************************************************************************
*    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: Mp00267

------------------------------------------------------------------------
Map name: signs

------------------------------------------------------------------------
Domain: Signed permutations

------------------------------------------------------------------------
Codomain: Binary words

------------------------------------------------------------------------
Description: The binary word recording the signs of a signed permutation.

This map sends a signed permutation $\pi\in\mathfrak H_n$ to the binary word $w$ of length $n$ such that $w_i = 0$ if $\pi(i) > 0$.

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

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

def mapping(pi):
    return Words([0, 1], len(pi))([0 if e > 0 else 1 for e in pi])

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

[1]              => 0
[-1]             => 1
[1,2]            => 00
[1,-2]           => 01
[-1,2]           => 10
[-1,-2]          => 11
[2,1]            => 00
[2,-1]           => 01
[-2,1]           => 10
[-2,-1]          => 11
[1,2,3]          => 000
[1,2,-3]         => 001
[1,-2,3]         => 010
[1,-2,-3]        => 011
[-1,2,3]         => 100
[-1,2,-3]        => 101
[-1,-2,3]        => 110
[-1,-2,-3]       => 111
[1,3,2]          => 000
[1,3,-2]         => 001
[1,-3,2]         => 010
[1,-3,-2]        => 011
[-1,3,2]         => 100
[-1,3,-2]        => 101
[-1,-3,2]        => 110
[-1,-3,-2]       => 111
[2,1,3]          => 000
[2,1,-3]         => 001
[2,-1,3]         => 010
[2,-1,-3]        => 011
[-2,1,3]         => 100
[-2,1,-3]        => 101
[-2,-1,3]        => 110
[-2,-1,-3]       => 111
[2,3,1]          => 000
[2,3,-1]         => 001
[2,-3,1]         => 010
[2,-3,-1]        => 011
[-2,3,1]         => 100
[-2,3,-1]        => 101
[-2,-3,1]        => 110
[-2,-3,-1]       => 111
[3,1,2]          => 000
[3,1,-2]         => 001
[3,-1,2]         => 010
[3,-1,-2]        => 011
[-3,1,2]         => 100
[-3,1,-2]        => 101
[-3,-1,2]        => 110
[-3,-1,-2]       => 111
[3,2,1]          => 000
[3,2,-1]         => 001
[3,-2,1]         => 010
[3,-2,-1]        => 011
[-3,2,1]         => 100
[-3,2,-1]        => 101
[-3,-2,1]        => 110
[-3,-2,-1]       => 111
[1,2,3,4]        => 0000
[1,2,3,-4]       => 0001
[1,2,-3,4]       => 0010
[1,2,-3,-4]      => 0011
[1,-2,3,4]       => 0100
[1,-2,3,-4]      => 0101
[1,-2,-3,4]      => 0110
[1,-2,-3,-4]     => 0111
[-1,2,3,4]       => 1000
[-1,2,3,-4]      => 1001
[-1,2,-3,4]      => 1010
[-1,2,-3,-4]     => 1011
[-1,-2,3,4]      => 1100
[-1,-2,3,-4]     => 1101
[-1,-2,-3,4]     => 1110
[-1,-2,-3,-4]    => 1111
[1,2,4,3]        => 0000
[1,2,4,-3]       => 0001
[1,2,-4,3]       => 0010
[1,2,-4,-3]      => 0011
[1,-2,4,3]       => 0100
[1,-2,4,-3]      => 0101
[1,-2,-4,3]      => 0110
[1,-2,-4,-3]     => 0111
[-1,2,4,3]       => 1000
[-1,2,4,-3]      => 1001
[-1,2,-4,3]      => 1010
[-1,2,-4,-3]     => 1011
[-1,-2,4,3]      => 1100
[-1,-2,4,-3]     => 1101
[-1,-2,-4,3]     => 1110
[-1,-2,-4,-3]    => 1111
[1,3,2,4]        => 0000
[1,3,2,-4]       => 0001
[1,3,-2,4]       => 0010
[1,3,-2,-4]      => 0011
[1,-3,2,4]       => 0100
[1,-3,2,-4]      => 0101
[1,-3,-2,4]      => 0110
[1,-3,-2,-4]     => 0111
[-1,3,2,4]       => 1000
[-1,3,2,-4]      => 1001
[-1,3,-2,4]      => 1010
[-1,3,-2,-4]     => 1011
[-1,-3,2,4]      => 1100
[-1,-3,2,-4]     => 1101
[-1,-3,-2,4]     => 1110
[-1,-3,-2,-4]    => 1111
[1,3,4,2]        => 0000
[1,3,4,-2]       => 0001
[1,3,-4,2]       => 0010
[1,3,-4,-2]      => 0011
[1,-3,4,2]       => 0100
[1,-3,4,-2]      => 0101
[1,-3,-4,2]      => 0110
[1,-3,-4,-2]     => 0111
[-1,3,4,2]       => 1000
[-1,3,4,-2]      => 1001
[-1,3,-4,2]      => 1010
[-1,3,-4,-2]     => 1011
[-1,-3,4,2]      => 1100
[-1,-3,4,-2]     => 1101
[-1,-3,-4,2]     => 1110
[-1,-3,-4,-2]    => 1111
[1,4,2,3]        => 0000
[1,4,2,-3]       => 0001
