[[1,1],[1,1],[1,1],[1,1]]                 => 6
[[3],[1],[1],[1],[1],[1]]                 => 9
[[3],[2],[1],[1],[1]]                     => 9
[[3],[2],[2],[1]]                         => 8
[[3],[3],[1],[1]]                         => 7
[[3],[3],[2]]                             => 6
[[2,1],[1],[1],[1],[1],[1]]               => 10
[[2,1],[2],[1],[1],[1]]                   => 9
[[2,1],[2],[2],[1]]                       => 8
[[2,1],[1,1],[1],[1],[1]]                 => 9
[[2,1],[1,1],[1,1],[1]]                   => 8
[[2,1],[2,1],[1],[1]]                     => 8
[[2,1],[2,1],[2]]                         => 6
[[2,1],[2,1],[1,1]]                       => 7
[[1,1,1],[1],[1],[1],[1],[1]]             => 8
[[1,1,1],[1,1],[1],[1],[1]]               => 7
[[1,1,1],[1,1],[1,1],[1]]                 => 6
[[1,1,1],[1,1,1],[1],[1]]                 => 6
[[1,1,1],[1,1,1],[1,1]]                   => 5
[[4],[1],[1],[1],[1]]                     => 8
[[4],[2],[1],[1]]                         => 8
[[4],[2],[2]]                             => 6
[[4],[3],[1]]                             => 7
[[4],[4]]                                 => 4
[[3,1],[1],[1],[1],[1]]                   => 9
[[3,1],[2],[1],[1]]                       => 9
[[3,1],[2],[2]]                           => 7
[[3,1],[1,1],[1],[1]]                     => 8
[[3,1],[1,1],[1,1]]                       => 7
[[3,1],[3],[1]]                           => 7
[[3,1],[2,1],[1]]                         => 8
[[3,1],[3,1]]                             => 5
[[2,2],[1],[1],[1],[1]]                   => 8
[[2,2],[2],[1],[1]]                       => 7
[[2,2],[2],[2]]                           => 5
[[2,2],[1,1],[1],[1]]                     => 7
[[2,2],[1,1],[1,1]]                       => 6
[[2,2],[2,1],[1]]                         => 7
[[2,2],[2,2]]                             => 4
[[2,1,1],[1],[1],[1],[1]]                 => 9
[[2,1,1],[2],[1],[1]]                     => 8
[[2,1,1],[2],[2]]                         => 6
[[2,1,1],[1,1],[1],[1]]                   => 8
[[2,1,1],[1,1],[1,1]]                     => 7
[[2,1,1],[2,1],[1]]                       => 7
[[2,1,1],[1,1,1],[1]]                     => 7
[[2,1,1],[2,1,1]]                         => 5
[[1,1,1,1],[1],[1],[1],[1]]               => 7
[[1,1,1,1],[1,1],[1],[1]]                 => 6
[[1,1,1,1],[1,1],[1,1]]                   => 5
[[1,1,1,1],[1,1,1],[1]]                   => 5
[[1,1,1,1],[1,1,1,1]]                     => 4
[[5],[1],[1],[1]]                         => 7
[[5],[2],[1]]                             => 7
[[5],[3]]                                 => 5
[[4,1],[1],[1],[1]]                       => 8
[[4,1],[2],[1]]                           => 8
[[4,1],[1,1],[1]]                         => 7
[[4,1],[3]]                               => 6
[[4,1],[2,1]]                             => 6
[[3,2],[1],[1],[1]]                       => 8
[[3,2],[2],[1]]                           => 8
[[3,2],[1,1],[1]]                         => 7
[[3,2],[3]]                               => 5
[[3,2],[2,1]]                             => 7
[[3,1,1],[1],[1],[1]]                     => 8
[[3,1,1],[2],[1]]                         => 8
[[3,1,1],[1,1],[1]]                       => 7
[[3,1,1],[3]]                             => 5
[[3,1,1],[2,1]]                           => 6
[[3,1,1],[1,1,1]]                         => 6
[[2,2,1],[1],[1],[1]]                     => 8
[[2,2,1],[2],[1]]                         => 7
[[2,2,1],[1,1],[1]]                       => 7
[[2,2,1],[2,1]]                           => 6
[[2,2,1],[1,1,1]]                         => 6
[[2,1,1,1],[1],[1],[1]]                   => 8
[[2,1,1,1],[2],[1]]                       => 7
[[2,1,1,1],[1,1],[1]]                     => 7
[[2,1,1,1],[2,1]]                         => 5
[[2,1,1,1],[1,1,1]]                       => 6
[[1,1,1,1,1],[1],[1],[1]]                 => 6
[[1,1,1,1,1],[1,1],[1]]                   => 5
[[1,1,1,1,1],[1,1,1]]                     => 4
[[6],[1],[1]]                             => 6
[[6],[2]]                                 => 5
[[5,1],[1],[1]]                           => 7
[[5,1],[2]]                               => 6
[[5,1],[1,1]]                             => 6
[[4,2],[1],[1]]                           => 7
[[4,2],[2]]                               => 6
[[4,2],[1,1]]                             => 6
[[4,1,1],[1],[1]]                         => 7
[[4,1,1],[2]]                             => 6
[[4,1,1],[1,1]]                           => 6
[[3,3],[1],[1]]                           => 6
[[3,3],[2]]                               => 5
[[3,3],[1,1]]                             => 5
[[3,2,1],[1],[1]]                         => 8
[[3,2,1],[2]]                             => 7
[[3,2,1],[1,1]]                           => 7
[[3,1,1,1],[1],[1]]                       => 7
[[3,1,1,1],[2]]                           => 6
[[3,1,1,1],[1,1]]                         => 6
[[2,2,2],[1],[1]]                         => 6
[[2,2,2],[2]]                             => 4
[[2,2,2],[1,1]]                           => 5
[[2,2,1,1],[1],[1]]                       => 7
[[2,2,1,1],[2]]                           => 5
[[2,2,1,1],[1,1]]                         => 6
[[2,1,1,1,1],[1],[1]]                     => 7
[[2,1,1,1,1],[2]]                         => 5
[[2,1,1,1,1],[1,1]]                       => 6
[[1,1,1,1,1,1],[1],[1]]                   => 5
[[1,1,1,1,1,1],[1,1]]                     => 4
[[7],[1]]                                 => 5
[[6,1],[1]]                               => 6
[[5,2],[1]]                               => 6
