Identifier
Mp00166:
Signed permutations
—even cycle type⟶
Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
Mp00317: Integer partitions —odd parts⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
Images
[1] => [1] => 1 => 1
[1,2] => [1,1] => 11 => 11
[1,-2] => [1] => 1 => 1
[-1,2] => [1] => 1 => 1
[2,1] => [2] => 0 => 0
[-2,-1] => [2] => 0 => 0
[1,2,3] => [1,1,1] => 111 => 111
[1,2,-3] => [1,1] => 11 => 11
[1,-2,3] => [1,1] => 11 => 11
[1,-2,-3] => [1] => 1 => 1
[-1,2,3] => [1,1] => 11 => 11
[-1,2,-3] => [1] => 1 => 1
[-1,-2,3] => [1] => 1 => 1
[1,3,2] => [2,1] => 01 => 01
[1,3,-2] => [1] => 1 => 1
[1,-3,2] => [1] => 1 => 1
[1,-3,-2] => [2,1] => 01 => 01
[-1,3,2] => [2] => 0 => 0
[-1,-3,-2] => [2] => 0 => 0
[2,1,3] => [2,1] => 01 => 01
[2,1,-3] => [2] => 0 => 0
[2,-1,3] => [1] => 1 => 1
[-2,1,3] => [1] => 1 => 1
[-2,-1,3] => [2,1] => 01 => 01
[-2,-1,-3] => [2] => 0 => 0
[2,3,1] => [3] => 1 => 1
[2,-3,-1] => [3] => 1 => 1
[-2,3,-1] => [3] => 1 => 1
[-2,-3,1] => [3] => 1 => 1
[3,1,2] => [3] => 1 => 1
[3,-1,-2] => [3] => 1 => 1
[-3,1,-2] => [3] => 1 => 1
[-3,-1,2] => [3] => 1 => 1
[3,2,1] => [2,1] => 01 => 01
[3,2,-1] => [1] => 1 => 1
[3,-2,1] => [2] => 0 => 0
[-3,2,1] => [1] => 1 => 1
[-3,2,-1] => [2,1] => 01 => 01
[-3,-2,-1] => [2] => 0 => 0
[1,2,3,4] => [1,1,1,1] => 1111 => 1111
[1,2,3,-4] => [1,1,1] => 111 => 111
[1,2,-3,4] => [1,1,1] => 111 => 111
[1,2,-3,-4] => [1,1] => 11 => 11
[1,-2,3,4] => [1,1,1] => 111 => 111
[1,-2,3,-4] => [1,1] => 11 => 11
[1,-2,-3,4] => [1,1] => 11 => 11
[1,-2,-3,-4] => [1] => 1 => 1
[-1,2,3,4] => [1,1,1] => 111 => 111
[-1,2,3,-4] => [1,1] => 11 => 11
[-1,2,-3,4] => [1,1] => 11 => 11
[-1,2,-3,-4] => [1] => 1 => 1
[-1,-2,3,4] => [1,1] => 11 => 11
[-1,-2,3,-4] => [1] => 1 => 1
[-1,-2,-3,4] => [1] => 1 => 1
[1,2,4,3] => [2,1,1] => 011 => 011
[1,2,4,-3] => [1,1] => 11 => 11
[1,2,-4,3] => [1,1] => 11 => 11
[1,2,-4,-3] => [2,1,1] => 011 => 011
[1,-2,4,3] => [2,1] => 01 => 01
[1,-2,4,-3] => [1] => 1 => 1
[1,-2,-4,3] => [1] => 1 => 1
[1,-2,-4,-3] => [2,1] => 01 => 01
[-1,2,4,3] => [2,1] => 01 => 01
[-1,2,4,-3] => [1] => 1 => 1
[-1,2,-4,3] => [1] => 1 => 1
[-1,2,-4,-3] => [2,1] => 01 => 01
[-1,-2,4,3] => [2] => 0 => 0
[-1,-2,-4,-3] => [2] => 0 => 0
[1,3,2,4] => [2,1,1] => 011 => 011
[1,3,2,-4] => [2,1] => 01 => 01
[1,3,-2,4] => [1,1] => 11 => 11
[1,3,-2,-4] => [1] => 1 => 1
[1,-3,2,4] => [1,1] => 11 => 11
[1,-3,2,-4] => [1] => 1 => 1
[1,-3,-2,4] => [2,1,1] => 011 => 011
[1,-3,-2,-4] => [2,1] => 01 => 01
[-1,3,2,4] => [2,1] => 01 => 01
[-1,3,2,-4] => [2] => 0 => 0
[-1,3,-2,4] => [1] => 1 => 1
[-1,-3,2,4] => [1] => 1 => 1
[-1,-3,-2,4] => [2,1] => 01 => 01
[-1,-3,-2,-4] => [2] => 0 => 0
[1,3,4,2] => [3,1] => 11 => 11
[1,3,4,-2] => [1] => 1 => 1
[1,3,-4,2] => [1] => 1 => 1
[1,3,-4,-2] => [3,1] => 11 => 11
[1,-3,4,2] => [1] => 1 => 1
[1,-3,4,-2] => [3,1] => 11 => 11
[1,-3,-4,2] => [3,1] => 11 => 11
[1,-3,-4,-2] => [1] => 1 => 1
[-1,3,4,2] => [3] => 1 => 1
[-1,3,-4,-2] => [3] => 1 => 1
[-1,-3,4,-2] => [3] => 1 => 1
[-1,-3,-4,2] => [3] => 1 => 1
[1,4,2,3] => [3,1] => 11 => 11
[1,4,2,-3] => [1] => 1 => 1
[1,4,-2,3] => [1] => 1 => 1
[1,4,-2,-3] => [3,1] => 11 => 11
[1,-4,2,3] => [1] => 1 => 1
[1,-4,2,-3] => [3,1] => 11 => 11
[1,-4,-2,3] => [3,1] => 11 => 11
>>> Load all 4842 entries. <<<
[1,-4,-2,-3] => [1] => 1 => 1
[-1,4,2,3] => [3] => 1 => 1
[-1,4,-2,-3] => [3] => 1 => 1
[-1,-4,2,-3] => [3] => 1 => 1
[-1,-4,-2,3] => [3] => 1 => 1
[1,4,3,2] => [2,1,1] => 011 => 011
[1,4,3,-2] => [1,1] => 11 => 11
[1,4,-3,2] => [2,1] => 01 => 01
[1,4,-3,-2] => [1] => 1 => 1
[1,-4,3,2] => [1,1] => 11 => 11
[1,-4,3,-2] => [2,1,1] => 011 => 011
[1,-4,-3,2] => [1] => 1 => 1
[1,-4,-3,-2] => [2,1] => 01 => 01
[-1,4,3,2] => [2,1] => 01 => 01
[-1,4,3,-2] => [1] => 1 => 1
[-1,4,-3,2] => [2] => 0 => 0
[-1,-4,3,2] => [1] => 1 => 1
[-1,-4,3,-2] => [2,1] => 01 => 01
[-1,-4,-3,-2] => [2] => 0 => 0
[2,1,3,4] => [2,1,1] => 011 => 011
[2,1,3,-4] => [2,1] => 01 => 01
[2,1,-3,4] => [2,1] => 01 => 01
[2,1,-3,-4] => [2] => 0 => 0
[2,-1,3,4] => [1,1] => 11 => 11
[2,-1,3,-4] => [1] => 1 => 1
[2,-1,-3,4] => [1] => 1 => 1
[-2,1,3,4] => [1,1] => 11 => 11
[-2,1,3,-4] => [1] => 1 => 1
[-2,1,-3,4] => [1] => 1 => 1
[-2,-1,3,4] => [2,1,1] => 011 => 011
[-2,-1,3,-4] => [2,1] => 01 => 01
[-2,-1,-3,4] => [2,1] => 01 => 01
[-2,-1,-3,-4] => [2] => 0 => 0
[2,1,4,3] => [2,2] => 00 => 00
[2,1,4,-3] => [2] => 0 => 0
[2,1,-4,3] => [2] => 0 => 0
[2,1,-4,-3] => [2,2] => 00 => 00
[2,-1,4,3] => [2] => 0 => 0
[2,-1,-4,-3] => [2] => 0 => 0
[-2,1,4,3] => [2] => 0 => 0
[-2,1,-4,-3] => [2] => 0 => 0
[-2,-1,4,3] => [2,2] => 00 => 00
[-2,-1,4,-3] => [2] => 0 => 0
[-2,-1,-4,3] => [2] => 0 => 0
[-2,-1,-4,-3] => [2,2] => 00 => 00
[2,3,1,4] => [3,1] => 11 => 11
[2,3,1,-4] => [3] => 1 => 1
[2,3,-1,4] => [1] => 1 => 1
[2,-3,1,4] => [1] => 1 => 1
[2,-3,-1,4] => [3,1] => 11 => 11
[2,-3,-1,-4] => [3] => 1 => 1
[-2,3,1,4] => [1] => 1 => 1
[-2,3,-1,4] => [3,1] => 11 => 11
[-2,3,-1,-4] => [3] => 1 => 1
[-2,-3,1,4] => [3,1] => 11 => 11
[-2,-3,1,-4] => [3] => 1 => 1
[-2,-3,-1,4] => [1] => 1 => 1
[2,3,4,1] => [4] => 0 => 0
[2,3,-4,-1] => [4] => 0 => 0
[2,-3,4,-1] => [4] => 0 => 0
[2,-3,-4,1] => [4] => 0 => 0
[-2,3,4,-1] => [4] => 0 => 0
[-2,3,-4,1] => [4] => 0 => 0
[-2,-3,4,1] => [4] => 0 => 0
[-2,-3,-4,-1] => [4] => 0 => 0
[2,4,1,3] => [4] => 0 => 0
[2,4,-1,-3] => [4] => 0 => 0
[2,-4,1,-3] => [4] => 0 => 0
[2,-4,-1,3] => [4] => 0 => 0
[-2,4,1,-3] => [4] => 0 => 0
[-2,4,-1,3] => [4] => 0 => 0
[-2,-4,1,3] => [4] => 0 => 0
[-2,-4,-1,-3] => [4] => 0 => 0
[2,4,3,1] => [3,1] => 11 => 11
[2,4,3,-1] => [1] => 1 => 1
[2,4,-3,1] => [3] => 1 => 1
[2,-4,3,1] => [1] => 1 => 1
[2,-4,3,-1] => [3,1] => 11 => 11
[2,-4,-3,-1] => [3] => 1 => 1
[-2,4,3,1] => [1] => 1 => 1
[-2,4,3,-1] => [3,1] => 11 => 11
[-2,4,-3,-1] => [3] => 1 => 1
[-2,-4,3,1] => [3,1] => 11 => 11
[-2,-4,3,-1] => [1] => 1 => 1
[-2,-4,-3,1] => [3] => 1 => 1
[3,1,2,4] => [3,1] => 11 => 11
[3,1,2,-4] => [3] => 1 => 1
[3,1,-2,4] => [1] => 1 => 1
[3,-1,2,4] => [1] => 1 => 1
[3,-1,-2,4] => [3,1] => 11 => 11
[3,-1,-2,-4] => [3] => 1 => 1
[-3,1,2,4] => [1] => 1 => 1
[-3,1,-2,4] => [3,1] => 11 => 11
[-3,1,-2,-4] => [3] => 1 => 1
[-3,-1,2,4] => [3,1] => 11 => 11
[-3,-1,2,-4] => [3] => 1 => 1
[-3,-1,-2,4] => [1] => 1 => 1
[3,1,4,2] => [4] => 0 => 0
[3,1,-4,-2] => [4] => 0 => 0
[3,-1,4,-2] => [4] => 0 => 0
[3,-1,-4,2] => [4] => 0 => 0
[-3,1,4,-2] => [4] => 0 => 0
[-3,1,-4,2] => [4] => 0 => 0
[-3,-1,4,2] => [4] => 0 => 0
[-3,-1,-4,-2] => [4] => 0 => 0
[3,2,1,4] => [2,1,1] => 011 => 011
[3,2,1,-4] => [2,1] => 01 => 01
[3,2,-1,4] => [1,1] => 11 => 11
[3,2,-1,-4] => [1] => 1 => 1
[3,-2,1,4] => [2,1] => 01 => 01
[3,-2,1,-4] => [2] => 0 => 0
[3,-2,-1,4] => [1] => 1 => 1
[-3,2,1,4] => [1,1] => 11 => 11
[-3,2,1,-4] => [1] => 1 => 1
[-3,2,-1,4] => [2,1,1] => 011 => 011
[-3,2,-1,-4] => [2,1] => 01 => 01
[-3,-2,1,4] => [1] => 1 => 1
[-3,-2,-1,4] => [2,1] => 01 => 01
[-3,-2,-1,-4] => [2] => 0 => 0
[3,2,4,1] => [3,1] => 11 => 11
[3,2,4,-1] => [1] => 1 => 1
[3,2,-4,1] => [1] => 1 => 1
[3,2,-4,-1] => [3,1] => 11 => 11
[3,-2,4,1] => [3] => 1 => 1
[3,-2,-4,-1] => [3] => 1 => 1
[-3,2,4,1] => [1] => 1 => 1
[-3,2,4,-1] => [3,1] => 11 => 11
[-3,2,-4,1] => [3,1] => 11 => 11
[-3,2,-4,-1] => [1] => 1 => 1
[-3,-2,4,-1] => [3] => 1 => 1
[-3,-2,-4,1] => [3] => 1 => 1
[3,4,1,2] => [2,2] => 00 => 00
[3,4,1,-2] => [2] => 0 => 0
[3,4,-1,2] => [2] => 0 => 0
[3,-4,1,2] => [2] => 0 => 0
[3,-4,1,-2] => [2,2] => 00 => 00
[3,-4,-1,-2] => [2] => 0 => 0
[-3,4,1,2] => [2] => 0 => 0
[-3,4,-1,2] => [2,2] => 00 => 00
[-3,4,-1,-2] => [2] => 0 => 0
[-3,-4,1,-2] => [2] => 0 => 0
[-3,-4,-1,2] => [2] => 0 => 0
[-3,-4,-1,-2] => [2,2] => 00 => 00
[3,4,2,1] => [4] => 0 => 0
[3,4,-2,-1] => [4] => 0 => 0
[3,-4,2,-1] => [4] => 0 => 0
[3,-4,-2,1] => [4] => 0 => 0
[-3,4,2,-1] => [4] => 0 => 0
[-3,4,-2,1] => [4] => 0 => 0
[-3,-4,2,1] => [4] => 0 => 0
[-3,-4,-2,-1] => [4] => 0 => 0
[4,1,2,3] => [4] => 0 => 0
[4,1,-2,-3] => [4] => 0 => 0
[4,-1,2,-3] => [4] => 0 => 0
[4,-1,-2,3] => [4] => 0 => 0
[-4,1,2,-3] => [4] => 0 => 0
[-4,1,-2,3] => [4] => 0 => 0
[-4,-1,2,3] => [4] => 0 => 0
[-4,-1,-2,-3] => [4] => 0 => 0