[1,4,-2,3]       => 0010
[1,4,-2,-3]      => 0011
[1,-4,2,3]       => 0100
[1,-4,2,-3]      => 0101
[1,-4,-2,3]      => 0110
[1,-4,-2,-3]     => 0111
[-1,4,2,3]       => 1000
[-1,4,2,-3]      => 1001
[-1,4,-2,3]      => 1010
[-1,4,-2,-3]     => 1011
[-1,-4,2,3]      => 1100
[-1,-4,2,-3]     => 1101
[-1,-4,-2,3]     => 1110
[-1,-4,-2,-3]    => 1111
[1,4,3,2]        => 0000
[1,4,3,-2]       => 0001
[1,4,-3,2]       => 0010
[1,4,-3,-2]      => 0011
[1,-4,3,2]       => 0100
[1,-4,3,-2]      => 0101
[1,-4,-3,2]      => 0110
[1,-4,-3,-2]     => 0111
[-1,4,3,2]       => 1000
[-1,4,3,-2]      => 1001
[-1,4,-3,2]      => 1010
[-1,4,-3,-2]     => 1011
[-1,-4,3,2]      => 1100
[-1,-4,3,-2]     => 1101
[-1,-4,-3,2]     => 1110
[-1,-4,-3,-2]    => 1111
[2,1,3,4]        => 0000
[2,1,3,-4]       => 0001
[2,1,-3,4]       => 0010
[2,1,-3,-4]      => 0011
[2,-1,3,4]       => 0100
[2,-1,3,-4]      => 0101
[2,-1,-3,4]      => 0110
[2,-1,-3,-4]     => 0111
[-2,1,3,4]       => 1000
[-2,1,3,-4]      => 1001
[-2,1,-3,4]      => 1010
[-2,1,-3,-4]     => 1011
[-2,-1,3,4]      => 1100
[-2,-1,3,-4]     => 1101
[-2,-1,-3,4]     => 1110
[-2,-1,-3,-4]    => 1111
[2,1,4,3]        => 0000
[2,1,4,-3]       => 0001
[2,1,-4,3]       => 0010
[2,1,-4,-3]      => 0011
[2,-1,4,3]       => 0100
[2,-1,4,-3]      => 0101
[2,-1,-4,3]      => 0110
[2,-1,-4,-3]     => 0111
[-2,1,4,3]       => 1000
[-2,1,4,-3]      => 1001
[-2,1,-4,3]      => 1010
[-2,1,-4,-3]     => 1011
[-2,-1,4,3]      => 1100
[-2,-1,4,-3]     => 1101
[-2,-1,-4,3]     => 1110
[-2,-1,-4,-3]    => 1111
[2,3,1,4]        => 0000
[2,3,1,-4]       => 0001
[2,3,-1,4]       => 0010
[2,3,-1,-4]      => 0011
[2,-3,1,4]       => 0100
[2,-3,1,-4]      => 0101
[2,-3,-1,4]      => 0110
[2,-3,-1,-4]     => 0111
[-2,3,1,4]       => 1000
[-2,3,1,-4]      => 1001
[-2,3,-1,4]      => 1010
[-2,3,-1,-4]     => 1011
[-2,-3,1,4]      => 1100
[-2,-3,1,-4]     => 1101
[-2,-3,-1,4]     => 1110
[-2,-3,-1,-4]    => 1111
[2,3,4,1]        => 0000
[2,3,4,-1]       => 0001
[2,3,-4,1]       => 0010
[2,3,-4,-1]      => 0011
[2,-3,4,1]       => 0100
[2,-3,4,-1]      => 0101
[2,-3,-4,1]      => 0110
[2,-3,-4,-1]     => 0111
[-2,3,4,1]       => 1000
[-2,3,4,-1]      => 1001
[-2,3,-4,1]      => 1010
[-2,3,-4,-1]     => 1011
[-2,-3,4,1]      => 1100
[-2,-3,4,-1]     => 1101
[-2,-3,-4,1]     => 1110
[-2,-3,-4,-1]    => 1111
[2,4,1,3]        => 0000
[2,4,1,-3]       => 0001
[2,4,-1,3]       => 0010
[2,4,-1,-3]      => 0011
[2,-4,1,3]       => 0100
[2,-4,1,-3]      => 0101
[2,-4,-1,3]      => 0110
[2,-4,-1,-3]     => 0111
[-2,4,1,3]       => 1000
[-2,4,1,-3]      => 1001
[-2,4,-1,3]      => 1010
[-2,4,-1,-3]     => 1011
[-2,-4,1,3]      => 1100
[-2,-4,1,-3]     => 1101
[-2,-4,-1,3]     => 1110
[-2,-4,-1,-3]    => 1111
[2,4,3,1]        => 0000
[2,4,3,-1]       => 0001
[2,4,-3,1]       => 0010
[2,4,-3,-1]      => 0011
[2,-4,3,1]       => 0100
[2,-4,3,-1]      => 0101
[2,-4,-3,1]      => 0110
[2,-4,-3,-1]     => 0111
[-2,4,3,1]       => 1000
[-2,4,3,-1]      => 1001
[-2,4,-3,1]      => 1010
[-2,4,-3,-1]     => 1011
[-2,-4,3,1]      => 1100
[-2,-4,3,-1]     => 1101
[-2,-4,-3,1]     => 1110
[-2,-4,-3,-1]    => 1111
[3,1,2,4]        => 0000
[3,1,2,-4]       => 0001
[3,1,-2,4]       => 0010
[3,1,-2,-4]      => 0011
[3,-1,2,4]       => 0100
[3,-1,2,-4]      => 0101
[3,-1,-2,4]      => 0110
[3,-1,-2,-4]     => 0111
[-3,1,2,4]       => 1000
[-3,1,2,-4]      => 1001
[-3,1,-2,4]      => 1010
[-3,1,-2,-4]     => 1011
[-3,-1,2,4]      => 1100
[-3,-1,2,-4]     => 1101
[-3,-1,-2,4]     => 1110
[-3,-1,-2,-4]    => 1111
[3,1,4,2]        => 0000
[3,1,4,-2]       => 0001
[3,1,-4,2]       => 0010
[3,1,-4,-2]      => 0011
[3,-1,4,2]       => 0100
[3,-1,4,-2]      => 0101
[3,-1,-4,2]      => 0110
[3,-1,-4,-2]     => 0111
[-3,1,4,2]       => 1000
[-3,1,4,-2]      => 1001
[-3,1,-4,2]      => 1010
[-3,1,-4,-2]     => 1011
[-3,-1,4,2]      => 1100
[-3,-1,4,-2]     => 1101
[-3,-1,-4,2]     => 1110
[-3,-1,-4,-2]    => 1111
[3,2,1,4]        => 0000