[[5,1,1],[1]]                             => 6
[[4,3],[1]]                               => 6
[[4,2,1],[1]]                             => 7
[[4,1,1,1],[1]]                           => 6
[[3,3,1],[1]]                             => 6
[[3,2,2],[1]]                             => 6
[[3,2,1,1],[1]]                           => 7
[[3,1,1,1,1],[1]]                         => 6
[[2,2,2,1],[1]]                           => 6
[[2,2,1,1,1],[1]]                         => 6
[[2,1,1,1,1,1],[1]]                       => 6
[[1,1,1,1,1,1,1],[1]]                     => 4
[[8]]                                     => 3
[[7,1]]                                   => 4
[[6,2]]                                   => 4
[[6,1,1]]                                 => 4
[[5,3]]                                   => 4
[[5,2,1]]                                 => 5
[[5,1,1,1]]                               => 4
[[4,4]]                                   => 3
[[4,3,1]]                                 => 5
[[4,2,2]]                                 => 4
[[4,2,1,1]]                               => 5
[[4,1,1,1,1]]                             => 4
[[3,3,2]]                                 => 4
[[3,3,1,1]]                               => 4
[[3,2,2,1]]                               => 5
[[3,2,1,1,1]]                             => 5
[[3,1,1,1,1,1]]                           => 4
[[2,2,2,2]]                               => 3
[[2,2,2,1,1]]                             => 4
[[2,2,1,1,1,1]]                           => 4
[[2,1,1,1,1,1,1]]                         => 4
[[1,1,1,1,1,1,1,1]]                       => 3
[[1],[1],[1],[1],[1],[1],[1],[1],[1]]     => 11
[[2],[1],[1],[1],[1],[1],[1],[1]]         => 11
[[2],[2],[1],[1],[1],[1],[1]]             => 10
[[2],[2],[2],[1],[1],[1]]                 => 9
[[2],[2],[2],[2],[1]]                     => 8
[[1,1],[1],[1],[1],[1],[1],[1],[1]]       => 10
[[1,1],[1,1],[1],[1],[1],[1],[1]]         => 9
[[1,1],[1,1],[1,1],[1],[1],[1]]           => 8
[[1,1],[1,1],[1,1],[1,1],[1]]             => 7
[[3],[1],[1],[1],[1],[1],[1]]             => 10
[[3],[2],[1],[1],[1],[1]]                 => 10
[[3],[2],[2],[1],[1]]                     => 9
[[3],[2],[2],[2]]                         => 7
[[3],[3],[1],[1],[1]]                     => 8
[[3],[3],[2],[1]]                         => 8
[[3],[3],[3]]                             => 5
[[2,1],[1],[1],[1],[1],[1],[1]]           => 11
[[2,1],[2],[1],[1],[1],[1]]               => 10
[[2,1],[2],[2],[1],[1]]                   => 9
[[2,1],[2],[2],[2]]                       => 7
[[2,1],[1,1],[1],[1],[1],[1]]             => 10
[[2,1],[1,1],[1,1],[1],[1]]               => 9
[[2,1],[1,1],[1,1],[1,1]]                 => 8
[[2,1],[2,1],[1],[1],[1]]                 => 9
[[2,1],[2,1],[2],[1]]                     => 8
[[2,1],[2,1],[1,1],[1]]                   => 8
[[2,1],[2,1],[2,1]]                       => 6
[[1,1,1],[1],[1],[1],[1],[1],[1]]         => 9
[[1,1,1],[1,1],[1],[1],[1],[1]]           => 8
[[1,1,1],[1,1],[1,1],[1],[1]]             => 7
[[1,1,1],[1,1],[1,1],[1,1]]               => 6
[[1,1,1],[1,1,1],[1],[1],[1]]             => 7
[[1,1,1],[1,1,1],[1,1],[1]]               => 6
[[1,1,1],[1,1,1],[1,1,1]]                 => 5
[[4],[1],[1],[1],[1],[1]]                 => 9
[[4],[2],[1],[1],[1]]                     => 9
[[4],[2],[2],[1]]                         => 8
[[4],[3],[1],[1]]                         => 8
[[4],[3],[2]]                             => 7
[[4],[4],[1]]                             => 6
[[3,1],[1],[1],[1],[1],[1]]               => 10
[[3,1],[2],[1],[1],[1]]                   => 10
[[3,1],[2],[2],[1]]                       => 9
[[3,1],[1,1],[1],[1],[1]]                 => 9
[[3,1],[1,1],[1,1],[1]]                   => 8
[[3,1],[3],[1],[1]]                       => 8
[[3,1],[3],[2]]                           => 7
[[3,1],[2,1],[1],[1]]                     => 9
[[3,1],[2,1],[2]]                         => 7
[[3,1],[2,1],[1,1]]                       => 8
[[3,1],[3,1],[1]]                         => 7
[[2,2],[1],[1],[1],[1],[1]]               => 9
[[2,2],[2],[1],[1],[1]]                   => 8
[[2,2],[2],[2],[1]]                       => 7
[[2,2],[1,1],[1],[1],[1]]                 => 8
[[2,2],[1,1],[1,1],[1]]                   => 7
[[2,2],[2,1],[1],[1]]                     => 8
[[2,2],[2,1],[2]]                         => 6
[[2,2],[2,1],[1,1]]                       => 7
[[2,2],[2,2],[1]]                         => 6
[[2,1,1],[1],[1],[1],[1],[1]]             => 10
[[2,1,1],[2],[1],[1],[1]]                 => 9
[[2,1,1],[2],[2],[1]]                     => 8
[[2,1,1],[1,1],[1],[1],[1]]               => 9
[[2,1,1],[1,1],[1,1],[1]]                 => 8
[[2,1,1],[2,1],[1],[1]]                   => 8
[[2,1,1],[2,1],[2]]                       => 6
[[2,1,1],[2,1],[1,1]]                     => 7
[[2,1,1],[1,1,1],[1],[1]]                 => 8
[[2,1,1],[1,1,1],[1,1]]                   => 7
[[2,1,1],[2,1,1],[1]]                     => 7
[[1,1,1,1],[1],[1],[1],[1],[1]]           => 8
[[1,1,1,1],[1,1],[1],[1],[1]]             => 7
[[1,1,1,1],[1,1],[1,1],[1]]               => 6
[[1,1,1,1],[1,1,1],[1],[1]]               => 6
[[1,1,1,1],[1,1,1],[1,1]]                 => 5
[[1,1,1,1],[1,1,1,1],[1]]                 => 5
[[5],[1],[1],[1],[1]]                     => 8
[[5],[2],[1],[1]]                         => 8
[[5],[2],[2]]                             => 6
[[5],[3],[1]]                             => 7
[[5],[4]]                                 => 5
[[4,1],[1],[1],[1],[1]]                   => 9
