Identifier
Mp00161:
Signed permutations
—reverse⟶
Signed permutations
Mp00267: Signed permutations —signs⟶ Binary words
Mp00261: Binary words —Burrows-Wheeler⟶ Binary words
Mp00267: Signed permutations —signs⟶ Binary words
Mp00261: Binary words —Burrows-Wheeler⟶ Binary words
Images
[1] => [1] => 0 => 0
[-1] => [-1] => 1 => 1
[1,2] => [2,1] => 00 => 00
[1,-2] => [-2,1] => 10 => 10
[-1,2] => [2,-1] => 01 => 10
[-1,-2] => [-2,-1] => 11 => 11
[2,1] => [1,2] => 00 => 00
[2,-1] => [-1,2] => 10 => 10
[-2,1] => [1,-2] => 01 => 10
[-2,-1] => [-1,-2] => 11 => 11
[1,2,3] => [3,2,1] => 000 => 000
[1,2,-3] => [-3,2,1] => 100 => 100
[1,-2,3] => [3,-2,1] => 010 => 100
[1,-2,-3] => [-3,-2,1] => 110 => 110
[-1,2,3] => [3,2,-1] => 001 => 100
[-1,2,-3] => [-3,2,-1] => 101 => 110
[-1,-2,3] => [3,-2,-1] => 011 => 110
[-1,-2,-3] => [-3,-2,-1] => 111 => 111
[1,3,2] => [2,3,1] => 000 => 000
[1,3,-2] => [-2,3,1] => 100 => 100
[1,-3,2] => [2,-3,1] => 010 => 100
[1,-3,-2] => [-2,-3,1] => 110 => 110
[-1,3,2] => [2,3,-1] => 001 => 100
[-1,3,-2] => [-2,3,-1] => 101 => 110
[-1,-3,2] => [2,-3,-1] => 011 => 110
[-1,-3,-2] => [-2,-3,-1] => 111 => 111
[2,1,3] => [3,1,2] => 000 => 000
[2,1,-3] => [-3,1,2] => 100 => 100
[2,-1,3] => [3,-1,2] => 010 => 100
[2,-1,-3] => [-3,-1,2] => 110 => 110
[-2,1,3] => [3,1,-2] => 001 => 100
[-2,1,-3] => [-3,1,-2] => 101 => 110
[-2,-1,3] => [3,-1,-2] => 011 => 110
[-2,-1,-3] => [-3,-1,-2] => 111 => 111
[2,3,1] => [1,3,2] => 000 => 000
[2,3,-1] => [-1,3,2] => 100 => 100
[2,-3,1] => [1,-3,2] => 010 => 100
[2,-3,-1] => [-1,-3,2] => 110 => 110
[-2,3,1] => [1,3,-2] => 001 => 100
[-2,3,-1] => [-1,3,-2] => 101 => 110
[-2,-3,1] => [1,-3,-2] => 011 => 110
[-2,-3,-1] => [-1,-3,-2] => 111 => 111
[3,1,2] => [2,1,3] => 000 => 000
[3,1,-2] => [-2,1,3] => 100 => 100
[3,-1,2] => [2,-1,3] => 010 => 100
[3,-1,-2] => [-2,-1,3] => 110 => 110
[-3,1,2] => [2,1,-3] => 001 => 100
[-3,1,-2] => [-2,1,-3] => 101 => 110
[-3,-1,2] => [2,-1,-3] => 011 => 110
[-3,-1,-2] => [-2,-1,-3] => 111 => 111
[3,2,1] => [1,2,3] => 000 => 000
[3,2,-1] => [-1,2,3] => 100 => 100
[3,-2,1] => [1,-2,3] => 010 => 100
[3,-2,-1] => [-1,-2,3] => 110 => 110
[-3,2,1] => [1,2,-3] => 001 => 100
[-3,2,-1] => [-1,2,-3] => 101 => 110
[-3,-2,1] => [1,-2,-3] => 011 => 110
[-3,-2,-1] => [-1,-2,-3] => 111 => 111
[1,2,3,4] => [4,3,2,1] => 0000 => 0000
[1,2,3,-4] => [-4,3,2,1] => 1000 => 1000
[1,2,-3,4] => [4,-3,2,1] => 0100 => 1000
[1,2,-3,-4] => [-4,-3,2,1] => 1100 => 1010
[1,-2,3,4] => [4,3,-2,1] => 0010 => 1000
[1,-2,3,-4] => [-4,3,-2,1] => 1010 => 1100
[1,-2,-3,4] => [4,-3,-2,1] => 0110 => 1010
[1,-2,-3,-4] => [-4,-3,-2,1] => 1110 => 1110
[-1,2,3,4] => [4,3,2,-1] => 0001 => 1000
[-1,2,3,-4] => [-4,3,2,-1] => 1001 => 1010
[-1,2,-3,4] => [4,-3,2,-1] => 0101 => 1100
[-1,2,-3,-4] => [-4,-3,2,-1] => 1101 => 1110
[-1,-2,3,4] => [4,3,-2,-1] => 0011 => 1010
[-1,-2,3,-4] => [-4,3,-2,-1] => 1011 => 1110
[-1,-2,-3,4] => [4,-3,-2,-1] => 0111 => 1110
[-1,-2,-3,-4] => [-4,-3,-2,-1] => 1111 => 1111
[1,2,4,3] => [3,4,2,1] => 0000 => 0000
[1,2,4,-3] => [-3,4,2,1] => 1000 => 1000
[1,2,-4,3] => [3,-4,2,1] => 0100 => 1000
[1,2,-4,-3] => [-3,-4,2,1] => 1100 => 1010
[1,-2,4,3] => [3,4,-2,1] => 0010 => 1000
[1,-2,4,-3] => [-3,4,-2,1] => 1010 => 1100
[1,-2,-4,3] => [3,-4,-2,1] => 0110 => 1010
[1,-2,-4,-3] => [-3,-4,-2,1] => 1110 => 1110
[-1,2,4,3] => [3,4,2,-1] => 0001 => 1000
[-1,2,4,-3] => [-3,4,2,-1] => 1001 => 1010
[-1,2,-4,3] => [3,-4,2,-1] => 0101 => 1100
[-1,2,-4,-3] => [-3,-4,2,-1] => 1101 => 1110
[-1,-2,4,3] => [3,4,-2,-1] => 0011 => 1010
[-1,-2,4,-3] => [-3,4,-2,-1] => 1011 => 1110
[-1,-2,-4,3] => [3,-4,-2,-1] => 0111 => 1110
[-1,-2,-4,-3] => [-3,-4,-2,-1] => 1111 => 1111
[1,3,2,4] => [4,2,3,1] => 0000 => 0000
[1,3,2,-4] => [-4,2,3,1] => 1000 => 1000
[1,3,-2,4] => [4,-2,3,1] => 0100 => 1000
[1,3,-2,-4] => [-4,-2,3,1] => 1100 => 1010
[1,-3,2,4] => [4,2,-3,1] => 0010 => 1000
[1,-3,2,-4] => [-4,2,-3,1] => 1010 => 1100
[1,-3,-2,4] => [4,-2,-3,1] => 0110 => 1010
[1,-3,-2,-4] => [-4,-2,-3,1] => 1110 => 1110
[-1,3,2,4] => [4,2,3,-1] => 0001 => 1000
[-1,3,2,-4] => [-4,2,3,-1] => 1001 => 1010
[-1,3,-2,4] => [4,-2,3,-1] => 0101 => 1100
>>> Load all 4452 entries. <<<
[-1,3,-2,-4] => [-4,-2,3,-1] => 1101 => 1110
[-1,-3,2,4] => [4,2,-3,-1] => 0011 => 1010
[-1,-3,2,-4] => [-4,2,-3,-1] => 1011 => 1110
[-1,-3,-2,4] => [4,-2,-3,-1] => 0111 => 1110
[-1,-3,-2,-4] => [-4,-2,-3,-1] => 1111 => 1111
[1,3,4,2] => [2,4,3,1] => 0000 => 0000
[1,3,4,-2] => [-2,4,3,1] => 1000 => 1000
[1,3,-4,2] => [2,-4,3,1] => 0100 => 1000
[1,3,-4,-2] => [-2,-4,3,1] => 1100 => 1010
[1,-3,4,2] => [2,4,-3,1] => 0010 => 1000
[1,-3,4,-2] => [-2,4,-3,1] => 1010 => 1100
[1,-3,-4,2] => [2,-4,-3,1] => 0110 => 1010
[1,-3,-4,-2] => [-2,-4,-3,1] => 1110 => 1110
[-1,3,4,2] => [2,4,3,-1] => 0001 => 1000
[-1,3,4,-2] => [-2,4,3,-1] => 1001 => 1010
[-1,3,-4,2] => [2,-4,3,-1] => 0101 => 1100
[-1,3,-4,-2] => [-2,-4,3,-1] => 1101 => 1110
[-1,-3,4,2] => [2,4,-3,-1] => 0011 => 1010
[-1,-3,4,-2] => [-2,4,-3,-1] => 1011 => 1110
[-1,-3,-4,2] => [2,-4,-3,-1] => 0111 => 1110
[-1,-3,-4,-2] => [-2,-4,-3,-1] => 1111 => 1111
[1,4,2,3] => [3,2,4,1] => 0000 => 0000
[1,4,2,-3] => [-3,2,4,1] => 1000 => 1000
[1,4,-2,3] => [3,-2,4,1] => 0100 => 1000
[1,4,-2,-3] => [-3,-2,4,1] => 1100 => 1010
[1,-4,2,3] => [3,2,-4,1] => 0010 => 1000
[1,-4,2,-3] => [-3,2,-4,1] => 1010 => 1100
[1,-4,-2,3] => [3,-2,-4,1] => 0110 => 1010
[1,-4,-2,-3] => [-3,-2,-4,1] => 1110 => 1110
[-1,4,2,3] => [3,2,4,-1] => 0001 => 1000
[-1,4,2,-3] => [-3,2,4,-1] => 1001 => 1010
[-1,4,-2,3] => [3,-2,4,-1] => 0101 => 1100
[-1,4,-2,-3] => [-3,-2,4,-1] => 1101 => 1110
[-1,-4,2,3] => [3,2,-4,-1] => 0011 => 1010
[-1,-4,2,-3] => [-3,2,-4,-1] => 1011 => 1110
[-1,-4,-2,3] => [3,-2,-4,-1] => 0111 => 1110
[-1,-4,-2,-3] => [-3,-2,-4,-1] => 1111 => 1111
[1,4,3,2] => [2,3,4,1] => 0000 => 0000
[1,4,3,-2] => [-2,3,4,1] => 1000 => 1000
[1,4,-3,2] => [2,-3,4,1] => 0100 => 1000
[1,4,-3,-2] => [-2,-3,4,1] => 1100 => 1010
[1,-4,3,2] => [2,3,-4,1] => 0010 => 1000
[1,-4,3,-2] => [-2,3,-4,1] => 1010 => 1100
[1,-4,-3,2] => [2,-3,-4,1] => 0110 => 1010
[1,-4,-3,-2] => [-2,-3,-4,1] => 1110 => 1110
[-1,4,3,2] => [2,3,4,-1] => 0001 => 1000
[-1,4,3,-2] => [-2,3,4,-1] => 1001 => 1010
[-1,4,-3,2] => [2,-3,4,-1] => 0101 => 1100
[-1,4,-3,-2] => [-2,-3,4,-1] => 1101 => 1110
[-1,-4,3,2] => [2,3,-4,-1] => 0011 => 1010
[-1,-4,3,-2] => [-2,3,-4,-1] => 1011 => 1110
[-1,-4,-3,2] => [2,-3,-4,-1] => 0111 => 1110
[-1,-4,-3,-2] => [-2,-3,-4,-1] => 1111 => 1111
[2,1,3,4] => [4,3,1,2] => 0000 => 0000
[2,1,3,-4] => [-4,3,1,2] => 1000 => 1000
[2,1,-3,4] => [4,-3,1,2] => 0100 => 1000
[2,1,-3,-4] => [-4,-3,1,2] => 1100 => 1010
[2,-1,3,4] => [4,3,-1,2] => 0010 => 1000
[2,-1,3,-4] => [-4,3,-1,2] => 1010 => 1100
[2,-1,-3,4] => [4,-3,-1,2] => 0110 => 1010
[2,-1,-3,-4] => [-4,-3,-1,2] => 1110 => 1110
[-2,1,3,4] => [4,3,1,-2] => 0001 => 1000
[-2,1,3,-4] => [-4,3,1,-2] => 1001 => 1010
[-2,1,-3,4] => [4,-3,1,-2] => 0101 => 1100
[-2,1,-3,-4] => [-4,-3,1,-2] => 1101 => 1110
[-2,-1,3,4] => [4,3,-1,-2] => 0011 => 1010
[-2,-1,3,-4] => [-4,3,-1,-2] => 1011 => 1110
[-2,-1,-3,4] => [4,-3,-1,-2] => 0111 => 1110
[-2,-1,-3,-4] => [-4,-3,-1,-2] => 1111 => 1111
[2,1,4,3] => [3,4,1,2] => 0000 => 0000
[2,1,4,-3] => [-3,4,1,2] => 1000 => 1000
[2,1,-4,3] => [3,-4,1,2] => 0100 => 1000
[2,1,-4,-3] => [-3,-4,1,2] => 1100 => 1010
[2,-1,4,3] => [3,4,-1,2] => 0010 => 1000
[2,-1,4,-3] => [-3,4,-1,2] => 1010 => 1100
[2,-1,-4,3] => [3,-4,-1,2] => 0110 => 1010
[2,-1,-4,-3] => [-3,-4,-1,2] => 1110 => 1110
[-2,1,4,3] => [3,4,1,-2] => 0001 => 1000
[-2,1,4,-3] => [-3,4,1,-2] => 1001 => 1010
[-2,1,-4,3] => [3,-4,1,-2] => 0101 => 1100
[-2,1,-4,-3] => [-3,-4,1,-2] => 1101 => 1110
[-2,-1,4,3] => [3,4,-1,-2] => 0011 => 1010
[-2,-1,4,-3] => [-3,4,-1,-2] => 1011 => 1110
[-2,-1,-4,3] => [3,-4,-1,-2] => 0111 => 1110
[-2,-1,-4,-3] => [-3,-4,-1,-2] => 1111 => 1111
[2,3,1,4] => [4,1,3,2] => 0000 => 0000
[2,3,1,-4] => [-4,1,3,2] => 1000 => 1000
[2,3,-1,4] => [4,-1,3,2] => 0100 => 1000
[2,3,-1,-4] => [-4,-1,3,2] => 1100 => 1010
[2,-3,1,4] => [4,1,-3,2] => 0010 => 1000
[2,-3,1,-4] => [-4,1,-3,2] => 1010 => 1100
[2,-3,-1,4] => [4,-1,-3,2] => 0110 => 1010
[2,-3,-1,-4] => [-4,-1,-3,2] => 1110 => 1110
[-2,3,1,4] => [4,1,3,-2] => 0001 => 1000
[-2,3,1,-4] => [-4,1,3,-2] => 1001 => 1010
[-2,3,-1,4] => [4,-1,3,-2] => 0101 => 1100
[-2,3,-1,-4] => [-4,-1,3,-2] => 1101 => 1110
[-2,-3,1,4] => [4,1,-3,-2] => 0011 => 1010
[-2,-3,1,-4] => [-4,1,-3,-2] => 1011 => 1110
[-2,-3,-1,4] => [4,-1,-3,-2] => 0111 => 1110
[-2,-3,-1,-4] => [-4,-1,-3,-2] => 1111 => 1111
[2,3,4,1] => [1,4,3,2] => 0000 => 0000
[2,3,4,-1] => [-1,4,3,2] => 1000 => 1000
[2,3,-4,1] => [1,-4,3,2] => 0100 => 1000
[2,3,-4,-1] => [-1,-4,3,2] => 1100 => 1010
[2,-3,4,1] => [1,4,-3,2] => 0010 => 1000
[2,-3,4,-1] => [-1,4,-3,2] => 1010 => 1100
[2,-3,-4,1] => [1,-4,-3,2] => 0110 => 1010
[2,-3,-4,-1] => [-1,-4,-3,2] => 1110 => 1110
[-2,3,4,1] => [1,4,3,-2] => 0001 => 1000
[-2,3,4,-1] => [-1,4,3,-2] => 1001 => 1010
[-2,3,-4,1] => [1,-4,3,-2] => 0101 => 1100
[-2,3,-4,-1] => [-1,-4,3,-2] => 1101 => 1110
[-2,-3,4,1] => [1,4,-3,-2] => 0011 => 1010
[-2,-3,4,-1] => [-1,4,-3,-2] => 1011 => 1110
[-2,-3,-4,1] => [1,-4,-3,-2] => 0111 => 1110
[-2,-3,-4,-1] => [-1,-4,-3,-2] => 1111 => 1111
[2,4,1,3] => [3,1,4,2] => 0000 => 0000
[2,4,1,-3] => [-3,1,4,2] => 1000 => 1000
[2,4,-1,3] => [3,-1,4,2] => 0100 => 1000
[2,4,-1,-3] => [-3,-1,4,2] => 1100 => 1010
[2,-4,1,3] => [3,1,-4,2] => 0010 => 1000
[2,-4,1,-3] => [-3,1,-4,2] => 1010 => 1100
[2,-4,-1,3] => [3,-1,-4,2] => 0110 => 1010
[2,-4,-1,-3] => [-3,-1,-4,2] => 1110 => 1110
[-2,4,1,3] => [3,1,4,-2] => 0001 => 1000
[-2,4,1,-3] => [-3,1,4,-2] => 1001 => 1010
[-2,4,-1,3] => [3,-1,4,-2] => 0101 => 1100
[-2,4,-1,-3] => [-3,-1,4,-2] => 1101 => 1110
[-2,-4,1,3] => [3,1,-4,-2] => 0011 => 1010
[-2,-4,1,-3] => [-3,1,-4,-2] => 1011 => 1110
[-2,-4,-1,3] => [3,-1,-4,-2] => 0111 => 1110
[-2,-4,-1,-3] => [-3,-1,-4,-2] => 1111 => 1111
[2,4,3,1] => [1,3,4,2] => 0000 => 0000
[2,4,3,-1] => [-1,3,4,2] => 1000 => 1000
[2,4,-3,1] => [1,-3,4,2] => 0100 => 1000
[2,4,-3,-1] => [-1,-3,4,2] => 1100 => 1010
[2,-4,3,1] => [1,3,-4,2] => 0010 => 1000
[2,-4,3,-1] => [-1,3,-4,2] => 1010 => 1100
[2,-4,-3,1] => [1,-3,-4,2] => 0110 => 1010
[2,-4,-3,-1] => [-1,-3,-4,2] => 1110 => 1110
[-2,4,3,1] => [1,3,4,-2] => 0001 => 1000
[-2,4,3,-1] => [-1,3,4,-2] => 1001 => 1010
[-2,4,-3,1] => [1,-3,4,-2] => 0101 => 1100
[-2,4,-3,-1] => [-1,-3,4,-2] => 1101 => 1110
[-2,-4,3,1] => [1,3,-4,-2] => 0011 => 1010
[-2,-4,3,-1] => [-1,3,-4,-2] => 1011 => 1110
[-2,-4,-3,1] => [1,-3,-4,-2] => 0111 => 1110
[-2,-4,-3,-1] => [-1,-3,-4,-2] => 1111 => 1111
[3,1,2,4] => [4,2,1,3] => 0000 => 0000
[3,1,2,-4] => [-4,2,1,3] => 1000 => 1000
[3,1,-2,4] => [4,-2,1,3] => 0100 => 1000
[3,1,-2,-4] => [-4,-2,1,3] => 1100 => 1010
[3,-1,2,4] => [4,2,-1,3] => 0010 => 1000
[3,-1,2,-4] => [-4,2,-1,3] => 1010 => 1100
[3,-1,-2,4] => [4,-2,-1,3] => 0110 => 1010
[3,-1,-2,-4] => [-4,-2,-1,3] => 1110 => 1110
[-3,1,2,4] => [4,2,1,-3] => 0001 => 1000
[-3,1,2,-4] => [-4,2,1,-3] => 1001 => 1010
[-3,1,-2,4] => [4,-2,1,-3] => 0101 => 1100
[-3,1,-2,-4] => [-4,-2,1,-3] => 1101 => 1110
[-3,-1,2,4] => [4,2,-1,-3] => 0011 => 1010
[-3,-1,2,-4] => [-4,2,-1,-3] => 1011 => 1110
[-3,-1,-2,4] => [4,-2,-1,-3] => 0111 => 1110
[-3,-1,-2,-4] => [-4,-2,-1,-3] => 1111 => 1111
[3,1,4,2] => [2,4,1,3] => 0000 => 0000
[3,1,4,-2] => [-2,4,1,3] => 1000 => 1000
[3,1,-4,2] => [2,-4,1,3] => 0100 => 1000
[3,1,-4,-2] => [-2,-4,1,3] => 1100 => 1010
[3,-1,4,2] => [2,4,-1,3] => 0010 => 1000
[3,-1,4,-2] => [-2,4,-1,3] => 1010 => 1100
[3,-1,-4,2] => [2,-4,-1,3] => 0110 => 1010
[3,-1,-4,-2] => [-2,-4,-1,3] => 1110 => 1110
[-3,1,4,2] => [2,4,1,-3] => 0001 => 1000
[-3,1,4,-2] => [-2,4,1,-3] => 1001 => 1010
[-3,1,-4,2] => [2,-4,1,-3] => 0101 => 1100
[-3,1,-4,-2] => [-2,-4,1,-3] => 1101 => 1110
[-3,-1,4,2] => [2,4,-1,-3] => 0011 => 1010
[-3,-1,4,-2] => [-2,4,-1,-3] => 1011 => 1110
[-3,-1,-4,2] => [2,-4,-1,-3] => 0111 => 1110
[-3,-1,-4,-2] => [-2,-4,-1,-3] => 1111 => 1111
[3,2,1,4] => [4,1,2,3] => 0000 => 0000
[3,2,1,-4] => [-4,1,2,3] => 1000 => 1000
[3,2,-1,4] => [4,-1,2,3] => 0100 => 1000
[3,2,-1,-4] => [-4,-1,2,3] => 1100 => 1010
[3,-2,1,4] => [4,1,-2,3] => 0010 => 1000
[3,-2,1,-4] => [-4,1,-2,3] => 1010 => 1100
[3,-2,-1,4] => [4,-1,-2,3] => 0110 => 1010
[3,-2,-1,-4] => [-4,-1,-2,3] => 1110 => 1110
[-3,2,1,4] => [4,1,2,-3] => 0001 => 1000
[-3,2,1,-4] => [-4,1,2,-3] => 1001 => 1010
[-3,2,-1,4] => [4,-1,2,-3] => 0101 => 1100
[-3,2,-1,-4] => [-4,-1,2,-3] => 1101 => 1110
[-3,-2,1,4] => [4,1,-2,-3] => 0011 => 1010
[-3,-2,1,-4] => [-4,1,-2,-3] => 1011 => 1110
[-3,-2,-1,4] => [4,-1,-2,-3] => 0111 => 1110
[-3,-2,-1,-4] => [-4,-1,-2,-3] => 1111 => 1111
[3,2,4,1] => [1,4,2,3] => 0000 => 0000
[3,2,4,-1] => [-1,4,2,3] => 1000 => 1000
[3,2,-4,1] => [1,-4,2,3] => 0100 => 1000
[3,2,-4,-1] => [-1,-4,2,3] => 1100 => 1010
[3,-2,4,1] => [1,4,-2,3] => 0010 => 1000
[3,-2,4,-1] => [-1,4,-2,3] => 1010 => 1100
[3,-2,-4,1] => [1,-4,-2,3] => 0110 => 1010
[3,-2,-4,-1] => [-1,-4,-2,3] => 1110 => 1110
[-3,2,4,1] => [1,4,2,-3] => 0001 => 1000
[-3,2,4,-1] => [-1,4,2,-3] => 1001 => 1010
[-3,2,-4,1] => [1,-4,2,-3] => 0101 => 1100
[-3,2,-4,-1] => [-1,-4,2,-3] => 1101 => 1110
[-3,-2,4,1] => [1,4,-2,-3] => 0011 => 1010
[-3,-2,4,-1] => [-1,4,-2,-3] => 1011 => 1110
[-3,-2,-4,1] => [1,-4,-2,-3] => 0111 => 1110
[-3,-2,-4,-1] => [-1,-4,-2,-3] => 1111 => 1111
[3,4,1,2] => [2,1,4,3] => 0000 => 0000
[3,4,1,-2] => [-2,1,4,3] => 1000 => 1000
[3,4,-1,2] => [2,-1,4,3] => 0100 => 1000
[3,4,-1,-2] => [-2,-1,4,3] => 1100 => 1010
[3,-4,1,2] => [2,1,-4,3] => 0010 => 1000
[3,-4,1,-2] => [-2,1,-4,3] => 1010 => 1100
[3,-4,-1,2] => [2,-1,-4,3] => 0110 => 1010
[3,-4,-1,-2] => [-2,-1,-4,3] => 1110 => 1110
[-3,4,1,2] => [2,1,4,-3] => 0001 => 1000
[-3,4,1,-2] => [-2,1,4,-3] => 1001 => 1010
[-3,4,-1,2] => [2,-1,4,-3] => 0101 => 1100
[-3,4,-1,-2] => [-2,-1,4,-3] => 1101 => 1110
[-3,-4,1,2] => [2,1,-4,-3] => 0011 => 1010
[-3,-4,1,-2] => [-2,1,-4,-3] => 1011 => 1110
[-3,-4,-1,2] => [2,-1,-4,-3] => 0111 => 1110
[-3,-4,-1,-2] => [-2,-1,-4,-3] => 1111 => 1111
[3,4,2,1] => [1,2,4,3] => 0000 => 0000
[3,4,2,-1] => [-1,2,4,3] => 1000 => 1000
[3,4,-2,1] => [1,-2,4,3] => 0100 => 1000
[3,4,-2,-1] => [-1,-2,4,3] => 1100 => 1010
[3,-4,2,1] => [1,2,-4,3] => 0010 => 1000
[3,-4,2,-1] => [-1,2,-4,3] => 1010 => 1100
[3,-4,-2,1] => [1,-2,-4,3] => 0110 => 1010
[3,-4,-2,-1] => [-1,-2,-4,3] => 1110 => 1110
[-3,4,2,1] => [1,2,4,-3] => 0001 => 1000
[-3,4,2,-1] => [-1,2,4,-3] => 1001 => 1010
[-3,4,-2,1] => [1,-2,4,-3] => 0101 => 1100
[-3,4,-2,-1] => [-1,-2,4,-3] => 1101 => 1110
[-3,-4,2,1] => [1,2,-4,-3] => 0011 => 1010
[-3,-4,2,-1] => [-1,2,-4,-3] => 1011 => 1110
[-3,-4,-2,1] => [1,-2,-4,-3] => 0111 => 1110
[-3,-4,-2,-1] => [-1,-2,-4,-3] => 1111 => 1111
[4,1,2,3] => [3,2,1,4] => 0000 => 0000
[4,1,2,-3] => [-3,2,1,4] => 1000 => 1000
[4,1,-2,3] => [3,-2,1,4] => 0100 => 1000
[4,1,-2,-3] => [-3,-2,1,4] => 1100 => 1010
[4,-1,2,3] => [3,2,-1,4] => 0010 => 1000
[4,-1,2,-3] => [-3,2,-1,4] => 1010 => 1100
[4,-1,-2,3] => [3,-2,-1,4] => 0110 => 1010
[4,-1,-2,-3] => [-3,-2,-1,4] => 1110 => 1110
[-4,1,2,3] => [3,2,1,-4] => 0001 => 1000
[-4,1,2,-3] => [-3,2,1,-4] => 1001 => 1010
[-4,1,-2,3] => [3,-2,1,-4] => 0101 => 1100
[-4,1,-2,-3] => [-3,-2,1,-4] => 1101 => 1110
[-4,-1,2,3] => [3,2,-1,-4] => 0011 => 1010
[-4,-1,2,-3] => [-3,2,-1,-4] => 1011 => 1110
[-4,-1,-2,3] => [3,-2,-1,-4] => 0111 => 1110
[-4,-1,-2,-3] => [-3,-2,-1,-4] => 1111 => 1111
[4,1,3,2] => [2,3,1,4] => 0000 => 0000
[4,1,3,-2] => [-2,3,1,4] => 1000 => 1000
[4,1,-3,2] => [2,-3,1,4] => 0100 => 1000
[4,1,-3,-2] => [-2,-3,1,4] => 1100 => 1010
[4,-1,3,2] => [2,3,-1,4] => 0010 => 1000
[4,-1,3,-2] => [-2,3,-1,4] => 1010 => 1100
[4,-1,-3,2] => [2,-3,-1,4] => 0110 => 1010
[4,-1,-3,-2] => [-2,-3,-1,4] => 1110 => 1110
[-4,1,3,2] => [2,3,1,-4] => 0001 => 1000
[-4,1,3,-2] => [-2,3,1,-4] => 1001 => 1010
[-4,1,-3,2] => [2,-3,1,-4] => 0101 => 1100
[-4,1,-3,-2] => [-2,-3,1,-4] => 1101 => 1110
[-4,-1,3,2] => [2,3,-1,-4] => 0011 => 1010
[-4,-1,3,-2] => [-2,3,-1,-4] => 1011 => 1110
[-4,-1,-3,2] => [2,-3,-1,-4] => 0111 => 1110
[-4,-1,-3,-2] => [-2,-3,-1,-4] => 1111 => 1111
[4,2,1,3] => [3,1,2,4] => 0000 => 0000
[4,2,1,-3] => [-3,1,2,4] => 1000 => 1000
[4,2,-1,3] => [3,-1,2,4] => 0100 => 1000
[4,2,-1,-3] => [-3,-1,2,4] => 1100 => 1010
[4,-2,1,3] => [3,1,-2,4] => 0010 => 1000
[4,-2,1,-3] => [-3,1,-2,4] => 1010 => 1100
[4,-2,-1,3] => [3,-1,-2,4] => 0110 => 1010
[4,-2,-1,-3] => [-3,-1,-2,4] => 1110 => 1110
[-4,2,1,3] => [3,1,2,-4] => 0001 => 1000
[-4,2,1,-3] => [-3,1,2,-4] => 1001 => 1010
[-4,2,-1,3] => [3,-1,2,-4] => 0101 => 1100
[-4,2,-1,-3] => [-3,-1,2,-4] => 1101 => 1110
[-4,-2,1,3] => [3,1,-2,-4] => 0011 => 1010
[-4,-2,1,-3] => [-3,1,-2,-4] => 1011 => 1110
[-4,-2,-1,3] => [3,-1,-2,-4] => 0111 => 1110
[-4,-2,-1,-3] => [-3,-1,-2,-4] => 1111 => 1111
[4,2,3,1] => [1,3,2,4] => 0000 => 0000
[4,2,3,-1] => [-1,3,2,4] => 1000 => 1000
[4,2,-3,1] => [1,-3,2,4] => 0100 => 1000
[4,2,-3,-1] => [-1,-3,2,4] => 1100 => 1010
[4,-2,3,1] => [1,3,-2,4] => 0010 => 1000
[4,-2,3,-1] => [-1,3,-2,4] => 1010 => 1100
[4,-2,-3,1] => [1,-3,-2,4] => 0110 => 1010
[4,-2,-3,-1] => [-1,-3,-2,4] => 1110 => 1110
[-4,2,3,1] => [1,3,2,-4] => 0001 => 1000
[-4,2,3,-1] => [-1,3,2,-4] => 1001 => 1010
[-4,2,-3,1] => [1,-3,2,-4] => 0101 => 1100
[-4,2,-3,-1] => [-1,-3,2,-4] => 1101 => 1110
[-4,-2,3,1] => [1,3,-2,-4] => 0011 => 1010
[-4,-2,3,-1] => [-1,3,-2,-4] => 1011 => 1110
[-4,-2,-3,1] => [1,-3,-2,-4] => 0111 => 1110
[-4,-2,-3,-1] => [-1,-3,-2,-4] => 1111 => 1111
[4,3,1,2] => [2,1,3,4] => 0000 => 0000
[4,3,1,-2] => [-2,1,3,4] => 1000 => 1000
[4,3,-1,2] => [2,-1,3,4] => 0100 => 1000
[4,3,-1,-2] => [-2,-1,3,4] => 1100 => 1010
[4,-3,1,2] => [2,1,-3,4] => 0010 => 1000
[4,-3,1,-2] => [-2,1,-3,4] => 1010 => 1100
[4,-3,-1,2] => [2,-1,-3,4] => 0110 => 1010
[4,-3,-1,-2] => [-2,-1,-3,4] => 1110 => 1110
[-4,3,1,2] => [2,1,3,-4] => 0001 => 1000
[-4,3,1,-2] => [-2,1,3,-4] => 1001 => 1010
[-4,3,-1,2] => [2,-1,3,-4] => 0101 => 1100
[-4,3,-1,-2] => [-2,-1,3,-4] => 1101 => 1110
[-4,-3,1,2] => [2,1,-3,-4] => 0011 => 1010
[-4,-3,1,-2] => [-2,1,-3,-4] => 1011 => 1110
[-4,-3,-1,2] => [2,-1,-3,-4] => 0111 => 1110
[-4,-3,-1,-2] => [-2,-1,-3,-4] => 1111 => 1111
[4,3,2,1] => [1,2,3,4] => 0000 => 0000
[4,3,2,-1] => [-1,2,3,4] => 1000 => 1000
[4,3,-2,1] => [1,-2,3,4] => 0100 => 1000
[4,3,-2,-1] => [-1,-2,3,4] => 1100 => 1010
[4,-3,2,1] => [1,2,-3,4] => 0010 => 1000
[4,-3,2,-1] => [-1,2,-3,4] => 1010 => 1100
[4,-3,-2,1] => [1,-2,-3,4] => 0110 => 1010
[4,-3,-2,-1] => [-1,-2,-3,4] => 1110 => 1110
[-4,3,2,1] => [1,2,3,-4] => 0001 => 1000
[-4,3,2,-1] => [-1,2,3,-4] => 1001 => 1010
[-4,3,-2,1] => [1,-2,3,-4] => 0101 => 1100
[-4,3,-2,-1] => [-1,-2,3,-4] => 1101 => 1110
[-4,-3,2,1] => [1,2,-3,-4] => 0011 => 1010
[-4,-3,2,-1] => [-1,2,-3,-4] => 1011 => 1110
[-4,-3,-2,1] => [1,-2,-3,-4] => 0111 => 1110
[-4,-3,-2,-1] => [-1,-2,-3,-4] => 1111 => 1111
[1,2,3,4,5] => [5,4,3,2,1] => 00000 => 00000
[1,2,3,4,-5] => [-5,4,3,2,1] => 10000 => 10000
[1,2,3,-4,5] => [5,-4,3,2,1] => 01000 => 10000
[1,2,3,-4,-5] => [-5,-4,3,2,1] => 11000 => 10010
[1,2,-3,4,5] => [5,4,-3,2,1] => 00100 => 10000
[1,2,-3,4,-5] => [-5,4,-3,2,1] => 10100 => 11000
[1,2,-3,-4,5] => [5,-4,-3,2,1] => 01100 => 10010
[1,2,-3,-4,-5] => [-5,-4,-3,2,1] => 11100 => 10110
[1,-2,3,4,5] => [5,4,3,-2,1] => 00010 => 10000
[1,-2,3,4,-5] => [-5,4,3,-2,1] => 10010 => 11000
[1,-2,3,-4,5] => [5,-4,3,-2,1] => 01010 => 11000
[1,-2,3,-4,-5] => [-5,-4,3,-2,1] => 11010 => 11100
[1,-2,-3,4,5] => [5,4,-3,-2,1] => 00110 => 10010
[1,-2,-3,4,-5] => [-5,4,-3,-2,1] => 10110 => 11100
[1,-2,-3,-4,5] => [5,-4,-3,-2,1] => 01110 => 10110
[1,-2,-3,-4,-5] => [-5,-4,-3,-2,1] => 11110 => 11110
[-1,2,3,4,5] => [5,4,3,2,-1] => 00001 => 10000
[-1,2,3,4,-5] => [-5,4,3,2,-1] => 10001 => 10010
[-1,2,3,-4,5] => [5,-4,3,2,-1] => 01001 => 11000
[-1,2,3,-4,-5] => [-5,-4,3,2,-1] => 11001 => 10110
[-1,2,-3,4,5] => [5,4,-3,2,-1] => 00101 => 11000
[-1,2,-3,4,-5] => [-5,4,-3,2,-1] => 10101 => 11100
[-1,2,-3,-4,5] => [5,-4,-3,2,-1] => 01101 => 11100
[-1,2,-3,-4,-5] => [-5,-4,-3,2,-1] => 11101 => 11110
[-1,-2,3,4,5] => [5,4,3,-2,-1] => 00011 => 10010
[-1,-2,3,4,-5] => [-5,4,3,-2,-1] => 10011 => 10110
[-1,-2,3,-4,5] => [5,-4,3,-2,-1] => 01011 => 11100
[-1,-2,3,-4,-5] => [-5,-4,3,-2,-1] => 11011 => 11110
[-1,-2,-3,4,5] => [5,4,-3,-2,-1] => 00111 => 10110
[-1,-2,-3,4,-5] => [-5,4,-3,-2,-1] => 10111 => 11110
[-1,-2,-3,-4,5] => [5,-4,-3,-2,-1] => 01111 => 11110
[-1,-2,-3,-4,-5] => [-5,-4,-3,-2,-1] => 11111 => 11111
[1,2,3,5,4] => [4,5,3,2,1] => 00000 => 00000
[1,2,3,5,-4] => [-4,5,3,2,1] => 10000 => 10000
[1,2,3,-5,4] => [4,-5,3,2,1] => 01000 => 10000
[1,2,3,-5,-4] => [-4,-5,3,2,1] => 11000 => 10010
[1,2,-3,5,4] => [4,5,-3,2,1] => 00100 => 10000
[1,2,-3,5,-4] => [-4,5,-3,2,1] => 10100 => 11000
[1,2,-3,-5,4] => [4,-5,-3,2,1] => 01100 => 10010
[1,2,-3,-5,-4] => [-4,-5,-3,2,1] => 11100 => 10110
[1,-2,3,5,4] => [4,5,3,-2,1] => 00010 => 10000
[1,-2,3,5,-4] => [-4,5,3,-2,1] => 10010 => 11000
[1,-2,3,-5,4] => [4,-5,3,-2,1] => 01010 => 11000
[1,-2,3,-5,-4] => [-4,-5,3,-2,1] => 11010 => 11100
[1,-2,-3,5,4] => [4,5,-3,-2,1] => 00110 => 10010
[1,-2,-3,5,-4] => [-4,5,-3,-2,1] => 10110 => 11100
[1,-2,-3,-5,4] => [4,-5,-3,-2,1] => 01110 => 10110
[1,-2,-3,-5,-4] => [-4,-5,-3,-2,1] => 11110 => 11110
[-1,2,3,5,4] => [4,5,3,2,-1] => 00001 => 10000
[-1,2,3,5,-4] => [-4,5,3,2,-1] => 10001 => 10010
[-1,2,3,-5,4] => [4,-5,3,2,-1] => 01001 => 11000
[-1,2,3,-5,-4] => [-4,-5,3,2,-1] => 11001 => 10110
[-1,2,-3,5,4] => [4,5,-3,2,-1] => 00101 => 11000
[-1,2,-3,5,-4] => [-4,5,-3,2,-1] => 10101 => 11100
[-1,2,-3,-5,4] => [4,-5,-3,2,-1] => 01101 => 11100
[-1,2,-3,-5,-4] => [-4,-5,-3,2,-1] => 11101 => 11110
[-1,-2,3,5,4] => [4,5,3,-2,-1] => 00011 => 10010
[-1,-2,3,5,-4] => [-4,5,3,-2,-1] => 10011 => 10110
[-1,-2,3,-5,4] => [4,-5,3,-2,-1] => 01011 => 11100
[-1,-2,3,-5,-4] => [-4,-5,3,-2,-1] => 11011 => 11110
[-1,-2,-3,5,4] => [4,5,-3,-2,-1] => 00111 => 10110
[-1,-2,-3,5,-4] => [-4,5,-3,-2,-1] => 10111 => 11110
[-1,-2,-3,-5,4] => [4,-5,-3,-2,-1] => 01111 => 11110
[-1,-2,-3,-5,-4] => [-4,-5,-3,-2,-1] => 11111 => 11111
[1,2,4,3,5] => [5,3,4,2,1] => 00000 => 00000
[1,2,4,3,-5] => [-5,3,4,2,1] => 10000 => 10000
[1,2,4,-3,5] => [5,-3,4,2,1] => 01000 => 10000
[1,2,4,-3,-5] => [-5,-3,4,2,1] => 11000 => 10010
[1,2,-4,3,5] => [5,3,-4,2,1] => 00100 => 10000
[1,2,-4,3,-5] => [-5,3,-4,2,1] => 10100 => 11000
[1,2,-4,-3,5] => [5,-3,-4,2,1] => 01100 => 10010
[1,2,-4,-3,-5] => [-5,-3,-4,2,1] => 11100 => 10110
[1,-2,4,3,5] => [5,3,4,-2,1] => 00010 => 10000
[1,-2,4,3,-5] => [-5,3,4,-2,1] => 10010 => 11000
[1,-2,4,-3,5] => [5,-3,4,-2,1] => 01010 => 11000
[1,-2,4,-3,-5] => [-5,-3,4,-2,1] => 11010 => 11100
[1,-2,-4,3,5] => [5,3,-4,-2,1] => 00110 => 10010
[1,-2,-4,3,-5] => [-5,3,-4,-2,1] => 10110 => 11100
[1,-2,-4,-3,5] => [5,-3,-4,-2,1] => 01110 => 10110
[1,-2,-4,-3,-5] => [-5,-3,-4,-2,1] => 11110 => 11110
[-1,2,4,3,5] => [5,3,4,2,-1] => 00001 => 10000
[-1,2,4,3,-5] => [-5,3,4,2,-1] => 10001 => 10010
[-1,2,4,-3,5] => [5,-3,4,2,-1] => 01001 => 11000
[-1,2,4,-3,-5] => [-5,-3,4,2,-1] => 11001 => 10110
[-1,2,-4,3,5] => [5,3,-4,2,-1] => 00101 => 11000
[-1,2,-4,3,-5] => [-5,3,-4,2,-1] => 10101 => 11100
[-1,2,-4,-3,5] => [5,-3,-4,2,-1] => 01101 => 11100
[-1,2,-4,-3,-5] => [-5,-3,-4,2,-1] => 11101 => 11110
[-1,-2,4,3,5] => [5,3,4,-2,-1] => 00011 => 10010
[-1,-2,4,3,-5] => [-5,3,4,-2,-1] => 10011 => 10110
[-1,-2,4,-3,5] => [5,-3,4,-2,-1] => 01011 => 11100
[-1,-2,4,-3,-5] => [-5,-3,4,-2,-1] => 11011 => 11110
[-1,-2,-4,3,5] => [5,3,-4,-2,-1] => 00111 => 10110
[-1,-2,-4,3,-5] => [-5,3,-4,-2,-1] => 10111 => 11110
[-1,-2,-4,-3,5] => [5,-3,-4,-2,-1] => 01111 => 11110
[-1,-2,-4,-3,-5] => [-5,-3,-4,-2,-1] => 11111 => 11111
[1,2,4,5,3] => [3,5,4,2,1] => 00000 => 00000
[1,2,4,5,-3] => [-3,5,4,2,1] => 10000 => 10000
[1,2,4,-5,3] => [3,-5,4,2,1] => 01000 => 10000
[1,2,4,-5,-3] => [-3,-5,4,2,1] => 11000 => 10010
[1,2,-4,5,3] => [3,5,-4,2,1] => 00100 => 10000
[1,2,-4,5,-3] => [-3,5,-4,2,1] => 10100 => 11000
[1,2,-4,-5,3] => [3,-5,-4,2,1] => 01100 => 10010
[1,2,-4,-5,-3] => [-3,-5,-4,2,1] => 11100 => 10110
[1,-2,4,5,3] => [3,5,4,-2,1] => 00010 => 10000
[1,-2,4,5,-3] => [-3,5,4,-2,1] => 10010 => 11000
[1,-2,4,-5,3] => [3,-5,4,-2,1] => 01010 => 11000
[1,-2,4,-5,-3] => [-3,-5,4,-2,1] => 11010 => 11100
[1,-2,-4,5,3] => [3,5,-4,-2,1] => 00110 => 10010
[1,-2,-4,5,-3] => [-3,5,-4,-2,1] => 10110 => 11100
[1,-2,-4,-5,3] => [3,-5,-4,-2,1] => 01110 => 10110
[1,-2,-4,-5,-3] => [-3,-5,-4,-2,1] => 11110 => 11110
[-1,2,4,5,3] => [3,5,4,2,-1] => 00001 => 10000
[-1,2,4,5,-3] => [-3,5,4,2,-1] => 10001 => 10010
[-1,2,4,-5,3] => [3,-5,4,2,-1] => 01001 => 11000
[-1,2,4,-5,-3] => [-3,-5,4,2,-1] => 11001 => 10110
[-1,2,-4,5,3] => [3,5,-4,2,-1] => 00101 => 11000
[-1,2,-4,5,-3] => [-3,5,-4,2,-1] => 10101 => 11100
[-1,2,-4,-5,3] => [3,-5,-4,2,-1] => 01101 => 11100
[-1,2,-4,-5,-3] => [-3,-5,-4,2,-1] => 11101 => 11110
[-1,-2,4,5,3] => [3,5,4,-2,-1] => 00011 => 10010
[-1,-2,4,5,-3] => [-3,5,4,-2,-1] => 10011 => 10110
[-1,-2,4,-5,3] => [3,-5,4,-2,-1] => 01011 => 11100
[-1,-2,4,-5,-3] => [-3,-5,4,-2,-1] => 11011 => 11110
[-1,-2,-4,5,3] => [3,5,-4,-2,-1] => 00111 => 10110
[-1,-2,-4,5,-3] => [-3,5,-4,-2,-1] => 10111 => 11110
[-1,-2,-4,-5,3] => [3,-5,-4,-2,-1] => 01111 => 11110
[-1,-2,-4,-5,-3] => [-3,-5,-4,-2,-1] => 11111 => 11111
[1,2,5,3,4] => [4,3,5,2,1] => 00000 => 00000
[1,2,5,3,-4] => [-4,3,5,2,1] => 10000 => 10000
[1,2,5,-3,4] => [4,-3,5,2,1] => 01000 => 10000
[1,2,5,-3,-4] => [-4,-3,5,2,1] => 11000 => 10010
[1,2,-5,3,4] => [4,3,-5,2,1] => 00100 => 10000
[1,2,-5,3,-4] => [-4,3,-5,2,1] => 10100 => 11000
[1,2,-5,-3,4] => [4,-3,-5,2,1] => 01100 => 10010
[1,2,-5,-3,-4] => [-4,-3,-5,2,1] => 11100 => 10110
[1,-2,5,3,4] => [4,3,5,-2,1] => 00010 => 10000
[1,-2,5,3,-4] => [-4,3,5,-2,1] => 10010 => 11000
[1,-2,5,-3,4] => [4,-3,5,-2,1] => 01010 => 11000
[1,-2,5,-3,-4] => [-4,-3,5,-2,1] => 11010 => 11100
[1,-2,-5,3,4] => [4,3,-5,-2,1] => 00110 => 10010
[1,-2,-5,3,-4] => [-4,3,-5,-2,1] => 10110 => 11100
[1,-2,-5,-3,4] => [4,-3,-5,-2,1] => 01110 => 10110
[1,-2,-5,-3,-4] => [-4,-3,-5,-2,1] => 11110 => 11110
[-1,2,5,3,4] => [4,3,5,2,-1] => 00001 => 10000
[-1,2,5,3,-4] => [-4,3,5,2,-1] => 10001 => 10010
[-1,2,5,-3,4] => [4,-3,5,2,-1] => 01001 => 11000
[-1,2,5,-3,-4] => [-4,-3,5,2,-1] => 11001 => 10110
[-1,2,-5,3,4] => [4,3,-5,2,-1] => 00101 => 11000
[-1,2,-5,3,-4] => [-4,3,-5,2,-1] => 10101 => 11100
[-1,2,-5,-3,4] => [4,-3,-5,2,-1] => 01101 => 11100
[-1,2,-5,-3,-4] => [-4,-3,-5,2,-1] => 11101 => 11110
[-1,-2,5,3,4] => [4,3,5,-2,-1] => 00011 => 10010
[-1,-2,5,3,-4] => [-4,3,5,-2,-1] => 10011 => 10110
[-1,-2,5,-3,4] => [4,-3,5,-2,-1] => 01011 => 11100
[-1,-2,5,-3,-4] => [-4,-3,5,-2,-1] => 11011 => 11110
[-1,-2,-5,3,4] => [4,3,-5,-2,-1] => 00111 => 10110
[-1,-2,-5,3,-4] => [-4,3,-5,-2,-1] => 10111 => 11110
[-1,-2,-5,-3,4] => [4,-3,-5,-2,-1] => 01111 => 11110
[-1,-2,-5,-3,-4] => [-4,-3,-5,-2,-1] => 11111 => 11111
[1,2,5,4,3] => [3,4,5,2,1] => 00000 => 00000
[1,2,5,4,-3] => [-3,4,5,2,1] => 10000 => 10000
[1,2,5,-4,3] => [3,-4,5,2,1] => 01000 => 10000
[1,2,5,-4,-3] => [-3,-4,5,2,1] => 11000 => 10010
[1,2,-5,4,3] => [3,4,-5,2,1] => 00100 => 10000
[1,2,-5,4,-3] => [-3,4,-5,2,1] => 10100 => 11000
[1,2,-5,-4,3] => [3,-4,-5,2,1] => 01100 => 10010
[1,2,-5,-4,-3] => [-3,-4,-5,2,1] => 11100 => 10110
[1,-2,5,4,3] => [3,4,5,-2,1] => 00010 => 10000
[1,-2,5,4,-3] => [-3,4,5,-2,1] => 10010 => 11000
[1,-2,5,-4,3] => [3,-4,5,-2,1] => 01010 => 11000
[1,-2,5,-4,-3] => [-3,-4,5,-2,1] => 11010 => 11100
[1,-2,-5,4,3] => [3,4,-5,-2,1] => 00110 => 10010
[1,-2,-5,4,-3] => [-3,4,-5,-2,1] => 10110 => 11100
[1,-2,-5,-4,3] => [3,-4,-5,-2,1] => 01110 => 10110
[1,-2,-5,-4,-3] => [-3,-4,-5,-2,1] => 11110 => 11110