[3,2,1,-4]       => 0001
[3,2,-1,4]       => 0010
[3,2,-1,-4]      => 0011
[3,-2,1,4]       => 0100
[3,-2,1,-4]      => 0101
[3,-2,-1,4]      => 0110
[3,-2,-1,-4]     => 0111
[-3,2,1,4]       => 1000
[-3,2,1,-4]      => 1001
[-3,2,-1,4]      => 1010
[-3,2,-1,-4]     => 1011
[-3,-2,1,4]      => 1100
[-3,-2,1,-4]     => 1101
[-3,-2,-1,4]     => 1110
[-3,-2,-1,-4]    => 1111
[3,2,4,1]        => 0000
[3,2,4,-1]       => 0001
[3,2,-4,1]       => 0010
[3,2,-4,-1]      => 0011
[3,-2,4,1]       => 0100
[3,-2,4,-1]      => 0101
[3,-2,-4,1]      => 0110
[3,-2,-4,-1]     => 0111
[-3,2,4,1]       => 1000
[-3,2,4,-1]      => 1001
[-3,2,-4,1]      => 1010
[-3,2,-4,-1]     => 1011
[-3,-2,4,1]      => 1100
[-3,-2,4,-1]     => 1101
[-3,-2,-4,1]     => 1110
[-3,-2,-4,-1]    => 1111
[3,4,1,2]        => 0000
[3,4,1,-2]       => 0001
[3,4,-1,2]       => 0010
[3,4,-1,-2]      => 0011
[3,-4,1,2]       => 0100
[3,-4,1,-2]      => 0101
[3,-4,-1,2]      => 0110
[3,-4,-1,-2]     => 0111
[-3,4,1,2]       => 1000
[-3,4,1,-2]      => 1001
[-3,4,-1,2]      => 1010
[-3,4,-1,-2]     => 1011
[-3,-4,1,2]      => 1100
[-3,-4,1,-2]     => 1101
[-3,-4,-1,2]     => 1110
[-3,-4,-1,-2]    => 1111
[3,4,2,1]        => 0000
[3,4,2,-1]       => 0001
[3,4,-2,1]       => 0010
[3,4,-2,-1]      => 0011
[3,-4,2,1]       => 0100
[3,-4,2,-1]      => 0101
[3,-4,-2,1]      => 0110
[3,-4,-2,-1]     => 0111
[-3,4,2,1]       => 1000
[-3,4,2,-1]      => 1001
[-3,4,-2,1]      => 1010
[-3,4,-2,-1]     => 1011
[-3,-4,2,1]      => 1100
[-3,-4,2,-1]     => 1101
[-3,-4,-2,1]     => 1110
[-3,-4,-2,-1]    => 1111
[4,1,2,3]        => 0000
[4,1,2,-3]       => 0001
[4,1,-2,3]       => 0010
[4,1,-2,-3]      => 0011
[4,-1,2,3]       => 0100
[4,-1,2,-3]      => 0101
[4,-1,-2,3]      => 0110
[4,-1,-2,-3]     => 0111
[-4,1,2,3]       => 1000
[-4,1,2,-3]      => 1001
[-4,1,-2,3]      => 1010
[-4,1,-2,-3]     => 1011
[-4,-1,2,3]      => 1100
[-4,-1,2,-3]     => 1101
[-4,-1,-2,3]     => 1110
[-4,-1,-2,-3]    => 1111
[4,1,3,2]        => 0000
[4,1,3,-2]       => 0001
[4,1,-3,2]       => 0010
[4,1,-3,-2]      => 0011
[4,-1,3,2]       => 0100
[4,-1,3,-2]      => 0101
[4,-1,-3,2]      => 0110
[4,-1,-3,-2]     => 0111
[-4,1,3,2]       => 1000
[-4,1,3,-2]      => 1001
[-4,1,-3,2]      => 1010
[-4,1,-3,-2]     => 1011
[-4,-1,3,2]      => 1100
[-4,-1,3,-2]     => 1101
[-4,-1,-3,2]     => 1110
[-4,-1,-3,-2]    => 1111
[4,2,1,3]        => 0000
[4,2,1,-3]       => 0001
[4,2,-1,3]       => 0010
[4,2,-1,-3]      => 0011
[4,-2,1,3]       => 0100
[4,-2,1,-3]      => 0101
[4,-2,-1,3]      => 0110
[4,-2,-1,-3]     => 0111
[-4,2,1,3]       => 1000
[-4,2,1,-3]      => 1001
[-4,2,-1,3]      => 1010
[-4,2,-1,-3]     => 1011
[-4,-2,1,3]      => 1100
[-4,-2,1,-3]     => 1101
[-4,-2,-1,3]     => 1110
[-4,-2,-1,-3]    => 1111
[4,2,3,1]        => 0000
[4,2,3,-1]       => 0001
[4,2,-3,1]       => 0010
[4,2,-3,-1]      => 0011
[4,-2,3,1]       => 0100
[4,-2,3,-1]      => 0101
[4,-2,-3,1]      => 0110
[4,-2,-3,-1]     => 0111
[-4,2,3,1]       => 1000
[-4,2,3,-1]      => 1001
[-4,2,-3,1]      => 1010
[-4,2,-3,-1]     => 1011
[-4,-2,3,1]      => 1100
[-4,-2,3,-1]     => 1101
[-4,-2,-3,1]     => 1110
[-4,-2,-3,-1]    => 1111
[4,3,1,2]        => 0000
[4,3,1,-2]       => 0001
[4,3,-1,2]       => 0010
[4,3,-1,-2]      => 0011
[4,-3,1,2]       => 0100
[4,-3,1,-2]      => 0101
[4,-3,-1,2]      => 0110
[4,-3,-1,-2]     => 0111
[-4,3,1,2]       => 1000
[-4,3,1,-2]      => 1001
[-4,3,-1,2]      => 1010
[-4,3,-1,-2]     => 1011
[-4,-3,1,2]      => 1100
[-4,-3,1,-2]     => 1101
[-4,-3,-1,2]     => 1110
[-4,-3,-1,-2]    => 1111
[4,3,2,1]        => 0000
[4,3,2,-1]       => 0001
[4,3,-2,1]       => 0010
[4,3,-2,-1]      => 0011
[4,-3,2,1]       => 0100
[4,-3,2,-1]      => 0101
[4,-3,-2,1]      => 0110
[4,-3,-2,-1]     => 0111
[-4,3,2,1]       => 1000
[-4,3,2,-1]      => 1001
[-4,3,-2,1]      => 1010
[-4,3,-2,-1]     => 1011
[-4,-3,2,1]      => 1100
[-4,-3,2,-1]     => 1101
[-4,-3,-2,1]     => 1110
[-4,-3,-2,-1]    => 1111
[1,2,3,4,5]      => 00000