[[4,1],[2],[1],[1]]                       => 9
[[4,1],[2],[2]]                           => 7
[[4,1],[1,1],[1],[1]]                     => 8
[[4,1],[1,1],[1,1]]                       => 7
[[4,1],[3],[1]]                           => 8
[[4,1],[2,1],[1]]                         => 8
[[4,1],[4]]                               => 5
[[4,1],[3,1]]                             => 6
[[3,2],[1],[1],[1],[1]]                   => 9
[[3,2],[2],[1],[1]]                       => 9
[[3,2],[2],[2]]                           => 7
[[3,2],[1,1],[1],[1]]                     => 8
[[3,2],[1,1],[1,1]]                       => 7
[[3,2],[3],[1]]                           => 7
[[3,2],[2,1],[1]]                         => 9
[[3,2],[3,1]]                             => 6
[[3,2],[2,2]]                             => 6
[[3,1,1],[1],[1],[1],[1]]                 => 9
[[3,1,1],[2],[1],[1]]                     => 9
[[3,1,1],[2],[2]]                         => 7
[[3,1,1],[1,1],[1],[1]]                   => 8
[[3,1,1],[1,1],[1,1]]                     => 7
[[3,1,1],[3],[1]]                         => 7
[[3,1,1],[2,1],[1]]                       => 8
[[3,1,1],[1,1,1],[1]]                     => 7
[[3,1,1],[3,1]]                           => 5
[[3,1,1],[2,1,1]]                         => 6
[[2,2,1],[1],[1],[1],[1]]                 => 9
[[2,2,1],[2],[1],[1]]                     => 8
[[2,2,1],[2],[2]]                         => 6
[[2,2,1],[1,1],[1],[1]]                   => 8
[[2,2,1],[1,1],[1,1]]                     => 7
[[2,2,1],[2,1],[1]]                       => 8
[[2,2,1],[1,1,1],[1]]                     => 7
[[2,2,1],[2,2]]                           => 5
[[2,2,1],[2,1,1]]                         => 6
[[2,1,1,1],[1],[1],[1],[1]]               => 9
[[2,1,1,1],[2],[1],[1]]                   => 8
[[2,1,1,1],[2],[2]]                       => 6
[[2,1,1,1],[1,1],[1],[1]]                 => 8
[[2,1,1,1],[1,1],[1,1]]                   => 7
[[2,1,1,1],[2,1],[1]]                     => 7
[[2,1,1,1],[1,1,1],[1]]                   => 7
[[2,1,1,1],[2,1,1]]                       => 5
[[2,1,1,1],[1,1,1,1]]                     => 6
[[1,1,1,1,1],[1],[1],[1],[1]]             => 7
[[1,1,1,1,1],[1,1],[1],[1]]               => 6
[[1,1,1,1,1],[1,1],[1,1]]                 => 5
[[1,1,1,1,1],[1,1,1],[1]]                 => 5
[[1,1,1,1,1],[1,1,1,1]]                   => 4
[[6],[1],[1],[1]]                         => 7
[[6],[2],[1]]                             => 7
[[6],[3]]                                 => 5
[[5,1],[1],[1],[1]]                       => 8
[[5,1],[2],[1]]                           => 8
[[5,1],[1,1],[1]]                         => 7
[[5,1],[3]]                               => 6
[[5,1],[2,1]]                             => 6
[[4,2],[1],[1],[1]]                       => 8
[[4,2],[2],[1]]                           => 8
[[4,2],[1,1],[1]]                         => 7
[[4,2],[3]]                               => 6
[[4,2],[2,1]]                             => 7
[[4,1,1],[1],[1],[1]]                     => 8
[[4,1,1],[2],[1]]                         => 8
[[4,1,1],[1,1],[1]]                       => 7
[[4,1,1],[3]]                             => 6
[[4,1,1],[2,1]]                           => 6
[[4,1,1],[1,1,1]]                         => 6
[[3,3],[1],[1],[1]]                       => 7
[[3,3],[2],[1]]                           => 7
[[3,3],[1,1],[1]]                         => 6
[[3,3],[3]]                               => 4
[[3,3],[2,1]]                             => 6
[[3,2,1],[1],[1],[1]]                     => 9
[[3,2,1],[2],[1]]                         => 9
[[3,2,1],[1,1],[1]]                       => 8
[[3,2,1],[3]]                             => 6
[[3,2,1],[2,1]]                           => 8
[[3,2,1],[1,1,1]]                         => 7
[[3,1,1,1],[1],[1],[1]]                   => 8
[[3,1,1,1],[2],[1]]                       => 8
[[3,1,1,1],[1,1],[1]]                     => 7
[[3,1,1,1],[3]]                           => 5
[[3,1,1,1],[2,1]]                         => 6
[[3,1,1,1],[1,1,1]]                       => 6
[[2,2,2],[1],[1],[1]]                     => 7
[[2,2,2],[2],[1]]                         => 6
[[2,2,2],[1,1],[1]]                       => 6
[[2,2,2],[2,1]]                           => 5
[[2,2,2],[1,1,1]]                         => 5
[[2,2,1,1],[1],[1],[1]]                   => 8
[[2,2,1,1],[2],[1]]                       => 7
[[2,2,1,1],[1,1],[1]]                     => 7
[[2,2,1,1],[2,1]]                         => 6
[[2,2,1,1],[1,1,1]]                       => 6
[[2,1,1,1,1],[1],[1],[1]]                 => 8
[[2,1,1,1,1],[2],[1]]                     => 7
[[2,1,1,1,1],[1,1],[1]]                   => 7
[[2,1,1,1,1],[2,1]]                       => 5
[[2,1,1,1,1],[1,1,1]]                     => 6
[[1,1,1,1,1,1],[1],[1],[1]]               => 6
[[1,1,1,1,1,1],[1,1],[1]]                 => 5
[[1,1,1,1,1,1],[1,1,1]]                   => 4
[[7],[1],[1]]                             => 6
[[7],[2]]                                 => 5
[[6,1],[1],[1]]                           => 7
[[6,1],[2]]                               => 6
[[6,1],[1,1]]                             => 6
[[5,2],[1],[1]]                           => 7
[[5,2],[2]]                               => 6
[[5,2],[1,1]]                             => 6
[[5,1,1],[1],[1]]                         => 7
[[5,1,1],[2]]                             => 6
[[5,1,1],[1,1]]                           => 6
[[4,3],[1],[1]]                           => 7
[[4,3],[2]]                               => 6
[[4,3],[1,1]]                             => 6