[4,1,3,2] => [3,1] => 11 => 11
[4,1,3,-2] => [1] => 1 => 1
[4,1,-3,2] => [3] => 1 => 1
[4,-1,3,2] => [1] => 1 => 1
[4,-1,3,-2] => [3,1] => 11 => 11
[4,-1,-3,-2] => [3] => 1 => 1
[-4,1,3,2] => [1] => 1 => 1
[-4,1,3,-2] => [3,1] => 11 => 11
[-4,1,-3,-2] => [3] => 1 => 1
[-4,-1,3,2] => [3,1] => 11 => 11
[-4,-1,3,-2] => [1] => 1 => 1
[-4,-1,-3,2] => [3] => 1 => 1
[4,2,1,3] => [3,1] => 11 => 11
[4,2,1,-3] => [1] => 1 => 1
[4,2,-1,3] => [1] => 1 => 1
[4,2,-1,-3] => [3,1] => 11 => 11
[4,-2,1,3] => [3] => 1 => 1
[4,-2,-1,-3] => [3] => 1 => 1
[-4,2,1,3] => [1] => 1 => 1
[-4,2,1,-3] => [3,1] => 11 => 11
[-4,2,-1,3] => [3,1] => 11 => 11
[-4,2,-1,-3] => [1] => 1 => 1
[-4,-2,1,-3] => [3] => 1 => 1
[-4,-2,-1,3] => [3] => 1 => 1
[4,2,3,1] => [2,1,1] => 011 => 011
[4,2,3,-1] => [1,1] => 11 => 11
[4,2,-3,1] => [2,1] => 01 => 01
[4,2,-3,-1] => [1] => 1 => 1
[4,-2,3,1] => [2,1] => 01 => 01
[4,-2,3,-1] => [1] => 1 => 1
[4,-2,-3,1] => [2] => 0 => 0
[-4,2,3,1] => [1,1] => 11 => 11
[-4,2,3,-1] => [2,1,1] => 011 => 011
[-4,2,-3,1] => [1] => 1 => 1
[-4,2,-3,-1] => [2,1] => 01 => 01
[-4,-2,3,1] => [1] => 1 => 1
[-4,-2,3,-1] => [2,1] => 01 => 01
[-4,-2,-3,-1] => [2] => 0 => 0
[4,3,1,2] => [4] => 0 => 0
[4,3,-1,-2] => [4] => 0 => 0
[4,-3,1,-2] => [4] => 0 => 0
[4,-3,-1,2] => [4] => 0 => 0
[-4,3,1,-2] => [4] => 0 => 0
[-4,3,-1,2] => [4] => 0 => 0
[-4,-3,1,2] => [4] => 0 => 0
[-4,-3,-1,-2] => [4] => 0 => 0
[4,3,2,1] => [2,2] => 00 => 00
[4,3,2,-1] => [2] => 0 => 0
[4,3,-2,1] => [2] => 0 => 0
[4,-3,2,1] => [2] => 0 => 0
[4,-3,-2,1] => [2,2] => 00 => 00
[4,-3,-2,-1] => [2] => 0 => 0
[-4,3,2,1] => [2] => 0 => 0
[-4,3,2,-1] => [2,2] => 00 => 00
[-4,3,-2,-1] => [2] => 0 => 0
[-4,-3,2,-1] => [2] => 0 => 0
[-4,-3,-2,1] => [2] => 0 => 0
[-4,-3,-2,-1] => [2,2] => 00 => 00
[1,2,3,4,5] => [1,1,1,1,1] => 11111 => 11111
[1,2,3,4,-5] => [1,1,1,1] => 1111 => 1111
[1,2,3,-4,5] => [1,1,1,1] => 1111 => 1111
[1,2,3,-4,-5] => [1,1,1] => 111 => 111
[1,2,-3,4,5] => [1,1,1,1] => 1111 => 1111
[1,2,-3,4,-5] => [1,1,1] => 111 => 111
[1,2,-3,-4,5] => [1,1,1] => 111 => 111
[1,2,-3,-4,-5] => [1,1] => 11 => 11
[1,-2,3,4,5] => [1,1,1,1] => 1111 => 1111
[1,-2,3,4,-5] => [1,1,1] => 111 => 111
[1,-2,3,-4,5] => [1,1,1] => 111 => 111
[1,-2,3,-4,-5] => [1,1] => 11 => 11
[1,-2,-3,4,5] => [1,1,1] => 111 => 111
[1,-2,-3,4,-5] => [1,1] => 11 => 11
[1,-2,-3,-4,5] => [1,1] => 11 => 11
[1,-2,-3,-4,-5] => [1] => 1 => 1
[-1,2,3,4,5] => [1,1,1,1] => 1111 => 1111
[-1,2,3,4,-5] => [1,1,1] => 111 => 111
[-1,2,3,-4,5] => [1,1,1] => 111 => 111
[-1,2,3,-4,-5] => [1,1] => 11 => 11
[-1,2,-3,4,5] => [1,1,1] => 111 => 111
[-1,2,-3,4,-5] => [1,1] => 11 => 11
[-1,2,-3,-4,5] => [1,1] => 11 => 11
[-1,2,-3,-4,-5] => [1] => 1 => 1
[-1,-2,3,4,5] => [1,1,1] => 111 => 111
[-1,-2,3,4,-5] => [1,1] => 11 => 11
[-1,-2,3,-4,5] => [1,1] => 11 => 11
[-1,-2,3,-4,-5] => [1] => 1 => 1
[-1,-2,-3,4,5] => [1,1] => 11 => 11
[-1,-2,-3,4,-5] => [1] => 1 => 1
[-1,-2,-3,-4,5] => [1] => 1 => 1
[1,2,3,5,4] => [2,1,1,1] => 0111 => 0111
[1,2,3,5,-4] => [1,1,1] => 111 => 111
[1,2,3,-5,4] => [1,1,1] => 111 => 111
[1,2,3,-5,-4] => [2,1,1,1] => 0111 => 0111
[1,2,-3,5,4] => [2,1,1] => 011 => 011
[1,2,-3,5,-4] => [1,1] => 11 => 11
[1,2,-3,-5,4] => [1,1] => 11 => 11
[1,2,-3,-5,-4] => [2,1,1] => 011 => 011
[1,-2,3,5,4] => [2,1,1] => 011 => 011
[1,-2,3,5,-4] => [1,1] => 11 => 11
[1,-2,3,-5,4] => [1,1] => 11 => 11
[1,-2,3,-5,-4] => [2,1,1] => 011 => 011
[1,-2,-3,5,4] => [2,1] => 01 => 01
[1,-2,-3,5,-4] => [1] => 1 => 1
[1,-2,-3,-5,4] => [1] => 1 => 1
[1,-2,-3,-5,-4] => [2,1] => 01 => 01
[-1,2,3,5,4] => [2,1,1] => 011 => 011
[-1,2,3,5,-4] => [1,1] => 11 => 11
[-1,2,3,-5,4] => [1,1] => 11 => 11
[-1,2,3,-5,-4] => [2,1,1] => 011 => 011
[-1,2,-3,5,4] => [2,1] => 01 => 01
[-1,2,-3,5,-4] => [1] => 1 => 1
[-1,2,-3,-5,4] => [1] => 1 => 1
[-1,2,-3,-5,-4] => [2,1] => 01 => 01
[-1,-2,3,5,4] => [2,1] => 01 => 01
[-1,-2,3,5,-4] => [1] => 1 => 1
[-1,-2,3,-5,4] => [1] => 1 => 1
[-1,-2,3,-5,-4] => [2,1] => 01 => 01
[-1,-2,-3,5,4] => [2] => 0 => 0
[-1,-2,-3,-5,-4] => [2] => 0 => 0
[1,2,4,3,5] => [2,1,1,1] => 0111 => 0111
[1,2,4,3,-5] => [2,1,1] => 011 => 011
[1,2,4,-3,5] => [1,1,1] => 111 => 111
[1,2,4,-3,-5] => [1,1] => 11 => 11
[1,2,-4,3,5] => [1,1,1] => 111 => 111
[1,2,-4,3,-5] => [1,1] => 11 => 11
[1,2,-4,-3,5] => [2,1,1,1] => 0111 => 0111
[1,2,-4,-3,-5] => [2,1,1] => 011 => 011
[1,-2,4,3,5] => [2,1,1] => 011 => 011
[1,-2,4,3,-5] => [2,1] => 01 => 01
[1,-2,4,-3,5] => [1,1] => 11 => 11
[1,-2,4,-3,-5] => [1] => 1 => 1
[1,-2,-4,3,5] => [1,1] => 11 => 11
[1,-2,-4,3,-5] => [1] => 1 => 1
[1,-2,-4,-3,5] => [2,1,1] => 011 => 011
[1,-2,-4,-3,-5] => [2,1] => 01 => 01
[-1,2,4,3,5] => [2,1,1] => 011 => 011
[-1,2,4,3,-5] => [2,1] => 01 => 01
[-1,2,4,-3,5] => [1,1] => 11 => 11
[-1,2,4,-3,-5] => [1] => 1 => 1
[-1,2,-4,3,5] => [1,1] => 11 => 11
[-1,2,-4,3,-5] => [1] => 1 => 1
[-1,2,-4,-3,5] => [2,1,1] => 011 => 011
[-1,2,-4,-3,-5] => [2,1] => 01 => 01
[-1,-2,4,3,5] => [2,1] => 01 => 01
[-1,-2,4,3,-5] => [2] => 0 => 0
[-1,-2,4,-3,5] => [1] => 1 => 1
[-1,-2,-4,3,5] => [1] => 1 => 1
[-1,-2,-4,-3,5] => [2,1] => 01 => 01
[-1,-2,-4,-3,-5] => [2] => 0 => 0
[1,2,4,5,3] => [3,1,1] => 111 => 111
[1,2,4,5,-3] => [1,1] => 11 => 11
[1,2,4,-5,3] => [1,1] => 11 => 11
[1,2,4,-5,-3] => [3,1,1] => 111 => 111
[1,2,-4,5,3] => [1,1] => 11 => 11
[1,2,-4,5,-3] => [3,1,1] => 111 => 111
[1,2,-4,-5,3] => [3,1,1] => 111 => 111
[1,2,-4,-5,-3] => [1,1] => 11 => 11
[1,-2,4,5,3] => [3,1] => 11 => 11
[1,-2,4,5,-3] => [1] => 1 => 1
[1,-2,4,-5,3] => [1] => 1 => 1
[1,-2,4,-5,-3] => [3,1] => 11 => 11
[1,-2,-4,5,3] => [1] => 1 => 1
[1,-2,-4,5,-3] => [3,1] => 11 => 11
[1,-2,-4,-5,3] => [3,1] => 11 => 11
[1,-2,-4,-5,-3] => [1] => 1 => 1
[-1,2,4,5,3] => [3,1] => 11 => 11
[-1,2,4,5,-3] => [1] => 1 => 1
[-1,2,4,-5,3] => [1] => 1 => 1
[-1,2,4,-5,-3] => [3,1] => 11 => 11
[-1,2,-4,5,3] => [1] => 1 => 1
[-1,2,-4,5,-3] => [3,1] => 11 => 11
[-1,2,-4,-5,3] => [3,1] => 11 => 11
[-1,2,-4,-5,-3] => [1] => 1 => 1
[-1,-2,4,5,3] => [3] => 1 => 1
[-1,-2,4,-5,-3] => [3] => 1 => 1
[-1,-2,-4,5,-3] => [3] => 1 => 1
[-1,-2,-4,-5,3] => [3] => 1 => 1
[1,2,5,3,4] => [3,1,1] => 111 => 111
[1,2,5,3,-4] => [1,1] => 11 => 11
[1,2,5,-3,4] => [1,1] => 11 => 11
[1,2,5,-3,-4] => [3,1,1] => 111 => 111
[1,2,-5,3,4] => [1,1] => 11 => 11
[1,2,-5,3,-4] => [3,1,1] => 111 => 111
[1,2,-5,-3,4] => [3,1,1] => 111 => 111
[1,2,-5,-3,-4] => [1,1] => 11 => 11
[1,-2,5,3,4] => [3,1] => 11 => 11
[1,-2,5,3,-4] => [1] => 1 => 1
[1,-2,5,-3,4] => [1] => 1 => 1
[1,-2,5,-3,-4] => [3,1] => 11 => 11
[1,-2,-5,3,4] => [1] => 1 => 1
[1,-2,-5,3,-4] => [3,1] => 11 => 11
[1,-2,-5,-3,4] => [3,1] => 11 => 11
[1,-2,-5,-3,-4] => [1] => 1 => 1
[-1,2,5,3,4] => [3,1] => 11 => 11
[-1,2,5,3,-4] => [1] => 1 => 1
[-1,2,5,-3,4] => [1] => 1 => 1
[-1,2,5,-3,-4] => [3,1] => 11 => 11
[-1,2,-5,3,4] => [1] => 1 => 1
[-1,2,-5,3,-4] => [3,1] => 11 => 11
[-1,2,-5,-3,4] => [3,1] => 11 => 11
[-1,2,-5,-3,-4] => [1] => 1 => 1
[-1,-2,5,3,4] => [3] => 1 => 1
[-1,-2,5,-3,-4] => [3] => 1 => 1
[-1,-2,-5,3,-4] => [3] => 1 => 1
[-1,-2,-5,-3,4] => [3] => 1 => 1
[1,2,5,4,3] => [2,1,1,1] => 0111 => 0111
[1,2,5,4,-3] => [1,1,1] => 111 => 111
[1,2,5,-4,3] => [2,1,1] => 011 => 011
[1,2,5,-4,-3] => [1,1] => 11 => 11
[1,2,-5,4,3] => [1,1,1] => 111 => 111
[1,2,-5,4,-3] => [2,1,1,1] => 0111 => 0111
[1,2,-5,-4,3] => [1,1] => 11 => 11
[1,2,-5,-4,-3] => [2,1,1] => 011 => 011
[1,-2,5,4,3] => [2,1,1] => 011 => 011
[1,-2,5,4,-3] => [1,1] => 11 => 11
[1,-2,5,-4,3] => [2,1] => 01 => 01
[1,-2,5,-4,-3] => [1] => 1 => 1
[1,-2,-5,4,3] => [1,1] => 11 => 11
[1,-2,-5,4,-3] => [2,1,1] => 011 => 011
[1,-2,-5,-4,3] => [1] => 1 => 1
[1,-2,-5,-4,-3] => [2,1] => 01 => 01
[-1,2,5,4,3] => [2,1,1] => 011 => 011
[-1,2,5,4,-3] => [1,1] => 11 => 11
[-1,2,5,-4,3] => [2,1] => 01 => 01
[-1,2,5,-4,-3] => [1] => 1 => 1
[-1,2,-5,4,3] => [1,1] => 11 => 11
[-1,2,-5,4,-3] => [2,1,1] => 011 => 011
[-1,2,-5,-4,3] => [1] => 1 => 1
[-1,2,-5,-4,-3] => [2,1] => 01 => 01
[-1,-2,5,4,3] => [2,1] => 01 => 01
[-1,-2,5,4,-3] => [1] => 1 => 1
[-1,-2,5,-4,3] => [2] => 0 => 0
[-1,-2,-5,4,3] => [1] => 1 => 1
[-1,-2,-5,4,-3] => [2,1] => 01 => 01
[-1,-2,-5,-4,-3] => [2] => 0 => 0
