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

------------------------------------------------------------------------
Map identifier: Mp00103

------------------------------------------------------------------------
Map name: peeling map

------------------------------------------------------------------------
Domain: Dyck paths

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

------------------------------------------------------------------------
Description: Send a Dyck path to its peeled Dyck path.

------------------------------------------------------------------------
References: [1]   Stump, C. More bijective Catalan combinatorics on permutations and on signed permutations [[MathSciNet:3153083]]

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

def mapping(D):
    n = D.semilength()
    area = D.to_area_sequence()
    new_area = []
    touch_sequences = []
    touches = []
    for i in range(n-1):
        if area[i+1] == 0:
            touches.append(i+1)
            if len(touches) > 1:
                touch_sequences.append(touches)
                touches = []
            elif area[i] == 0:
                touches = []
            new_area.append(0)
        elif area[i+1] == 1:
            new_area.append(0)
            touches.append(i+1)
        else:
            new_area.append(area[i+1]-2)
    new_area.append(0)
    if area[n - 1] != 0:
        touches.append(n)
        if len(touches) > 1:
            touch_sequences.append(touches)
    return DyckWords().from_area_sequence(new_area)


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

[1,0]                             => [1,0]
[1,0,1,0]                         => [1,0,1,0]
[1,1,0,0]                         => [1,0,1,0]
[1,0,1,0,1,0]                     => [1,0,1,0,1,0]
[1,0,1,1,0,0]                     => [1,0,1,0,1,0]
[1,1,0,0,1,0]                     => [1,0,1,0,1,0]
[1,1,0,1,0,0]                     => [1,0,1,0,1,0]
[1,1,1,0,0,0]                     => [1,0,1,0,1,0]
[1,0,1,0,1,0,1,0]                 => [1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0]                 => [1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0]                 => [1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0]                 => [1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0]                 => [1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0]                 => [1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0]                 => [1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0]                 => [1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0]                 => [1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0]                 => [1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0]                 => [1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0]                 => [1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0]                 => [1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0]                 => [1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0]             => [1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0]             => [1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0]             => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0]             => [1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0]             => [1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0]             => [1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0]             => [1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0]             => [1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0]             => [1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0]         => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0]         => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0]         => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0]         => [1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0]         => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0]         => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0]         => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0]         => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0]         => [1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0]         => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0]         => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0]         => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0]         => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0]         => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0]         => [1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0]         => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0]         => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0]         => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0]         => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0]         => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0]         => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0]         => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0]         => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0]         => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0]         => [1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0]         => [1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0]         => [1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0]         => [1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0]         => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0]         => [1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0]         => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0]         => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0]         => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0]         => [1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0]         => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0]         => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]     => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]     => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]     => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]     => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]     => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]     => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]     => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]     => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]     => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]     => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]     => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]     => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]     => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]     => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]     => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]     => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]     => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]     => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]     => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]     => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]     => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]     => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]     => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]     => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]     => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]     => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]     => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]     => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]     => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]     => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]     => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]     => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]     => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]     => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]     => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]     => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]     => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]     => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]     => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]     => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]     => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]     => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]     => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]     => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]     => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]     => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]     => [1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]     => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]     => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]     => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]     => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]     => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]     => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]     => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]     => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]     => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]     => [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]     => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]     => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]     => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]     => [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]     => [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]     => [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]     => [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]     => [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]     => [1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]     => [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]     => [1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]     => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]     => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]     => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]     => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]     => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]     => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]     => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]     => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]     => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]     => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]     => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]     => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]     => [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]     => [1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]     => [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]     => [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]     => [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]     => [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]     => [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]     => [1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]     => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]     => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]     => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]     => [1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]     => [1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]     => [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]     => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]

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Created: Jan 29, 2020 at 13:25 by FindStatCrew

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Last Updated: May 11, 2021 at 15:01 by Martin Rubey