[[4,2,1],[1],[1]]                         => 8
[[4,2,1],[2]]                             => 7
[[4,2,1],[1,1]]                           => 7
[[4,1,1,1],[1],[1]]                       => 7
[[4,1,1,1],[2]]                           => 6
[[4,1,1,1],[1,1]]                         => 6
[[3,3,1],[1],[1]]                         => 7
[[3,3,1],[2]]                             => 6
[[3,3,1],[1,1]]                           => 6
[[3,2,2],[1],[1]]                         => 7
[[3,2,2],[2]]                             => 6
[[3,2,2],[1,1]]                           => 6
[[3,2,1,1],[1],[1]]                       => 8
[[3,2,1,1],[2]]                           => 7
[[3,2,1,1],[1,1]]                         => 7
[[3,1,1,1,1],[1],[1]]                     => 7
[[3,1,1,1,1],[2]]                         => 6
[[3,1,1,1,1],[1,1]]                       => 6
[[2,2,2,1],[1],[1]]                       => 7
[[2,2,2,1],[2]]                           => 5
[[2,2,2,1],[1,1]]                         => 6
[[2,2,1,1,1],[1],[1]]                     => 7
[[2,2,1,1,1],[2]]                         => 5
[[2,2,1,1,1],[1,1]]                       => 6
[[2,1,1,1,1,1],[1],[1]]                   => 7
[[2,1,1,1,1,1],[2]]                       => 5
[[2,1,1,1,1,1],[1,1]]                     => 6
[[1,1,1,1,1,1,1],[1],[1]]                 => 5
[[1,1,1,1,1,1,1],[1,1]]                   => 4
[[8],[1]]                                 => 5
[[7,1],[1]]                               => 6
[[6,2],[1]]                               => 6
[[6,1,1],[1]]                             => 6
[[5,3],[1]]                               => 6
[[5,2,1],[1]]                             => 7
[[5,1,1,1],[1]]                           => 6
[[4,4],[1]]                               => 5
[[4,3,1],[1]]                             => 7
[[4,2,2],[1]]                             => 6
[[4,2,1,1],[1]]                           => 7
[[4,1,1,1,1],[1]]                         => 6
[[3,3,2],[1]]                             => 6
[[3,3,1,1],[1]]                           => 6
[[3,2,2,1],[1]]                           => 7
[[3,2,1,1,1],[1]]                         => 7
[[3,1,1,1,1,1],[1]]                       => 6
[[2,2,2,2],[1]]                           => 5
[[2,2,2,1,1],[1]]                         => 6
[[2,2,1,1,1,1],[1]]                       => 6
[[2,1,1,1,1,1,1],[1]]                     => 6
[[1,1,1,1,1,1,1,1],[1]]                   => 4
[[9]]                                     => 3
[[8,1]]                                   => 4
[[7,2]]                                   => 4
[[7,1,1]]                                 => 4
[[6,3]]                                   => 4
[[6,2,1]]                                 => 5
[[6,1,1,1]]                               => 4
[[5,4]]                                   => 4
[[5,3,1]]                                 => 5
[[5,2,2]]                                 => 4
[[5,2,1,1]]                               => 5
[[5,1,1,1,1]]                             => 4
[[4,4,1]]                                 => 4
[[4,3,2]]                                 => 5
[[4,3,1,1]]                               => 5
[[4,2,2,1]]                               => 5
[[4,2,1,1,1]]                             => 5
[[4,1,1,1,1,1]]                           => 4
[[3,3,3]]                                 => 3
[[3,3,2,1]]                               => 5
[[3,3,1,1,1]]                             => 4
[[3,2,2,2]]                               => 4
[[3,2,2,1,1]]                             => 5
[[3,2,1,1,1,1]]                           => 5
[[3,1,1,1,1,1,1]]                         => 4
[[2,2,2,2,1]]                             => 4
[[2,2,2,1,1,1]]                           => 4
[[2,2,1,1,1,1,1]]                         => 4
[[2,1,1,1,1,1,1,1]]                       => 4
[[1,1,1,1,1,1,1,1,1]]                     => 3
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => 12
[[2],[1],[1],[1],[1],[1],[1],[1],[1]]     => 12
[[2],[2],[1],[1],[1],[1],[1],[1]]         => 11
[[2],[2],[2],[1],[1],[1],[1]]             => 10
[[2],[2],[2],[2],[1],[1]]                 => 9
[[2],[2],[2],[2],[2]]                     => 7
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]]   => 11
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]]     => 10
[[1,1],[1,1],[1,1],[1],[1],[1],[1]]       => 9
[[1,1],[1,1],[1,1],[1,1],[1],[1]]         => 8
[[1,1],[1,1],[1,1],[1,1],[1,1]]           => 7
[[3],[1],[1],[1],[1],[1],[1],[1]]         => 11
[[3],[2],[1],[1],[1],[1],[1]]             => 11
[[3],[2],[2],[1],[1],[1]]                 => 10
[[3],[2],[2],[2],[1]]                     => 9
[[3],[3],[1],[1],[1],[1]]                 => 9
[[3],[3],[2],[1],[1]]                     => 9
[[3],[3],[2],[2]]                         => 7
[[3],[3],[3],[1]]                         => 7
[[2,1],[1],[1],[1],[1],[1],[1],[1]]       => 12
[[2,1],[2],[1],[1],[1],[1],[1]]           => 11
[[2,1],[2],[2],[1],[1],[1]]               => 10
[[2,1],[2],[2],[2],[1]]                   => 9
[[2,1],[1,1],[1],[1],[1],[1],[1]]         => 11
[[2,1],[1,1],[1,1],[1],[1],[1]]           => 10
[[2,1],[1,1],[1,1],[1,1],[1]]             => 9
[[2,1],[2,1],[1],[1],[1],[1]]             => 10
[[2,1],[2,1],[2],[1],[1]]                 => 9
[[2,1],[2,1],[2],[2]]                     => 7
[[2,1],[2,1],[1,1],[1],[1]]               => 9
[[2,1],[2,1],[1,1],[1,1]]                 => 8
[[2,1],[2,1],[2,1],[1]]                   => 8
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]]     => 10
[[1,1,1],[1,1],[1],[1],[1],[1],[1]]       => 9
