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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         *
*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                   *
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-----------------------------------------------------------------------------
Statistic identifier: St000010

-----------------------------------------------------------------------------
Collection: Integer partitions

-----------------------------------------------------------------------------
Description: The length of the partition.

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

-----------------------------------------------------------------------------
Code:
def statistic(x):
    return x.length()

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

[]                                  => 0
[1]                                 => 1
[2]                                 => 1
[1,1]                               => 2
[3]                                 => 1
[2,1]                               => 2
[1,1,1]                             => 3
[4]                                 => 1
[3,1]                               => 2
[2,2]                               => 2
[2,1,1]                             => 3
[1,1,1,1]                           => 4
[5]                                 => 1
[4,1]                               => 2
[3,2]                               => 2
[3,1,1]                             => 3
[2,2,1]                             => 3
[2,1,1,1]                           => 4
[1,1,1,1,1]                         => 5
[6]                                 => 1
[5,1]                               => 2
[4,2]                               => 2
[4,1,1]                             => 3
[3,3]                               => 2
[3,2,1]                             => 3
[3,1,1,1]                           => 4
[2,2,2]                             => 3
[2,2,1,1]                           => 4
[2,1,1,1,1]                         => 5
[1,1,1,1,1,1]                       => 6
[7]                                 => 1
[6,1]                               => 2
[5,2]                               => 2
[5,1,1]                             => 3
[4,3]                               => 2
[4,2,1]                             => 3
[4,1,1,1]                           => 4
[3,3,1]                             => 3
[3,2,2]                             => 3
[3,2,1,1]                           => 4
[3,1,1,1,1]                         => 5
[2,2,2,1]                           => 4
[2,2,1,1,1]                         => 5
[2,1,1,1,1,1]                       => 6
[1,1,1,1,1,1,1]                     => 7
[8]                                 => 1
[7,1]                               => 2
[6,2]                               => 2
[6,1,1]                             => 3
[5,3]                               => 2
[5,2,1]                             => 3
[5,1,1,1]                           => 4
[4,4]                               => 2
[4,3,1]                             => 3
[4,2,2]                             => 3
[4,2,1,1]                           => 4
[4,1,1,1,1]                         => 5
[3,3,2]                             => 3
[3,3,1,1]                           => 4
[3,2,2,1]                           => 4
[3,2,1,1,1]                         => 5
[3,1,1,1,1,1]                       => 6
[2,2,2,2]                           => 4
[2,2,2,1,1]                         => 5
[2,2,1,1,1,1]                       => 6
[2,1,1,1,1,1,1]                     => 7
[1,1,1,1,1,1,1,1]                   => 8
[9]                                 => 1
[8,1]                               => 2
[7,2]                               => 2
[7,1,1]                             => 3
[6,3]                               => 2
[6,2,1]                             => 3
[6,1,1,1]                           => 4
[5,4]                               => 2
[5,3,1]                             => 3
[5,2,2]                             => 3
[5,2,1,1]                           => 4
[5,1,1,1,1]                         => 5
[4,4,1]                             => 3
[4,3,2]                             => 3
[4,3,1,1]                           => 4
[4,2,2,1]                           => 4
[4,2,1,1,1]                         => 5
[4,1,1,1,1,1]                       => 6
[3,3,3]                             => 3
[3,3,2,1]                           => 4
[3,3,1,1,1]                         => 5
[3,2,2,2]                           => 4
[3,2,2,1,1]                         => 5
[3,2,1,1,1,1]                       => 6
[3,1,1,1,1,1,1]                     => 7
[2,2,2,2,1]                         => 5
[2,2,2,1,1,1]                       => 6
[2,2,1,1,1,1,1]                     => 7
[2,1,1,1,1,1,1,1]                   => 8
[1,1,1,1,1,1,1,1,1]                 => 9
[10]                                => 1
[9,1]                               => 2
[8,2]                               => 2
[8,1,1]                             => 3
[7,3]                               => 2
[7,2,1]                             => 3
[7,1,1,1]                           => 4
[6,4]                               => 2
[6,3,1]                             => 3
[6,2,2]                             => 3
[6,2,1,1]                           => 4
[6,1,1,1,1]                         => 5
[5,5]                               => 2
[5,4,1]                             => 3
[5,3,2]                             => 3
[5,3,1,1]                           => 4
[5,2,2,1]                           => 4
[5,2,1,1,1]                         => 5
[5,1,1,1,1,1]                       => 6
[4,4,2]                             => 3
[4,4,1,1]                           => 4
[4,3,3]                             => 3
[4,3,2,1]                           => 4
[4,3,1,1,1]                         => 5
[4,2,2,2]                           => 4
[4,2,2,1,1]                         => 5
[4,2,1,1,1,1]                       => 6
[4,1,1,1,1,1,1]                     => 7
[3,3,3,1]                           => 4
[3,3,2,2]                           => 4
[3,3,2,1,1]                         => 5
[3,3,1,1,1,1]                       => 6
[3,2,2,2,1]                         => 5
[3,2,2,1,1,1]                       => 6
[3,2,1,1,1,1,1]                     => 7
[3,1,1,1,1,1,1,1]                   => 8
[2,2,2,2,2]                         => 5
[2,2,2,2,1,1]                       => 6
[2,2,2,1,1,1,1]                     => 7