[-1,2,5,4,3] => [3,4,5,2,-1] => 00001 => 10000
[-1,2,5,4,-3] => [-3,4,5,2,-1] => 10001 => 10010
[-1,2,5,-4,3] => [3,-4,5,2,-1] => 01001 => 11000
[-1,2,5,-4,-3] => [-3,-4,5,2,-1] => 11001 => 10110
[-1,2,-5,4,3] => [3,4,-5,2,-1] => 00101 => 11000
[-1,2,-5,4,-3] => [-3,4,-5,2,-1] => 10101 => 11100
[-1,2,-5,-4,3] => [3,-4,-5,2,-1] => 01101 => 11100
[-1,2,-5,-4,-3] => [-3,-4,-5,2,-1] => 11101 => 11110
[-1,-2,5,4,3] => [3,4,5,-2,-1] => 00011 => 10010
[-1,-2,5,4,-3] => [-3,4,5,-2,-1] => 10011 => 10110
[-1,-2,5,-4,3] => [3,-4,5,-2,-1] => 01011 => 11100
[-1,-2,5,-4,-3] => [-3,-4,5,-2,-1] => 11011 => 11110
[-1,-2,-5,4,3] => [3,4,-5,-2,-1] => 00111 => 10110
[-1,-2,-5,4,-3] => [-3,4,-5,-2,-1] => 10111 => 11110
[-1,-2,-5,-4,3] => [3,-4,-5,-2,-1] => 01111 => 11110
[-1,-2,-5,-4,-3] => [-3,-4,-5,-2,-1] => 11111 => 11111
[1,3,2,4,5] => [5,4,2,3,1] => 00000 => 00000
[1,3,2,4,-5] => [-5,4,2,3,1] => 10000 => 10000
[1,3,2,-4,5] => [5,-4,2,3,1] => 01000 => 10000
[1,3,2,-4,-5] => [-5,-4,2,3,1] => 11000 => 10010
[1,3,-2,4,5] => [5,4,-2,3,1] => 00100 => 10000
[1,3,-2,4,-5] => [-5,4,-2,3,1] => 10100 => 11000
[1,3,-2,-4,5] => [5,-4,-2,3,1] => 01100 => 10010
[1,3,-2,-4,-5] => [-5,-4,-2,3,1] => 11100 => 10110
[1,-3,2,4,5] => [5,4,2,-3,1] => 00010 => 10000
[1,-3,2,4,-5] => [-5,4,2,-3,1] => 10010 => 11000
[1,-3,2,-4,5] => [5,-4,2,-3,1] => 01010 => 11000
[1,-3,2,-4,-5] => [-5,-4,2,-3,1] => 11010 => 11100
[1,-3,-2,4,5] => [5,4,-2,-3,1] => 00110 => 10010
[1,-3,-2,4,-5] => [-5,4,-2,-3,1] => 10110 => 11100
[1,-3,-2,-4,5] => [5,-4,-2,-3,1] => 01110 => 10110
[1,-3,-2,-4,-5] => [-5,-4,-2,-3,1] => 11110 => 11110
[-1,3,2,4,5] => [5,4,2,3,-1] => 00001 => 10000
[-1,3,2,4,-5] => [-5,4,2,3,-1] => 10001 => 10010
[-1,3,2,-4,5] => [5,-4,2,3,-1] => 01001 => 11000
[-1,3,2,-4,-5] => [-5,-4,2,3,-1] => 11001 => 10110
[-1,3,-2,4,5] => [5,4,-2,3,-1] => 00101 => 11000
[-1,3,-2,4,-5] => [-5,4,-2,3,-1] => 10101 => 11100
[-1,3,-2,-4,5] => [5,-4,-2,3,-1] => 01101 => 11100
[-1,3,-2,-4,-5] => [-5,-4,-2,3,-1] => 11101 => 11110
[-1,-3,2,4,5] => [5,4,2,-3,-1] => 00011 => 10010
[-1,-3,2,4,-5] => [-5,4,2,-3,-1] => 10011 => 10110
[-1,-3,2,-4,5] => [5,-4,2,-3,-1] => 01011 => 11100
[-1,-3,2,-4,-5] => [-5,-4,2,-3,-1] => 11011 => 11110
[-1,-3,-2,4,5] => [5,4,-2,-3,-1] => 00111 => 10110
[-1,-3,-2,4,-5] => [-5,4,-2,-3,-1] => 10111 => 11110
[-1,-3,-2,-4,5] => [5,-4,-2,-3,-1] => 01111 => 11110
[-1,-3,-2,-4,-5] => [-5,-4,-2,-3,-1] => 11111 => 11111
[1,3,2,5,4] => [4,5,2,3,1] => 00000 => 00000
[1,3,2,5,-4] => [-4,5,2,3,1] => 10000 => 10000
[1,3,2,-5,4] => [4,-5,2,3,1] => 01000 => 10000
[1,3,2,-5,-4] => [-4,-5,2,3,1] => 11000 => 10010
[1,3,-2,5,4] => [4,5,-2,3,1] => 00100 => 10000
[1,3,-2,5,-4] => [-4,5,-2,3,1] => 10100 => 11000
[1,3,-2,-5,4] => [4,-5,-2,3,1] => 01100 => 10010
[1,3,-2,-5,-4] => [-4,-5,-2,3,1] => 11100 => 10110
[1,-3,2,5,4] => [4,5,2,-3,1] => 00010 => 10000
[1,-3,2,5,-4] => [-4,5,2,-3,1] => 10010 => 11000
[1,-3,2,-5,4] => [4,-5,2,-3,1] => 01010 => 11000
[1,-3,2,-5,-4] => [-4,-5,2,-3,1] => 11010 => 11100
[1,-3,-2,5,4] => [4,5,-2,-3,1] => 00110 => 10010
[1,-3,-2,5,-4] => [-4,5,-2,-3,1] => 10110 => 11100
[1,-3,-2,-5,4] => [4,-5,-2,-3,1] => 01110 => 10110
[1,-3,-2,-5,-4] => [-4,-5,-2,-3,1] => 11110 => 11110
[-1,3,2,5,4] => [4,5,2,3,-1] => 00001 => 10000
[-1,3,2,5,-4] => [-4,5,2,3,-1] => 10001 => 10010
[-1,3,2,-5,4] => [4,-5,2,3,-1] => 01001 => 11000
[-1,3,2,-5,-4] => [-4,-5,2,3,-1] => 11001 => 10110
[-1,3,-2,5,4] => [4,5,-2,3,-1] => 00101 => 11000
[-1,3,-2,5,-4] => [-4,5,-2,3,-1] => 10101 => 11100
[-1,3,-2,-5,4] => [4,-5,-2,3,-1] => 01101 => 11100
[-1,3,-2,-5,-4] => [-4,-5,-2,3,-1] => 11101 => 11110
[-1,-3,2,5,4] => [4,5,2,-3,-1] => 00011 => 10010
[-1,-3,2,5,-4] => [-4,5,2,-3,-1] => 10011 => 10110
[-1,-3,2,-5,4] => [4,-5,2,-3,-1] => 01011 => 11100
[-1,-3,2,-5,-4] => [-4,-5,2,-3,-1] => 11011 => 11110
[-1,-3,-2,5,4] => [4,5,-2,-3,-1] => 00111 => 10110
[-1,-3,-2,5,-4] => [-4,5,-2,-3,-1] => 10111 => 11110
[-1,-3,-2,-5,4] => [4,-5,-2,-3,-1] => 01111 => 11110
[-1,-3,-2,-5,-4] => [-4,-5,-2,-3,-1] => 11111 => 11111
[1,3,4,2,5] => [5,2,4,3,1] => 00000 => 00000
[1,3,4,2,-5] => [-5,2,4,3,1] => 10000 => 10000
[1,3,4,-2,5] => [5,-2,4,3,1] => 01000 => 10000
[1,3,4,-2,-5] => [-5,-2,4,3,1] => 11000 => 10010
[1,3,-4,2,5] => [5,2,-4,3,1] => 00100 => 10000
[1,3,-4,2,-5] => [-5,2,-4,3,1] => 10100 => 11000
[1,3,-4,-2,5] => [5,-2,-4,3,1] => 01100 => 10010
[1,3,-4,-2,-5] => [-5,-2,-4,3,1] => 11100 => 10110
[1,-3,4,2,5] => [5,2,4,-3,1] => 00010 => 10000
[1,-3,4,2,-5] => [-5,2,4,-3,1] => 10010 => 11000
[1,-3,4,-2,5] => [5,-2,4,-3,1] => 01010 => 11000
[1,-3,4,-2,-5] => [-5,-2,4,-3,1] => 11010 => 11100
[1,-3,-4,2,5] => [5,2,-4,-3,1] => 00110 => 10010
[1,-3,-4,2,-5] => [-5,2,-4,-3,1] => 10110 => 11100
[1,-3,-4,-2,5] => [5,-2,-4,-3,1] => 01110 => 10110
[1,-3,-4,-2,-5] => [-5,-2,-4,-3,1] => 11110 => 11110
[-1,3,4,2,5] => [5,2,4,3,-1] => 00001 => 10000
[-1,3,4,2,-5] => [-5,2,4,3,-1] => 10001 => 10010
[-1,3,4,-2,5] => [5,-2,4,3,-1] => 01001 => 11000
[-1,3,4,-2,-5] => [-5,-2,4,3,-1] => 11001 => 10110
[-1,3,-4,2,5] => [5,2,-4,3,-1] => 00101 => 11000
[-1,3,-4,2,-5] => [-5,2,-4,3,-1] => 10101 => 11100
[-1,3,-4,-2,5] => [5,-2,-4,3,-1] => 01101 => 11100
[-1,3,-4,-2,-5] => [-5,-2,-4,3,-1] => 11101 => 11110
[-1,-3,4,2,5] => [5,2,4,-3,-1] => 00011 => 10010
[-1,-3,4,2,-5] => [-5,2,4,-3,-1] => 10011 => 10110
[-1,-3,4,-2,5] => [5,-2,4,-3,-1] => 01011 => 11100
[-1,-3,4,-2,-5] => [-5,-2,4,-3,-1] => 11011 => 11110
[-1,-3,-4,2,5] => [5,2,-4,-3,-1] => 00111 => 10110
[-1,-3,-4,2,-5] => [-5,2,-4,-3,-1] => 10111 => 11110
[-1,-3,-4,-2,5] => [5,-2,-4,-3,-1] => 01111 => 11110
[-1,-3,-4,-2,-5] => [-5,-2,-4,-3,-1] => 11111 => 11111
[1,3,4,5,2] => [2,5,4,3,1] => 00000 => 00000
[1,3,4,5,-2] => [-2,5,4,3,1] => 10000 => 10000
[1,3,4,-5,2] => [2,-5,4,3,1] => 01000 => 10000
[1,3,4,-5,-2] => [-2,-5,4,3,1] => 11000 => 10010
[1,3,-4,5,2] => [2,5,-4,3,1] => 00100 => 10000
[1,3,-4,5,-2] => [-2,5,-4,3,1] => 10100 => 11000
[1,3,-4,-5,2] => [2,-5,-4,3,1] => 01100 => 10010
[1,3,-4,-5,-2] => [-2,-5,-4,3,1] => 11100 => 10110
[1,-3,4,5,2] => [2,5,4,-3,1] => 00010 => 10000
[1,-3,4,5,-2] => [-2,5,4,-3,1] => 10010 => 11000
[1,-3,4,-5,2] => [2,-5,4,-3,1] => 01010 => 11000
[1,-3,4,-5,-2] => [-2,-5,4,-3,1] => 11010 => 11100
[1,-3,-4,5,2] => [2,5,-4,-3,1] => 00110 => 10010
[1,-3,-4,5,-2] => [-2,5,-4,-3,1] => 10110 => 11100
[1,-3,-4,-5,2] => [2,-5,-4,-3,1] => 01110 => 10110
[1,-3,-4,-5,-2] => [-2,-5,-4,-3,1] => 11110 => 11110
[-1,3,4,5,2] => [2,5,4,3,-1] => 00001 => 10000
[-1,3,4,5,-2] => [-2,5,4,3,-1] => 10001 => 10010
[-1,3,4,-5,2] => [2,-5,4,3,-1] => 01001 => 11000
[-1,3,4,-5,-2] => [-2,-5,4,3,-1] => 11001 => 10110
[-1,3,-4,5,2] => [2,5,-4,3,-1] => 00101 => 11000
[-1,3,-4,5,-2] => [-2,5,-4,3,-1] => 10101 => 11100
[-1,3,-4,-5,2] => [2,-5,-4,3,-1] => 01101 => 11100
[-1,3,-4,-5,-2] => [-2,-5,-4,3,-1] => 11101 => 11110
[-1,-3,4,5,2] => [2,5,4,-3,-1] => 00011 => 10010
[-1,-3,4,5,-2] => [-2,5,4,-3,-1] => 10011 => 10110
[-1,-3,4,-5,2] => [2,-5,4,-3,-1] => 01011 => 11100
[-1,-3,4,-5,-2] => [-2,-5,4,-3,-1] => 11011 => 11110
[-1,-3,-4,5,2] => [2,5,-4,-3,-1] => 00111 => 10110
[-1,-3,-4,5,-2] => [-2,5,-4,-3,-1] => 10111 => 11110
[-1,-3,-4,-5,2] => [2,-5,-4,-3,-1] => 01111 => 11110
[-1,-3,-4,-5,-2] => [-2,-5,-4,-3,-1] => 11111 => 11111
[1,3,5,2,4] => [4,2,5,3,1] => 00000 => 00000
[1,3,5,2,-4] => [-4,2,5,3,1] => 10000 => 10000
[1,3,5,-2,4] => [4,-2,5,3,1] => 01000 => 10000
[1,3,5,-2,-4] => [-4,-2,5,3,1] => 11000 => 10010
[1,3,-5,2,4] => [4,2,-5,3,1] => 00100 => 10000
[1,3,-5,2,-4] => [-4,2,-5,3,1] => 10100 => 11000
[1,3,-5,-2,4] => [4,-2,-5,3,1] => 01100 => 10010
[1,3,-5,-2,-4] => [-4,-2,-5,3,1] => 11100 => 10110
[1,-3,5,2,4] => [4,2,5,-3,1] => 00010 => 10000
[1,-3,5,2,-4] => [-4,2,5,-3,1] => 10010 => 11000
[1,-3,5,-2,4] => [4,-2,5,-3,1] => 01010 => 11000
[1,-3,5,-2,-4] => [-4,-2,5,-3,1] => 11010 => 11100
[1,-3,-5,2,4] => [4,2,-5,-3,1] => 00110 => 10010
[1,-3,-5,2,-4] => [-4,2,-5,-3,1] => 10110 => 11100
[1,-3,-5,-2,4] => [4,-2,-5,-3,1] => 01110 => 10110
[1,-3,-5,-2,-4] => [-4,-2,-5,-3,1] => 11110 => 11110
[-1,3,5,2,4] => [4,2,5,3,-1] => 00001 => 10000
[-1,3,5,2,-4] => [-4,2,5,3,-1] => 10001 => 10010
[-1,3,5,-2,4] => [4,-2,5,3,-1] => 01001 => 11000
[-1,3,5,-2,-4] => [-4,-2,5,3,-1] => 11001 => 10110
[-1,3,-5,2,4] => [4,2,-5,3,-1] => 00101 => 11000
[-1,3,-5,2,-4] => [-4,2,-5,3,-1] => 10101 => 11100
[-1,3,-5,-2,4] => [4,-2,-5,3,-1] => 01101 => 11100
[-1,3,-5,-2,-4] => [-4,-2,-5,3,-1] => 11101 => 11110
[-1,-3,5,2,4] => [4,2,5,-3,-1] => 00011 => 10010
[-1,-3,5,2,-4] => [-4,2,5,-3,-1] => 10011 => 10110
[-1,-3,5,-2,4] => [4,-2,5,-3,-1] => 01011 => 11100
[-1,-3,5,-2,-4] => [-4,-2,5,-3,-1] => 11011 => 11110
[-1,-3,-5,2,4] => [4,2,-5,-3,-1] => 00111 => 10110
[-1,-3,-5,2,-4] => [-4,2,-5,-3,-1] => 10111 => 11110
[-1,-3,-5,-2,4] => [4,-2,-5,-3,-1] => 01111 => 11110
[-1,-3,-5,-2,-4] => [-4,-2,-5,-3,-1] => 11111 => 11111
[1,3,5,4,2] => [2,4,5,3,1] => 00000 => 00000
[1,3,5,4,-2] => [-2,4,5,3,1] => 10000 => 10000
[1,3,5,-4,2] => [2,-4,5,3,1] => 01000 => 10000
[1,3,5,-4,-2] => [-2,-4,5,3,1] => 11000 => 10010
[1,3,-5,4,2] => [2,4,-5,3,1] => 00100 => 10000
[1,3,-5,4,-2] => [-2,4,-5,3,1] => 10100 => 11000
[1,3,-5,-4,2] => [2,-4,-5,3,1] => 01100 => 10010
[1,3,-5,-4,-2] => [-2,-4,-5,3,1] => 11100 => 10110
[1,-3,5,4,2] => [2,4,5,-3,1] => 00010 => 10000
[1,-3,5,4,-2] => [-2,4,5,-3,1] => 10010 => 11000
[1,-3,5,-4,2] => [2,-4,5,-3,1] => 01010 => 11000
[1,-3,5,-4,-2] => [-2,-4,5,-3,1] => 11010 => 11100
[1,-3,-5,4,2] => [2,4,-5,-3,1] => 00110 => 10010
[1,-3,-5,4,-2] => [-2,4,-5,-3,1] => 10110 => 11100
[1,-3,-5,-4,2] => [2,-4,-5,-3,1] => 01110 => 10110
[1,-3,-5,-4,-2] => [-2,-4,-5,-3,1] => 11110 => 11110
[-1,3,5,4,2] => [2,4,5,3,-1] => 00001 => 10000
[-1,3,5,4,-2] => [-2,4,5,3,-1] => 10001 => 10010
[-1,3,5,-4,2] => [2,-4,5,3,-1] => 01001 => 11000
[-1,3,5,-4,-2] => [-2,-4,5,3,-1] => 11001 => 10110
[-1,3,-5,4,2] => [2,4,-5,3,-1] => 00101 => 11000
[-1,3,-5,4,-2] => [-2,4,-5,3,-1] => 10101 => 11100
[-1,3,-5,-4,2] => [2,-4,-5,3,-1] => 01101 => 11100
[-1,3,-5,-4,-2] => [-2,-4,-5,3,-1] => 11101 => 11110
[-1,-3,5,4,2] => [2,4,5,-3,-1] => 00011 => 10010
[-1,-3,5,4,-2] => [-2,4,5,-3,-1] => 10011 => 10110
[-1,-3,5,-4,2] => [2,-4,5,-3,-1] => 01011 => 11100
[-1,-3,5,-4,-2] => [-2,-4,5,-3,-1] => 11011 => 11110
[-1,-3,-5,4,2] => [2,4,-5,-3,-1] => 00111 => 10110
[-1,-3,-5,4,-2] => [-2,4,-5,-3,-1] => 10111 => 11110
[-1,-3,-5,-4,2] => [2,-4,-5,-3,-1] => 01111 => 11110
[-1,-3,-5,-4,-2] => [-2,-4,-5,-3,-1] => 11111 => 11111
[1,4,2,3,5] => [5,3,2,4,1] => 00000 => 00000
[1,4,2,3,-5] => [-5,3,2,4,1] => 10000 => 10000
[1,4,2,-3,5] => [5,-3,2,4,1] => 01000 => 10000
[1,4,2,-3,-5] => [-5,-3,2,4,1] => 11000 => 10010
[1,4,-2,3,5] => [5,3,-2,4,1] => 00100 => 10000
[1,4,-2,3,-5] => [-5,3,-2,4,1] => 10100 => 11000
[1,4,-2,-3,5] => [5,-3,-2,4,1] => 01100 => 10010
[1,4,-2,-3,-5] => [-5,-3,-2,4,1] => 11100 => 10110
[1,-4,2,3,5] => [5,3,2,-4,1] => 00010 => 10000
[1,-4,2,3,-5] => [-5,3,2,-4,1] => 10010 => 11000
[1,-4,2,-3,5] => [5,-3,2,-4,1] => 01010 => 11000
[1,-4,2,-3,-5] => [-5,-3,2,-4,1] => 11010 => 11100
[1,-4,-2,3,5] => [5,3,-2,-4,1] => 00110 => 10010
[1,-4,-2,3,-5] => [-5,3,-2,-4,1] => 10110 => 11100
[1,-4,-2,-3,5] => [5,-3,-2,-4,1] => 01110 => 10110
[1,-4,-2,-3,-5] => [-5,-3,-2,-4,1] => 11110 => 11110
[-1,4,2,3,5] => [5,3,2,4,-1] => 00001 => 10000
[-1,4,2,3,-5] => [-5,3,2,4,-1] => 10001 => 10010
[-1,4,2,-3,5] => [5,-3,2,4,-1] => 01001 => 11000
[-1,4,2,-3,-5] => [-5,-3,2,4,-1] => 11001 => 10110
[-1,4,-2,3,5] => [5,3,-2,4,-1] => 00101 => 11000
[-1,4,-2,3,-5] => [-5,3,-2,4,-1] => 10101 => 11100
[-1,4,-2,-3,5] => [5,-3,-2,4,-1] => 01101 => 11100
[-1,4,-2,-3,-5] => [-5,-3,-2,4,-1] => 11101 => 11110
[-1,-4,2,3,5] => [5,3,2,-4,-1] => 00011 => 10010
[-1,-4,2,3,-5] => [-5,3,2,-4,-1] => 10011 => 10110
[-1,-4,2,-3,5] => [5,-3,2,-4,-1] => 01011 => 11100
[-1,-4,2,-3,-5] => [-5,-3,2,-4,-1] => 11011 => 11110
[-1,-4,-2,3,5] => [5,3,-2,-4,-1] => 00111 => 10110
[-1,-4,-2,3,-5] => [-5,3,-2,-4,-1] => 10111 => 11110
[-1,-4,-2,-3,5] => [5,-3,-2,-4,-1] => 01111 => 11110
[-1,-4,-2,-3,-5] => [-5,-3,-2,-4,-1] => 11111 => 11111
[1,4,2,5,3] => [3,5,2,4,1] => 00000 => 00000
[1,4,2,5,-3] => [-3,5,2,4,1] => 10000 => 10000
[1,4,2,-5,3] => [3,-5,2,4,1] => 01000 => 10000
[1,4,2,-5,-3] => [-3,-5,2,4,1] => 11000 => 10010
[1,4,-2,5,3] => [3,5,-2,4,1] => 00100 => 10000
[1,4,-2,5,-3] => [-3,5,-2,4,1] => 10100 => 11000
[1,4,-2,-5,3] => [3,-5,-2,4,1] => 01100 => 10010
[1,4,-2,-5,-3] => [-3,-5,-2,4,1] => 11100 => 10110
[1,-4,2,5,3] => [3,5,2,-4,1] => 00010 => 10000
[1,-4,2,5,-3] => [-3,5,2,-4,1] => 10010 => 11000
[1,-4,2,-5,3] => [3,-5,2,-4,1] => 01010 => 11000
[1,-4,2,-5,-3] => [-3,-5,2,-4,1] => 11010 => 11100
[1,-4,-2,5,3] => [3,5,-2,-4,1] => 00110 => 10010
[1,-4,-2,5,-3] => [-3,5,-2,-4,1] => 10110 => 11100
[1,-4,-2,-5,3] => [3,-5,-2,-4,1] => 01110 => 10110
[1,-4,-2,-5,-3] => [-3,-5,-2,-4,1] => 11110 => 11110
[-1,4,2,5,3] => [3,5,2,4,-1] => 00001 => 10000
[-1,4,2,5,-3] => [-3,5,2,4,-1] => 10001 => 10010
[-1,4,2,-5,3] => [3,-5,2,4,-1] => 01001 => 11000
[-1,4,2,-5,-3] => [-3,-5,2,4,-1] => 11001 => 10110
[-1,4,-2,5,3] => [3,5,-2,4,-1] => 00101 => 11000
[-1,4,-2,5,-3] => [-3,5,-2,4,-1] => 10101 => 11100
[-1,4,-2,-5,3] => [3,-5,-2,4,-1] => 01101 => 11100
[-1,4,-2,-5,-3] => [-3,-5,-2,4,-1] => 11101 => 11110
[-1,-4,2,5,3] => [3,5,2,-4,-1] => 00011 => 10010
[-1,-4,2,5,-3] => [-3,5,2,-4,-1] => 10011 => 10110
[-1,-4,2,-5,3] => [3,-5,2,-4,-1] => 01011 => 11100
[-1,-4,2,-5,-3] => [-3,-5,2,-4,-1] => 11011 => 11110
[-1,-4,-2,5,3] => [3,5,-2,-4,-1] => 00111 => 10110
[-1,-4,-2,5,-3] => [-3,5,-2,-4,-1] => 10111 => 11110
[-1,-4,-2,-5,3] => [3,-5,-2,-4,-1] => 01111 => 11110
[-1,-4,-2,-5,-3] => [-3,-5,-2,-4,-1] => 11111 => 11111
[1,4,3,2,5] => [5,2,3,4,1] => 00000 => 00000
[1,4,3,2,-5] => [-5,2,3,4,1] => 10000 => 10000
[1,4,3,-2,5] => [5,-2,3,4,1] => 01000 => 10000
[1,4,3,-2,-5] => [-5,-2,3,4,1] => 11000 => 10010
[1,4,-3,2,5] => [5,2,-3,4,1] => 00100 => 10000
[1,4,-3,2,-5] => [-5,2,-3,4,1] => 10100 => 11000
[1,4,-3,-2,5] => [5,-2,-3,4,1] => 01100 => 10010
[1,4,-3,-2,-5] => [-5,-2,-3,4,1] => 11100 => 10110
[1,-4,3,2,5] => [5,2,3,-4,1] => 00010 => 10000
[1,-4,3,2,-5] => [-5,2,3,-4,1] => 10010 => 11000
[1,-4,3,-2,5] => [5,-2,3,-4,1] => 01010 => 11000
[1,-4,3,-2,-5] => [-5,-2,3,-4,1] => 11010 => 11100
[1,-4,-3,2,5] => [5,2,-3,-4,1] => 00110 => 10010
[1,-4,-3,2,-5] => [-5,2,-3,-4,1] => 10110 => 11100
[1,-4,-3,-2,5] => [5,-2,-3,-4,1] => 01110 => 10110
[1,-4,-3,-2,-5] => [-5,-2,-3,-4,1] => 11110 => 11110
[-1,4,3,2,5] => [5,2,3,4,-1] => 00001 => 10000
[-1,4,3,2,-5] => [-5,2,3,4,-1] => 10001 => 10010
[-1,4,3,-2,5] => [5,-2,3,4,-1] => 01001 => 11000
[-1,4,3,-2,-5] => [-5,-2,3,4,-1] => 11001 => 10110
[-1,4,-3,2,5] => [5,2,-3,4,-1] => 00101 => 11000
[-1,4,-3,2,-5] => [-5,2,-3,4,-1] => 10101 => 11100
[-1,4,-3,-2,5] => [5,-2,-3,4,-1] => 01101 => 11100
[-1,4,-3,-2,-5] => [-5,-2,-3,4,-1] => 11101 => 11110
[-1,-4,3,2,5] => [5,2,3,-4,-1] => 00011 => 10010
[-1,-4,3,2,-5] => [-5,2,3,-4,-1] => 10011 => 10110
[-1,-4,3,-2,5] => [5,-2,3,-4,-1] => 01011 => 11100
[-1,-4,3,-2,-5] => [-5,-2,3,-4,-1] => 11011 => 11110
[-1,-4,-3,2,5] => [5,2,-3,-4,-1] => 00111 => 10110
[-1,-4,-3,2,-5] => [-5,2,-3,-4,-1] => 10111 => 11110
[-1,-4,-3,-2,5] => [5,-2,-3,-4,-1] => 01111 => 11110
[-1,-4,-3,-2,-5] => [-5,-2,-3,-4,-1] => 11111 => 11111
[1,4,3,5,2] => [2,5,3,4,1] => 00000 => 00000
[1,4,3,5,-2] => [-2,5,3,4,1] => 10000 => 10000
[1,4,3,-5,2] => [2,-5,3,4,1] => 01000 => 10000
[1,4,3,-5,-2] => [-2,-5,3,4,1] => 11000 => 10010
[1,4,-3,5,2] => [2,5,-3,4,1] => 00100 => 10000
[1,4,-3,5,-2] => [-2,5,-3,4,1] => 10100 => 11000
[1,4,-3,-5,2] => [2,-5,-3,4,1] => 01100 => 10010
[1,4,-3,-5,-2] => [-2,-5,-3,4,1] => 11100 => 10110
[1,-4,3,5,2] => [2,5,3,-4,1] => 00010 => 10000
[1,-4,3,5,-2] => [-2,5,3,-4,1] => 10010 => 11000
[1,-4,3,-5,2] => [2,-5,3,-4,1] => 01010 => 11000
[1,-4,3,-5,-2] => [-2,-5,3,-4,1] => 11010 => 11100
[1,-4,-3,5,2] => [2,5,-3,-4,1] => 00110 => 10010
[1,-4,-3,5,-2] => [-2,5,-3,-4,1] => 10110 => 11100
[1,-4,-3,-5,2] => [2,-5,-3,-4,1] => 01110 => 10110
[1,-4,-3,-5,-2] => [-2,-5,-3,-4,1] => 11110 => 11110
[-1,4,3,5,2] => [2,5,3,4,-1] => 00001 => 10000
[-1,4,3,5,-2] => [-2,5,3,4,-1] => 10001 => 10010
[-1,4,3,-5,2] => [2,-5,3,4,-1] => 01001 => 11000
[-1,4,3,-5,-2] => [-2,-5,3,4,-1] => 11001 => 10110
[-1,4,-3,5,2] => [2,5,-3,4,-1] => 00101 => 11000
[-1,4,-3,5,-2] => [-2,5,-3,4,-1] => 10101 => 11100
[-1,4,-3,-5,2] => [2,-5,-3,4,-1] => 01101 => 11100
[-1,4,-3,-5,-2] => [-2,-5,-3,4,-1] => 11101 => 11110
[-1,-4,3,5,2] => [2,5,3,-4,-1] => 00011 => 10010
[-1,-4,3,5,-2] => [-2,5,3,-4,-1] => 10011 => 10110
[-1,-4,3,-5,2] => [2,-5,3,-4,-1] => 01011 => 11100
[-1,-4,3,-5,-2] => [-2,-5,3,-4,-1] => 11011 => 11110
[-1,-4,-3,5,2] => [2,5,-3,-4,-1] => 00111 => 10110
[-1,-4,-3,5,-2] => [-2,5,-3,-4,-1] => 10111 => 11110
[-1,-4,-3,-5,2] => [2,-5,-3,-4,-1] => 01111 => 11110
[-1,-4,-3,-5,-2] => [-2,-5,-3,-4,-1] => 11111 => 11111
[1,4,5,2,3] => [3,2,5,4,1] => 00000 => 00000
[1,4,5,2,-3] => [-3,2,5,4,1] => 10000 => 10000
[1,4,5,-2,3] => [3,-2,5,4,1] => 01000 => 10000
[1,4,5,-2,-3] => [-3,-2,5,4,1] => 11000 => 10010
[1,4,-5,2,3] => [3,2,-5,4,1] => 00100 => 10000
[1,4,-5,2,-3] => [-3,2,-5,4,1] => 10100 => 11000
[1,4,-5,-2,3] => [3,-2,-5,4,1] => 01100 => 10010
[1,4,-5,-2,-3] => [-3,-2,-5,4,1] => 11100 => 10110
[1,-4,5,2,3] => [3,2,5,-4,1] => 00010 => 10000
[1,-4,5,2,-3] => [-3,2,5,-4,1] => 10010 => 11000
[1,-4,5,-2,3] => [3,-2,5,-4,1] => 01010 => 11000
[1,-4,5,-2,-3] => [-3,-2,5,-4,1] => 11010 => 11100
[1,-4,-5,2,3] => [3,2,-5,-4,1] => 00110 => 10010
[1,-4,-5,2,-3] => [-3,2,-5,-4,1] => 10110 => 11100
[1,-4,-5,-2,3] => [3,-2,-5,-4,1] => 01110 => 10110
[1,-4,-5,-2,-3] => [-3,-2,-5,-4,1] => 11110 => 11110
[-1,4,5,2,3] => [3,2,5,4,-1] => 00001 => 10000
[-1,4,5,2,-3] => [-3,2,5,4,-1] => 10001 => 10010
[-1,4,5,-2,3] => [3,-2,5,4,-1] => 01001 => 11000
[-1,4,5,-2,-3] => [-3,-2,5,4,-1] => 11001 => 10110
[-1,4,-5,2,3] => [3,2,-5,4,-1] => 00101 => 11000
[-1,4,-5,2,-3] => [-3,2,-5,4,-1] => 10101 => 11100
[-1,4,-5,-2,3] => [3,-2,-5,4,-1] => 01101 => 11100
[-1,4,-5,-2,-3] => [-3,-2,-5,4,-1] => 11101 => 11110
[-1,-4,5,2,3] => [3,2,5,-4,-1] => 00011 => 10010
[-1,-4,5,2,-3] => [-3,2,5,-4,-1] => 10011 => 10110
[-1,-4,5,-2,3] => [3,-2,5,-4,-1] => 01011 => 11100
[-1,-4,5,-2,-3] => [-3,-2,5,-4,-1] => 11011 => 11110
[-1,-4,-5,2,3] => [3,2,-5,-4,-1] => 00111 => 10110
[-1,-4,-5,2,-3] => [-3,2,-5,-4,-1] => 10111 => 11110
[-1,-4,-5,-2,3] => [3,-2,-5,-4,-1] => 01111 => 11110
[-1,-4,-5,-2,-3] => [-3,-2,-5,-4,-1] => 11111 => 11111
[1,4,5,3,2] => [2,3,5,4,1] => 00000 => 00000
[1,4,5,3,-2] => [-2,3,5,4,1] => 10000 => 10000
[1,4,5,-3,2] => [2,-3,5,4,1] => 01000 => 10000
[1,4,5,-3,-2] => [-2,-3,5,4,1] => 11000 => 10010
[1,4,-5,3,2] => [2,3,-5,4,1] => 00100 => 10000
[1,4,-5,3,-2] => [-2,3,-5,4,1] => 10100 => 11000
[1,4,-5,-3,2] => [2,-3,-5,4,1] => 01100 => 10010
[1,4,-5,-3,-2] => [-2,-3,-5,4,1] => 11100 => 10110
[1,-4,5,3,2] => [2,3,5,-4,1] => 00010 => 10000
[1,-4,5,3,-2] => [-2,3,5,-4,1] => 10010 => 11000
[1,-4,5,-3,2] => [2,-3,5,-4,1] => 01010 => 11000
[1,-4,5,-3,-2] => [-2,-3,5,-4,1] => 11010 => 11100
[1,-4,-5,3,2] => [2,3,-5,-4,1] => 00110 => 10010
[1,-4,-5,3,-2] => [-2,3,-5,-4,1] => 10110 => 11100
[1,-4,-5,-3,2] => [2,-3,-5,-4,1] => 01110 => 10110
[1,-4,-5,-3,-2] => [-2,-3,-5,-4,1] => 11110 => 11110
[-1,4,5,3,2] => [2,3,5,4,-1] => 00001 => 10000
[-1,4,5,3,-2] => [-2,3,5,4,-1] => 10001 => 10010
[-1,4,5,-3,2] => [2,-3,5,4,-1] => 01001 => 11000
[-1,4,5,-3,-2] => [-2,-3,5,4,-1] => 11001 => 10110
[-1,4,-5,3,2] => [2,3,-5,4,-1] => 00101 => 11000
[-1,4,-5,3,-2] => [-2,3,-5,4,-1] => 10101 => 11100
[-1,4,-5,-3,2] => [2,-3,-5,4,-1] => 01101 => 11100
[-1,4,-5,-3,-2] => [-2,-3,-5,4,-1] => 11101 => 11110
[-1,-4,5,3,2] => [2,3,5,-4,-1] => 00011 => 10010
[-1,-4,5,3,-2] => [-2,3,5,-4,-1] => 10011 => 10110
[-1,-4,5,-3,2] => [2,-3,5,-4,-1] => 01011 => 11100
[-1,-4,5,-3,-2] => [-2,-3,5,-4,-1] => 11011 => 11110
[-1,-4,-5,3,2] => [2,3,-5,-4,-1] => 00111 => 10110
[-1,-4,-5,3,-2] => [-2,3,-5,-4,-1] => 10111 => 11110
[-1,-4,-5,-3,2] => [2,-3,-5,-4,-1] => 01111 => 11110
[-1,-4,-5,-3,-2] => [-2,-3,-5,-4,-1] => 11111 => 11111
[1,5,2,3,4] => [4,3,2,5,1] => 00000 => 00000
[1,5,2,3,-4] => [-4,3,2,5,1] => 10000 => 10000
[1,5,2,-3,4] => [4,-3,2,5,1] => 01000 => 10000
[1,5,2,-3,-4] => [-4,-3,2,5,1] => 11000 => 10010
[1,5,-2,3,4] => [4,3,-2,5,1] => 00100 => 10000
[1,5,-2,3,-4] => [-4,3,-2,5,1] => 10100 => 11000
[1,5,-2,-3,4] => [4,-3,-2,5,1] => 01100 => 10010
[1,5,-2,-3,-4] => [-4,-3,-2,5,1] => 11100 => 10110
[1,-5,2,3,4] => [4,3,2,-5,1] => 00010 => 10000
[1,-5,2,3,-4] => [-4,3,2,-5,1] => 10010 => 11000
[1,-5,2,-3,4] => [4,-3,2,-5,1] => 01010 => 11000
[1,-5,2,-3,-4] => [-4,-3,2,-5,1] => 11010 => 11100
[1,-5,-2,3,4] => [4,3,-2,-5,1] => 00110 => 10010
[1,-5,-2,3,-4] => [-4,3,-2,-5,1] => 10110 => 11100
[1,-5,-2,-3,4] => [4,-3,-2,-5,1] => 01110 => 10110
[1,-5,-2,-3,-4] => [-4,-3,-2,-5,1] => 11110 => 11110
[-1,5,2,3,4] => [4,3,2,5,-1] => 00001 => 10000
[-1,5,2,3,-4] => [-4,3,2,5,-1] => 10001 => 10010
[-1,5,2,-3,4] => [4,-3,2,5,-1] => 01001 => 11000
[-1,5,2,-3,-4] => [-4,-3,2,5,-1] => 11001 => 10110
[-1,5,-2,3,4] => [4,3,-2,5,-1] => 00101 => 11000
[-1,5,-2,3,-4] => [-4,3,-2,5,-1] => 10101 => 11100
[-1,5,-2,-3,4] => [4,-3,-2,5,-1] => 01101 => 11100
[-1,5,-2,-3,-4] => [-4,-3,-2,5,-1] => 11101 => 11110
[-1,-5,2,3,4] => [4,3,2,-5,-1] => 00011 => 10010
[-1,-5,2,3,-4] => [-4,3,2,-5,-1] => 10011 => 10110
[-1,-5,2,-3,4] => [4,-3,2,-5,-1] => 01011 => 11100
[-1,-5,2,-3,-4] => [-4,-3,2,-5,-1] => 11011 => 11110
[-1,-5,-2,3,4] => [4,3,-2,-5,-1] => 00111 => 10110
[-1,-5,-2,3,-4] => [-4,3,-2,-5,-1] => 10111 => 11110
[-1,-5,-2,-3,4] => [4,-3,-2,-5,-1] => 01111 => 11110
[-1,-5,-2,-3,-4] => [-4,-3,-2,-5,-1] => 11111 => 11111
[1,5,2,4,3] => [3,4,2,5,1] => 00000 => 00000
[1,5,2,4,-3] => [-3,4,2,5,1] => 10000 => 10000
[1,5,2,-4,3] => [3,-4,2,5,1] => 01000 => 10000
[1,5,2,-4,-3] => [-3,-4,2,5,1] => 11000 => 10010
[1,5,-2,4,3] => [3,4,-2,5,1] => 00100 => 10000
[1,5,-2,4,-3] => [-3,4,-2,5,1] => 10100 => 11000
[1,5,-2,-4,3] => [3,-4,-2,5,1] => 01100 => 10010
[1,5,-2,-4,-3] => [-3,-4,-2,5,1] => 11100 => 10110
[1,-5,2,4,3] => [3,4,2,-5,1] => 00010 => 10000
[1,-5,2,4,-3] => [-3,4,2,-5,1] => 10010 => 11000
[1,-5,2,-4,3] => [3,-4,2,-5,1] => 01010 => 11000
[1,-5,2,-4,-3] => [-3,-4,2,-5,1] => 11010 => 11100
[1,-5,-2,4,3] => [3,4,-2,-5,1] => 00110 => 10010
[1,-5,-2,4,-3] => [-3,4,-2,-5,1] => 10110 => 11100
[1,-5,-2,-4,3] => [3,-4,-2,-5,1] => 01110 => 10110
[1,-5,-2,-4,-3] => [-3,-4,-2,-5,1] => 11110 => 11110
[-1,5,2,4,3] => [3,4,2,5,-1] => 00001 => 10000
[-1,5,2,4,-3] => [-3,4,2,5,-1] => 10001 => 10010
[-1,5,2,-4,3] => [3,-4,2,5,-1] => 01001 => 11000
[-1,5,2,-4,-3] => [-3,-4,2,5,-1] => 11001 => 10110
[-1,5,-2,4,3] => [3,4,-2,5,-1] => 00101 => 11000
[-1,5,-2,4,-3] => [-3,4,-2,5,-1] => 10101 => 11100
[-1,5,-2,-4,3] => [3,-4,-2,5,-1] => 01101 => 11100
[-1,5,-2,-4,-3] => [-3,-4,-2,5,-1] => 11101 => 11110
[-1,-5,2,4,3] => [3,4,2,-5,-1] => 00011 => 10010
[-1,-5,2,4,-3] => [-3,4,2,-5,-1] => 10011 => 10110
[-1,-5,2,-4,3] => [3,-4,2,-5,-1] => 01011 => 11100
[-1,-5,2,-4,-3] => [-3,-4,2,-5,-1] => 11011 => 11110
[-1,-5,-2,4,3] => [3,4,-2,-5,-1] => 00111 => 10110
[-1,-5,-2,4,-3] => [-3,4,-2,-5,-1] => 10111 => 11110
[-1,-5,-2,-4,3] => [3,-4,-2,-5,-1] => 01111 => 11110
[-1,-5,-2,-4,-3] => [-3,-4,-2,-5,-1] => 11111 => 11111
[1,5,3,2,4] => [4,2,3,5,1] => 00000 => 00000
[1,5,3,2,-4] => [-4,2,3,5,1] => 10000 => 10000
[1,5,3,-2,4] => [4,-2,3,5,1] => 01000 => 10000
[1,5,3,-2,-4] => [-4,-2,3,5,1] => 11000 => 10010
[1,5,-3,2,4] => [4,2,-3,5,1] => 00100 => 10000
[1,5,-3,2,-4] => [-4,2,-3,5,1] => 10100 => 11000
[1,5,-3,-2,4] => [4,-2,-3,5,1] => 01100 => 10010
[1,5,-3,-2,-4] => [-4,-2,-3,5,1] => 11100 => 10110
[1,-5,3,2,4] => [4,2,3,-5,1] => 00010 => 10000
[1,-5,3,2,-4] => [-4,2,3,-5,1] => 10010 => 11000
[1,-5,3,-2,4] => [4,-2,3,-5,1] => 01010 => 11000
[1,-5,3,-2,-4] => [-4,-2,3,-5,1] => 11010 => 11100
[1,-5,-3,2,4] => [4,2,-3,-5,1] => 00110 => 10010
[1,-5,-3,2,-4] => [-4,2,-3,-5,1] => 10110 => 11100
[1,-5,-3,-2,4] => [4,-2,-3,-5,1] => 01110 => 10110
[1,-5,-3,-2,-4] => [-4,-2,-3,-5,1] => 11110 => 11110
[-1,5,3,2,4] => [4,2,3,5,-1] => 00001 => 10000
[-1,5,3,2,-4] => [-4,2,3,5,-1] => 10001 => 10010
[-1,5,3,-2,4] => [4,-2,3,5,-1] => 01001 => 11000
[-1,5,3,-2,-4] => [-4,-2,3,5,-1] => 11001 => 10110
[-1,5,-3,2,4] => [4,2,-3,5,-1] => 00101 => 11000
[-1,5,-3,2,-4] => [-4,2,-3,5,-1] => 10101 => 11100
[-1,5,-3,-2,4] => [4,-2,-3,5,-1] => 01101 => 11100
[-1,5,-3,-2,-4] => [-4,-2,-3,5,-1] => 11101 => 11110
[-1,-5,3,2,4] => [4,2,3,-5,-1] => 00011 => 10010
[-1,-5,3,2,-4] => [-4,2,3,-5,-1] => 10011 => 10110
[-1,-5,3,-2,4] => [4,-2,3,-5,-1] => 01011 => 11100
[-1,-5,3,-2,-4] => [-4,-2,3,-5,-1] => 11011 => 11110
[-1,-5,-3,2,4] => [4,2,-3,-5,-1] => 00111 => 10110
[-1,-5,-3,2,-4] => [-4,2,-3,-5,-1] => 10111 => 11110
[-1,-5,-3,-2,4] => [4,-2,-3,-5,-1] => 01111 => 11110
[-1,-5,-3,-2,-4] => [-4,-2,-3,-5,-1] => 11111 => 11111
[1,5,3,4,2] => [2,4,3,5,1] => 00000 => 00000
[1,5,3,4,-2] => [-2,4,3,5,1] => 10000 => 10000
[1,5,3,-4,2] => [2,-4,3,5,1] => 01000 => 10000
[1,5,3,-4,-2] => [-2,-4,3,5,1] => 11000 => 10010
[1,5,-3,4,2] => [2,4,-3,5,1] => 00100 => 10000
[1,5,-3,4,-2] => [-2,4,-3,5,1] => 10100 => 11000
[1,5,-3,-4,2] => [2,-4,-3,5,1] => 01100 => 10010
[1,5,-3,-4,-2] => [-2,-4,-3,5,1] => 11100 => 10110
[1,-5,3,4,2] => [2,4,3,-5,1] => 00010 => 10000
[1,-5,3,4,-2] => [-2,4,3,-5,1] => 10010 => 11000
[1,-5,3,-4,2] => [2,-4,3,-5,1] => 01010 => 11000
[1,-5,3,-4,-2] => [-2,-4,3,-5,1] => 11010 => 11100
[1,-5,-3,4,2] => [2,4,-3,-5,1] => 00110 => 10010
[1,-5,-3,4,-2] => [-2,4,-3,-5,1] => 10110 => 11100
[1,-5,-3,-4,2] => [2,-4,-3,-5,1] => 01110 => 10110
[1,-5,-3,-4,-2] => [-2,-4,-3,-5,1] => 11110 => 11110
[-1,5,3,4,2] => [2,4,3,5,-1] => 00001 => 10000
[-1,5,3,4,-2] => [-2,4,3,5,-1] => 10001 => 10010
[-1,5,3,-4,2] => [2,-4,3,5,-1] => 01001 => 11000
[-1,5,3,-4,-2] => [-2,-4,3,5,-1] => 11001 => 10110
[-1,5,-3,4,2] => [2,4,-3,5,-1] => 00101 => 11000
[-1,5,-3,4,-2] => [-2,4,-3,5,-1] => 10101 => 11100
[-1,5,-3,-4,2] => [2,-4,-3,5,-1] => 01101 => 11100
[-1,5,-3,-4,-2] => [-2,-4,-3,5,-1] => 11101 => 11110
[-1,-5,3,4,2] => [2,4,3,-5,-1] => 00011 => 10010
[-1,-5,3,4,-2] => [-2,4,3,-5,-1] => 10011 => 10110
[-1,-5,3,-4,2] => [2,-4,3,-5,-1] => 01011 => 11100
[-1,-5,3,-4,-2] => [-2,-4,3,-5,-1] => 11011 => 11110
[-1,-5,-3,4,2] => [2,4,-3,-5,-1] => 00111 => 10110
[-1,-5,-3,4,-2] => [-2,4,-3,-5,-1] => 10111 => 11110
[-1,-5,-3,-4,2] => [2,-4,-3,-5,-1] => 01111 => 11110
[-1,-5,-3,-4,-2] => [-2,-4,-3,-5,-1] => 11111 => 11111
[1,5,4,2,3] => [3,2,4,5,1] => 00000 => 00000
[1,5,4,2,-3] => [-3,2,4,5,1] => 10000 => 10000
[1,5,4,-2,3] => [3,-2,4,5,1] => 01000 => 10000
[1,5,4,-2,-3] => [-3,-2,4,5,1] => 11000 => 10010
[1,5,-4,2,3] => [3,2,-4,5,1] => 00100 => 10000
[1,5,-4,2,-3] => [-3,2,-4,5,1] => 10100 => 11000
[1,5,-4,-2,3] => [3,-2,-4,5,1] => 01100 => 10010
[1,5,-4,-2,-3] => [-3,-2,-4,5,1] => 11100 => 10110
[1,-5,4,2,3] => [3,2,4,-5,1] => 00010 => 10000
[1,-5,4,2,-3] => [-3,2,4,-5,1] => 10010 => 11000
[1,-5,4,-2,3] => [3,-2,4,-5,1] => 01010 => 11000
[1,-5,4,-2,-3] => [-3,-2,4,-5,1] => 11010 => 11100
[1,-5,-4,2,3] => [3,2,-4,-5,1] => 00110 => 10010
[1,-5,-4,2,-3] => [-3,2,-4,-5,1] => 10110 => 11100
[1,-5,-4,-2,3] => [3,-2,-4,-5,1] => 01110 => 10110
[1,-5,-4,-2,-3] => [-3,-2,-4,-5,1] => 11110 => 11110
[-1,5,4,2,3] => [3,2,4,5,-1] => 00001 => 10000
[-1,5,4,2,-3] => [-3,2,4,5,-1] => 10001 => 10010
[-1,5,4,-2,3] => [3,-2,4,5,-1] => 01001 => 11000
[-1,5,4,-2,-3] => [-3,-2,4,5,-1] => 11001 => 10110
[-1,5,-4,2,3] => [3,2,-4,5,-1] => 00101 => 11000
[-1,5,-4,2,-3] => [-3,2,-4,5,-1] => 10101 => 11100
[-1,5,-4,-2,3] => [3,-2,-4,5,-1] => 01101 => 11100
[-1,5,-4,-2,-3] => [-3,-2,-4,5,-1] => 11101 => 11110