[[1,1,1],[1,1],[1,1],[1],[1],[1]]         => 8
[[1,1,1],[1,1],[1,1],[1,1],[1]]           => 7
[[1,1,1],[1,1,1],[1],[1],[1],[1]]         => 8
[[1,1,1],[1,1,1],[1,1],[1],[1]]           => 7
[[1,1,1],[1,1,1],[1,1],[1,1]]             => 6
[[1,1,1],[1,1,1],[1,1,1],[1]]             => 6
[[4],[1],[1],[1],[1],[1],[1]]             => 10
[[4],[2],[1],[1],[1],[1]]                 => 10
[[4],[2],[2],[1],[1]]                     => 9
[[4],[2],[2],[2]]                         => 7
[[4],[3],[1],[1],[1]]                     => 9
[[4],[3],[2],[1]]                         => 9
[[4],[3],[3]]                             => 6
[[4],[4],[1],[1]]                         => 7
[[4],[4],[2]]                             => 6
[[3,1],[1],[1],[1],[1],[1],[1]]           => 11
[[3,1],[2],[1],[1],[1],[1]]               => 11
[[3,1],[2],[2],[1],[1]]                   => 10
[[3,1],[2],[2],[2]]                       => 8
[[3,1],[1,1],[1],[1],[1],[1]]             => 10
[[3,1],[1,1],[1,1],[1],[1]]               => 9
[[3,1],[1,1],[1,1],[1,1]]                 => 8
[[3,1],[3],[1],[1],[1]]                   => 9
[[3,1],[3],[2],[1]]                       => 9
[[3,1],[3],[3]]                           => 6
[[3,1],[2,1],[1],[1],[1]]                 => 10
[[3,1],[2,1],[2],[1]]                     => 9
[[3,1],[2,1],[1,1],[1]]                   => 9
[[3,1],[2,1],[2,1]]                       => 7
[[3,1],[3,1],[1],[1]]                     => 8
[[3,1],[3,1],[2]]                         => 7
[[3,1],[3,1],[1,1]]                       => 7
[[2,2],[1],[1],[1],[1],[1],[1]]           => 10
[[2,2],[2],[1],[1],[1],[1]]               => 9
[[2,2],[2],[2],[1],[1]]                   => 8
[[2,2],[2],[2],[2]]                       => 6
[[2,2],[1,1],[1],[1],[1],[1]]             => 9
[[2,2],[1,1],[1,1],[1],[1]]               => 8
[[2,2],[1,1],[1,1],[1,1]]                 => 7
[[2,2],[2,1],[1],[1],[1]]                 => 9
[[2,2],[2,1],[2],[1]]                     => 8
[[2,2],[2,1],[1,1],[1]]                   => 8
[[2,2],[2,1],[2,1]]                       => 6
[[2,2],[2,2],[1],[1]]                     => 7
[[2,2],[2,2],[2]]                         => 5
[[2,2],[2,2],[1,1]]                       => 6
[[2,1,1],[1],[1],[1],[1],[1],[1]]         => 11
[[2,1,1],[2],[1],[1],[1],[1]]             => 10
[[2,1,1],[2],[2],[1],[1]]                 => 9
[[2,1,1],[2],[2],[2]]                     => 7
[[2,1,1],[1,1],[1],[1],[1],[1]]           => 10
[[2,1,1],[1,1],[1,1],[1],[1]]             => 9
[[2,1,1],[1,1],[1,1],[1,1]]               => 8
[[2,1,1],[2,1],[1],[1],[1]]               => 9
[[2,1,1],[2,1],[2],[1]]                   => 8
[[2,1,1],[2,1],[1,1],[1]]                 => 8
[[2,1,1],[2,1],[2,1]]                     => 6
[[2,1,1],[1,1,1],[1],[1],[1]]             => 9
[[2,1,1],[1,1,1],[1,1],[1]]               => 8
[[2,1,1],[1,1,1],[1,1,1]]                 => 7
[[2,1,1],[2,1,1],[1],[1]]                 => 8
[[2,1,1],[2,1,1],[2]]                     => 6
[[2,1,1],[2,1,1],[1,1]]                   => 7
[[1,1,1,1],[1],[1],[1],[1],[1],[1]]       => 9
[[1,1,1,1],[1,1],[1],[1],[1],[1]]         => 8
[[1,1,1,1],[1,1],[1,1],[1],[1]]           => 7
[[1,1,1,1],[1,1],[1,1],[1,1]]             => 6
[[1,1,1,1],[1,1,1],[1],[1],[1]]           => 7
[[1,1,1,1],[1,1,1],[1,1],[1]]             => 6
[[1,1,1,1],[1,1,1],[1,1,1]]               => 5
[[1,1,1,1],[1,1,1,1],[1],[1]]             => 6
[[1,1,1,1],[1,1,1,1],[1,1]]               => 5
[[5],[1],[1],[1],[1],[1]]                 => 9
[[5],[2],[1],[1],[1]]                     => 9
[[5],[2],[2],[1]]                         => 8
[[5],[3],[1],[1]]                         => 8
[[5],[3],[2]]                             => 7
[[5],[4],[1]]                             => 7
[[5],[5]]                                 => 4
[[4,1],[1],[1],[1],[1],[1]]               => 10
[[4,1],[2],[1],[1],[1]]                   => 10
[[4,1],[2],[2],[1]]                       => 9
[[4,1],[1,1],[1],[1],[1]]                 => 9
[[4,1],[1,1],[1,1],[1]]                   => 8
[[4,1],[3],[1],[1]]                       => 9
[[4,1],[3],[2]]                           => 8
[[4,1],[2,1],[1],[1]]                     => 9
[[4,1],[2,1],[2]]                         => 7
[[4,1],[2,1],[1,1]]                       => 8
[[4,1],[4],[1]]                           => 7
[[4,1],[3,1],[1]]                         => 8
[[4,1],[4,1]]                             => 5
[[3,2],[1],[1],[1],[1],[1]]               => 10
[[3,2],[2],[1],[1],[1]]                   => 10
[[3,2],[2],[2],[1]]                       => 9
[[3,2],[1,1],[1],[1],[1]]                 => 9
[[3,2],[1,1],[1,1],[1]]                   => 8
[[3,2],[3],[1],[1]]                       => 8
[[3,2],[3],[2]]                           => 7
[[3,2],[2,1],[1],[1]]                     => 10
[[3,2],[2,1],[2]]                         => 8
[[3,2],[2,1],[1,1]]                       => 9
[[3,2],[3,1],[1]]                         => 8
[[3,2],[2,2],[1]]                         => 8
[[3,2],[3,2]]                             => 5
[[3,1,1],[1],[1],[1],[1],[1]]             => 10
[[3,1,1],[2],[1],[1],[1]]                 => 10
[[3,1,1],[2],[2],[1]]                     => 9
[[3,1,1],[1,1],[1],[1],[1]]               => 9
[[3,1,1],[1,1],[1,1],[1]]                 => 8
[[3,1,1],[3],[1],[1]]                     => 8
[[3,1,1],[3],[2]]                         => 7
[[3,1,1],[2,1],[1],[1]]                   => 9
[[3,1,1],[2,1],[2]]                       => 7
[[3,1,1],[2,1],[1,1]]                     => 8
[[3,1,1],[1,1,1],[1],[1]]                 => 8
[[3,1,1],[1,1,1],[1,1]]                   => 7
[[3,1,1],[3,1],[1]]                       => 7