[2,2,1,1,1,1,1,1]                   => 8
[2,1,1,1,1,1,1,1,1]                 => 9
[1,1,1,1,1,1,1,1,1,1]               => 10
[11]                                => 1
[10,1]                              => 2
[9,2]                               => 2
[9,1,1]                             => 3
[8,3]                               => 2
[8,2,1]                             => 3
[8,1,1,1]                           => 4
[7,4]                               => 2
[7,3,1]                             => 3
[7,2,2]                             => 3
[7,2,1,1]                           => 4
[7,1,1,1,1]                         => 5
[6,5]                               => 2
[6,4,1]                             => 3
[6,3,2]                             => 3
[6,3,1,1]                           => 4
[6,2,2,1]                           => 4
[6,2,1,1,1]                         => 5
[6,1,1,1,1,1]                       => 6
[5,5,1]                             => 3
[5,4,2]                             => 3
[5,4,1,1]                           => 4
[5,3,3]                             => 3
[5,3,2,1]                           => 4
[5,3,1,1,1]                         => 5
[5,2,2,2]                           => 4
[5,2,2,1,1]                         => 5
[5,2,1,1,1,1]                       => 6
[5,1,1,1,1,1,1]                     => 7
[4,4,3]                             => 3
[4,4,2,1]                           => 4
[4,4,1,1,1]                         => 5
[4,3,3,1]                           => 4
[4,3,2,2]                           => 4
[4,3,2,1,1]                         => 5
[4,3,1,1,1,1]                       => 6
[4,2,2,2,1]                         => 5
[4,2,2,1,1,1]                       => 6
[4,2,1,1,1,1,1]                     => 7
[4,1,1,1,1,1,1,1]                   => 8
[3,3,3,2]                           => 4
[3,3,3,1,1]                         => 5
[3,3,2,2,1]                         => 5
[3,3,2,1,1,1]                       => 6
[3,3,1,1,1,1,1]                     => 7
[3,2,2,2,2]                         => 5
[3,2,2,2,1,1]                       => 6
[3,2,2,1,1,1,1]                     => 7
[3,2,1,1,1,1,1,1]                   => 8
[3,1,1,1,1,1,1,1,1]                 => 9
[2,2,2,2,2,1]                       => 6
[2,2,2,2,1,1,1]                     => 7
[2,2,2,1,1,1,1,1]                   => 8
[2,2,1,1,1,1,1,1,1]                 => 9
[2,1,1,1,1,1,1,1,1,1]               => 10
[1,1,1,1,1,1,1,1,1,1,1]             => 11
[12]                                => 1
[11,1]                              => 2
[10,2]                              => 2
[10,1,1]                            => 3
[9,3]                               => 2
[9,2,1]                             => 3
[9,1,1,1]                           => 4
[8,4]                               => 2
[8,3,1]                             => 3
[8,2,2]                             => 3
[8,2,1,1]                           => 4
[8,1,1,1,1]                         => 5
[7,5]                               => 2
[7,4,1]                             => 3
[7,3,2]                             => 3
[7,3,1,1]                           => 4
[7,2,2,1]                           => 4
[7,2,1,1,1]                         => 5
[7,1,1,1,1,1]                       => 6
[6,6]                               => 2
[6,5,1]                             => 3
[6,4,2]                             => 3
[6,4,1,1]                           => 4
[6,3,3]                             => 3
[6,3,2,1]                           => 4
[6,3,1,1,1]                         => 5
[6,2,2,2]                           => 4
[6,2,2,1,1]                         => 5
[6,2,1,1,1,1]                       => 6
[6,1,1,1,1,1,1]                     => 7
[5,5,2]                             => 3
[5,5,1,1]                           => 4
[5,4,3]                             => 3
[5,4,2,1]                           => 4
[5,4,1,1,1]                         => 5
[5,3,3,1]                           => 4
[5,3,2,2]                           => 4
[5,3,2,1,1]                         => 5
[5,3,1,1,1,1]                       => 6
[5,2,2,2,1]                         => 5
[5,2,2,1,1,1]                       => 6
[5,2,1,1,1,1,1]                     => 7
[5,1,1,1,1,1,1,1]                   => 8
[4,4,4]                             => 3
[4,4,3,1]                           => 4
[4,4,2,2]                           => 4
[4,4,2,1,1]                         => 5
[4,4,1,1,1,1]                       => 6
[4,3,3,2]                           => 4
[4,3,3,1,1]                         => 5
[4,3,2,2,1]                         => 5
[4,3,2,1,1,1]                       => 6
[4,3,1,1,1,1,1]                     => 7
[4,2,2,2,2]                         => 5
[4,2,2,2,1,1]                       => 6
[4,2,2,1,1,1,1]                     => 7
[4,2,1,1,1,1,1,1]                   => 8
[4,1,1,1,1,1,1,1,1]                 => 9
[3,3,3,3]                           => 4
[3,3,3,2,1]                         => 5
[3,3,3,1,1,1]                       => 6
[3,3,2,2,2]                         => 5
[3,3,2,2,1,1]                       => 6
[3,3,2,1,1,1,1]                     => 7
[3,3,1,1,1,1,1,1]                   => 8
[3,2,2,2,2,1]                       => 6
[3,2,2,2,1,1,1]                     => 7
[3,2,2,1,1,1,1,1]                   => 8
[3,2,1,1,1,1,1,1,1]                 => 9
[3,1,1,1,1,1,1,1,1,1]               => 10
[2,2,2,2,2,2]                       => 6
[2,2,2,2,2,1,1]                     => 7
[2,2,2,2,1,1,1,1]                   => 8
[2,2,2,1,1,1,1,1,1]                 => 9
[2,2,1,1,1,1,1,1,1,1]               => 10
[2,1,1,1,1,1,1,1,1,1,1]             => 11
[1,1,1,1,1,1,1,1,1,1,1,1]           => 12
[13]                                => 1
[12,1]                              => 2
[11,2]                              => 2
[11,1,1]                            => 3
[10,3]                              => 2
[10,2,1]                            => 3
[10,1,1,1]                          => 4
[9,4]                               => 2
[9,3,1]                             => 3
[9,2,2]                             => 3
[9,2,1,1]                           => 4
[9,1,1,1,1]                         => 5
[8,5]                               => 2
[8,4,1]                             => 3
[8,3,2]                             => 3
[8,3,1,1]                           => 4
[8,2,2,1]                           => 4
[8,2,1,1,1]                         => 5
[8,1,1,1,1,1]                       => 6