[1,3,2,4,5] => [2,1,1,1] => 0111 => 0111
[1,3,2,4,-5] => [2,1,1] => 011 => 011
[1,3,2,-4,5] => [2,1,1] => 011 => 011
[1,3,2,-4,-5] => [2,1] => 01 => 01
[1,3,-2,4,5] => [1,1,1] => 111 => 111
[1,3,-2,4,-5] => [1,1] => 11 => 11
[1,3,-2,-4,5] => [1,1] => 11 => 11
[1,3,-2,-4,-5] => [1] => 1 => 1
[1,-3,2,4,5] => [1,1,1] => 111 => 111
[1,-3,2,4,-5] => [1,1] => 11 => 11
[1,-3,2,-4,5] => [1,1] => 11 => 11
[1,-3,2,-4,-5] => [1] => 1 => 1
[1,-3,-2,4,5] => [2,1,1,1] => 0111 => 0111
[1,-3,-2,4,-5] => [2,1,1] => 011 => 011
[1,-3,-2,-4,5] => [2,1,1] => 011 => 011
[1,-3,-2,-4,-5] => [2,1] => 01 => 01
[-1,3,2,4,5] => [2,1,1] => 011 => 011
[-1,3,2,4,-5] => [2,1] => 01 => 01
[-1,3,2,-4,5] => [2,1] => 01 => 01
[-1,3,2,-4,-5] => [2] => 0 => 0
[-1,3,-2,4,5] => [1,1] => 11 => 11
[-1,3,-2,4,-5] => [1] => 1 => 1
[-1,3,-2,-4,5] => [1] => 1 => 1
[-1,-3,2,4,5] => [1,1] => 11 => 11
[-1,-3,2,4,-5] => [1] => 1 => 1
[-1,-3,2,-4,5] => [1] => 1 => 1
[-1,-3,-2,4,5] => [2,1,1] => 011 => 011
[-1,-3,-2,4,-5] => [2,1] => 01 => 01
[-1,-3,-2,-4,5] => [2,1] => 01 => 01
[-1,-3,-2,-4,-5] => [2] => 0 => 0
[1,3,2,5,4] => [2,2,1] => 001 => 001
[1,3,2,5,-4] => [2,1] => 01 => 01
[1,3,2,-5,4] => [2,1] => 01 => 01
[1,3,2,-5,-4] => [2,2,1] => 001 => 001
[1,3,-2,5,4] => [2,1] => 01 => 01
[1,3,-2,5,-4] => [1] => 1 => 1
[1,3,-2,-5,4] => [1] => 1 => 1
[1,3,-2,-5,-4] => [2,1] => 01 => 01
[1,-3,2,5,4] => [2,1] => 01 => 01
[1,-3,2,5,-4] => [1] => 1 => 1
[1,-3,2,-5,4] => [1] => 1 => 1
[1,-3,2,-5,-4] => [2,1] => 01 => 01
[1,-3,-2,5,4] => [2,2,1] => 001 => 001
[1,-3,-2,5,-4] => [2,1] => 01 => 01
[1,-3,-2,-5,4] => [2,1] => 01 => 01
[1,-3,-2,-5,-4] => [2,2,1] => 001 => 001
[-1,3,2,5,4] => [2,2] => 00 => 00
[-1,3,2,5,-4] => [2] => 0 => 0
[-1,3,2,-5,4] => [2] => 0 => 0
[-1,3,2,-5,-4] => [2,2] => 00 => 00
[-1,3,-2,5,4] => [2] => 0 => 0
[-1,3,-2,-5,-4] => [2] => 0 => 0
[-1,-3,2,5,4] => [2] => 0 => 0
[-1,-3,2,-5,-4] => [2] => 0 => 0
[-1,-3,-2,5,4] => [2,2] => 00 => 00
[-1,-3,-2,5,-4] => [2] => 0 => 0
[-1,-3,-2,-5,4] => [2] => 0 => 0
[-1,-3,-2,-5,-4] => [2,2] => 00 => 00
[1,3,4,2,5] => [3,1,1] => 111 => 111
[1,3,4,2,-5] => [3,1] => 11 => 11
[1,3,4,-2,5] => [1,1] => 11 => 11
[1,3,4,-2,-5] => [1] => 1 => 1
[1,3,-4,2,5] => [1,1] => 11 => 11
[1,3,-4,2,-5] => [1] => 1 => 1
[1,3,-4,-2,5] => [3,1,1] => 111 => 111
[1,3,-4,-2,-5] => [3,1] => 11 => 11
[1,-3,4,2,5] => [1,1] => 11 => 11
[1,-3,4,2,-5] => [1] => 1 => 1
[1,-3,4,-2,5] => [3,1,1] => 111 => 111
[1,-3,4,-2,-5] => [3,1] => 11 => 11
[1,-3,-4,2,5] => [3,1,1] => 111 => 111
[1,-3,-4,2,-5] => [3,1] => 11 => 11
[1,-3,-4,-2,5] => [1,1] => 11 => 11
[1,-3,-4,-2,-5] => [1] => 1 => 1
[-1,3,4,2,5] => [3,1] => 11 => 11
[-1,3,4,2,-5] => [3] => 1 => 1
[-1,3,4,-2,5] => [1] => 1 => 1
[-1,3,-4,2,5] => [1] => 1 => 1
[-1,3,-4,-2,5] => [3,1] => 11 => 11
[-1,3,-4,-2,-5] => [3] => 1 => 1
[-1,-3,4,2,5] => [1] => 1 => 1
[-1,-3,4,-2,5] => [3,1] => 11 => 11
[-1,-3,4,-2,-5] => [3] => 1 => 1
[-1,-3,-4,2,5] => [3,1] => 11 => 11
[-1,-3,-4,2,-5] => [3] => 1 => 1
[-1,-3,-4,-2,5] => [1] => 1 => 1
[1,3,4,5,2] => [4,1] => 01 => 01
[1,3,4,5,-2] => [1] => 1 => 1
[1,3,4,-5,2] => [1] => 1 => 1
[1,3,4,-5,-2] => [4,1] => 01 => 01
[1,3,-4,5,2] => [1] => 1 => 1
[1,3,-4,5,-2] => [4,1] => 01 => 01
[1,3,-4,-5,2] => [4,1] => 01 => 01
[1,3,-4,-5,-2] => [1] => 1 => 1
[1,-3,4,5,2] => [1] => 1 => 1
[1,-3,4,5,-2] => [4,1] => 01 => 01
[1,-3,4,-5,2] => [4,1] => 01 => 01
[1,-3,4,-5,-2] => [1] => 1 => 1
[1,-3,-4,5,2] => [4,1] => 01 => 01
[1,-3,-4,5,-2] => [1] => 1 => 1
[1,-3,-4,-5,2] => [1] => 1 => 1
[1,-3,-4,-5,-2] => [4,1] => 01 => 01
[-1,3,4,5,2] => [4] => 0 => 0
[-1,3,4,-5,-2] => [4] => 0 => 0
[-1,3,-4,5,-2] => [4] => 0 => 0
[-1,3,-4,-5,2] => [4] => 0 => 0
[-1,-3,4,5,-2] => [4] => 0 => 0
[-1,-3,4,-5,2] => [4] => 0 => 0
[-1,-3,-4,5,2] => [4] => 0 => 0
[-1,-3,-4,-5,-2] => [4] => 0 => 0
[1,3,5,2,4] => [4,1] => 01 => 01
[1,3,5,2,-4] => [1] => 1 => 1
[1,3,5,-2,4] => [1] => 1 => 1
[1,3,5,-2,-4] => [4,1] => 01 => 01
[1,3,-5,2,4] => [1] => 1 => 1
[1,3,-5,2,-4] => [4,1] => 01 => 01
[1,3,-5,-2,4] => [4,1] => 01 => 01
[1,3,-5,-2,-4] => [1] => 1 => 1
[1,-3,5,2,4] => [1] => 1 => 1
[1,-3,5,2,-4] => [4,1] => 01 => 01
[1,-3,5,-2,4] => [4,1] => 01 => 01
[1,-3,5,-2,-4] => [1] => 1 => 1
[1,-3,-5,2,4] => [4,1] => 01 => 01
[1,-3,-5,2,-4] => [1] => 1 => 1
[1,-3,-5,-2,4] => [1] => 1 => 1
[1,-3,-5,-2,-4] => [4,1] => 01 => 01
[-1,3,5,2,4] => [4] => 0 => 0
[-1,3,5,-2,-4] => [4] => 0 => 0
[-1,3,-5,2,-4] => [4] => 0 => 0
[-1,3,-5,-2,4] => [4] => 0 => 0
[-1,-3,5,2,-4] => [4] => 0 => 0
[-1,-3,5,-2,4] => [4] => 0 => 0
[-1,-3,-5,2,4] => [4] => 0 => 0
[-1,-3,-5,-2,-4] => [4] => 0 => 0
[1,3,5,4,2] => [3,1,1] => 111 => 111
[1,3,5,4,-2] => [1,1] => 11 => 11
[1,3,5,-4,2] => [3,1] => 11 => 11
[1,3,5,-4,-2] => [1] => 1 => 1
[1,3,-5,4,2] => [1,1] => 11 => 11
[1,3,-5,4,-2] => [3,1,1] => 111 => 111
[1,3,-5,-4,2] => [1] => 1 => 1
[1,3,-5,-4,-2] => [3,1] => 11 => 11
[1,-3,5,4,2] => [1,1] => 11 => 11
[1,-3,5,4,-2] => [3,1,1] => 111 => 111
[1,-3,5,-4,2] => [1] => 1 => 1
[1,-3,5,-4,-2] => [3,1] => 11 => 11
[1,-3,-5,4,2] => [3,1,1] => 111 => 111
[1,-3,-5,4,-2] => [1,1] => 11 => 11
[1,-3,-5,-4,2] => [3,1] => 11 => 11
[1,-3,-5,-4,-2] => [1] => 1 => 1
[-1,3,5,4,2] => [3,1] => 11 => 11
[-1,3,5,4,-2] => [1] => 1 => 1
[-1,3,5,-4,2] => [3] => 1 => 1
[-1,3,-5,4,2] => [1] => 1 => 1
[-1,3,-5,4,-2] => [3,1] => 11 => 11
[-1,3,-5,-4,-2] => [3] => 1 => 1
[-1,-3,5,4,2] => [1] => 1 => 1
[-1,-3,5,4,-2] => [3,1] => 11 => 11
[-1,-3,5,-4,-2] => [3] => 1 => 1
[-1,-3,-5,4,2] => [3,1] => 11 => 11
[-1,-3,-5,4,-2] => [1] => 1 => 1
[-1,-3,-5,-4,2] => [3] => 1 => 1
[1,4,2,3,5] => [3,1,1] => 111 => 111
[1,4,2,3,-5] => [3,1] => 11 => 11
[1,4,2,-3,5] => [1,1] => 11 => 11
[1,4,2,-3,-5] => [1] => 1 => 1
[1,4,-2,3,5] => [1,1] => 11 => 11
[1,4,-2,3,-5] => [1] => 1 => 1
[1,4,-2,-3,5] => [3,1,1] => 111 => 111
[1,4,-2,-3,-5] => [3,1] => 11 => 11
[1,-4,2,3,5] => [1,1] => 11 => 11
[1,-4,2,3,-5] => [1] => 1 => 1
[1,-4,2,-3,5] => [3,1,1] => 111 => 111
[1,-4,2,-3,-5] => [3,1] => 11 => 11
[1,-4,-2,3,5] => [3,1,1] => 111 => 111
[1,-4,-2,3,-5] => [3,1] => 11 => 11
[1,-4,-2,-3,5] => [1,1] => 11 => 11
[1,-4,-2,-3,-5] => [1] => 1 => 1
[-1,4,2,3,5] => [3,1] => 11 => 11
[-1,4,2,3,-5] => [3] => 1 => 1
[-1,4,2,-3,5] => [1] => 1 => 1
[-1,4,-2,3,5] => [1] => 1 => 1
[-1,4,-2,-3,5] => [3,1] => 11 => 11
[-1,4,-2,-3,-5] => [3] => 1 => 1
[-1,-4,2,3,5] => [1] => 1 => 1
[-1,-4,2,-3,5] => [3,1] => 11 => 11
[-1,-4,2,-3,-5] => [3] => 1 => 1
[-1,-4,-2,3,5] => [3,1] => 11 => 11
[-1,-4,-2,3,-5] => [3] => 1 => 1
[-1,-4,-2,-3,5] => [1] => 1 => 1
[1,4,2,5,3] => [4,1] => 01 => 01
[1,4,2,5,-3] => [1] => 1 => 1
[1,4,2,-5,3] => [1] => 1 => 1
[1,4,2,-5,-3] => [4,1] => 01 => 01
[1,4,-2,5,3] => [1] => 1 => 1
[1,4,-2,5,-3] => [4,1] => 01 => 01
[1,4,-2,-5,3] => [4,1] => 01 => 01
[1,4,-2,-5,-3] => [1] => 1 => 1
[1,-4,2,5,3] => [1] => 1 => 1
[1,-4,2,5,-3] => [4,1] => 01 => 01
[1,-4,2,-5,3] => [4,1] => 01 => 01
[1,-4,2,-5,-3] => [1] => 1 => 1
[1,-4,-2,5,3] => [4,1] => 01 => 01
[1,-4,-2,5,-3] => [1] => 1 => 1
[1,-4,-2,-5,3] => [1] => 1 => 1
[1,-4,-2,-5,-3] => [4,1] => 01 => 01
[-1,4,2,5,3] => [4] => 0 => 0
[-1,4,2,-5,-3] => [4] => 0 => 0
[-1,4,-2,5,-3] => [4] => 0 => 0
[-1,4,-2,-5,3] => [4] => 0 => 0
[-1,-4,2,5,-3] => [4] => 0 => 0
[-1,-4,2,-5,3] => [4] => 0 => 0
[-1,-4,-2,5,3] => [4] => 0 => 0
[-1,-4,-2,-5,-3] => [4] => 0 => 0
[1,4,3,2,5] => [2,1,1,1] => 0111 => 0111
[1,4,3,2,-5] => [2,1,1] => 011 => 011
[1,4,3,-2,5] => [1,1,1] => 111 => 111
[1,4,3,-2,-5] => [1,1] => 11 => 11
[1,4,-3,2,5] => [2,1,1] => 011 => 011
[1,4,-3,2,-5] => [2,1] => 01 => 01
[1,4,-3,-2,5] => [1,1] => 11 => 11
[1,4,-3,-2,-5] => [1] => 1 => 1
[1,-4,3,2,5] => [1,1,1] => 111 => 111
[1,-4,3,2,-5] => [1,1] => 11 => 11
[1,-4,3,-2,5] => [2,1,1,1] => 0111 => 0111
[1,-4,3,-2,-5] => [2,1,1] => 011 => 011
[1,-4,-3,2,5] => [1,1] => 11 => 11
[1,-4,-3,2,-5] => [1] => 1 => 1
[1,-4,-3,-2,5] => [2,1,1] => 011 => 011
[1,-4,-3,-2,-5] => [2,1] => 01 => 01
[-1,4,3,2,5] => [2,1,1] => 011 => 011
[-1,4,3,2,-5] => [2,1] => 01 => 01
[-1,4,3,-2,5] => [1,1] => 11 => 11
[-1,4,3,-2,-5] => [1] => 1 => 1
[-1,4,-3,2,5] => [2,1] => 01 => 01
[-1,4,-3,2,-5] => [2] => 0 => 0
[-1,4,-3,-2,5] => [1] => 1 => 1