[1,2,3,4,-5]     => 00001
[1,2,3,-4,5]     => 00010
[1,2,3,-4,-5]    => 00011
[1,2,-3,4,5]     => 00100
[1,2,-3,4,-5]    => 00101
[1,2,-3,-4,5]    => 00110
[1,2,-3,-4,-5]   => 00111
[1,-2,3,4,5]     => 01000
[1,-2,3,4,-5]    => 01001
[1,-2,3,-4,5]    => 01010
[1,-2,3,-4,-5]   => 01011
[1,-2,-3,4,5]    => 01100
[1,-2,-3,4,-5]   => 01101
[1,-2,-3,-4,5]   => 01110
[1,-2,-3,-4,-5]  => 01111
[-1,2,3,4,5]     => 10000
[-1,2,3,4,-5]    => 10001
[-1,2,3,-4,5]    => 10010
[-1,2,3,-4,-5]   => 10011
[-1,2,-3,4,5]    => 10100
[-1,2,-3,4,-5]   => 10101
[-1,2,-3,-4,5]   => 10110
[-1,2,-3,-4,-5]  => 10111
[-1,-2,3,4,5]    => 11000
[-1,-2,3,4,-5]   => 11001
[-1,-2,3,-4,5]   => 11010
[-1,-2,3,-4,-5]  => 11011
[-1,-2,-3,4,5]   => 11100
[-1,-2,-3,4,-5]  => 11101
[-1,-2,-3,-4,5]  => 11110
[-1,-2,-3,-4,-5] => 11111
[1,2,3,5,4]      => 00000
[1,2,3,5,-4]     => 00001
[1,2,3,-5,4]     => 00010
[1,2,3,-5,-4]    => 00011
[1,2,-3,5,4]     => 00100
[1,2,-3,5,-4]    => 00101
[1,2,-3,-5,4]    => 00110
[1,2,-3,-5,-4]   => 00111
[1,-2,3,5,4]     => 01000
[1,-2,3,5,-4]    => 01001
[1,-2,3,-5,4]    => 01010
[1,-2,3,-5,-4]   => 01011
[1,-2,-3,5,4]    => 01100
[1,-2,-3,5,-4]   => 01101
[1,-2,-3,-5,4]   => 01110
[1,-2,-3,-5,-4]  => 01111
[-1,2,3,5,4]     => 10000
[-1,2,3,5,-4]    => 10001
[-1,2,3,-5,4]    => 10010
[-1,2,3,-5,-4]   => 10011
[-1,2,-3,5,4]    => 10100
[-1,2,-3,5,-4]   => 10101
[-1,2,-3,-5,4]   => 10110
[-1,2,-3,-5,-4]  => 10111
[-1,-2,3,5,4]    => 11000
[-1,-2,3,5,-4]   => 11001
[-1,-2,3,-5,4]   => 11010
[-1,-2,3,-5,-4]  => 11011
[-1,-2,-3,5,4]   => 11100
[-1,-2,-3,5,-4]  => 11101
[-1,-2,-3,-5,4]  => 11110
[-1,-2,-3,-5,-4] => 11111
[1,2,4,3,5]      => 00000
[1,2,4,3,-5]     => 00001
[1,2,4,-3,5]     => 00010
[1,2,4,-3,-5]    => 00011
[1,2,-4,3,5]     => 00100
[1,2,-4,3,-5]    => 00101
[1,2,-4,-3,5]    => 00110
[1,2,-4,-3,-5]   => 00111
[1,-2,4,3,5]     => 01000
[1,-2,4,3,-5]    => 01001
[1,-2,4,-3,5]    => 01010
[1,-2,4,-3,-5]   => 01011
[1,-2,-4,3,5]    => 01100
[1,-2,-4,3,-5]   => 01101
[1,-2,-4,-3,5]   => 01110
[1,-2,-4,-3,-5]  => 01111
[-1,2,4,3,5]     => 10000
[-1,2,4,3,-5]    => 10001
[-1,2,4,-3,5]    => 10010
[-1,2,4,-3,-5]   => 10011
[-1,2,-4,3,5]    => 10100
[-1,2,-4,3,-5]   => 10101
[-1,2,-4,-3,5]   => 10110
[-1,2,-4,-3,-5]  => 10111
[-1,-2,4,3,5]    => 11000
[-1,-2,4,3,-5]   => 11001
[-1,-2,4,-3,5]   => 11010
[-1,-2,4,-3,-5]  => 11011
[-1,-2,-4,3,5]   => 11100
[-1,-2,-4,3,-5]  => 11101
[-1,-2,-4,-3,5]  => 11110
[-1,-2,-4,-3,-5] => 11111
[1,2,4,5,3]      => 00000
[1,2,4,5,-3]     => 00001
[1,2,4,-5,3]     => 00010
[1,2,4,-5,-3]    => 00011
[1,2,-4,5,3]     => 00100
[1,2,-4,5,-3]    => 00101
[1,2,-4,-5,3]    => 00110
[1,2,-4,-5,-3]   => 00111
[1,-2,4,5,3]     => 01000
[1,-2,4,5,-3]    => 01001
[1,-2,4,-5,3]    => 01010
[1,-2,4,-5,-3]   => 01011
[1,-2,-4,5,3]    => 01100
[1,-2,-4,5,-3]   => 01101
[1,-2,-4,-5,3]   => 01110
[1,-2,-4,-5,-3]  => 01111
[-1,2,4,5,3]     => 10000
[-1,2,4,5,-3]    => 10001
[-1,2,4,-5,3]    => 10010
[-1,2,4,-5,-3]   => 10011
[-1,2,-4,5,3]    => 10100
[-1,2,-4,5,-3]   => 10101
[-1,2,-4,-5,3]   => 10110
[-1,2,-4,-5,-3]  => 10111
[-1,-2,4,5,3]    => 11000
[-1,-2,4,5,-3]   => 11001
[-1,-2,4,-5,3]   => 11010
[-1,-2,4,-5,-3]  => 11011
[-1,-2,-4,5,3]   => 11100
[-1,-2,-4,5,-3]  => 11101
[-1,-2,-4,-5,3]  => 11110
[-1,-2,-4,-5,-3] => 11111
[1,2,5,3,4]      => 00000
[1,2,5,3,-4]     => 00001
[1,2,5,-3,4]     => 00010
[1,2,5,-3,-4]    => 00011
[1,2,-5,3,4]     => 00100
[1,2,-5,3,-4]    => 00101
[1,2,-5,-3,4]    => 00110
[1,2,-5,-3,-4]   => 00111
[1,-2,5,3,4]     => 01000
[1,-2,5,3,-4]    => 01001
[1,-2,5,-3,4]    => 01010
[1,-2,5,-3,-4]   => 01011
[1,-2,-5,3,4]    => 01100
[1,-2,-5,3,-4]   => 01101
[1,-2,-5,-3,4]   => 01110
[1,-2,-5,-3,-4]  => 01111
[-1,2,5,3,4]     => 10000
[-1,2,5,3,-4]    => 10001
[-1,2,5,-3,4]    => 10010
[-1,2,5,-3,-4]   => 10011
[-1,2,-5,3,4]    => 10100
[-1,2,-5,3,-4]   => 10101
[-1,2,-5,-3,4]   => 10110
[-1,2,-5,-3,-4]  => 10111
[-1,-2,5,3,4]    => 11000
[-1,-2,5,3,-4]   => 11001