[7,6]                               => 2
[7,5,1]                             => 3
[7,4,2]                             => 3
[7,4,1,1]                           => 4
[7,3,3]                             => 3
[7,3,2,1]                           => 4
[7,3,1,1,1]                         => 5
[7,2,2,2]                           => 4
[7,2,2,1,1]                         => 5
[7,2,1,1,1,1]                       => 6
[7,1,1,1,1,1,1]                     => 7
[6,6,1]                             => 3
[6,5,2]                             => 3
[6,5,1,1]                           => 4
[6,4,3]                             => 3
[6,4,2,1]                           => 4
[6,4,1,1,1]                         => 5
[6,3,3,1]                           => 4
[6,3,2,2]                           => 4
[6,3,2,1,1]                         => 5
[6,3,1,1,1,1]                       => 6
[6,2,2,2,1]                         => 5
[6,2,2,1,1,1]                       => 6
[6,2,1,1,1,1,1]                     => 7
[6,1,1,1,1,1,1,1]                   => 8
[5,5,3]                             => 3
[5,5,2,1]                           => 4
[5,5,1,1,1]                         => 5
[5,4,4]                             => 3
[5,4,3,1]                           => 4
[5,4,2,2]                           => 4
[5,4,2,1,1]                         => 5
[5,4,1,1,1,1]                       => 6
[5,3,3,2]                           => 4
[5,3,3,1,1]                         => 5
[5,3,2,2,1]                         => 5
[5,3,2,1,1,1]                       => 6
[5,3,1,1,1,1,1]                     => 7
[5,2,2,2,2]                         => 5
[5,2,2,2,1,1]                       => 6
[5,2,2,1,1,1,1]                     => 7
[5,2,1,1,1,1,1,1]                   => 8
[5,1,1,1,1,1,1,1,1]                 => 9
[4,4,4,1]                           => 4
[4,4,3,2]                           => 4
[4,4,3,1,1]                         => 5
[4,4,2,2,1]                         => 5
[4,4,2,1,1,1]                       => 6
[4,4,1,1,1,1,1]                     => 7
[4,3,3,3]                           => 4
[4,3,3,2,1]                         => 5
[4,3,3,1,1,1]                       => 6
[4,3,2,2,2]                         => 5
[4,3,2,2,1,1]                       => 6
[4,3,2,1,1,1,1]                     => 7
[4,3,1,1,1,1,1,1]                   => 8
[4,2,2,2,2,1]                       => 6
[4,2,2,2,1,1,1]                     => 7
[4,2,2,1,1,1,1,1]                   => 8
[4,2,1,1,1,1,1,1,1]                 => 9
[4,1,1,1,1,1,1,1,1,1]               => 10
[3,3,3,3,1]                         => 5
[3,3,3,2,2]                         => 5
[3,3,3,2,1,1]                       => 6
[3,3,3,1,1,1,1]                     => 7
[3,3,2,2,2,1]                       => 6
[3,3,2,2,1,1,1]                     => 7
[3,3,2,1,1,1,1,1]                   => 8
[3,3,1,1,1,1,1,1,1]                 => 9
[3,2,2,2,2,2]                       => 6
[3,2,2,2,2,1,1]                     => 7
[3,2,2,2,1,1,1,1]                   => 8
[3,2,2,1,1,1,1,1,1]                 => 9
[3,2,1,1,1,1,1,1,1,1]               => 10
[3,1,1,1,1,1,1,1,1,1,1]             => 11
[2,2,2,2,2,2,1]                     => 7
[2,2,2,2,2,1,1,1]                   => 8
[2,2,2,2,1,1,1,1,1]                 => 9
[2,2,2,1,1,1,1,1,1,1]               => 10
[2,2,1,1,1,1,1,1,1,1,1]             => 11
[2,1,1,1,1,1,1,1,1,1,1,1]           => 12
[1,1,1,1,1,1,1,1,1,1,1,1,1]         => 13
[14]                                => 1
[13,1]                              => 2
[12,2]                              => 2
[12,1,1]                            => 3
[11,3]                              => 2
[11,2,1]                            => 3
[11,1,1,1]                          => 4
[10,4]                              => 2
[10,3,1]                            => 3
[10,2,2]                            => 3
[10,2,1,1]                          => 4
[10,1,1,1,1]                        => 5
[9,5]                               => 2
[9,4,1]                             => 3
[9,3,2]                             => 3
[9,3,1,1]                           => 4
[9,2,2,1]                           => 4
[9,2,1,1,1]                         => 5
[9,1,1,1,1,1]                       => 6
[8,6]                               => 2
[8,5,1]                             => 3
[8,4,2]                             => 3
[8,4,1,1]                           => 4
[8,3,3]                             => 3
[8,3,2,1]                           => 4
[8,3,1,1,1]                         => 5
[8,2,2,2]                           => 4
[8,2,2,1,1]                         => 5
[8,2,1,1,1,1]                       => 6
[8,1,1,1,1,1,1]                     => 7
[7,7]                               => 2
[7,6,1]                             => 3
[7,5,2]                             => 3
[7,5,1,1]                           => 4
[7,4,3]                             => 3
[7,4,2,1]                           => 4
[7,4,1,1,1]                         => 5
[7,3,3,1]                           => 4
[7,3,2,2]                           => 4
[7,3,2,1,1]                         => 5
[7,3,1,1,1,1]                       => 6
[7,2,2,2,1]                         => 5
[7,2,2,1,1,1]                       => 6
[7,2,1,1,1,1,1]                     => 7
[7,1,1,1,1,1,1,1]                   => 8
[6,6,2]                             => 3
[6,6,1,1]                           => 4
[6,5,3]                             => 3
[6,5,2,1]                           => 4
[6,5,1,1,1]                         => 5
[6,4,4]                             => 3
[6,4,3,1]                           => 4
[6,4,2,2]                           => 4
[6,4,2,1,1]                         => 5
[6,4,1,1,1,1]                       => 6
[6,3,3,2]                           => 4
[6,3,3,1,1]                         => 5
[6,3,2,2,1]                         => 5
[6,3,2,1,1,1]                       => 6
[6,3,1,1,1,1,1]                     => 7
[6,2,2,2,2]                         => 5
[6,2,2,2,1,1]                       => 6
[6,2,2,1,1,1,1]                     => 7
[6,2,1,1,1,1,1,1]                   => 8
[6,1,1,1,1,1,1,1,1]                 => 9
[5,5,4]                             => 3
[5,5,3,1]                           => 4
[5,5,2,2]                           => 4
[5,5,2,1,1]                         => 5
[5,5,1,1,1,1]                       => 6
[5,4,4,1]                           => 4
[5,4,3,2]                           => 4
[5,4,3,1,1]                         => 5
[5,4,2,2,1]                         => 5