[-1,-4,3,2,5] => [1,1] => 11 => 11
[-1,-4,3,2,-5] => [1] => 1 => 1
[-1,-4,3,-2,5] => [2,1,1] => 011 => 011
[-1,-4,3,-2,-5] => [2,1] => 01 => 01
[-1,-4,-3,2,5] => [1] => 1 => 1
[-1,-4,-3,-2,5] => [2,1] => 01 => 01
[-1,-4,-3,-2,-5] => [2] => 0 => 0
[1,4,3,5,2] => [3,1,1] => 111 => 111
[1,4,3,5,-2] => [1,1] => 11 => 11
[1,4,3,-5,2] => [1,1] => 11 => 11
[1,4,3,-5,-2] => [3,1,1] => 111 => 111
[1,4,-3,5,2] => [3,1] => 11 => 11
[1,4,-3,5,-2] => [1] => 1 => 1
[1,4,-3,-5,2] => [1] => 1 => 1
[1,4,-3,-5,-2] => [3,1] => 11 => 11
[1,-4,3,5,2] => [1,1] => 11 => 11
[1,-4,3,5,-2] => [3,1,1] => 111 => 111
[1,-4,3,-5,2] => [3,1,1] => 111 => 111
[1,-4,3,-5,-2] => [1,1] => 11 => 11
[1,-4,-3,5,2] => [1] => 1 => 1
[1,-4,-3,5,-2] => [3,1] => 11 => 11
[1,-4,-3,-5,2] => [3,1] => 11 => 11
[1,-4,-3,-5,-2] => [1] => 1 => 1
[-1,4,3,5,2] => [3,1] => 11 => 11
[-1,4,3,5,-2] => [1] => 1 => 1
[-1,4,3,-5,2] => [1] => 1 => 1
[-1,4,3,-5,-2] => [3,1] => 11 => 11
[-1,4,-3,5,2] => [3] => 1 => 1
[-1,4,-3,-5,-2] => [3] => 1 => 1
[-1,-4,3,5,2] => [1] => 1 => 1
[-1,-4,3,5,-2] => [3,1] => 11 => 11
[-1,-4,3,-5,2] => [3,1] => 11 => 11
[-1,-4,3,-5,-2] => [1] => 1 => 1
[-1,-4,-3,5,-2] => [3] => 1 => 1
[-1,-4,-3,-5,2] => [3] => 1 => 1
[1,4,5,2,3] => [2,2,1] => 001 => 001
[1,4,5,2,-3] => [2,1] => 01 => 01
[1,4,5,-2,3] => [2,1] => 01 => 01
[1,4,5,-2,-3] => [1] => 1 => 1
[1,4,-5,2,3] => [2,1] => 01 => 01
[1,4,-5,2,-3] => [2,2,1] => 001 => 001
[1,4,-5,-2,3] => [1] => 1 => 1
[1,4,-5,-2,-3] => [2,1] => 01 => 01
[1,-4,5,2,3] => [2,1] => 01 => 01
[1,-4,5,2,-3] => [1] => 1 => 1
[1,-4,5,-2,3] => [2,2,1] => 001 => 001
[1,-4,5,-2,-3] => [2,1] => 01 => 01
[1,-4,-5,2,3] => [1] => 1 => 1
[1,-4,-5,2,-3] => [2,1] => 01 => 01
[1,-4,-5,-2,3] => [2,1] => 01 => 01
[1,-4,-5,-2,-3] => [2,2,1] => 001 => 001
[-1,4,5,2,3] => [2,2] => 00 => 00
[-1,4,5,2,-3] => [2] => 0 => 0
[-1,4,5,-2,3] => [2] => 0 => 0
[-1,4,-5,2,3] => [2] => 0 => 0
[-1,4,-5,2,-3] => [2,2] => 00 => 00
[-1,4,-5,-2,-3] => [2] => 0 => 0
[-1,-4,5,2,3] => [2] => 0 => 0
[-1,-4,5,-2,3] => [2,2] => 00 => 00
[-1,-4,5,-2,-3] => [2] => 0 => 0
[-1,-4,-5,2,-3] => [2] => 0 => 0
[-1,-4,-5,-2,3] => [2] => 0 => 0
[-1,-4,-5,-2,-3] => [2,2] => 00 => 00
[1,4,5,3,2] => [4,1] => 01 => 01
[1,4,5,3,-2] => [1] => 1 => 1
[1,4,5,-3,2] => [1] => 1 => 1
[1,4,5,-3,-2] => [4,1] => 01 => 01
[1,4,-5,3,2] => [1] => 1 => 1
[1,4,-5,3,-2] => [4,1] => 01 => 01
[1,4,-5,-3,2] => [4,1] => 01 => 01
[1,4,-5,-3,-2] => [1] => 1 => 1
[1,-4,5,3,2] => [1] => 1 => 1
[1,-4,5,3,-2] => [4,1] => 01 => 01
[1,-4,5,-3,2] => [4,1] => 01 => 01
[1,-4,5,-3,-2] => [1] => 1 => 1
[1,-4,-5,3,2] => [4,1] => 01 => 01
[1,-4,-5,3,-2] => [1] => 1 => 1
[1,-4,-5,-3,2] => [1] => 1 => 1
[1,-4,-5,-3,-2] => [4,1] => 01 => 01
[-1,4,5,3,2] => [4] => 0 => 0
[-1,4,5,-3,-2] => [4] => 0 => 0
[-1,4,-5,3,-2] => [4] => 0 => 0
[-1,4,-5,-3,2] => [4] => 0 => 0
[-1,-4,5,3,-2] => [4] => 0 => 0
[-1,-4,5,-3,2] => [4] => 0 => 0
[-1,-4,-5,3,2] => [4] => 0 => 0
[-1,-4,-5,-3,-2] => [4] => 0 => 0
[1,5,2,3,4] => [4,1] => 01 => 01
[1,5,2,3,-4] => [1] => 1 => 1
[1,5,2,-3,4] => [1] => 1 => 1
[1,5,2,-3,-4] => [4,1] => 01 => 01
[1,5,-2,3,4] => [1] => 1 => 1
[1,5,-2,3,-4] => [4,1] => 01 => 01
[1,5,-2,-3,4] => [4,1] => 01 => 01
[1,5,-2,-3,-4] => [1] => 1 => 1
[1,-5,2,3,4] => [1] => 1 => 1
[1,-5,2,3,-4] => [4,1] => 01 => 01
[1,-5,2,-3,4] => [4,1] => 01 => 01
[1,-5,2,-3,-4] => [1] => 1 => 1
[1,-5,-2,3,4] => [4,1] => 01 => 01
[1,-5,-2,3,-4] => [1] => 1 => 1
[1,-5,-2,-3,4] => [1] => 1 => 1
[1,-5,-2,-3,-4] => [4,1] => 01 => 01
[-1,5,2,3,4] => [4] => 0 => 0
[-1,5,2,-3,-4] => [4] => 0 => 0
[-1,5,-2,3,-4] => [4] => 0 => 0
[-1,5,-2,-3,4] => [4] => 0 => 0
[-1,-5,2,3,-4] => [4] => 0 => 0
[-1,-5,2,-3,4] => [4] => 0 => 0
[-1,-5,-2,3,4] => [4] => 0 => 0
[-1,-5,-2,-3,-4] => [4] => 0 => 0
[1,5,2,4,3] => [3,1,1] => 111 => 111
[1,5,2,4,-3] => [1,1] => 11 => 11
[1,5,2,-4,3] => [3,1] => 11 => 11
[1,5,2,-4,-3] => [1] => 1 => 1
[1,5,-2,4,3] => [1,1] => 11 => 11
[1,5,-2,4,-3] => [3,1,1] => 111 => 111
[1,5,-2,-4,3] => [1] => 1 => 1
[1,5,-2,-4,-3] => [3,1] => 11 => 11
[1,-5,2,4,3] => [1,1] => 11 => 11
[1,-5,2,4,-3] => [3,1,1] => 111 => 111
[1,-5,2,-4,3] => [1] => 1 => 1
[1,-5,2,-4,-3] => [3,1] => 11 => 11
[1,-5,-2,4,3] => [3,1,1] => 111 => 111
[1,-5,-2,4,-3] => [1,1] => 11 => 11
[1,-5,-2,-4,3] => [3,1] => 11 => 11
[1,-5,-2,-4,-3] => [1] => 1 => 1
[-1,5,2,4,3] => [3,1] => 11 => 11
[-1,5,2,4,-3] => [1] => 1 => 1
[-1,5,2,-4,3] => [3] => 1 => 1
[-1,5,-2,4,3] => [1] => 1 => 1
[-1,5,-2,4,-3] => [3,1] => 11 => 11
[-1,5,-2,-4,-3] => [3] => 1 => 1
[-1,-5,2,4,3] => [1] => 1 => 1
[-1,-5,2,4,-3] => [3,1] => 11 => 11
[-1,-5,2,-4,-3] => [3] => 1 => 1
[-1,-5,-2,4,3] => [3,1] => 11 => 11
[-1,-5,-2,4,-3] => [1] => 1 => 1
[-1,-5,-2,-4,3] => [3] => 1 => 1
[1,5,3,2,4] => [3,1,1] => 111 => 111
[1,5,3,2,-4] => [1,1] => 11 => 11
[1,5,3,-2,4] => [1,1] => 11 => 11
[1,5,3,-2,-4] => [3,1,1] => 111 => 111
[1,5,-3,2,4] => [3,1] => 11 => 11
[1,5,-3,2,-4] => [1] => 1 => 1
[1,5,-3,-2,4] => [1] => 1 => 1
[1,5,-3,-2,-4] => [3,1] => 11 => 11
[1,-5,3,2,4] => [1,1] => 11 => 11
[1,-5,3,2,-4] => [3,1,1] => 111 => 111
[1,-5,3,-2,4] => [3,1,1] => 111 => 111
[1,-5,3,-2,-4] => [1,1] => 11 => 11
[1,-5,-3,2,4] => [1] => 1 => 1
[1,-5,-3,2,-4] => [3,1] => 11 => 11
[1,-5,-3,-2,4] => [3,1] => 11 => 11
[1,-5,-3,-2,-4] => [1] => 1 => 1
[-1,5,3,2,4] => [3,1] => 11 => 11
[-1,5,3,2,-4] => [1] => 1 => 1
[-1,5,3,-2,4] => [1] => 1 => 1
[-1,5,3,-2,-4] => [3,1] => 11 => 11
[-1,5,-3,2,4] => [3] => 1 => 1
[-1,5,-3,-2,-4] => [3] => 1 => 1
[-1,-5,3,2,4] => [1] => 1 => 1
[-1,-5,3,2,-4] => [3,1] => 11 => 11
[-1,-5,3,-2,4] => [3,1] => 11 => 11
[-1,-5,3,-2,-4] => [1] => 1 => 1
[-1,-5,-3,2,-4] => [3] => 1 => 1
[-1,-5,-3,-2,4] => [3] => 1 => 1
[1,5,3,4,2] => [2,1,1,1] => 0111 => 0111
[1,5,3,4,-2] => [1,1,1] => 111 => 111
[1,5,3,-4,2] => [2,1,1] => 011 => 011
[1,5,3,-4,-2] => [1,1] => 11 => 11
[1,5,-3,4,2] => [2,1,1] => 011 => 011
[1,5,-3,4,-2] => [1,1] => 11 => 11
[1,5,-3,-4,2] => [2,1] => 01 => 01
[1,5,-3,-4,-2] => [1] => 1 => 1
[1,-5,3,4,2] => [1,1,1] => 111 => 111
[1,-5,3,4,-2] => [2,1,1,1] => 0111 => 0111
[1,-5,3,-4,2] => [1,1] => 11 => 11
[1,-5,3,-4,-2] => [2,1,1] => 011 => 011
[1,-5,-3,4,2] => [1,1] => 11 => 11
[1,-5,-3,4,-2] => [2,1,1] => 011 => 011
[1,-5,-3,-4,2] => [1] => 1 => 1
[1,-5,-3,-4,-2] => [2,1] => 01 => 01
[-1,5,3,4,2] => [2,1,1] => 011 => 011
[-1,5,3,4,-2] => [1,1] => 11 => 11
[-1,5,3,-4,2] => [2,1] => 01 => 01
[-1,5,3,-4,-2] => [1] => 1 => 1
[-1,5,-3,4,2] => [2,1] => 01 => 01
[-1,5,-3,4,-2] => [1] => 1 => 1
[-1,5,-3,-4,2] => [2] => 0 => 0
[-1,-5,3,4,2] => [1,1] => 11 => 11
[-1,-5,3,4,-2] => [2,1,1] => 011 => 011
[-1,-5,3,-4,2] => [1] => 1 => 1
[-1,-5,3,-4,-2] => [2,1] => 01 => 01
[-1,-5,-3,4,2] => [1] => 1 => 1
[-1,-5,-3,4,-2] => [2,1] => 01 => 01
[-1,-5,-3,-4,-2] => [2] => 0 => 0
[1,5,4,2,3] => [4,1] => 01 => 01
[1,5,4,2,-3] => [1] => 1 => 1
[1,5,4,-2,3] => [1] => 1 => 1
[1,5,4,-2,-3] => [4,1] => 01 => 01
[1,5,-4,2,3] => [1] => 1 => 1
[1,5,-4,2,-3] => [4,1] => 01 => 01
[1,5,-4,-2,3] => [4,1] => 01 => 01
[1,5,-4,-2,-3] => [1] => 1 => 1
[1,-5,4,2,3] => [1] => 1 => 1
[1,-5,4,2,-3] => [4,1] => 01 => 01
[1,-5,4,-2,3] => [4,1] => 01 => 01
[1,-5,4,-2,-3] => [1] => 1 => 1
[1,-5,-4,2,3] => [4,1] => 01 => 01
[1,-5,-4,2,-3] => [1] => 1 => 1
[1,-5,-4,-2,3] => [1] => 1 => 1
[1,-5,-4,-2,-3] => [4,1] => 01 => 01
[-1,5,4,2,3] => [4] => 0 => 0
[-1,5,4,-2,-3] => [4] => 0 => 0
[-1,5,-4,2,-3] => [4] => 0 => 0
[-1,5,-4,-2,3] => [4] => 0 => 0
[-1,-5,4,2,-3] => [4] => 0 => 0
[-1,-5,4,-2,3] => [4] => 0 => 0
[-1,-5,-4,2,3] => [4] => 0 => 0
[-1,-5,-4,-2,-3] => [4] => 0 => 0
[1,5,4,3,2] => [2,2,1] => 001 => 001
[1,5,4,3,-2] => [2,1] => 01 => 01
[1,5,4,-3,2] => [2,1] => 01 => 01
[1,5,4,-3,-2] => [1] => 1 => 1
[1,5,-4,3,2] => [2,1] => 01 => 01
[1,5,-4,3,-2] => [1] => 1 => 1
[1,5,-4,-3,2] => [2,2,1] => 001 => 001
[1,5,-4,-3,-2] => [2,1] => 01 => 01
[1,-5,4,3,2] => [2,1] => 01 => 01
[1,-5,4,3,-2] => [2,2,1] => 001 => 001
[1,-5,4,-3,2] => [1] => 1 => 1
[1,-5,4,-3,-2] => [2,1] => 01 => 01
[1,-5,-4,3,2] => [1] => 1 => 1
[1,-5,-4,3,-2] => [2,1] => 01 => 01
[1,-5,-4,-3,2] => [2,1] => 01 => 01
[1,-5,-4,-3,-2] => [2,2,1] => 001 => 001