[-1,-5,4,2,3] => [3,2,4,-5,-1] => 00011 => 10010
[-1,-5,4,2,-3] => [-3,2,4,-5,-1] => 10011 => 10110
[-1,-5,4,-2,3] => [3,-2,4,-5,-1] => 01011 => 11100
[-1,-5,4,-2,-3] => [-3,-2,4,-5,-1] => 11011 => 11110
[-1,-5,-4,2,3] => [3,2,-4,-5,-1] => 00111 => 10110
[-1,-5,-4,2,-3] => [-3,2,-4,-5,-1] => 10111 => 11110
[-1,-5,-4,-2,3] => [3,-2,-4,-5,-1] => 01111 => 11110
[-1,-5,-4,-2,-3] => [-3,-2,-4,-5,-1] => 11111 => 11111
[1,5,4,3,2] => [2,3,4,5,1] => 00000 => 00000
[1,5,4,3,-2] => [-2,3,4,5,1] => 10000 => 10000
[1,5,4,-3,2] => [2,-3,4,5,1] => 01000 => 10000
[1,5,4,-3,-2] => [-2,-3,4,5,1] => 11000 => 10010
[1,5,-4,3,2] => [2,3,-4,5,1] => 00100 => 10000
[1,5,-4,3,-2] => [-2,3,-4,5,1] => 10100 => 11000
[1,5,-4,-3,2] => [2,-3,-4,5,1] => 01100 => 10010
[1,5,-4,-3,-2] => [-2,-3,-4,5,1] => 11100 => 10110
[1,-5,4,3,2] => [2,3,4,-5,1] => 00010 => 10000
[1,-5,4,3,-2] => [-2,3,4,-5,1] => 10010 => 11000
[1,-5,4,-3,2] => [2,-3,4,-5,1] => 01010 => 11000
[1,-5,4,-3,-2] => [-2,-3,4,-5,1] => 11010 => 11100
[1,-5,-4,3,2] => [2,3,-4,-5,1] => 00110 => 10010
[1,-5,-4,3,-2] => [-2,3,-4,-5,1] => 10110 => 11100
[1,-5,-4,-3,2] => [2,-3,-4,-5,1] => 01110 => 10110
[1,-5,-4,-3,-2] => [-2,-3,-4,-5,1] => 11110 => 11110
[-1,5,4,3,2] => [2,3,4,5,-1] => 00001 => 10000
[-1,5,4,3,-2] => [-2,3,4,5,-1] => 10001 => 10010
[-1,5,4,-3,2] => [2,-3,4,5,-1] => 01001 => 11000
[-1,5,4,-3,-2] => [-2,-3,4,5,-1] => 11001 => 10110
[-1,5,-4,3,2] => [2,3,-4,5,-1] => 00101 => 11000
[-1,5,-4,3,-2] => [-2,3,-4,5,-1] => 10101 => 11100
[-1,5,-4,-3,2] => [2,-3,-4,5,-1] => 01101 => 11100
[-1,5,-4,-3,-2] => [-2,-3,-4,5,-1] => 11101 => 11110
[-1,-5,4,3,2] => [2,3,4,-5,-1] => 00011 => 10010
[-1,-5,4,3,-2] => [-2,3,4,-5,-1] => 10011 => 10110
[-1,-5,4,-3,2] => [2,-3,4,-5,-1] => 01011 => 11100
[-1,-5,4,-3,-2] => [-2,-3,4,-5,-1] => 11011 => 11110
[-1,-5,-4,3,2] => [2,3,-4,-5,-1] => 00111 => 10110
[-1,-5,-4,3,-2] => [-2,3,-4,-5,-1] => 10111 => 11110
[-1,-5,-4,-3,2] => [2,-3,-4,-5,-1] => 01111 => 11110
[-1,-5,-4,-3,-2] => [-2,-3,-4,-5,-1] => 11111 => 11111
[2,1,3,4,5] => [5,4,3,1,2] => 00000 => 00000
[2,1,3,4,-5] => [-5,4,3,1,2] => 10000 => 10000
[2,1,3,-4,5] => [5,-4,3,1,2] => 01000 => 10000
[2,1,3,-4,-5] => [-5,-4,3,1,2] => 11000 => 10010
[2,1,-3,4,5] => [5,4,-3,1,2] => 00100 => 10000
[2,1,-3,4,-5] => [-5,4,-3,1,2] => 10100 => 11000
[2,1,-3,-4,5] => [5,-4,-3,1,2] => 01100 => 10010
[2,1,-3,-4,-5] => [-5,-4,-3,1,2] => 11100 => 10110
[2,-1,3,4,5] => [5,4,3,-1,2] => 00010 => 10000
[2,-1,3,4,-5] => [-5,4,3,-1,2] => 10010 => 11000
[2,-1,3,-4,5] => [5,-4,3,-1,2] => 01010 => 11000
[2,-1,3,-4,-5] => [-5,-4,3,-1,2] => 11010 => 11100
[2,-1,-3,4,5] => [5,4,-3,-1,2] => 00110 => 10010
[2,-1,-3,4,-5] => [-5,4,-3,-1,2] => 10110 => 11100
[2,-1,-3,-4,5] => [5,-4,-3,-1,2] => 01110 => 10110
[2,-1,-3,-4,-5] => [-5,-4,-3,-1,2] => 11110 => 11110
[-2,1,3,4,5] => [5,4,3,1,-2] => 00001 => 10000
[-2,1,3,4,-5] => [-5,4,3,1,-2] => 10001 => 10010
[-2,1,3,-4,5] => [5,-4,3,1,-2] => 01001 => 11000
[-2,1,3,-4,-5] => [-5,-4,3,1,-2] => 11001 => 10110
[-2,1,-3,4,5] => [5,4,-3,1,-2] => 00101 => 11000
[-2,1,-3,4,-5] => [-5,4,-3,1,-2] => 10101 => 11100
[-2,1,-3,-4,5] => [5,-4,-3,1,-2] => 01101 => 11100
[-2,1,-3,-4,-5] => [-5,-4,-3,1,-2] => 11101 => 11110
[-2,-1,3,4,5] => [5,4,3,-1,-2] => 00011 => 10010
[-2,-1,3,4,-5] => [-5,4,3,-1,-2] => 10011 => 10110
[-2,-1,3,-4,5] => [5,-4,3,-1,-2] => 01011 => 11100
[-2,-1,3,-4,-5] => [-5,-4,3,-1,-2] => 11011 => 11110
[-2,-1,-3,4,5] => [5,4,-3,-1,-2] => 00111 => 10110
[-2,-1,-3,4,-5] => [-5,4,-3,-1,-2] => 10111 => 11110
[-2,-1,-3,-4,5] => [5,-4,-3,-1,-2] => 01111 => 11110
[-2,-1,-3,-4,-5] => [-5,-4,-3,-1,-2] => 11111 => 11111
[2,1,3,5,4] => [4,5,3,1,2] => 00000 => 00000
[2,1,3,5,-4] => [-4,5,3,1,2] => 10000 => 10000
[2,1,3,-5,4] => [4,-5,3,1,2] => 01000 => 10000
[2,1,3,-5,-4] => [-4,-5,3,1,2] => 11000 => 10010
[2,1,-3,5,4] => [4,5,-3,1,2] => 00100 => 10000
[2,1,-3,5,-4] => [-4,5,-3,1,2] => 10100 => 11000
[2,1,-3,-5,4] => [4,-5,-3,1,2] => 01100 => 10010
[2,1,-3,-5,-4] => [-4,-5,-3,1,2] => 11100 => 10110
[2,-1,3,5,4] => [4,5,3,-1,2] => 00010 => 10000
[2,-1,3,5,-4] => [-4,5,3,-1,2] => 10010 => 11000
[2,-1,3,-5,4] => [4,-5,3,-1,2] => 01010 => 11000
[2,-1,3,-5,-4] => [-4,-5,3,-1,2] => 11010 => 11100
[2,-1,-3,5,4] => [4,5,-3,-1,2] => 00110 => 10010
[2,-1,-3,5,-4] => [-4,5,-3,-1,2] => 10110 => 11100
[2,-1,-3,-5,4] => [4,-5,-3,-1,2] => 01110 => 10110
[2,-1,-3,-5,-4] => [-4,-5,-3,-1,2] => 11110 => 11110
[-2,1,3,5,4] => [4,5,3,1,-2] => 00001 => 10000
[-2,1,3,5,-4] => [-4,5,3,1,-2] => 10001 => 10010
[-2,1,3,-5,4] => [4,-5,3,1,-2] => 01001 => 11000
[-2,1,3,-5,-4] => [-4,-5,3,1,-2] => 11001 => 10110
[-2,1,-3,5,4] => [4,5,-3,1,-2] => 00101 => 11000
[-2,1,-3,5,-4] => [-4,5,-3,1,-2] => 10101 => 11100
[-2,1,-3,-5,4] => [4,-5,-3,1,-2] => 01101 => 11100
[-2,1,-3,-5,-4] => [-4,-5,-3,1,-2] => 11101 => 11110
[-2,-1,3,5,4] => [4,5,3,-1,-2] => 00011 => 10010
[-2,-1,3,5,-4] => [-4,5,3,-1,-2] => 10011 => 10110
[-2,-1,3,-5,4] => [4,-5,3,-1,-2] => 01011 => 11100
[-2,-1,3,-5,-4] => [-4,-5,3,-1,-2] => 11011 => 11110
[-2,-1,-3,5,4] => [4,5,-3,-1,-2] => 00111 => 10110
[-2,-1,-3,5,-4] => [-4,5,-3,-1,-2] => 10111 => 11110
[-2,-1,-3,-5,4] => [4,-5,-3,-1,-2] => 01111 => 11110
[-2,-1,-3,-5,-4] => [-4,-5,-3,-1,-2] => 11111 => 11111
[2,1,4,3,5] => [5,3,4,1,2] => 00000 => 00000
[2,1,4,3,-5] => [-5,3,4,1,2] => 10000 => 10000
[2,1,4,-3,5] => [5,-3,4,1,2] => 01000 => 10000
[2,1,4,-3,-5] => [-5,-3,4,1,2] => 11000 => 10010
[2,1,-4,3,5] => [5,3,-4,1,2] => 00100 => 10000
[2,1,-4,3,-5] => [-5,3,-4,1,2] => 10100 => 11000
[2,1,-4,-3,5] => [5,-3,-4,1,2] => 01100 => 10010
[2,1,-4,-3,-5] => [-5,-3,-4,1,2] => 11100 => 10110
[2,-1,4,3,5] => [5,3,4,-1,2] => 00010 => 10000
[2,-1,4,3,-5] => [-5,3,4,-1,2] => 10010 => 11000
[2,-1,4,-3,5] => [5,-3,4,-1,2] => 01010 => 11000
[2,-1,4,-3,-5] => [-5,-3,4,-1,2] => 11010 => 11100
[2,-1,-4,3,5] => [5,3,-4,-1,2] => 00110 => 10010
[2,-1,-4,3,-5] => [-5,3,-4,-1,2] => 10110 => 11100
[2,-1,-4,-3,5] => [5,-3,-4,-1,2] => 01110 => 10110
[2,-1,-4,-3,-5] => [-5,-3,-4,-1,2] => 11110 => 11110
[-2,1,4,3,5] => [5,3,4,1,-2] => 00001 => 10000
[-2,1,4,3,-5] => [-5,3,4,1,-2] => 10001 => 10010
[-2,1,4,-3,5] => [5,-3,4,1,-2] => 01001 => 11000
[-2,1,4,-3,-5] => [-5,-3,4,1,-2] => 11001 => 10110
[-2,1,-4,3,5] => [5,3,-4,1,-2] => 00101 => 11000
[-2,1,-4,3,-5] => [-5,3,-4,1,-2] => 10101 => 11100
[-2,1,-4,-3,5] => [5,-3,-4,1,-2] => 01101 => 11100
[-2,1,-4,-3,-5] => [-5,-3,-4,1,-2] => 11101 => 11110
[-2,-1,4,3,5] => [5,3,4,-1,-2] => 00011 => 10010
[-2,-1,4,3,-5] => [-5,3,4,-1,-2] => 10011 => 10110
[-2,-1,4,-3,5] => [5,-3,4,-1,-2] => 01011 => 11100
[-2,-1,4,-3,-5] => [-5,-3,4,-1,-2] => 11011 => 11110
[-2,-1,-4,3,5] => [5,3,-4,-1,-2] => 00111 => 10110
[-2,-1,-4,3,-5] => [-5,3,-4,-1,-2] => 10111 => 11110
[-2,-1,-4,-3,5] => [5,-3,-4,-1,-2] => 01111 => 11110
[-2,-1,-4,-3,-5] => [-5,-3,-4,-1,-2] => 11111 => 11111
[2,1,4,5,3] => [3,5,4,1,2] => 00000 => 00000
[2,1,4,5,-3] => [-3,5,4,1,2] => 10000 => 10000
[2,1,4,-5,3] => [3,-5,4,1,2] => 01000 => 10000
[2,1,4,-5,-3] => [-3,-5,4,1,2] => 11000 => 10010
[2,1,-4,5,3] => [3,5,-4,1,2] => 00100 => 10000
[2,1,-4,5,-3] => [-3,5,-4,1,2] => 10100 => 11000
[2,1,-4,-5,3] => [3,-5,-4,1,2] => 01100 => 10010
[2,1,-4,-5,-3] => [-3,-5,-4,1,2] => 11100 => 10110
[2,-1,4,5,3] => [3,5,4,-1,2] => 00010 => 10000
[2,-1,4,5,-3] => [-3,5,4,-1,2] => 10010 => 11000
[2,-1,4,-5,3] => [3,-5,4,-1,2] => 01010 => 11000
[2,-1,4,-5,-3] => [-3,-5,4,-1,2] => 11010 => 11100
[2,-1,-4,5,3] => [3,5,-4,-1,2] => 00110 => 10010
[2,-1,-4,5,-3] => [-3,5,-4,-1,2] => 10110 => 11100
[2,-1,-4,-5,3] => [3,-5,-4,-1,2] => 01110 => 10110
[2,-1,-4,-5,-3] => [-3,-5,-4,-1,2] => 11110 => 11110
[-2,1,4,5,3] => [3,5,4,1,-2] => 00001 => 10000
[-2,1,4,5,-3] => [-3,5,4,1,-2] => 10001 => 10010
[-2,1,4,-5,3] => [3,-5,4,1,-2] => 01001 => 11000
[-2,1,4,-5,-3] => [-3,-5,4,1,-2] => 11001 => 10110
[-2,1,-4,5,3] => [3,5,-4,1,-2] => 00101 => 11000
[-2,1,-4,5,-3] => [-3,5,-4,1,-2] => 10101 => 11100
[-2,1,-4,-5,3] => [3,-5,-4,1,-2] => 01101 => 11100
[-2,1,-4,-5,-3] => [-3,-5,-4,1,-2] => 11101 => 11110
[-2,-1,4,5,3] => [3,5,4,-1,-2] => 00011 => 10010
[-2,-1,4,5,-3] => [-3,5,4,-1,-2] => 10011 => 10110
[-2,-1,4,-5,3] => [3,-5,4,-1,-2] => 01011 => 11100
[-2,-1,4,-5,-3] => [-3,-5,4,-1,-2] => 11011 => 11110
[-2,-1,-4,5,3] => [3,5,-4,-1,-2] => 00111 => 10110
[-2,-1,-4,5,-3] => [-3,5,-4,-1,-2] => 10111 => 11110
[-2,-1,-4,-5,3] => [3,-5,-4,-1,-2] => 01111 => 11110
[-2,-1,-4,-5,-3] => [-3,-5,-4,-1,-2] => 11111 => 11111
[2,1,5,3,4] => [4,3,5,1,2] => 00000 => 00000
[2,1,5,3,-4] => [-4,3,5,1,2] => 10000 => 10000
[2,1,5,-3,4] => [4,-3,5,1,2] => 01000 => 10000
[2,1,5,-3,-4] => [-4,-3,5,1,2] => 11000 => 10010
[2,1,-5,3,4] => [4,3,-5,1,2] => 00100 => 10000
[2,1,-5,3,-4] => [-4,3,-5,1,2] => 10100 => 11000
[2,1,-5,-3,4] => [4,-3,-5,1,2] => 01100 => 10010
[2,1,-5,-3,-4] => [-4,-3,-5,1,2] => 11100 => 10110
[2,-1,5,3,4] => [4,3,5,-1,2] => 00010 => 10000
[2,-1,5,3,-4] => [-4,3,5,-1,2] => 10010 => 11000
[2,-1,5,-3,4] => [4,-3,5,-1,2] => 01010 => 11000
[2,-1,5,-3,-4] => [-4,-3,5,-1,2] => 11010 => 11100
[2,-1,-5,3,4] => [4,3,-5,-1,2] => 00110 => 10010
[2,-1,-5,3,-4] => [-4,3,-5,-1,2] => 10110 => 11100
[2,-1,-5,-3,4] => [4,-3,-5,-1,2] => 01110 => 10110
[2,-1,-5,-3,-4] => [-4,-3,-5,-1,2] => 11110 => 11110
[-2,1,5,3,4] => [4,3,5,1,-2] => 00001 => 10000
[-2,1,5,3,-4] => [-4,3,5,1,-2] => 10001 => 10010
[-2,1,5,-3,4] => [4,-3,5,1,-2] => 01001 => 11000
[-2,1,5,-3,-4] => [-4,-3,5,1,-2] => 11001 => 10110
[-2,1,-5,3,4] => [4,3,-5,1,-2] => 00101 => 11000
[-2,1,-5,3,-4] => [-4,3,-5,1,-2] => 10101 => 11100
[-2,1,-5,-3,4] => [4,-3,-5,1,-2] => 01101 => 11100
[-2,1,-5,-3,-4] => [-4,-3,-5,1,-2] => 11101 => 11110
[-2,-1,5,3,4] => [4,3,5,-1,-2] => 00011 => 10010
[-2,-1,5,3,-4] => [-4,3,5,-1,-2] => 10011 => 10110
[-2,-1,5,-3,4] => [4,-3,5,-1,-2] => 01011 => 11100
[-2,-1,5,-3,-4] => [-4,-3,5,-1,-2] => 11011 => 11110
[-2,-1,-5,3,4] => [4,3,-5,-1,-2] => 00111 => 10110
[-2,-1,-5,3,-4] => [-4,3,-5,-1,-2] => 10111 => 11110
[-2,-1,-5,-3,4] => [4,-3,-5,-1,-2] => 01111 => 11110
[-2,-1,-5,-3,-4] => [-4,-3,-5,-1,-2] => 11111 => 11111
[2,1,5,4,3] => [3,4,5,1,2] => 00000 => 00000
[2,1,5,4,-3] => [-3,4,5,1,2] => 10000 => 10000
[2,1,5,-4,3] => [3,-4,5,1,2] => 01000 => 10000
[2,1,5,-4,-3] => [-3,-4,5,1,2] => 11000 => 10010
[2,1,-5,4,3] => [3,4,-5,1,2] => 00100 => 10000
[2,1,-5,4,-3] => [-3,4,-5,1,2] => 10100 => 11000
[2,1,-5,-4,3] => [3,-4,-5,1,2] => 01100 => 10010
[2,1,-5,-4,-3] => [-3,-4,-5,1,2] => 11100 => 10110
[2,-1,5,4,3] => [3,4,5,-1,2] => 00010 => 10000
[2,-1,5,4,-3] => [-3,4,5,-1,2] => 10010 => 11000
[2,-1,5,-4,3] => [3,-4,5,-1,2] => 01010 => 11000
[2,-1,5,-4,-3] => [-3,-4,5,-1,2] => 11010 => 11100
[2,-1,-5,4,3] => [3,4,-5,-1,2] => 00110 => 10010
[2,-1,-5,4,-3] => [-3,4,-5,-1,2] => 10110 => 11100
[2,-1,-5,-4,3] => [3,-4,-5,-1,2] => 01110 => 10110
[2,-1,-5,-4,-3] => [-3,-4,-5,-1,2] => 11110 => 11110
[-2,1,5,4,3] => [3,4,5,1,-2] => 00001 => 10000
[-2,1,5,4,-3] => [-3,4,5,1,-2] => 10001 => 10010
[-2,1,5,-4,3] => [3,-4,5,1,-2] => 01001 => 11000
[-2,1,5,-4,-3] => [-3,-4,5,1,-2] => 11001 => 10110
[-2,1,-5,4,3] => [3,4,-5,1,-2] => 00101 => 11000
[-2,1,-5,4,-3] => [-3,4,-5,1,-2] => 10101 => 11100
[-2,1,-5,-4,3] => [3,-4,-5,1,-2] => 01101 => 11100
[-2,1,-5,-4,-3] => [-3,-4,-5,1,-2] => 11101 => 11110
[-2,-1,5,4,3] => [3,4,5,-1,-2] => 00011 => 10010
[-2,-1,5,4,-3] => [-3,4,5,-1,-2] => 10011 => 10110
[-2,-1,5,-4,3] => [3,-4,5,-1,-2] => 01011 => 11100
[-2,-1,5,-4,-3] => [-3,-4,5,-1,-2] => 11011 => 11110
[-2,-1,-5,4,3] => [3,4,-5,-1,-2] => 00111 => 10110
[-2,-1,-5,4,-3] => [-3,4,-5,-1,-2] => 10111 => 11110
[-2,-1,-5,-4,3] => [3,-4,-5,-1,-2] => 01111 => 11110
[-2,-1,-5,-4,-3] => [-3,-4,-5,-1,-2] => 11111 => 11111
[2,3,1,4,5] => [5,4,1,3,2] => 00000 => 00000
[2,3,1,4,-5] => [-5,4,1,3,2] => 10000 => 10000
[2,3,1,-4,5] => [5,-4,1,3,2] => 01000 => 10000
[2,3,1,-4,-5] => [-5,-4,1,3,2] => 11000 => 10010
[2,3,-1,4,5] => [5,4,-1,3,2] => 00100 => 10000
[2,3,-1,4,-5] => [-5,4,-1,3,2] => 10100 => 11000
[2,3,-1,-4,5] => [5,-4,-1,3,2] => 01100 => 10010
[2,3,-1,-4,-5] => [-5,-4,-1,3,2] => 11100 => 10110
[2,-3,1,4,5] => [5,4,1,-3,2] => 00010 => 10000
[2,-3,1,4,-5] => [-5,4,1,-3,2] => 10010 => 11000
[2,-3,1,-4,5] => [5,-4,1,-3,2] => 01010 => 11000
[2,-3,1,-4,-5] => [-5,-4,1,-3,2] => 11010 => 11100
[2,-3,-1,4,5] => [5,4,-1,-3,2] => 00110 => 10010
[2,-3,-1,4,-5] => [-5,4,-1,-3,2] => 10110 => 11100
[2,-3,-1,-4,5] => [5,-4,-1,-3,2] => 01110 => 10110
[2,-3,-1,-4,-5] => [-5,-4,-1,-3,2] => 11110 => 11110
[-2,3,1,4,5] => [5,4,1,3,-2] => 00001 => 10000
[-2,3,1,4,-5] => [-5,4,1,3,-2] => 10001 => 10010
[-2,3,1,-4,5] => [5,-4,1,3,-2] => 01001 => 11000
[-2,3,1,-4,-5] => [-5,-4,1,3,-2] => 11001 => 10110
[-2,3,-1,4,5] => [5,4,-1,3,-2] => 00101 => 11000
[-2,3,-1,4,-5] => [-5,4,-1,3,-2] => 10101 => 11100
[-2,3,-1,-4,5] => [5,-4,-1,3,-2] => 01101 => 11100
[-2,3,-1,-4,-5] => [-5,-4,-1,3,-2] => 11101 => 11110
[-2,-3,1,4,5] => [5,4,1,-3,-2] => 00011 => 10010
[-2,-3,1,4,-5] => [-5,4,1,-3,-2] => 10011 => 10110
[-2,-3,1,-4,5] => [5,-4,1,-3,-2] => 01011 => 11100
[-2,-3,1,-4,-5] => [-5,-4,1,-3,-2] => 11011 => 11110
[-2,-3,-1,4,5] => [5,4,-1,-3,-2] => 00111 => 10110
[-2,-3,-1,4,-5] => [-5,4,-1,-3,-2] => 10111 => 11110
[-2,-3,-1,-4,5] => [5,-4,-1,-3,-2] => 01111 => 11110
[-2,-3,-1,-4,-5] => [-5,-4,-1,-3,-2] => 11111 => 11111
[2,3,1,5,4] => [4,5,1,3,2] => 00000 => 00000
[2,3,1,5,-4] => [-4,5,1,3,2] => 10000 => 10000
[2,3,1,-5,4] => [4,-5,1,3,2] => 01000 => 10000
[2,3,1,-5,-4] => [-4,-5,1,3,2] => 11000 => 10010
[2,3,-1,5,4] => [4,5,-1,3,2] => 00100 => 10000
[2,3,-1,5,-4] => [-4,5,-1,3,2] => 10100 => 11000
[2,3,-1,-5,4] => [4,-5,-1,3,2] => 01100 => 10010
[2,3,-1,-5,-4] => [-4,-5,-1,3,2] => 11100 => 10110
[2,-3,1,5,4] => [4,5,1,-3,2] => 00010 => 10000
[2,-3,1,5,-4] => [-4,5,1,-3,2] => 10010 => 11000
[2,-3,1,-5,4] => [4,-5,1,-3,2] => 01010 => 11000
[2,-3,1,-5,-4] => [-4,-5,1,-3,2] => 11010 => 11100
[2,-3,-1,5,4] => [4,5,-1,-3,2] => 00110 => 10010
[2,-3,-1,5,-4] => [-4,5,-1,-3,2] => 10110 => 11100
[2,-3,-1,-5,4] => [4,-5,-1,-3,2] => 01110 => 10110
[2,-3,-1,-5,-4] => [-4,-5,-1,-3,2] => 11110 => 11110
[-2,3,1,5,4] => [4,5,1,3,-2] => 00001 => 10000
[-2,3,1,5,-4] => [-4,5,1,3,-2] => 10001 => 10010
[-2,3,1,-5,4] => [4,-5,1,3,-2] => 01001 => 11000
[-2,3,1,-5,-4] => [-4,-5,1,3,-2] => 11001 => 10110
[-2,3,-1,5,4] => [4,5,-1,3,-2] => 00101 => 11000
[-2,3,-1,5,-4] => [-4,5,-1,3,-2] => 10101 => 11100
[-2,3,-1,-5,4] => [4,-5,-1,3,-2] => 01101 => 11100
[-2,3,-1,-5,-4] => [-4,-5,-1,3,-2] => 11101 => 11110
[-2,-3,1,5,4] => [4,5,1,-3,-2] => 00011 => 10010
[-2,-3,1,5,-4] => [-4,5,1,-3,-2] => 10011 => 10110
[-2,-3,1,-5,4] => [4,-5,1,-3,-2] => 01011 => 11100
[-2,-3,1,-5,-4] => [-4,-5,1,-3,-2] => 11011 => 11110
[-2,-3,-1,5,4] => [4,5,-1,-3,-2] => 00111 => 10110
[-2,-3,-1,5,-4] => [-4,5,-1,-3,-2] => 10111 => 11110
[-2,-3,-1,-5,4] => [4,-5,-1,-3,-2] => 01111 => 11110
[-2,-3,-1,-5,-4] => [-4,-5,-1,-3,-2] => 11111 => 11111
[2,3,4,1,5] => [5,1,4,3,2] => 00000 => 00000
[2,3,4,1,-5] => [-5,1,4,3,2] => 10000 => 10000
[2,3,4,-1,5] => [5,-1,4,3,2] => 01000 => 10000
[2,3,4,-1,-5] => [-5,-1,4,3,2] => 11000 => 10010
[2,3,-4,1,5] => [5,1,-4,3,2] => 00100 => 10000
[2,3,-4,1,-5] => [-5,1,-4,3,2] => 10100 => 11000
[2,3,-4,-1,5] => [5,-1,-4,3,2] => 01100 => 10010
[2,3,-4,-1,-5] => [-5,-1,-4,3,2] => 11100 => 10110
[2,-3,4,1,5] => [5,1,4,-3,2] => 00010 => 10000
[2,-3,4,1,-5] => [-5,1,4,-3,2] => 10010 => 11000
[2,-3,4,-1,5] => [5,-1,4,-3,2] => 01010 => 11000
[2,-3,4,-1,-5] => [-5,-1,4,-3,2] => 11010 => 11100
[2,-3,-4,1,5] => [5,1,-4,-3,2] => 00110 => 10010
[2,-3,-4,1,-5] => [-5,1,-4,-3,2] => 10110 => 11100
[2,-3,-4,-1,5] => [5,-1,-4,-3,2] => 01110 => 10110
[2,-3,-4,-1,-5] => [-5,-1,-4,-3,2] => 11110 => 11110
[-2,3,4,1,5] => [5,1,4,3,-2] => 00001 => 10000
[-2,3,4,1,-5] => [-5,1,4,3,-2] => 10001 => 10010
[-2,3,4,-1,5] => [5,-1,4,3,-2] => 01001 => 11000
[-2,3,4,-1,-5] => [-5,-1,4,3,-2] => 11001 => 10110
[-2,3,-4,1,5] => [5,1,-4,3,-2] => 00101 => 11000
[-2,3,-4,1,-5] => [-5,1,-4,3,-2] => 10101 => 11100
[-2,3,-4,-1,5] => [5,-1,-4,3,-2] => 01101 => 11100
[-2,3,-4,-1,-5] => [-5,-1,-4,3,-2] => 11101 => 11110
[-2,-3,4,1,5] => [5,1,4,-3,-2] => 00011 => 10010
[-2,-3,4,1,-5] => [-5,1,4,-3,-2] => 10011 => 10110
[-2,-3,4,-1,5] => [5,-1,4,-3,-2] => 01011 => 11100
[-2,-3,4,-1,-5] => [-5,-1,4,-3,-2] => 11011 => 11110
[-2,-3,-4,1,5] => [5,1,-4,-3,-2] => 00111 => 10110
[-2,-3,-4,1,-5] => [-5,1,-4,-3,-2] => 10111 => 11110
[-2,-3,-4,-1,5] => [5,-1,-4,-3,-2] => 01111 => 11110
[-2,-3,-4,-1,-5] => [-5,-1,-4,-3,-2] => 11111 => 11111
[2,3,4,5,1] => [1,5,4,3,2] => 00000 => 00000
[2,3,4,5,-1] => [-1,5,4,3,2] => 10000 => 10000
[2,3,4,-5,1] => [1,-5,4,3,2] => 01000 => 10000
[2,3,4,-5,-1] => [-1,-5,4,3,2] => 11000 => 10010
[2,3,-4,5,1] => [1,5,-4,3,2] => 00100 => 10000
[2,3,-4,5,-1] => [-1,5,-4,3,2] => 10100 => 11000
[2,3,-4,-5,1] => [1,-5,-4,3,2] => 01100 => 10010
[2,3,-4,-5,-1] => [-1,-5,-4,3,2] => 11100 => 10110
[2,-3,4,5,1] => [1,5,4,-3,2] => 00010 => 10000
[2,-3,4,5,-1] => [-1,5,4,-3,2] => 10010 => 11000
[2,-3,4,-5,1] => [1,-5,4,-3,2] => 01010 => 11000
[2,-3,4,-5,-1] => [-1,-5,4,-3,2] => 11010 => 11100
[2,-3,-4,5,1] => [1,5,-4,-3,2] => 00110 => 10010
[2,-3,-4,5,-1] => [-1,5,-4,-3,2] => 10110 => 11100
[2,-3,-4,-5,1] => [1,-5,-4,-3,2] => 01110 => 10110
[2,-3,-4,-5,-1] => [-1,-5,-4,-3,2] => 11110 => 11110
[-2,3,4,5,1] => [1,5,4,3,-2] => 00001 => 10000
[-2,3,4,5,-1] => [-1,5,4,3,-2] => 10001 => 10010
[-2,3,4,-5,1] => [1,-5,4,3,-2] => 01001 => 11000
[-2,3,4,-5,-1] => [-1,-5,4,3,-2] => 11001 => 10110
[-2,3,-4,5,1] => [1,5,-4,3,-2] => 00101 => 11000
[-2,3,-4,5,-1] => [-1,5,-4,3,-2] => 10101 => 11100
[-2,3,-4,-5,1] => [1,-5,-4,3,-2] => 01101 => 11100
[-2,3,-4,-5,-1] => [-1,-5,-4,3,-2] => 11101 => 11110
[-2,-3,4,5,1] => [1,5,4,-3,-2] => 00011 => 10010
[-2,-3,4,5,-1] => [-1,5,4,-3,-2] => 10011 => 10110
[-2,-3,4,-5,1] => [1,-5,4,-3,-2] => 01011 => 11100
[-2,-3,4,-5,-1] => [-1,-5,4,-3,-2] => 11011 => 11110
[-2,-3,-4,5,1] => [1,5,-4,-3,-2] => 00111 => 10110
[-2,-3,-4,5,-1] => [-1,5,-4,-3,-2] => 10111 => 11110
[-2,-3,-4,-5,1] => [1,-5,-4,-3,-2] => 01111 => 11110
[-2,-3,-4,-5,-1] => [-1,-5,-4,-3,-2] => 11111 => 11111
[2,3,5,1,4] => [4,1,5,3,2] => 00000 => 00000
[2,3,5,1,-4] => [-4,1,5,3,2] => 10000 => 10000
[2,3,5,-1,4] => [4,-1,5,3,2] => 01000 => 10000
[2,3,5,-1,-4] => [-4,-1,5,3,2] => 11000 => 10010
[2,3,-5,1,4] => [4,1,-5,3,2] => 00100 => 10000
[2,3,-5,1,-4] => [-4,1,-5,3,2] => 10100 => 11000
[2,3,-5,-1,4] => [4,-1,-5,3,2] => 01100 => 10010
[2,3,-5,-1,-4] => [-4,-1,-5,3,2] => 11100 => 10110
[2,-3,5,1,4] => [4,1,5,-3,2] => 00010 => 10000
[2,-3,5,1,-4] => [-4,1,5,-3,2] => 10010 => 11000
[2,-3,5,-1,4] => [4,-1,5,-3,2] => 01010 => 11000
[2,-3,5,-1,-4] => [-4,-1,5,-3,2] => 11010 => 11100
[2,-3,-5,1,4] => [4,1,-5,-3,2] => 00110 => 10010
[2,-3,-5,1,-4] => [-4,1,-5,-3,2] => 10110 => 11100
[2,-3,-5,-1,4] => [4,-1,-5,-3,2] => 01110 => 10110
[2,-3,-5,-1,-4] => [-4,-1,-5,-3,2] => 11110 => 11110
[-2,3,5,1,4] => [4,1,5,3,-2] => 00001 => 10000
[-2,3,5,1,-4] => [-4,1,5,3,-2] => 10001 => 10010
[-2,3,5,-1,4] => [4,-1,5,3,-2] => 01001 => 11000
[-2,3,5,-1,-4] => [-4,-1,5,3,-2] => 11001 => 10110
[-2,3,-5,1,4] => [4,1,-5,3,-2] => 00101 => 11000
[-2,3,-5,1,-4] => [-4,1,-5,3,-2] => 10101 => 11100
[-2,3,-5,-1,4] => [4,-1,-5,3,-2] => 01101 => 11100
[-2,3,-5,-1,-4] => [-4,-1,-5,3,-2] => 11101 => 11110
[-2,-3,5,1,4] => [4,1,5,-3,-2] => 00011 => 10010
[-2,-3,5,1,-4] => [-4,1,5,-3,-2] => 10011 => 10110
[-2,-3,5,-1,4] => [4,-1,5,-3,-2] => 01011 => 11100
[-2,-3,5,-1,-4] => [-4,-1,5,-3,-2] => 11011 => 11110
[-2,-3,-5,1,4] => [4,1,-5,-3,-2] => 00111 => 10110
[-2,-3,-5,1,-4] => [-4,1,-5,-3,-2] => 10111 => 11110
[-2,-3,-5,-1,4] => [4,-1,-5,-3,-2] => 01111 => 11110
[-2,-3,-5,-1,-4] => [-4,-1,-5,-3,-2] => 11111 => 11111
[2,3,5,4,1] => [1,4,5,3,2] => 00000 => 00000
[2,3,5,4,-1] => [-1,4,5,3,2] => 10000 => 10000
[2,3,5,-4,1] => [1,-4,5,3,2] => 01000 => 10000
[2,3,5,-4,-1] => [-1,-4,5,3,2] => 11000 => 10010
[2,3,-5,4,1] => [1,4,-5,3,2] => 00100 => 10000
[2,3,-5,4,-1] => [-1,4,-5,3,2] => 10100 => 11000
[2,3,-5,-4,1] => [1,-4,-5,3,2] => 01100 => 10010
[2,3,-5,-4,-1] => [-1,-4,-5,3,2] => 11100 => 10110
[2,-3,5,4,1] => [1,4,5,-3,2] => 00010 => 10000
[2,-3,5,4,-1] => [-1,4,5,-3,2] => 10010 => 11000
[2,-3,5,-4,1] => [1,-4,5,-3,2] => 01010 => 11000
[2,-3,5,-4,-1] => [-1,-4,5,-3,2] => 11010 => 11100
[2,-3,-5,4,1] => [1,4,-5,-3,2] => 00110 => 10010
[2,-3,-5,4,-1] => [-1,4,-5,-3,2] => 10110 => 11100
[2,-3,-5,-4,1] => [1,-4,-5,-3,2] => 01110 => 10110
[2,-3,-5,-4,-1] => [-1,-4,-5,-3,2] => 11110 => 11110
[-2,3,5,4,1] => [1,4,5,3,-2] => 00001 => 10000
[-2,3,5,4,-1] => [-1,4,5,3,-2] => 10001 => 10010
[-2,3,5,-4,1] => [1,-4,5,3,-2] => 01001 => 11000
[-2,3,5,-4,-1] => [-1,-4,5,3,-2] => 11001 => 10110
[-2,3,-5,4,1] => [1,4,-5,3,-2] => 00101 => 11000
[-2,3,-5,4,-1] => [-1,4,-5,3,-2] => 10101 => 11100
[-2,3,-5,-4,1] => [1,-4,-5,3,-2] => 01101 => 11100
[-2,3,-5,-4,-1] => [-1,-4,-5,3,-2] => 11101 => 11110
[-2,-3,5,4,1] => [1,4,5,-3,-2] => 00011 => 10010
[-2,-3,5,4,-1] => [-1,4,5,-3,-2] => 10011 => 10110
[-2,-3,5,-4,1] => [1,-4,5,-3,-2] => 01011 => 11100
[-2,-3,5,-4,-1] => [-1,-4,5,-3,-2] => 11011 => 11110
[-2,-3,-5,4,1] => [1,4,-5,-3,-2] => 00111 => 10110
[-2,-3,-5,4,-1] => [-1,4,-5,-3,-2] => 10111 => 11110
[-2,-3,-5,-4,1] => [1,-4,-5,-3,-2] => 01111 => 11110
[-2,-3,-5,-4,-1] => [-1,-4,-5,-3,-2] => 11111 => 11111
[2,4,1,3,5] => [5,3,1,4,2] => 00000 => 00000
[2,4,1,3,-5] => [-5,3,1,4,2] => 10000 => 10000
[2,4,1,-3,5] => [5,-3,1,4,2] => 01000 => 10000
[2,4,1,-3,-5] => [-5,-3,1,4,2] => 11000 => 10010
[2,4,-1,3,5] => [5,3,-1,4,2] => 00100 => 10000
[2,4,-1,3,-5] => [-5,3,-1,4,2] => 10100 => 11000
[2,4,-1,-3,5] => [5,-3,-1,4,2] => 01100 => 10010
[2,4,-1,-3,-5] => [-5,-3,-1,4,2] => 11100 => 10110
[2,-4,1,3,5] => [5,3,1,-4,2] => 00010 => 10000
[2,-4,1,3,-5] => [-5,3,1,-4,2] => 10010 => 11000
[2,-4,1,-3,5] => [5,-3,1,-4,2] => 01010 => 11000
[2,-4,1,-3,-5] => [-5,-3,1,-4,2] => 11010 => 11100
[2,-4,-1,3,5] => [5,3,-1,-4,2] => 00110 => 10010
[2,-4,-1,3,-5] => [-5,3,-1,-4,2] => 10110 => 11100
[2,-4,-1,-3,5] => [5,-3,-1,-4,2] => 01110 => 10110
[2,-4,-1,-3,-5] => [-5,-3,-1,-4,2] => 11110 => 11110
[-2,4,1,3,5] => [5,3,1,4,-2] => 00001 => 10000
[-2,4,1,3,-5] => [-5,3,1,4,-2] => 10001 => 10010
[-2,4,1,-3,5] => [5,-3,1,4,-2] => 01001 => 11000
[-2,4,1,-3,-5] => [-5,-3,1,4,-2] => 11001 => 10110
[-2,4,-1,3,5] => [5,3,-1,4,-2] => 00101 => 11000
[-2,4,-1,3,-5] => [-5,3,-1,4,-2] => 10101 => 11100
[-2,4,-1,-3,5] => [5,-3,-1,4,-2] => 01101 => 11100
[-2,4,-1,-3,-5] => [-5,-3,-1,4,-2] => 11101 => 11110
[-2,-4,1,3,5] => [5,3,1,-4,-2] => 00011 => 10010
[-2,-4,1,3,-5] => [-5,3,1,-4,-2] => 10011 => 10110
[-2,-4,1,-3,5] => [5,-3,1,-4,-2] => 01011 => 11100
[-2,-4,1,-3,-5] => [-5,-3,1,-4,-2] => 11011 => 11110
[-2,-4,-1,3,5] => [5,3,-1,-4,-2] => 00111 => 10110
[-2,-4,-1,3,-5] => [-5,3,-1,-4,-2] => 10111 => 11110
[-2,-4,-1,-3,5] => [5,-3,-1,-4,-2] => 01111 => 11110
[-2,-4,-1,-3,-5] => [-5,-3,-1,-4,-2] => 11111 => 11111
[2,4,1,5,3] => [3,5,1,4,2] => 00000 => 00000
[2,4,1,5,-3] => [-3,5,1,4,2] => 10000 => 10000
[2,4,1,-5,3] => [3,-5,1,4,2] => 01000 => 10000
[2,4,1,-5,-3] => [-3,-5,1,4,2] => 11000 => 10010
[2,4,-1,5,3] => [3,5,-1,4,2] => 00100 => 10000
[2,4,-1,5,-3] => [-3,5,-1,4,2] => 10100 => 11000
[2,4,-1,-5,3] => [3,-5,-1,4,2] => 01100 => 10010
[2,4,-1,-5,-3] => [-3,-5,-1,4,2] => 11100 => 10110
[2,-4,1,5,3] => [3,5,1,-4,2] => 00010 => 10000
[2,-4,1,5,-3] => [-3,5,1,-4,2] => 10010 => 11000
[2,-4,1,-5,3] => [3,-5,1,-4,2] => 01010 => 11000
[2,-4,1,-5,-3] => [-3,-5,1,-4,2] => 11010 => 11100
[2,-4,-1,5,3] => [3,5,-1,-4,2] => 00110 => 10010
[2,-4,-1,5,-3] => [-3,5,-1,-4,2] => 10110 => 11100
[2,-4,-1,-5,3] => [3,-5,-1,-4,2] => 01110 => 10110
[2,-4,-1,-5,-3] => [-3,-5,-1,-4,2] => 11110 => 11110
[-2,4,1,5,3] => [3,5,1,4,-2] => 00001 => 10000
[-2,4,1,5,-3] => [-3,5,1,4,-2] => 10001 => 10010
[-2,4,1,-5,3] => [3,-5,1,4,-2] => 01001 => 11000
[-2,4,1,-5,-3] => [-3,-5,1,4,-2] => 11001 => 10110
[-2,4,-1,5,3] => [3,5,-1,4,-2] => 00101 => 11000
[-2,4,-1,5,-3] => [-3,5,-1,4,-2] => 10101 => 11100
[-2,4,-1,-5,3] => [3,-5,-1,4,-2] => 01101 => 11100
[-2,4,-1,-5,-3] => [-3,-5,-1,4,-2] => 11101 => 11110
[-2,-4,1,5,3] => [3,5,1,-4,-2] => 00011 => 10010
[-2,-4,1,5,-3] => [-3,5,1,-4,-2] => 10011 => 10110
[-2,-4,1,-5,3] => [3,-5,1,-4,-2] => 01011 => 11100
[-2,-4,1,-5,-3] => [-3,-5,1,-4,-2] => 11011 => 11110
[-2,-4,-1,5,3] => [3,5,-1,-4,-2] => 00111 => 10110
[-2,-4,-1,5,-3] => [-3,5,-1,-4,-2] => 10111 => 11110
[-2,-4,-1,-5,3] => [3,-5,-1,-4,-2] => 01111 => 11110
[-2,-4,-1,-5,-3] => [-3,-5,-1,-4,-2] => 11111 => 11111
[2,4,3,1,5] => [5,1,3,4,2] => 00000 => 00000
[2,4,3,1,-5] => [-5,1,3,4,2] => 10000 => 10000
[2,4,3,-1,5] => [5,-1,3,4,2] => 01000 => 10000
[2,4,3,-1,-5] => [-5,-1,3,4,2] => 11000 => 10010
[2,4,-3,1,5] => [5,1,-3,4,2] => 00100 => 10000
[2,4,-3,1,-5] => [-5,1,-3,4,2] => 10100 => 11000
[2,4,-3,-1,5] => [5,-1,-3,4,2] => 01100 => 10010
[2,4,-3,-1,-5] => [-5,-1,-3,4,2] => 11100 => 10110
[2,-4,3,1,5] => [5,1,3,-4,2] => 00010 => 10000
[2,-4,3,1,-5] => [-5,1,3,-4,2] => 10010 => 11000
[2,-4,3,-1,5] => [5,-1,3,-4,2] => 01010 => 11000
[2,-4,3,-1,-5] => [-5,-1,3,-4,2] => 11010 => 11100
[2,-4,-3,1,5] => [5,1,-3,-4,2] => 00110 => 10010
[2,-4,-3,1,-5] => [-5,1,-3,-4,2] => 10110 => 11100
[2,-4,-3,-1,5] => [5,-1,-3,-4,2] => 01110 => 10110
[2,-4,-3,-1,-5] => [-5,-1,-3,-4,2] => 11110 => 11110
[-2,4,3,1,5] => [5,1,3,4,-2] => 00001 => 10000
[-2,4,3,1,-5] => [-5,1,3,4,-2] => 10001 => 10010
[-2,4,3,-1,5] => [5,-1,3,4,-2] => 01001 => 11000
[-2,4,3,-1,-5] => [-5,-1,3,4,-2] => 11001 => 10110
[-2,4,-3,1,5] => [5,1,-3,4,-2] => 00101 => 11000
[-2,4,-3,1,-5] => [-5,1,-3,4,-2] => 10101 => 11100
[-2,4,-3,-1,5] => [5,-1,-3,4,-2] => 01101 => 11100
[-2,4,-3,-1,-5] => [-5,-1,-3,4,-2] => 11101 => 11110
[-2,-4,3,1,5] => [5,1,3,-4,-2] => 00011 => 10010
[-2,-4,3,1,-5] => [-5,1,3,-4,-2] => 10011 => 10110
[-2,-4,3,-1,5] => [5,-1,3,-4,-2] => 01011 => 11100
[-2,-4,3,-1,-5] => [-5,-1,3,-4,-2] => 11011 => 11110
[-2,-4,-3,1,5] => [5,1,-3,-4,-2] => 00111 => 10110
[-2,-4,-3,1,-5] => [-5,1,-3,-4,-2] => 10111 => 11110
[-2,-4,-3,-1,5] => [5,-1,-3,-4,-2] => 01111 => 11110
[-2,-4,-3,-1,-5] => [-5,-1,-3,-4,-2] => 11111 => 11111
[2,4,3,5,1] => [1,5,3,4,2] => 00000 => 00000
[2,4,3,5,-1] => [-1,5,3,4,2] => 10000 => 10000
[2,4,3,-5,1] => [1,-5,3,4,2] => 01000 => 10000
[2,4,3,-5,-1] => [-1,-5,3,4,2] => 11000 => 10010
[2,4,-3,5,1] => [1,5,-3,4,2] => 00100 => 10000
[2,4,-3,5,-1] => [-1,5,-3,4,2] => 10100 => 11000
[2,4,-3,-5,1] => [1,-5,-3,4,2] => 01100 => 10010
[2,4,-3,-5,-1] => [-1,-5,-3,4,2] => 11100 => 10110
[2,-4,3,5,1] => [1,5,3,-4,2] => 00010 => 10000
[2,-4,3,5,-1] => [-1,5,3,-4,2] => 10010 => 11000
[2,-4,3,-5,1] => [1,-5,3,-4,2] => 01010 => 11000
[2,-4,3,-5,-1] => [-1,-5,3,-4,2] => 11010 => 11100
[2,-4,-3,5,1] => [1,5,-3,-4,2] => 00110 => 10010
[2,-4,-3,5,-1] => [-1,5,-3,-4,2] => 10110 => 11100
[2,-4,-3,-5,1] => [1,-5,-3,-4,2] => 01110 => 10110
[2,-4,-3,-5,-1] => [-1,-5,-3,-4,2] => 11110 => 11110
[-2,4,3,5,1] => [1,5,3,4,-2] => 00001 => 10000
[-2,4,3,5,-1] => [-1,5,3,4,-2] => 10001 => 10010
[-2,4,3,-5,1] => [1,-5,3,4,-2] => 01001 => 11000
[-2,4,3,-5,-1] => [-1,-5,3,4,-2] => 11001 => 10110
[-2,4,-3,5,1] => [1,5,-3,4,-2] => 00101 => 11000
[-2,4,-3,5,-1] => [-1,5,-3,4,-2] => 10101 => 11100
[-2,4,-3,-5,1] => [1,-5,-3,4,-2] => 01101 => 11100
[-2,4,-3,-5,-1] => [-1,-5,-3,4,-2] => 11101 => 11110
[-2,-4,3,5,1] => [1,5,3,-4,-2] => 00011 => 10010
[-2,-4,3,5,-1] => [-1,5,3,-4,-2] => 10011 => 10110
[-2,-4,3,-5,1] => [1,-5,3,-4,-2] => 01011 => 11100
[-2,-4,3,-5,-1] => [-1,-5,3,-4,-2] => 11011 => 11110
[-2,-4,-3,5,1] => [1,5,-3,-4,-2] => 00111 => 10110
[-2,-4,-3,5,-1] => [-1,5,-3,-4,-2] => 10111 => 11110
[-2,-4,-3,-5,1] => [1,-5,-3,-4,-2] => 01111 => 11110
[-2,-4,-3,-5,-1] => [-1,-5,-3,-4,-2] => 11111 => 11111