[5,4,2,1,1,1]                       => 6
[5,4,1,1,1,1,1]                     => 7
[5,3,3,3]                           => 4
[5,3,3,2,1]                         => 5
[5,3,3,1,1,1]                       => 6
[5,3,2,2,2]                         => 5
[5,3,2,2,1,1]                       => 6
[5,3,2,1,1,1,1]                     => 7
[5,3,1,1,1,1,1,1]                   => 8
[5,2,2,2,2,1]                       => 6
[5,2,2,2,1,1,1]                     => 7
[5,2,2,1,1,1,1,1]                   => 8
[5,2,1,1,1,1,1,1,1]                 => 9
[5,1,1,1,1,1,1,1,1,1]               => 10
[4,4,4,2]                           => 4
[4,4,4,1,1]                         => 5
[4,4,3,3]                           => 4
[4,4,3,2,1]                         => 5
[4,4,3,1,1,1]                       => 6
[4,4,2,2,2]                         => 5
[4,4,2,2,1,1]                       => 6
[4,4,2,1,1,1,1]                     => 7
[4,4,1,1,1,1,1,1]                   => 8
[4,3,3,3,1]                         => 5
[4,3,3,2,2]                         => 5
[4,3,3,2,1,1]                       => 6
[4,3,3,1,1,1,1]                     => 7
[4,3,2,2,2,1]                       => 6
[4,3,2,2,1,1,1]                     => 7
[4,3,2,1,1,1,1,1]                   => 8
[4,3,1,1,1,1,1,1,1]                 => 9
[4,2,2,2,2,2]                       => 6
[4,2,2,2,2,1,1]                     => 7
[4,2,2,2,1,1,1,1]                   => 8
[4,2,2,1,1,1,1,1,1]                 => 9
[4,2,1,1,1,1,1,1,1,1]               => 10
[4,1,1,1,1,1,1,1,1,1,1]             => 11
[3,3,3,3,2]                         => 5
[3,3,3,3,1,1]                       => 6
[3,3,3,2,2,1]                       => 6
[3,3,3,2,1,1,1]                     => 7
[3,3,3,1,1,1,1,1]                   => 8
[3,3,2,2,2,2]                       => 6
[3,3,2,2,2,1,1]                     => 7
[3,3,2,2,1,1,1,1]                   => 8
[3,3,2,1,1,1,1,1,1]                 => 9
[3,3,1,1,1,1,1,1,1,1]               => 10
[3,2,2,2,2,2,1]                     => 7
[3,2,2,2,2,1,1,1]                   => 8
[3,2,2,2,1,1,1,1,1]                 => 9
[3,2,2,1,1,1,1,1,1,1]               => 10
[3,2,1,1,1,1,1,1,1,1,1]             => 11
[3,1,1,1,1,1,1,1,1,1,1,1]           => 12
[2,2,2,2,2,2,2]                     => 7
[2,2,2,2,2,2,1,1]                   => 8
[2,2,2,2,2,1,1,1,1]                 => 9
[2,2,2,2,1,1,1,1,1,1]               => 10
[2,2,2,1,1,1,1,1,1,1,1]             => 11
[2,2,1,1,1,1,1,1,1,1,1,1]           => 12
[2,1,1,1,1,1,1,1,1,1,1,1,1]         => 13
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]       => 14
[15]                                => 1
[14,1]                              => 2
[13,2]                              => 2
[13,1,1]                            => 3
[12,3]                              => 2
[12,2,1]                            => 3
[12,1,1,1]                          => 4
[11,4]                              => 2
[11,3,1]                            => 3
[11,2,2]                            => 3
[11,2,1,1]                          => 4
[11,1,1,1,1]                        => 5
[10,5]                              => 2
[10,4,1]                            => 3
[10,3,2]                            => 3
[10,3,1,1]                          => 4
[10,2,2,1]                          => 4
[10,2,1,1,1]                        => 5
[10,1,1,1,1,1]                      => 6
[9,6]                               => 2
[9,5,1]                             => 3
[9,4,2]                             => 3
[9,4,1,1]                           => 4
[9,3,3]                             => 3
[9,3,2,1]                           => 4
[9,3,1,1,1]                         => 5
[9,2,2,2]                           => 4
[9,2,2,1,1]                         => 5
[9,2,1,1,1,1]                       => 6
[9,1,1,1,1,1,1]                     => 7
[8,7]                               => 2
[8,6,1]                             => 3
[8,5,2]                             => 3
[8,5,1,1]                           => 4
[8,4,3]                             => 3
[8,4,2,1]                           => 4
[8,4,1,1,1]                         => 5
[8,3,3,1]                           => 4
[8,3,2,2]                           => 4
[8,3,2,1,1]                         => 5
[8,3,1,1,1,1]                       => 6
[8,2,2,2,1]                         => 5
[8,2,2,1,1,1]                       => 6
[8,2,1,1,1,1,1]                     => 7
[8,1,1,1,1,1,1,1]                   => 8
[7,7,1]                             => 3
[7,6,2]                             => 3
[7,6,1,1]                           => 4
[7,5,3]                             => 3
[7,5,2,1]                           => 4
[7,5,1,1,1]                         => 5
[7,4,4]                             => 3
[7,4,3,1]                           => 4
[7,4,2,2]                           => 4
[7,4,2,1,1]                         => 5
[7,4,1,1,1,1]                       => 6
[7,3,3,2]                           => 4
[7,3,3,1,1]                         => 5
[7,3,2,2,1]                         => 5
[7,3,2,1,1,1]                       => 6
[7,3,1,1,1,1,1]                     => 7
[7,2,2,2,2]                         => 5
[7,2,2,2,1,1]                       => 6
[7,2,2,1,1,1,1]                     => 7
[7,2,1,1,1,1,1,1]                   => 8
[7,1,1,1,1,1,1,1,1]                 => 9
[6,6,3]                             => 3
[6,6,2,1]                           => 4
[6,6,1,1,1]                         => 5
[6,5,4]                             => 3
[6,5,3,1]                           => 4
[6,5,2,2]                           => 4
[6,5,2,1,1]                         => 5
[6,5,1,1,1,1]                       => 6
[6,4,4,1]                           => 4
[6,4,3,2]                           => 4
[6,4,3,1,1]                         => 5
[6,4,2,2,1]                         => 5
[6,4,2,1,1,1]                       => 6
[6,4,1,1,1,1,1]                     => 7
[6,3,3,3]                           => 4
[6,3,3,2,1]                         => 5
[6,3,3,1,1,1]                       => 6
[6,3,2,2,2]                         => 5
[6,3,2,2,1,1]                       => 6
[6,3,2,1,1,1,1]                     => 7
[6,3,1,1,1,1,1,1]                   => 8
[6,2,2,2,2,1]                       => 6
[6,2,2,2,1,1,1]                     => 7
[6,2,2,1,1,1,1,1]                   => 8
[6,2,1,1,1,1,1,1,1]                 => 9
[6,1,1,1,1,1,1,1,1,1]               => 10
[5,5,5]                             => 3