[-1,5,4,3,2] => [2,2] => 00 => 00
[-1,5,4,3,-2] => [2] => 0 => 0
[-1,5,4,-3,2] => [2] => 0 => 0
[-1,5,-4,3,2] => [2] => 0 => 0
[-1,5,-4,-3,2] => [2,2] => 00 => 00
[-1,5,-4,-3,-2] => [2] => 0 => 0
[-1,-5,4,3,2] => [2] => 0 => 0
[-1,-5,4,3,-2] => [2,2] => 00 => 00
[-1,-5,4,-3,-2] => [2] => 0 => 0
[-1,-5,-4,3,-2] => [2] => 0 => 0
[-1,-5,-4,-3,2] => [2] => 0 => 0
[-1,-5,-4,-3,-2] => [2,2] => 00 => 00
[2,1,3,4,5] => [2,1,1,1] => 0111 => 0111
[2,1,3,4,-5] => [2,1,1] => 011 => 011
[2,1,3,-4,5] => [2,1,1] => 011 => 011
[2,1,3,-4,-5] => [2,1] => 01 => 01
[2,1,-3,4,5] => [2,1,1] => 011 => 011
[2,1,-3,4,-5] => [2,1] => 01 => 01
[2,1,-3,-4,5] => [2,1] => 01 => 01
[2,1,-3,-4,-5] => [2] => 0 => 0
[2,-1,3,4,5] => [1,1,1] => 111 => 111
[2,-1,3,4,-5] => [1,1] => 11 => 11
[2,-1,3,-4,5] => [1,1] => 11 => 11
[2,-1,3,-4,-5] => [1] => 1 => 1
[2,-1,-3,4,5] => [1,1] => 11 => 11
[2,-1,-3,4,-5] => [1] => 1 => 1
[2,-1,-3,-4,5] => [1] => 1 => 1
[-2,1,3,4,5] => [1,1,1] => 111 => 111
[-2,1,3,4,-5] => [1,1] => 11 => 11
[-2,1,3,-4,5] => [1,1] => 11 => 11
[-2,1,3,-4,-5] => [1] => 1 => 1
[-2,1,-3,4,5] => [1,1] => 11 => 11
[-2,1,-3,4,-5] => [1] => 1 => 1
[-2,1,-3,-4,5] => [1] => 1 => 1
[-2,-1,3,4,5] => [2,1,1,1] => 0111 => 0111
[-2,-1,3,4,-5] => [2,1,1] => 011 => 011
[-2,-1,3,-4,5] => [2,1,1] => 011 => 011
[-2,-1,3,-4,-5] => [2,1] => 01 => 01
[-2,-1,-3,4,5] => [2,1,1] => 011 => 011
[-2,-1,-3,4,-5] => [2,1] => 01 => 01
[-2,-1,-3,-4,5] => [2,1] => 01 => 01
[-2,-1,-3,-4,-5] => [2] => 0 => 0
[2,1,3,5,4] => [2,2,1] => 001 => 001
[2,1,3,5,-4] => [2,1] => 01 => 01
[2,1,3,-5,4] => [2,1] => 01 => 01
[2,1,3,-5,-4] => [2,2,1] => 001 => 001
[2,1,-3,5,4] => [2,2] => 00 => 00
[2,1,-3,5,-4] => [2] => 0 => 0
[2,1,-3,-5,4] => [2] => 0 => 0
[2,1,-3,-5,-4] => [2,2] => 00 => 00
[2,-1,3,5,4] => [2,1] => 01 => 01
[2,-1,3,5,-4] => [1] => 1 => 1
[2,-1,3,-5,4] => [1] => 1 => 1
[2,-1,3,-5,-4] => [2,1] => 01 => 01
[2,-1,-3,5,4] => [2] => 0 => 0
[2,-1,-3,-5,-4] => [2] => 0 => 0
[-2,1,3,5,4] => [2,1] => 01 => 01
[-2,1,3,5,-4] => [1] => 1 => 1
[-2,1,3,-5,4] => [1] => 1 => 1
[-2,1,3,-5,-4] => [2,1] => 01 => 01
[-2,1,-3,5,4] => [2] => 0 => 0
[-2,1,-3,-5,-4] => [2] => 0 => 0
[-2,-1,3,5,4] => [2,2,1] => 001 => 001
[-2,-1,3,5,-4] => [2,1] => 01 => 01
[-2,-1,3,-5,4] => [2,1] => 01 => 01
[-2,-1,3,-5,-4] => [2,2,1] => 001 => 001
[-2,-1,-3,5,4] => [2,2] => 00 => 00
[-2,-1,-3,5,-4] => [2] => 0 => 0
[-2,-1,-3,-5,4] => [2] => 0 => 0
[-2,-1,-3,-5,-4] => [2,2] => 00 => 00
[2,1,4,3,5] => [2,2,1] => 001 => 001
[2,1,4,3,-5] => [2,2] => 00 => 00
[2,1,4,-3,5] => [2,1] => 01 => 01
[2,1,4,-3,-5] => [2] => 0 => 0
[2,1,-4,3,5] => [2,1] => 01 => 01
[2,1,-4,3,-5] => [2] => 0 => 0
[2,1,-4,-3,5] => [2,2,1] => 001 => 001
[2,1,-4,-3,-5] => [2,2] => 00 => 00
[2,-1,4,3,5] => [2,1] => 01 => 01
[2,-1,4,3,-5] => [2] => 0 => 0
[2,-1,4,-3,5] => [1] => 1 => 1
[2,-1,-4,3,5] => [1] => 1 => 1
[2,-1,-4,-3,5] => [2,1] => 01 => 01
[2,-1,-4,-3,-5] => [2] => 0 => 0
[-2,1,4,3,5] => [2,1] => 01 => 01
[-2,1,4,3,-5] => [2] => 0 => 0
[-2,1,4,-3,5] => [1] => 1 => 1
[-2,1,-4,3,5] => [1] => 1 => 1
[-2,1,-4,-3,5] => [2,1] => 01 => 01
[-2,1,-4,-3,-5] => [2] => 0 => 0
[-2,-1,4,3,5] => [2,2,1] => 001 => 001
[-2,-1,4,3,-5] => [2,2] => 00 => 00
[-2,-1,4,-3,5] => [2,1] => 01 => 01
[-2,-1,4,-3,-5] => [2] => 0 => 0
[-2,-1,-4,3,5] => [2,1] => 01 => 01
[-2,-1,-4,3,-5] => [2] => 0 => 0
[-2,-1,-4,-3,5] => [2,2,1] => 001 => 001
[-2,-1,-4,-3,-5] => [2,2] => 00 => 00
[2,1,4,5,3] => [3,2] => 10 => 10
[2,1,4,5,-3] => [2] => 0 => 0
[2,1,4,-5,3] => [2] => 0 => 0
[2,1,4,-5,-3] => [3,2] => 10 => 10
[2,1,-4,5,3] => [2] => 0 => 0
[2,1,-4,5,-3] => [3,2] => 10 => 10
[2,1,-4,-5,3] => [3,2] => 10 => 10
[2,1,-4,-5,-3] => [2] => 0 => 0
[2,-1,4,5,3] => [3] => 1 => 1
[2,-1,4,-5,-3] => [3] => 1 => 1
[2,-1,-4,5,-3] => [3] => 1 => 1
[2,-1,-4,-5,3] => [3] => 1 => 1
[-2,1,4,5,3] => [3] => 1 => 1
[-2,1,4,-5,-3] => [3] => 1 => 1
[-2,1,-4,5,-3] => [3] => 1 => 1
[-2,1,-4,-5,3] => [3] => 1 => 1
[-2,-1,4,5,3] => [3,2] => 10 => 10
[-2,-1,4,5,-3] => [2] => 0 => 0
[-2,-1,4,-5,3] => [2] => 0 => 0
[-2,-1,4,-5,-3] => [3,2] => 10 => 10
[-2,-1,-4,5,3] => [2] => 0 => 0
[-2,-1,-4,5,-3] => [3,2] => 10 => 10
[-2,-1,-4,-5,3] => [3,2] => 10 => 10
[-2,-1,-4,-5,-3] => [2] => 0 => 0
[2,1,5,3,4] => [3,2] => 10 => 10
[2,1,5,3,-4] => [2] => 0 => 0
[2,1,5,-3,4] => [2] => 0 => 0
[2,1,5,-3,-4] => [3,2] => 10 => 10
[2,1,-5,3,4] => [2] => 0 => 0
[2,1,-5,3,-4] => [3,2] => 10 => 10
[2,1,-5,-3,4] => [3,2] => 10 => 10
[2,1,-5,-3,-4] => [2] => 0 => 0
[2,-1,5,3,4] => [3] => 1 => 1
[2,-1,5,-3,-4] => [3] => 1 => 1
[2,-1,-5,3,-4] => [3] => 1 => 1
[2,-1,-5,-3,4] => [3] => 1 => 1
[-2,1,5,3,4] => [3] => 1 => 1
[-2,1,5,-3,-4] => [3] => 1 => 1
[-2,1,-5,3,-4] => [3] => 1 => 1
[-2,1,-5,-3,4] => [3] => 1 => 1
[-2,-1,5,3,4] => [3,2] => 10 => 10
[-2,-1,5,3,-4] => [2] => 0 => 0
[-2,-1,5,-3,4] => [2] => 0 => 0
[-2,-1,5,-3,-4] => [3,2] => 10 => 10
[-2,-1,-5,3,4] => [2] => 0 => 0
[-2,-1,-5,3,-4] => [3,2] => 10 => 10
[-2,-1,-5,-3,4] => [3,2] => 10 => 10
[-2,-1,-5,-3,-4] => [2] => 0 => 0
[2,1,5,4,3] => [2,2,1] => 001 => 001
[2,1,5,4,-3] => [2,1] => 01 => 01
[2,1,5,-4,3] => [2,2] => 00 => 00
[2,1,5,-4,-3] => [2] => 0 => 0
[2,1,-5,4,3] => [2,1] => 01 => 01
[2,1,-5,4,-3] => [2,2,1] => 001 => 001
[2,1,-5,-4,3] => [2] => 0 => 0
[2,1,-5,-4,-3] => [2,2] => 00 => 00
[2,-1,5,4,3] => [2,1] => 01 => 01
[2,-1,5,4,-3] => [1] => 1 => 1
[2,-1,5,-4,3] => [2] => 0 => 0
[2,-1,-5,4,3] => [1] => 1 => 1
[2,-1,-5,4,-3] => [2,1] => 01 => 01
[2,-1,-5,-4,-3] => [2] => 0 => 0
[-2,1,5,4,3] => [2,1] => 01 => 01
[-2,1,5,4,-3] => [1] => 1 => 1
[-2,1,5,-4,3] => [2] => 0 => 0
[-2,1,-5,4,3] => [1] => 1 => 1
[-2,1,-5,4,-3] => [2,1] => 01 => 01
[-2,1,-5,-4,-3] => [2] => 0 => 0
[-2,-1,5,4,3] => [2,2,1] => 001 => 001
[-2,-1,5,4,-3] => [2,1] => 01 => 01
[-2,-1,5,-4,3] => [2,2] => 00 => 00
[-2,-1,5,-4,-3] => [2] => 0 => 0
[-2,-1,-5,4,3] => [2,1] => 01 => 01
[-2,-1,-5,4,-3] => [2,2,1] => 001 => 001
[-2,-1,-5,-4,3] => [2] => 0 => 0
[-2,-1,-5,-4,-3] => [2,2] => 00 => 00
[2,3,1,4,5] => [3,1,1] => 111 => 111
[2,3,1,4,-5] => [3,1] => 11 => 11
[2,3,1,-4,5] => [3,1] => 11 => 11
[2,3,1,-4,-5] => [3] => 1 => 1
[2,3,-1,4,5] => [1,1] => 11 => 11
[2,3,-1,4,-5] => [1] => 1 => 1
[2,3,-1,-4,5] => [1] => 1 => 1
[2,-3,1,4,5] => [1,1] => 11 => 11
[2,-3,1,4,-5] => [1] => 1 => 1
[2,-3,1,-4,5] => [1] => 1 => 1
[2,-3,-1,4,5] => [3,1,1] => 111 => 111
[2,-3,-1,4,-5] => [3,1] => 11 => 11
[2,-3,-1,-4,5] => [3,1] => 11 => 11
[2,-3,-1,-4,-5] => [3] => 1 => 1
[-2,3,1,4,5] => [1,1] => 11 => 11
[-2,3,1,4,-5] => [1] => 1 => 1
[-2,3,1,-4,5] => [1] => 1 => 1
[-2,3,-1,4,5] => [3,1,1] => 111 => 111
[-2,3,-1,4,-5] => [3,1] => 11 => 11
[-2,3,-1,-4,5] => [3,1] => 11 => 11
[-2,3,-1,-4,-5] => [3] => 1 => 1
[-2,-3,1,4,5] => [3,1,1] => 111 => 111
[-2,-3,1,4,-5] => [3,1] => 11 => 11
[-2,-3,1,-4,5] => [3,1] => 11 => 11
[-2,-3,1,-4,-5] => [3] => 1 => 1
[-2,-3,-1,4,5] => [1,1] => 11 => 11
[-2,-3,-1,4,-5] => [1] => 1 => 1
[-2,-3,-1,-4,5] => [1] => 1 => 1
[2,3,1,5,4] => [3,2] => 10 => 10
[2,3,1,5,-4] => [3] => 1 => 1
[2,3,1,-5,4] => [3] => 1 => 1
[2,3,1,-5,-4] => [3,2] => 10 => 10
[2,3,-1,5,4] => [2] => 0 => 0
[2,3,-1,-5,-4] => [2] => 0 => 0
[2,-3,1,5,4] => [2] => 0 => 0
[2,-3,1,-5,-4] => [2] => 0 => 0
[2,-3,-1,5,4] => [3,2] => 10 => 10
[2,-3,-1,5,-4] => [3] => 1 => 1
[2,-3,-1,-5,4] => [3] => 1 => 1
[2,-3,-1,-5,-4] => [3,2] => 10 => 10
[-2,3,1,5,4] => [2] => 0 => 0
[-2,3,1,-5,-4] => [2] => 0 => 0
[-2,3,-1,5,4] => [3,2] => 10 => 10
[-2,3,-1,5,-4] => [3] => 1 => 1
[-2,3,-1,-5,4] => [3] => 1 => 1
[-2,3,-1,-5,-4] => [3,2] => 10 => 10
[-2,-3,1,5,4] => [3,2] => 10 => 10
[-2,-3,1,5,-4] => [3] => 1 => 1
[-2,-3,1,-5,4] => [3] => 1 => 1
[-2,-3,1,-5,-4] => [3,2] => 10 => 10
[-2,-3,-1,5,4] => [2] => 0 => 0
[-2,-3,-1,-5,-4] => [2] => 0 => 0
[2,3,4,1,5] => [4,1] => 01 => 01
[2,3,4,1,-5] => [4] => 0 => 0
[2,3,4,-1,5] => [1] => 1 => 1
[2,3,-4,1,5] => [1] => 1 => 1
[2,3,-4,-1,5] => [4,1] => 01 => 01
[2,3,-4,-1,-5] => [4] => 0 => 0
[2,-3,4,1,5] => [1] => 1 => 1
[2,-3,4,-1,5] => [4,1] => 01 => 01
[2,-3,4,-1,-5] => [4] => 0 => 0
[2,-3,-4,1,5] => [4,1] => 01 => 01
[2,-3,-4,1,-5] => [4] => 0 => 0
[2,-3,-4,-1,5] => [1] => 1 => 1