[2,4,5,1,3] => [3,1,5,4,2] => 00000 => 00000
[2,4,5,1,-3] => [-3,1,5,4,2] => 10000 => 10000
[2,4,5,-1,3] => [3,-1,5,4,2] => 01000 => 10000
[2,4,5,-1,-3] => [-3,-1,5,4,2] => 11000 => 10010
[2,4,-5,1,3] => [3,1,-5,4,2] => 00100 => 10000
[2,4,-5,1,-3] => [-3,1,-5,4,2] => 10100 => 11000
[2,4,-5,-1,3] => [3,-1,-5,4,2] => 01100 => 10010
[2,4,-5,-1,-3] => [-3,-1,-5,4,2] => 11100 => 10110
[2,-4,5,1,3] => [3,1,5,-4,2] => 00010 => 10000
[2,-4,5,1,-3] => [-3,1,5,-4,2] => 10010 => 11000
[2,-4,5,-1,3] => [3,-1,5,-4,2] => 01010 => 11000
[2,-4,5,-1,-3] => [-3,-1,5,-4,2] => 11010 => 11100
[2,-4,-5,1,3] => [3,1,-5,-4,2] => 00110 => 10010
[2,-4,-5,1,-3] => [-3,1,-5,-4,2] => 10110 => 11100
[2,-4,-5,-1,3] => [3,-1,-5,-4,2] => 01110 => 10110
[2,-4,-5,-1,-3] => [-3,-1,-5,-4,2] => 11110 => 11110
[-2,4,5,1,3] => [3,1,5,4,-2] => 00001 => 10000
[-2,4,5,1,-3] => [-3,1,5,4,-2] => 10001 => 10010
[-2,4,5,-1,3] => [3,-1,5,4,-2] => 01001 => 11000
[-2,4,5,-1,-3] => [-3,-1,5,4,-2] => 11001 => 10110
[-2,4,-5,1,3] => [3,1,-5,4,-2] => 00101 => 11000
[-2,4,-5,1,-3] => [-3,1,-5,4,-2] => 10101 => 11100
[-2,4,-5,-1,3] => [3,-1,-5,4,-2] => 01101 => 11100
[-2,4,-5,-1,-3] => [-3,-1,-5,4,-2] => 11101 => 11110
[-2,-4,5,1,3] => [3,1,5,-4,-2] => 00011 => 10010
[-2,-4,5,1,-3] => [-3,1,5,-4,-2] => 10011 => 10110
[-2,-4,5,-1,3] => [3,-1,5,-4,-2] => 01011 => 11100
[-2,-4,5,-1,-3] => [-3,-1,5,-4,-2] => 11011 => 11110
[-2,-4,-5,1,3] => [3,1,-5,-4,-2] => 00111 => 10110
[-2,-4,-5,1,-3] => [-3,1,-5,-4,-2] => 10111 => 11110
[-2,-4,-5,-1,3] => [3,-1,-5,-4,-2] => 01111 => 11110
[-2,-4,-5,-1,-3] => [-3,-1,-5,-4,-2] => 11111 => 11111
[2,4,5,3,1] => [1,3,5,4,2] => 00000 => 00000
[2,4,5,3,-1] => [-1,3,5,4,2] => 10000 => 10000
[2,4,5,-3,1] => [1,-3,5,4,2] => 01000 => 10000
[2,4,5,-3,-1] => [-1,-3,5,4,2] => 11000 => 10010
[2,4,-5,3,1] => [1,3,-5,4,2] => 00100 => 10000
[2,4,-5,3,-1] => [-1,3,-5,4,2] => 10100 => 11000
[2,4,-5,-3,1] => [1,-3,-5,4,2] => 01100 => 10010
[2,4,-5,-3,-1] => [-1,-3,-5,4,2] => 11100 => 10110
[2,-4,5,3,1] => [1,3,5,-4,2] => 00010 => 10000
[2,-4,5,3,-1] => [-1,3,5,-4,2] => 10010 => 11000
[2,-4,5,-3,1] => [1,-3,5,-4,2] => 01010 => 11000
[2,-4,5,-3,-1] => [-1,-3,5,-4,2] => 11010 => 11100
[2,-4,-5,3,1] => [1,3,-5,-4,2] => 00110 => 10010
[2,-4,-5,3,-1] => [-1,3,-5,-4,2] => 10110 => 11100
[2,-4,-5,-3,1] => [1,-3,-5,-4,2] => 01110 => 10110
[2,-4,-5,-3,-1] => [-1,-3,-5,-4,2] => 11110 => 11110
[-2,4,5,3,1] => [1,3,5,4,-2] => 00001 => 10000
[-2,4,5,3,-1] => [-1,3,5,4,-2] => 10001 => 10010
[-2,4,5,-3,1] => [1,-3,5,4,-2] => 01001 => 11000
[-2,4,5,-3,-1] => [-1,-3,5,4,-2] => 11001 => 10110
[-2,4,-5,3,1] => [1,3,-5,4,-2] => 00101 => 11000
[-2,4,-5,3,-1] => [-1,3,-5,4,-2] => 10101 => 11100
[-2,4,-5,-3,1] => [1,-3,-5,4,-2] => 01101 => 11100
[-2,4,-5,-3,-1] => [-1,-3,-5,4,-2] => 11101 => 11110
[-2,-4,5,3,1] => [1,3,5,-4,-2] => 00011 => 10010
[-2,-4,5,3,-1] => [-1,3,5,-4,-2] => 10011 => 10110
[-2,-4,5,-3,1] => [1,-3,5,-4,-2] => 01011 => 11100
[-2,-4,5,-3,-1] => [-1,-3,5,-4,-2] => 11011 => 11110
[-2,-4,-5,3,1] => [1,3,-5,-4,-2] => 00111 => 10110
[-2,-4,-5,3,-1] => [-1,3,-5,-4,-2] => 10111 => 11110
[-2,-4,-5,-3,1] => [1,-3,-5,-4,-2] => 01111 => 11110
[-2,-4,-5,-3,-1] => [-1,-3,-5,-4,-2] => 11111 => 11111
[2,5,1,3,4] => [4,3,1,5,2] => 00000 => 00000
[2,5,1,3,-4] => [-4,3,1,5,2] => 10000 => 10000
[2,5,1,-3,4] => [4,-3,1,5,2] => 01000 => 10000
[2,5,1,-3,-4] => [-4,-3,1,5,2] => 11000 => 10010
[2,5,-1,3,4] => [4,3,-1,5,2] => 00100 => 10000
[2,5,-1,3,-4] => [-4,3,-1,5,2] => 10100 => 11000
[2,5,-1,-3,4] => [4,-3,-1,5,2] => 01100 => 10010
[2,5,-1,-3,-4] => [-4,-3,-1,5,2] => 11100 => 10110
[2,-5,1,3,4] => [4,3,1,-5,2] => 00010 => 10000
[2,-5,1,3,-4] => [-4,3,1,-5,2] => 10010 => 11000
[2,-5,1,-3,4] => [4,-3,1,-5,2] => 01010 => 11000
[2,-5,1,-3,-4] => [-4,-3,1,-5,2] => 11010 => 11100
[2,-5,-1,3,4] => [4,3,-1,-5,2] => 00110 => 10010
[2,-5,-1,3,-4] => [-4,3,-1,-5,2] => 10110 => 11100
[2,-5,-1,-3,4] => [4,-3,-1,-5,2] => 01110 => 10110
[2,-5,-1,-3,-4] => [-4,-3,-1,-5,2] => 11110 => 11110
[-2,5,1,3,4] => [4,3,1,5,-2] => 00001 => 10000
[-2,5,1,3,-4] => [-4,3,1,5,-2] => 10001 => 10010
[-2,5,1,-3,4] => [4,-3,1,5,-2] => 01001 => 11000
[-2,5,1,-3,-4] => [-4,-3,1,5,-2] => 11001 => 10110
[-2,5,-1,3,4] => [4,3,-1,5,-2] => 00101 => 11000
[-2,5,-1,3,-4] => [-4,3,-1,5,-2] => 10101 => 11100
[-2,5,-1,-3,4] => [4,-3,-1,5,-2] => 01101 => 11100
[-2,5,-1,-3,-4] => [-4,-3,-1,5,-2] => 11101 => 11110
[-2,-5,1,3,4] => [4,3,1,-5,-2] => 00011 => 10010
[-2,-5,1,3,-4] => [-4,3,1,-5,-2] => 10011 => 10110
[-2,-5,1,-3,4] => [4,-3,1,-5,-2] => 01011 => 11100
[-2,-5,1,-3,-4] => [-4,-3,1,-5,-2] => 11011 => 11110
[-2,-5,-1,3,4] => [4,3,-1,-5,-2] => 00111 => 10110
[-2,-5,-1,3,-4] => [-4,3,-1,-5,-2] => 10111 => 11110
[-2,-5,-1,-3,4] => [4,-3,-1,-5,-2] => 01111 => 11110
[-2,-5,-1,-3,-4] => [-4,-3,-1,-5,-2] => 11111 => 11111
[2,5,1,4,3] => [3,4,1,5,2] => 00000 => 00000
[2,5,1,4,-3] => [-3,4,1,5,2] => 10000 => 10000
[2,5,1,-4,3] => [3,-4,1,5,2] => 01000 => 10000
[2,5,1,-4,-3] => [-3,-4,1,5,2] => 11000 => 10010
[2,5,-1,4,3] => [3,4,-1,5,2] => 00100 => 10000
[2,5,-1,4,-3] => [-3,4,-1,5,2] => 10100 => 11000
[2,5,-1,-4,3] => [3,-4,-1,5,2] => 01100 => 10010
[2,5,-1,-4,-3] => [-3,-4,-1,5,2] => 11100 => 10110
[2,-5,1,4,3] => [3,4,1,-5,2] => 00010 => 10000
[2,-5,1,4,-3] => [-3,4,1,-5,2] => 10010 => 11000
[2,-5,1,-4,3] => [3,-4,1,-5,2] => 01010 => 11000
[2,-5,1,-4,-3] => [-3,-4,1,-5,2] => 11010 => 11100
[2,-5,-1,4,3] => [3,4,-1,-5,2] => 00110 => 10010
[2,-5,-1,4,-3] => [-3,4,-1,-5,2] => 10110 => 11100
[2,-5,-1,-4,3] => [3,-4,-1,-5,2] => 01110 => 10110
[2,-5,-1,-4,-3] => [-3,-4,-1,-5,2] => 11110 => 11110
[-2,5,1,4,3] => [3,4,1,5,-2] => 00001 => 10000
[-2,5,1,4,-3] => [-3,4,1,5,-2] => 10001 => 10010
[-2,5,1,-4,3] => [3,-4,1,5,-2] => 01001 => 11000
[-2,5,1,-4,-3] => [-3,-4,1,5,-2] => 11001 => 10110
[-2,5,-1,4,3] => [3,4,-1,5,-2] => 00101 => 11000
[-2,5,-1,4,-3] => [-3,4,-1,5,-2] => 10101 => 11100
[-2,5,-1,-4,3] => [3,-4,-1,5,-2] => 01101 => 11100
[-2,5,-1,-4,-3] => [-3,-4,-1,5,-2] => 11101 => 11110
[-2,-5,1,4,3] => [3,4,1,-5,-2] => 00011 => 10010
[-2,-5,1,4,-3] => [-3,4,1,-5,-2] => 10011 => 10110
[-2,-5,1,-4,3] => [3,-4,1,-5,-2] => 01011 => 11100
[-2,-5,1,-4,-3] => [-3,-4,1,-5,-2] => 11011 => 11110
[-2,-5,-1,4,3] => [3,4,-1,-5,-2] => 00111 => 10110
[-2,-5,-1,4,-3] => [-3,4,-1,-5,-2] => 10111 => 11110
[-2,-5,-1,-4,3] => [3,-4,-1,-5,-2] => 01111 => 11110
[-2,-5,-1,-4,-3] => [-3,-4,-1,-5,-2] => 11111 => 11111
[2,5,3,1,4] => [4,1,3,5,2] => 00000 => 00000
[2,5,3,1,-4] => [-4,1,3,5,2] => 10000 => 10000
[2,5,3,-1,4] => [4,-1,3,5,2] => 01000 => 10000
[2,5,3,-1,-4] => [-4,-1,3,5,2] => 11000 => 10010
[2,5,-3,1,4] => [4,1,-3,5,2] => 00100 => 10000
[2,5,-3,1,-4] => [-4,1,-3,5,2] => 10100 => 11000
[2,5,-3,-1,4] => [4,-1,-3,5,2] => 01100 => 10010
[2,5,-3,-1,-4] => [-4,-1,-3,5,2] => 11100 => 10110
[2,-5,3,1,4] => [4,1,3,-5,2] => 00010 => 10000
[2,-5,3,1,-4] => [-4,1,3,-5,2] => 10010 => 11000
[2,-5,3,-1,4] => [4,-1,3,-5,2] => 01010 => 11000
[2,-5,3,-1,-4] => [-4,-1,3,-5,2] => 11010 => 11100
[2,-5,-3,1,4] => [4,1,-3,-5,2] => 00110 => 10010
[2,-5,-3,1,-4] => [-4,1,-3,-5,2] => 10110 => 11100
[2,-5,-3,-1,4] => [4,-1,-3,-5,2] => 01110 => 10110
[2,-5,-3,-1,-4] => [-4,-1,-3,-5,2] => 11110 => 11110
[-2,5,3,1,4] => [4,1,3,5,-2] => 00001 => 10000
[-2,5,3,1,-4] => [-4,1,3,5,-2] => 10001 => 10010
[-2,5,3,-1,4] => [4,-1,3,5,-2] => 01001 => 11000
[-2,5,3,-1,-4] => [-4,-1,3,5,-2] => 11001 => 10110
[-2,5,-3,1,4] => [4,1,-3,5,-2] => 00101 => 11000
[-2,5,-3,1,-4] => [-4,1,-3,5,-2] => 10101 => 11100
[-2,5,-3,-1,4] => [4,-1,-3,5,-2] => 01101 => 11100
[-2,5,-3,-1,-4] => [-4,-1,-3,5,-2] => 11101 => 11110
[-2,-5,3,1,4] => [4,1,3,-5,-2] => 00011 => 10010
[-2,-5,3,1,-4] => [-4,1,3,-5,-2] => 10011 => 10110
[-2,-5,3,-1,4] => [4,-1,3,-5,-2] => 01011 => 11100
[-2,-5,3,-1,-4] => [-4,-1,3,-5,-2] => 11011 => 11110
[-2,-5,-3,1,4] => [4,1,-3,-5,-2] => 00111 => 10110
[-2,-5,-3,1,-4] => [-4,1,-3,-5,-2] => 10111 => 11110
[-2,-5,-3,-1,4] => [4,-1,-3,-5,-2] => 01111 => 11110
[-2,-5,-3,-1,-4] => [-4,-1,-3,-5,-2] => 11111 => 11111
[2,5,3,4,1] => [1,4,3,5,2] => 00000 => 00000
[2,5,3,4,-1] => [-1,4,3,5,2] => 10000 => 10000
[2,5,3,-4,1] => [1,-4,3,5,2] => 01000 => 10000
[2,5,3,-4,-1] => [-1,-4,3,5,2] => 11000 => 10010
[2,5,-3,4,1] => [1,4,-3,5,2] => 00100 => 10000
[2,5,-3,4,-1] => [-1,4,-3,5,2] => 10100 => 11000
[2,5,-3,-4,1] => [1,-4,-3,5,2] => 01100 => 10010
[2,5,-3,-4,-1] => [-1,-4,-3,5,2] => 11100 => 10110
[2,-5,3,4,1] => [1,4,3,-5,2] => 00010 => 10000
[2,-5,3,4,-1] => [-1,4,3,-5,2] => 10010 => 11000
[2,-5,3,-4,1] => [1,-4,3,-5,2] => 01010 => 11000
[2,-5,3,-4,-1] => [-1,-4,3,-5,2] => 11010 => 11100
[2,-5,-3,4,1] => [1,4,-3,-5,2] => 00110 => 10010
[2,-5,-3,4,-1] => [-1,4,-3,-5,2] => 10110 => 11100
[2,-5,-3,-4,1] => [1,-4,-3,-5,2] => 01110 => 10110
[2,-5,-3,-4,-1] => [-1,-4,-3,-5,2] => 11110 => 11110
[-2,5,3,4,1] => [1,4,3,5,-2] => 00001 => 10000
[-2,5,3,4,-1] => [-1,4,3,5,-2] => 10001 => 10010
[-2,5,3,-4,1] => [1,-4,3,5,-2] => 01001 => 11000
[-2,5,3,-4,-1] => [-1,-4,3,5,-2] => 11001 => 10110
[-2,5,-3,4,1] => [1,4,-3,5,-2] => 00101 => 11000
[-2,5,-3,4,-1] => [-1,4,-3,5,-2] => 10101 => 11100
[-2,5,-3,-4,1] => [1,-4,-3,5,-2] => 01101 => 11100
[-2,5,-3,-4,-1] => [-1,-4,-3,5,-2] => 11101 => 11110
[-2,-5,3,4,1] => [1,4,3,-5,-2] => 00011 => 10010
[-2,-5,3,4,-1] => [-1,4,3,-5,-2] => 10011 => 10110
[-2,-5,3,-4,1] => [1,-4,3,-5,-2] => 01011 => 11100
[-2,-5,3,-4,-1] => [-1,-4,3,-5,-2] => 11011 => 11110
[-2,-5,-3,4,1] => [1,4,-3,-5,-2] => 00111 => 10110
[-2,-5,-3,4,-1] => [-1,4,-3,-5,-2] => 10111 => 11110
[-2,-5,-3,-4,1] => [1,-4,-3,-5,-2] => 01111 => 11110
[-2,-5,-3,-4,-1] => [-1,-4,-3,-5,-2] => 11111 => 11111
[2,5,4,1,3] => [3,1,4,5,2] => 00000 => 00000
[2,5,4,1,-3] => [-3,1,4,5,2] => 10000 => 10000
[2,5,4,-1,3] => [3,-1,4,5,2] => 01000 => 10000
[2,5,4,-1,-3] => [-3,-1,4,5,2] => 11000 => 10010
[2,5,-4,1,3] => [3,1,-4,5,2] => 00100 => 10000
[2,5,-4,1,-3] => [-3,1,-4,5,2] => 10100 => 11000
[2,5,-4,-1,3] => [3,-1,-4,5,2] => 01100 => 10010
[2,5,-4,-1,-3] => [-3,-1,-4,5,2] => 11100 => 10110
[2,-5,4,1,3] => [3,1,4,-5,2] => 00010 => 10000
[2,-5,4,1,-3] => [-3,1,4,-5,2] => 10010 => 11000
[2,-5,4,-1,3] => [3,-1,4,-5,2] => 01010 => 11000
[2,-5,4,-1,-3] => [-3,-1,4,-5,2] => 11010 => 11100
[2,-5,-4,1,3] => [3,1,-4,-5,2] => 00110 => 10010
[2,-5,-4,1,-3] => [-3,1,-4,-5,2] => 10110 => 11100
[2,-5,-4,-1,3] => [3,-1,-4,-5,2] => 01110 => 10110
[2,-5,-4,-1,-3] => [-3,-1,-4,-5,2] => 11110 => 11110
[-2,5,4,1,3] => [3,1,4,5,-2] => 00001 => 10000
[-2,5,4,1,-3] => [-3,1,4,5,-2] => 10001 => 10010
[-2,5,4,-1,3] => [3,-1,4,5,-2] => 01001 => 11000
[-2,5,4,-1,-3] => [-3,-1,4,5,-2] => 11001 => 10110
[-2,5,-4,1,3] => [3,1,-4,5,-2] => 00101 => 11000
[-2,5,-4,1,-3] => [-3,1,-4,5,-2] => 10101 => 11100
[-2,5,-4,-1,3] => [3,-1,-4,5,-2] => 01101 => 11100
[-2,5,-4,-1,-3] => [-3,-1,-4,5,-2] => 11101 => 11110
[-2,-5,4,1,3] => [3,1,4,-5,-2] => 00011 => 10010
[-2,-5,4,1,-3] => [-3,1,4,-5,-2] => 10011 => 10110
[-2,-5,4,-1,3] => [3,-1,4,-5,-2] => 01011 => 11100
[-2,-5,4,-1,-3] => [-3,-1,4,-5,-2] => 11011 => 11110
[-2,-5,-4,1,3] => [3,1,-4,-5,-2] => 00111 => 10110
[-2,-5,-4,1,-3] => [-3,1,-4,-5,-2] => 10111 => 11110
[-2,-5,-4,-1,3] => [3,-1,-4,-5,-2] => 01111 => 11110
[-2,-5,-4,-1,-3] => [-3,-1,-4,-5,-2] => 11111 => 11111
[2,5,4,3,1] => [1,3,4,5,2] => 00000 => 00000
[2,5,4,3,-1] => [-1,3,4,5,2] => 10000 => 10000
[2,5,4,-3,1] => [1,-3,4,5,2] => 01000 => 10000
[2,5,4,-3,-1] => [-1,-3,4,5,2] => 11000 => 10010
[2,5,-4,3,1] => [1,3,-4,5,2] => 00100 => 10000
[2,5,-4,3,-1] => [-1,3,-4,5,2] => 10100 => 11000
[2,5,-4,-3,1] => [1,-3,-4,5,2] => 01100 => 10010
[2,5,-4,-3,-1] => [-1,-3,-4,5,2] => 11100 => 10110
[2,-5,4,3,1] => [1,3,4,-5,2] => 00010 => 10000
[2,-5,4,3,-1] => [-1,3,4,-5,2] => 10010 => 11000
[2,-5,4,-3,1] => [1,-3,4,-5,2] => 01010 => 11000
[2,-5,4,-3,-1] => [-1,-3,4,-5,2] => 11010 => 11100
[2,-5,-4,3,1] => [1,3,-4,-5,2] => 00110 => 10010
[2,-5,-4,3,-1] => [-1,3,-4,-5,2] => 10110 => 11100
[2,-5,-4,-3,1] => [1,-3,-4,-5,2] => 01110 => 10110
[2,-5,-4,-3,-1] => [-1,-3,-4,-5,2] => 11110 => 11110
[-2,5,4,3,1] => [1,3,4,5,-2] => 00001 => 10000
[-2,5,4,3,-1] => [-1,3,4,5,-2] => 10001 => 10010
[-2,5,4,-3,1] => [1,-3,4,5,-2] => 01001 => 11000
[-2,5,4,-3,-1] => [-1,-3,4,5,-2] => 11001 => 10110
[-2,5,-4,3,1] => [1,3,-4,5,-2] => 00101 => 11000
[-2,5,-4,3,-1] => [-1,3,-4,5,-2] => 10101 => 11100
[-2,5,-4,-3,1] => [1,-3,-4,5,-2] => 01101 => 11100
[-2,5,-4,-3,-1] => [-1,-3,-4,5,-2] => 11101 => 11110
[-2,-5,4,3,1] => [1,3,4,-5,-2] => 00011 => 10010
[-2,-5,4,3,-1] => [-1,3,4,-5,-2] => 10011 => 10110
[-2,-5,4,-3,1] => [1,-3,4,-5,-2] => 01011 => 11100
[-2,-5,4,-3,-1] => [-1,-3,4,-5,-2] => 11011 => 11110
[-2,-5,-4,3,1] => [1,3,-4,-5,-2] => 00111 => 10110
[-2,-5,-4,3,-1] => [-1,3,-4,-5,-2] => 10111 => 11110
[-2,-5,-4,-3,1] => [1,-3,-4,-5,-2] => 01111 => 11110
[-2,-5,-4,-3,-1] => [-1,-3,-4,-5,-2] => 11111 => 11111
[3,1,2,4,5] => [5,4,2,1,3] => 00000 => 00000
[3,1,2,4,-5] => [-5,4,2,1,3] => 10000 => 10000
[3,1,2,-4,5] => [5,-4,2,1,3] => 01000 => 10000
[3,1,2,-4,-5] => [-5,-4,2,1,3] => 11000 => 10010
[3,1,-2,4,5] => [5,4,-2,1,3] => 00100 => 10000
[3,1,-2,4,-5] => [-5,4,-2,1,3] => 10100 => 11000
[3,1,-2,-4,5] => [5,-4,-2,1,3] => 01100 => 10010
[3,1,-2,-4,-5] => [-5,-4,-2,1,3] => 11100 => 10110
[3,-1,2,4,5] => [5,4,2,-1,3] => 00010 => 10000
[3,-1,2,4,-5] => [-5,4,2,-1,3] => 10010 => 11000
[3,-1,2,-4,5] => [5,-4,2,-1,3] => 01010 => 11000
[3,-1,2,-4,-5] => [-5,-4,2,-1,3] => 11010 => 11100
[3,-1,-2,4,5] => [5,4,-2,-1,3] => 00110 => 10010
[3,-1,-2,4,-5] => [-5,4,-2,-1,3] => 10110 => 11100
[3,-1,-2,-4,5] => [5,-4,-2,-1,3] => 01110 => 10110
[3,-1,-2,-4,-5] => [-5,-4,-2,-1,3] => 11110 => 11110
[-3,1,2,4,5] => [5,4,2,1,-3] => 00001 => 10000
[-3,1,2,4,-5] => [-5,4,2,1,-3] => 10001 => 10010
[-3,1,2,-4,5] => [5,-4,2,1,-3] => 01001 => 11000
[-3,1,2,-4,-5] => [-5,-4,2,1,-3] => 11001 => 10110
[-3,1,-2,4,5] => [5,4,-2,1,-3] => 00101 => 11000
[-3,1,-2,4,-5] => [-5,4,-2,1,-3] => 10101 => 11100
[-3,1,-2,-4,5] => [5,-4,-2,1,-3] => 01101 => 11100
[-3,1,-2,-4,-5] => [-5,-4,-2,1,-3] => 11101 => 11110
[-3,-1,2,4,5] => [5,4,2,-1,-3] => 00011 => 10010
[-3,-1,2,4,-5] => [-5,4,2,-1,-3] => 10011 => 10110
[-3,-1,2,-4,5] => [5,-4,2,-1,-3] => 01011 => 11100
[-3,-1,2,-4,-5] => [-5,-4,2,-1,-3] => 11011 => 11110
[-3,-1,-2,4,5] => [5,4,-2,-1,-3] => 00111 => 10110
[-3,-1,-2,4,-5] => [-5,4,-2,-1,-3] => 10111 => 11110
[-3,-1,-2,-4,5] => [5,-4,-2,-1,-3] => 01111 => 11110
[-3,-1,-2,-4,-5] => [-5,-4,-2,-1,-3] => 11111 => 11111
[3,1,2,5,4] => [4,5,2,1,3] => 00000 => 00000
[3,1,2,5,-4] => [-4,5,2,1,3] => 10000 => 10000
[3,1,2,-5,4] => [4,-5,2,1,3] => 01000 => 10000
[3,1,2,-5,-4] => [-4,-5,2,1,3] => 11000 => 10010
[3,1,-2,5,4] => [4,5,-2,1,3] => 00100 => 10000
[3,1,-2,5,-4] => [-4,5,-2,1,3] => 10100 => 11000
[3,1,-2,-5,4] => [4,-5,-2,1,3] => 01100 => 10010
[3,1,-2,-5,-4] => [-4,-5,-2,1,3] => 11100 => 10110
[3,-1,2,5,4] => [4,5,2,-1,3] => 00010 => 10000
[3,-1,2,5,-4] => [-4,5,2,-1,3] => 10010 => 11000
[3,-1,2,-5,4] => [4,-5,2,-1,3] => 01010 => 11000
[3,-1,2,-5,-4] => [-4,-5,2,-1,3] => 11010 => 11100
[3,-1,-2,5,4] => [4,5,-2,-1,3] => 00110 => 10010
[3,-1,-2,5,-4] => [-4,5,-2,-1,3] => 10110 => 11100
[3,-1,-2,-5,4] => [4,-5,-2,-1,3] => 01110 => 10110
[3,-1,-2,-5,-4] => [-4,-5,-2,-1,3] => 11110 => 11110
[-3,1,2,5,4] => [4,5,2,1,-3] => 00001 => 10000
[-3,1,2,5,-4] => [-4,5,2,1,-3] => 10001 => 10010
[-3,1,2,-5,4] => [4,-5,2,1,-3] => 01001 => 11000
[-3,1,2,-5,-4] => [-4,-5,2,1,-3] => 11001 => 10110
[-3,1,-2,5,4] => [4,5,-2,1,-3] => 00101 => 11000
[-3,1,-2,5,-4] => [-4,5,-2,1,-3] => 10101 => 11100
[-3,1,-2,-5,4] => [4,-5,-2,1,-3] => 01101 => 11100
[-3,1,-2,-5,-4] => [-4,-5,-2,1,-3] => 11101 => 11110
[-3,-1,2,5,4] => [4,5,2,-1,-3] => 00011 => 10010
[-3,-1,2,5,-4] => [-4,5,2,-1,-3] => 10011 => 10110
[-3,-1,2,-5,4] => [4,-5,2,-1,-3] => 01011 => 11100
[-3,-1,2,-5,-4] => [-4,-5,2,-1,-3] => 11011 => 11110
[-3,-1,-2,5,4] => [4,5,-2,-1,-3] => 00111 => 10110
[-3,-1,-2,5,-4] => [-4,5,-2,-1,-3] => 10111 => 11110
[-3,-1,-2,-5,4] => [4,-5,-2,-1,-3] => 01111 => 11110
[-3,-1,-2,-5,-4] => [-4,-5,-2,-1,-3] => 11111 => 11111
[3,1,4,2,5] => [5,2,4,1,3] => 00000 => 00000
[3,1,4,2,-5] => [-5,2,4,1,3] => 10000 => 10000
[3,1,4,-2,5] => [5,-2,4,1,3] => 01000 => 10000
[3,1,4,-2,-5] => [-5,-2,4,1,3] => 11000 => 10010
[3,1,-4,2,5] => [5,2,-4,1,3] => 00100 => 10000
[3,1,-4,2,-5] => [-5,2,-4,1,3] => 10100 => 11000
[3,1,-4,-2,5] => [5,-2,-4,1,3] => 01100 => 10010
[3,1,-4,-2,-5] => [-5,-2,-4,1,3] => 11100 => 10110
[3,-1,4,2,5] => [5,2,4,-1,3] => 00010 => 10000
[3,-1,4,2,-5] => [-5,2,4,-1,3] => 10010 => 11000
[3,-1,4,-2,5] => [5,-2,4,-1,3] => 01010 => 11000
[3,-1,4,-2,-5] => [-5,-2,4,-1,3] => 11010 => 11100
[3,-1,-4,2,5] => [5,2,-4,-1,3] => 00110 => 10010
[3,-1,-4,2,-5] => [-5,2,-4,-1,3] => 10110 => 11100
[3,-1,-4,-2,5] => [5,-2,-4,-1,3] => 01110 => 10110
[3,-1,-4,-2,-5] => [-5,-2,-4,-1,3] => 11110 => 11110
[-3,1,4,2,5] => [5,2,4,1,-3] => 00001 => 10000
[-3,1,4,2,-5] => [-5,2,4,1,-3] => 10001 => 10010
[-3,1,4,-2,5] => [5,-2,4,1,-3] => 01001 => 11000
[-3,1,4,-2,-5] => [-5,-2,4,1,-3] => 11001 => 10110
[-3,1,-4,2,5] => [5,2,-4,1,-3] => 00101 => 11000
[-3,1,-4,2,-5] => [-5,2,-4,1,-3] => 10101 => 11100
[-3,1,-4,-2,5] => [5,-2,-4,1,-3] => 01101 => 11100
[-3,1,-4,-2,-5] => [-5,-2,-4,1,-3] => 11101 => 11110
[-3,-1,4,2,5] => [5,2,4,-1,-3] => 00011 => 10010
[-3,-1,4,2,-5] => [-5,2,4,-1,-3] => 10011 => 10110
[-3,-1,4,-2,5] => [5,-2,4,-1,-3] => 01011 => 11100
[-3,-1,4,-2,-5] => [-5,-2,4,-1,-3] => 11011 => 11110
[-3,-1,-4,2,5] => [5,2,-4,-1,-3] => 00111 => 10110
[-3,-1,-4,2,-5] => [-5,2,-4,-1,-3] => 10111 => 11110
[-3,-1,-4,-2,5] => [5,-2,-4,-1,-3] => 01111 => 11110
[-3,-1,-4,-2,-5] => [-5,-2,-4,-1,-3] => 11111 => 11111
[3,1,4,5,2] => [2,5,4,1,3] => 00000 => 00000
[3,1,4,5,-2] => [-2,5,4,1,3] => 10000 => 10000
[3,1,4,-5,2] => [2,-5,4,1,3] => 01000 => 10000
[3,1,4,-5,-2] => [-2,-5,4,1,3] => 11000 => 10010
[3,1,-4,5,2] => [2,5,-4,1,3] => 00100 => 10000
[3,1,-4,5,-2] => [-2,5,-4,1,3] => 10100 => 11000
[3,1,-4,-5,2] => [2,-5,-4,1,3] => 01100 => 10010
[3,1,-4,-5,-2] => [-2,-5,-4,1,3] => 11100 => 10110
[3,-1,4,5,2] => [2,5,4,-1,3] => 00010 => 10000
[3,-1,4,5,-2] => [-2,5,4,-1,3] => 10010 => 11000
[3,-1,4,-5,2] => [2,-5,4,-1,3] => 01010 => 11000
[3,-1,4,-5,-2] => [-2,-5,4,-1,3] => 11010 => 11100
[3,-1,-4,5,2] => [2,5,-4,-1,3] => 00110 => 10010
[3,-1,-4,5,-2] => [-2,5,-4,-1,3] => 10110 => 11100
[3,-1,-4,-5,2] => [2,-5,-4,-1,3] => 01110 => 10110
[3,-1,-4,-5,-2] => [-2,-5,-4,-1,3] => 11110 => 11110
[-3,1,4,5,2] => [2,5,4,1,-3] => 00001 => 10000
[-3,1,4,5,-2] => [-2,5,4,1,-3] => 10001 => 10010
[-3,1,4,-5,2] => [2,-5,4,1,-3] => 01001 => 11000
[-3,1,4,-5,-2] => [-2,-5,4,1,-3] => 11001 => 10110
[-3,1,-4,5,2] => [2,5,-4,1,-3] => 00101 => 11000
[-3,1,-4,5,-2] => [-2,5,-4,1,-3] => 10101 => 11100
[-3,1,-4,-5,2] => [2,-5,-4,1,-3] => 01101 => 11100
[-3,1,-4,-5,-2] => [-2,-5,-4,1,-3] => 11101 => 11110
[-3,-1,4,5,2] => [2,5,4,-1,-3] => 00011 => 10010
[-3,-1,4,5,-2] => [-2,5,4,-1,-3] => 10011 => 10110
[-3,-1,4,-5,2] => [2,-5,4,-1,-3] => 01011 => 11100
[-3,-1,4,-5,-2] => [-2,-5,4,-1,-3] => 11011 => 11110
[-3,-1,-4,5,2] => [2,5,-4,-1,-3] => 00111 => 10110
[-3,-1,-4,5,-2] => [-2,5,-4,-1,-3] => 10111 => 11110
[-3,-1,-4,-5,2] => [2,-5,-4,-1,-3] => 01111 => 11110
[-3,-1,-4,-5,-2] => [-2,-5,-4,-1,-3] => 11111 => 11111
[3,1,5,2,4] => [4,2,5,1,3] => 00000 => 00000
[3,1,5,2,-4] => [-4,2,5,1,3] => 10000 => 10000
[3,1,5,-2,4] => [4,-2,5,1,3] => 01000 => 10000
[3,1,5,-2,-4] => [-4,-2,5,1,3] => 11000 => 10010
[3,1,-5,2,4] => [4,2,-5,1,3] => 00100 => 10000
[3,1,-5,2,-4] => [-4,2,-5,1,3] => 10100 => 11000
[3,1,-5,-2,4] => [4,-2,-5,1,3] => 01100 => 10010
[3,1,-5,-2,-4] => [-4,-2,-5,1,3] => 11100 => 10110
[3,-1,5,2,4] => [4,2,5,-1,3] => 00010 => 10000
[3,-1,5,2,-4] => [-4,2,5,-1,3] => 10010 => 11000
[3,-1,5,-2,4] => [4,-2,5,-1,3] => 01010 => 11000
[3,-1,5,-2,-4] => [-4,-2,5,-1,3] => 11010 => 11100
[3,-1,-5,2,4] => [4,2,-5,-1,3] => 00110 => 10010
[3,-1,-5,2,-4] => [-4,2,-5,-1,3] => 10110 => 11100
[3,-1,-5,-2,4] => [4,-2,-5,-1,3] => 01110 => 10110
[3,-1,-5,-2,-4] => [-4,-2,-5,-1,3] => 11110 => 11110
[-3,1,5,2,4] => [4,2,5,1,-3] => 00001 => 10000
[-3,1,5,2,-4] => [-4,2,5,1,-3] => 10001 => 10010
[-3,1,5,-2,4] => [4,-2,5,1,-3] => 01001 => 11000
[-3,1,5,-2,-4] => [-4,-2,5,1,-3] => 11001 => 10110
[-3,1,-5,2,4] => [4,2,-5,1,-3] => 00101 => 11000
[-3,1,-5,2,-4] => [-4,2,-5,1,-3] => 10101 => 11100
[-3,1,-5,-2,4] => [4,-2,-5,1,-3] => 01101 => 11100
[-3,1,-5,-2,-4] => [-4,-2,-5,1,-3] => 11101 => 11110
[-3,-1,5,2,4] => [4,2,5,-1,-3] => 00011 => 10010
[-3,-1,5,2,-4] => [-4,2,5,-1,-3] => 10011 => 10110
[-3,-1,5,-2,4] => [4,-2,5,-1,-3] => 01011 => 11100
[-3,-1,5,-2,-4] => [-4,-2,5,-1,-3] => 11011 => 11110
[-3,-1,-5,2,4] => [4,2,-5,-1,-3] => 00111 => 10110
[-3,-1,-5,2,-4] => [-4,2,-5,-1,-3] => 10111 => 11110
[-3,-1,-5,-2,4] => [4,-2,-5,-1,-3] => 01111 => 11110
[-3,-1,-5,-2,-4] => [-4,-2,-5,-1,-3] => 11111 => 11111
[3,1,5,4,2] => [2,4,5,1,3] => 00000 => 00000
[3,1,5,4,-2] => [-2,4,5,1,3] => 10000 => 10000
[3,1,5,-4,2] => [2,-4,5,1,3] => 01000 => 10000
[3,1,5,-4,-2] => [-2,-4,5,1,3] => 11000 => 10010
[3,1,-5,4,2] => [2,4,-5,1,3] => 00100 => 10000
[3,1,-5,4,-2] => [-2,4,-5,1,3] => 10100 => 11000
[3,1,-5,-4,2] => [2,-4,-5,1,3] => 01100 => 10010
[3,1,-5,-4,-2] => [-2,-4,-5,1,3] => 11100 => 10110
[3,-1,5,4,2] => [2,4,5,-1,3] => 00010 => 10000
[3,-1,5,4,-2] => [-2,4,5,-1,3] => 10010 => 11000
[3,-1,5,-4,2] => [2,-4,5,-1,3] => 01010 => 11000
[3,-1,5,-4,-2] => [-2,-4,5,-1,3] => 11010 => 11100
[3,-1,-5,4,2] => [2,4,-5,-1,3] => 00110 => 10010
[3,-1,-5,4,-2] => [-2,4,-5,-1,3] => 10110 => 11100
[3,-1,-5,-4,2] => [2,-4,-5,-1,3] => 01110 => 10110
[3,-1,-5,-4,-2] => [-2,-4,-5,-1,3] => 11110 => 11110
[-3,1,5,4,2] => [2,4,5,1,-3] => 00001 => 10000
[-3,1,5,4,-2] => [-2,4,5,1,-3] => 10001 => 10010
[-3,1,5,-4,2] => [2,-4,5,1,-3] => 01001 => 11000
[-3,1,5,-4,-2] => [-2,-4,5,1,-3] => 11001 => 10110
[-3,1,-5,4,2] => [2,4,-5,1,-3] => 00101 => 11000
[-3,1,-5,4,-2] => [-2,4,-5,1,-3] => 10101 => 11100
[-3,1,-5,-4,2] => [2,-4,-5,1,-3] => 01101 => 11100
[-3,1,-5,-4,-2] => [-2,-4,-5,1,-3] => 11101 => 11110
[-3,-1,5,4,2] => [2,4,5,-1,-3] => 00011 => 10010
[-3,-1,5,4,-2] => [-2,4,5,-1,-3] => 10011 => 10110
[-3,-1,5,-4,2] => [2,-4,5,-1,-3] => 01011 => 11100
[-3,-1,5,-4,-2] => [-2,-4,5,-1,-3] => 11011 => 11110
[-3,-1,-5,4,2] => [2,4,-5,-1,-3] => 00111 => 10110
[-3,-1,-5,4,-2] => [-2,4,-5,-1,-3] => 10111 => 11110
[-3,-1,-5,-4,2] => [2,-4,-5,-1,-3] => 01111 => 11110
[-3,-1,-5,-4,-2] => [-2,-4,-5,-1,-3] => 11111 => 11111
[3,2,1,4,5] => [5,4,1,2,3] => 00000 => 00000
[3,2,1,4,-5] => [-5,4,1,2,3] => 10000 => 10000
[3,2,1,-4,5] => [5,-4,1,2,3] => 01000 => 10000
[3,2,1,-4,-5] => [-5,-4,1,2,3] => 11000 => 10010
[3,2,-1,4,5] => [5,4,-1,2,3] => 00100 => 10000
[3,2,-1,4,-5] => [-5,4,-1,2,3] => 10100 => 11000
[3,2,-1,-4,5] => [5,-4,-1,2,3] => 01100 => 10010
[3,2,-1,-4,-5] => [-5,-4,-1,2,3] => 11100 => 10110
[3,-2,1,4,5] => [5,4,1,-2,3] => 00010 => 10000
[3,-2,1,4,-5] => [-5,4,1,-2,3] => 10010 => 11000
[3,-2,1,-4,5] => [5,-4,1,-2,3] => 01010 => 11000
[3,-2,1,-4,-5] => [-5,-4,1,-2,3] => 11010 => 11100
[3,-2,-1,4,5] => [5,4,-1,-2,3] => 00110 => 10010
[3,-2,-1,4,-5] => [-5,4,-1,-2,3] => 10110 => 11100
[3,-2,-1,-4,5] => [5,-4,-1,-2,3] => 01110 => 10110
[3,-2,-1,-4,-5] => [-5,-4,-1,-2,3] => 11110 => 11110
[-3,2,1,4,5] => [5,4,1,2,-3] => 00001 => 10000
[-3,2,1,4,-5] => [-5,4,1,2,-3] => 10001 => 10010
[-3,2,1,-4,5] => [5,-4,1,2,-3] => 01001 => 11000
[-3,2,1,-4,-5] => [-5,-4,1,2,-3] => 11001 => 10110
[-3,2,-1,4,5] => [5,4,-1,2,-3] => 00101 => 11000
[-3,2,-1,4,-5] => [-5,4,-1,2,-3] => 10101 => 11100
[-3,2,-1,-4,5] => [5,-4,-1,2,-3] => 01101 => 11100
[-3,2,-1,-4,-5] => [-5,-4,-1,2,-3] => 11101 => 11110
[-3,-2,1,4,5] => [5,4,1,-2,-3] => 00011 => 10010
[-3,-2,1,4,-5] => [-5,4,1,-2,-3] => 10011 => 10110
[-3,-2,1,-4,5] => [5,-4,1,-2,-3] => 01011 => 11100
[-3,-2,1,-4,-5] => [-5,-4,1,-2,-3] => 11011 => 11110
[-3,-2,-1,4,5] => [5,4,-1,-2,-3] => 00111 => 10110
[-3,-2,-1,4,-5] => [-5,4,-1,-2,-3] => 10111 => 11110
[-3,-2,-1,-4,5] => [5,-4,-1,-2,-3] => 01111 => 11110
[-3,-2,-1,-4,-5] => [-5,-4,-1,-2,-3] => 11111 => 11111
[3,2,1,5,4] => [4,5,1,2,3] => 00000 => 00000
[3,2,1,5,-4] => [-4,5,1,2,3] => 10000 => 10000
[3,2,1,-5,4] => [4,-5,1,2,3] => 01000 => 10000
[3,2,1,-5,-4] => [-4,-5,1,2,3] => 11000 => 10010
[3,2,-1,5,4] => [4,5,-1,2,3] => 00100 => 10000
[3,2,-1,5,-4] => [-4,5,-1,2,3] => 10100 => 11000
[3,2,-1,-5,4] => [4,-5,-1,2,3] => 01100 => 10010
[3,2,-1,-5,-4] => [-4,-5,-1,2,3] => 11100 => 10110
[3,-2,1,5,4] => [4,5,1,-2,3] => 00010 => 10000
[3,-2,1,5,-4] => [-4,5,1,-2,3] => 10010 => 11000
[3,-2,1,-5,4] => [4,-5,1,-2,3] => 01010 => 11000
[3,-2,1,-5,-4] => [-4,-5,1,-2,3] => 11010 => 11100
[3,-2,-1,5,4] => [4,5,-1,-2,3] => 00110 => 10010
[3,-2,-1,5,-4] => [-4,5,-1,-2,3] => 10110 => 11100
[3,-2,-1,-5,4] => [4,-5,-1,-2,3] => 01110 => 10110
[3,-2,-1,-5,-4] => [-4,-5,-1,-2,3] => 11110 => 11110
[-3,2,1,5,4] => [4,5,1,2,-3] => 00001 => 10000
[-3,2,1,5,-4] => [-4,5,1,2,-3] => 10001 => 10010
[-3,2,1,-5,4] => [4,-5,1,2,-3] => 01001 => 11000
[-3,2,1,-5,-4] => [-4,-5,1,2,-3] => 11001 => 10110
[-3,2,-1,5,4] => [4,5,-1,2,-3] => 00101 => 11000
[-3,2,-1,5,-4] => [-4,5,-1,2,-3] => 10101 => 11100
[-3,2,-1,-5,4] => [4,-5,-1,2,-3] => 01101 => 11100
[-3,2,-1,-5,-4] => [-4,-5,-1,2,-3] => 11101 => 11110
[-3,-2,1,5,4] => [4,5,1,-2,-3] => 00011 => 10010
[-3,-2,1,5,-4] => [-4,5,1,-2,-3] => 10011 => 10110
[-3,-2,1,-5,4] => [4,-5,1,-2,-3] => 01011 => 11100
[-3,-2,1,-5,-4] => [-4,-5,1,-2,-3] => 11011 => 11110
[-3,-2,-1,5,4] => [4,5,-1,-2,-3] => 00111 => 10110
[-3,-2,-1,5,-4] => [-4,5,-1,-2,-3] => 10111 => 11110
[-3,-2,-1,-5,4] => [4,-5,-1,-2,-3] => 01111 => 11110
[-3,-2,-1,-5,-4] => [-4,-5,-1,-2,-3] => 11111 => 11111
[3,2,4,1,5] => [5,1,4,2,3] => 00000 => 00000
[3,2,4,1,-5] => [-5,1,4,2,3] => 10000 => 10000
[3,2,4,-1,5] => [5,-1,4,2,3] => 01000 => 10000
[3,2,4,-1,-5] => [-5,-1,4,2,3] => 11000 => 10010
[3,2,-4,1,5] => [5,1,-4,2,3] => 00100 => 10000
[3,2,-4,1,-5] => [-5,1,-4,2,3] => 10100 => 11000
[3,2,-4,-1,5] => [5,-1,-4,2,3] => 01100 => 10010
[3,2,-4,-1,-5] => [-5,-1,-4,2,3] => 11100 => 10110
[3,-2,4,1,5] => [5,1,4,-2,3] => 00010 => 10000
[3,-2,4,1,-5] => [-5,1,4,-2,3] => 10010 => 11000
[3,-2,4,-1,5] => [5,-1,4,-2,3] => 01010 => 11000
[3,-2,4,-1,-5] => [-5,-1,4,-2,3] => 11010 => 11100
[3,-2,-4,1,5] => [5,1,-4,-2,3] => 00110 => 10010
[3,-2,-4,1,-5] => [-5,1,-4,-2,3] => 10110 => 11100
[3,-2,-4,-1,5] => [5,-1,-4,-2,3] => 01110 => 10110
[3,-2,-4,-1,-5] => [-5,-1,-4,-2,3] => 11110 => 11110
[-3,2,4,1,5] => [5,1,4,2,-3] => 00001 => 10000
[-3,2,4,1,-5] => [-5,1,4,2,-3] => 10001 => 10010
[-3,2,4,-1,5] => [5,-1,4,2,-3] => 01001 => 11000
[-3,2,4,-1,-5] => [-5,-1,4,2,-3] => 11001 => 10110
[-3,2,-4,1,5] => [5,1,-4,2,-3] => 00101 => 11000
[-3,2,-4,1,-5] => [-5,1,-4,2,-3] => 10101 => 11100
[-3,2,-4,-1,5] => [5,-1,-4,2,-3] => 01101 => 11100
[-3,2,-4,-1,-5] => [-5,-1,-4,2,-3] => 11101 => 11110
[-3,-2,4,1,5] => [5,1,4,-2,-3] => 00011 => 10010
[-3,-2,4,1,-5] => [-5,1,4,-2,-3] => 10011 => 10110
[-3,-2,4,-1,5] => [5,-1,4,-2,-3] => 01011 => 11100
[-3,-2,4,-1,-5] => [-5,-1,4,-2,-3] => 11011 => 11110
[-3,-2,-4,1,5] => [5,1,-4,-2,-3] => 00111 => 10110
[-3,-2,-4,1,-5] => [-5,1,-4,-2,-3] => 10111 => 11110
[-3,-2,-4,-1,5] => [5,-1,-4,-2,-3] => 01111 => 11110
[-3,-2,-4,-1,-5] => [-5,-1,-4,-2,-3] => 11111 => 11111
[3,2,4,5,1] => [1,5,4,2,3] => 00000 => 00000
[3,2,4,5,-1] => [-1,5,4,2,3] => 10000 => 10000
[3,2,4,-5,1] => [1,-5,4,2,3] => 01000 => 10000
[3,2,4,-5,-1] => [-1,-5,4,2,3] => 11000 => 10010
[3,2,-4,5,1] => [1,5,-4,2,3] => 00100 => 10000
[3,2,-4,5,-1] => [-1,5,-4,2,3] => 10100 => 11000
[3,2,-4,-5,1] => [1,-5,-4,2,3] => 01100 => 10010
[3,2,-4,-5,-1] => [-1,-5,-4,2,3] => 11100 => 10110