[[3,1,1],[2,1,1],[1]]                     => 8
[[3,1,1],[3,1,1]]                         => 5
[[2,2,1],[1],[1],[1],[1],[1]]             => 10
[[2,2,1],[2],[1],[1],[1]]                 => 9
[[2,2,1],[2],[2],[1]]                     => 8
[[2,2,1],[1,1],[1],[1],[1]]               => 9
[[2,2,1],[1,1],[1,1],[1]]                 => 8
[[2,2,1],[2,1],[1],[1]]                   => 9
[[2,2,1],[2,1],[2]]                       => 7
[[2,2,1],[2,1],[1,1]]                     => 8
[[2,2,1],[1,1,1],[1],[1]]                 => 8
[[2,2,1],[1,1,1],[1,1]]                   => 7
[[2,2,1],[2,2],[1]]                       => 7
[[2,2,1],[2,1,1],[1]]                     => 8
[[2,2,1],[2,2,1]]                         => 5
[[2,1,1,1],[1],[1],[1],[1],[1]]           => 10
[[2,1,1,1],[2],[1],[1],[1]]               => 9
[[2,1,1,1],[2],[2],[1]]                   => 8
[[2,1,1,1],[1,1],[1],[1],[1]]             => 9
[[2,1,1,1],[1,1],[1,1],[1]]               => 8
[[2,1,1,1],[2,1],[1],[1]]                 => 8
[[2,1,1,1],[2,1],[2]]                     => 6
[[2,1,1,1],[2,1],[1,1]]                   => 7
[[2,1,1,1],[1,1,1],[1],[1]]               => 8
[[2,1,1,1],[1,1,1],[1,1]]                 => 7
[[2,1,1,1],[2,1,1],[1]]                   => 7
[[2,1,1,1],[1,1,1,1],[1]]                 => 7
[[2,1,1,1],[2,1,1,1]]                     => 5
[[1,1,1,1,1],[1],[1],[1],[1],[1]]         => 8
[[1,1,1,1,1],[1,1],[1],[1],[1]]           => 7
[[1,1,1,1,1],[1,1],[1,1],[1]]             => 6
[[1,1,1,1,1],[1,1,1],[1],[1]]             => 6
[[1,1,1,1,1],[1,1,1],[1,1]]               => 5
[[1,1,1,1,1],[1,1,1,1],[1]]               => 5
[[1,1,1,1,1],[1,1,1,1,1]]                 => 4
[[6],[1],[1],[1],[1]]                     => 8
[[6],[2],[1],[1]]                         => 8
[[6],[2],[2]]                             => 6
[[6],[3],[1]]                             => 7
[[6],[4]]                                 => 5
[[5,1],[1],[1],[1],[1]]                   => 9
[[5,1],[2],[1],[1]]                       => 9
[[5,1],[2],[2]]                           => 7
[[5,1],[1,1],[1],[1]]                     => 8
[[5,1],[1,1],[1,1]]                       => 7
[[5,1],[3],[1]]                           => 8
[[5,1],[2,1],[1]]                         => 8
[[5,1],[4]]                               => 6
[[5,1],[3,1]]                             => 6
[[4,2],[1],[1],[1],[1]]                   => 9
[[4,2],[2],[1],[1]]                       => 9
[[4,2],[2],[2]]                           => 7
[[4,2],[1,1],[1],[1]]                     => 8
[[4,2],[1,1],[1,1]]                       => 7
[[4,2],[3],[1]]                           => 8
[[4,2],[2,1],[1]]                         => 9
[[4,2],[4]]                               => 5
[[4,2],[3,1]]                             => 7
[[4,2],[2,2]]                             => 6
[[4,1,1],[1],[1],[1],[1]]                 => 9
[[4,1,1],[2],[1],[1]]                     => 9
[[4,1,1],[2],[2]]                         => 7
[[4,1,1],[1,1],[1],[1]]                   => 8
[[4,1,1],[1,1],[1,1]]                     => 7
[[4,1,1],[3],[1]]                         => 8
[[4,1,1],[2,1],[1]]                       => 8
[[4,1,1],[1,1,1],[1]]                     => 7
[[4,1,1],[4]]                             => 5
[[4,1,1],[3,1]]                           => 6
[[4,1,1],[2,1,1]]                         => 6
[[3,3],[1],[1],[1],[1]]                   => 8
[[3,3],[2],[1],[1]]                       => 8
[[3,3],[2],[2]]                           => 6
[[3,3],[1,1],[1],[1]]                     => 7
[[3,3],[1,1],[1,1]]                       => 6
[[3,3],[3],[1]]                           => 6
[[3,3],[2,1],[1]]                         => 8
[[3,3],[3,1]]                             => 5
[[3,3],[2,2]]                             => 5
[[3,2,1],[1],[1],[1],[1]]                 => 10
[[3,2,1],[2],[1],[1]]                     => 10
[[3,2,1],[2],[2]]                         => 8
[[3,2,1],[1,1],[1],[1]]                   => 9
[[3,2,1],[1,1],[1,1]]                     => 8
[[3,2,1],[3],[1]]                         => 8
[[3,2,1],[2,1],[1]]                       => 10
[[3,2,1],[1,1,1],[1]]                     => 8
[[3,2,1],[3,1]]                           => 7
[[3,2,1],[2,2]]                           => 7
[[3,2,1],[2,1,1]]                         => 8
[[3,1,1,1],[1],[1],[1],[1]]               => 9
[[3,1,1,1],[2],[1],[1]]                   => 9
[[3,1,1,1],[2],[2]]                       => 7
[[3,1,1,1],[1,1],[1],[1]]                 => 8
[[3,1,1,1],[1,1],[1,1]]                   => 7
[[3,1,1,1],[3],[1]]                       => 7
[[3,1,1,1],[2,1],[1]]                     => 8
[[3,1,1,1],[1,1,1],[1]]                   => 7
[[3,1,1,1],[3,1]]                         => 5
[[3,1,1,1],[2,1,1]]                       => 6
[[3,1,1,1],[1,1,1,1]]                     => 6
[[2,2,2],[1],[1],[1],[1]]                 => 8
[[2,2,2],[2],[1],[1]]                     => 7
[[2,2,2],[2],[2]]                         => 5
[[2,2,2],[1,1],[1],[1]]                   => 7
[[2,2,2],[1,1],[1,1]]                     => 6
[[2,2,2],[2,1],[1]]                       => 7
[[2,2,2],[1,1,1],[1]]                     => 6
[[2,2,2],[2,2]]                           => 4
[[2,2,2],[2,1,1]]                         => 5
[[2,2,1,1],[1],[1],[1],[1]]               => 9
[[2,2,1,1],[2],[1],[1]]                   => 8
[[2,2,1,1],[2],[2]]                       => 6
[[2,2,1,1],[1,1],[1],[1]]                 => 8
[[2,2,1,1],[1,1],[1,1]]                   => 7
[[2,2,1,1],[2,1],[1]]                     => 8
[[2,2,1,1],[1,1,1],[1]]                   => 7
