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*    www.FindStat.org - The Combinatorial Statistic Finder             *
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------------------------------------------------------------------------
Map identifier: Mp00179

------------------------------------------------------------------------
Map name: to skew partition

------------------------------------------------------------------------
Domain: Integer partitions

------------------------------------------------------------------------
Codomain: Skew partitions

------------------------------------------------------------------------
Description: The partition regarded as a skew partition.

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

------------------------------------------------------------------------
Code:

def mapping(la):
    return SkewPartition((la, []))

------------------------------------------------------------------------
Map images:

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

-----------------------------------------------------------------------------
Created: Sep 22, 2020 at 11:07 by Martin Rubey

-----------------------------------------------------------------------------
Last Updated: Sep 22, 2020 at 11:07 by Martin Rubey