[-2,3,4,1,5] => [1] => 1 => 1
[-2,3,4,-1,5] => [4,1] => 01 => 01
[-2,3,4,-1,-5] => [4] => 0 => 0
[-2,3,-4,1,5] => [4,1] => 01 => 01
[-2,3,-4,1,-5] => [4] => 0 => 0
[-2,3,-4,-1,5] => [1] => 1 => 1
[-2,-3,4,1,5] => [4,1] => 01 => 01
[-2,-3,4,1,-5] => [4] => 0 => 0
[-2,-3,4,-1,5] => [1] => 1 => 1
[-2,-3,-4,1,5] => [1] => 1 => 1
[-2,-3,-4,-1,5] => [4,1] => 01 => 01
[-2,-3,-4,-1,-5] => [4] => 0 => 0
[2,3,4,5,1] => [5] => 1 => 1
[2,3,4,-5,-1] => [5] => 1 => 1
[2,3,-4,5,-1] => [5] => 1 => 1
[2,3,-4,-5,1] => [5] => 1 => 1
[2,-3,4,5,-1] => [5] => 1 => 1
[2,-3,4,-5,1] => [5] => 1 => 1
[2,-3,-4,5,1] => [5] => 1 => 1
[2,-3,-4,-5,-1] => [5] => 1 => 1
[-2,3,4,5,-1] => [5] => 1 => 1
[-2,3,4,-5,1] => [5] => 1 => 1
[-2,3,-4,5,1] => [5] => 1 => 1
[-2,3,-4,-5,-1] => [5] => 1 => 1
[-2,-3,4,5,1] => [5] => 1 => 1
[-2,-3,4,-5,-1] => [5] => 1 => 1
[-2,-3,-4,5,-1] => [5] => 1 => 1
[-2,-3,-4,-5,1] => [5] => 1 => 1
[2,3,5,1,4] => [5] => 1 => 1
[2,3,5,-1,-4] => [5] => 1 => 1
[2,3,-5,1,-4] => [5] => 1 => 1
[2,3,-5,-1,4] => [5] => 1 => 1
[2,-3,5,1,-4] => [5] => 1 => 1
[2,-3,5,-1,4] => [5] => 1 => 1
[2,-3,-5,1,4] => [5] => 1 => 1
[2,-3,-5,-1,-4] => [5] => 1 => 1
[-2,3,5,1,-4] => [5] => 1 => 1
[-2,3,5,-1,4] => [5] => 1 => 1
[-2,3,-5,1,4] => [5] => 1 => 1
[-2,3,-5,-1,-4] => [5] => 1 => 1
[-2,-3,5,1,4] => [5] => 1 => 1
[-2,-3,5,-1,-4] => [5] => 1 => 1
[-2,-3,-5,1,-4] => [5] => 1 => 1
[-2,-3,-5,-1,4] => [5] => 1 => 1
[2,3,5,4,1] => [4,1] => 01 => 01
[2,3,5,4,-1] => [1] => 1 => 1
[2,3,5,-4,1] => [4] => 0 => 0
[2,3,-5,4,1] => [1] => 1 => 1
[2,3,-5,4,-1] => [4,1] => 01 => 01
[2,3,-5,-4,-1] => [4] => 0 => 0
[2,-3,5,4,1] => [1] => 1 => 1
[2,-3,5,4,-1] => [4,1] => 01 => 01
[2,-3,5,-4,-1] => [4] => 0 => 0
[2,-3,-5,4,1] => [4,1] => 01 => 01
[2,-3,-5,4,-1] => [1] => 1 => 1
[2,-3,-5,-4,1] => [4] => 0 => 0
[-2,3,5,4,1] => [1] => 1 => 1
[-2,3,5,4,-1] => [4,1] => 01 => 01
[-2,3,5,-4,-1] => [4] => 0 => 0
[-2,3,-5,4,1] => [4,1] => 01 => 01
[-2,3,-5,4,-1] => [1] => 1 => 1
[-2,3,-5,-4,1] => [4] => 0 => 0
[-2,-3,5,4,1] => [4,1] => 01 => 01
[-2,-3,5,4,-1] => [1] => 1 => 1
[-2,-3,5,-4,1] => [4] => 0 => 0
[-2,-3,-5,4,1] => [1] => 1 => 1
[-2,-3,-5,4,-1] => [4,1] => 01 => 01
[-2,-3,-5,-4,-1] => [4] => 0 => 0
[2,4,1,3,5] => [4,1] => 01 => 01
[2,4,1,3,-5] => [4] => 0 => 0
[2,4,1,-3,5] => [1] => 1 => 1
[2,4,-1,3,5] => [1] => 1 => 1
[2,4,-1,-3,5] => [4,1] => 01 => 01
[2,4,-1,-3,-5] => [4] => 0 => 0
[2,-4,1,3,5] => [1] => 1 => 1
[2,-4,1,-3,5] => [4,1] => 01 => 01
[2,-4,1,-3,-5] => [4] => 0 => 0
[2,-4,-1,3,5] => [4,1] => 01 => 01
[2,-4,-1,3,-5] => [4] => 0 => 0
[2,-4,-1,-3,5] => [1] => 1 => 1
[-2,4,1,3,5] => [1] => 1 => 1
[-2,4,1,-3,5] => [4,1] => 01 => 01
[-2,4,1,-3,-5] => [4] => 0 => 0
[-2,4,-1,3,5] => [4,1] => 01 => 01
[-2,4,-1,3,-5] => [4] => 0 => 0
[-2,4,-1,-3,5] => [1] => 1 => 1
[-2,-4,1,3,5] => [4,1] => 01 => 01
[-2,-4,1,3,-5] => [4] => 0 => 0
[-2,-4,1,-3,5] => [1] => 1 => 1
[-2,-4,-1,3,5] => [1] => 1 => 1
[-2,-4,-1,-3,5] => [4,1] => 01 => 01
[-2,-4,-1,-3,-5] => [4] => 0 => 0
[2,4,1,5,3] => [5] => 1 => 1
[2,4,1,-5,-3] => [5] => 1 => 1
[2,4,-1,5,-3] => [5] => 1 => 1
[2,4,-1,-5,3] => [5] => 1 => 1
[2,-4,1,5,-3] => [5] => 1 => 1
[2,-4,1,-5,3] => [5] => 1 => 1
[2,-4,-1,5,3] => [5] => 1 => 1
[2,-4,-1,-5,-3] => [5] => 1 => 1
[-2,4,1,5,-3] => [5] => 1 => 1
[-2,4,1,-5,3] => [5] => 1 => 1
[-2,4,-1,5,3] => [5] => 1 => 1
[-2,4,-1,-5,-3] => [5] => 1 => 1
[-2,-4,1,5,3] => [5] => 1 => 1
[-2,-4,1,-5,-3] => [5] => 1 => 1
[-2,-4,-1,5,-3] => [5] => 1 => 1
[-2,-4,-1,-5,3] => [5] => 1 => 1
[2,4,3,1,5] => [3,1,1] => 111 => 111
[2,4,3,1,-5] => [3,1] => 11 => 11
[2,4,3,-1,5] => [1,1] => 11 => 11
[2,4,3,-1,-5] => [1] => 1 => 1
[2,4,-3,1,5] => [3,1] => 11 => 11
[2,4,-3,1,-5] => [3] => 1 => 1
[2,4,-3,-1,5] => [1] => 1 => 1
[2,-4,3,1,5] => [1,1] => 11 => 11
[2,-4,3,1,-5] => [1] => 1 => 1
[2,-4,3,-1,5] => [3,1,1] => 111 => 111
[2,-4,3,-1,-5] => [3,1] => 11 => 11
[2,-4,-3,1,5] => [1] => 1 => 1
[2,-4,-3,-1,5] => [3,1] => 11 => 11
[2,-4,-3,-1,-5] => [3] => 1 => 1
[-2,4,3,1,5] => [1,1] => 11 => 11
[-2,4,3,1,-5] => [1] => 1 => 1
[-2,4,3,-1,5] => [3,1,1] => 111 => 111
[-2,4,3,-1,-5] => [3,1] => 11 => 11
[-2,4,-3,1,5] => [1] => 1 => 1
[-2,4,-3,-1,5] => [3,1] => 11 => 11
[-2,4,-3,-1,-5] => [3] => 1 => 1
[-2,-4,3,1,5] => [3,1,1] => 111 => 111
[-2,-4,3,1,-5] => [3,1] => 11 => 11
[-2,-4,3,-1,5] => [1,1] => 11 => 11
[-2,-4,3,-1,-5] => [1] => 1 => 1
[-2,-4,-3,1,5] => [3,1] => 11 => 11
[-2,-4,-3,1,-5] => [3] => 1 => 1
[-2,-4,-3,-1,5] => [1] => 1 => 1
[2,4,3,5,1] => [4,1] => 01 => 01
[2,4,3,5,-1] => [1] => 1 => 1
[2,4,3,-5,1] => [1] => 1 => 1
[2,4,3,-5,-1] => [4,1] => 01 => 01
[2,4,-3,5,1] => [4] => 0 => 0
[2,4,-3,-5,-1] => [4] => 0 => 0
[2,-4,3,5,1] => [1] => 1 => 1
[2,-4,3,5,-1] => [4,1] => 01 => 01
[2,-4,3,-5,1] => [4,1] => 01 => 01
[2,-4,3,-5,-1] => [1] => 1 => 1
[2,-4,-3,5,-1] => [4] => 0 => 0
[2,-4,-3,-5,1] => [4] => 0 => 0
[-2,4,3,5,1] => [1] => 1 => 1
[-2,4,3,5,-1] => [4,1] => 01 => 01
[-2,4,3,-5,1] => [4,1] => 01 => 01
[-2,4,3,-5,-1] => [1] => 1 => 1
[-2,4,-3,5,-1] => [4] => 0 => 0
[-2,4,-3,-5,1] => [4] => 0 => 0
[-2,-4,3,5,1] => [4,1] => 01 => 01
[-2,-4,3,5,-1] => [1] => 1 => 1
[-2,-4,3,-5,1] => [1] => 1 => 1
[-2,-4,3,-5,-1] => [4,1] => 01 => 01
[-2,-4,-3,5,1] => [4] => 0 => 0
[-2,-4,-3,-5,-1] => [4] => 0 => 0
[2,4,5,1,3] => [3,2] => 10 => 10
[2,4,5,1,-3] => [3] => 1 => 1
[2,4,5,-1,3] => [2] => 0 => 0
[2,4,-5,1,3] => [3] => 1 => 1
[2,4,-5,1,-3] => [3,2] => 10 => 10
[2,4,-5,-1,-3] => [2] => 0 => 0
[2,-4,5,1,3] => [2] => 0 => 0
[2,-4,5,-1,3] => [3,2] => 10 => 10
[2,-4,5,-1,-3] => [3] => 1 => 1
[2,-4,-5,1,-3] => [2] => 0 => 0
[2,-4,-5,-1,3] => [3] => 1 => 1
[2,-4,-5,-1,-3] => [3,2] => 10 => 10
[-2,4,5,1,3] => [2] => 0 => 0
[-2,4,5,-1,3] => [3,2] => 10 => 10
[-2,4,5,-1,-3] => [3] => 1 => 1
[-2,4,-5,1,-3] => [2] => 0 => 0
[-2,4,-5,-1,3] => [3] => 1 => 1
[-2,4,-5,-1,-3] => [3,2] => 10 => 10
[-2,-4,5,1,3] => [3,2] => 10 => 10
[-2,-4,5,1,-3] => [3] => 1 => 1
[-2,-4,5,-1,3] => [2] => 0 => 0
[-2,-4,-5,1,3] => [3] => 1 => 1
[-2,-4,-5,1,-3] => [3,2] => 10 => 10
[-2,-4,-5,-1,-3] => [2] => 0 => 0
[2,4,5,3,1] => [5] => 1 => 1
[2,4,5,-3,-1] => [5] => 1 => 1
[2,4,-5,3,-1] => [5] => 1 => 1
[2,4,-5,-3,1] => [5] => 1 => 1
[2,-4,5,3,-1] => [5] => 1 => 1
[2,-4,5,-3,1] => [5] => 1 => 1
[2,-4,-5,3,1] => [5] => 1 => 1
[2,-4,-5,-3,-1] => [5] => 1 => 1
[-2,4,5,3,-1] => [5] => 1 => 1
[-2,4,5,-3,1] => [5] => 1 => 1
[-2,4,-5,3,1] => [5] => 1 => 1
[-2,4,-5,-3,-1] => [5] => 1 => 1
[-2,-4,5,3,1] => [5] => 1 => 1
[-2,-4,5,-3,-1] => [5] => 1 => 1
[-2,-4,-5,3,-1] => [5] => 1 => 1
[-2,-4,-5,-3,1] => [5] => 1 => 1
[2,5,1,3,4] => [5] => 1 => 1
[2,5,1,-3,-4] => [5] => 1 => 1
[2,5,-1,3,-4] => [5] => 1 => 1
[2,5,-1,-3,4] => [5] => 1 => 1
[2,-5,1,3,-4] => [5] => 1 => 1
[2,-5,1,-3,4] => [5] => 1 => 1
[2,-5,-1,3,4] => [5] => 1 => 1
[2,-5,-1,-3,-4] => [5] => 1 => 1
[-2,5,1,3,-4] => [5] => 1 => 1
[-2,5,1,-3,4] => [5] => 1 => 1
[-2,5,-1,3,4] => [5] => 1 => 1
[-2,5,-1,-3,-4] => [5] => 1 => 1
[-2,-5,1,3,4] => [5] => 1 => 1
[-2,-5,1,-3,-4] => [5] => 1 => 1
[-2,-5,-1,3,-4] => [5] => 1 => 1
[-2,-5,-1,-3,4] => [5] => 1 => 1
[2,5,1,4,3] => [4,1] => 01 => 01
[2,5,1,4,-3] => [1] => 1 => 1
[2,5,1,-4,3] => [4] => 0 => 0
[2,5,-1,4,3] => [1] => 1 => 1
[2,5,-1,4,-3] => [4,1] => 01 => 01
[2,5,-1,-4,-3] => [4] => 0 => 0
[2,-5,1,4,3] => [1] => 1 => 1
[2,-5,1,4,-3] => [4,1] => 01 => 01
[2,-5,1,-4,-3] => [4] => 0 => 0
[2,-5,-1,4,3] => [4,1] => 01 => 01
[2,-5,-1,4,-3] => [1] => 1 => 1
[2,-5,-1,-4,3] => [4] => 0 => 0
[-2,5,1,4,3] => [1] => 1 => 1
[-2,5,1,4,-3] => [4,1] => 01 => 01
[-2,5,1,-4,-3] => [4] => 0 => 0
[-2,5,-1,4,3] => [4,1] => 01 => 01
[-2,5,-1,4,-3] => [1] => 1 => 1
[-2,5,-1,-4,3] => [4] => 0 => 0
[-2,-5,1,4,3] => [4,1] => 01 => 01
[-2,-5,1,4,-3] => [1] => 1 => 1
[-2,-5,1,-4,3] => [4] => 0 => 0
[-2,-5,-1,4,3] => [1] => 1 => 1
[-2,-5,-1,4,-3] => [4,1] => 01 => 01
[-2,-5,-1,-4,-3] => [4] => 0 => 0
[2,5,3,1,4] => [4,1] => 01 => 01
[2,5,3,1,-4] => [1] => 1 => 1
[2,5,3,-1,4] => [1] => 1 => 1
[2,5,3,-1,-4] => [4,1] => 01 => 01
[2,5,-3,1,4] => [4] => 0 => 0
[2,5,-3,-1,-4] => [4] => 0 => 0
[2,-5,3,1,4] => [1] => 1 => 1
[2,-5,3,1,-4] => [4,1] => 01 => 01
[2,-5,3,-1,4] => [4,1] => 01 => 01