[3,-2,4,5,1] => [1,5,4,-2,3] => 00010 => 10000
[3,-2,4,5,-1] => [-1,5,4,-2,3] => 10010 => 11000
[3,-2,4,-5,1] => [1,-5,4,-2,3] => 01010 => 11000
[3,-2,4,-5,-1] => [-1,-5,4,-2,3] => 11010 => 11100
[3,-2,-4,5,1] => [1,5,-4,-2,3] => 00110 => 10010
[3,-2,-4,5,-1] => [-1,5,-4,-2,3] => 10110 => 11100
[3,-2,-4,-5,1] => [1,-5,-4,-2,3] => 01110 => 10110
[3,-2,-4,-5,-1] => [-1,-5,-4,-2,3] => 11110 => 11110
[-3,2,4,5,1] => [1,5,4,2,-3] => 00001 => 10000
[-3,2,4,5,-1] => [-1,5,4,2,-3] => 10001 => 10010
[-3,2,4,-5,1] => [1,-5,4,2,-3] => 01001 => 11000
[-3,2,4,-5,-1] => [-1,-5,4,2,-3] => 11001 => 10110
[-3,2,-4,5,1] => [1,5,-4,2,-3] => 00101 => 11000
[-3,2,-4,5,-1] => [-1,5,-4,2,-3] => 10101 => 11100
[-3,2,-4,-5,1] => [1,-5,-4,2,-3] => 01101 => 11100
[-3,2,-4,-5,-1] => [-1,-5,-4,2,-3] => 11101 => 11110
[-3,-2,4,5,1] => [1,5,4,-2,-3] => 00011 => 10010
[-3,-2,4,5,-1] => [-1,5,4,-2,-3] => 10011 => 10110
[-3,-2,4,-5,1] => [1,-5,4,-2,-3] => 01011 => 11100
[-3,-2,4,-5,-1] => [-1,-5,4,-2,-3] => 11011 => 11110
[-3,-2,-4,5,1] => [1,5,-4,-2,-3] => 00111 => 10110
[-3,-2,-4,5,-1] => [-1,5,-4,-2,-3] => 10111 => 11110
[-3,-2,-4,-5,1] => [1,-5,-4,-2,-3] => 01111 => 11110
[-3,-2,-4,-5,-1] => [-1,-5,-4,-2,-3] => 11111 => 11111
[3,2,5,1,4] => [4,1,5,2,3] => 00000 => 00000
[3,2,5,1,-4] => [-4,1,5,2,3] => 10000 => 10000
[3,2,5,-1,4] => [4,-1,5,2,3] => 01000 => 10000
[3,2,5,-1,-4] => [-4,-1,5,2,3] => 11000 => 10010
[3,2,-5,1,4] => [4,1,-5,2,3] => 00100 => 10000
[3,2,-5,1,-4] => [-4,1,-5,2,3] => 10100 => 11000
[3,2,-5,-1,4] => [4,-1,-5,2,3] => 01100 => 10010
[3,2,-5,-1,-4] => [-4,-1,-5,2,3] => 11100 => 10110
[3,-2,5,1,4] => [4,1,5,-2,3] => 00010 => 10000
[3,-2,5,1,-4] => [-4,1,5,-2,3] => 10010 => 11000
[3,-2,5,-1,4] => [4,-1,5,-2,3] => 01010 => 11000
[3,-2,5,-1,-4] => [-4,-1,5,-2,3] => 11010 => 11100
[3,-2,-5,1,4] => [4,1,-5,-2,3] => 00110 => 10010
[3,-2,-5,1,-4] => [-4,1,-5,-2,3] => 10110 => 11100
[3,-2,-5,-1,4] => [4,-1,-5,-2,3] => 01110 => 10110
[3,-2,-5,-1,-4] => [-4,-1,-5,-2,3] => 11110 => 11110
[-3,2,5,1,4] => [4,1,5,2,-3] => 00001 => 10000
[-3,2,5,1,-4] => [-4,1,5,2,-3] => 10001 => 10010
[-3,2,5,-1,4] => [4,-1,5,2,-3] => 01001 => 11000
[-3,2,5,-1,-4] => [-4,-1,5,2,-3] => 11001 => 10110
[-3,2,-5,1,4] => [4,1,-5,2,-3] => 00101 => 11000
[-3,2,-5,1,-4] => [-4,1,-5,2,-3] => 10101 => 11100
[-3,2,-5,-1,4] => [4,-1,-5,2,-3] => 01101 => 11100
[-3,2,-5,-1,-4] => [-4,-1,-5,2,-3] => 11101 => 11110
[-3,-2,5,1,4] => [4,1,5,-2,-3] => 00011 => 10010
[-3,-2,5,1,-4] => [-4,1,5,-2,-3] => 10011 => 10110
[-3,-2,5,-1,4] => [4,-1,5,-2,-3] => 01011 => 11100
[-3,-2,5,-1,-4] => [-4,-1,5,-2,-3] => 11011 => 11110
[-3,-2,-5,1,4] => [4,1,-5,-2,-3] => 00111 => 10110
[-3,-2,-5,1,-4] => [-4,1,-5,-2,-3] => 10111 => 11110
[-3,-2,-5,-1,4] => [4,-1,-5,-2,-3] => 01111 => 11110
[-3,-2,-5,-1,-4] => [-4,-1,-5,-2,-3] => 11111 => 11111
[3,2,5,4,1] => [1,4,5,2,3] => 00000 => 00000
[3,2,5,4,-1] => [-1,4,5,2,3] => 10000 => 10000
[3,2,5,-4,1] => [1,-4,5,2,3] => 01000 => 10000
[3,2,5,-4,-1] => [-1,-4,5,2,3] => 11000 => 10010
[3,2,-5,4,1] => [1,4,-5,2,3] => 00100 => 10000
[3,2,-5,4,-1] => [-1,4,-5,2,3] => 10100 => 11000
[3,2,-5,-4,1] => [1,-4,-5,2,3] => 01100 => 10010
[3,2,-5,-4,-1] => [-1,-4,-5,2,3] => 11100 => 10110
[3,-2,5,4,1] => [1,4,5,-2,3] => 00010 => 10000
[3,-2,5,4,-1] => [-1,4,5,-2,3] => 10010 => 11000
[3,-2,5,-4,1] => [1,-4,5,-2,3] => 01010 => 11000
[3,-2,5,-4,-1] => [-1,-4,5,-2,3] => 11010 => 11100
[3,-2,-5,4,1] => [1,4,-5,-2,3] => 00110 => 10010
[3,-2,-5,4,-1] => [-1,4,-5,-2,3] => 10110 => 11100
[3,-2,-5,-4,1] => [1,-4,-5,-2,3] => 01110 => 10110
[3,-2,-5,-4,-1] => [-1,-4,-5,-2,3] => 11110 => 11110
[-3,2,5,4,1] => [1,4,5,2,-3] => 00001 => 10000
[-3,2,5,4,-1] => [-1,4,5,2,-3] => 10001 => 10010
[-3,2,5,-4,1] => [1,-4,5,2,-3] => 01001 => 11000
[-3,2,5,-4,-1] => [-1,-4,5,2,-3] => 11001 => 10110
[-3,2,-5,4,1] => [1,4,-5,2,-3] => 00101 => 11000
[-3,2,-5,4,-1] => [-1,4,-5,2,-3] => 10101 => 11100
[-3,2,-5,-4,1] => [1,-4,-5,2,-3] => 01101 => 11100
[-3,2,-5,-4,-1] => [-1,-4,-5,2,-3] => 11101 => 11110
[-3,-2,5,4,1] => [1,4,5,-2,-3] => 00011 => 10010
[-3,-2,5,4,-1] => [-1,4,5,-2,-3] => 10011 => 10110
[-3,-2,5,-4,1] => [1,-4,5,-2,-3] => 01011 => 11100
[-3,-2,5,-4,-1] => [-1,-4,5,-2,-3] => 11011 => 11110
[-3,-2,-5,4,1] => [1,4,-5,-2,-3] => 00111 => 10110
[-3,-2,-5,4,-1] => [-1,4,-5,-2,-3] => 10111 => 11110
[-3,-2,-5,-4,1] => [1,-4,-5,-2,-3] => 01111 => 11110
[-3,-2,-5,-4,-1] => [-1,-4,-5,-2,-3] => 11111 => 11111
[3,4,1,2,5] => [5,2,1,4,3] => 00000 => 00000
[3,4,1,2,-5] => [-5,2,1,4,3] => 10000 => 10000
[3,4,1,-2,5] => [5,-2,1,4,3] => 01000 => 10000
[3,4,1,-2,-5] => [-5,-2,1,4,3] => 11000 => 10010
[3,4,-1,2,5] => [5,2,-1,4,3] => 00100 => 10000
[3,4,-1,2,-5] => [-5,2,-1,4,3] => 10100 => 11000
[3,4,-1,-2,5] => [5,-2,-1,4,3] => 01100 => 10010
[3,4,-1,-2,-5] => [-5,-2,-1,4,3] => 11100 => 10110
[3,-4,1,2,5] => [5,2,1,-4,3] => 00010 => 10000
[3,-4,1,2,-5] => [-5,2,1,-4,3] => 10010 => 11000
[3,-4,1,-2,5] => [5,-2,1,-4,3] => 01010 => 11000
[3,-4,1,-2,-5] => [-5,-2,1,-4,3] => 11010 => 11100
[3,-4,-1,2,5] => [5,2,-1,-4,3] => 00110 => 10010
[3,-4,-1,2,-5] => [-5,2,-1,-4,3] => 10110 => 11100
[3,-4,-1,-2,5] => [5,-2,-1,-4,3] => 01110 => 10110
[3,-4,-1,-2,-5] => [-5,-2,-1,-4,3] => 11110 => 11110
[-3,4,1,2,5] => [5,2,1,4,-3] => 00001 => 10000
[-3,4,1,2,-5] => [-5,2,1,4,-3] => 10001 => 10010
[-3,4,1,-2,5] => [5,-2,1,4,-3] => 01001 => 11000
[-3,4,1,-2,-5] => [-5,-2,1,4,-3] => 11001 => 10110
[-3,4,-1,2,5] => [5,2,-1,4,-3] => 00101 => 11000
[-3,4,-1,2,-5] => [-5,2,-1,4,-3] => 10101 => 11100
[-3,4,-1,-2,5] => [5,-2,-1,4,-3] => 01101 => 11100
[-3,4,-1,-2,-5] => [-5,-2,-1,4,-3] => 11101 => 11110
[-3,-4,1,2,5] => [5,2,1,-4,-3] => 00011 => 10010
[-3,-4,1,2,-5] => [-5,2,1,-4,-3] => 10011 => 10110
[-3,-4,1,-2,5] => [5,-2,1,-4,-3] => 01011 => 11100
[-3,-4,1,-2,-5] => [-5,-2,1,-4,-3] => 11011 => 11110
[-3,-4,-1,2,5] => [5,2,-1,-4,-3] => 00111 => 10110
[-3,-4,-1,2,-5] => [-5,2,-1,-4,-3] => 10111 => 11110
[-3,-4,-1,-2,5] => [5,-2,-1,-4,-3] => 01111 => 11110
[-3,-4,-1,-2,-5] => [-5,-2,-1,-4,-3] => 11111 => 11111
[3,4,1,5,2] => [2,5,1,4,3] => 00000 => 00000
[3,4,1,5,-2] => [-2,5,1,4,3] => 10000 => 10000
[3,4,1,-5,2] => [2,-5,1,4,3] => 01000 => 10000
[3,4,1,-5,-2] => [-2,-5,1,4,3] => 11000 => 10010
[3,4,-1,5,2] => [2,5,-1,4,3] => 00100 => 10000
[3,4,-1,5,-2] => [-2,5,-1,4,3] => 10100 => 11000
[3,4,-1,-5,2] => [2,-5,-1,4,3] => 01100 => 10010
[3,4,-1,-5,-2] => [-2,-5,-1,4,3] => 11100 => 10110
[3,-4,1,5,2] => [2,5,1,-4,3] => 00010 => 10000
[3,-4,1,5,-2] => [-2,5,1,-4,3] => 10010 => 11000
[3,-4,1,-5,2] => [2,-5,1,-4,3] => 01010 => 11000
[3,-4,1,-5,-2] => [-2,-5,1,-4,3] => 11010 => 11100
[3,-4,-1,5,2] => [2,5,-1,-4,3] => 00110 => 10010
[3,-4,-1,5,-2] => [-2,5,-1,-4,3] => 10110 => 11100
[3,-4,-1,-5,2] => [2,-5,-1,-4,3] => 01110 => 10110
[3,-4,-1,-5,-2] => [-2,-5,-1,-4,3] => 11110 => 11110
[-3,4,1,5,2] => [2,5,1,4,-3] => 00001 => 10000
[-3,4,1,5,-2] => [-2,5,1,4,-3] => 10001 => 10010
[-3,4,1,-5,2] => [2,-5,1,4,-3] => 01001 => 11000
[-3,4,1,-5,-2] => [-2,-5,1,4,-3] => 11001 => 10110
[-3,4,-1,5,2] => [2,5,-1,4,-3] => 00101 => 11000
[-3,4,-1,5,-2] => [-2,5,-1,4,-3] => 10101 => 11100
[-3,4,-1,-5,2] => [2,-5,-1,4,-3] => 01101 => 11100
[-3,4,-1,-5,-2] => [-2,-5,-1,4,-3] => 11101 => 11110
[-3,-4,1,5,2] => [2,5,1,-4,-3] => 00011 => 10010
[-3,-4,1,5,-2] => [-2,5,1,-4,-3] => 10011 => 10110
[-3,-4,1,-5,2] => [2,-5,1,-4,-3] => 01011 => 11100
[-3,-4,1,-5,-2] => [-2,-5,1,-4,-3] => 11011 => 11110
[-3,-4,-1,5,2] => [2,5,-1,-4,-3] => 00111 => 10110
[-3,-4,-1,5,-2] => [-2,5,-1,-4,-3] => 10111 => 11110
[-3,-4,-1,-5,2] => [2,-5,-1,-4,-3] => 01111 => 11110
[-3,-4,-1,-5,-2] => [-2,-5,-1,-4,-3] => 11111 => 11111
[3,4,2,1,5] => [5,1,2,4,3] => 00000 => 00000
[3,4,2,1,-5] => [-5,1,2,4,3] => 10000 => 10000
[3,4,2,-1,5] => [5,-1,2,4,3] => 01000 => 10000
[3,4,2,-1,-5] => [-5,-1,2,4,3] => 11000 => 10010
[3,4,-2,1,5] => [5,1,-2,4,3] => 00100 => 10000
[3,4,-2,1,-5] => [-5,1,-2,4,3] => 10100 => 11000
[3,4,-2,-1,5] => [5,-1,-2,4,3] => 01100 => 10010
[3,4,-2,-1,-5] => [-5,-1,-2,4,3] => 11100 => 10110
[3,-4,2,1,5] => [5,1,2,-4,3] => 00010 => 10000
[3,-4,2,1,-5] => [-5,1,2,-4,3] => 10010 => 11000
[3,-4,2,-1,5] => [5,-1,2,-4,3] => 01010 => 11000
[3,-4,2,-1,-5] => [-5,-1,2,-4,3] => 11010 => 11100
[3,-4,-2,1,5] => [5,1,-2,-4,3] => 00110 => 10010
[3,-4,-2,1,-5] => [-5,1,-2,-4,3] => 10110 => 11100
[3,-4,-2,-1,5] => [5,-1,-2,-4,3] => 01110 => 10110
[3,-4,-2,-1,-5] => [-5,-1,-2,-4,3] => 11110 => 11110
[-3,4,2,1,5] => [5,1,2,4,-3] => 00001 => 10000
[-3,4,2,1,-5] => [-5,1,2,4,-3] => 10001 => 10010
[-3,4,2,-1,5] => [5,-1,2,4,-3] => 01001 => 11000
[-3,4,2,-1,-5] => [-5,-1,2,4,-3] => 11001 => 10110
[-3,4,-2,1,5] => [5,1,-2,4,-3] => 00101 => 11000
[-3,4,-2,1,-5] => [-5,1,-2,4,-3] => 10101 => 11100
[-3,4,-2,-1,5] => [5,-1,-2,4,-3] => 01101 => 11100
[-3,4,-2,-1,-5] => [-5,-1,-2,4,-3] => 11101 => 11110
[-3,-4,2,1,5] => [5,1,2,-4,-3] => 00011 => 10010
[-3,-4,2,1,-5] => [-5,1,2,-4,-3] => 10011 => 10110
[-3,-4,2,-1,5] => [5,-1,2,-4,-3] => 01011 => 11100
[-3,-4,2,-1,-5] => [-5,-1,2,-4,-3] => 11011 => 11110
[-3,-4,-2,1,5] => [5,1,-2,-4,-3] => 00111 => 10110
[-3,-4,-2,1,-5] => [-5,1,-2,-4,-3] => 10111 => 11110
[-3,-4,-2,-1,5] => [5,-1,-2,-4,-3] => 01111 => 11110
[-3,-4,-2,-1,-5] => [-5,-1,-2,-4,-3] => 11111 => 11111
[3,4,2,5,1] => [1,5,2,4,3] => 00000 => 00000
[3,4,2,5,-1] => [-1,5,2,4,3] => 10000 => 10000
[3,4,2,-5,1] => [1,-5,2,4,3] => 01000 => 10000
[3,4,2,-5,-1] => [-1,-5,2,4,3] => 11000 => 10010
[3,4,-2,5,1] => [1,5,-2,4,3] => 00100 => 10000
[3,4,-2,5,-1] => [-1,5,-2,4,3] => 10100 => 11000
[3,4,-2,-5,1] => [1,-5,-2,4,3] => 01100 => 10010
[3,4,-2,-5,-1] => [-1,-5,-2,4,3] => 11100 => 10110
[3,-4,2,5,1] => [1,5,2,-4,3] => 00010 => 10000
[3,-4,2,5,-1] => [-1,5,2,-4,3] => 10010 => 11000
[3,-4,2,-5,1] => [1,-5,2,-4,3] => 01010 => 11000
[3,-4,2,-5,-1] => [-1,-5,2,-4,3] => 11010 => 11100
[3,-4,-2,5,1] => [1,5,-2,-4,3] => 00110 => 10010
[3,-4,-2,5,-1] => [-1,5,-2,-4,3] => 10110 => 11100
[3,-4,-2,-5,1] => [1,-5,-2,-4,3] => 01110 => 10110
[3,-4,-2,-5,-1] => [-1,-5,-2,-4,3] => 11110 => 11110
[-3,4,2,5,1] => [1,5,2,4,-3] => 00001 => 10000
[-3,4,2,5,-1] => [-1,5,2,4,-3] => 10001 => 10010
[-3,4,2,-5,1] => [1,-5,2,4,-3] => 01001 => 11000
[-3,4,2,-5,-1] => [-1,-5,2,4,-3] => 11001 => 10110
[-3,4,-2,5,1] => [1,5,-2,4,-3] => 00101 => 11000
[-3,4,-2,5,-1] => [-1,5,-2,4,-3] => 10101 => 11100
[-3,4,-2,-5,1] => [1,-5,-2,4,-3] => 01101 => 11100
[-3,4,-2,-5,-1] => [-1,-5,-2,4,-3] => 11101 => 11110
[-3,-4,2,5,1] => [1,5,2,-4,-3] => 00011 => 10010
[-3,-4,2,5,-1] => [-1,5,2,-4,-3] => 10011 => 10110
[-3,-4,2,-5,1] => [1,-5,2,-4,-3] => 01011 => 11100
[-3,-4,2,-5,-1] => [-1,-5,2,-4,-3] => 11011 => 11110
[-3,-4,-2,5,1] => [1,5,-2,-4,-3] => 00111 => 10110
[-3,-4,-2,5,-1] => [-1,5,-2,-4,-3] => 10111 => 11110
[-3,-4,-2,-5,1] => [1,-5,-2,-4,-3] => 01111 => 11110
[-3,-4,-2,-5,-1] => [-1,-5,-2,-4,-3] => 11111 => 11111
[3,4,5,1,2] => [2,1,5,4,3] => 00000 => 00000
[3,4,5,1,-2] => [-2,1,5,4,3] => 10000 => 10000
[3,4,5,-1,2] => [2,-1,5,4,3] => 01000 => 10000
[3,4,5,-1,-2] => [-2,-1,5,4,3] => 11000 => 10010
[3,4,-5,1,2] => [2,1,-5,4,3] => 00100 => 10000
[3,4,-5,1,-2] => [-2,1,-5,4,3] => 10100 => 11000
[3,4,-5,-1,2] => [2,-1,-5,4,3] => 01100 => 10010
[3,4,-5,-1,-2] => [-2,-1,-5,4,3] => 11100 => 10110
[3,-4,5,1,2] => [2,1,5,-4,3] => 00010 => 10000
[3,-4,5,1,-2] => [-2,1,5,-4,3] => 10010 => 11000
[3,-4,5,-1,2] => [2,-1,5,-4,3] => 01010 => 11000
[3,-4,5,-1,-2] => [-2,-1,5,-4,3] => 11010 => 11100
[3,-4,-5,1,2] => [2,1,-5,-4,3] => 00110 => 10010
[3,-4,-5,1,-2] => [-2,1,-5,-4,3] => 10110 => 11100
[3,-4,-5,-1,2] => [2,-1,-5,-4,3] => 01110 => 10110
[3,-4,-5,-1,-2] => [-2,-1,-5,-4,3] => 11110 => 11110
[-3,4,5,1,2] => [2,1,5,4,-3] => 00001 => 10000
[-3,4,5,1,-2] => [-2,1,5,4,-3] => 10001 => 10010
[-3,4,5,-1,2] => [2,-1,5,4,-3] => 01001 => 11000
[-3,4,5,-1,-2] => [-2,-1,5,4,-3] => 11001 => 10110
[-3,4,-5,1,2] => [2,1,-5,4,-3] => 00101 => 11000
[-3,4,-5,1,-2] => [-2,1,-5,4,-3] => 10101 => 11100
[-3,4,-5,-1,2] => [2,-1,-5,4,-3] => 01101 => 11100
[-3,4,-5,-1,-2] => [-2,-1,-5,4,-3] => 11101 => 11110
[-3,-4,5,1,2] => [2,1,5,-4,-3] => 00011 => 10010
[-3,-4,5,1,-2] => [-2,1,5,-4,-3] => 10011 => 10110
[-3,-4,5,-1,2] => [2,-1,5,-4,-3] => 01011 => 11100
[-3,-4,5,-1,-2] => [-2,-1,5,-4,-3] => 11011 => 11110
[-3,-4,-5,1,2] => [2,1,-5,-4,-3] => 00111 => 10110
[-3,-4,-5,1,-2] => [-2,1,-5,-4,-3] => 10111 => 11110
[-3,-4,-5,-1,2] => [2,-1,-5,-4,-3] => 01111 => 11110
[-3,-4,-5,-1,-2] => [-2,-1,-5,-4,-3] => 11111 => 11111
[3,4,5,2,1] => [1,2,5,4,3] => 00000 => 00000
[3,4,5,2,-1] => [-1,2,5,4,3] => 10000 => 10000
[3,4,5,-2,1] => [1,-2,5,4,3] => 01000 => 10000
[3,4,5,-2,-1] => [-1,-2,5,4,3] => 11000 => 10010
[3,4,-5,2,1] => [1,2,-5,4,3] => 00100 => 10000
[3,4,-5,2,-1] => [-1,2,-5,4,3] => 10100 => 11000
[3,4,-5,-2,1] => [1,-2,-5,4,3] => 01100 => 10010
[3,4,-5,-2,-1] => [-1,-2,-5,4,3] => 11100 => 10110
[3,-4,5,2,1] => [1,2,5,-4,3] => 00010 => 10000
[3,-4,5,2,-1] => [-1,2,5,-4,3] => 10010 => 11000
[3,-4,5,-2,1] => [1,-2,5,-4,3] => 01010 => 11000
[3,-4,5,-2,-1] => [-1,-2,5,-4,3] => 11010 => 11100
[3,-4,-5,2,1] => [1,2,-5,-4,3] => 00110 => 10010
[3,-4,-5,2,-1] => [-1,2,-5,-4,3] => 10110 => 11100
[3,-4,-5,-2,1] => [1,-2,-5,-4,3] => 01110 => 10110
[3,-4,-5,-2,-1] => [-1,-2,-5,-4,3] => 11110 => 11110
[-3,4,5,2,1] => [1,2,5,4,-3] => 00001 => 10000
[-3,4,5,2,-1] => [-1,2,5,4,-3] => 10001 => 10010
[-3,4,5,-2,1] => [1,-2,5,4,-3] => 01001 => 11000
[-3,4,5,-2,-1] => [-1,-2,5,4,-3] => 11001 => 10110
[-3,4,-5,2,1] => [1,2,-5,4,-3] => 00101 => 11000
[-3,4,-5,2,-1] => [-1,2,-5,4,-3] => 10101 => 11100
[-3,4,-5,-2,1] => [1,-2,-5,4,-3] => 01101 => 11100
[-3,4,-5,-2,-1] => [-1,-2,-5,4,-3] => 11101 => 11110
[-3,-4,5,2,1] => [1,2,5,-4,-3] => 00011 => 10010
[-3,-4,5,2,-1] => [-1,2,5,-4,-3] => 10011 => 10110
[-3,-4,5,-2,1] => [1,-2,5,-4,-3] => 01011 => 11100
[-3,-4,5,-2,-1] => [-1,-2,5,-4,-3] => 11011 => 11110
[-3,-4,-5,2,1] => [1,2,-5,-4,-3] => 00111 => 10110
[-3,-4,-5,2,-1] => [-1,2,-5,-4,-3] => 10111 => 11110
[-3,-4,-5,-2,1] => [1,-2,-5,-4,-3] => 01111 => 11110
[-3,-4,-5,-2,-1] => [-1,-2,-5,-4,-3] => 11111 => 11111
[3,5,1,2,4] => [4,2,1,5,3] => 00000 => 00000
[3,5,1,2,-4] => [-4,2,1,5,3] => 10000 => 10000
[3,5,1,-2,4] => [4,-2,1,5,3] => 01000 => 10000
[3,5,1,-2,-4] => [-4,-2,1,5,3] => 11000 => 10010
[3,5,-1,2,4] => [4,2,-1,5,3] => 00100 => 10000
[3,5,-1,2,-4] => [-4,2,-1,5,3] => 10100 => 11000
[3,5,-1,-2,4] => [4,-2,-1,5,3] => 01100 => 10010
[3,5,-1,-2,-4] => [-4,-2,-1,5,3] => 11100 => 10110
[3,-5,1,2,4] => [4,2,1,-5,3] => 00010 => 10000
[3,-5,1,2,-4] => [-4,2,1,-5,3] => 10010 => 11000
[3,-5,1,-2,4] => [4,-2,1,-5,3] => 01010 => 11000
[3,-5,1,-2,-4] => [-4,-2,1,-5,3] => 11010 => 11100
[3,-5,-1,2,4] => [4,2,-1,-5,3] => 00110 => 10010
[3,-5,-1,2,-4] => [-4,2,-1,-5,3] => 10110 => 11100
[3,-5,-1,-2,4] => [4,-2,-1,-5,3] => 01110 => 10110
[3,-5,-1,-2,-4] => [-4,-2,-1,-5,3] => 11110 => 11110
[-3,5,1,2,4] => [4,2,1,5,-3] => 00001 => 10000
[-3,5,1,2,-4] => [-4,2,1,5,-3] => 10001 => 10010
[-3,5,1,-2,4] => [4,-2,1,5,-3] => 01001 => 11000
[-3,5,1,-2,-4] => [-4,-2,1,5,-3] => 11001 => 10110
[-3,5,-1,2,4] => [4,2,-1,5,-3] => 00101 => 11000
[-3,5,-1,2,-4] => [-4,2,-1,5,-3] => 10101 => 11100
[-3,5,-1,-2,4] => [4,-2,-1,5,-3] => 01101 => 11100
[-3,5,-1,-2,-4] => [-4,-2,-1,5,-3] => 11101 => 11110
[-3,-5,1,2,4] => [4,2,1,-5,-3] => 00011 => 10010
[-3,-5,1,2,-4] => [-4,2,1,-5,-3] => 10011 => 10110
[-3,-5,1,-2,4] => [4,-2,1,-5,-3] => 01011 => 11100
[-3,-5,1,-2,-4] => [-4,-2,1,-5,-3] => 11011 => 11110
[-3,-5,-1,2,4] => [4,2,-1,-5,-3] => 00111 => 10110
[-3,-5,-1,2,-4] => [-4,2,-1,-5,-3] => 10111 => 11110
[-3,-5,-1,-2,4] => [4,-2,-1,-5,-3] => 01111 => 11110
[-3,-5,-1,-2,-4] => [-4,-2,-1,-5,-3] => 11111 => 11111
[3,5,1,4,2] => [2,4,1,5,3] => 00000 => 00000
[3,5,1,4,-2] => [-2,4,1,5,3] => 10000 => 10000
[3,5,1,-4,2] => [2,-4,1,5,3] => 01000 => 10000
[3,5,1,-4,-2] => [-2,-4,1,5,3] => 11000 => 10010
[3,5,-1,4,2] => [2,4,-1,5,3] => 00100 => 10000
[3,5,-1,4,-2] => [-2,4,-1,5,3] => 10100 => 11000
[3,5,-1,-4,2] => [2,-4,-1,5,3] => 01100 => 10010
[3,5,-1,-4,-2] => [-2,-4,-1,5,3] => 11100 => 10110
[3,-5,1,4,2] => [2,4,1,-5,3] => 00010 => 10000
[3,-5,1,4,-2] => [-2,4,1,-5,3] => 10010 => 11000
[3,-5,1,-4,2] => [2,-4,1,-5,3] => 01010 => 11000
[3,-5,1,-4,-2] => [-2,-4,1,-5,3] => 11010 => 11100
[3,-5,-1,4,2] => [2,4,-1,-5,3] => 00110 => 10010
[3,-5,-1,4,-2] => [-2,4,-1,-5,3] => 10110 => 11100
[3,-5,-1,-4,2] => [2,-4,-1,-5,3] => 01110 => 10110
[3,-5,-1,-4,-2] => [-2,-4,-1,-5,3] => 11110 => 11110
[-3,5,1,4,2] => [2,4,1,5,-3] => 00001 => 10000
[-3,5,1,4,-2] => [-2,4,1,5,-3] => 10001 => 10010
[-3,5,1,-4,2] => [2,-4,1,5,-3] => 01001 => 11000
[-3,5,1,-4,-2] => [-2,-4,1,5,-3] => 11001 => 10110
[-3,5,-1,4,2] => [2,4,-1,5,-3] => 00101 => 11000
[-3,5,-1,4,-2] => [-2,4,-1,5,-3] => 10101 => 11100
[-3,5,-1,-4,2] => [2,-4,-1,5,-3] => 01101 => 11100
[-3,5,-1,-4,-2] => [-2,-4,-1,5,-3] => 11101 => 11110
[-3,-5,1,4,2] => [2,4,1,-5,-3] => 00011 => 10010
[-3,-5,1,4,-2] => [-2,4,1,-5,-3] => 10011 => 10110
[-3,-5,1,-4,2] => [2,-4,1,-5,-3] => 01011 => 11100
[-3,-5,1,-4,-2] => [-2,-4,1,-5,-3] => 11011 => 11110
[-3,-5,-1,4,2] => [2,4,-1,-5,-3] => 00111 => 10110
[-3,-5,-1,4,-2] => [-2,4,-1,-5,-3] => 10111 => 11110
[-3,-5,-1,-4,2] => [2,-4,-1,-5,-3] => 01111 => 11110
[-3,-5,-1,-4,-2] => [-2,-4,-1,-5,-3] => 11111 => 11111
[3,5,2,1,4] => [4,1,2,5,3] => 00000 => 00000
[3,5,2,1,-4] => [-4,1,2,5,3] => 10000 => 10000
[3,5,2,-1,4] => [4,-1,2,5,3] => 01000 => 10000
[3,5,2,-1,-4] => [-4,-1,2,5,3] => 11000 => 10010
[3,5,-2,1,4] => [4,1,-2,5,3] => 00100 => 10000
[3,5,-2,1,-4] => [-4,1,-2,5,3] => 10100 => 11000
[3,5,-2,-1,4] => [4,-1,-2,5,3] => 01100 => 10010
[3,5,-2,-1,-4] => [-4,-1,-2,5,3] => 11100 => 10110
[3,-5,2,1,4] => [4,1,2,-5,3] => 00010 => 10000
[3,-5,2,1,-4] => [-4,1,2,-5,3] => 10010 => 11000
[3,-5,2,-1,4] => [4,-1,2,-5,3] => 01010 => 11000
[3,-5,2,-1,-4] => [-4,-1,2,-5,3] => 11010 => 11100
[3,-5,-2,1,4] => [4,1,-2,-5,3] => 00110 => 10010
[3,-5,-2,1,-4] => [-4,1,-2,-5,3] => 10110 => 11100
[3,-5,-2,-1,4] => [4,-1,-2,-5,3] => 01110 => 10110
[3,-5,-2,-1,-4] => [-4,-1,-2,-5,3] => 11110 => 11110
[-3,5,2,1,4] => [4,1,2,5,-3] => 00001 => 10000
[-3,5,2,1,-4] => [-4,1,2,5,-3] => 10001 => 10010
[-3,5,2,-1,4] => [4,-1,2,5,-3] => 01001 => 11000
[-3,5,2,-1,-4] => [-4,-1,2,5,-3] => 11001 => 10110
[-3,5,-2,1,4] => [4,1,-2,5,-3] => 00101 => 11000
[-3,5,-2,1,-4] => [-4,1,-2,5,-3] => 10101 => 11100
[-3,5,-2,-1,4] => [4,-1,-2,5,-3] => 01101 => 11100
[-3,5,-2,-1,-4] => [-4,-1,-2,5,-3] => 11101 => 11110
[-3,-5,2,1,4] => [4,1,2,-5,-3] => 00011 => 10010
[-3,-5,2,1,-4] => [-4,1,2,-5,-3] => 10011 => 10110
[-3,-5,2,-1,4] => [4,-1,2,-5,-3] => 01011 => 11100
[-3,-5,2,-1,-4] => [-4,-1,2,-5,-3] => 11011 => 11110
[-3,-5,-2,1,4] => [4,1,-2,-5,-3] => 00111 => 10110
[-3,-5,-2,1,-4] => [-4,1,-2,-5,-3] => 10111 => 11110
[-3,-5,-2,-1,4] => [4,-1,-2,-5,-3] => 01111 => 11110
[-3,-5,-2,-1,-4] => [-4,-1,-2,-5,-3] => 11111 => 11111
[3,5,2,4,1] => [1,4,2,5,3] => 00000 => 00000
[3,5,2,4,-1] => [-1,4,2,5,3] => 10000 => 10000
[3,5,2,-4,1] => [1,-4,2,5,3] => 01000 => 10000
[3,5,2,-4,-1] => [-1,-4,2,5,3] => 11000 => 10010
[3,5,-2,4,1] => [1,4,-2,5,3] => 00100 => 10000
[3,5,-2,4,-1] => [-1,4,-2,5,3] => 10100 => 11000
[3,5,-2,-4,1] => [1,-4,-2,5,3] => 01100 => 10010
[3,5,-2,-4,-1] => [-1,-4,-2,5,3] => 11100 => 10110
[3,-5,2,4,1] => [1,4,2,-5,3] => 00010 => 10000
[3,-5,2,4,-1] => [-1,4,2,-5,3] => 10010 => 11000
[3,-5,2,-4,1] => [1,-4,2,-5,3] => 01010 => 11000
[3,-5,2,-4,-1] => [-1,-4,2,-5,3] => 11010 => 11100
[3,-5,-2,4,1] => [1,4,-2,-5,3] => 00110 => 10010
[3,-5,-2,4,-1] => [-1,4,-2,-5,3] => 10110 => 11100
[3,-5,-2,-4,1] => [1,-4,-2,-5,3] => 01110 => 10110
[3,-5,-2,-4,-1] => [-1,-4,-2,-5,3] => 11110 => 11110
[-3,5,2,4,1] => [1,4,2,5,-3] => 00001 => 10000
[-3,5,2,4,-1] => [-1,4,2,5,-3] => 10001 => 10010
[-3,5,2,-4,1] => [1,-4,2,5,-3] => 01001 => 11000
[-3,5,2,-4,-1] => [-1,-4,2,5,-3] => 11001 => 10110
[-3,5,-2,4,1] => [1,4,-2,5,-3] => 00101 => 11000
[-3,5,-2,4,-1] => [-1,4,-2,5,-3] => 10101 => 11100
[-3,5,-2,-4,1] => [1,-4,-2,5,-3] => 01101 => 11100
[-3,5,-2,-4,-1] => [-1,-4,-2,5,-3] => 11101 => 11110
[-3,-5,2,4,1] => [1,4,2,-5,-3] => 00011 => 10010
[-3,-5,2,4,-1] => [-1,4,2,-5,-3] => 10011 => 10110
[-3,-5,2,-4,1] => [1,-4,2,-5,-3] => 01011 => 11100
[-3,-5,2,-4,-1] => [-1,-4,2,-5,-3] => 11011 => 11110
[-3,-5,-2,4,1] => [1,4,-2,-5,-3] => 00111 => 10110
[-3,-5,-2,4,-1] => [-1,4,-2,-5,-3] => 10111 => 11110
[-3,-5,-2,-4,1] => [1,-4,-2,-5,-3] => 01111 => 11110
[-3,-5,-2,-4,-1] => [-1,-4,-2,-5,-3] => 11111 => 11111
[3,5,4,1,2] => [2,1,4,5,3] => 00000 => 00000
[3,5,4,1,-2] => [-2,1,4,5,3] => 10000 => 10000
[3,5,4,-1,2] => [2,-1,4,5,3] => 01000 => 10000
[3,5,4,-1,-2] => [-2,-1,4,5,3] => 11000 => 10010
[3,5,-4,1,2] => [2,1,-4,5,3] => 00100 => 10000
[3,5,-4,1,-2] => [-2,1,-4,5,3] => 10100 => 11000
[3,5,-4,-1,2] => [2,-1,-4,5,3] => 01100 => 10010
[3,5,-4,-1,-2] => [-2,-1,-4,5,3] => 11100 => 10110
[3,-5,4,1,2] => [2,1,4,-5,3] => 00010 => 10000
[3,-5,4,1,-2] => [-2,1,4,-5,3] => 10010 => 11000
[3,-5,4,-1,2] => [2,-1,4,-5,3] => 01010 => 11000
[3,-5,4,-1,-2] => [-2,-1,4,-5,3] => 11010 => 11100
[3,-5,-4,1,2] => [2,1,-4,-5,3] => 00110 => 10010
[3,-5,-4,1,-2] => [-2,1,-4,-5,3] => 10110 => 11100
[3,-5,-4,-1,2] => [2,-1,-4,-5,3] => 01110 => 10110
[3,-5,-4,-1,-2] => [-2,-1,-4,-5,3] => 11110 => 11110
[-3,5,4,1,2] => [2,1,4,5,-3] => 00001 => 10000
[-3,5,4,1,-2] => [-2,1,4,5,-3] => 10001 => 10010
[-3,5,4,-1,2] => [2,-1,4,5,-3] => 01001 => 11000
[-3,5,4,-1,-2] => [-2,-1,4,5,-3] => 11001 => 10110
[-3,5,-4,1,2] => [2,1,-4,5,-3] => 00101 => 11000
[-3,5,-4,1,-2] => [-2,1,-4,5,-3] => 10101 => 11100
[-3,5,-4,-1,2] => [2,-1,-4,5,-3] => 01101 => 11100
[-3,5,-4,-1,-2] => [-2,-1,-4,5,-3] => 11101 => 11110
[-3,-5,4,1,2] => [2,1,4,-5,-3] => 00011 => 10010
[-3,-5,4,1,-2] => [-2,1,4,-5,-3] => 10011 => 10110
[-3,-5,4,-1,2] => [2,-1,4,-5,-3] => 01011 => 11100
[-3,-5,4,-1,-2] => [-2,-1,4,-5,-3] => 11011 => 11110
[-3,-5,-4,1,2] => [2,1,-4,-5,-3] => 00111 => 10110
[-3,-5,-4,1,-2] => [-2,1,-4,-5,-3] => 10111 => 11110
[-3,-5,-4,-1,2] => [2,-1,-4,-5,-3] => 01111 => 11110
[-3,-5,-4,-1,-2] => [-2,-1,-4,-5,-3] => 11111 => 11111
[3,5,4,2,1] => [1,2,4,5,3] => 00000 => 00000
[3,5,4,2,-1] => [-1,2,4,5,3] => 10000 => 10000
[3,5,4,-2,1] => [1,-2,4,5,3] => 01000 => 10000
[3,5,4,-2,-1] => [-1,-2,4,5,3] => 11000 => 10010
[3,5,-4,2,1] => [1,2,-4,5,3] => 00100 => 10000
[3,5,-4,2,-1] => [-1,2,-4,5,3] => 10100 => 11000
[3,5,-4,-2,1] => [1,-2,-4,5,3] => 01100 => 10010
[3,5,-4,-2,-1] => [-1,-2,-4,5,3] => 11100 => 10110
[3,-5,4,2,1] => [1,2,4,-5,3] => 00010 => 10000
[3,-5,4,2,-1] => [-1,2,4,-5,3] => 10010 => 11000
[3,-5,4,-2,1] => [1,-2,4,-5,3] => 01010 => 11000
[3,-5,4,-2,-1] => [-1,-2,4,-5,3] => 11010 => 11100
[3,-5,-4,2,1] => [1,2,-4,-5,3] => 00110 => 10010
[3,-5,-4,2,-1] => [-1,2,-4,-5,3] => 10110 => 11100
[3,-5,-4,-2,1] => [1,-2,-4,-5,3] => 01110 => 10110
[3,-5,-4,-2,-1] => [-1,-2,-4,-5,3] => 11110 => 11110
[-3,5,4,2,1] => [1,2,4,5,-3] => 00001 => 10000
[-3,5,4,2,-1] => [-1,2,4,5,-3] => 10001 => 10010
[-3,5,4,-2,1] => [1,-2,4,5,-3] => 01001 => 11000
[-3,5,4,-2,-1] => [-1,-2,4,5,-3] => 11001 => 10110
[-3,5,-4,2,1] => [1,2,-4,5,-3] => 00101 => 11000
[-3,5,-4,2,-1] => [-1,2,-4,5,-3] => 10101 => 11100
[-3,5,-4,-2,1] => [1,-2,-4,5,-3] => 01101 => 11100
[-3,5,-4,-2,-1] => [-1,-2,-4,5,-3] => 11101 => 11110
[-3,-5,4,2,1] => [1,2,4,-5,-3] => 00011 => 10010
[-3,-5,4,2,-1] => [-1,2,4,-5,-3] => 10011 => 10110
[-3,-5,4,-2,1] => [1,-2,4,-5,-3] => 01011 => 11100
[-3,-5,4,-2,-1] => [-1,-2,4,-5,-3] => 11011 => 11110
[-3,-5,-4,2,1] => [1,2,-4,-5,-3] => 00111 => 10110
[-3,-5,-4,2,-1] => [-1,2,-4,-5,-3] => 10111 => 11110
[-3,-5,-4,-2,1] => [1,-2,-4,-5,-3] => 01111 => 11110
[-3,-5,-4,-2,-1] => [-1,-2,-4,-5,-3] => 11111 => 11111
[4,1,2,3,5] => [5,3,2,1,4] => 00000 => 00000
[4,1,2,3,-5] => [-5,3,2,1,4] => 10000 => 10000
[4,1,2,-3,5] => [5,-3,2,1,4] => 01000 => 10000
[4,1,2,-3,-5] => [-5,-3,2,1,4] => 11000 => 10010
[4,1,-2,3,5] => [5,3,-2,1,4] => 00100 => 10000
[4,1,-2,3,-5] => [-5,3,-2,1,4] => 10100 => 11000
[4,1,-2,-3,5] => [5,-3,-2,1,4] => 01100 => 10010
[4,1,-2,-3,-5] => [-5,-3,-2,1,4] => 11100 => 10110
[4,-1,2,3,5] => [5,3,2,-1,4] => 00010 => 10000
[4,-1,2,3,-5] => [-5,3,2,-1,4] => 10010 => 11000
[4,-1,2,-3,5] => [5,-3,2,-1,4] => 01010 => 11000
[4,-1,2,-3,-5] => [-5,-3,2,-1,4] => 11010 => 11100
[4,-1,-2,3,5] => [5,3,-2,-1,4] => 00110 => 10010
[4,-1,-2,3,-5] => [-5,3,-2,-1,4] => 10110 => 11100
[4,-1,-2,-3,5] => [5,-3,-2,-1,4] => 01110 => 10110
[4,-1,-2,-3,-5] => [-5,-3,-2,-1,4] => 11110 => 11110
[-4,1,2,3,5] => [5,3,2,1,-4] => 00001 => 10000
[-4,1,2,3,-5] => [-5,3,2,1,-4] => 10001 => 10010
[-4,1,2,-3,5] => [5,-3,2,1,-4] => 01001 => 11000
[-4,1,2,-3,-5] => [-5,-3,2,1,-4] => 11001 => 10110
[-4,1,-2,3,5] => [5,3,-2,1,-4] => 00101 => 11000
[-4,1,-2,3,-5] => [-5,3,-2,1,-4] => 10101 => 11100
[-4,1,-2,-3,5] => [5,-3,-2,1,-4] => 01101 => 11100
[-4,1,-2,-3,-5] => [-5,-3,-2,1,-4] => 11101 => 11110
[-4,-1,2,3,5] => [5,3,2,-1,-4] => 00011 => 10010
[-4,-1,2,3,-5] => [-5,3,2,-1,-4] => 10011 => 10110
[-4,-1,2,-3,5] => [5,-3,2,-1,-4] => 01011 => 11100
[-4,-1,2,-3,-5] => [-5,-3,2,-1,-4] => 11011 => 11110
[-4,-1,-2,3,5] => [5,3,-2,-1,-4] => 00111 => 10110
[-4,-1,-2,3,-5] => [-5,3,-2,-1,-4] => 10111 => 11110
[-4,-1,-2,-3,5] => [5,-3,-2,-1,-4] => 01111 => 11110
[-4,-1,-2,-3,-5] => [-5,-3,-2,-1,-4] => 11111 => 11111
[4,1,2,5,3] => [3,5,2,1,4] => 00000 => 00000
[4,1,2,5,-3] => [-3,5,2,1,4] => 10000 => 10000
[4,1,2,-5,3] => [3,-5,2,1,4] => 01000 => 10000
[4,1,2,-5,-3] => [-3,-5,2,1,4] => 11000 => 10010
[4,1,-2,5,3] => [3,5,-2,1,4] => 00100 => 10000
[4,1,-2,5,-3] => [-3,5,-2,1,4] => 10100 => 11000
[4,1,-2,-5,3] => [3,-5,-2,1,4] => 01100 => 10010
[4,1,-2,-5,-3] => [-3,-5,-2,1,4] => 11100 => 10110
[4,-1,2,5,3] => [3,5,2,-1,4] => 00010 => 10000
[4,-1,2,5,-3] => [-3,5,2,-1,4] => 10010 => 11000
[4,-1,2,-5,3] => [3,-5,2,-1,4] => 01010 => 11000
[4,-1,2,-5,-3] => [-3,-5,2,-1,4] => 11010 => 11100
[4,-1,-2,5,3] => [3,5,-2,-1,4] => 00110 => 10010
[4,-1,-2,5,-3] => [-3,5,-2,-1,4] => 10110 => 11100
[4,-1,-2,-5,3] => [3,-5,-2,-1,4] => 01110 => 10110
[4,-1,-2,-5,-3] => [-3,-5,-2,-1,4] => 11110 => 11110
[-4,1,2,5,3] => [3,5,2,1,-4] => 00001 => 10000
[-4,1,2,5,-3] => [-3,5,2,1,-4] => 10001 => 10010
[-4,1,2,-5,3] => [3,-5,2,1,-4] => 01001 => 11000
[-4,1,2,-5,-3] => [-3,-5,2,1,-4] => 11001 => 10110
[-4,1,-2,5,3] => [3,5,-2,1,-4] => 00101 => 11000
[-4,1,-2,5,-3] => [-3,5,-2,1,-4] => 10101 => 11100
[-4,1,-2,-5,3] => [3,-5,-2,1,-4] => 01101 => 11100
[-4,1,-2,-5,-3] => [-3,-5,-2,1,-4] => 11101 => 11110
[-4,-1,2,5,3] => [3,5,2,-1,-4] => 00011 => 10010
[-4,-1,2,5,-3] => [-3,5,2,-1,-4] => 10011 => 10110
[-4,-1,2,-5,3] => [3,-5,2,-1,-4] => 01011 => 11100
[-4,-1,2,-5,-3] => [-3,-5,2,-1,-4] => 11011 => 11110
[-4,-1,-2,5,3] => [3,5,-2,-1,-4] => 00111 => 10110
[-4,-1,-2,5,-3] => [-3,5,-2,-1,-4] => 10111 => 11110
[-4,-1,-2,-5,3] => [3,-5,-2,-1,-4] => 01111 => 11110
[-4,-1,-2,-5,-3] => [-3,-5,-2,-1,-4] => 11111 => 11111
[4,1,3,2,5] => [5,2,3,1,4] => 00000 => 00000
[4,1,3,2,-5] => [-5,2,3,1,4] => 10000 => 10000
[4,1,3,-2,5] => [5,-2,3,1,4] => 01000 => 10000
[4,1,3,-2,-5] => [-5,-2,3,1,4] => 11000 => 10010
[4,1,-3,2,5] => [5,2,-3,1,4] => 00100 => 10000
[4,1,-3,2,-5] => [-5,2,-3,1,4] => 10100 => 11000
[4,1,-3,-2,5] => [5,-2,-3,1,4] => 01100 => 10010
[4,1,-3,-2,-5] => [-5,-2,-3,1,4] => 11100 => 10110
[4,-1,3,2,5] => [5,2,3,-1,4] => 00010 => 10000
[4,-1,3,2,-5] => [-5,2,3,-1,4] => 10010 => 11000
[4,-1,3,-2,5] => [5,-2,3,-1,4] => 01010 => 11000
[4,-1,3,-2,-5] => [-5,-2,3,-1,4] => 11010 => 11100
[4,-1,-3,2,5] => [5,2,-3,-1,4] => 00110 => 10010
[4,-1,-3,2,-5] => [-5,2,-3,-1,4] => 10110 => 11100
[4,-1,-3,-2,5] => [5,-2,-3,-1,4] => 01110 => 10110
[4,-1,-3,-2,-5] => [-5,-2,-3,-1,4] => 11110 => 11110