[[2,2,1,1],[2,2]]                         => 5
[[2,2,1,1],[2,1,1]]                       => 6
[[2,2,1,1],[1,1,1,1]]                     => 6
[[2,1,1,1,1],[1],[1],[1],[1]]             => 9
[[2,1,1,1,1],[2],[1],[1]]                 => 8
[[2,1,1,1,1],[2],[2]]                     => 6
[[2,1,1,1,1],[1,1],[1],[1]]               => 8
[[2,1,1,1,1],[1,1],[1,1]]                 => 7
[[2,1,1,1,1],[2,1],[1]]                   => 7
[[2,1,1,1,1],[1,1,1],[1]]                 => 7
[[2,1,1,1,1],[2,1,1]]                     => 5
[[2,1,1,1,1],[1,1,1,1]]                   => 6
[[1,1,1,1,1,1],[1],[1],[1],[1]]           => 7
[[1,1,1,1,1,1],[1,1],[1],[1]]             => 6
[[1,1,1,1,1,1],[1,1],[1,1]]               => 5
[[1,1,1,1,1,1],[1,1,1],[1]]               => 5
[[1,1,1,1,1,1],[1,1,1,1]]                 => 4
[[7],[1],[1],[1]]                         => 7
[[7],[2],[1]]                             => 7
[[7],[3]]                                 => 5
[[6,1],[1],[1],[1]]                       => 8
[[6,1],[2],[1]]                           => 8
[[6,1],[1,1],[1]]                         => 7
[[6,1],[3]]                               => 6
[[6,1],[2,1]]                             => 6
[[5,2],[1],[1],[1]]                       => 8
[[5,2],[2],[1]]                           => 8
[[5,2],[1,1],[1]]                         => 7
[[5,2],[3]]                               => 6
[[5,2],[2,1]]                             => 7
[[5,1,1],[1],[1],[1]]                     => 8
[[5,1,1],[2],[1]]                         => 8
[[5,1,1],[1,1],[1]]                       => 7
[[5,1,1],[3]]                             => 6
[[5,1,1],[2,1]]                           => 6
[[5,1,1],[1,1,1]]                         => 6
[[4,3],[1],[1],[1]]                       => 8
[[4,3],[2],[1]]                           => 8
[[4,3],[1,1],[1]]                         => 7
[[4,3],[3]]                               => 6
[[4,3],[2,1]]                             => 7
[[4,2,1],[1],[1],[1]]                     => 9
[[4,2,1],[2],[1]]                         => 9
[[4,2,1],[1,1],[1]]                       => 8
[[4,2,1],[3]]                             => 7
[[4,2,1],[2,1]]                           => 8
[[4,2,1],[1,1,1]]                         => 7
[[4,1,1,1],[1],[1],[1]]                   => 8
[[4,1,1,1],[2],[1]]                       => 8
[[4,1,1,1],[1,1],[1]]                     => 7
[[4,1,1,1],[3]]                           => 6
[[4,1,1,1],[2,1]]                         => 6
[[4,1,1,1],[1,1,1]]                       => 6
[[3,3,1],[1],[1],[1]]                     => 8
[[3,3,1],[2],[1]]                         => 8
[[3,3,1],[1,1],[1]]                       => 7
[[3,3,1],[3]]                             => 5
[[3,3,1],[2,1]]                           => 7
[[3,3,1],[1,1,1]]                         => 6
[[3,2,2],[1],[1],[1]]                     => 8
[[3,2,2],[2],[1]]                         => 8
[[3,2,2],[1,1],[1]]                       => 7
[[3,2,2],[3]]                             => 5
[[3,2,2],[2,1]]                           => 7
[[3,2,2],[1,1,1]]                         => 6
[[3,2,1,1],[1],[1],[1]]                   => 9
[[3,2,1,1],[2],[1]]                       => 9
[[3,2,1,1],[1,1],[1]]                     => 8
[[3,2,1,1],[3]]                           => 6
[[3,2,1,1],[2,1]]                         => 8
[[3,2,1,1],[1,1,1]]                       => 7
[[3,1,1,1,1],[1],[1],[1]]                 => 8
[[3,1,1,1,1],[2],[1]]                     => 8
[[3,1,1,1,1],[1,1],[1]]                   => 7
[[3,1,1,1,1],[3]]                         => 5
[[3,1,1,1,1],[2,1]]                       => 6
[[3,1,1,1,1],[1,1,1]]                     => 6
[[2,2,2,1],[1],[1],[1]]                   => 8
[[2,2,2,1],[2],[1]]                       => 7
[[2,2,2,1],[1,1],[1]]                     => 7
[[2,2,2,1],[2,1]]                         => 6
[[2,2,2,1],[1,1,1]]                       => 6
[[2,2,1,1,1],[1],[1],[1]]                 => 8
[[2,2,1,1,1],[2],[1]]                     => 7
[[2,2,1,1,1],[1,1],[1]]                   => 7
[[2,2,1,1,1],[2,1]]                       => 6
[[2,2,1,1,1],[1,1,1]]                     => 6
[[2,1,1,1,1,1],[1],[1],[1]]               => 8
[[2,1,1,1,1,1],[2],[1]]                   => 7
[[2,1,1,1,1,1],[1,1],[1]]                 => 7
[[2,1,1,1,1,1],[2,1]]                     => 5
[[2,1,1,1,1,1],[1,1,1]]                   => 6
[[1,1,1,1,1,1,1],[1],[1],[1]]             => 6
[[1,1,1,1,1,1,1],[1,1],[1]]               => 5
[[1,1,1,1,1,1,1],[1,1,1]]                 => 4
[[8],[1],[1]]                             => 6
[[8],[2]]                                 => 5
[[7,1],[1],[1]]                           => 7
[[7,1],[2]]                               => 6
[[7,1],[1,1]]                             => 6
[[6,2],[1],[1]]                           => 7
[[6,2],[2]]                               => 6
[[6,2],[1,1]]                             => 6
[[6,1,1],[1],[1]]                         => 7
[[6,1,1],[2]]                             => 6
[[6,1,1],[1,1]]                           => 6
[[5,3],[1],[1]]                           => 7
[[5,3],[2]]                               => 6
[[5,3],[1,1]]                             => 6
[[5,2,1],[1],[1]]                         => 8
[[5,2,1],[2]]                             => 7
[[5,2,1],[1,1]]                           => 7
[[5,1,1,1],[1],[1]]                       => 7
[[5,1,1,1],[2]]                           => 6
[[5,1,1,1],[1,1]]                         => 6
[[4,4],[1],[1]]                           => 6
[[4,4],[2]]                               => 5
[[4,4],[1,1]]                             => 5