[2,-5,3,-1,-4] => [1] => 1 => 1
[2,-5,-3,1,-4] => [4] => 0 => 0
[2,-5,-3,-1,4] => [4] => 0 => 0
[-2,5,3,1,4] => [1] => 1 => 1
[-2,5,3,1,-4] => [4,1] => 01 => 01
[-2,5,3,-1,4] => [4,1] => 01 => 01
[-2,5,3,-1,-4] => [1] => 1 => 1
[-2,5,-3,1,-4] => [4] => 0 => 0
[-2,5,-3,-1,4] => [4] => 0 => 0
[-2,-5,3,1,4] => [4,1] => 01 => 01
[-2,-5,3,1,-4] => [1] => 1 => 1
[-2,-5,3,-1,4] => [1] => 1 => 1
[-2,-5,3,-1,-4] => [4,1] => 01 => 01
[-2,-5,-3,1,4] => [4] => 0 => 0
[-2,-5,-3,-1,-4] => [4] => 0 => 0
[2,5,3,4,1] => [3,1,1] => 111 => 111
[2,5,3,4,-1] => [1,1] => 11 => 11
[2,5,3,-4,1] => [3,1] => 11 => 11
[2,5,3,-4,-1] => [1] => 1 => 1
[2,5,-3,4,1] => [3,1] => 11 => 11
[2,5,-3,4,-1] => [1] => 1 => 1
[2,5,-3,-4,1] => [3] => 1 => 1
[2,-5,3,4,1] => [1,1] => 11 => 11
[2,-5,3,4,-1] => [3,1,1] => 111 => 111
[2,-5,3,-4,1] => [1] => 1 => 1
[2,-5,3,-4,-1] => [3,1] => 11 => 11
[2,-5,-3,4,1] => [1] => 1 => 1
[2,-5,-3,4,-1] => [3,1] => 11 => 11
[2,-5,-3,-4,-1] => [3] => 1 => 1
[-2,5,3,4,1] => [1,1] => 11 => 11
[-2,5,3,4,-1] => [3,1,1] => 111 => 111
[-2,5,3,-4,1] => [1] => 1 => 1
[-2,5,3,-4,-1] => [3,1] => 11 => 11
[-2,5,-3,4,1] => [1] => 1 => 1
[-2,5,-3,4,-1] => [3,1] => 11 => 11
[-2,5,-3,-4,-1] => [3] => 1 => 1
[-2,-5,3,4,1] => [3,1,1] => 111 => 111
[-2,-5,3,4,-1] => [1,1] => 11 => 11
[-2,-5,3,-4,1] => [3,1] => 11 => 11
[-2,-5,3,-4,-1] => [1] => 1 => 1
[-2,-5,-3,4,1] => [3,1] => 11 => 11
[-2,-5,-3,4,-1] => [1] => 1 => 1
[-2,-5,-3,-4,1] => [3] => 1 => 1
[2,5,4,1,3] => [5] => 1 => 1
[2,5,4,-1,-3] => [5] => 1 => 1
[2,5,-4,1,-3] => [5] => 1 => 1
[2,5,-4,-1,3] => [5] => 1 => 1
[2,-5,4,1,-3] => [5] => 1 => 1
[2,-5,4,-1,3] => [5] => 1 => 1
[2,-5,-4,1,3] => [5] => 1 => 1
[2,-5,-4,-1,-3] => [5] => 1 => 1
[-2,5,4,1,-3] => [5] => 1 => 1
[-2,5,4,-1,3] => [5] => 1 => 1
[-2,5,-4,1,3] => [5] => 1 => 1
[-2,5,-4,-1,-3] => [5] => 1 => 1
[-2,-5,4,1,3] => [5] => 1 => 1
[-2,-5,4,-1,-3] => [5] => 1 => 1
[-2,-5,-4,1,-3] => [5] => 1 => 1
[-2,-5,-4,-1,3] => [5] => 1 => 1
[2,5,4,3,1] => [3,2] => 10 => 10
[2,5,4,3,-1] => [2] => 0 => 0
[2,5,4,-3,1] => [3] => 1 => 1
[2,5,-4,3,1] => [3] => 1 => 1
[2,5,-4,-3,1] => [3,2] => 10 => 10
[2,5,-4,-3,-1] => [2] => 0 => 0
[2,-5,4,3,1] => [2] => 0 => 0
[2,-5,4,3,-1] => [3,2] => 10 => 10
[2,-5,4,-3,-1] => [3] => 1 => 1
[2,-5,-4,3,-1] => [3] => 1 => 1
[2,-5,-4,-3,1] => [2] => 0 => 0
[2,-5,-4,-3,-1] => [3,2] => 10 => 10
[-2,5,4,3,1] => [2] => 0 => 0
[-2,5,4,3,-1] => [3,2] => 10 => 10
[-2,5,4,-3,-1] => [3] => 1 => 1
[-2,5,-4,3,-1] => [3] => 1 => 1
[-2,5,-4,-3,1] => [2] => 0 => 0
[-2,5,-4,-3,-1] => [3,2] => 10 => 10
[-2,-5,4,3,1] => [3,2] => 10 => 10
[-2,-5,4,3,-1] => [2] => 0 => 0
[-2,-5,4,-3,1] => [3] => 1 => 1
[-2,-5,-4,3,1] => [3] => 1 => 1
[-2,-5,-4,-3,1] => [3,2] => 10 => 10
[-2,-5,-4,-3,-1] => [2] => 0 => 0
[3,1,2,4,5] => [3,1,1] => 111 => 111
[3,1,2,4,-5] => [3,1] => 11 => 11
[3,1,2,-4,5] => [3,1] => 11 => 11
[3,1,2,-4,-5] => [3] => 1 => 1
[3,1,-2,4,5] => [1,1] => 11 => 11
[3,1,-2,4,-5] => [1] => 1 => 1
[3,1,-2,-4,5] => [1] => 1 => 1
[3,-1,2,4,5] => [1,1] => 11 => 11
[3,-1,2,4,-5] => [1] => 1 => 1
[3,-1,2,-4,5] => [1] => 1 => 1
[3,-1,-2,4,5] => [3,1,1] => 111 => 111
[3,-1,-2,4,-5] => [3,1] => 11 => 11
[3,-1,-2,-4,5] => [3,1] => 11 => 11
[3,-1,-2,-4,-5] => [3] => 1 => 1
[-3,1,2,4,5] => [1,1] => 11 => 11
[-3,1,2,4,-5] => [1] => 1 => 1
[-3,1,2,-4,5] => [1] => 1 => 1
[-3,1,-2,4,5] => [3,1,1] => 111 => 111
[-3,1,-2,4,-5] => [3,1] => 11 => 11
[-3,1,-2,-4,5] => [3,1] => 11 => 11
[-3,1,-2,-4,-5] => [3] => 1 => 1
[-3,-1,2,4,5] => [3,1,1] => 111 => 111
[-3,-1,2,4,-5] => [3,1] => 11 => 11
[-3,-1,2,-4,5] => [3,1] => 11 => 11
[-3,-1,2,-4,-5] => [3] => 1 => 1
[-3,-1,-2,4,5] => [1,1] => 11 => 11
[-3,-1,-2,4,-5] => [1] => 1 => 1
[-3,-1,-2,-4,5] => [1] => 1 => 1
[3,1,2,5,4] => [3,2] => 10 => 10
[3,1,2,5,-4] => [3] => 1 => 1
[3,1,2,-5,4] => [3] => 1 => 1
[3,1,2,-5,-4] => [3,2] => 10 => 10
[3,1,-2,5,4] => [2] => 0 => 0
[3,1,-2,-5,-4] => [2] => 0 => 0
[3,-1,2,5,4] => [2] => 0 => 0
[3,-1,2,-5,-4] => [2] => 0 => 0
[3,-1,-2,5,4] => [3,2] => 10 => 10
[3,-1,-2,5,-4] => [3] => 1 => 1
[3,-1,-2,-5,4] => [3] => 1 => 1
[3,-1,-2,-5,-4] => [3,2] => 10 => 10
[-3,1,2,5,4] => [2] => 0 => 0
[-3,1,2,-5,-4] => [2] => 0 => 0
[-3,1,-2,5,4] => [3,2] => 10 => 10
[-3,1,-2,5,-4] => [3] => 1 => 1
[-3,1,-2,-5,4] => [3] => 1 => 1
[-3,1,-2,-5,-4] => [3,2] => 10 => 10
[-3,-1,2,5,4] => [3,2] => 10 => 10
[-3,-1,2,5,-4] => [3] => 1 => 1
[-3,-1,2,-5,4] => [3] => 1 => 1
[-3,-1,2,-5,-4] => [3,2] => 10 => 10
[-3,-1,-2,5,4] => [2] => 0 => 0
[-3,-1,-2,-5,-4] => [2] => 0 => 0
[3,1,4,2,5] => [4,1] => 01 => 01
[3,1,4,2,-5] => [4] => 0 => 0
[3,1,4,-2,5] => [1] => 1 => 1
[3,1,-4,2,5] => [1] => 1 => 1
[3,1,-4,-2,5] => [4,1] => 01 => 01
[3,1,-4,-2,-5] => [4] => 0 => 0
[3,-1,4,2,5] => [1] => 1 => 1
[3,-1,4,-2,5] => [4,1] => 01 => 01
[3,-1,4,-2,-5] => [4] => 0 => 0
[3,-1,-4,2,5] => [4,1] => 01 => 01
[3,-1,-4,2,-5] => [4] => 0 => 0
[3,-1,-4,-2,5] => [1] => 1 => 1
[-3,1,4,2,5] => [1] => 1 => 1
[-3,1,4,-2,5] => [4,1] => 01 => 01
[-3,1,4,-2,-5] => [4] => 0 => 0
[-3,1,-4,2,5] => [4,1] => 01 => 01
[-3,1,-4,2,-5] => [4] => 0 => 0
[-3,1,-4,-2,5] => [1] => 1 => 1
[-3,-1,4,2,5] => [4,1] => 01 => 01
[-3,-1,4,2,-5] => [4] => 0 => 0
[-3,-1,4,-2,5] => [1] => 1 => 1
[-3,-1,-4,2,5] => [1] => 1 => 1
[-3,-1,-4,-2,5] => [4,1] => 01 => 01
[-3,-1,-4,-2,-5] => [4] => 0 => 0
[3,1,4,5,2] => [5] => 1 => 1
[3,1,4,-5,-2] => [5] => 1 => 1
[3,1,-4,5,-2] => [5] => 1 => 1
[3,1,-4,-5,2] => [5] => 1 => 1
[3,-1,4,5,-2] => [5] => 1 => 1
[3,-1,4,-5,2] => [5] => 1 => 1
[3,-1,-4,5,2] => [5] => 1 => 1
[3,-1,-4,-5,-2] => [5] => 1 => 1
[-3,1,4,5,-2] => [5] => 1 => 1
[-3,1,4,-5,2] => [5] => 1 => 1
[-3,1,-4,5,2] => [5] => 1 => 1
[-3,1,-4,-5,-2] => [5] => 1 => 1
[-3,-1,4,5,2] => [5] => 1 => 1
[-3,-1,4,-5,-2] => [5] => 1 => 1
[-3,-1,-4,5,-2] => [5] => 1 => 1
[-3,-1,-4,-5,2] => [5] => 1 => 1
[3,1,5,2,4] => [5] => 1 => 1
[3,1,5,-2,-4] => [5] => 1 => 1
[3,1,-5,2,-4] => [5] => 1 => 1
[3,1,-5,-2,4] => [5] => 1 => 1
[3,-1,5,2,-4] => [5] => 1 => 1
[3,-1,5,-2,4] => [5] => 1 => 1
[3,-1,-5,2,4] => [5] => 1 => 1
[3,-1,-5,-2,-4] => [5] => 1 => 1
[-3,1,5,2,-4] => [5] => 1 => 1
[-3,1,5,-2,4] => [5] => 1 => 1
[-3,1,-5,2,4] => [5] => 1 => 1
[-3,1,-5,-2,-4] => [5] => 1 => 1
[-3,-1,5,2,4] => [5] => 1 => 1
[-3,-1,5,-2,-4] => [5] => 1 => 1
[-3,-1,-5,2,-4] => [5] => 1 => 1
[-3,-1,-5,-2,4] => [5] => 1 => 1
[3,1,5,4,2] => [4,1] => 01 => 01
[3,1,5,4,-2] => [1] => 1 => 1
[3,1,5,-4,2] => [4] => 0 => 0
[3,1,-5,4,2] => [1] => 1 => 1
[3,1,-5,4,-2] => [4,1] => 01 => 01
[3,1,-5,-4,-2] => [4] => 0 => 0
[3,-1,5,4,2] => [1] => 1 => 1
[3,-1,5,4,-2] => [4,1] => 01 => 01
[3,-1,5,-4,-2] => [4] => 0 => 0
[3,-1,-5,4,2] => [4,1] => 01 => 01
[3,-1,-5,4,-2] => [1] => 1 => 1
[3,-1,-5,-4,2] => [4] => 0 => 0
[-3,1,5,4,2] => [1] => 1 => 1
[-3,1,5,4,-2] => [4,1] => 01 => 01
[-3,1,5,-4,-2] => [4] => 0 => 0
[-3,1,-5,4,2] => [4,1] => 01 => 01
[-3,1,-5,4,-2] => [1] => 1 => 1
[-3,1,-5,-4,2] => [4] => 0 => 0
[-3,-1,5,4,2] => [4,1] => 01 => 01
[-3,-1,5,4,-2] => [1] => 1 => 1
[-3,-1,5,-4,2] => [4] => 0 => 0
[-3,-1,-5,4,2] => [1] => 1 => 1
[-3,-1,-5,4,-2] => [4,1] => 01 => 01
[-3,-1,-5,-4,-2] => [4] => 0 => 0
[3,2,1,4,5] => [2,1,1,1] => 0111 => 0111
[3,2,1,4,-5] => [2,1,1] => 011 => 011
[3,2,1,-4,5] => [2,1,1] => 011 => 011
[3,2,1,-4,-5] => [2,1] => 01 => 01
[3,2,-1,4,5] => [1,1,1] => 111 => 111
[3,2,-1,4,-5] => [1,1] => 11 => 11
[3,2,-1,-4,5] => [1,1] => 11 => 11
[3,2,-1,-4,-5] => [1] => 1 => 1
[3,-2,1,4,5] => [2,1,1] => 011 => 011
[3,-2,1,4,-5] => [2,1] => 01 => 01
[3,-2,1,-4,5] => [2,1] => 01 => 01
[3,-2,1,-4,-5] => [2] => 0 => 0
[3,-2,-1,4,5] => [1,1] => 11 => 11
[3,-2,-1,4,-5] => [1] => 1 => 1
[3,-2,-1,-4,5] => [1] => 1 => 1
[-3,2,1,4,5] => [1,1,1] => 111 => 111
[-3,2,1,4,-5] => [1,1] => 11 => 11
[-3,2,1,-4,5] => [1,1] => 11 => 11
[-3,2,1,-4,-5] => [1] => 1 => 1
[-3,2,-1,4,5] => [2,1,1,1] => 0111 => 0111
[-3,2,-1,4,-5] => [2,1,1] => 011 => 011
[-3,2,-1,-4,5] => [2,1,1] => 011 => 011
[-3,2,-1,-4,-5] => [2,1] => 01 => 01
[-3,-2,1,4,5] => [1,1] => 11 => 11
[-3,-2,1,4,-5] => [1] => 1 => 1
[-3,-2,1,-4,5] => [1] => 1 => 1
[-3,-2,-1,4,5] => [2,1,1] => 011 => 011
[-3,-2,-1,4,-5] => [2,1] => 01 => 01