[-4,1,3,2,5] => [5,2,3,1,-4] => 00001 => 10000
[-4,1,3,2,-5] => [-5,2,3,1,-4] => 10001 => 10010
[-4,1,3,-2,5] => [5,-2,3,1,-4] => 01001 => 11000
[-4,1,3,-2,-5] => [-5,-2,3,1,-4] => 11001 => 10110
[-4,1,-3,2,5] => [5,2,-3,1,-4] => 00101 => 11000
[-4,1,-3,2,-5] => [-5,2,-3,1,-4] => 10101 => 11100
[-4,1,-3,-2,5] => [5,-2,-3,1,-4] => 01101 => 11100
[-4,1,-3,-2,-5] => [-5,-2,-3,1,-4] => 11101 => 11110
[-4,-1,3,2,5] => [5,2,3,-1,-4] => 00011 => 10010
[-4,-1,3,2,-5] => [-5,2,3,-1,-4] => 10011 => 10110
[-4,-1,3,-2,5] => [5,-2,3,-1,-4] => 01011 => 11100
[-4,-1,3,-2,-5] => [-5,-2,3,-1,-4] => 11011 => 11110
[-4,-1,-3,2,5] => [5,2,-3,-1,-4] => 00111 => 10110
[-4,-1,-3,2,-5] => [-5,2,-3,-1,-4] => 10111 => 11110
[-4,-1,-3,-2,5] => [5,-2,-3,-1,-4] => 01111 => 11110
[-4,-1,-3,-2,-5] => [-5,-2,-3,-1,-4] => 11111 => 11111
[4,1,3,5,2] => [2,5,3,1,4] => 00000 => 00000
[4,1,3,5,-2] => [-2,5,3,1,4] => 10000 => 10000
[4,1,3,-5,2] => [2,-5,3,1,4] => 01000 => 10000
[4,1,3,-5,-2] => [-2,-5,3,1,4] => 11000 => 10010
[4,1,-3,5,2] => [2,5,-3,1,4] => 00100 => 10000
[4,1,-3,5,-2] => [-2,5,-3,1,4] => 10100 => 11000
[4,1,-3,-5,2] => [2,-5,-3,1,4] => 01100 => 10010
[4,1,-3,-5,-2] => [-2,-5,-3,1,4] => 11100 => 10110
[4,-1,3,5,2] => [2,5,3,-1,4] => 00010 => 10000
[4,-1,3,5,-2] => [-2,5,3,-1,4] => 10010 => 11000
[4,-1,3,-5,2] => [2,-5,3,-1,4] => 01010 => 11000
[4,-1,3,-5,-2] => [-2,-5,3,-1,4] => 11010 => 11100
[4,-1,-3,5,2] => [2,5,-3,-1,4] => 00110 => 10010
[4,-1,-3,5,-2] => [-2,5,-3,-1,4] => 10110 => 11100
[4,-1,-3,-5,2] => [2,-5,-3,-1,4] => 01110 => 10110
[4,-1,-3,-5,-2] => [-2,-5,-3,-1,4] => 11110 => 11110
[-4,1,3,5,2] => [2,5,3,1,-4] => 00001 => 10000
[-4,1,3,5,-2] => [-2,5,3,1,-4] => 10001 => 10010
[-4,1,3,-5,2] => [2,-5,3,1,-4] => 01001 => 11000
[-4,1,3,-5,-2] => [-2,-5,3,1,-4] => 11001 => 10110
[-4,1,-3,5,2] => [2,5,-3,1,-4] => 00101 => 11000
[-4,1,-3,5,-2] => [-2,5,-3,1,-4] => 10101 => 11100
[-4,1,-3,-5,2] => [2,-5,-3,1,-4] => 01101 => 11100
[-4,1,-3,-5,-2] => [-2,-5,-3,1,-4] => 11101 => 11110
[-4,-1,3,5,2] => [2,5,3,-1,-4] => 00011 => 10010
[-4,-1,3,5,-2] => [-2,5,3,-1,-4] => 10011 => 10110
[-4,-1,3,-5,2] => [2,-5,3,-1,-4] => 01011 => 11100
[-4,-1,3,-5,-2] => [-2,-5,3,-1,-4] => 11011 => 11110
[-4,-1,-3,5,2] => [2,5,-3,-1,-4] => 00111 => 10110
[-4,-1,-3,5,-2] => [-2,5,-3,-1,-4] => 10111 => 11110
[-4,-1,-3,-5,2] => [2,-5,-3,-1,-4] => 01111 => 11110
[-4,-1,-3,-5,-2] => [-2,-5,-3,-1,-4] => 11111 => 11111
[4,1,5,2,3] => [3,2,5,1,4] => 00000 => 00000
[4,1,5,2,-3] => [-3,2,5,1,4] => 10000 => 10000
[4,1,5,-2,3] => [3,-2,5,1,4] => 01000 => 10000
[4,1,5,-2,-3] => [-3,-2,5,1,4] => 11000 => 10010
[4,1,-5,2,3] => [3,2,-5,1,4] => 00100 => 10000
[4,1,-5,2,-3] => [-3,2,-5,1,4] => 10100 => 11000
[4,1,-5,-2,3] => [3,-2,-5,1,4] => 01100 => 10010
[4,1,-5,-2,-3] => [-3,-2,-5,1,4] => 11100 => 10110
[4,-1,5,2,3] => [3,2,5,-1,4] => 00010 => 10000
[4,-1,5,2,-3] => [-3,2,5,-1,4] => 10010 => 11000
[4,-1,5,-2,3] => [3,-2,5,-1,4] => 01010 => 11000
[4,-1,5,-2,-3] => [-3,-2,5,-1,4] => 11010 => 11100
[4,-1,-5,2,3] => [3,2,-5,-1,4] => 00110 => 10010
[4,-1,-5,2,-3] => [-3,2,-5,-1,4] => 10110 => 11100
[4,-1,-5,-2,3] => [3,-2,-5,-1,4] => 01110 => 10110
[4,-1,-5,-2,-3] => [-3,-2,-5,-1,4] => 11110 => 11110
[-4,1,5,2,3] => [3,2,5,1,-4] => 00001 => 10000
[-4,1,5,2,-3] => [-3,2,5,1,-4] => 10001 => 10010
[-4,1,5,-2,3] => [3,-2,5,1,-4] => 01001 => 11000
[-4,1,5,-2,-3] => [-3,-2,5,1,-4] => 11001 => 10110
[-4,1,-5,2,3] => [3,2,-5,1,-4] => 00101 => 11000
[-4,1,-5,2,-3] => [-3,2,-5,1,-4] => 10101 => 11100
[-4,1,-5,-2,3] => [3,-2,-5,1,-4] => 01101 => 11100
[-4,1,-5,-2,-3] => [-3,-2,-5,1,-4] => 11101 => 11110
[-4,-1,5,2,3] => [3,2,5,-1,-4] => 00011 => 10010
[-4,-1,5,2,-3] => [-3,2,5,-1,-4] => 10011 => 10110
[-4,-1,5,-2,3] => [3,-2,5,-1,-4] => 01011 => 11100
[-4,-1,5,-2,-3] => [-3,-2,5,-1,-4] => 11011 => 11110
[-4,-1,-5,2,3] => [3,2,-5,-1,-4] => 00111 => 10110
[-4,-1,-5,2,-3] => [-3,2,-5,-1,-4] => 10111 => 11110
[-4,-1,-5,-2,3] => [3,-2,-5,-1,-4] => 01111 => 11110
[-4,-1,-5,-2,-3] => [-3,-2,-5,-1,-4] => 11111 => 11111
[4,1,5,3,2] => [2,3,5,1,4] => 00000 => 00000
[4,1,5,3,-2] => [-2,3,5,1,4] => 10000 => 10000
[4,1,5,-3,2] => [2,-3,5,1,4] => 01000 => 10000
[4,1,5,-3,-2] => [-2,-3,5,1,4] => 11000 => 10010
[4,1,-5,3,2] => [2,3,-5,1,4] => 00100 => 10000
[4,1,-5,3,-2] => [-2,3,-5,1,4] => 10100 => 11000
[4,1,-5,-3,2] => [2,-3,-5,1,4] => 01100 => 10010
[4,1,-5,-3,-2] => [-2,-3,-5,1,4] => 11100 => 10110
[4,-1,5,3,2] => [2,3,5,-1,4] => 00010 => 10000
[4,-1,5,3,-2] => [-2,3,5,-1,4] => 10010 => 11000
[4,-1,5,-3,2] => [2,-3,5,-1,4] => 01010 => 11000
[4,-1,5,-3,-2] => [-2,-3,5,-1,4] => 11010 => 11100
[4,-1,-5,3,2] => [2,3,-5,-1,4] => 00110 => 10010
[4,-1,-5,3,-2] => [-2,3,-5,-1,4] => 10110 => 11100
[4,-1,-5,-3,2] => [2,-3,-5,-1,4] => 01110 => 10110
[4,-1,-5,-3,-2] => [-2,-3,-5,-1,4] => 11110 => 11110
[-4,1,5,3,2] => [2,3,5,1,-4] => 00001 => 10000
[-4,1,5,3,-2] => [-2,3,5,1,-4] => 10001 => 10010
[-4,1,5,-3,2] => [2,-3,5,1,-4] => 01001 => 11000
[-4,1,5,-3,-2] => [-2,-3,5,1,-4] => 11001 => 10110
[-4,1,-5,3,2] => [2,3,-5,1,-4] => 00101 => 11000
[-4,1,-5,3,-2] => [-2,3,-5,1,-4] => 10101 => 11100
[-4,1,-5,-3,2] => [2,-3,-5,1,-4] => 01101 => 11100
[-4,1,-5,-3,-2] => [-2,-3,-5,1,-4] => 11101 => 11110
[-4,-1,5,3,2] => [2,3,5,-1,-4] => 00011 => 10010
[-4,-1,5,3,-2] => [-2,3,5,-1,-4] => 10011 => 10110
[-4,-1,5,-3,2] => [2,-3,5,-1,-4] => 01011 => 11100
[-4,-1,5,-3,-2] => [-2,-3,5,-1,-4] => 11011 => 11110
[-4,-1,-5,3,2] => [2,3,-5,-1,-4] => 00111 => 10110
[-4,-1,-5,3,-2] => [-2,3,-5,-1,-4] => 10111 => 11110
[-4,-1,-5,-3,2] => [2,-3,-5,-1,-4] => 01111 => 11110
[-4,-1,-5,-3,-2] => [-2,-3,-5,-1,-4] => 11111 => 11111
[4,2,1,3,5] => [5,3,1,2,4] => 00000 => 00000
[4,2,1,3,-5] => [-5,3,1,2,4] => 10000 => 10000
[4,2,1,-3,5] => [5,-3,1,2,4] => 01000 => 10000
[4,2,1,-3,-5] => [-5,-3,1,2,4] => 11000 => 10010
[4,2,-1,3,5] => [5,3,-1,2,4] => 00100 => 10000
[4,2,-1,3,-5] => [-5,3,-1,2,4] => 10100 => 11000
[4,2,-1,-3,5] => [5,-3,-1,2,4] => 01100 => 10010
[4,2,-1,-3,-5] => [-5,-3,-1,2,4] => 11100 => 10110
[4,-2,1,3,5] => [5,3,1,-2,4] => 00010 => 10000
[4,-2,1,3,-5] => [-5,3,1,-2,4] => 10010 => 11000
[4,-2,1,-3,5] => [5,-3,1,-2,4] => 01010 => 11000
[4,-2,1,-3,-5] => [-5,-3,1,-2,4] => 11010 => 11100
[4,-2,-1,3,5] => [5,3,-1,-2,4] => 00110 => 10010
[4,-2,-1,3,-5] => [-5,3,-1,-2,4] => 10110 => 11100
[4,-2,-1,-3,5] => [5,-3,-1,-2,4] => 01110 => 10110
[4,-2,-1,-3,-5] => [-5,-3,-1,-2,4] => 11110 => 11110
[-4,2,1,3,5] => [5,3,1,2,-4] => 00001 => 10000
[-4,2,1,3,-5] => [-5,3,1,2,-4] => 10001 => 10010
[-4,2,1,-3,5] => [5,-3,1,2,-4] => 01001 => 11000
[-4,2,1,-3,-5] => [-5,-3,1,2,-4] => 11001 => 10110
[-4,2,-1,3,5] => [5,3,-1,2,-4] => 00101 => 11000
[-4,2,-1,3,-5] => [-5,3,-1,2,-4] => 10101 => 11100
[-4,2,-1,-3,5] => [5,-3,-1,2,-4] => 01101 => 11100
[-4,2,-1,-3,-5] => [-5,-3,-1,2,-4] => 11101 => 11110
[-4,-2,1,3,5] => [5,3,1,-2,-4] => 00011 => 10010
[-4,-2,1,3,-5] => [-5,3,1,-2,-4] => 10011 => 10110
[-4,-2,1,-3,5] => [5,-3,1,-2,-4] => 01011 => 11100
[-4,-2,1,-3,-5] => [-5,-3,1,-2,-4] => 11011 => 11110
[-4,-2,-1,3,5] => [5,3,-1,-2,-4] => 00111 => 10110
[-4,-2,-1,3,-5] => [-5,3,-1,-2,-4] => 10111 => 11110
[-4,-2,-1,-3,5] => [5,-3,-1,-2,-4] => 01111 => 11110
[-4,-2,-1,-3,-5] => [-5,-3,-1,-2,-4] => 11111 => 11111
[4,2,1,5,3] => [3,5,1,2,4] => 00000 => 00000
[4,2,1,5,-3] => [-3,5,1,2,4] => 10000 => 10000
[4,2,1,-5,3] => [3,-5,1,2,4] => 01000 => 10000
[4,2,1,-5,-3] => [-3,-5,1,2,4] => 11000 => 10010
[4,2,-1,5,3] => [3,5,-1,2,4] => 00100 => 10000
[4,2,-1,5,-3] => [-3,5,-1,2,4] => 10100 => 11000
[4,2,-1,-5,3] => [3,-5,-1,2,4] => 01100 => 10010
[4,2,-1,-5,-3] => [-3,-5,-1,2,4] => 11100 => 10110
[4,-2,1,5,3] => [3,5,1,-2,4] => 00010 => 10000
[4,-2,1,5,-3] => [-3,5,1,-2,4] => 10010 => 11000
[4,-2,1,-5,3] => [3,-5,1,-2,4] => 01010 => 11000
[4,-2,1,-5,-3] => [-3,-5,1,-2,4] => 11010 => 11100
[4,-2,-1,5,3] => [3,5,-1,-2,4] => 00110 => 10010
[4,-2,-1,5,-3] => [-3,5,-1,-2,4] => 10110 => 11100
[4,-2,-1,-5,3] => [3,-5,-1,-2,4] => 01110 => 10110
[4,-2,-1,-5,-3] => [-3,-5,-1,-2,4] => 11110 => 11110
[-4,2,1,5,3] => [3,5,1,2,-4] => 00001 => 10000
[-4,2,1,5,-3] => [-3,5,1,2,-4] => 10001 => 10010
[-4,2,1,-5,3] => [3,-5,1,2,-4] => 01001 => 11000
[-4,2,1,-5,-3] => [-3,-5,1,2,-4] => 11001 => 10110
[-4,2,-1,5,3] => [3,5,-1,2,-4] => 00101 => 11000
[-4,2,-1,5,-3] => [-3,5,-1,2,-4] => 10101 => 11100
[-4,2,-1,-5,3] => [3,-5,-1,2,-4] => 01101 => 11100
[-4,2,-1,-5,-3] => [-3,-5,-1,2,-4] => 11101 => 11110
[-4,-2,1,5,3] => [3,5,1,-2,-4] => 00011 => 10010
[-4,-2,1,5,-3] => [-3,5,1,-2,-4] => 10011 => 10110
[-4,-2,1,-5,3] => [3,-5,1,-2,-4] => 01011 => 11100
[-4,-2,1,-5,-3] => [-3,-5,1,-2,-4] => 11011 => 11110
[-4,-2,-1,5,3] => [3,5,-1,-2,-4] => 00111 => 10110
[-4,-2,-1,5,-3] => [-3,5,-1,-2,-4] => 10111 => 11110
[-4,-2,-1,-5,3] => [3,-5,-1,-2,-4] => 01111 => 11110
[-4,-2,-1,-5,-3] => [-3,-5,-1,-2,-4] => 11111 => 11111
[4,2,3,1,5] => [5,1,3,2,4] => 00000 => 00000
[4,2,3,1,-5] => [-5,1,3,2,4] => 10000 => 10000
[4,2,3,-1,5] => [5,-1,3,2,4] => 01000 => 10000
[4,2,3,-1,-5] => [-5,-1,3,2,4] => 11000 => 10010
[4,2,-3,1,5] => [5,1,-3,2,4] => 00100 => 10000
[4,2,-3,1,-5] => [-5,1,-3,2,4] => 10100 => 11000
[4,2,-3,-1,5] => [5,-1,-3,2,4] => 01100 => 10010
[4,2,-3,-1,-5] => [-5,-1,-3,2,4] => 11100 => 10110
[4,-2,3,1,5] => [5,1,3,-2,4] => 00010 => 10000
[4,-2,3,1,-5] => [-5,1,3,-2,4] => 10010 => 11000
[4,-2,3,-1,5] => [5,-1,3,-2,4] => 01010 => 11000
[4,-2,3,-1,-5] => [-5,-1,3,-2,4] => 11010 => 11100
[4,-2,-3,1,5] => [5,1,-3,-2,4] => 00110 => 10010
[4,-2,-3,1,-5] => [-5,1,-3,-2,4] => 10110 => 11100
[4,-2,-3,-1,5] => [5,-1,-3,-2,4] => 01110 => 10110
[4,-2,-3,-1,-5] => [-5,-1,-3,-2,4] => 11110 => 11110
[-4,2,3,1,5] => [5,1,3,2,-4] => 00001 => 10000
[-4,2,3,1,-5] => [-5,1,3,2,-4] => 10001 => 10010
[-4,2,3,-1,5] => [5,-1,3,2,-4] => 01001 => 11000
[-4,2,3,-1,-5] => [-5,-1,3,2,-4] => 11001 => 10110
[-4,2,-3,1,5] => [5,1,-3,2,-4] => 00101 => 11000
[-4,2,-3,1,-5] => [-5,1,-3,2,-4] => 10101 => 11100
[-4,2,-3,-1,5] => [5,-1,-3,2,-4] => 01101 => 11100
[-4,2,-3,-1,-5] => [-5,-1,-3,2,-4] => 11101 => 11110
[-4,-2,3,1,5] => [5,1,3,-2,-4] => 00011 => 10010
[-4,-2,3,1,-5] => [-5,1,3,-2,-4] => 10011 => 10110
[-4,-2,3,-1,5] => [5,-1,3,-2,-4] => 01011 => 11100
[-4,-2,3,-1,-5] => [-5,-1,3,-2,-4] => 11011 => 11110
[-4,-2,-3,1,5] => [5,1,-3,-2,-4] => 00111 => 10110
[-4,-2,-3,1,-5] => [-5,1,-3,-2,-4] => 10111 => 11110
[-4,-2,-3,-1,5] => [5,-1,-3,-2,-4] => 01111 => 11110
[-4,-2,-3,-1,-5] => [-5,-1,-3,-2,-4] => 11111 => 11111
[4,2,3,5,1] => [1,5,3,2,4] => 00000 => 00000
[4,2,3,5,-1] => [-1,5,3,2,4] => 10000 => 10000
[4,2,3,-5,1] => [1,-5,3,2,4] => 01000 => 10000
[4,2,3,-5,-1] => [-1,-5,3,2,4] => 11000 => 10010
[4,2,-3,5,1] => [1,5,-3,2,4] => 00100 => 10000
[4,2,-3,5,-1] => [-1,5,-3,2,4] => 10100 => 11000
[4,2,-3,-5,1] => [1,-5,-3,2,4] => 01100 => 10010
[4,2,-3,-5,-1] => [-1,-5,-3,2,4] => 11100 => 10110
[4,-2,3,5,1] => [1,5,3,-2,4] => 00010 => 10000
[4,-2,3,5,-1] => [-1,5,3,-2,4] => 10010 => 11000
[4,-2,3,-5,1] => [1,-5,3,-2,4] => 01010 => 11000
[4,-2,3,-5,-1] => [-1,-5,3,-2,4] => 11010 => 11100
[4,-2,-3,5,1] => [1,5,-3,-2,4] => 00110 => 10010
[4,-2,-3,5,-1] => [-1,5,-3,-2,4] => 10110 => 11100
[4,-2,-3,-5,1] => [1,-5,-3,-2,4] => 01110 => 10110
[4,-2,-3,-5,-1] => [-1,-5,-3,-2,4] => 11110 => 11110
[-4,2,3,5,1] => [1,5,3,2,-4] => 00001 => 10000
[-4,2,3,5,-1] => [-1,5,3,2,-4] => 10001 => 10010
[-4,2,3,-5,1] => [1,-5,3,2,-4] => 01001 => 11000
[-4,2,3,-5,-1] => [-1,-5,3,2,-4] => 11001 => 10110
[-4,2,-3,5,1] => [1,5,-3,2,-4] => 00101 => 11000
[-4,2,-3,5,-1] => [-1,5,-3,2,-4] => 10101 => 11100
[-4,2,-3,-5,1] => [1,-5,-3,2,-4] => 01101 => 11100
[-4,2,-3,-5,-1] => [-1,-5,-3,2,-4] => 11101 => 11110
[-4,-2,3,5,1] => [1,5,3,-2,-4] => 00011 => 10010
[-4,-2,3,5,-1] => [-1,5,3,-2,-4] => 10011 => 10110
[-4,-2,3,-5,1] => [1,-5,3,-2,-4] => 01011 => 11100
[-4,-2,3,-5,-1] => [-1,-5,3,-2,-4] => 11011 => 11110
[-4,-2,-3,5,1] => [1,5,-3,-2,-4] => 00111 => 10110
[-4,-2,-3,5,-1] => [-1,5,-3,-2,-4] => 10111 => 11110
[-4,-2,-3,-5,1] => [1,-5,-3,-2,-4] => 01111 => 11110
[-4,-2,-3,-5,-1] => [-1,-5,-3,-2,-4] => 11111 => 11111
[4,2,5,1,3] => [3,1,5,2,4] => 00000 => 00000
[4,2,5,1,-3] => [-3,1,5,2,4] => 10000 => 10000
[4,2,5,-1,3] => [3,-1,5,2,4] => 01000 => 10000
[4,2,5,-1,-3] => [-3,-1,5,2,4] => 11000 => 10010
[4,2,-5,1,3] => [3,1,-5,2,4] => 00100 => 10000
[4,2,-5,1,-3] => [-3,1,-5,2,4] => 10100 => 11000
[4,2,-5,-1,3] => [3,-1,-5,2,4] => 01100 => 10010
[4,2,-5,-1,-3] => [-3,-1,-5,2,4] => 11100 => 10110
[4,-2,5,1,3] => [3,1,5,-2,4] => 00010 => 10000
[4,-2,5,1,-3] => [-3,1,5,-2,4] => 10010 => 11000
[4,-2,5,-1,3] => [3,-1,5,-2,4] => 01010 => 11000
[4,-2,5,-1,-3] => [-3,-1,5,-2,4] => 11010 => 11100
[4,-2,-5,1,3] => [3,1,-5,-2,4] => 00110 => 10010
[4,-2,-5,1,-3] => [-3,1,-5,-2,4] => 10110 => 11100
[4,-2,-5,-1,3] => [3,-1,-5,-2,4] => 01110 => 10110
[4,-2,-5,-1,-3] => [-3,-1,-5,-2,4] => 11110 => 11110
[-4,2,5,1,3] => [3,1,5,2,-4] => 00001 => 10000
[-4,2,5,1,-3] => [-3,1,5,2,-4] => 10001 => 10010
[-4,2,5,-1,3] => [3,-1,5,2,-4] => 01001 => 11000
[-4,2,5,-1,-3] => [-3,-1,5,2,-4] => 11001 => 10110
[-4,2,-5,1,3] => [3,1,-5,2,-4] => 00101 => 11000
[-4,2,-5,1,-3] => [-3,1,-5,2,-4] => 10101 => 11100
[-4,2,-5,-1,3] => [3,-1,-5,2,-4] => 01101 => 11100
[-4,2,-5,-1,-3] => [-3,-1,-5,2,-4] => 11101 => 11110
[-4,-2,5,1,3] => [3,1,5,-2,-4] => 00011 => 10010
[-4,-2,5,1,-3] => [-3,1,5,-2,-4] => 10011 => 10110
[-4,-2,5,-1,3] => [3,-1,5,-2,-4] => 01011 => 11100
[-4,-2,5,-1,-3] => [-3,-1,5,-2,-4] => 11011 => 11110
[-4,-2,-5,1,3] => [3,1,-5,-2,-4] => 00111 => 10110
[-4,-2,-5,1,-3] => [-3,1,-5,-2,-4] => 10111 => 11110
[-4,-2,-5,-1,3] => [3,-1,-5,-2,-4] => 01111 => 11110
[-4,-2,-5,-1,-3] => [-3,-1,-5,-2,-4] => 11111 => 11111
[4,2,5,3,1] => [1,3,5,2,4] => 00000 => 00000
[4,2,5,3,-1] => [-1,3,5,2,4] => 10000 => 10000
[4,2,5,-3,1] => [1,-3,5,2,4] => 01000 => 10000
[4,2,5,-3,-1] => [-1,-3,5,2,4] => 11000 => 10010
[4,2,-5,3,1] => [1,3,-5,2,4] => 00100 => 10000
[4,2,-5,3,-1] => [-1,3,-5,2,4] => 10100 => 11000
[4,2,-5,-3,1] => [1,-3,-5,2,4] => 01100 => 10010
[4,2,-5,-3,-1] => [-1,-3,-5,2,4] => 11100 => 10110
[4,-2,5,3,1] => [1,3,5,-2,4] => 00010 => 10000
[4,-2,5,3,-1] => [-1,3,5,-2,4] => 10010 => 11000
[4,-2,5,-3,1] => [1,-3,5,-2,4] => 01010 => 11000
[4,-2,5,-3,-1] => [-1,-3,5,-2,4] => 11010 => 11100
[4,-2,-5,3,1] => [1,3,-5,-2,4] => 00110 => 10010
[4,-2,-5,3,-1] => [-1,3,-5,-2,4] => 10110 => 11100
[4,-2,-5,-3,1] => [1,-3,-5,-2,4] => 01110 => 10110
[4,-2,-5,-3,-1] => [-1,-3,-5,-2,4] => 11110 => 11110
[-4,2,5,3,1] => [1,3,5,2,-4] => 00001 => 10000
[-4,2,5,3,-1] => [-1,3,5,2,-4] => 10001 => 10010
[-4,2,5,-3,1] => [1,-3,5,2,-4] => 01001 => 11000
[-4,2,5,-3,-1] => [-1,-3,5,2,-4] => 11001 => 10110
[-4,2,-5,3,1] => [1,3,-5,2,-4] => 00101 => 11000
[-4,2,-5,3,-1] => [-1,3,-5,2,-4] => 10101 => 11100
[-4,2,-5,-3,1] => [1,-3,-5,2,-4] => 01101 => 11100
[-4,2,-5,-3,-1] => [-1,-3,-5,2,-4] => 11101 => 11110
[-4,-2,5,3,1] => [1,3,5,-2,-4] => 00011 => 10010
[-4,-2,5,3,-1] => [-1,3,5,-2,-4] => 10011 => 10110
[-4,-2,5,-3,1] => [1,-3,5,-2,-4] => 01011 => 11100
[-4,-2,5,-3,-1] => [-1,-3,5,-2,-4] => 11011 => 11110
[-4,-2,-5,3,1] => [1,3,-5,-2,-4] => 00111 => 10110
[-4,-2,-5,3,-1] => [-1,3,-5,-2,-4] => 10111 => 11110
[-4,-2,-5,-3,1] => [1,-3,-5,-2,-4] => 01111 => 11110
[-4,-2,-5,-3,-1] => [-1,-3,-5,-2,-4] => 11111 => 11111
[4,3,1,2,5] => [5,2,1,3,4] => 00000 => 00000
[4,3,1,2,-5] => [-5,2,1,3,4] => 10000 => 10000
[4,3,1,-2,5] => [5,-2,1,3,4] => 01000 => 10000
[4,3,1,-2,-5] => [-5,-2,1,3,4] => 11000 => 10010
[4,3,-1,2,5] => [5,2,-1,3,4] => 00100 => 10000
[4,3,-1,2,-5] => [-5,2,-1,3,4] => 10100 => 11000
[4,3,-1,-2,5] => [5,-2,-1,3,4] => 01100 => 10010
[4,3,-1,-2,-5] => [-5,-2,-1,3,4] => 11100 => 10110
[4,-3,1,2,5] => [5,2,1,-3,4] => 00010 => 10000
[4,-3,1,2,-5] => [-5,2,1,-3,4] => 10010 => 11000
[4,-3,1,-2,5] => [5,-2,1,-3,4] => 01010 => 11000
[4,-3,1,-2,-5] => [-5,-2,1,-3,4] => 11010 => 11100
[4,-3,-1,2,5] => [5,2,-1,-3,4] => 00110 => 10010
[4,-3,-1,2,-5] => [-5,2,-1,-3,4] => 10110 => 11100
[4,-3,-1,-2,5] => [5,-2,-1,-3,4] => 01110 => 10110
[4,-3,-1,-2,-5] => [-5,-2,-1,-3,4] => 11110 => 11110
[-4,3,1,2,5] => [5,2,1,3,-4] => 00001 => 10000
[-4,3,1,2,-5] => [-5,2,1,3,-4] => 10001 => 10010
[-4,3,1,-2,5] => [5,-2,1,3,-4] => 01001 => 11000
[-4,3,1,-2,-5] => [-5,-2,1,3,-4] => 11001 => 10110
[-4,3,-1,2,5] => [5,2,-1,3,-4] => 00101 => 11000
[-4,3,-1,2,-5] => [-5,2,-1,3,-4] => 10101 => 11100
[-4,3,-1,-2,5] => [5,-2,-1,3,-4] => 01101 => 11100
[-4,3,-1,-2,-5] => [-5,-2,-1,3,-4] => 11101 => 11110
[-4,-3,1,2,5] => [5,2,1,-3,-4] => 00011 => 10010
[-4,-3,1,2,-5] => [-5,2,1,-3,-4] => 10011 => 10110
[-4,-3,1,-2,5] => [5,-2,1,-3,-4] => 01011 => 11100
[-4,-3,1,-2,-5] => [-5,-2,1,-3,-4] => 11011 => 11110
[-4,-3,-1,2,5] => [5,2,-1,-3,-4] => 00111 => 10110
[-4,-3,-1,2,-5] => [-5,2,-1,-3,-4] => 10111 => 11110
[-4,-3,-1,-2,5] => [5,-2,-1,-3,-4] => 01111 => 11110
[-4,-3,-1,-2,-5] => [-5,-2,-1,-3,-4] => 11111 => 11111
[4,3,1,5,2] => [2,5,1,3,4] => 00000 => 00000
[4,3,1,5,-2] => [-2,5,1,3,4] => 10000 => 10000
[4,3,1,-5,2] => [2,-5,1,3,4] => 01000 => 10000
[4,3,1,-5,-2] => [-2,-5,1,3,4] => 11000 => 10010
[4,3,-1,5,2] => [2,5,-1,3,4] => 00100 => 10000
[4,3,-1,5,-2] => [-2,5,-1,3,4] => 10100 => 11000
[4,3,-1,-5,2] => [2,-5,-1,3,4] => 01100 => 10010
[4,3,-1,-5,-2] => [-2,-5,-1,3,4] => 11100 => 10110
[4,-3,1,5,2] => [2,5,1,-3,4] => 00010 => 10000
[4,-3,1,5,-2] => [-2,5,1,-3,4] => 10010 => 11000
[4,-3,1,-5,2] => [2,-5,1,-3,4] => 01010 => 11000
[4,-3,1,-5,-2] => [-2,-5,1,-3,4] => 11010 => 11100
[4,-3,-1,5,2] => [2,5,-1,-3,4] => 00110 => 10010
[4,-3,-1,5,-2] => [-2,5,-1,-3,4] => 10110 => 11100
[4,-3,-1,-5,2] => [2,-5,-1,-3,4] => 01110 => 10110
[4,-3,-1,-5,-2] => [-2,-5,-1,-3,4] => 11110 => 11110
[-4,3,1,5,2] => [2,5,1,3,-4] => 00001 => 10000
[-4,3,1,5,-2] => [-2,5,1,3,-4] => 10001 => 10010
[-4,3,1,-5,2] => [2,-5,1,3,-4] => 01001 => 11000
[-4,3,1,-5,-2] => [-2,-5,1,3,-4] => 11001 => 10110
[-4,3,-1,5,2] => [2,5,-1,3,-4] => 00101 => 11000
[-4,3,-1,5,-2] => [-2,5,-1,3,-4] => 10101 => 11100
[-4,3,-1,-5,2] => [2,-5,-1,3,-4] => 01101 => 11100
[-4,3,-1,-5,-2] => [-2,-5,-1,3,-4] => 11101 => 11110
[-4,-3,1,5,2] => [2,5,1,-3,-4] => 00011 => 10010
[-4,-3,1,5,-2] => [-2,5,1,-3,-4] => 10011 => 10110
[-4,-3,1,-5,2] => [2,-5,1,-3,-4] => 01011 => 11100
[-4,-3,1,-5,-2] => [-2,-5,1,-3,-4] => 11011 => 11110
[-4,-3,-1,5,2] => [2,5,-1,-3,-4] => 00111 => 10110
[-4,-3,-1,5,-2] => [-2,5,-1,-3,-4] => 10111 => 11110
[-4,-3,-1,-5,2] => [2,-5,-1,-3,-4] => 01111 => 11110
[-4,-3,-1,-5,-2] => [-2,-5,-1,-3,-4] => 11111 => 11111
[4,3,2,1,5] => [5,1,2,3,4] => 00000 => 00000
[4,3,2,1,-5] => [-5,1,2,3,4] => 10000 => 10000
[4,3,2,-1,5] => [5,-1,2,3,4] => 01000 => 10000
[4,3,2,-1,-5] => [-5,-1,2,3,4] => 11000 => 10010
[4,3,-2,1,5] => [5,1,-2,3,4] => 00100 => 10000
[4,3,-2,1,-5] => [-5,1,-2,3,4] => 10100 => 11000
[4,3,-2,-1,5] => [5,-1,-2,3,4] => 01100 => 10010
[4,3,-2,-1,-5] => [-5,-1,-2,3,4] => 11100 => 10110
[4,-3,2,1,5] => [5,1,2,-3,4] => 00010 => 10000
[4,-3,2,1,-5] => [-5,1,2,-3,4] => 10010 => 11000
[4,-3,2,-1,5] => [5,-1,2,-3,4] => 01010 => 11000
[4,-3,2,-1,-5] => [-5,-1,2,-3,4] => 11010 => 11100
[4,-3,-2,1,5] => [5,1,-2,-3,4] => 00110 => 10010
[4,-3,-2,1,-5] => [-5,1,-2,-3,4] => 10110 => 11100
[4,-3,-2,-1,5] => [5,-1,-2,-3,4] => 01110 => 10110
[4,-3,-2,-1,-5] => [-5,-1,-2,-3,4] => 11110 => 11110
[-4,3,2,1,5] => [5,1,2,3,-4] => 00001 => 10000
[-4,3,2,1,-5] => [-5,1,2,3,-4] => 10001 => 10010
[-4,3,2,-1,5] => [5,-1,2,3,-4] => 01001 => 11000
[-4,3,2,-1,-5] => [-5,-1,2,3,-4] => 11001 => 10110
[-4,3,-2,1,5] => [5,1,-2,3,-4] => 00101 => 11000
[-4,3,-2,1,-5] => [-5,1,-2,3,-4] => 10101 => 11100
[-4,3,-2,-1,5] => [5,-1,-2,3,-4] => 01101 => 11100
[-4,3,-2,-1,-5] => [-5,-1,-2,3,-4] => 11101 => 11110
[-4,-3,2,1,5] => [5,1,2,-3,-4] => 00011 => 10010
[-4,-3,2,1,-5] => [-5,1,2,-3,-4] => 10011 => 10110
[-4,-3,2,-1,5] => [5,-1,2,-3,-4] => 01011 => 11100
[-4,-3,2,-1,-5] => [-5,-1,2,-3,-4] => 11011 => 11110
[-4,-3,-2,1,5] => [5,1,-2,-3,-4] => 00111 => 10110
[-4,-3,-2,1,-5] => [-5,1,-2,-3,-4] => 10111 => 11110
[-4,-3,-2,-1,5] => [5,-1,-2,-3,-4] => 01111 => 11110
[-4,-3,-2,-1,-5] => [-5,-1,-2,-3,-4] => 11111 => 11111
[4,3,2,5,1] => [1,5,2,3,4] => 00000 => 00000
[4,3,2,5,-1] => [-1,5,2,3,4] => 10000 => 10000
[4,3,2,-5,1] => [1,-5,2,3,4] => 01000 => 10000
[4,3,2,-5,-1] => [-1,-5,2,3,4] => 11000 => 10010
[4,3,-2,5,1] => [1,5,-2,3,4] => 00100 => 10000
[4,3,-2,5,-1] => [-1,5,-2,3,4] => 10100 => 11000
[4,3,-2,-5,1] => [1,-5,-2,3,4] => 01100 => 10010
[4,3,-2,-5,-1] => [-1,-5,-2,3,4] => 11100 => 10110
[4,-3,2,5,1] => [1,5,2,-3,4] => 00010 => 10000
[4,-3,2,5,-1] => [-1,5,2,-3,4] => 10010 => 11000
[4,-3,2,-5,1] => [1,-5,2,-3,4] => 01010 => 11000
[4,-3,2,-5,-1] => [-1,-5,2,-3,4] => 11010 => 11100
[4,-3,-2,5,1] => [1,5,-2,-3,4] => 00110 => 10010
[4,-3,-2,5,-1] => [-1,5,-2,-3,4] => 10110 => 11100
[4,-3,-2,-5,1] => [1,-5,-2,-3,4] => 01110 => 10110
[4,-3,-2,-5,-1] => [-1,-5,-2,-3,4] => 11110 => 11110
[-4,3,2,5,1] => [1,5,2,3,-4] => 00001 => 10000
[-4,3,2,5,-1] => [-1,5,2,3,-4] => 10001 => 10010
[-4,3,2,-5,1] => [1,-5,2,3,-4] => 01001 => 11000
[-4,3,2,-5,-1] => [-1,-5,2,3,-4] => 11001 => 10110
[-4,3,-2,5,1] => [1,5,-2,3,-4] => 00101 => 11000
[-4,3,-2,5,-1] => [-1,5,-2,3,-4] => 10101 => 11100
[-4,3,-2,-5,1] => [1,-5,-2,3,-4] => 01101 => 11100
[-4,3,-2,-5,-1] => [-1,-5,-2,3,-4] => 11101 => 11110
[-4,-3,2,5,1] => [1,5,2,-3,-4] => 00011 => 10010
[-4,-3,2,5,-1] => [-1,5,2,-3,-4] => 10011 => 10110
[-4,-3,2,-5,1] => [1,-5,2,-3,-4] => 01011 => 11100
[-4,-3,2,-5,-1] => [-1,-5,2,-3,-4] => 11011 => 11110
[-4,-3,-2,5,1] => [1,5,-2,-3,-4] => 00111 => 10110
[-4,-3,-2,5,-1] => [-1,5,-2,-3,-4] => 10111 => 11110
[-4,-3,-2,-5,1] => [1,-5,-2,-3,-4] => 01111 => 11110
[-4,-3,-2,-5,-1] => [-1,-5,-2,-3,-4] => 11111 => 11111
[4,3,5,1,2] => [2,1,5,3,4] => 00000 => 00000
[4,3,5,1,-2] => [-2,1,5,3,4] => 10000 => 10000
[4,3,5,-1,2] => [2,-1,5,3,4] => 01000 => 10000
[4,3,5,-1,-2] => [-2,-1,5,3,4] => 11000 => 10010
[4,3,-5,1,2] => [2,1,-5,3,4] => 00100 => 10000
[4,3,-5,1,-2] => [-2,1,-5,3,4] => 10100 => 11000
[4,3,-5,-1,2] => [2,-1,-5,3,4] => 01100 => 10010
[4,3,-5,-1,-2] => [-2,-1,-5,3,4] => 11100 => 10110
[4,-3,5,1,2] => [2,1,5,-3,4] => 00010 => 10000
[4,-3,5,1,-2] => [-2,1,5,-3,4] => 10010 => 11000
[4,-3,5,-1,2] => [2,-1,5,-3,4] => 01010 => 11000
[4,-3,5,-1,-2] => [-2,-1,5,-3,4] => 11010 => 11100
[4,-3,-5,1,2] => [2,1,-5,-3,4] => 00110 => 10010
[4,-3,-5,1,-2] => [-2,1,-5,-3,4] => 10110 => 11100
[4,-3,-5,-1,2] => [2,-1,-5,-3,4] => 01110 => 10110
[4,-3,-5,-1,-2] => [-2,-1,-5,-3,4] => 11110 => 11110
[-4,3,5,1,2] => [2,1,5,3,-4] => 00001 => 10000
[-4,3,5,1,-2] => [-2,1,5,3,-4] => 10001 => 10010
[-4,3,5,-1,2] => [2,-1,5,3,-4] => 01001 => 11000
[-4,3,5,-1,-2] => [-2,-1,5,3,-4] => 11001 => 10110
[-4,3,-5,1,2] => [2,1,-5,3,-4] => 00101 => 11000
[-4,3,-5,1,-2] => [-2,1,-5,3,-4] => 10101 => 11100
[-4,3,-5,-1,2] => [2,-1,-5,3,-4] => 01101 => 11100
[-4,3,-5,-1,-2] => [-2,-1,-5,3,-4] => 11101 => 11110
[-4,-3,5,1,2] => [2,1,5,-3,-4] => 00011 => 10010
[-4,-3,5,1,-2] => [-2,1,5,-3,-4] => 10011 => 10110
[-4,-3,5,-1,2] => [2,-1,5,-3,-4] => 01011 => 11100
[-4,-3,5,-1,-2] => [-2,-1,5,-3,-4] => 11011 => 11110
[-4,-3,-5,1,2] => [2,1,-5,-3,-4] => 00111 => 10110
[-4,-3,-5,1,-2] => [-2,1,-5,-3,-4] => 10111 => 11110
[-4,-3,-5,-1,2] => [2,-1,-5,-3,-4] => 01111 => 11110
[-4,-3,-5,-1,-2] => [-2,-1,-5,-3,-4] => 11111 => 11111
[4,3,5,2,1] => [1,2,5,3,4] => 00000 => 00000
[4,3,5,2,-1] => [-1,2,5,3,4] => 10000 => 10000
[4,3,5,-2,1] => [1,-2,5,3,4] => 01000 => 10000
[4,3,5,-2,-1] => [-1,-2,5,3,4] => 11000 => 10010
[4,3,-5,2,1] => [1,2,-5,3,4] => 00100 => 10000
[4,3,-5,2,-1] => [-1,2,-5,3,4] => 10100 => 11000
[4,3,-5,-2,1] => [1,-2,-5,3,4] => 01100 => 10010
[4,3,-5,-2,-1] => [-1,-2,-5,3,4] => 11100 => 10110
[4,-3,5,2,1] => [1,2,5,-3,4] => 00010 => 10000
[4,-3,5,2,-1] => [-1,2,5,-3,4] => 10010 => 11000
[4,-3,5,-2,1] => [1,-2,5,-3,4] => 01010 => 11000
[4,-3,5,-2,-1] => [-1,-2,5,-3,4] => 11010 => 11100
[4,-3,-5,2,1] => [1,2,-5,-3,4] => 00110 => 10010
[4,-3,-5,2,-1] => [-1,2,-5,-3,4] => 10110 => 11100
[4,-3,-5,-2,1] => [1,-2,-5,-3,4] => 01110 => 10110
[4,-3,-5,-2,-1] => [-1,-2,-5,-3,4] => 11110 => 11110
[-4,3,5,2,1] => [1,2,5,3,-4] => 00001 => 10000
[-4,3,5,2,-1] => [-1,2,5,3,-4] => 10001 => 10010
[-4,3,5,-2,1] => [1,-2,5,3,-4] => 01001 => 11000
[-4,3,5,-2,-1] => [-1,-2,5,3,-4] => 11001 => 10110
[-4,3,-5,2,1] => [1,2,-5,3,-4] => 00101 => 11000
[-4,3,-5,2,-1] => [-1,2,-5,3,-4] => 10101 => 11100
[-4,3,-5,-2,1] => [1,-2,-5,3,-4] => 01101 => 11100
[-4,3,-5,-2,-1] => [-1,-2,-5,3,-4] => 11101 => 11110
[-4,-3,5,2,1] => [1,2,5,-3,-4] => 00011 => 10010
[-4,-3,5,2,-1] => [-1,2,5,-3,-4] => 10011 => 10110
[-4,-3,5,-2,1] => [1,-2,5,-3,-4] => 01011 => 11100
[-4,-3,5,-2,-1] => [-1,-2,5,-3,-4] => 11011 => 11110
[-4,-3,-5,2,1] => [1,2,-5,-3,-4] => 00111 => 10110
[-4,-3,-5,2,-1] => [-1,2,-5,-3,-4] => 10111 => 11110
[-4,-3,-5,-2,1] => [1,-2,-5,-3,-4] => 01111 => 11110
[-4,-3,-5,-2,-1] => [-1,-2,-5,-3,-4] => 11111 => 11111
[4,5,1,2,3] => [3,2,1,5,4] => 00000 => 00000
[4,5,1,2,-3] => [-3,2,1,5,4] => 10000 => 10000
[4,5,1,-2,3] => [3,-2,1,5,4] => 01000 => 10000
[4,5,1,-2,-3] => [-3,-2,1,5,4] => 11000 => 10010
[4,5,-1,2,3] => [3,2,-1,5,4] => 00100 => 10000
[4,5,-1,2,-3] => [-3,2,-1,5,4] => 10100 => 11000
[4,5,-1,-2,3] => [3,-2,-1,5,4] => 01100 => 10010
[4,5,-1,-2,-3] => [-3,-2,-1,5,4] => 11100 => 10110
[4,-5,1,2,3] => [3,2,1,-5,4] => 00010 => 10000
[4,-5,1,2,-3] => [-3,2,1,-5,4] => 10010 => 11000
[4,-5,1,-2,3] => [3,-2,1,-5,4] => 01010 => 11000
[4,-5,1,-2,-3] => [-3,-2,1,-5,4] => 11010 => 11100
[4,-5,-1,2,3] => [3,2,-1,-5,4] => 00110 => 10010
[4,-5,-1,2,-3] => [-3,2,-1,-5,4] => 10110 => 11100
[4,-5,-1,-2,3] => [3,-2,-1,-5,4] => 01110 => 10110
[4,-5,-1,-2,-3] => [-3,-2,-1,-5,4] => 11110 => 11110
[-4,5,1,2,3] => [3,2,1,5,-4] => 00001 => 10000
[-4,5,1,2,-3] => [-3,2,1,5,-4] => 10001 => 10010
[-4,5,1,-2,3] => [3,-2,1,5,-4] => 01001 => 11000
[-4,5,1,-2,-3] => [-3,-2,1,5,-4] => 11001 => 10110
[-4,5,-1,2,3] => [3,2,-1,5,-4] => 00101 => 11000
[-4,5,-1,2,-3] => [-3,2,-1,5,-4] => 10101 => 11100
[-4,5,-1,-2,3] => [3,-2,-1,5,-4] => 01101 => 11100
[-4,5,-1,-2,-3] => [-3,-2,-1,5,-4] => 11101 => 11110
[-4,-5,1,2,3] => [3,2,1,-5,-4] => 00011 => 10010
[-4,-5,1,2,-3] => [-3,2,1,-5,-4] => 10011 => 10110
[-4,-5,1,-2,3] => [3,-2,1,-5,-4] => 01011 => 11100
[-4,-5,1,-2,-3] => [-3,-2,1,-5,-4] => 11011 => 11110
[-4,-5,-1,2,3] => [3,2,-1,-5,-4] => 00111 => 10110
[-4,-5,-1,2,-3] => [-3,2,-1,-5,-4] => 10111 => 11110
[-4,-5,-1,-2,3] => [3,-2,-1,-5,-4] => 01111 => 11110
[-4,-5,-1,-2,-3] => [-3,-2,-1,-5,-4] => 11111 => 11111
[4,5,1,3,2] => [2,3,1,5,4] => 00000 => 00000
[4,5,1,3,-2] => [-2,3,1,5,4] => 10000 => 10000
[4,5,1,-3,2] => [2,-3,1,5,4] => 01000 => 10000
[4,5,1,-3,-2] => [-2,-3,1,5,4] => 11000 => 10010
[4,5,-1,3,2] => [2,3,-1,5,4] => 00100 => 10000
[4,5,-1,3,-2] => [-2,3,-1,5,4] => 10100 => 11000
[4,5,-1,-3,2] => [2,-3,-1,5,4] => 01100 => 10010
[4,5,-1,-3,-2] => [-2,-3,-1,5,4] => 11100 => 10110
[4,-5,1,3,2] => [2,3,1,-5,4] => 00010 => 10000
[4,-5,1,3,-2] => [-2,3,1,-5,4] => 10010 => 11000
[4,-5,1,-3,2] => [2,-3,1,-5,4] => 01010 => 11000
[4,-5,1,-3,-2] => [-2,-3,1,-5,4] => 11010 => 11100
[4,-5,-1,3,2] => [2,3,-1,-5,4] => 00110 => 10010
[4,-5,-1,3,-2] => [-2,3,-1,-5,4] => 10110 => 11100
[4,-5,-1,-3,2] => [2,-3,-1,-5,4] => 01110 => 10110
[4,-5,-1,-3,-2] => [-2,-3,-1,-5,4] => 11110 => 11110
[-4,5,1,3,2] => [2,3,1,5,-4] => 00001 => 10000
[-4,5,1,3,-2] => [-2,3,1,5,-4] => 10001 => 10010
[-4,5,1,-3,2] => [2,-3,1,5,-4] => 01001 => 11000
[-4,5,1,-3,-2] => [-2,-3,1,5,-4] => 11001 => 10110
[-4,5,-1,3,2] => [2,3,-1,5,-4] => 00101 => 11000
[-4,5,-1,3,-2] => [-2,3,-1,5,-4] => 10101 => 11100
[-4,5,-1,-3,2] => [2,-3,-1,5,-4] => 01101 => 11100
[-4,5,-1,-3,-2] => [-2,-3,-1,5,-4] => 11101 => 11110