[5,5,4,1]                           => 4
[5,5,3,2]                           => 4
[5,5,3,1,1]                         => 5
[5,5,2,2,1]                         => 5
[5,5,2,1,1,1]                       => 6
[5,5,1,1,1,1,1]                     => 7
[5,4,4,2]                           => 4
[5,4,4,1,1]                         => 5
[5,4,3,3]                           => 4
[5,4,3,2,1]                         => 5
[5,4,3,1,1,1]                       => 6
[5,4,2,2,2]                         => 5
[5,4,2,2,1,1]                       => 6
[5,4,2,1,1,1,1]                     => 7
[5,4,1,1,1,1,1,1]                   => 8
[5,3,3,3,1]                         => 5
[5,3,3,2,2]                         => 5
[5,3,3,2,1,1]                       => 6
[5,3,3,1,1,1,1]                     => 7
[5,3,2,2,2,1]                       => 6
[5,3,2,2,1,1,1]                     => 7
[5,3,2,1,1,1,1,1]                   => 8
[5,3,1,1,1,1,1,1,1]                 => 9
[5,2,2,2,2,2]                       => 6
[5,2,2,2,2,1,1]                     => 7
[5,2,2,2,1,1,1,1]                   => 8
[5,2,2,1,1,1,1,1,1]                 => 9
[5,2,1,1,1,1,1,1,1,1]               => 10
[5,1,1,1,1,1,1,1,1,1,1]             => 11
[4,4,4,3]                           => 4
[4,4,4,2,1]                         => 5
[4,4,4,1,1,1]                       => 6
[4,4,3,3,1]                         => 5
[4,4,3,2,2]                         => 5
[4,4,3,2,1,1]                       => 6
[4,4,3,1,1,1,1]                     => 7
[4,4,2,2,2,1]                       => 6
[4,4,2,2,1,1,1]                     => 7
[4,4,2,1,1,1,1,1]                   => 8
[4,4,1,1,1,1,1,1,1]                 => 9
[4,3,3,3,2]                         => 5
[4,3,3,3,1,1]                       => 6
[4,3,3,2,2,1]                       => 6
[4,3,3,2,1,1,1]                     => 7
[4,3,3,1,1,1,1,1]                   => 8
[4,3,2,2,2,2]                       => 6
[4,3,2,2,2,1,1]                     => 7
[4,3,2,2,1,1,1,1]                   => 8
[4,3,2,1,1,1,1,1,1]                 => 9
[4,3,1,1,1,1,1,1,1,1]               => 10
[4,2,2,2,2,2,1]                     => 7
[4,2,2,2,2,1,1,1]                   => 8
[4,2,2,2,1,1,1,1,1]                 => 9
[4,2,2,1,1,1,1,1,1,1]               => 10
[4,2,1,1,1,1,1,1,1,1,1]             => 11
[4,1,1,1,1,1,1,1,1,1,1,1]           => 12
[3,3,3,3,3]                         => 5
[3,3,3,3,2,1]                       => 6
[3,3,3,3,1,1,1]                     => 7
[3,3,3,2,2,2]                       => 6
[3,3,3,2,2,1,1]                     => 7
[3,3,3,2,1,1,1,1]                   => 8
[3,3,3,1,1,1,1,1,1]                 => 9
[3,3,2,2,2,2,1]                     => 7
[3,3,2,2,2,1,1,1]                   => 8
[3,3,2,2,1,1,1,1,1]                 => 9
[3,3,2,1,1,1,1,1,1,1]               => 10
[3,3,1,1,1,1,1,1,1,1,1]             => 11
[3,2,2,2,2,2,2]                     => 7
[3,2,2,2,2,2,1,1]                   => 8
[3,2,2,2,2,1,1,1,1]                 => 9
[3,2,2,2,1,1,1,1,1,1]               => 10
[3,2,2,1,1,1,1,1,1,1,1]             => 11
[3,2,1,1,1,1,1,1,1,1,1,1]           => 12
[3,1,1,1,1,1,1,1,1,1,1,1,1]         => 13
[2,2,2,2,2,2,2,1]                   => 8
[2,2,2,2,2,2,1,1,1]                 => 9
[2,2,2,2,2,1,1,1,1,1]               => 10
[2,2,2,2,1,1,1,1,1,1,1]             => 11
[2,2,2,1,1,1,1,1,1,1,1,1]           => 12
[2,2,1,1,1,1,1,1,1,1,1,1,1]         => 13
[2,1,1,1,1,1,1,1,1,1,1,1,1,1]       => 14
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]     => 15
[16]                                => 1
[15,1]                              => 2
[14,2]                              => 2
[14,1,1]                            => 3
[13,3]                              => 2
[13,2,1]                            => 3
[13,1,1,1]                          => 4
[12,4]                              => 2
[12,3,1]                            => 3
[12,2,2]                            => 3
[12,2,1,1]                          => 4
[12,1,1,1,1]                        => 5
[11,5]                              => 2
[11,4,1]                            => 3
[11,3,2]                            => 3
[11,3,1,1]                          => 4
[11,2,2,1]                          => 4
[11,2,1,1,1]                        => 5
[11,1,1,1,1,1]                      => 6
[10,6]                              => 2
[10,5,1]                            => 3
[10,4,2]                            => 3
[10,4,1,1]                          => 4
[10,3,3]                            => 3
[10,3,2,1]                          => 4
[10,3,1,1,1]                        => 5
[10,2,2,2]                          => 4
[10,2,2,1,1]                        => 5
[10,2,1,1,1,1]                      => 6
[10,1,1,1,1,1,1]                    => 7
[9,7]                               => 2
[9,6,1]                             => 3
[9,5,2]                             => 3
[9,5,1,1]                           => 4
[9,4,3]                             => 3
[9,4,2,1]                           => 4
[9,4,1,1,1]                         => 5
[9,3,3,1]                           => 4
[9,3,2,2]                           => 4
[9,3,2,1,1]                         => 5
[9,3,1,1,1,1]                       => 6
[9,2,2,2,1]                         => 5
[9,2,2,1,1,1]                       => 6
[9,2,1,1,1,1,1]                     => 7
[9,1,1,1,1,1,1,1]                   => 8
[8,8]                               => 2
[8,7,1]                             => 3
[8,6,2]                             => 3
[8,6,1,1]                           => 4
[8,5,3]                             => 3
[8,5,2,1]                           => 4
[8,5,1,1,1]                         => 5
[8,4,4]                             => 3
[8,4,3,1]                           => 4
[8,4,2,2]                           => 4
[8,4,2,1,1]                         => 5
[8,4,1,1,1,1]                       => 6
[8,3,3,2]                           => 4
[8,3,3,1,1]                         => 5
[8,3,2,2,1]                         => 5
[8,3,2,1,1,1]                       => 6
[8,3,1,1,1,1,1]                     => 7
[8,2,2,2,2]                         => 5
[8,2,2,2,1,1]                       => 6
[8,2,2,1,1,1,1]                     => 7
[8,2,1,1,1,1,1,1]                   => 8
[8,1,1,1,1,1,1,1,1]                 => 9
[7,7,2]                             => 3
[7,7,1,1]                           => 4
[7,6,3]                             => 3
[7,6,2,1]                           => 4
[7,6,1,1,1]                         => 5