[[4,3,1],[1],[1]]                         => 8
[[4,3,1],[2]]                             => 7
[[4,3,1],[1,1]]                           => 7
[[4,2,2],[1],[1]]                         => 7
[[4,2,2],[2]]                             => 6
[[4,2,2],[1,1]]                           => 6
[[4,2,1,1],[1],[1]]                       => 8
[[4,2,1,1],[2]]                           => 7
[[4,2,1,1],[1,1]]                         => 7
[[4,1,1,1,1],[1],[1]]                     => 7
[[4,1,1,1,1],[2]]                         => 6
[[4,1,1,1,1],[1,1]]                       => 6
[[3,3,2],[1],[1]]                         => 7
[[3,3,2],[2]]                             => 6
[[3,3,2],[1,1]]                           => 6
[[3,3,1,1],[1],[1]]                       => 7
[[3,3,1,1],[2]]                           => 6
[[3,3,1,1],[1,1]]                         => 6
[[3,2,2,1],[1],[1]]                       => 8
[[3,2,2,1],[2]]                           => 7
[[3,2,2,1],[1,1]]                         => 7
[[3,2,1,1,1],[1],[1]]                     => 8
[[3,2,1,1,1],[2]]                         => 7
[[3,2,1,1,1],[1,1]]                       => 7
[[3,1,1,1,1,1],[1],[1]]                   => 7
[[3,1,1,1,1,1],[2]]                       => 6
[[3,1,1,1,1,1],[1,1]]                     => 6
[[2,2,2,2],[1],[1]]                       => 6
[[2,2,2,2],[2]]                           => 4
[[2,2,2,2],[1,1]]                         => 5
[[2,2,2,1,1],[1],[1]]                     => 7
[[2,2,2,1,1],[2]]                         => 5
[[2,2,2,1,1],[1,1]]                       => 6
[[2,2,1,1,1,1],[1],[1]]                   => 7
[[2,2,1,1,1,1],[2]]                       => 5
[[2,2,1,1,1,1],[1,1]]                     => 6
[[2,1,1,1,1,1,1],[1],[1]]                 => 7
[[2,1,1,1,1,1,1],[2]]                     => 5
[[2,1,1,1,1,1,1],[1,1]]                   => 6
[[1,1,1,1,1,1,1,1],[1],[1]]               => 5
[[1,1,1,1,1,1,1,1],[1,1]]                 => 4
[[9],[1]]                                 => 5
[[8,1],[1]]                               => 6
[[7,2],[1]]                               => 6
[[7,1,1],[1]]                             => 6
[[6,3],[1]]                               => 6
[[6,2,1],[1]]                             => 7
[[6,1,1,1],[1]]                           => 6
[[5,4],[1]]                               => 6
[[5,3,1],[1]]                             => 7
[[5,2,2],[1]]                             => 6
[[5,2,1,1],[1]]                           => 7
[[5,1,1,1,1],[1]]                         => 6
[[4,4,1],[1]]                             => 6
[[4,3,2],[1]]                             => 7
[[4,3,1,1],[1]]                           => 7
[[4,2,2,1],[1]]                           => 7
[[4,2,1,1,1],[1]]                         => 7
[[4,1,1,1,1,1],[1]]                       => 6
[[3,3,3],[1]]                             => 5
[[3,3,2,1],[1]]                           => 7
[[3,3,1,1,1],[1]]                         => 6
[[3,2,2,2],[1]]                           => 6
[[3,2,2,1,1],[1]]                         => 7
[[3,2,1,1,1,1],[1]]                       => 7
[[3,1,1,1,1,1,1],[1]]                     => 6
[[2,2,2,2,1],[1]]                         => 6
[[2,2,2,1,1,1],[1]]                       => 6
[[2,2,1,1,1,1,1],[1]]                     => 6
[[2,1,1,1,1,1,1,1],[1]]                   => 6
[[1,1,1,1,1,1,1,1,1],[1]]                 => 4
[[10]]                                    => 3
[[9,1]]                                   => 4
[[8,2]]                                   => 4
[[8,1,1]]                                 => 4
[[7,3]]                                   => 4
[[7,2,1]]                                 => 5
[[7,1,1,1]]                               => 4
[[6,4]]                                   => 4
[[6,3,1]]                                 => 5
[[6,2,2]]                                 => 4
[[6,2,1,1]]                               => 5
[[6,1,1,1,1]]                             => 4
[[5,5]]                                   => 3
[[5,4,1]]                                 => 5
[[5,3,2]]                                 => 5
[[5,3,1,1]]                               => 5
[[5,2,2,1]]                               => 5
[[5,2,1,1,1]]                             => 5
[[5,1,1,1,1,1]]                           => 4
[[4,4,2]]                                 => 4
[[4,4,1,1]]                               => 4
[[4,3,3]]                                 => 4
[[4,3,2,1]]                               => 6
[[4,3,1,1,1]]                             => 5
[[4,2,2,2]]                               => 4
[[4,2,2,1,1]]                             => 5
[[4,2,1,1,1,1]]                           => 5
[[4,1,1,1,1,1,1]]                         => 4
[[3,3,3,1]]                               => 4
[[3,3,2,2]]                               => 4
[[3,3,2,1,1]]                             => 5
[[3,3,1,1,1,1]]                           => 4
[[3,2,2,2,1]]                             => 5
[[3,2,2,1,1,1]]                           => 5
[[3,2,1,1,1,1,1]]                         => 5
[[3,1,1,1,1,1,1,1]]                       => 4
[[2,2,2,2,2]]                             => 3
[[2,2,2,2,1,1]]                           => 4
[[2,2,2,1,1,1,1]]                         => 4
[[2,2,1,1,1,1,1,1]]                       => 4
[[2,1,1,1,1,1,1,1,1]]                     => 4
[[1,1,1,1,1,1,1,1,1,1]]                   => 3

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Created: Aug 28, 2023 at 09:50 by Martin Rubey

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Last Updated: Aug 28, 2023 at 09:50 by Martin Rubey