************************************************************************
*    www.FindStat.org - The Combinatorial Statistic Finder             *
*                                                                      *
*    Copyright (C) 2013 The FindStatCrew <info@findstat.org>           *
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*    useful, but WITHOUT ANY WARRANTY; without even the implied        *
*    warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  *
************************************************************************

------------------------------------------------------------------------
Map identifier: Mp00043

------------------------------------------------------------------------
Map name: to Dyck path

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

------------------------------------------------------------------------
Codomain: Dyck paths

------------------------------------------------------------------------
Description: Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.

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

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

def mapping(elt):
    return elt.to_dyck_word()

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

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

-----------------------------------------------------------------------------
Created: Jan 19, 2020 at 07:28 by FindStatCrew

-----------------------------------------------------------------------------
Last Updated: Jan 19, 2020 at 07:28 by Martin Rubey