[7,5,4]                             => 3
[7,5,3,1]                           => 4
[7,5,2,2]                           => 4
[7,5,2,1,1]                         => 5
[7,5,1,1,1,1]                       => 6
[7,4,4,1]                           => 4
[7,4,3,2]                           => 4
[7,4,3,1,1]                         => 5
[7,4,2,2,1]                         => 5
[7,4,2,1,1,1]                       => 6
[7,4,1,1,1,1,1]                     => 7
[7,3,3,3]                           => 4
[7,3,3,2,1]                         => 5
[7,3,3,1,1,1]                       => 6
[7,3,2,2,2]                         => 5
[7,3,2,2,1,1]                       => 6
[7,3,2,1,1,1,1]                     => 7
[7,3,1,1,1,1,1,1]                   => 8
[7,2,2,2,2,1]                       => 6
[7,2,2,2,1,1,1]                     => 7
[7,2,2,1,1,1,1,1]                   => 8
[7,2,1,1,1,1,1,1,1]                 => 9
[7,1,1,1,1,1,1,1,1,1]               => 10
[6,6,4]                             => 3
[6,6,3,1]                           => 4
[6,6,2,2]                           => 4
[6,6,2,1,1]                         => 5
[6,6,1,1,1,1]                       => 6
[6,5,5]                             => 3
[6,5,4,1]                           => 4
[6,5,3,2]                           => 4
[6,5,3,1,1]                         => 5
[6,5,2,2,1]                         => 5
[6,5,2,1,1,1]                       => 6
[6,5,1,1,1,1,1]                     => 7
[6,4,4,2]                           => 4
[6,4,4,1,1]                         => 5
[6,4,3,3]                           => 4
[6,4,3,2,1]                         => 5
[6,4,3,1,1,1]                       => 6
[6,4,2,2,2]                         => 5
[6,4,2,2,1,1]                       => 6
[6,4,2,1,1,1,1]                     => 7
[6,4,1,1,1,1,1,1]                   => 8
[6,3,3,3,1]                         => 5
[6,3,3,2,2]                         => 5
[6,3,3,2,1,1]                       => 6
[6,3,3,1,1,1,1]                     => 7
[6,3,2,2,2,1]                       => 6
[6,3,2,2,1,1,1]                     => 7
[6,3,2,1,1,1,1,1]                   => 8
[6,3,1,1,1,1,1,1,1]                 => 9
[6,2,2,2,2,2]                       => 6
[6,2,2,2,2,1,1]                     => 7
[6,2,2,2,1,1,1,1]                   => 8
[6,2,2,1,1,1,1,1,1]                 => 9
[6,2,1,1,1,1,1,1,1,1]               => 10
[6,1,1,1,1,1,1,1,1,1,1]             => 11
[5,5,5,1]                           => 4
[5,5,4,2]                           => 4
[5,5,4,1,1]                         => 5
[5,5,3,3]                           => 4
[5,5,3,2,1]                         => 5
[5,5,3,1,1,1]                       => 6
[5,5,2,2,2]                         => 5
[5,5,2,2,1,1]                       => 6
[5,5,2,1,1,1,1]                     => 7
[5,5,1,1,1,1,1,1]                   => 8
[5,4,4,3]                           => 4
[5,4,4,2,1]                         => 5
[5,4,4,1,1,1]                       => 6
[5,4,3,3,1]                         => 5
[5,4,3,2,2]                         => 5
[5,4,3,2,1,1]                       => 6
[5,4,3,1,1,1,1]                     => 7
[5,4,2,2,2,1]                       => 6
[5,4,2,2,1,1,1]                     => 7
[5,4,2,1,1,1,1,1]                   => 8
[5,4,1,1,1,1,1,1,1]                 => 9
[5,3,3,3,2]                         => 5
[5,3,3,3,1,1]                       => 6
[5,3,3,2,2,1]                       => 6
[5,3,3,2,1,1,1]                     => 7
[5,3,3,1,1,1,1,1]                   => 8
[5,3,2,2,2,2]                       => 6
[5,3,2,2,2,1,1]                     => 7
[5,3,2,2,1,1,1,1]                   => 8
[5,3,2,1,1,1,1,1,1]                 => 9
[5,3,1,1,1,1,1,1,1,1]               => 10
[5,2,2,2,2,2,1]                     => 7
[5,2,2,2,2,1,1,1]                   => 8
[5,2,2,2,1,1,1,1,1]                 => 9
[5,2,2,1,1,1,1,1,1,1]               => 10
[5,2,1,1,1,1,1,1,1,1,1]             => 11
[5,1,1,1,1,1,1,1,1,1,1,1]           => 12
[4,4,4,4]                           => 4
[4,4,4,3,1]                         => 5
[4,4,4,2,2]                         => 5
[4,4,4,2,1,1]                       => 6
[4,4,4,1,1,1,1]                     => 7
[4,4,3,3,2]                         => 5
[4,4,3,3,1,1]                       => 6
[4,4,3,2,2,1]                       => 6
[4,4,3,2,1,1,1]                     => 7
[4,4,3,1,1,1,1,1]                   => 8
[4,4,2,2,2,2]                       => 6
[4,4,2,2,2,1,1]                     => 7
[4,4,2,2,1,1,1,1]                   => 8
[4,4,2,1,1,1,1,1,1]                 => 9
[4,4,1,1,1,1,1,1,1,1]               => 10
[4,3,3,3,3]                         => 5
[4,3,3,3,2,1]                       => 6
[4,3,3,3,1,1,1]                     => 7
[4,3,3,2,2,2]                       => 6
[4,3,3,2,2,1,1]                     => 7
[4,3,3,2,1,1,1,1]                   => 8
[4,3,3,1,1,1,1,1,1]                 => 9
[4,3,2,2,2,2,1]                     => 7
[4,3,2,2,2,1,1,1]                   => 8
[4,3,2,2,1,1,1,1,1]                 => 9
[4,3,2,1,1,1,1,1,1,1]               => 10
[4,3,1,1,1,1,1,1,1,1,1]             => 11
[4,2,2,2,2,2,2]                     => 7
[4,2,2,2,2,2,1,1]                   => 8
[4,2,2,2,2,1,1,1,1]                 => 9
[4,2,2,2,1,1,1,1,1,1]               => 10
[4,2,2,1,1,1,1,1,1,1,1]             => 11
[4,2,1,1,1,1,1,1,1,1,1,1]           => 12
[4,1,1,1,1,1,1,1,1,1,1,1,1]         => 13
[3,3,3,3,3,1]                       => 6
[3,3,3,3,2,2]                       => 6
[3,3,3,3,2,1,1]                     => 7
[3,3,3,3,1,1,1,1]                   => 8
[3,3,3,2,2,2,1]                     => 7
[3,3,3,2,2,1,1,1]                   => 8
[3,3,3,2,1,1,1,1,1]                 => 9
[3,3,3,1,1,1,1,1,1,1]               => 10
[3,3,2,2,2,2,2]                     => 7
[3,3,2,2,2,2,1,1]                   => 8
[3,3,2,2,2,1,1,1,1]                 => 9
[3,3,2,2,1,1,1,1,1,1]               => 10
[3,3,2,1,1,1,1,1,1,1,1]             => 11
[3,3,1,1,1,1,1,1,1,1,1,1]           => 12
[3,2,2,2,2,2,2,1]                   => 8
[3,2,2,2,2,2,1,1,1]                 => 9
[3,2,2,2,2,1,1,1,1,1]               => 10
[3,2,2,2,1,1,1,1,1,1,1]             => 11
[3,2,2,1,1,1,1,1,1,1,1,1]           => 12
[3,2,1,1,1,1,1,1,1,1,1,1,1]         => 13
[3,1,1,1,1,1,1,1,1,1,1,1,1,1]       => 14
[2,2,2,2,2,2,2,2]                   => 8
[2,2,2,2,2,2,2,1,1]                 => 9
[2,2,2,2,2,2,1,1,1,1]               => 10
[2,2,2,2,2,1,1,1,1,1,1]             => 11
[2,2,2,2,1,1,1,1,1,1,1,1]           => 12