[-4,-5,1,3,2] => [2,3,1,-5,-4] => 00011 => 10010
[-4,-5,1,3,-2] => [-2,3,1,-5,-4] => 10011 => 10110
[-4,-5,1,-3,2] => [2,-3,1,-5,-4] => 01011 => 11100
[-4,-5,1,-3,-2] => [-2,-3,1,-5,-4] => 11011 => 11110
[-4,-5,-1,3,2] => [2,3,-1,-5,-4] => 00111 => 10110
[-4,-5,-1,3,-2] => [-2,3,-1,-5,-4] => 10111 => 11110
[-4,-5,-1,-3,2] => [2,-3,-1,-5,-4] => 01111 => 11110
[-4,-5,-1,-3,-2] => [-2,-3,-1,-5,-4] => 11111 => 11111
[4,5,2,1,3] => [3,1,2,5,4] => 00000 => 00000
[4,5,2,1,-3] => [-3,1,2,5,4] => 10000 => 10000
[4,5,2,-1,3] => [3,-1,2,5,4] => 01000 => 10000
[4,5,2,-1,-3] => [-3,-1,2,5,4] => 11000 => 10010
[4,5,-2,1,3] => [3,1,-2,5,4] => 00100 => 10000
[4,5,-2,1,-3] => [-3,1,-2,5,4] => 10100 => 11000
[4,5,-2,-1,3] => [3,-1,-2,5,4] => 01100 => 10010
[4,5,-2,-1,-3] => [-3,-1,-2,5,4] => 11100 => 10110
[4,-5,2,1,3] => [3,1,2,-5,4] => 00010 => 10000
[4,-5,2,1,-3] => [-3,1,2,-5,4] => 10010 => 11000
[4,-5,2,-1,3] => [3,-1,2,-5,4] => 01010 => 11000
[4,-5,2,-1,-3] => [-3,-1,2,-5,4] => 11010 => 11100
[4,-5,-2,1,3] => [3,1,-2,-5,4] => 00110 => 10010
[4,-5,-2,1,-3] => [-3,1,-2,-5,4] => 10110 => 11100
[4,-5,-2,-1,3] => [3,-1,-2,-5,4] => 01110 => 10110
[4,-5,-2,-1,-3] => [-3,-1,-2,-5,4] => 11110 => 11110
[-4,5,2,1,3] => [3,1,2,5,-4] => 00001 => 10000
[-4,5,2,1,-3] => [-3,1,2,5,-4] => 10001 => 10010
[-4,5,2,-1,3] => [3,-1,2,5,-4] => 01001 => 11000
[-4,5,2,-1,-3] => [-3,-1,2,5,-4] => 11001 => 10110
[-4,5,-2,1,3] => [3,1,-2,5,-4] => 00101 => 11000
[-4,5,-2,1,-3] => [-3,1,-2,5,-4] => 10101 => 11100
[-4,5,-2,-1,3] => [3,-1,-2,5,-4] => 01101 => 11100
[-4,5,-2,-1,-3] => [-3,-1,-2,5,-4] => 11101 => 11110
[-4,-5,2,1,3] => [3,1,2,-5,-4] => 00011 => 10010
[-4,-5,2,1,-3] => [-3,1,2,-5,-4] => 10011 => 10110
[-4,-5,2,-1,3] => [3,-1,2,-5,-4] => 01011 => 11100
[-4,-5,2,-1,-3] => [-3,-1,2,-5,-4] => 11011 => 11110
[-4,-5,-2,1,3] => [3,1,-2,-5,-4] => 00111 => 10110
[-4,-5,-2,1,-3] => [-3,1,-2,-5,-4] => 10111 => 11110
[-4,-5,-2,-1,3] => [3,-1,-2,-5,-4] => 01111 => 11110
[-4,-5,-2,-1,-3] => [-3,-1,-2,-5,-4] => 11111 => 11111
[4,5,2,3,1] => [1,3,2,5,4] => 00000 => 00000
[4,5,2,3,-1] => [-1,3,2,5,4] => 10000 => 10000
[4,5,2,-3,1] => [1,-3,2,5,4] => 01000 => 10000
[4,5,2,-3,-1] => [-1,-3,2,5,4] => 11000 => 10010
[4,5,-2,3,1] => [1,3,-2,5,4] => 00100 => 10000
[4,5,-2,3,-1] => [-1,3,-2,5,4] => 10100 => 11000
[4,5,-2,-3,1] => [1,-3,-2,5,4] => 01100 => 10010
[4,5,-2,-3,-1] => [-1,-3,-2,5,4] => 11100 => 10110
[4,-5,2,3,1] => [1,3,2,-5,4] => 00010 => 10000
[4,-5,2,3,-1] => [-1,3,2,-5,4] => 10010 => 11000
[4,-5,2,-3,1] => [1,-3,2,-5,4] => 01010 => 11000
[4,-5,2,-3,-1] => [-1,-3,2,-5,4] => 11010 => 11100
[4,-5,-2,3,1] => [1,3,-2,-5,4] => 00110 => 10010
[4,-5,-2,3,-1] => [-1,3,-2,-5,4] => 10110 => 11100
[4,-5,-2,-3,1] => [1,-3,-2,-5,4] => 01110 => 10110
[4,-5,-2,-3,-1] => [-1,-3,-2,-5,4] => 11110 => 11110
[-4,5,2,3,1] => [1,3,2,5,-4] => 00001 => 10000
[-4,5,2,3,-1] => [-1,3,2,5,-4] => 10001 => 10010
[-4,5,2,-3,1] => [1,-3,2,5,-4] => 01001 => 11000
[-4,5,2,-3,-1] => [-1,-3,2,5,-4] => 11001 => 10110
[-4,5,-2,3,1] => [1,3,-2,5,-4] => 00101 => 11000
[-4,5,-2,3,-1] => [-1,3,-2,5,-4] => 10101 => 11100
[-4,5,-2,-3,1] => [1,-3,-2,5,-4] => 01101 => 11100
[-4,5,-2,-3,-1] => [-1,-3,-2,5,-4] => 11101 => 11110
[-4,-5,2,3,1] => [1,3,2,-5,-4] => 00011 => 10010
[-4,-5,2,3,-1] => [-1,3,2,-5,-4] => 10011 => 10110
[-4,-5,2,-3,1] => [1,-3,2,-5,-4] => 01011 => 11100
[-4,-5,2,-3,-1] => [-1,-3,2,-5,-4] => 11011 => 11110
[-4,-5,-2,3,1] => [1,3,-2,-5,-4] => 00111 => 10110
[-4,-5,-2,3,-1] => [-1,3,-2,-5,-4] => 10111 => 11110
[-4,-5,-2,-3,1] => [1,-3,-2,-5,-4] => 01111 => 11110
[-4,-5,-2,-3,-1] => [-1,-3,-2,-5,-4] => 11111 => 11111
[4,5,3,1,2] => [2,1,3,5,4] => 00000 => 00000
[4,5,3,1,-2] => [-2,1,3,5,4] => 10000 => 10000
[4,5,3,-1,2] => [2,-1,3,5,4] => 01000 => 10000
[4,5,3,-1,-2] => [-2,-1,3,5,4] => 11000 => 10010
[4,5,-3,1,2] => [2,1,-3,5,4] => 00100 => 10000
[4,5,-3,1,-2] => [-2,1,-3,5,4] => 10100 => 11000
[4,5,-3,-1,2] => [2,-1,-3,5,4] => 01100 => 10010
[4,5,-3,-1,-2] => [-2,-1,-3,5,4] => 11100 => 10110
[4,-5,3,1,2] => [2,1,3,-5,4] => 00010 => 10000
[4,-5,3,1,-2] => [-2,1,3,-5,4] => 10010 => 11000
[4,-5,3,-1,2] => [2,-1,3,-5,4] => 01010 => 11000
[4,-5,3,-1,-2] => [-2,-1,3,-5,4] => 11010 => 11100
[4,-5,-3,1,2] => [2,1,-3,-5,4] => 00110 => 10010
[4,-5,-3,1,-2] => [-2,1,-3,-5,4] => 10110 => 11100
[4,-5,-3,-1,2] => [2,-1,-3,-5,4] => 01110 => 10110
[4,-5,-3,-1,-2] => [-2,-1,-3,-5,4] => 11110 => 11110
[-4,5,3,1,2] => [2,1,3,5,-4] => 00001 => 10000
[-4,5,3,1,-2] => [-2,1,3,5,-4] => 10001 => 10010
[-4,5,3,-1,2] => [2,-1,3,5,-4] => 01001 => 11000
[-4,5,3,-1,-2] => [-2,-1,3,5,-4] => 11001 => 10110
[-4,5,-3,1,2] => [2,1,-3,5,-4] => 00101 => 11000
[-4,5,-3,1,-2] => [-2,1,-3,5,-4] => 10101 => 11100
[-4,5,-3,-1,2] => [2,-1,-3,5,-4] => 01101 => 11100
[-4,5,-3,-1,-2] => [-2,-1,-3,5,-4] => 11101 => 11110
[-4,-5,3,1,2] => [2,1,3,-5,-4] => 00011 => 10010
[-4,-5,3,1,-2] => [-2,1,3,-5,-4] => 10011 => 10110
[-4,-5,3,-1,2] => [2,-1,3,-5,-4] => 01011 => 11100
[-4,-5,3,-1,-2] => [-2,-1,3,-5,-4] => 11011 => 11110
[-4,-5,-3,1,2] => [2,1,-3,-5,-4] => 00111 => 10110
[-4,-5,-3,1,-2] => [-2,1,-3,-5,-4] => 10111 => 11110
[-4,-5,-3,-1,2] => [2,-1,-3,-5,-4] => 01111 => 11110
[-4,-5,-3,-1,-2] => [-2,-1,-3,-5,-4] => 11111 => 11111
[4,5,3,2,1] => [1,2,3,5,4] => 00000 => 00000
[4,5,3,2,-1] => [-1,2,3,5,4] => 10000 => 10000
[4,5,3,-2,1] => [1,-2,3,5,4] => 01000 => 10000
[4,5,3,-2,-1] => [-1,-2,3,5,4] => 11000 => 10010
[4,5,-3,2,1] => [1,2,-3,5,4] => 00100 => 10000
[4,5,-3,2,-1] => [-1,2,-3,5,4] => 10100 => 11000
[4,5,-3,-2,1] => [1,-2,-3,5,4] => 01100 => 10010
[4,5,-3,-2,-1] => [-1,-2,-3,5,4] => 11100 => 10110
[4,-5,3,2,1] => [1,2,3,-5,4] => 00010 => 10000
[4,-5,3,2,-1] => [-1,2,3,-5,4] => 10010 => 11000
[4,-5,3,-2,1] => [1,-2,3,-5,4] => 01010 => 11000
[4,-5,3,-2,-1] => [-1,-2,3,-5,4] => 11010 => 11100
[4,-5,-3,2,1] => [1,2,-3,-5,4] => 00110 => 10010
[4,-5,-3,2,-1] => [-1,2,-3,-5,4] => 10110 => 11100
[4,-5,-3,-2,1] => [1,-2,-3,-5,4] => 01110 => 10110
[4,-5,-3,-2,-1] => [-1,-2,-3,-5,4] => 11110 => 11110
[-4,5,3,2,1] => [1,2,3,5,-4] => 00001 => 10000
[-4,5,3,2,-1] => [-1,2,3,5,-4] => 10001 => 10010
[-4,5,3,-2,1] => [1,-2,3,5,-4] => 01001 => 11000
[-4,5,3,-2,-1] => [-1,-2,3,5,-4] => 11001 => 10110
[-4,5,-3,2,1] => [1,2,-3,5,-4] => 00101 => 11000
[-4,5,-3,2,-1] => [-1,2,-3,5,-4] => 10101 => 11100
[-4,5,-3,-2,1] => [1,-2,-3,5,-4] => 01101 => 11100
[-4,5,-3,-2,-1] => [-1,-2,-3,5,-4] => 11101 => 11110
[-4,-5,3,2,1] => [1,2,3,-5,-4] => 00011 => 10010
[-4,-5,3,2,-1] => [-1,2,3,-5,-4] => 10011 => 10110
[-4,-5,3,-2,1] => [1,-2,3,-5,-4] => 01011 => 11100
[-4,-5,3,-2,-1] => [-1,-2,3,-5,-4] => 11011 => 11110
[-4,-5,-3,2,1] => [1,2,-3,-5,-4] => 00111 => 10110
[-4,-5,-3,2,-1] => [-1,2,-3,-5,-4] => 10111 => 11110
[-4,-5,-3,-2,1] => [1,-2,-3,-5,-4] => 01111 => 11110
[-4,-5,-3,-2,-1] => [-1,-2,-3,-5,-4] => 11111 => 11111
[5,1,2,3,4] => [4,3,2,1,5] => 00000 => 00000
[5,1,2,3,-4] => [-4,3,2,1,5] => 10000 => 10000
[5,1,2,-3,4] => [4,-3,2,1,5] => 01000 => 10000
[5,1,2,-3,-4] => [-4,-3,2,1,5] => 11000 => 10010
[5,1,-2,3,4] => [4,3,-2,1,5] => 00100 => 10000
[5,1,-2,3,-4] => [-4,3,-2,1,5] => 10100 => 11000
[5,1,-2,-3,4] => [4,-3,-2,1,5] => 01100 => 10010
[5,1,-2,-3,-4] => [-4,-3,-2,1,5] => 11100 => 10110
[5,-1,2,3,4] => [4,3,2,-1,5] => 00010 => 10000
[5,-1,2,3,-4] => [-4,3,2,-1,5] => 10010 => 11000
[5,-1,2,-3,4] => [4,-3,2,-1,5] => 01010 => 11000
[5,-1,2,-3,-4] => [-4,-3,2,-1,5] => 11010 => 11100
[5,-1,-2,3,4] => [4,3,-2,-1,5] => 00110 => 10010
[5,-1,-2,3,-4] => [-4,3,-2,-1,5] => 10110 => 11100
[5,-1,-2,-3,4] => [4,-3,-2,-1,5] => 01110 => 10110
[5,-1,-2,-3,-4] => [-4,-3,-2,-1,5] => 11110 => 11110
[-5,1,2,3,4] => [4,3,2,1,-5] => 00001 => 10000
[-5,1,2,3,-4] => [-4,3,2,1,-5] => 10001 => 10010
[-5,1,2,-3,4] => [4,-3,2,1,-5] => 01001 => 11000
[-5,1,2,-3,-4] => [-4,-3,2,1,-5] => 11001 => 10110
[-5,1,-2,3,4] => [4,3,-2,1,-5] => 00101 => 11000
[-5,1,-2,3,-4] => [-4,3,-2,1,-5] => 10101 => 11100
[-5,1,-2,-3,4] => [4,-3,-2,1,-5] => 01101 => 11100
[-5,1,-2,-3,-4] => [-4,-3,-2,1,-5] => 11101 => 11110
[-5,-1,2,3,4] => [4,3,2,-1,-5] => 00011 => 10010
[-5,-1,2,3,-4] => [-4,3,2,-1,-5] => 10011 => 10110
[-5,-1,2,-3,4] => [4,-3,2,-1,-5] => 01011 => 11100
[-5,-1,2,-3,-4] => [-4,-3,2,-1,-5] => 11011 => 11110
[-5,-1,-2,3,4] => [4,3,-2,-1,-5] => 00111 => 10110
[-5,-1,-2,3,-4] => [-4,3,-2,-1,-5] => 10111 => 11110
[-5,-1,-2,-3,4] => [4,-3,-2,-1,-5] => 01111 => 11110
[-5,-1,-2,-3,-4] => [-4,-3,-2,-1,-5] => 11111 => 11111
[5,1,2,4,3] => [3,4,2,1,5] => 00000 => 00000
[5,1,2,4,-3] => [-3,4,2,1,5] => 10000 => 10000
[5,1,2,-4,3] => [3,-4,2,1,5] => 01000 => 10000
[5,1,2,-4,-3] => [-3,-4,2,1,5] => 11000 => 10010
[5,1,-2,4,3] => [3,4,-2,1,5] => 00100 => 10000
[5,1,-2,4,-3] => [-3,4,-2,1,5] => 10100 => 11000
[5,1,-2,-4,3] => [3,-4,-2,1,5] => 01100 => 10010
[5,1,-2,-4,-3] => [-3,-4,-2,1,5] => 11100 => 10110
[5,-1,2,4,3] => [3,4,2,-1,5] => 00010 => 10000
[5,-1,2,4,-3] => [-3,4,2,-1,5] => 10010 => 11000
[5,-1,2,-4,3] => [3,-4,2,-1,5] => 01010 => 11000
[5,-1,2,-4,-3] => [-3,-4,2,-1,5] => 11010 => 11100
[5,-1,-2,4,3] => [3,4,-2,-1,5] => 00110 => 10010
[5,-1,-2,4,-3] => [-3,4,-2,-1,5] => 10110 => 11100
[5,-1,-2,-4,3] => [3,-4,-2,-1,5] => 01110 => 10110
[5,-1,-2,-4,-3] => [-3,-4,-2,-1,5] => 11110 => 11110
[-5,1,2,4,3] => [3,4,2,1,-5] => 00001 => 10000
[-5,1,2,4,-3] => [-3,4,2,1,-5] => 10001 => 10010
[-5,1,2,-4,3] => [3,-4,2,1,-5] => 01001 => 11000
[-5,1,2,-4,-3] => [-3,-4,2,1,-5] => 11001 => 10110
[-5,1,-2,4,3] => [3,4,-2,1,-5] => 00101 => 11000
[-5,1,-2,4,-3] => [-3,4,-2,1,-5] => 10101 => 11100
[-5,1,-2,-4,3] => [3,-4,-2,1,-5] => 01101 => 11100
[-5,1,-2,-4,-3] => [-3,-4,-2,1,-5] => 11101 => 11110
[-5,-1,2,4,3] => [3,4,2,-1,-5] => 00011 => 10010
[-5,-1,2,4,-3] => [-3,4,2,-1,-5] => 10011 => 10110
[-5,-1,2,-4,3] => [3,-4,2,-1,-5] => 01011 => 11100
[-5,-1,2,-4,-3] => [-3,-4,2,-1,-5] => 11011 => 11110
[-5,-1,-2,4,3] => [3,4,-2,-1,-5] => 00111 => 10110
[-5,-1,-2,4,-3] => [-3,4,-2,-1,-5] => 10111 => 11110
[-5,-1,-2,-4,3] => [3,-4,-2,-1,-5] => 01111 => 11110
[-5,-1,-2,-4,-3] => [-3,-4,-2,-1,-5] => 11111 => 11111
[5,1,3,2,4] => [4,2,3,1,5] => 00000 => 00000
[5,1,3,2,-4] => [-4,2,3,1,5] => 10000 => 10000
[5,1,3,-2,4] => [4,-2,3,1,5] => 01000 => 10000
[5,1,3,-2,-4] => [-4,-2,3,1,5] => 11000 => 10010
[5,1,-3,2,4] => [4,2,-3,1,5] => 00100 => 10000
[5,1,-3,2,-4] => [-4,2,-3,1,5] => 10100 => 11000
[5,1,-3,-2,4] => [4,-2,-3,1,5] => 01100 => 10010
[5,1,-3,-2,-4] => [-4,-2,-3,1,5] => 11100 => 10110
[5,-1,3,2,4] => [4,2,3,-1,5] => 00010 => 10000
[5,-1,3,2,-4] => [-4,2,3,-1,5] => 10010 => 11000
[5,-1,3,-2,4] => [4,-2,3,-1,5] => 01010 => 11000
[5,-1,3,-2,-4] => [-4,-2,3,-1,5] => 11010 => 11100
[5,-1,-3,2,4] => [4,2,-3,-1,5] => 00110 => 10010
[5,-1,-3,2,-4] => [-4,2,-3,-1,5] => 10110 => 11100
[5,-1,-3,-2,4] => [4,-2,-3,-1,5] => 01110 => 10110
[5,-1,-3,-2,-4] => [-4,-2,-3,-1,5] => 11110 => 11110
[-5,1,3,2,4] => [4,2,3,1,-5] => 00001 => 10000
[-5,1,3,2,-4] => [-4,2,3,1,-5] => 10001 => 10010
[-5,1,3,-2,4] => [4,-2,3,1,-5] => 01001 => 11000
[-5,1,3,-2,-4] => [-4,-2,3,1,-5] => 11001 => 10110
[-5,1,-3,2,4] => [4,2,-3,1,-5] => 00101 => 11000
[-5,1,-3,2,-4] => [-4,2,-3,1,-5] => 10101 => 11100
[-5,1,-3,-2,4] => [4,-2,-3,1,-5] => 01101 => 11100
[-5,1,-3,-2,-4] => [-4,-2,-3,1,-5] => 11101 => 11110
[-5,-1,3,2,4] => [4,2,3,-1,-5] => 00011 => 10010
[-5,-1,3,2,-4] => [-4,2,3,-1,-5] => 10011 => 10110
[-5,-1,3,-2,4] => [4,-2,3,-1,-5] => 01011 => 11100
[-5,-1,3,-2,-4] => [-4,-2,3,-1,-5] => 11011 => 11110
[-5,-1,-3,2,4] => [4,2,-3,-1,-5] => 00111 => 10110
[-5,-1,-3,2,-4] => [-4,2,-3,-1,-5] => 10111 => 11110
[-5,-1,-3,-2,4] => [4,-2,-3,-1,-5] => 01111 => 11110
[-5,-1,-3,-2,-4] => [-4,-2,-3,-1,-5] => 11111 => 11111
[5,1,3,4,2] => [2,4,3,1,5] => 00000 => 00000
[5,1,3,4,-2] => [-2,4,3,1,5] => 10000 => 10000
[5,1,3,-4,2] => [2,-4,3,1,5] => 01000 => 10000
[5,1,3,-4,-2] => [-2,-4,3,1,5] => 11000 => 10010
[5,1,-3,4,2] => [2,4,-3,1,5] => 00100 => 10000
[5,1,-3,4,-2] => [-2,4,-3,1,5] => 10100 => 11000
[5,1,-3,-4,2] => [2,-4,-3,1,5] => 01100 => 10010
[5,1,-3,-4,-2] => [-2,-4,-3,1,5] => 11100 => 10110
[5,-1,3,4,2] => [2,4,3,-1,5] => 00010 => 10000
[5,-1,3,4,-2] => [-2,4,3,-1,5] => 10010 => 11000
[5,-1,3,-4,2] => [2,-4,3,-1,5] => 01010 => 11000
[5,-1,3,-4,-2] => [-2,-4,3,-1,5] => 11010 => 11100
[5,-1,-3,4,2] => [2,4,-3,-1,5] => 00110 => 10010
[5,-1,-3,4,-2] => [-2,4,-3,-1,5] => 10110 => 11100
[5,-1,-3,-4,2] => [2,-4,-3,-1,5] => 01110 => 10110
[5,-1,-3,-4,-2] => [-2,-4,-3,-1,5] => 11110 => 11110
[-5,1,3,4,2] => [2,4,3,1,-5] => 00001 => 10000
[-5,1,3,4,-2] => [-2,4,3,1,-5] => 10001 => 10010
[-5,1,3,-4,2] => [2,-4,3,1,-5] => 01001 => 11000
[-5,1,3,-4,-2] => [-2,-4,3,1,-5] => 11001 => 10110
[-5,1,-3,4,2] => [2,4,-3,1,-5] => 00101 => 11000
[-5,1,-3,4,-2] => [-2,4,-3,1,-5] => 10101 => 11100
[-5,1,-3,-4,2] => [2,-4,-3,1,-5] => 01101 => 11100
[-5,1,-3,-4,-2] => [-2,-4,-3,1,-5] => 11101 => 11110
[-5,-1,3,4,2] => [2,4,3,-1,-5] => 00011 => 10010
[-5,-1,3,4,-2] => [-2,4,3,-1,-5] => 10011 => 10110
[-5,-1,3,-4,2] => [2,-4,3,-1,-5] => 01011 => 11100
[-5,-1,3,-4,-2] => [-2,-4,3,-1,-5] => 11011 => 11110
[-5,-1,-3,4,2] => [2,4,-3,-1,-5] => 00111 => 10110
[-5,-1,-3,4,-2] => [-2,4,-3,-1,-5] => 10111 => 11110
[-5,-1,-3,-4,2] => [2,-4,-3,-1,-5] => 01111 => 11110
[-5,-1,-3,-4,-2] => [-2,-4,-3,-1,-5] => 11111 => 11111
[5,1,4,2,3] => [3,2,4,1,5] => 00000 => 00000
[5,1,4,2,-3] => [-3,2,4,1,5] => 10000 => 10000
[5,1,4,-2,3] => [3,-2,4,1,5] => 01000 => 10000
[5,1,4,-2,-3] => [-3,-2,4,1,5] => 11000 => 10010
[5,1,-4,2,3] => [3,2,-4,1,5] => 00100 => 10000
[5,1,-4,2,-3] => [-3,2,-4,1,5] => 10100 => 11000
[5,1,-4,-2,3] => [3,-2,-4,1,5] => 01100 => 10010
[5,1,-4,-2,-3] => [-3,-2,-4,1,5] => 11100 => 10110
[5,-1,4,2,3] => [3,2,4,-1,5] => 00010 => 10000
[5,-1,4,2,-3] => [-3,2,4,-1,5] => 10010 => 11000
[5,-1,4,-2,3] => [3,-2,4,-1,5] => 01010 => 11000
[5,-1,4,-2,-3] => [-3,-2,4,-1,5] => 11010 => 11100
[5,-1,-4,2,3] => [3,2,-4,-1,5] => 00110 => 10010
[5,-1,-4,2,-3] => [-3,2,-4,-1,5] => 10110 => 11100
[5,-1,-4,-2,3] => [3,-2,-4,-1,5] => 01110 => 10110
[5,-1,-4,-2,-3] => [-3,-2,-4,-1,5] => 11110 => 11110
[-5,1,4,2,3] => [3,2,4,1,-5] => 00001 => 10000
[-5,1,4,2,-3] => [-3,2,4,1,-5] => 10001 => 10010
[-5,1,4,-2,3] => [3,-2,4,1,-5] => 01001 => 11000
[-5,1,4,-2,-3] => [-3,-2,4,1,-5] => 11001 => 10110
[-5,1,-4,2,3] => [3,2,-4,1,-5] => 00101 => 11000
[-5,1,-4,2,-3] => [-3,2,-4,1,-5] => 10101 => 11100
[-5,1,-4,-2,3] => [3,-2,-4,1,-5] => 01101 => 11100
[-5,1,-4,-2,-3] => [-3,-2,-4,1,-5] => 11101 => 11110
[-5,-1,4,2,3] => [3,2,4,-1,-5] => 00011 => 10010
[-5,-1,4,2,-3] => [-3,2,4,-1,-5] => 10011 => 10110
[-5,-1,4,-2,3] => [3,-2,4,-1,-5] => 01011 => 11100
[-5,-1,4,-2,-3] => [-3,-2,4,-1,-5] => 11011 => 11110
[-5,-1,-4,2,3] => [3,2,-4,-1,-5] => 00111 => 10110
[-5,-1,-4,2,-3] => [-3,2,-4,-1,-5] => 10111 => 11110
[-5,-1,-4,-2,3] => [3,-2,-4,-1,-5] => 01111 => 11110
[-5,-1,-4,-2,-3] => [-3,-2,-4,-1,-5] => 11111 => 11111
[5,1,4,3,2] => [2,3,4,1,5] => 00000 => 00000
[5,1,4,3,-2] => [-2,3,4,1,5] => 10000 => 10000
[5,1,4,-3,2] => [2,-3,4,1,5] => 01000 => 10000
[5,1,4,-3,-2] => [-2,-3,4,1,5] => 11000 => 10010
[5,1,-4,3,2] => [2,3,-4,1,5] => 00100 => 10000
[5,1,-4,3,-2] => [-2,3,-4,1,5] => 10100 => 11000
[5,1,-4,-3,2] => [2,-3,-4,1,5] => 01100 => 10010
[5,1,-4,-3,-2] => [-2,-3,-4,1,5] => 11100 => 10110
[5,-1,4,3,2] => [2,3,4,-1,5] => 00010 => 10000
[5,-1,4,3,-2] => [-2,3,4,-1,5] => 10010 => 11000
[5,-1,4,-3,2] => [2,-3,4,-1,5] => 01010 => 11000
[5,-1,4,-3,-2] => [-2,-3,4,-1,5] => 11010 => 11100
[5,-1,-4,3,2] => [2,3,-4,-1,5] => 00110 => 10010
[5,-1,-4,3,-2] => [-2,3,-4,-1,5] => 10110 => 11100
[5,-1,-4,-3,2] => [2,-3,-4,-1,5] => 01110 => 10110
[5,-1,-4,-3,-2] => [-2,-3,-4,-1,5] => 11110 => 11110
[-5,1,4,3,2] => [2,3,4,1,-5] => 00001 => 10000
[-5,1,4,3,-2] => [-2,3,4,1,-5] => 10001 => 10010
[-5,1,4,-3,2] => [2,-3,4,1,-5] => 01001 => 11000
[-5,1,4,-3,-2] => [-2,-3,4,1,-5] => 11001 => 10110
[-5,1,-4,3,2] => [2,3,-4,1,-5] => 00101 => 11000
[-5,1,-4,3,-2] => [-2,3,-4,1,-5] => 10101 => 11100
[-5,1,-4,-3,2] => [2,-3,-4,1,-5] => 01101 => 11100
[-5,1,-4,-3,-2] => [-2,-3,-4,1,-5] => 11101 => 11110
[-5,-1,4,3,2] => [2,3,4,-1,-5] => 00011 => 10010
[-5,-1,4,3,-2] => [-2,3,4,-1,-5] => 10011 => 10110
[-5,-1,4,-3,2] => [2,-3,4,-1,-5] => 01011 => 11100
[-5,-1,4,-3,-2] => [-2,-3,4,-1,-5] => 11011 => 11110
[-5,-1,-4,3,2] => [2,3,-4,-1,-5] => 00111 => 10110
[-5,-1,-4,3,-2] => [-2,3,-4,-1,-5] => 10111 => 11110
[-5,-1,-4,-3,2] => [2,-3,-4,-1,-5] => 01111 => 11110
[-5,-1,-4,-3,-2] => [-2,-3,-4,-1,-5] => 11111 => 11111
[5,2,1,3,4] => [4,3,1,2,5] => 00000 => 00000
[5,2,1,3,-4] => [-4,3,1,2,5] => 10000 => 10000
[5,2,1,-3,4] => [4,-3,1,2,5] => 01000 => 10000
[5,2,1,-3,-4] => [-4,-3,1,2,5] => 11000 => 10010
[5,2,-1,3,4] => [4,3,-1,2,5] => 00100 => 10000
[5,2,-1,3,-4] => [-4,3,-1,2,5] => 10100 => 11000
[5,2,-1,-3,4] => [4,-3,-1,2,5] => 01100 => 10010
[5,2,-1,-3,-4] => [-4,-3,-1,2,5] => 11100 => 10110
[5,-2,1,3,4] => [4,3,1,-2,5] => 00010 => 10000
[5,-2,1,3,-4] => [-4,3,1,-2,5] => 10010 => 11000
[5,-2,1,-3,4] => [4,-3,1,-2,5] => 01010 => 11000
[5,-2,1,-3,-4] => [-4,-3,1,-2,5] => 11010 => 11100
[5,-2,-1,3,4] => [4,3,-1,-2,5] => 00110 => 10010
[5,-2,-1,3,-4] => [-4,3,-1,-2,5] => 10110 => 11100
[5,-2,-1,-3,4] => [4,-3,-1,-2,5] => 01110 => 10110
[5,-2,-1,-3,-4] => [-4,-3,-1,-2,5] => 11110 => 11110
[-5,2,1,3,4] => [4,3,1,2,-5] => 00001 => 10000
[-5,2,1,3,-4] => [-4,3,1,2,-5] => 10001 => 10010
[-5,2,1,-3,4] => [4,-3,1,2,-5] => 01001 => 11000
[-5,2,1,-3,-4] => [-4,-3,1,2,-5] => 11001 => 10110
[-5,2,-1,3,4] => [4,3,-1,2,-5] => 00101 => 11000
[-5,2,-1,3,-4] => [-4,3,-1,2,-5] => 10101 => 11100
[-5,2,-1,-3,4] => [4,-3,-1,2,-5] => 01101 => 11100
[-5,2,-1,-3,-4] => [-4,-3,-1,2,-5] => 11101 => 11110
[-5,-2,1,3,4] => [4,3,1,-2,-5] => 00011 => 10010
[-5,-2,1,3,-4] => [-4,3,1,-2,-5] => 10011 => 10110
[-5,-2,1,-3,4] => [4,-3,1,-2,-5] => 01011 => 11100
[-5,-2,1,-3,-4] => [-4,-3,1,-2,-5] => 11011 => 11110
[-5,-2,-1,3,4] => [4,3,-1,-2,-5] => 00111 => 10110
[-5,-2,-1,3,-4] => [-4,3,-1,-2,-5] => 10111 => 11110
[-5,-2,-1,-3,4] => [4,-3,-1,-2,-5] => 01111 => 11110
[-5,-2,-1,-3,-4] => [-4,-3,-1,-2,-5] => 11111 => 11111
[5,2,1,4,3] => [3,4,1,2,5] => 00000 => 00000
[5,2,1,4,-3] => [-3,4,1,2,5] => 10000 => 10000
[5,2,1,-4,3] => [3,-4,1,2,5] => 01000 => 10000
[5,2,1,-4,-3] => [-3,-4,1,2,5] => 11000 => 10010
[5,2,-1,4,3] => [3,4,-1,2,5] => 00100 => 10000
[5,2,-1,4,-3] => [-3,4,-1,2,5] => 10100 => 11000
[5,2,-1,-4,3] => [3,-4,-1,2,5] => 01100 => 10010
[5,2,-1,-4,-3] => [-3,-4,-1,2,5] => 11100 => 10110
[5,-2,1,4,3] => [3,4,1,-2,5] => 00010 => 10000
[5,-2,1,4,-3] => [-3,4,1,-2,5] => 10010 => 11000
[5,-2,1,-4,3] => [3,-4,1,-2,5] => 01010 => 11000
[5,-2,1,-4,-3] => [-3,-4,1,-2,5] => 11010 => 11100
[5,-2,-1,4,3] => [3,4,-1,-2,5] => 00110 => 10010
[5,-2,-1,4,-3] => [-3,4,-1,-2,5] => 10110 => 11100
[5,-2,-1,-4,3] => [3,-4,-1,-2,5] => 01110 => 10110
[5,-2,-1,-4,-3] => [-3,-4,-1,-2,5] => 11110 => 11110
[-5,2,1,4,3] => [3,4,1,2,-5] => 00001 => 10000
[-5,2,1,4,-3] => [-3,4,1,2,-5] => 10001 => 10010
[-5,2,1,-4,3] => [3,-4,1,2,-5] => 01001 => 11000
[-5,2,1,-4,-3] => [-3,-4,1,2,-5] => 11001 => 10110
[-5,2,-1,4,3] => [3,4,-1,2,-5] => 00101 => 11000
[-5,2,-1,4,-3] => [-3,4,-1,2,-5] => 10101 => 11100
[-5,2,-1,-4,3] => [3,-4,-1,2,-5] => 01101 => 11100
[-5,2,-1,-4,-3] => [-3,-4,-1,2,-5] => 11101 => 11110
[-5,-2,1,4,3] => [3,4,1,-2,-5] => 00011 => 10010
[-5,-2,1,4,-3] => [-3,4,1,-2,-5] => 10011 => 10110
[-5,-2,1,-4,3] => [3,-4,1,-2,-5] => 01011 => 11100
[-5,-2,1,-4,-3] => [-3,-4,1,-2,-5] => 11011 => 11110
[-5,-2,-1,4,3] => [3,4,-1,-2,-5] => 00111 => 10110
[-5,-2,-1,4,-3] => [-3,4,-1,-2,-5] => 10111 => 11110
[-5,-2,-1,-4,3] => [3,-4,-1,-2,-5] => 01111 => 11110
[-5,-2,-1,-4,-3] => [-3,-4,-1,-2,-5] => 11111 => 11111
[5,2,3,1,4] => [4,1,3,2,5] => 00000 => 00000
[5,2,3,1,-4] => [-4,1,3,2,5] => 10000 => 10000
[5,2,3,-1,4] => [4,-1,3,2,5] => 01000 => 10000
[5,2,3,-1,-4] => [-4,-1,3,2,5] => 11000 => 10010
[5,2,-3,1,4] => [4,1,-3,2,5] => 00100 => 10000
[5,2,-3,1,-4] => [-4,1,-3,2,5] => 10100 => 11000
[5,2,-3,-1,4] => [4,-1,-3,2,5] => 01100 => 10010
[5,2,-3,-1,-4] => [-4,-1,-3,2,5] => 11100 => 10110
[5,-2,3,1,4] => [4,1,3,-2,5] => 00010 => 10000
[5,-2,3,1,-4] => [-4,1,3,-2,5] => 10010 => 11000
[5,-2,3,-1,4] => [4,-1,3,-2,5] => 01010 => 11000
[5,-2,3,-1,-4] => [-4,-1,3,-2,5] => 11010 => 11100
[5,-2,-3,1,4] => [4,1,-3,-2,5] => 00110 => 10010
[5,-2,-3,1,-4] => [-4,1,-3,-2,5] => 10110 => 11100
[5,-2,-3,-1,4] => [4,-1,-3,-2,5] => 01110 => 10110
[5,-2,-3,-1,-4] => [-4,-1,-3,-2,5] => 11110 => 11110
[-5,2,3,1,4] => [4,1,3,2,-5] => 00001 => 10000
[-5,2,3,1,-4] => [-4,1,3,2,-5] => 10001 => 10010
[-5,2,3,-1,4] => [4,-1,3,2,-5] => 01001 => 11000
[-5,2,3,-1,-4] => [-4,-1,3,2,-5] => 11001 => 10110
[-5,2,-3,1,4] => [4,1,-3,2,-5] => 00101 => 11000
[-5,2,-3,1,-4] => [-4,1,-3,2,-5] => 10101 => 11100
[-5,2,-3,-1,4] => [4,-1,-3,2,-5] => 01101 => 11100
[-5,2,-3,-1,-4] => [-4,-1,-3,2,-5] => 11101 => 11110
[-5,-2,3,1,4] => [4,1,3,-2,-5] => 00011 => 10010
[-5,-2,3,1,-4] => [-4,1,3,-2,-5] => 10011 => 10110
[-5,-2,3,-1,4] => [4,-1,3,-2,-5] => 01011 => 11100
[-5,-2,3,-1,-4] => [-4,-1,3,-2,-5] => 11011 => 11110
[-5,-2,-3,1,4] => [4,1,-3,-2,-5] => 00111 => 10110
[-5,-2,-3,1,-4] => [-4,1,-3,-2,-5] => 10111 => 11110
[-5,-2,-3,-1,4] => [4,-1,-3,-2,-5] => 01111 => 11110
[-5,-2,-3,-1,-4] => [-4,-1,-3,-2,-5] => 11111 => 11111
[5,2,3,4,1] => [1,4,3,2,5] => 00000 => 00000
[5,2,3,4,-1] => [-1,4,3,2,5] => 10000 => 10000
[5,2,3,-4,1] => [1,-4,3,2,5] => 01000 => 10000
[5,2,3,-4,-1] => [-1,-4,3,2,5] => 11000 => 10010
[5,2,-3,4,1] => [1,4,-3,2,5] => 00100 => 10000
[5,2,-3,4,-1] => [-1,4,-3,2,5] => 10100 => 11000
[5,2,-3,-4,1] => [1,-4,-3,2,5] => 01100 => 10010
[5,2,-3,-4,-1] => [-1,-4,-3,2,5] => 11100 => 10110
[5,-2,3,4,1] => [1,4,3,-2,5] => 00010 => 10000
[5,-2,3,4,-1] => [-1,4,3,-2,5] => 10010 => 11000
[5,-2,3,-4,1] => [1,-4,3,-2,5] => 01010 => 11000
[5,-2,3,-4,-1] => [-1,-4,3,-2,5] => 11010 => 11100
[5,-2,-3,4,1] => [1,4,-3,-2,5] => 00110 => 10010
[5,-2,-3,4,-1] => [-1,4,-3,-2,5] => 10110 => 11100
[5,-2,-3,-4,1] => [1,-4,-3,-2,5] => 01110 => 10110
[5,-2,-3,-4,-1] => [-1,-4,-3,-2,5] => 11110 => 11110
[-5,2,3,4,1] => [1,4,3,2,-5] => 00001 => 10000
[-5,2,3,4,-1] => [-1,4,3,2,-5] => 10001 => 10010
[-5,2,3,-4,1] => [1,-4,3,2,-5] => 01001 => 11000
[-5,2,3,-4,-1] => [-1,-4,3,2,-5] => 11001 => 10110
[-5,2,-3,4,1] => [1,4,-3,2,-5] => 00101 => 11000
[-5,2,-3,4,-1] => [-1,4,-3,2,-5] => 10101 => 11100
[-5,2,-3,-4,1] => [1,-4,-3,2,-5] => 01101 => 11100
[-5,2,-3,-4,-1] => [-1,-4,-3,2,-5] => 11101 => 11110
[-5,-2,3,4,1] => [1,4,3,-2,-5] => 00011 => 10010
[-5,-2,3,4,-1] => [-1,4,3,-2,-5] => 10011 => 10110
[-5,-2,3,-4,1] => [1,-4,3,-2,-5] => 01011 => 11100
[-5,-2,3,-4,-1] => [-1,-4,3,-2,-5] => 11011 => 11110
[-5,-2,-3,4,1] => [1,4,-3,-2,-5] => 00111 => 10110
[-5,-2,-3,4,-1] => [-1,4,-3,-2,-5] => 10111 => 11110
[-5,-2,-3,-4,1] => [1,-4,-3,-2,-5] => 01111 => 11110
[-5,-2,-3,-4,-1] => [-1,-4,-3,-2,-5] => 11111 => 11111
[5,2,4,1,3] => [3,1,4,2,5] => 00000 => 00000
[5,2,4,1,-3] => [-3,1,4,2,5] => 10000 => 10000
[5,2,4,-1,3] => [3,-1,4,2,5] => 01000 => 10000
[5,2,4,-1,-3] => [-3,-1,4,2,5] => 11000 => 10010
[5,2,-4,1,3] => [3,1,-4,2,5] => 00100 => 10000
[5,2,-4,1,-3] => [-3,1,-4,2,5] => 10100 => 11000
[5,2,-4,-1,3] => [3,-1,-4,2,5] => 01100 => 10010
[5,2,-4,-1,-3] => [-3,-1,-4,2,5] => 11100 => 10110
[5,-2,4,1,3] => [3,1,4,-2,5] => 00010 => 10000
[5,-2,4,1,-3] => [-3,1,4,-2,5] => 10010 => 11000
[5,-2,4,-1,3] => [3,-1,4,-2,5] => 01010 => 11000
[5,-2,4,-1,-3] => [-3,-1,4,-2,5] => 11010 => 11100
[5,-2,-4,1,3] => [3,1,-4,-2,5] => 00110 => 10010
[5,-2,-4,1,-3] => [-3,1,-4,-2,5] => 10110 => 11100
[5,-2,-4,-1,3] => [3,-1,-4,-2,5] => 01110 => 10110
[5,-2,-4,-1,-3] => [-3,-1,-4,-2,5] => 11110 => 11110
[-5,2,4,1,3] => [3,1,4,2,-5] => 00001 => 10000
[-5,2,4,1,-3] => [-3,1,4,2,-5] => 10001 => 10010
[-5,2,4,-1,3] => [3,-1,4,2,-5] => 01001 => 11000
[-5,2,4,-1,-3] => [-3,-1,4,2,-5] => 11001 => 10110
[-5,2,-4,1,3] => [3,1,-4,2,-5] => 00101 => 11000
[-5,2,-4,1,-3] => [-3,1,-4,2,-5] => 10101 => 11100
[-5,2,-4,-1,3] => [3,-1,-4,2,-5] => 01101 => 11100
[-5,2,-4,-1,-3] => [-3,-1,-4,2,-5] => 11101 => 11110
[-5,-2,4,1,3] => [3,1,4,-2,-5] => 00011 => 10010
[-5,-2,4,1,-3] => [-3,1,4,-2,-5] => 10011 => 10110
[-5,-2,4,-1,3] => [3,-1,4,-2,-5] => 01011 => 11100
[-5,-2,4,-1,-3] => [-3,-1,4,-2,-5] => 11011 => 11110
[-5,-2,-4,1,3] => [3,1,-4,-2,-5] => 00111 => 10110
[-5,-2,-4,1,-3] => [-3,1,-4,-2,-5] => 10111 => 11110
[-5,-2,-4,-1,3] => [3,-1,-4,-2,-5] => 01111 => 11110
[-5,-2,-4,-1,-3] => [-3,-1,-4,-2,-5] => 11111 => 11111
[5,2,4,3,1] => [1,3,4,2,5] => 00000 => 00000
[5,2,4,3,-1] => [-1,3,4,2,5] => 10000 => 10000
[5,2,4,-3,1] => [1,-3,4,2,5] => 01000 => 10000
[5,2,4,-3,-1] => [-1,-3,4,2,5] => 11000 => 10010
[5,2,-4,3,1] => [1,3,-4,2,5] => 00100 => 10000
[5,2,-4,3,-1] => [-1,3,-4,2,5] => 10100 => 11000
[5,2,-4,-3,1] => [1,-3,-4,2,5] => 01100 => 10010
[5,2,-4,-3,-1] => [-1,-3,-4,2,5] => 11100 => 10110
[5,-2,4,3,1] => [1,3,4,-2,5] => 00010 => 10000
[5,-2,4,3,-1] => [-1,3,4,-2,5] => 10010 => 11000
[5,-2,4,-3,1] => [1,-3,4,-2,5] => 01010 => 11000
[5,-2,4,-3,-1] => [-1,-3,4,-2,5] => 11010 => 11100
[5,-2,-4,3,1] => [1,3,-4,-2,5] => 00110 => 10010
[5,-2,-4,3,-1] => [-1,3,-4,-2,5] => 10110 => 11100
[5,-2,-4,-3,1] => [1,-3,-4,-2,5] => 01110 => 10110
[5,-2,-4,-3,-1] => [-1,-3,-4,-2,5] => 11110 => 11110
[-5,2,4,3,1] => [1,3,4,2,-5] => 00001 => 10000
[-5,2,4,3,-1] => [-1,3,4,2,-5] => 10001 => 10010
[-5,2,4,-3,1] => [1,-3,4,2,-5] => 01001 => 11000
[-5,2,4,-3,-1] => [-1,-3,4,2,-5] => 11001 => 10110
[-5,2,-4,3,1] => [1,3,-4,2,-5] => 00101 => 11000
[-5,2,-4,3,-1] => [-1,3,-4,2,-5] => 10101 => 11100
[-5,2,-4,-3,1] => [1,-3,-4,2,-5] => 01101 => 11100
[-5,2,-4,-3,-1] => [-1,-3,-4,2,-5] => 11101 => 11110
[-5,-2,4,3,1] => [1,3,4,-2,-5] => 00011 => 10010
[-5,-2,4,3,-1] => [-1,3,4,-2,-5] => 10011 => 10110
[-5,-2,4,-3,1] => [1,-3,4,-2,-5] => 01011 => 11100
[-5,-2,4,-3,-1] => [-1,-3,4,-2,-5] => 11011 => 11110
[-5,-2,-4,3,1] => [1,3,-4,-2,-5] => 00111 => 10110
[-5,-2,-4,3,-1] => [-1,3,-4,-2,-5] => 10111 => 11110
[-5,-2,-4,-3,1] => [1,-3,-4,-2,-5] => 01111 => 11110
[-5,-2,-4,-3,-1] => [-1,-3,-4,-2,-5] => 11111 => 11111
[5,3,1,2,4] => [4,2,1,3,5] => 00000 => 00000
[5,3,1,2,-4] => [-4,2,1,3,5] => 10000 => 10000
[5,3,1,-2,4] => [4,-2,1,3,5] => 01000 => 10000
[5,3,1,-2,-4] => [-4,-2,1,3,5] => 11000 => 10010
[5,3,-1,2,4] => [4,2,-1,3,5] => 00100 => 10000
[5,3,-1,2,-4] => [-4,2,-1,3,5] => 10100 => 11000
[5,3,-1,-2,4] => [4,-2,-1,3,5] => 01100 => 10010
[5,3,-1,-2,-4] => [-4,-2,-1,3,5] => 11100 => 10110
[5,-3,1,2,4] => [4,2,1,-3,5] => 00010 => 10000
[5,-3,1,2,-4] => [-4,2,1,-3,5] => 10010 => 11000
[5,-3,1,-2,4] => [4,-2,1,-3,5] => 01010 => 11000
[5,-3,1,-2,-4] => [-4,-2,1,-3,5] => 11010 => 11100
[5,-3,-1,2,4] => [4,2,-1,-3,5] => 00110 => 10010
[5,-3,-1,2,-4] => [-4,2,-1,-3,5] => 10110 => 11100
[5,-3,-1,-2,4] => [4,-2,-1,-3,5] => 01110 => 10110
[5,-3,-1,-2,-4] => [-4,-2,-1,-3,5] => 11110 => 11110
[-5,3,1,2,4] => [4,2,1,3,-5] => 00001 => 10000
[-5,3,1,2,-4] => [-4,2,1,3,-5] => 10001 => 10010
[-5,3,1,-2,4] => [4,-2,1,3,-5] => 01001 => 11000
[-5,3,1,-2,-4] => [-4,-2,1,3,-5] => 11001 => 10110
[-5,3,-1,2,4] => [4,2,-1,3,-5] => 00101 => 11000
[-5,3,-1,2,-4] => [-4,2,-1,3,-5] => 10101 => 11100
[-5,3,-1,-2,4] => [4,-2,-1,3,-5] => 01101 => 11100
[-5,3,-1,-2,-4] => [-4,-2,-1,3,-5] => 11101 => 11110
[-5,-3,1,2,4] => [4,2,1,-3,-5] => 00011 => 10010
[-5,-3,1,2,-4] => [-4,2,1,-3,-5] => 10011 => 10110
[-5,-3,1,-2,4] => [4,-2,1,-3,-5] => 01011 => 11100
[-5,-3,1,-2,-4] => [-4,-2,1,-3,-5] => 11011 => 11110
[-5,-3,-1,2,4] => [4,2,-1,-3,-5] => 00111 => 10110
[-5,-3,-1,2,-4] => [-4,2,-1,-3,-5] => 10111 => 11110
[-5,-3,-1,-2,4] => [4,-2,-1,-3,-5] => 01111 => 11110
[-5,-3,-1,-2,-4] => [-4,-2,-1,-3,-5] => 11111 => 11111
