************************************************************************
*    www.FindStat.org - The Combinatorial Statistic Finder             *
*                                                                      *
*    Copyright (C) 2013 The FindStatCrew <info@findstat.org>           *
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************************************************************************

------------------------------------------------------------------------
Map identifier: Mp00127

------------------------------------------------------------------------
Map name: left-to-right-maxima to Dyck path

------------------------------------------------------------------------
Domain: Permutations

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

------------------------------------------------------------------------
Description: The left-to-right maxima of a permutation as a Dyck path.

Let $(c_1, \dots, c_k)$ be the rise composition [[Mp00102]] of the path.  Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.

Restricted to 321-avoiding permutations, this is the inverse of [[Mp00119]], restricted to 312-avoiding permutations, this is the inverse of [[Mp00031]].

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

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

def mapping(pi):
    l = [(0,0)]
    for i, e in enumerate(pi):
        if e > l[-1][1]:
            l.append((i,e))
    l.append((len(pi), len(pi)))
    D = []
    for i in range(len(l)-2):
        D.extend([1]*(l[i+1][1]-l[i][1])+[0]*(l[i+2][0]-l[i+1][0]))
    return DyckWord(D)

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

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

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Created: Jan 29, 2020 at 13:26 by FindStatCrew

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Last Updated: Jun 07, 2023 at 13:40 by Martin Rubey