[2,2,2,1,1,1,1,1,1,1,1,1,1]         => 13
[2,2,1,1,1,1,1,1,1,1,1,1,1,1]       => 14
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]     => 15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]   => 16
[17]                                => 1
[16,1]                              => 2
[15,2]                              => 2
[15,1,1]                            => 3
[14,3]                              => 2
[14,2,1]                            => 3
[14,1,1,1]                          => 4
[13,4]                              => 2
[13,3,1]                            => 3
[13,2,2]                            => 3
[13,2,1,1]                          => 4
[13,1,1,1,1]                        => 5
[12,5]                              => 2
[12,4,1]                            => 3
[12,3,2]                            => 3
[12,3,1,1]                          => 4
[12,2,2,1]                          => 4
[12,2,1,1,1]                        => 5
[12,1,1,1,1,1]                      => 6
[11,6]                              => 2
[11,5,1]                            => 3
[11,4,2]                            => 3
[11,4,1,1]                          => 4
[11,3,3]                            => 3
[11,3,2,1]                          => 4
[11,3,1,1,1]                        => 5
[11,2,2,2]                          => 4
[11,2,2,1,1]                        => 5
[11,2,1,1,1,1]                      => 6
[11,1,1,1,1,1,1]                    => 7
[10,7]                              => 2
[10,6,1]                            => 3
[10,5,2]                            => 3
[10,5,1,1]                          => 4
[10,4,3]                            => 3
[10,4,2,1]                          => 4
[10,4,1,1,1]                        => 5
[10,3,3,1]                          => 4
[10,3,2,2]                          => 4
[10,3,2,1,1]                        => 5
[10,3,1,1,1,1]                      => 6
[10,2,2,2,1]                        => 5
[10,2,2,1,1,1]                      => 6
[10,2,1,1,1,1,1]                    => 7
[10,1,1,1,1,1,1,1]                  => 8
[9,8]                               => 2
[9,7,1]                             => 3
[9,6,2]                             => 3
[9,6,1,1]                           => 4
[9,5,3]                             => 3
[9,5,2,1]                           => 4
[9,5,1,1,1]                         => 5
[9,4,4]                             => 3
[9,4,3,1]                           => 4
[9,4,2,2]                           => 4
[9,4,2,1,1]                         => 5
[9,4,1,1,1,1]                       => 6
[9,3,3,2]                           => 4
[9,3,3,1,1]                         => 5
[9,3,2,2,1]                         => 5
[9,3,2,1,1,1]                       => 6
[9,3,1,1,1,1,1]                     => 7
[9,2,2,2,2]                         => 5
[9,2,2,2,1,1]                       => 6
[9,2,2,1,1,1,1]                     => 7
[9,2,1,1,1,1,1,1]                   => 8
[9,1,1,1,1,1,1,1,1]                 => 9
[8,8,1]                             => 3
[8,7,2]                             => 3
[8,7,1,1]                           => 4
[8,6,3]                             => 3
[8,6,2,1]                           => 4
[8,6,1,1,1]                         => 5
[8,5,4]                             => 3
[8,5,3,1]                           => 4
[8,5,2,2]                           => 4
[8,5,2,1,1]                         => 5
[8,5,1,1,1,1]                       => 6
[8,4,4,1]                           => 4
[8,4,3,2]                           => 4
[8,4,3,1,1]                         => 5
[8,4,2,2,1]                         => 5
[8,4,2,1,1,1]                       => 6
[8,4,1,1,1,1,1]                     => 7
[8,3,3,3]                           => 4
[8,3,3,2,1]                         => 5
[8,3,3,1,1,1]                       => 6
[8,3,2,2,2]                         => 5
[8,3,2,2,1,1]                       => 6
[8,3,2,1,1,1,1]                     => 7
[8,3,1,1,1,1,1,1]                   => 8
[8,2,2,2,2,1]                       => 6
[8,2,2,2,1,1,1]                     => 7
[8,2,2,1,1,1,1,1]                   => 8
[8,2,1,1,1,1,1,1,1]                 => 9
[8,1,1,1,1,1,1,1,1,1]               => 10
[7,7,3]                             => 3
[7,7,2,1]                           => 4
[7,7,1,1,1]                         => 5
[7,6,4]                             => 3
[7,6,3,1]                           => 4
[7,6,2,2]                           => 4
[7,6,2,1,1]                         => 5
[7,6,1,1,1,1]                       => 6
[7,5,5]                             => 3
[7,5,4,1]                           => 4
[7,5,3,2]                           => 4
[7,5,3,1,1]                         => 5
[7,5,2,2,1]                         => 5
[7,5,2,1,1,1]                       => 6
[7,5,1,1,1,1,1]                     => 7
[7,4,4,2]                           => 4
[7,4,4,1,1]                         => 5
[7,4,3,3]                           => 4
[7,4,3,2,1]                         => 5
[7,4,3,1,1,1]                       => 6
[7,4,2,2,2]                         => 5
[7,4,2,2,1,1]                       => 6
[7,4,2,1,1,1,1]                     => 7
[7,4,1,1,1,1,1,1]                   => 8
[7,3,3,3,1]                         => 5
[7,3,3,2,2]                         => 5
[7,3,3,2,1,1]                       => 6
[7,3,3,1,1,1,1]                     => 7
[7,3,2,2,2,1]                       => 6
[7,3,2,2,1,1,1]                     => 7
[7,3,2,1,1,1,1,1]                   => 8
[7,3,1,1,1,1,1,1,1]                 => 9
[7,2,2,2,2,2]                       => 6
[7,2,2,2,2,1,1]                     => 7
[7,2,2,2,1,1,1,1]                   => 8
[7,2,2,1,1,1,1,1,1]                 => 9
[7,2,1,1,1,1,1,1,1,1]               => 10
[7,1,1,1,1,1,1,1,1,1,1]             => 11
[6,6,5]                             => 3
[6,6,4,1]                           => 4
[6,6,3,2]                           => 4
[6,6,3,1,1]                         => 5
[6,6,2,2,1]                         => 5
[6,6,2,1,1,1]                       => 6
[6,6,1,1,1,1,1]                     => 7
[6,5,5,1]                           => 4
[6,5,4,2]                           => 4
[6,5,4,1,1]                         => 5
[6,5,3,3]                           => 4
[6,5,3,2,1]                         => 5
[6,5,3,1,1,1]                       => 6
[6,5,2,2,2]                         => 5
[6,5,2,2,1,1]                       => 6
[6,5,2,1,1,1,1]                     => 7
[6,5,1,1,1,1,1,1]                   => 8