[5,3,1,4,2] => [2,4,1,3,5] => 00000 => 00000
[5,3,1,4,-2] => [-2,4,1,3,5] => 10000 => 10000
[5,3,1,-4,2] => [2,-4,1,3,5] => 01000 => 10000
[5,3,1,-4,-2] => [-2,-4,1,3,5] => 11000 => 10010
[5,3,-1,4,2] => [2,4,-1,3,5] => 00100 => 10000
[5,3,-1,4,-2] => [-2,4,-1,3,5] => 10100 => 11000
[5,3,-1,-4,2] => [2,-4,-1,3,5] => 01100 => 10010
[5,3,-1,-4,-2] => [-2,-4,-1,3,5] => 11100 => 10110
[5,-3,1,4,2] => [2,4,1,-3,5] => 00010 => 10000
[5,-3,1,4,-2] => [-2,4,1,-3,5] => 10010 => 11000
[5,-3,1,-4,2] => [2,-4,1,-3,5] => 01010 => 11000
[5,-3,1,-4,-2] => [-2,-4,1,-3,5] => 11010 => 11100
[5,-3,-1,4,2] => [2,4,-1,-3,5] => 00110 => 10010
[5,-3,-1,4,-2] => [-2,4,-1,-3,5] => 10110 => 11100
[5,-3,-1,-4,2] => [2,-4,-1,-3,5] => 01110 => 10110
[5,-3,-1,-4,-2] => [-2,-4,-1,-3,5] => 11110 => 11110
[-5,3,1,4,2] => [2,4,1,3,-5] => 00001 => 10000
[-5,3,1,4,-2] => [-2,4,1,3,-5] => 10001 => 10010
[-5,3,1,-4,2] => [2,-4,1,3,-5] => 01001 => 11000
[-5,3,1,-4,-2] => [-2,-4,1,3,-5] => 11001 => 10110
[-5,3,-1,4,2] => [2,4,-1,3,-5] => 00101 => 11000
[-5,3,-1,4,-2] => [-2,4,-1,3,-5] => 10101 => 11100
[-5,3,-1,-4,2] => [2,-4,-1,3,-5] => 01101 => 11100
[-5,3,-1,-4,-2] => [-2,-4,-1,3,-5] => 11101 => 11110
[-5,-3,1,4,2] => [2,4,1,-3,-5] => 00011 => 10010
[-5,-3,1,4,-2] => [-2,4,1,-3,-5] => 10011 => 10110
[-5,-3,1,-4,2] => [2,-4,1,-3,-5] => 01011 => 11100
[-5,-3,1,-4,-2] => [-2,-4,1,-3,-5] => 11011 => 11110
[-5,-3,-1,4,2] => [2,4,-1,-3,-5] => 00111 => 10110
[-5,-3,-1,4,-2] => [-2,4,-1,-3,-5] => 10111 => 11110
[-5,-3,-1,-4,2] => [2,-4,-1,-3,-5] => 01111 => 11110
[-5,-3,-1,-4,-2] => [-2,-4,-1,-3,-5] => 11111 => 11111
[5,3,2,1,4] => [4,1,2,3,5] => 00000 => 00000
[5,3,2,1,-4] => [-4,1,2,3,5] => 10000 => 10000
[5,3,2,-1,4] => [4,-1,2,3,5] => 01000 => 10000
[5,3,2,-1,-4] => [-4,-1,2,3,5] => 11000 => 10010
[5,3,-2,1,4] => [4,1,-2,3,5] => 00100 => 10000
[5,3,-2,1,-4] => [-4,1,-2,3,5] => 10100 => 11000
[5,3,-2,-1,4] => [4,-1,-2,3,5] => 01100 => 10010
[5,3,-2,-1,-4] => [-4,-1,-2,3,5] => 11100 => 10110
[5,-3,2,1,4] => [4,1,2,-3,5] => 00010 => 10000
[5,-3,2,1,-4] => [-4,1,2,-3,5] => 10010 => 11000
[5,-3,2,-1,4] => [4,-1,2,-3,5] => 01010 => 11000
[5,-3,2,-1,-4] => [-4,-1,2,-3,5] => 11010 => 11100
[5,-3,-2,1,4] => [4,1,-2,-3,5] => 00110 => 10010
[5,-3,-2,1,-4] => [-4,1,-2,-3,5] => 10110 => 11100
[5,-3,-2,-1,4] => [4,-1,-2,-3,5] => 01110 => 10110
[5,-3,-2,-1,-4] => [-4,-1,-2,-3,5] => 11110 => 11110
[-5,3,2,1,4] => [4,1,2,3,-5] => 00001 => 10000
[-5,3,2,1,-4] => [-4,1,2,3,-5] => 10001 => 10010
[-5,3,2,-1,4] => [4,-1,2,3,-5] => 01001 => 11000
[-5,3,2,-1,-4] => [-4,-1,2,3,-5] => 11001 => 10110
[-5,3,-2,1,4] => [4,1,-2,3,-5] => 00101 => 11000
[-5,3,-2,1,-4] => [-4,1,-2,3,-5] => 10101 => 11100
[-5,3,-2,-1,4] => [4,-1,-2,3,-5] => 01101 => 11100
[-5,3,-2,-1,-4] => [-4,-1,-2,3,-5] => 11101 => 11110
[-5,-3,2,1,4] => [4,1,2,-3,-5] => 00011 => 10010
[-5,-3,2,1,-4] => [-4,1,2,-3,-5] => 10011 => 10110
[-5,-3,2,-1,4] => [4,-1,2,-3,-5] => 01011 => 11100
[-5,-3,2,-1,-4] => [-4,-1,2,-3,-5] => 11011 => 11110
[-5,-3,-2,1,4] => [4,1,-2,-3,-5] => 00111 => 10110
[-5,-3,-2,1,-4] => [-4,1,-2,-3,-5] => 10111 => 11110
[-5,-3,-2,-1,4] => [4,-1,-2,-3,-5] => 01111 => 11110
[-5,-3,-2,-1,-4] => [-4,-1,-2,-3,-5] => 11111 => 11111
[5,3,2,4,1] => [1,4,2,3,5] => 00000 => 00000
[5,3,2,4,-1] => [-1,4,2,3,5] => 10000 => 10000
[5,3,2,-4,1] => [1,-4,2,3,5] => 01000 => 10000
[5,3,2,-4,-1] => [-1,-4,2,3,5] => 11000 => 10010
[5,3,-2,4,1] => [1,4,-2,3,5] => 00100 => 10000
[5,3,-2,4,-1] => [-1,4,-2,3,5] => 10100 => 11000
[5,3,-2,-4,1] => [1,-4,-2,3,5] => 01100 => 10010
[5,3,-2,-4,-1] => [-1,-4,-2,3,5] => 11100 => 10110
[5,-3,2,4,1] => [1,4,2,-3,5] => 00010 => 10000
[5,-3,2,4,-1] => [-1,4,2,-3,5] => 10010 => 11000
[5,-3,2,-4,1] => [1,-4,2,-3,5] => 01010 => 11000
[5,-3,2,-4,-1] => [-1,-4,2,-3,5] => 11010 => 11100
[5,-3,-2,4,1] => [1,4,-2,-3,5] => 00110 => 10010
[5,-3,-2,4,-1] => [-1,4,-2,-3,5] => 10110 => 11100
[5,-3,-2,-4,1] => [1,-4,-2,-3,5] => 01110 => 10110
[5,-3,-2,-4,-1] => [-1,-4,-2,-3,5] => 11110 => 11110
[-5,3,2,4,1] => [1,4,2,3,-5] => 00001 => 10000
[-5,3,2,4,-1] => [-1,4,2,3,-5] => 10001 => 10010
[-5,3,2,-4,1] => [1,-4,2,3,-5] => 01001 => 11000
[-5,3,2,-4,-1] => [-1,-4,2,3,-5] => 11001 => 10110
[-5,3,-2,4,1] => [1,4,-2,3,-5] => 00101 => 11000
[-5,3,-2,4,-1] => [-1,4,-2,3,-5] => 10101 => 11100
[-5,3,-2,-4,1] => [1,-4,-2,3,-5] => 01101 => 11100
[-5,3,-2,-4,-1] => [-1,-4,-2,3,-5] => 11101 => 11110
[-5,-3,2,4,1] => [1,4,2,-3,-5] => 00011 => 10010
[-5,-3,2,4,-1] => [-1,4,2,-3,-5] => 10011 => 10110
[-5,-3,2,-4,1] => [1,-4,2,-3,-5] => 01011 => 11100
[-5,-3,2,-4,-1] => [-1,-4,2,-3,-5] => 11011 => 11110
[-5,-3,-2,4,1] => [1,4,-2,-3,-5] => 00111 => 10110
[-5,-3,-2,4,-1] => [-1,4,-2,-3,-5] => 10111 => 11110
[-5,-3,-2,-4,1] => [1,-4,-2,-3,-5] => 01111 => 11110
[-5,-3,-2,-4,-1] => [-1,-4,-2,-3,-5] => 11111 => 11111
[5,3,4,1,2] => [2,1,4,3,5] => 00000 => 00000
[5,3,4,1,-2] => [-2,1,4,3,5] => 10000 => 10000
[5,3,4,-1,2] => [2,-1,4,3,5] => 01000 => 10000
[5,3,4,-1,-2] => [-2,-1,4,3,5] => 11000 => 10010
[5,3,-4,1,2] => [2,1,-4,3,5] => 00100 => 10000
[5,3,-4,1,-2] => [-2,1,-4,3,5] => 10100 => 11000
[5,3,-4,-1,2] => [2,-1,-4,3,5] => 01100 => 10010
[5,3,-4,-1,-2] => [-2,-1,-4,3,5] => 11100 => 10110
[5,-3,4,1,2] => [2,1,4,-3,5] => 00010 => 10000
[5,-3,4,1,-2] => [-2,1,4,-3,5] => 10010 => 11000
[5,-3,4,-1,2] => [2,-1,4,-3,5] => 01010 => 11000
[5,-3,4,-1,-2] => [-2,-1,4,-3,5] => 11010 => 11100
[5,-3,-4,1,2] => [2,1,-4,-3,5] => 00110 => 10010
[5,-3,-4,1,-2] => [-2,1,-4,-3,5] => 10110 => 11100
[5,-3,-4,-1,2] => [2,-1,-4,-3,5] => 01110 => 10110
[5,-3,-4,-1,-2] => [-2,-1,-4,-3,5] => 11110 => 11110
[-5,3,4,1,2] => [2,1,4,3,-5] => 00001 => 10000
[-5,3,4,1,-2] => [-2,1,4,3,-5] => 10001 => 10010
[-5,3,4,-1,2] => [2,-1,4,3,-5] => 01001 => 11000
[-5,3,4,-1,-2] => [-2,-1,4,3,-5] => 11001 => 10110
[-5,3,-4,1,2] => [2,1,-4,3,-5] => 00101 => 11000
[-5,3,-4,1,-2] => [-2,1,-4,3,-5] => 10101 => 11100
[-5,3,-4,-1,2] => [2,-1,-4,3,-5] => 01101 => 11100
[-5,3,-4,-1,-2] => [-2,-1,-4,3,-5] => 11101 => 11110
[-5,-3,4,1,2] => [2,1,4,-3,-5] => 00011 => 10010
[-5,-3,4,1,-2] => [-2,1,4,-3,-5] => 10011 => 10110
[-5,-3,4,-1,2] => [2,-1,4,-3,-5] => 01011 => 11100
[-5,-3,4,-1,-2] => [-2,-1,4,-3,-5] => 11011 => 11110
[-5,-3,-4,1,2] => [2,1,-4,-3,-5] => 00111 => 10110
[-5,-3,-4,1,-2] => [-2,1,-4,-3,-5] => 10111 => 11110
[-5,-3,-4,-1,2] => [2,-1,-4,-3,-5] => 01111 => 11110
[-5,-3,-4,-1,-2] => [-2,-1,-4,-3,-5] => 11111 => 11111
[5,3,4,2,1] => [1,2,4,3,5] => 00000 => 00000
[5,3,4,2,-1] => [-1,2,4,3,5] => 10000 => 10000
[5,3,4,-2,1] => [1,-2,4,3,5] => 01000 => 10000
[5,3,4,-2,-1] => [-1,-2,4,3,5] => 11000 => 10010
[5,3,-4,2,1] => [1,2,-4,3,5] => 00100 => 10000
[5,3,-4,2,-1] => [-1,2,-4,3,5] => 10100 => 11000
[5,3,-4,-2,1] => [1,-2,-4,3,5] => 01100 => 10010
[5,3,-4,-2,-1] => [-1,-2,-4,3,5] => 11100 => 10110
[5,-3,4,2,1] => [1,2,4,-3,5] => 00010 => 10000
[5,-3,4,2,-1] => [-1,2,4,-3,5] => 10010 => 11000
[5,-3,4,-2,1] => [1,-2,4,-3,5] => 01010 => 11000
[5,-3,4,-2,-1] => [-1,-2,4,-3,5] => 11010 => 11100
[5,-3,-4,2,1] => [1,2,-4,-3,5] => 00110 => 10010
[5,-3,-4,2,-1] => [-1,2,-4,-3,5] => 10110 => 11100
[5,-3,-4,-2,1] => [1,-2,-4,-3,5] => 01110 => 10110
[5,-3,-4,-2,-1] => [-1,-2,-4,-3,5] => 11110 => 11110
[-5,3,4,2,1] => [1,2,4,3,-5] => 00001 => 10000
[-5,3,4,2,-1] => [-1,2,4,3,-5] => 10001 => 10010
[-5,3,4,-2,1] => [1,-2,4,3,-5] => 01001 => 11000
[-5,3,4,-2,-1] => [-1,-2,4,3,-5] => 11001 => 10110
[-5,3,-4,2,1] => [1,2,-4,3,-5] => 00101 => 11000
[-5,3,-4,2,-1] => [-1,2,-4,3,-5] => 10101 => 11100
[-5,3,-4,-2,1] => [1,-2,-4,3,-5] => 01101 => 11100
[-5,3,-4,-2,-1] => [-1,-2,-4,3,-5] => 11101 => 11110
[-5,-3,4,2,1] => [1,2,4,-3,-5] => 00011 => 10010
[-5,-3,4,2,-1] => [-1,2,4,-3,-5] => 10011 => 10110
[-5,-3,4,-2,1] => [1,-2,4,-3,-5] => 01011 => 11100
[-5,-3,4,-2,-1] => [-1,-2,4,-3,-5] => 11011 => 11110
[-5,-3,-4,2,1] => [1,2,-4,-3,-5] => 00111 => 10110
[-5,-3,-4,2,-1] => [-1,2,-4,-3,-5] => 10111 => 11110
[-5,-3,-4,-2,1] => [1,-2,-4,-3,-5] => 01111 => 11110
[-5,-3,-4,-2,-1] => [-1,-2,-4,-3,-5] => 11111 => 11111
[5,4,1,2,3] => [3,2,1,4,5] => 00000 => 00000
[5,4,1,2,-3] => [-3,2,1,4,5] => 10000 => 10000
[5,4,1,-2,3] => [3,-2,1,4,5] => 01000 => 10000
[5,4,1,-2,-3] => [-3,-2,1,4,5] => 11000 => 10010
[5,4,-1,2,3] => [3,2,-1,4,5] => 00100 => 10000
[5,4,-1,2,-3] => [-3,2,-1,4,5] => 10100 => 11000
[5,4,-1,-2,3] => [3,-2,-1,4,5] => 01100 => 10010
[5,4,-1,-2,-3] => [-3,-2,-1,4,5] => 11100 => 10110
[5,-4,1,2,3] => [3,2,1,-4,5] => 00010 => 10000
[5,-4,1,2,-3] => [-3,2,1,-4,5] => 10010 => 11000
[5,-4,1,-2,3] => [3,-2,1,-4,5] => 01010 => 11000
[5,-4,1,-2,-3] => [-3,-2,1,-4,5] => 11010 => 11100
[5,-4,-1,2,3] => [3,2,-1,-4,5] => 00110 => 10010
[5,-4,-1,2,-3] => [-3,2,-1,-4,5] => 10110 => 11100
[5,-4,-1,-2,3] => [3,-2,-1,-4,5] => 01110 => 10110
[5,-4,-1,-2,-3] => [-3,-2,-1,-4,5] => 11110 => 11110
[-5,4,1,2,3] => [3,2,1,4,-5] => 00001 => 10000
[-5,4,1,2,-3] => [-3,2,1,4,-5] => 10001 => 10010
[-5,4,1,-2,3] => [3,-2,1,4,-5] => 01001 => 11000
[-5,4,1,-2,-3] => [-3,-2,1,4,-5] => 11001 => 10110
[-5,4,-1,2,3] => [3,2,-1,4,-5] => 00101 => 11000
[-5,4,-1,2,-3] => [-3,2,-1,4,-5] => 10101 => 11100
[-5,4,-1,-2,3] => [3,-2,-1,4,-5] => 01101 => 11100
[-5,4,-1,-2,-3] => [-3,-2,-1,4,-5] => 11101 => 11110
[-5,-4,1,2,3] => [3,2,1,-4,-5] => 00011 => 10010
[-5,-4,1,2,-3] => [-3,2,1,-4,-5] => 10011 => 10110
[-5,-4,1,-2,3] => [3,-2,1,-4,-5] => 01011 => 11100
[-5,-4,1,-2,-3] => [-3,-2,1,-4,-5] => 11011 => 11110
[-5,-4,-1,2,3] => [3,2,-1,-4,-5] => 00111 => 10110
[-5,-4,-1,2,-3] => [-3,2,-1,-4,-5] => 10111 => 11110
[-5,-4,-1,-2,3] => [3,-2,-1,-4,-5] => 01111 => 11110
[-5,-4,-1,-2,-3] => [-3,-2,-1,-4,-5] => 11111 => 11111
[5,4,1,3,2] => [2,3,1,4,5] => 00000 => 00000
[5,4,1,3,-2] => [-2,3,1,4,5] => 10000 => 10000
[5,4,1,-3,2] => [2,-3,1,4,5] => 01000 => 10000
[5,4,1,-3,-2] => [-2,-3,1,4,5] => 11000 => 10010
[5,4,-1,3,2] => [2,3,-1,4,5] => 00100 => 10000
[5,4,-1,3,-2] => [-2,3,-1,4,5] => 10100 => 11000
[5,4,-1,-3,2] => [2,-3,-1,4,5] => 01100 => 10010
[5,4,-1,-3,-2] => [-2,-3,-1,4,5] => 11100 => 10110
[5,-4,1,3,2] => [2,3,1,-4,5] => 00010 => 10000
[5,-4,1,3,-2] => [-2,3,1,-4,5] => 10010 => 11000
[5,-4,1,-3,2] => [2,-3,1,-4,5] => 01010 => 11000
[5,-4,1,-3,-2] => [-2,-3,1,-4,5] => 11010 => 11100
[5,-4,-1,3,2] => [2,3,-1,-4,5] => 00110 => 10010
[5,-4,-1,3,-2] => [-2,3,-1,-4,5] => 10110 => 11100
[5,-4,-1,-3,2] => [2,-3,-1,-4,5] => 01110 => 10110
[5,-4,-1,-3,-2] => [-2,-3,-1,-4,5] => 11110 => 11110
[-5,4,1,3,2] => [2,3,1,4,-5] => 00001 => 10000
[-5,4,1,3,-2] => [-2,3,1,4,-5] => 10001 => 10010
[-5,4,1,-3,2] => [2,-3,1,4,-5] => 01001 => 11000
[-5,4,1,-3,-2] => [-2,-3,1,4,-5] => 11001 => 10110
[-5,4,-1,3,2] => [2,3,-1,4,-5] => 00101 => 11000
[-5,4,-1,3,-2] => [-2,3,-1,4,-5] => 10101 => 11100
[-5,4,-1,-3,2] => [2,-3,-1,4,-5] => 01101 => 11100
[-5,4,-1,-3,-2] => [-2,-3,-1,4,-5] => 11101 => 11110
[-5,-4,1,3,2] => [2,3,1,-4,-5] => 00011 => 10010
[-5,-4,1,3,-2] => [-2,3,1,-4,-5] => 10011 => 10110
[-5,-4,1,-3,2] => [2,-3,1,-4,-5] => 01011 => 11100
[-5,-4,1,-3,-2] => [-2,-3,1,-4,-5] => 11011 => 11110
[-5,-4,-1,3,2] => [2,3,-1,-4,-5] => 00111 => 10110
[-5,-4,-1,3,-2] => [-2,3,-1,-4,-5] => 10111 => 11110
[-5,-4,-1,-3,2] => [2,-3,-1,-4,-5] => 01111 => 11110
[-5,-4,-1,-3,-2] => [-2,-3,-1,-4,-5] => 11111 => 11111
[5,4,2,1,3] => [3,1,2,4,5] => 00000 => 00000
[5,4,2,1,-3] => [-3,1,2,4,5] => 10000 => 10000
[5,4,2,-1,3] => [3,-1,2,4,5] => 01000 => 10000
[5,4,2,-1,-3] => [-3,-1,2,4,5] => 11000 => 10010
[5,4,-2,1,3] => [3,1,-2,4,5] => 00100 => 10000
[5,4,-2,1,-3] => [-3,1,-2,4,5] => 10100 => 11000
[5,4,-2,-1,3] => [3,-1,-2,4,5] => 01100 => 10010
[5,4,-2,-1,-3] => [-3,-1,-2,4,5] => 11100 => 10110
[5,-4,2,1,3] => [3,1,2,-4,5] => 00010 => 10000
[5,-4,2,1,-3] => [-3,1,2,-4,5] => 10010 => 11000
[5,-4,2,-1,3] => [3,-1,2,-4,5] => 01010 => 11000
[5,-4,2,-1,-3] => [-3,-1,2,-4,5] => 11010 => 11100
[5,-4,-2,1,3] => [3,1,-2,-4,5] => 00110 => 10010
[5,-4,-2,1,-3] => [-3,1,-2,-4,5] => 10110 => 11100
[5,-4,-2,-1,3] => [3,-1,-2,-4,5] => 01110 => 10110
[5,-4,-2,-1,-3] => [-3,-1,-2,-4,5] => 11110 => 11110
[-5,4,2,1,3] => [3,1,2,4,-5] => 00001 => 10000
[-5,4,2,1,-3] => [-3,1,2,4,-5] => 10001 => 10010
[-5,4,2,-1,3] => [3,-1,2,4,-5] => 01001 => 11000
[-5,4,2,-1,-3] => [-3,-1,2,4,-5] => 11001 => 10110
[-5,4,-2,1,3] => [3,1,-2,4,-5] => 00101 => 11000
[-5,4,-2,1,-3] => [-3,1,-2,4,-5] => 10101 => 11100
[-5,4,-2,-1,3] => [3,-1,-2,4,-5] => 01101 => 11100
[-5,4,-2,-1,-3] => [-3,-1,-2,4,-5] => 11101 => 11110
[-5,-4,2,1,3] => [3,1,2,-4,-5] => 00011 => 10010
[-5,-4,2,1,-3] => [-3,1,2,-4,-5] => 10011 => 10110
[-5,-4,2,-1,3] => [3,-1,2,-4,-5] => 01011 => 11100
[-5,-4,2,-1,-3] => [-3,-1,2,-4,-5] => 11011 => 11110
[-5,-4,-2,1,3] => [3,1,-2,-4,-5] => 00111 => 10110
[-5,-4,-2,1,-3] => [-3,1,-2,-4,-5] => 10111 => 11110
[-5,-4,-2,-1,3] => [3,-1,-2,-4,-5] => 01111 => 11110
[-5,-4,-2,-1,-3] => [-3,-1,-2,-4,-5] => 11111 => 11111
[5,4,2,3,1] => [1,3,2,4,5] => 00000 => 00000
[5,4,2,3,-1] => [-1,3,2,4,5] => 10000 => 10000
[5,4,2,-3,1] => [1,-3,2,4,5] => 01000 => 10000
[5,4,2,-3,-1] => [-1,-3,2,4,5] => 11000 => 10010
[5,4,-2,3,1] => [1,3,-2,4,5] => 00100 => 10000
[5,4,-2,3,-1] => [-1,3,-2,4,5] => 10100 => 11000
[5,4,-2,-3,1] => [1,-3,-2,4,5] => 01100 => 10010
[5,4,-2,-3,-1] => [-1,-3,-2,4,5] => 11100 => 10110
[5,-4,2,3,1] => [1,3,2,-4,5] => 00010 => 10000
[5,-4,2,3,-1] => [-1,3,2,-4,5] => 10010 => 11000
[5,-4,2,-3,1] => [1,-3,2,-4,5] => 01010 => 11000
[5,-4,2,-3,-1] => [-1,-3,2,-4,5] => 11010 => 11100
[5,-4,-2,3,1] => [1,3,-2,-4,5] => 00110 => 10010
[5,-4,-2,3,-1] => [-1,3,-2,-4,5] => 10110 => 11100
[5,-4,-2,-3,1] => [1,-3,-2,-4,5] => 01110 => 10110
[5,-4,-2,-3,-1] => [-1,-3,-2,-4,5] => 11110 => 11110
[-5,4,2,3,1] => [1,3,2,4,-5] => 00001 => 10000
[-5,4,2,3,-1] => [-1,3,2,4,-5] => 10001 => 10010
[-5,4,2,-3,1] => [1,-3,2,4,-5] => 01001 => 11000
[-5,4,2,-3,-1] => [-1,-3,2,4,-5] => 11001 => 10110
[-5,4,-2,3,1] => [1,3,-2,4,-5] => 00101 => 11000
[-5,4,-2,3,-1] => [-1,3,-2,4,-5] => 10101 => 11100
[-5,4,-2,-3,1] => [1,-3,-2,4,-5] => 01101 => 11100
[-5,4,-2,-3,-1] => [-1,-3,-2,4,-5] => 11101 => 11110
[-5,-4,2,3,1] => [1,3,2,-4,-5] => 00011 => 10010
[-5,-4,2,3,-1] => [-1,3,2,-4,-5] => 10011 => 10110
[-5,-4,2,-3,1] => [1,-3,2,-4,-5] => 01011 => 11100
[-5,-4,2,-3,-1] => [-1,-3,2,-4,-5] => 11011 => 11110
[-5,-4,-2,3,1] => [1,3,-2,-4,-5] => 00111 => 10110
[-5,-4,-2,3,-1] => [-1,3,-2,-4,-5] => 10111 => 11110
[-5,-4,-2,-3,1] => [1,-3,-2,-4,-5] => 01111 => 11110
[-5,-4,-2,-3,-1] => [-1,-3,-2,-4,-5] => 11111 => 11111
[5,4,3,1,2] => [2,1,3,4,5] => 00000 => 00000
[5,4,3,1,-2] => [-2,1,3,4,5] => 10000 => 10000
[5,4,3,-1,2] => [2,-1,3,4,5] => 01000 => 10000
[5,4,3,-1,-2] => [-2,-1,3,4,5] => 11000 => 10010
[5,4,-3,1,2] => [2,1,-3,4,5] => 00100 => 10000
[5,4,-3,1,-2] => [-2,1,-3,4,5] => 10100 => 11000
[5,4,-3,-1,2] => [2,-1,-3,4,5] => 01100 => 10010
[5,4,-3,-1,-2] => [-2,-1,-3,4,5] => 11100 => 10110
[5,-4,3,1,2] => [2,1,3,-4,5] => 00010 => 10000
[5,-4,3,1,-2] => [-2,1,3,-4,5] => 10010 => 11000
[5,-4,3,-1,2] => [2,-1,3,-4,5] => 01010 => 11000
[5,-4,3,-1,-2] => [-2,-1,3,-4,5] => 11010 => 11100
[5,-4,-3,1,2] => [2,1,-3,-4,5] => 00110 => 10010
[5,-4,-3,1,-2] => [-2,1,-3,-4,5] => 10110 => 11100
[5,-4,-3,-1,2] => [2,-1,-3,-4,5] => 01110 => 10110
[5,-4,-3,-1,-2] => [-2,-1,-3,-4,5] => 11110 => 11110
[-5,4,3,1,2] => [2,1,3,4,-5] => 00001 => 10000
[-5,4,3,1,-2] => [-2,1,3,4,-5] => 10001 => 10010
[-5,4,3,-1,2] => [2,-1,3,4,-5] => 01001 => 11000
[-5,4,3,-1,-2] => [-2,-1,3,4,-5] => 11001 => 10110
[-5,4,-3,1,2] => [2,1,-3,4,-5] => 00101 => 11000
[-5,4,-3,1,-2] => [-2,1,-3,4,-5] => 10101 => 11100
[-5,4,-3,-1,2] => [2,-1,-3,4,-5] => 01101 => 11100
[-5,4,-3,-1,-2] => [-2,-1,-3,4,-5] => 11101 => 11110
[-5,-4,3,1,2] => [2,1,3,-4,-5] => 00011 => 10010
[-5,-4,3,1,-2] => [-2,1,3,-4,-5] => 10011 => 10110
[-5,-4,3,-1,2] => [2,-1,3,-4,-5] => 01011 => 11100
[-5,-4,3,-1,-2] => [-2,-1,3,-4,-5] => 11011 => 11110
[-5,-4,-3,1,2] => [2,1,-3,-4,-5] => 00111 => 10110
[-5,-4,-3,1,-2] => [-2,1,-3,-4,-5] => 10111 => 11110
[-5,-4,-3,-1,2] => [2,-1,-3,-4,-5] => 01111 => 11110
[-5,-4,-3,-1,-2] => [-2,-1,-3,-4,-5] => 11111 => 11111
[5,4,3,2,1] => [1,2,3,4,5] => 00000 => 00000
[5,4,3,2,-1] => [-1,2,3,4,5] => 10000 => 10000
[5,4,3,-2,1] => [1,-2,3,4,5] => 01000 => 10000
[5,4,3,-2,-1] => [-1,-2,3,4,5] => 11000 => 10010
[5,4,-3,2,1] => [1,2,-3,4,5] => 00100 => 10000
[5,4,-3,2,-1] => [-1,2,-3,4,5] => 10100 => 11000
[5,4,-3,-2,1] => [1,-2,-3,4,5] => 01100 => 10010
[5,4,-3,-2,-1] => [-1,-2,-3,4,5] => 11100 => 10110
[5,-4,3,2,1] => [1,2,3,-4,5] => 00010 => 10000
[5,-4,3,2,-1] => [-1,2,3,-4,5] => 10010 => 11000
[5,-4,3,-2,1] => [1,-2,3,-4,5] => 01010 => 11000
[5,-4,3,-2,-1] => [-1,-2,3,-4,5] => 11010 => 11100
[5,-4,-3,2,1] => [1,2,-3,-4,5] => 00110 => 10010
[5,-4,-3,2,-1] => [-1,2,-3,-4,5] => 10110 => 11100
[5,-4,-3,-2,1] => [1,-2,-3,-4,5] => 01110 => 10110
[5,-4,-3,-2,-1] => [-1,-2,-3,-4,5] => 11110 => 11110
[-5,4,3,2,1] => [1,2,3,4,-5] => 00001 => 10000
[-5,4,3,2,-1] => [-1,2,3,4,-5] => 10001 => 10010
[-5,4,3,-2,1] => [1,-2,3,4,-5] => 01001 => 11000
[-5,4,3,-2,-1] => [-1,-2,3,4,-5] => 11001 => 10110
[-5,4,-3,2,1] => [1,2,-3,4,-5] => 00101 => 11000
[-5,4,-3,2,-1] => [-1,2,-3,4,-5] => 10101 => 11100
[-5,4,-3,-2,1] => [1,-2,-3,4,-5] => 01101 => 11100
[-5,4,-3,-2,-1] => [-1,-2,-3,4,-5] => 11101 => 11110
[-5,-4,3,2,1] => [1,2,3,-4,-5] => 00011 => 10010
[-5,-4,3,2,-1] => [-1,2,3,-4,-5] => 10011 => 10110
[-5,-4,3,-2,1] => [1,-2,3,-4,-5] => 01011 => 11100
[-5,-4,3,-2,-1] => [-1,-2,3,-4,-5] => 11011 => 11110
[-5,-4,-3,2,1] => [1,2,-3,-4,-5] => 00111 => 10110
[-5,-4,-3,2,-1] => [-1,2,-3,-4,-5] => 10111 => 11110
[-5,-4,-3,-2,1] => [1,-2,-3,-4,-5] => 01111 => 11110
[-5,-4,-3,-2,-1] => [-1,-2,-3,-4,-5] => 11111 => 11111
[6,2,3,4,5,-1] => [-1,5,4,3,2,6] => 100000 => 100000
[5,2,3,4,6,-1] => [-1,6,4,3,2,5] => 100000 => 100000
[4,2,3,6,5,-1] => [-1,5,6,3,2,4] => 100000 => 100000
[4,2,3,5,6,-1] => [-1,6,5,3,2,4] => 100000 => 100000
[3,2,6,4,5,-1] => [-1,5,4,6,2,3] => 100000 => 100000
[3,2,5,4,6,-1] => [-1,6,4,5,2,3] => 100000 => 100000
[3,2,4,6,5,-1] => [-1,5,6,4,2,3] => 100000 => 100000
[3,2,4,5,6,-1] => [-1,6,5,4,2,3] => 100000 => 100000
[2,6,3,4,5,-1] => [-1,5,4,3,6,2] => 100000 => 100000
[2,5,3,4,6,-1] => [-1,6,4,3,5,2] => 100000 => 100000
[2,4,3,6,5,-1] => [-1,5,6,3,4,2] => 100000 => 100000
[2,4,3,5,6,-1] => [-1,6,5,3,4,2] => 100000 => 100000
[5,6,2,3,4,-1] => [-1,4,3,2,6,5] => 100000 => 100000
[4,5,2,3,6,-1] => [-1,6,3,2,5,4] => 100000 => 100000
[3,4,2,5,6,-1] => [-1,6,5,2,4,3] => 100000 => 100000
[2,3,6,4,5,-1] => [-1,5,4,6,3,2] => 100000 => 100000
[2,3,5,4,6,-1] => [-1,6,4,5,3,2] => 100000 => 100000
[2,5,6,3,4,-1] => [-1,4,3,6,5,2] => 100000 => 100000
[2,4,5,3,6,-1] => [-1,6,3,5,4,2] => 100000 => 100000
[4,5,6,2,3,-1] => [-1,3,2,6,5,4] => 100000 => 100000
[3,4,5,2,6,-1] => [-1,6,2,5,4,3] => 100000 => 100000
[2,3,4,6,5,-1] => [-1,5,6,4,3,2] => 100000 => 100000
[2,4,5,6,3,-1] => [-1,3,6,5,4,2] => 100000 => 100000
[3,4,5,6,2,-1] => [-1,2,6,5,4,3] => 100000 => 100000
[2,3,4,5,6,-1] => [-1,6,5,4,3,2] => 100000 => 100000
[2,3,4,5,-1,6] => [6,-1,5,4,3,2] => 010000 => 100000
[2,3,4,-1,5,6] => [6,5,-1,4,3,2] => 001000 => 100000
[2,3,-1,4,5,6] => [6,5,4,-1,3,2] => 000100 => 100000
[2,3,6,5,4,-1] => [-1,4,5,6,3,2] => 100000 => 100000
[2,-1,3,4,5,6] => [6,5,4,3,-1,2] => 000010 => 100000
[2,6,3,5,4,-1] => [-1,4,5,3,6,2] => 100000 => 100000
[2,5,4,3,6,-1] => [-1,6,3,4,5,2] => 100000 => 100000
[2,6,4,3,5,-1] => [-1,5,3,4,6,2] => 100000 => 100000
[2,6,5,3,4,-1] => [-1,4,3,5,6,2] => 100000 => 100000
[2,6,5,4,3,-1] => [-1,3,4,5,6,2] => 100000 => 100000
[3,2,4,5,-1,6] => [6,-1,5,4,2,3] => 010000 => 100000
[3,2,6,5,4,-1] => [-1,4,5,6,2,3] => 100000 => 100000
[6,2,3,5,4,-1] => [-1,4,5,3,2,6] => 100000 => 100000
[5,2,4,3,6,-1] => [-1,6,3,4,2,5] => 100000 => 100000
[6,2,4,3,5,-1] => [-1,5,3,4,2,6] => 100000 => 100000
[6,2,5,3,4,-1] => [-1,4,3,5,2,6] => 100000 => 100000
[6,2,5,4,3,-1] => [-1,3,4,5,2,6] => 100000 => 100000
[4,3,2,5,6,-1] => [-1,6,5,2,3,4] => 100000 => 100000
[4,3,2,6,5,-1] => [-1,5,6,2,3,4] => 100000 => 100000
[5,3,2,4,6,-1] => [-1,6,4,2,3,5] => 100000 => 100000
[6,3,2,4,5,-1] => [-1,5,4,2,3,6] => 100000 => 100000
[6,3,2,5,4,-1] => [-1,4,5,2,3,6] => 100000 => 100000
[5,4,2,3,6,-1] => [-1,6,3,2,4,5] => 100000 => 100000
[6,4,2,3,5,-1] => [-1,5,3,2,4,6] => 100000 => 100000
[6,5,2,3,4,-1] => [-1,4,3,2,5,6] => 100000 => 100000
[6,5,2,4,3,-1] => [-1,3,4,2,5,6] => 100000 => 100000
[5,4,3,2,6,-1] => [-1,6,2,3,4,5] => 100000 => 100000
[6,4,3,2,5,-1] => [-1,5,2,3,4,6] => 100000 => 100000
[6,5,3,2,4,-1] => [-1,4,2,3,5,6] => 100000 => 100000
[6,5,4,2,3,-1] => [-1,3,2,4,5,6] => 100000 => 100000
[6,5,4,3,2,-1] => [-1,2,3,4,5,6] => 100000 => 100000
[3,4,5,6,-1,2] => [2,-1,6,5,4,3] => 010000 => 100000
[4,5,6,-1,2,3] => [3,2,-1,6,5,4] => 001000 => 100000
[2,-6,-5,-4,-3,1] => [1,-3,-4,-5,-6,2] => 011110 => 101110
[5,4,3,2,1,-6] => [-6,1,2,3,4,5] => 100000 => 100000
[5,4,3,1,2,-6] => [-6,2,1,3,4,5] => 100000 => 100000
[5,4,1,3,2,-6] => [-6,2,3,1,4,5] => 100000 => 100000
[5,4,2,1,3,-6] => [-6,3,1,2,4,5] => 100000 => 100000
[5,2,1,4,3,-6] => [-6,3,4,1,2,5] => 100000 => 100000
[5,3,2,1,4,-6] => [-6,4,1,2,3,5] => 100000 => 100000
[4,2,1,3,5,-6] => [-6,5,3,1,2,4] => 100000 => 100000
[2,1,4,3,5,-6] => [-6,5,3,4,1,2] => 100000 => 100000
[3,2,1,6,5,-4] => [-4,5,6,1,2,3] => 100000 => 100000
[4,3,2,1,6,-5] => [-5,6,1,2,3,4] => 100000 => 100000
[4,3,1,2,6,-5] => [-5,6,2,1,3,4] => 100000 => 100000
[1,-3,-4,-5,-6,2] => [2,-6,-5,-4,-3,1] => 011110 => 101110
[3,2,5,4,1,-6] => [-6,1,4,5,2,3] => 100000 => 100000
[6,4,3,1,2,-5] => [-5,2,1,3,4,6] => 100000 => 100000
[5,3,2,4,1,-6] => [-6,1,4,2,3,5] => 100000 => 100000
[4,3,5,2,1,-6] => [-6,1,2,5,3,4] => 100000 => 100000
[4,3,2,5,1,-6] => [-6,1,5,2,3,4] => 100000 => 100000
[3,2,4,1,5,-6] => [-6,5,1,4,2,3] => 100000 => 100000
[6,4,3,2,1,-5] => [-5,1,2,3,4,6] => 100000 => 100000
[6,4,2,1,3,-5] => [-5,3,1,2,4,6] => 100000 => 100000
[5,3,6,2,1,-4] => [-4,1,2,6,3,5] => 100000 => 100000
[5,3,2,1,6,-4] => [-4,6,1,2,3,5] => 100000 => 100000
[6,5,3,4,2,-1] => [-1,2,4,3,5,6] => 100000 => 100000
[6,4,5,3,2,-1] => [-1,2,3,5,4,6] => 100000 => 100000
[6,4,5,2,3,-1] => [-1,3,2,5,4,6] => 100000 => 100000
[6,4,3,5,2,-1] => [-1,2,5,3,4,6] => 100000 => 100000
[6,3,4,5,2,-1] => [-1,2,5,4,3,6] => 100000 => 100000
[6,3,4,2,5,-1] => [-1,5,2,4,3,6] => 100000 => 100000
[5,6,4,3,2,-1] => [-1,2,3,4,6,5] => 100000 => 100000
[5,6,4,2,3,-1] => [-1,3,2,4,6,5] => 100000 => 100000
[5,6,3,4,2,-1] => [-1,2,4,3,6,5] => 100000 => 100000
[5,6,3,2,4,-1] => [-1,4,2,3,6,5] => 100000 => 100000
[5,4,6,3,2,-1] => [-1,2,3,6,4,5] => 100000 => 100000
[5,4,6,2,3,-1] => [-1,3,2,6,4,5] => 100000 => 100000
[5,4,3,6,2,-1] => [-1,2,6,3,4,5] => 100000 => 100000
[5,3,4,6,2,-1] => [-1,2,6,4,3,5] => 100000 => 100000
[5,3,4,2,6,-1] => [-1,6,2,4,3,5] => 100000 => 100000
[4,5,6,3,2,-1] => [-1,2,3,6,5,4] => 100000 => 100000
[4,5,3,6,2,-1] => [-1,2,6,3,5,4] => 100000 => 100000
[4,5,3,2,6,-1] => [-1,6,2,3,5,4] => 100000 => 100000
[4,3,5,6,-1,2] => [2,-1,6,5,3,4] => 010000 => 100000
[4,3,5,6,2,-1] => [-1,2,6,5,3,4] => 100000 => 100000
[4,3,5,2,6,-1] => [-1,6,2,5,3,4] => 100000 => 100000
[2,6,4,5,3,-1] => [-1,3,5,4,6,2] => 100000 => 100000
[6,2,4,5,3,-1] => [-1,3,5,4,2,6] => 100000 => 100000
[6,3,5,4,2,-1] => [-1,2,4,5,3,6] => 100000 => 100000
[2,1,5,3,6,-4] => [-4,6,3,5,1,2] => 100000 => 100000
[5,2,1,6,3,-4] => [-4,3,6,1,2,5] => 100000 => 100000
[5,2,6,1,3,-4] => [-4,3,1,6,2,5] => 100000 => 100000
[6,3,1,4,2,-5] => [-5,2,4,1,3,6] => 100000 => 100000
[5,1,-4,6,2,-3] => [-3,2,6,-4,1,5] => 100100 => 110000
[6,1,-5,-4,-3,-2] => [-2,-3,-4,-5,1,6] => 111100 => 101110
[6,3,1,-2,-5,-4] => [-4,-5,-2,1,3,6] => 111000 => 100110
[1,-6,3,2,5,4] => [4,5,2,3,-6,1] => 000010 => 100000
[1,-6,4,3,5,2] => [2,5,3,4,-6,1] => 000010 => 100000
[1,-6,5,4,3,2] => [2,3,4,5,-6,1] => 000010 => 100000
[2,1,-6,5,4,3] => [3,4,5,-6,1,2] => 000100 => 100000
[2,1,3,-6,5,4] => [4,5,-6,3,1,2] => 001000 => 100000
[3,2,1,-6,5,4] => [4,5,-6,1,2,3] => 001000 => 100000
[4,3,2,1,-6,5] => [5,-6,1,2,3,4] => 010000 => 100000
[4,6,5,3,2,-1] => [-1,2,3,5,6,4] => 100000 => 100000
[3,6,5,4,2,-1] => [-1,2,4,5,6,3] => 100000 => 100000
[3,5,6,4,2,-1] => [-1,2,4,6,5,3] => 100000 => 100000
[3,5,4,6,2,-1] => [-1,2,6,4,5,3] => 100000 => 100000
[2,5,6,4,3,-1] => [-1,3,4,6,5,2] => 100000 => 100000
[2,5,4,6,3,-1] => [-1,3,6,4,5,2] => 100000 => 100000
[3,1,-4,-5,-6,2] => [2,-6,-5,-4,1,3] => 011100 => 100110
[6,5,4,3,1,-2] => [-2,1,3,4,5,6] => 100000 => 100000
[4,2,1,6,3,-5] => [-5,3,6,1,2,4] => 100000 => 100000
[6,5,4,2,1,-3] => [-3,1,2,4,5,6] => 100000 => 100000
[6,3,2,1,5,-4] => [-4,5,1,2,3,6] => 100000 => 100000
[6,5,3,2,1,-4] => [-4,1,2,3,5,6] => 100000 => 100000
[5,4,3,-6,2,1] => [1,2,-6,3,4,5] => 001000 => 100000
[3,1,6,5,4,-2] => [-2,4,5,6,1,3] => 100000 => 100000
[5,4,3,1,6,-2] => [-2,6,1,3,4,5] => 100000 => 100000
[4,3,6,5,1,-2] => [-2,1,5,6,3,4] => 100000 => 100000
[5,4,6,3,1,-2] => [-2,1,3,6,4,5] => 100000 => 100000
[3,2,6,5,1,-4] => [-4,1,5,6,2,3] => 100000 => 100000
[6,5,2,1,3,-4] => [-4,3,1,2,5,6] => 100000 => 100000
[6,2,1,5,3,-4] => [-4,3,5,1,2,6] => 100000 => 100000
[4,2,1,5,3,-6] => [-6,3,5,1,2,4] => 100000 => 100000
[6,3,2,5,1,-4] => [-4,1,5,2,3,6] => 100000 => 100000
[2,1,6,5,3,-4] => [-4,3,5,6,1,2] => 100000 => 100000
[5,1,6,-4,-3,-2] => [-2,-3,-4,6,1,5] => 111000 => 100110
[5,3,6,-4,1,-2] => [-2,1,-4,6,3,5] => 101000 => 101000
[6,4,3,5,1,-2] => [-2,1,5,3,4,6] => 100000 => 100000
[4,3,1,-6,-5,2] => [2,-5,-6,1,3,4] => 011000 => 100010
[3,1,-4,2,-6,5] => [5,-6,2,-4,1,3] => 010100 => 101000
[1,-5,4,2,-6,3] => [3,-6,2,4,-5,1] => 010010 => 110000
[5,1,-6,4,2,3] => [3,2,4,-6,1,5] => 000100 => 100000
[1,-5,2,-4,-6,3] => [3,-6,-4,2,-5,1] => 011010 => 110010
[1,-6,5,2,-4,3] => [3,-4,2,5,-6,1] => 010010 => 110000
[2,1,5,4,-6,3] => [3,-6,4,5,1,2] => 010000 => 100000
[6,1,-5,2,-4,3] => [3,-4,2,-5,1,6] => 010100 => 101000
[3,2,-6,1,5,4] => [4,5,1,-6,2,3] => 000100 => 100000
[6,3,1,-2,-5,4] => [4,-5,-2,1,3,6] => 011000 => 100010
[6,4,1,-3,-5,2] => [2,-5,-3,1,4,6] => 011000 => 100010
[5,3,1,-6,2,4] => [4,2,-6,1,3,5] => 001000 => 100000
[2,3,4,5,6,7,8,-1] => [-1,8,7,6,5,4,3,2] => 10000000 => 10000000
[2,-6,5,4,1,3] => [3,1,4,5,-6,2] => 000010 => 100000
[4,1,5,-3,2,6] => [6,2,-3,5,1,4] => 001000 => 100000
[5,3,1,-4,2,6] => [6,2,-4,1,3,5] => 001000 => 100000
[3,6,4,5,2,-1] => [-1,2,5,4,6,3] => 100000 => 100000
[4,6,5,2,3,-1] => [-1,3,2,5,6,4] => 100000 => 100000
[5,6,2,4,3,-1] => [-1,3,4,2,6,5] => 100000 => 100000
[6,4,1,-3,-5,-2] => [-2,-5,-3,1,4,6] => 111000 => 100110
[5,4,2,1,3,7,-6] => [-6,7,3,1,2,4,5] => 1000000 => 1000000
[4,3,2,1,6,7,-5] => [-5,7,6,1,2,3,4] => 1000000 => 1000000
[7,6,5,4,3,2,-1] => [-1,2,3,4,5,6,7] => 1000000 => 1000000
[3,1,-6,2,5,4] => [4,5,2,-6,1,3] => 000100 => 100000
[4,1,3,-6,2,5] => [5,2,-6,3,1,4] => 001000 => 100000
Map
reverse
Description
The reversal of a signed permutation.
Map
signs
Description
The binary word recording the signs of a signed permutation.
This map sends a signed permutation π∈Hn to the binary word w of length n such that wi=0 if π(i)>0.
This map sends a signed permutation π∈Hn to the binary word w of length n such that wi=0 if π(i)>0.
Map
Burrows-Wheeler
Description
The Burrows-Wheeler transform of a binary word.
The Burrows-Wheeler transform of a finite word w is obtained from w by first listing the conjugates of w in lexicographic order and then concatenating the final letters of the conjugates in this order.
The Burrows-Wheeler transform of a finite word w is obtained from w by first listing the conjugates of w in lexicographic order and then concatenating the final letters of the conjugates in this order.
searching the database
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