[-1,-2,5,-3,4]   => 11010
[-1,-2,5,-3,-4]  => 11011
[-1,-2,-5,3,4]   => 11100
[-1,-2,-5,3,-4]  => 11101
[-1,-2,-5,-3,4]  => 11110
[-1,-2,-5,-3,-4] => 11111
[1,2,5,4,3]      => 00000
[1,2,5,4,-3]     => 00001
[1,2,5,-4,3]     => 00010
[1,2,5,-4,-3]    => 00011
[1,2,-5,4,3]     => 00100
[1,2,-5,4,-3]    => 00101
[1,2,-5,-4,3]    => 00110
[1,2,-5,-4,-3]   => 00111
[1,-2,5,4,3]     => 01000
[1,-2,5,4,-3]    => 01001
[1,-2,5,-4,3]    => 01010
[1,-2,5,-4,-3]   => 01011
[1,-2,-5,4,3]    => 01100
[1,-2,-5,4,-3]   => 01101
[1,-2,-5,-4,3]   => 01110
[1,-2,-5,-4,-3]  => 01111
[-1,2,5,4,3]     => 10000
[-1,2,5,4,-3]    => 10001
[-1,2,5,-4,3]    => 10010
[-1,2,5,-4,-3]   => 10011
[-1,2,-5,4,3]    => 10100
[-1,2,-5,4,-3]   => 10101
[-1,2,-5,-4,3]   => 10110
[-1,2,-5,-4,-3]  => 10111
[-1,-2,5,4,3]    => 11000
[-1,-2,5,4,-3]   => 11001
[-1,-2,5,-4,3]   => 11010
[-1,-2,5,-4,-3]  => 11011
[-1,-2,-5,4,3]   => 11100
[-1,-2,-5,4,-3]  => 11101
[-1,-2,-5,-4,3]  => 11110
[-1,-2,-5,-4,-3] => 11111
[1,3,2,4,5]      => 00000
[1,3,2,4,-5]     => 00001
[1,3,2,-4,5]     => 00010
[1,3,2,-4,-5]    => 00011
[1,3,-2,4,5]     => 00100
[1,3,-2,4,-5]    => 00101
[1,3,-2,-4,5]    => 00110
[1,3,-2,-4,-5]   => 00111
[1,-3,2,4,5]     => 01000
[1,-3,2,4,-5]    => 01001
[1,-3,2,-4,5]    => 01010
[1,-3,2,-4,-5]   => 01011
[1,-3,-2,4,5]    => 01100
[1,-3,-2,4,-5]   => 01101
[1,-3,-2,-4,5]   => 01110
[1,-3,-2,-4,-5]  => 01111
[-1,3,2,4,5]     => 10000
[-1,3,2,4,-5]    => 10001
[-1,3,2,-4,5]    => 10010
[-1,3,2,-4,-5]   => 10011
[-1,3,-2,4,5]    => 10100
[-1,3,-2,4,-5]   => 10101
[-1,3,-2,-4,5]   => 10110
[-1,3,-2,-4,-5]  => 10111
[-1,-3,2,4,5]    => 11000
[-1,-3,2,4,-5]   => 11001
[-1,-3,2,-4,5]   => 11010
[-1,-3,2,-4,-5]  => 11011
[-1,-3,-2,4,5]   => 11100
[-1,-3,-2,4,-5]  => 11101
[-1,-3,-2,-4,5]  => 11110
[-1,-3,-2,-4,-5] => 11111
[1,3,2,5,4]      => 00000
[1,3,2,5,-4]     => 00001
[1,3,2,-5,4]     => 00010
[1,3,2,-5,-4]    => 00011
[1,3,-2,5,4]     => 00100
[1,3,-2,5,-4]    => 00101
[1,3,-2,-5,4]    => 00110
[1,3,-2,-5,-4]   => 00111
[1,-3,2,5,4]     => 01000
[1,-3,2,5,-4]    => 01001
[1,-3,2,-5,4]    => 01010
[1,-3,2,-5,-4]   => 01011
[1,-3,-2,5,4]    => 01100
[1,-3,-2,5,-4]   => 01101
[1,-3,-2,-5,4]   => 01110
[1,-3,-2,-5,-4]  => 01111
[-1,3,2,5,4]     => 10000
[-1,3,2,5,-4]    => 10001
[-1,3,2,-5,4]    => 10010
[-1,3,2,-5,-4]   => 10011
[-1,3,-2,5,4]    => 10100
[-1,3,-2,5,-4]   => 10101
[-1,3,-2,-5,4]   => 10110
[-1,3,-2,-5,-4]  => 10111
[-1,-3,2,5,4]    => 11000
[-1,-3,2,5,-4]   => 11001
[-1,-3,2,-5,4]   => 11010
[-1,-3,2,-5,-4]  => 11011
[-1,-3,-2,5,4]   => 11100
[-1,-3,-2,5,-4]  => 11101
[-1,-3,-2,-5,4]  => 11110
[-1,-3,-2,-5,-4] => 11111
[1,3,4,2,5]      => 00000
[1,3,4,2,-5]     => 00001
[1,3,4,-2,5]     => 00010
[1,3,4,-2,-5]    => 00011
[1,3,-4,2,5]     => 00100
[1,3,-4,2,-5]    => 00101
[1,3,-4,-2,5]    => 00110
[1,3,-4,-2,-5]   => 00111
[1,-3,4,2,5]     => 01000
[1,-3,4,2,-5]    => 01001
[1,-3,4,-2,5]    => 01010
[1,-3,4,-2,-5]   => 01011
[1,-3,-4,2,5]    => 01100
[1,-3,-4,2,-5]   => 01101
[1,-3,-4,-2,5]   => 01110
[1,-3,-4,-2,-5]  => 01111
[-1,3,4,2,5]     => 10000
[-1,3,4,2,-5]    => 10001
[-1,3,4,-2,5]    => 10010
[-1,3,4,-2,-5]   => 10011
[-1,3,-4,2,5]    => 10100
[-1,3,-4,2,-5]   => 10101
[-1,3,-4,-2,5]   => 10110
[-1,3,-4,-2,-5]  => 10111
[-1,-3,4,2,5]    => 11000
[-1,-3,4,2,-5]   => 11001
[-1,-3,4,-2,5]   => 11010
[-1,-3,4,-2,-5]  => 11011
[-1,-3,-4,2,5]   => 11100
[-1,-3,-4,2,-5]  => 11101
[-1,-3,-4,-2,5]  => 11110
[-1,-3,-4,-2,-5] => 11111
[1,3,4,5,2]      => 00000
[1,3,4,5,-2]     => 00001
[1,3,4,-5,2]     => 00010
[1,3,4,-5,-2]    => 00011
[1,3,-4,5,2]     => 00100
[1,3,-4,5,-2]    => 00101
[1,3,-4,-5,2]    => 00110
[1,3,-4,-5,-2]   => 00111
[1,-3,4,5,2]     => 01000
[1,-3,4,5,-2]    => 01001
[1,-3,4,-5,2]    => 01010
[1,-3,4,-5,-2]   => 01011
[1,-3,-4,5,2]    => 01100
[1,-3,-4,5,-2]   => 01101
[1,-3,-4,-5,2]   => 01110
[1,-3,-4,-5,-2]  => 01111
[-1,3,4,5,2]     => 10000
[-1,3,4,5,-2]    => 10001
[-1,3,4,-5,2]    => 10010
[-1,3,4,-5,-2]   => 10011