[6,4,4,3]                           => 4
[6,4,4,2,1]                         => 5
[6,4,4,1,1,1]                       => 6
[6,4,3,3,1]                         => 5
[6,4,3,2,2]                         => 5
[6,4,3,2,1,1]                       => 6
[6,4,3,1,1,1,1]                     => 7
[6,4,2,2,2,1]                       => 6
[6,4,2,2,1,1,1]                     => 7
[6,4,2,1,1,1,1,1]                   => 8
[6,4,1,1,1,1,1,1,1]                 => 9
[6,3,3,3,2]                         => 5
[6,3,3,3,1,1]                       => 6
[6,3,3,2,2,1]                       => 6
[6,3,3,2,1,1,1]                     => 7
[6,3,3,1,1,1,1,1]                   => 8
[6,3,2,2,2,2]                       => 6
[6,3,2,2,2,1,1]                     => 7
[6,3,2,2,1,1,1,1]                   => 8
[6,3,2,1,1,1,1,1,1]                 => 9
[6,3,1,1,1,1,1,1,1,1]               => 10
[6,2,2,2,2,2,1]                     => 7
[6,2,2,2,2,1,1,1]                   => 8
[6,2,2,2,1,1,1,1,1]                 => 9
[6,2,2,1,1,1,1,1,1,1]               => 10
[6,2,1,1,1,1,1,1,1,1,1]             => 11
[6,1,1,1,1,1,1,1,1,1,1,1]           => 12
[5,5,5,2]                           => 4
[5,5,5,1,1]                         => 5
[5,5,4,3]                           => 4
[5,5,4,2,1]                         => 5
[5,5,4,1,1,1]                       => 6
[5,5,3,3,1]                         => 5
[5,5,3,2,2]                         => 5
[5,5,3,2,1,1]                       => 6
[5,5,3,1,1,1,1]                     => 7
[5,5,2,2,2,1]                       => 6
[5,5,2,2,1,1,1]                     => 7
[5,5,2,1,1,1,1,1]                   => 8
[5,5,1,1,1,1,1,1,1]                 => 9
[5,4,4,4]                           => 4
[5,4,4,3,1]                         => 5
[5,4,4,2,2]                         => 5
[5,4,4,2,1,1]                       => 6
[5,4,4,1,1,1,1]                     => 7
[5,4,3,3,2]                         => 5
[5,4,3,3,1,1]                       => 6
[5,4,3,2,2,1]                       => 6
[5,4,3,2,1,1,1]                     => 7
[5,4,3,1,1,1,1,1]                   => 8
[5,4,2,2,2,2]                       => 6
[5,4,2,2,2,1,1]                     => 7
[5,4,2,2,1,1,1,1]                   => 8
[5,4,2,1,1,1,1,1,1]                 => 9
[5,4,1,1,1,1,1,1,1,1]               => 10
[5,3,3,3,3]                         => 5
[5,3,3,3,2,1]                       => 6
[5,3,3,3,1,1,1]                     => 7
[5,3,3,2,2,2]                       => 6
[5,3,3,2,2,1,1]                     => 7
[5,3,3,2,1,1,1,1]                   => 8
[5,3,3,1,1,1,1,1,1]                 => 9
[5,3,2,2,2,2,1]                     => 7
[5,3,2,2,2,1,1,1]                   => 8
[5,3,2,2,1,1,1,1,1]                 => 9
[5,3,2,1,1,1,1,1,1,1]               => 10
[5,3,1,1,1,1,1,1,1,1,1]             => 11
[5,2,2,2,2,2,2]                     => 7
[5,2,2,2,2,2,1,1]                   => 8
[5,2,2,2,2,1,1,1,1]                 => 9
[5,2,2,2,1,1,1,1,1,1]               => 10
[5,2,2,1,1,1,1,1,1,1,1]             => 11
[5,2,1,1,1,1,1,1,1,1,1,1]           => 12
[5,1,1,1,1,1,1,1,1,1,1,1,1]         => 13
[4,4,4,4,1]                         => 5
[4,4,4,3,2]                         => 5
[4,4,4,3,1,1]                       => 6
[4,4,4,2,2,1]                       => 6
[4,4,4,2,1,1,1]                     => 7
[4,4,4,1,1,1,1,1]                   => 8
[4,4,3,3,3]                         => 5
[4,4,3,3,2,1]                       => 6
[4,4,3,3,1,1,1]                     => 7
[4,4,3,2,2,2]                       => 6
[4,4,3,2,2,1,1]                     => 7
[4,4,3,2,1,1,1,1]                   => 8
[4,4,3,1,1,1,1,1,1]                 => 9
[4,4,2,2,2,2,1]                     => 7
[4,4,2,2,2,1,1,1]                   => 8
[4,4,2,2,1,1,1,1,1]                 => 9
[4,4,2,1,1,1,1,1,1,1]               => 10
[4,4,1,1,1,1,1,1,1,1,1]             => 11
[4,3,3,3,3,1]                       => 6
[4,3,3,3,2,2]                       => 6
[4,3,3,3,2,1,1]                     => 7
[4,3,3,3,1,1,1,1]                   => 8
[4,3,3,2,2,2,1]                     => 7
[4,3,3,2,2,1,1,1]                   => 8
[4,3,3,2,1,1,1,1,1]                 => 9
[4,3,3,1,1,1,1,1,1,1]               => 10
[4,3,2,2,2,2,2]                     => 7
[4,3,2,2,2,2,1,1]                   => 8
[4,3,2,2,2,1,1,1,1]                 => 9
[4,3,2,2,1,1,1,1,1,1]               => 10
[4,3,2,1,1,1,1,1,1,1,1]             => 11
[4,3,1,1,1,1,1,1,1,1,1,1]           => 12
[4,2,2,2,2,2,2,1]                   => 8
[4,2,2,2,2,2,1,1,1]                 => 9
[4,2,2,2,2,1,1,1,1,1]               => 10
[4,2,2,2,1,1,1,1,1,1,1]             => 11
[4,2,2,1,1,1,1,1,1,1,1,1]           => 12
[4,2,1,1,1,1,1,1,1,1,1,1,1]         => 13
[4,1,1,1,1,1,1,1,1,1,1,1,1,1]       => 14
[3,3,3,3,3,2]                       => 6
[3,3,3,3,3,1,1]                     => 7
[3,3,3,3,2,2,1]                     => 7
[3,3,3,3,2,1,1,1]                   => 8
[3,3,3,3,1,1,1,1,1]                 => 9
[3,3,3,2,2,2,2]                     => 7
[3,3,3,2,2,2,1,1]                   => 8
[3,3,3,2,2,1,1,1,1]                 => 9
[3,3,3,2,1,1,1,1,1,1]               => 10
[3,3,3,1,1,1,1,1,1,1,1]             => 11
[3,3,2,2,2,2,2,1]                   => 8
[3,3,2,2,2,2,1,1,1]                 => 9
[3,3,2,2,2,1,1,1,1,1]               => 10
[3,3,2,2,1,1,1,1,1,1,1]             => 11
[3,3,2,1,1,1,1,1,1,1,1,1]           => 12
[3,3,1,1,1,1,1,1,1,1,1,1,1]         => 13
[3,2,2,2,2,2,2,2]                   => 8
[3,2,2,2,2,2,2,1,1]                 => 9
[3,2,2,2,2,2,1,1,1,1]               => 10
[3,2,2,2,2,1,1,1,1,1,1]             => 11
[3,2,2,2,1,1,1,1,1,1,1,1]           => 12
[3,2,2,1,1,1,1,1,1,1,1,1,1]         => 13
[3,2,1,1,1,1,1,1,1,1,1,1,1,1]       => 14
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]     => 15
[2,2,2,2,2,2,2,2,1]                 => 9
[2,2,2,2,2,2,2,1,1,1]               => 10
[2,2,2,2,2,2,1,1,1,1,1]             => 11
[2,2,2,2,2,1,1,1,1,1,1,1]           => 12
[2,2,2,2,1,1,1,1,1,1,1,1,1]         => 13
[2,2,2,1,1,1,1,1,1,1,1,1,1,1]       => 14
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]     => 15
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]   => 16
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 17

-----------------------------------------------------------------------------
Created: Sep 22, 2011 at 17:49 by Chris Berg

-----------------------------------------------------------------------------
Last Updated: Dec 22, 2020 at 14:37 by Martin Rubey