[-1,3,-4,5,2]    => 10100
[-1,3,-4,5,-2]   => 10101
[-1,3,-4,-5,2]   => 10110
[-1,3,-4,-5,-2]  => 10111
[-1,-3,4,5,2]    => 11000
[-1,-3,4,5,-2]   => 11001
[-1,-3,4,-5,2]   => 11010
[-1,-3,4,-5,-2]  => 11011
[-1,-3,-4,5,2]   => 11100
[-1,-3,-4,5,-2]  => 11101
[-1,-3,-4,-5,2]  => 11110
[-1,-3,-4,-5,-2] => 11111
[1,3,5,2,4]      => 00000
[1,3,5,2,-4]     => 00001
[1,3,5,-2,4]     => 00010
[1,3,5,-2,-4]    => 00011
[1,3,-5,2,4]     => 00100
[1,3,-5,2,-4]    => 00101
[1,3,-5,-2,4]    => 00110
[1,3,-5,-2,-4]   => 00111
[1,-3,5,2,4]     => 01000
[1,-3,5,2,-4]    => 01001
[1,-3,5,-2,4]    => 01010
[1,-3,5,-2,-4]   => 01011
[1,-3,-5,2,4]    => 01100
[1,-3,-5,2,-4]   => 01101
[1,-3,-5,-2,4]   => 01110
[1,-3,-5,-2,-4]  => 01111
[-1,3,5,2,4]     => 10000
[-1,3,5,2,-4]    => 10001
[-1,3,5,-2,4]    => 10010
[-1,3,5,-2,-4]   => 10011
[-1,3,-5,2,4]    => 10100
[-1,3,-5,2,-4]   => 10101
[-1,3,-5,-2,4]   => 10110
[-1,3,-5,-2,-4]  => 10111
[-1,-3,5,2,4]    => 11000
[-1,-3,5,2,-4]   => 11001
[-1,-3,5,-2,4]   => 11010
[-1,-3,5,-2,-4]  => 11011
[-1,-3,-5,2,4]   => 11100
[-1,-3,-5,2,-4]  => 11101
[-1,-3,-5,-2,4]  => 11110
[-1,-3,-5,-2,-4] => 11111
[1,3,5,4,2]      => 00000
[1,3,5,4,-2]     => 00001
[1,3,5,-4,2]     => 00010
[1,3,5,-4,-2]    => 00011
[1,3,-5,4,2]     => 00100
[1,3,-5,4,-2]    => 00101
[1,3,-5,-4,2]    => 00110
[1,3,-5,-4,-2]   => 00111
[1,-3,5,4,2]     => 01000
[1,-3,5,4,-2]    => 01001
[1,-3,5,-4,2]    => 01010
[1,-3,5,-4,-2]   => 01011
[1,-3,-5,4,2]    => 01100
[1,-3,-5,4,-2]   => 01101
[1,-3,-5,-4,2]   => 01110
[1,-3,-5,-4,-2]  => 01111
[-1,3,5,4,2]     => 10000
[-1,3,5,4,-2]    => 10001
[-1,3,5,-4,2]    => 10010
[-1,3,5,-4,-2]   => 10011
[-1,3,-5,4,2]    => 10100
[-1,3,-5,4,-2]   => 10101
[-1,3,-5,-4,2]   => 10110
[-1,3,-5,-4,-2]  => 10111
[-1,-3,5,4,2]    => 11000
[-1,-3,5,4,-2]   => 11001
[-1,-3,5,-4,2]   => 11010
[-1,-3,5,-4,-2]  => 11011
[-1,-3,-5,4,2]   => 11100
[-1,-3,-5,4,-2]  => 11101
[-1,-3,-5,-4,2]  => 11110
[-1,-3,-5,-4,-2] => 11111
[1,4,2,3,5]      => 00000
[1,4,2,3,-5]     => 00001
[1,4,2,-3,5]     => 00010
[1,4,2,-3,-5]    => 00011
[1,4,-2,3,5]     => 00100
[1,4,-2,3,-5]    => 00101
[1,4,-2,-3,5]    => 00110
[1,4,-2,-3,-5]   => 00111
[1,-4,2,3,5]     => 01000
[1,-4,2,3,-5]    => 01001
[1,-4,2,-3,5]    => 01010
[1,-4,2,-3,-5]   => 01011
[1,-4,-2,3,5]    => 01100
[1,-4,-2,3,-5]   => 01101
[1,-4,-2,-3,5]   => 01110
[1,-4,-2,-3,-5]  => 01111
[-1,4,2,3,5]     => 10000
[-1,4,2,3,-5]    => 10001
[-1,4,2,-3,5]    => 10010
[-1,4,2,-3,-5]   => 10011
[-1,4,-2,3,5]    => 10100
[-1,4,-2,3,-5]   => 10101
[-1,4,-2,-3,5]   => 10110
[-1,4,-2,-3,-5]  => 10111
[-1,-4,2,3,5]    => 11000
[-1,-4,2,3,-5]   => 11001
[-1,-4,2,-3,5]   => 11010
[-1,-4,2,-3,-5]  => 11011
[-1,-4,-2,3,5]   => 11100
[-1,-4,-2,3,-5]  => 11101
[-1,-4,-2,-3,5]  => 11110
[-1,-4,-2,-3,-5] => 11111
[1,4,2,5,3]      => 00000
[1,4,2,5,-3]     => 00001
[1,4,2,-5,3]     => 00010
[1,4,2,-5,-3]    => 00011
[1,4,-2,5,3]     => 00100
[1,4,-2,5,-3]    => 00101
[1,4,-2,-5,3]    => 00110
[1,4,-2,-5,-3]   => 00111
[1,-4,2,5,3]     => 01000
[1,-4,2,5,-3]    => 01001
[1,-4,2,-5,3]    => 01010
[1,-4,2,-5,-3]   => 01011
[1,-4,-2,5,3]    => 01100
[1,-4,-2,5,-3]   => 01101
[1,-4,-2,-5,3]   => 01110
[1,-4,-2,-5,-3]  => 01111
[-1,4,2,5,3]     => 10000
[-1,4,2,5,-3]    => 10001
[-1,4,2,-5,3]    => 10010
[-1,4,2,-5,-3]   => 10011
[-1,4,-2,5,3]    => 10100
[-1,4,-2,5,-3]   => 10101
[-1,4,-2,-5,3]   => 10110
[-1,4,-2,-5,-3]  => 10111
[-1,-4,2,5,3]    => 11000
[-1,-4,2,5,-3]   => 11001
[-1,-4,2,-5,3]   => 11010
[-1,-4,2,-5,-3]  => 11011
[-1,-4,-2,5,3]   => 11100
[-1,-4,-2,5,-3]  => 11101
[-1,-4,-2,-5,3]  => 11110
[-1,-4,-2,-5,-3] => 11111
[1,4,3,2,5]      => 00000
[1,4,3,2,-5]     => 00001
[1,4,3,-2,5]     => 00010
[1,4,3,-2,-5]    => 00011
[1,4,-3,2,5]     => 00100
[1,4,-3,2,-5]    => 00101
[1,4,-3,-2,5]    => 00110
[1,4,-3,-2,-5]   => 00111
[1,-4,3,2,5]     => 01000
[1,-4,3,2,-5]    => 01001
[1,-4,3,-2,5]    => 01010
[1,-4,3,-2,-5]   => 01011
[1,-4,-3,2,5]    => 01100
[1,-4,-3,2,-5]   => 01101
[1,-4,-3,-2,5]   => 01110
[1,-4,-3,-2,-5]  => 01111
[-1,4,3,2,5]     => 10000
[-1,4,3,2,-5]    => 10001
[-1,4,3,-2,5]    => 10010
[-1,4,3,-2,-5]   => 10011
[-1,4,-3,2,5]    => 10100
[-1,4,-3,2,-5]   => 10101
[-1,4,-3,-2,5]   => 10110
[-1,4,-3,-2,-5]  => 10111
[-1,-4,3,2,5]    => 11000
[-1,-4,3,2,-5]   => 11001
[-1,-4,3,-2,5]   => 11010
[-1,-4,3,-2,-5]  => 11011
[-1,-4,-3,2,5]   => 11100
[-1,-4,-3,2,-5]  => 11101
[-1,-4,-3,-2,5]  => 11110
[-1,-4,-3,-2,-5] => 11111
[1,4,3,5,2]      => 00000
[1,4,3,5,-2]     => 00001
[1,4,3,-5,2]     => 00010
[1,4,3,-5,-2]    => 00011
[1,4,-3,5,2]     => 00100
[1,4,-3,5,-2]    => 00101
[1,4,-3,-5,2]    => 00110
[1,4,-3,-5,-2]   => 00111
[1,-4,3,5,2]     => 01000
[1,-4,3,5,-2]    => 01001
[1,-4,3,-5,2]    => 01010
[1,-4,3,-5,-2]   => 01011
[1,-4,-3,5,2]    => 01100
[1,-4,-3,5,-2]   => 01101
[1,-4,-3,-5,2]   => 01110
[1,-4,-3,-5,-2]  => 01111
[-1,4,3,5,2]     => 10000
[-1,4,3,5,-2]    => 10001
[-1,4,3,-5,2]    => 10010
[-1,4,3,-5,-2]   => 10011
[-1,4,-3,5,2]    => 10100
[-1,4,-3,5,-2]   => 10101
[-1,4,-3,-5,2]   => 10110
[-1,4,-3,-5,-2]  => 10111
[-1,-4,3,5,2]    => 11000
[-1,-4,3,5,-2]   => 11001
[-1,-4,3,-5,2]   => 11010
[-1,-4,3,-5,-2]  => 11011
[-1,-4,-3,5,2]   => 11100
[-1,-4,-3,5,-2]  => 11101
[-1,-4,-3,-5,2]  => 11110
[-1,-4,-3,-5,-2] => 11111
[1,4,5,2,3]      => 00000
[1,4,5,2,-3]     => 00001
[1,4,5,-2,3]     => 00010
[1,4,5,-2,-3]    => 00011
[1,4,-5,2,3]     => 00100
[1,4,-5,2,-3]    => 00101
[1,4,-5,-2,3]    => 00110
[1,4,-5,-2,-3]   => 00111
[1,-4,5,2,3]     => 01000
[1,-4,5,2,-3]    => 01001
[1,-4,5,-2,3]    => 01010
[1,-4,5,-2,-3]   => 01011
[1,-4,-5,2,3]    => 01100
[1,-4,-5,2,-3]   => 01101
[1,-4,-5,-2,3]   => 01110
[1,-4,-5,-2,-3]  => 01111
[-1,4,5,2,3]     => 10000
[-1,4,5,2,-3]    => 10001
[-1,4,5,-2,3]    => 10010
[-1,4,5,-2,-3]   => 10011
[-1,4,-5,2,3]    => 10100
[-1,4,-5,2,-3]   => 10101
[-1,4,-5,-2,3]   => 10110
[-1,4,-5,-2,-3]  => 10111
[-1,-4,5,2,3]    => 11000
[-1,-4,5,2,-3]   => 11001
[-1,-4,5,-2,3]   => 11010
[-1,-4,5,-2,-3]  => 11011
[-1,-4,-5,2,3]   => 11100
[-1,-4,-5,2,-3]  => 11101
[-1,-4,-5,-2,3]  => 11110
[-1,-4,-5,-2,-3] => 11111
[1,4,5,3,2]      => 00000
[1,4,5,3,-2]     => 00001
[1,4,5,-3,2]     => 00010
[1,4,5,-3,-2]    => 00011
[1,4,-5,3,2]     => 00100
[1,4,-5,3,-2]    => 00101
[1,4,-5,-3,2]    => 00110
[1,4,-5,-3,-2]   => 00111
[1,-4,5,3,2]     => 01000
[1,-4,5,3,-2]    => 01001
[1,-4,5,-3,2]    => 01010
[1,-4,5,-3,-2]   => 01011
[1,-4,-5,3,2]    => 01100
[1,-4,-5,3,-2]   => 01101
[1,-4,-5,-3,2]   => 01110
[1,-4,-5,-3,-2]  => 01111
[-1,4,5,3,2]     => 10000
[-1,4,5,3,-2]    => 10001
[-1,4,5,-3,2]    => 10010
[-1,4,5,-3,-2]   => 10011
[-1,4,-5,3,2]    => 10100
[-1,4,-5,3,-2]   => 10101
[-1,4,-5,-3,2]   => 10110
[-1,4,-5,-3,-2]  => 10111
[-1,-4,5,3,2]    => 11000
[-1,-4,5,3,-2]   => 11001
[-1,-4,5,-3,2]   => 11010
[-1,-4,5,-3,-2]  => 11011
[-1,-4,-5,3,2]   => 11100
[-1,-4,-5,3,-2]  => 11101
[-1,-4,-5,-3,2]  => 11110
[-1,-4,-5,-3,-2] => 11111
[1,5,2,3,4]      => 00000
[1,5,2,3,-4]     => 00001
[1,5,2,-3,4]     => 00010
[1,5,2,-3,-4]    => 00011
[1,5,-2,3,4]     => 00100
[1,5,-2,3,-4]    => 00101
[1,5,-2,-3,4]    => 00110
[1,5,-2,-3,-4]   => 00111
[1,-5,2,3,4]     => 01000
[1,-5,2,3,-4]    => 01001
[1,-5,2,-3,4]    => 01010
[1,-5,2,-3,-4]   => 01011
[1,-5,-2,3,4]    => 01100
[1,-5,-2,3,-4]   => 01101
[1,-5,-2,-3,4]   => 01110
[1,-5,-2,-3,-4]  => 01111
[-1,5,2,3,4]     => 10000
[-1,5,2,3,-4]    => 10001
[-1,5,2,-3,4]    => 10010
[-1,5,2,-3,-4]   => 10011
[-1,5,-2,3,4]    => 10100
[-1,5,-2,3,-4]   => 10101
[-1,5,-2,-3,4]   => 10110
[-1,5,-2,-3,-4]  => 10111
[-1,-5,2,3,4]    => 11000
[-1,-5,2,3,-4]   => 11001
[-1,-5,2,-3,4]   => 11010
[-1,-5,2,-3,-4]  => 11011
[-1,-5,-2,3,4]   => 11100
[-1,-5,-2,3,-4]  => 11101
[-1,-5,-2,-3,4]  => 11110
[-1,-5,-2,-3,-4] => 11111
[1,5,2,4,3]      => 00000
[1,5,2,4,-3]     => 00001
[1,5,2,-4,3]     => 00010
[1,5,2,-4,-3]    => 00011
[1,5,-2,4,3]     => 00100
[1,5,-2,4,-3]    => 00101
[1,5,-2,-4,3]    => 00110
[1,5,-2,-4,-3]   => 00111
[1,-5,2,4,3]     => 01000
[1,-5,2,4,-3]    => 01001
[1,-5,2,-4,3]    => 01010
[1,-5,2,-4,-3]   => 01011
[1,-5,-2,4,3]    => 01100
[1,-5,-2,4,-3]   => 01101
[1,-5,-2,-4,3]   => 01110
[1,-5,-2,-4,-3]  => 01111
[-1,5,2,4,3]     => 10000
[-1,5,2,4,-3]    => 10001
[-1,5,2,-4,3]    => 10010
[-1,5,2,-4,-3]   => 10011
[-1,5,-2,4,3]    => 10100
[-1,5,-2,4,-3]   => 10101
[-1,5,-2,-4,3]   => 10110
[-1,5,-2,-4,-3]  => 10111
[-1,-5,2,4,3]    => 11000
[-1,-5,2,4,-3]   => 11001
[-1,-5,2,-4,3]   => 11010
[-1,-5,2,-4,-3]  => 11011
[-1,-5,-2,4,3]   => 11100
[-1,-5,-2,4,-3]  => 11101
[-1,-5,-2,-4,3]  => 11110
[-1,-5,-2,-4,-3] => 11111
[1,5,3,2,4]      => 00000
[1,5,3,2,-4]     => 00001
[1,5,3,-2,4]     => 00010
[1,5,3,-2,-4]    => 00011
[1,5,-3,2,4]     => 00100
[1,5,-3,2,-4]    => 00101
[1,5,-3,-2,4]    => 00110
[1,5,-3,-2,-4]   => 00111
[1,-5,3,2,4]     => 01000
[1,-5,3,2,-4]    => 01001
[1,-5,3,-2,4]    => 01010
[1,-5,3,-2,-4]   => 01011
[1,-5,-3,2,4]    => 01100
[1,-5,-3,2,-4]   => 01101
[1,-5,-3,-2,4]   => 01110
[1,-5,-3,-2,-4]  => 01111
[-1,5,3,2,4]     => 10000
[-1,5,3,2,-4]    => 10001
[-1,5,3,-2,4]    => 10010
[-1,5,3,-2,-4]   => 10011
[-1,5,-3,2,4]    => 10100
[-1,5,-3,2,-4]   => 10101
[-1,5,-3,-2,4]   => 10110
[-1,5,-3,-2,-4]  => 10111
[-1,-5,3,2,4]    => 11000
[-1,-5,3,2,-4]   => 11001
[-1,-5,3,-2,4]   => 11010
[-1,-5,3,-2,-4]  => 11011
[-1,-5,-3,2,4]   => 11100
[-1,-5,-3,2,-4]  => 11101
[-1,-5,-3,-2,4]  => 11110
[-1,-5,-3,-2,-4] => 11111
[1,5,3,4,2]      => 00000
[1,5,3,4,-2]     => 00001
[1,5,3,-4,2]     => 00010
[1,5,3,-4,-2]    => 00011
[1,5,-3,4,2]     => 00100
[1,5,-3,4,-2]    => 00101
[1,5,-3,-4,2]    => 00110
[1,5,-3,-4,-2]   => 00111
[1,-5,3,4,2]     => 01000
[1,-5,3,4,-2]    => 01001
[1,-5,3,-4,2]    => 01010
[1,-5,3,-4,-2]   => 01011
[1,-5,-3,4,2]    => 01100
[1,-5,-3,4,-2]   => 01101
[1,-5,-3,-4,2]   => 01110
[1,-5,-3,-4,-2]  => 01111
[-1,5,3,4,2]     => 10000
[-1,5,3,4,-2]    => 10001
[-1,5,3,-4,2]    => 10010
[-1,5,3,-4,-2]   => 10011
[-1,5,-3,4,2]    => 10100
[-1,5,-3,4,-2]   => 10101
[-1,5,-3,-4,2]   => 10110
[-1,5,-3,-4,-2]  => 10111
[-1,-5,3,4,2]    => 11000
[-1,-5,3,4,-2]   => 11001
[-1,-5,3,-4,2]   => 11010
[-1,-5,3,-4,-2]  => 11011
[-1,-5,-3,4,2]   => 11100
[-1,-5,-3,4,-2]  => 11101
[-1,-5,-3,-4,2]  => 11110
[-1,-5,-3,-4,-2] => 11111
[1,5,4,2,3]      => 00000
[1,5,4,2,-3]     => 00001
[1,5,4,-2,3]     => 00010
[1,5,4,-2,-3]    => 00011
[1,5,-4,2,3]     => 00100
[1,5,-4,2,-3]    => 00101
[1,5,-4,-2,3]    => 00110
[1,5,-4,-2,-3]   => 00111
[1,-5,4,2,3]     => 01000
[1,-5,4,2,-3]    => 01001
[1,-5,4,-2,3]    => 01010
[1,-5,4,-2,-3]   => 01011
[1,-5,-4,2,3]    => 01100
[1,-5,-4,2,-3]   => 01101
[1,-5,-4,-2,3]   => 01110
[1,-5,-4,-2,-3]  => 01111
[-1,5,4,2,3]     => 10000
[-1,5,4,2,-3]    => 10001
[-1,5,4,-2,3]    => 10010
[-1,5,4,-2,-3]   => 10011
[-1,5,-4,2,3]    => 10100
[-1,5,-4,2,-3]   => 10101
[-1,5,-4,-2,3]   => 10110
[-1,5,-4,-2,-3]  => 10111
[-1,-5,4,2,3]    => 11000
[-1,-5,4,2,-3]   => 11001
[-1,-5,4,-2,3]   => 11010
[-1,-5,4,-2,-3]  => 11011
[-1,-5,-4,2,3]   => 11100
[-1,-5,-4,2,-3]  => 11101
[-1,-5,-4,-2,3]  => 11110
[-1,-5,-4,-2,-3] => 11111
[1,5,4,3,2]      => 00000
[1,5,4,3,-2]     => 00001
[1,5,4,-3,2]     => 00010
[1,5,4,-3,-2]    => 00011
[1,5,-4,3,2]     => 00100
[1,5,-4,3,-2]    => 00101
[1,5,-4,-3,2]    => 00110
[1,5,-4,-3,-2]   => 00111
[1,-5,4,3,2]     => 01000
[1,-5,4,3,-2]    => 01001
[1,-5,4,-3,2]    => 01010
[1,-5,4,-3,-2]   => 01011
[1,-5,-4,3,2]    => 01100
[1,-5,-4,3,-2]   => 01101
[1,-5,-4,-3,2]   => 01110
[1,-5,-4,-3,-2]  => 01111
[-1,5,4,3,2]     => 10000
[-1,5,4,3,-2]    => 10001
[-1,5,4,-3,2]    => 10010
[-1,5,4,-3,-2]   => 10011
[-1,5,-4,3,2]    => 10100
[-1,5,-4,3,-2]   => 10101

-----------------------------------------------------------------------------
Created: Dec 01, 2022 at 19:54 by Martin Rubey

-----------------------------------------------------------------------------
Last Updated: Dec 01, 2022 at 19:54 by Martin Rubey