[-3,-2,-1,-4,5] => [2,1] => 01 => 01
[-3,-2,-1,-4,-5] => [2] => 0 => 0
[3,2,1,5,4] => [2,2,1] => 001 => 001
[3,2,1,5,-4] => [2,1] => 01 => 01
[3,2,1,-5,4] => [2,1] => 01 => 01
[3,2,1,-5,-4] => [2,2,1] => 001 => 001
[3,2,-1,5,4] => [2,1] => 01 => 01
[3,2,-1,5,-4] => [1] => 1 => 1
[3,2,-1,-5,4] => [1] => 1 => 1
[3,2,-1,-5,-4] => [2,1] => 01 => 01
[3,-2,1,5,4] => [2,2] => 00 => 00
[3,-2,1,5,-4] => [2] => 0 => 0
[3,-2,1,-5,4] => [2] => 0 => 0
[3,-2,1,-5,-4] => [2,2] => 00 => 00
[3,-2,-1,5,4] => [2] => 0 => 0
[3,-2,-1,-5,-4] => [2] => 0 => 0
[-3,2,1,5,4] => [2,1] => 01 => 01
[-3,2,1,5,-4] => [1] => 1 => 1
[-3,2,1,-5,4] => [1] => 1 => 1
[-3,2,1,-5,-4] => [2,1] => 01 => 01
[-3,2,-1,5,4] => [2,2,1] => 001 => 001
[-3,2,-1,5,-4] => [2,1] => 01 => 01
[-3,2,-1,-5,4] => [2,1] => 01 => 01
[-3,2,-1,-5,-4] => [2,2,1] => 001 => 001
[-3,-2,1,5,4] => [2] => 0 => 0
[-3,-2,1,-5,-4] => [2] => 0 => 0
[-3,-2,-1,5,4] => [2,2] => 00 => 00
[-3,-2,-1,5,-4] => [2] => 0 => 0
[-3,-2,-1,-5,4] => [2] => 0 => 0
[-3,-2,-1,-5,-4] => [2,2] => 00 => 00
[3,2,4,1,5] => [3,1,1] => 111 => 111
[3,2,4,1,-5] => [3,1] => 11 => 11
[3,2,4,-1,5] => [1,1] => 11 => 11
[3,2,4,-1,-5] => [1] => 1 => 1
[3,2,-4,1,5] => [1,1] => 11 => 11
[3,2,-4,1,-5] => [1] => 1 => 1
[3,2,-4,-1,5] => [3,1,1] => 111 => 111
[3,2,-4,-1,-5] => [3,1] => 11 => 11
[3,-2,4,1,5] => [3,1] => 11 => 11
[3,-2,4,1,-5] => [3] => 1 => 1
[3,-2,4,-1,5] => [1] => 1 => 1
[3,-2,-4,1,5] => [1] => 1 => 1
[3,-2,-4,-1,5] => [3,1] => 11 => 11
[3,-2,-4,-1,-5] => [3] => 1 => 1
[-3,2,4,1,5] => [1,1] => 11 => 11
[-3,2,4,1,-5] => [1] => 1 => 1
[-3,2,4,-1,5] => [3,1,1] => 111 => 111
[-3,2,4,-1,-5] => [3,1] => 11 => 11
[-3,2,-4,1,5] => [3,1,1] => 111 => 111
[-3,2,-4,1,-5] => [3,1] => 11 => 11
[-3,2,-4,-1,5] => [1,1] => 11 => 11
[-3,2,-4,-1,-5] => [1] => 1 => 1
[-3,-2,4,1,5] => [1] => 1 => 1
[-3,-2,4,-1,5] => [3,1] => 11 => 11
[-3,-2,4,-1,-5] => [3] => 1 => 1
[-3,-2,-4,1,5] => [3,1] => 11 => 11
[-3,-2,-4,1,-5] => [3] => 1 => 1
[-3,-2,-4,-1,5] => [1] => 1 => 1
[3,2,4,5,1] => [4,1] => 01 => 01
[3,2,4,5,-1] => [1] => 1 => 1
[3,2,4,-5,1] => [1] => 1 => 1
[3,2,4,-5,-1] => [4,1] => 01 => 01
[3,2,-4,5,1] => [1] => 1 => 1
[3,2,-4,5,-1] => [4,1] => 01 => 01
[3,2,-4,-5,1] => [4,1] => 01 => 01
[3,2,-4,-5,-1] => [1] => 1 => 1
[3,-2,4,5,1] => [4] => 0 => 0
[3,-2,4,-5,-1] => [4] => 0 => 0
[3,-2,-4,5,-1] => [4] => 0 => 0
[3,-2,-4,-5,1] => [4] => 0 => 0
[-3,2,4,5,1] => [1] => 1 => 1
[-3,2,4,5,-1] => [4,1] => 01 => 01
[-3,2,4,-5,1] => [4,1] => 01 => 01
[-3,2,4,-5,-1] => [1] => 1 => 1
[-3,2,-4,5,1] => [4,1] => 01 => 01
[-3,2,-4,5,-1] => [1] => 1 => 1
[-3,2,-4,-5,1] => [1] => 1 => 1
[-3,2,-4,-5,-1] => [4,1] => 01 => 01
[-3,-2,4,5,-1] => [4] => 0 => 0
[-3,-2,4,-5,1] => [4] => 0 => 0
[-3,-2,-4,5,1] => [4] => 0 => 0
[-3,-2,-4,-5,-1] => [4] => 0 => 0
[3,2,5,1,4] => [4,1] => 01 => 01
[3,2,5,1,-4] => [1] => 1 => 1
[3,2,5,-1,4] => [1] => 1 => 1
[3,2,5,-1,-4] => [4,1] => 01 => 01
[3,2,-5,1,4] => [1] => 1 => 1
[3,2,-5,1,-4] => [4,1] => 01 => 01
[3,2,-5,-1,4] => [4,1] => 01 => 01
[3,2,-5,-1,-4] => [1] => 1 => 1
[3,-2,5,1,4] => [4] => 0 => 0
[3,-2,5,-1,-4] => [4] => 0 => 0
[3,-2,-5,1,-4] => [4] => 0 => 0
[3,-2,-5,-1,4] => [4] => 0 => 0
[-3,2,5,1,4] => [1] => 1 => 1
[-3,2,5,1,-4] => [4,1] => 01 => 01
[-3,2,5,-1,4] => [4,1] => 01 => 01
[-3,2,5,-1,-4] => [1] => 1 => 1
[-3,2,-5,1,4] => [4,1] => 01 => 01
[-3,2,-5,1,-4] => [1] => 1 => 1
[-3,2,-5,-1,4] => [1] => 1 => 1
[-3,2,-5,-1,-4] => [4,1] => 01 => 01
[-3,-2,5,1,-4] => [4] => 0 => 0
[-3,-2,5,-1,4] => [4] => 0 => 0
[-3,-2,-5,1,4] => [4] => 0 => 0
[-3,-2,-5,-1,-4] => [4] => 0 => 0
[3,2,5,4,1] => [3,1,1] => 111 => 111
[3,2,5,4,-1] => [1,1] => 11 => 11
[3,2,5,-4,1] => [3,1] => 11 => 11
[3,2,5,-4,-1] => [1] => 1 => 1
[3,2,-5,4,1] => [1,1] => 11 => 11
[3,2,-5,4,-1] => [3,1,1] => 111 => 111
[3,2,-5,-4,1] => [1] => 1 => 1
[3,2,-5,-4,-1] => [3,1] => 11 => 11
[3,-2,5,4,1] => [3,1] => 11 => 11
[3,-2,5,4,-1] => [1] => 1 => 1
[3,-2,5,-4,1] => [3] => 1 => 1
[3,-2,-5,4,1] => [1] => 1 => 1
[3,-2,-5,4,-1] => [3,1] => 11 => 11
[3,-2,-5,-4,-1] => [3] => 1 => 1
[-3,2,5,4,1] => [1,1] => 11 => 11
[-3,2,5,4,-1] => [3,1,1] => 111 => 111
[-3,2,5,-4,1] => [1] => 1 => 1
[-3,2,5,-4,-1] => [3,1] => 11 => 11
[-3,2,-5,4,1] => [3,1,1] => 111 => 111
[-3,2,-5,4,-1] => [1,1] => 11 => 11
[-3,2,-5,-4,1] => [3,1] => 11 => 11
[-3,2,-5,-4,-1] => [1] => 1 => 1
[-3,-2,5,4,1] => [1] => 1 => 1
[-3,-2,5,4,-1] => [3,1] => 11 => 11
[-3,-2,5,-4,-1] => [3] => 1 => 1
[-3,-2,-5,4,1] => [3,1] => 11 => 11
[-3,-2,-5,4,-1] => [1] => 1 => 1
[-3,-2,-5,-4,1] => [3] => 1 => 1
[3,4,1,2,5] => [2,2,1] => 001 => 001
[3,4,1,2,-5] => [2,2] => 00 => 00
[3,4,1,-2,5] => [2,1] => 01 => 01
[3,4,1,-2,-5] => [2] => 0 => 0
[3,4,-1,2,5] => [2,1] => 01 => 01
[3,4,-1,2,-5] => [2] => 0 => 0
[3,4,-1,-2,5] => [1] => 1 => 1
[3,-4,1,2,5] => [2,1] => 01 => 01
[3,-4,1,2,-5] => [2] => 0 => 0
[3,-4,1,-2,5] => [2,2,1] => 001 => 001
[3,-4,1,-2,-5] => [2,2] => 00 => 00
[3,-4,-1,2,5] => [1] => 1 => 1
[3,-4,-1,-2,5] => [2,1] => 01 => 01
[3,-4,-1,-2,-5] => [2] => 0 => 0
[-3,4,1,2,5] => [2,1] => 01 => 01
[-3,4,1,2,-5] => [2] => 0 => 0
[-3,4,1,-2,5] => [1] => 1 => 1
[-3,4,-1,2,5] => [2,2,1] => 001 => 001
[-3,4,-1,2,-5] => [2,2] => 00 => 00
[-3,4,-1,-2,5] => [2,1] => 01 => 01
[-3,4,-1,-2,-5] => [2] => 0 => 0
[-3,-4,1,2,5] => [1] => 1 => 1
[-3,-4,1,-2,5] => [2,1] => 01 => 01
[-3,-4,1,-2,-5] => [2] => 0 => 0
[-3,-4,-1,2,5] => [2,1] => 01 => 01
[-3,-4,-1,2,-5] => [2] => 0 => 0
[-3,-4,-1,-2,5] => [2,2,1] => 001 => 001
[-3,-4,-1,-2,-5] => [2,2] => 00 => 00
[3,4,1,5,2] => [3,2] => 10 => 10
[3,4,1,5,-2] => [2] => 0 => 0
[3,4,1,-5,2] => [2] => 0 => 0
[3,4,1,-5,-2] => [3,2] => 10 => 10
[3,4,-1,5,2] => [3] => 1 => 1
[3,4,-1,-5,-2] => [3] => 1 => 1
[3,-4,1,5,2] => [2] => 0 => 0
[3,-4,1,5,-2] => [3,2] => 10 => 10
[3,-4,1,-5,2] => [3,2] => 10 => 10
[3,-4,1,-5,-2] => [2] => 0 => 0
[3,-4,-1,5,-2] => [3] => 1 => 1
[3,-4,-1,-5,2] => [3] => 1 => 1
[-3,4,1,5,2] => [3] => 1 => 1
[-3,4,1,-5,-2] => [3] => 1 => 1
[-3,4,-1,5,2] => [3,2] => 10 => 10
[-3,4,-1,5,-2] => [2] => 0 => 0
[-3,4,-1,-5,2] => [2] => 0 => 0
[-3,4,-1,-5,-2] => [3,2] => 10 => 10
[-3,-4,1,5,-2] => [3] => 1 => 1
[-3,-4,1,-5,2] => [3] => 1 => 1
[-3,-4,-1,5,2] => [2] => 0 => 0
[-3,-4,-1,5,-2] => [3,2] => 10 => 10
[-3,-4,-1,-5,2] => [3,2] => 10 => 10
[-3,-4,-1,-5,-2] => [2] => 0 => 0
[3,4,2,1,5] => [4,1] => 01 => 01
[3,4,2,1,-5] => [4] => 0 => 0
[3,4,2,-1,5] => [1] => 1 => 1
[3,4,-2,1,5] => [1] => 1 => 1
[3,4,-2,-1,5] => [4,1] => 01 => 01
[3,4,-2,-1,-5] => [4] => 0 => 0
[3,-4,2,1,5] => [1] => 1 => 1
[3,-4,2,-1,5] => [4,1] => 01 => 01
[3,-4,2,-1,-5] => [4] => 0 => 0
[3,-4,-2,1,5] => [4,1] => 01 => 01
[3,-4,-2,1,-5] => [4] => 0 => 0
[3,-4,-2,-1,5] => [1] => 1 => 1
[-3,4,2,1,5] => [1] => 1 => 1
[-3,4,2,-1,5] => [4,1] => 01 => 01
[-3,4,2,-1,-5] => [4] => 0 => 0
[-3,4,-2,1,5] => [4,1] => 01 => 01
[-3,4,-2,1,-5] => [4] => 0 => 0
[-3,4,-2,-1,5] => [1] => 1 => 1
[-3,-4,2,1,5] => [4,1] => 01 => 01
[-3,-4,2,1,-5] => [4] => 0 => 0
[-3,-4,2,-1,5] => [1] => 1 => 1
[-3,-4,-2,1,5] => [1] => 1 => 1
[-3,-4,-2,-1,5] => [4,1] => 01 => 01
[-3,-4,-2,-1,-5] => [4] => 0 => 0
[3,4,2,5,1] => [5] => 1 => 1
[3,4,2,-5,-1] => [5] => 1 => 1
[3,4,-2,5,-1] => [5] => 1 => 1
[3,4,-2,-5,1] => [5] => 1 => 1
[3,-4,2,5,-1] => [5] => 1 => 1
[3,-4,2,-5,1] => [5] => 1 => 1
[3,-4,-2,5,1] => [5] => 1 => 1
[3,-4,-2,-5,-1] => [5] => 1 => 1
[-3,4,2,5,-1] => [5] => 1 => 1
[-3,4,2,-5,1] => [5] => 1 => 1
[-3,4,-2,5,1] => [5] => 1 => 1
[-3,4,-2,-5,-1] => [5] => 1 => 1
[-3,-4,2,5,1] => [5] => 1 => 1
[-3,-4,2,-5,-1] => [5] => 1 => 1
[-3,-4,-2,5,-1] => [5] => 1 => 1
[-3,-4,-2,-5,1] => [5] => 1 => 1
[3,4,5,1,2] => [5] => 1 => 1
[3,4,5,-1,-2] => [5] => 1 => 1
[3,4,-5,1,-2] => [5] => 1 => 1
[3,4,-5,-1,2] => [5] => 1 => 1
[3,-4,5,1,-2] => [5] => 1 => 1
[3,-4,5,-1,2] => [5] => 1 => 1
[3,-4,-5,1,2] => [5] => 1 => 1
[3,-4,-5,-1,-2] => [5] => 1 => 1
[-3,4,5,1,-2] => [5] => 1 => 1
[-3,4,5,-1,2] => [5] => 1 => 1
[-3,4,-5,1,2] => [5] => 1 => 1
[-3,4,-5,-1,-2] => [5] => 1 => 1
[-3,-4,5,1,2] => [5] => 1 => 1
[-3,-4,5,-1,-2] => [5] => 1 => 1
[-3,-4,-5,1,-2] => [5] => 1 => 1
[-3,-4,-5,-1,2] => [5] => 1 => 1
[3,4,5,2,1] => [3,2] => 10 => 10
[3,4,5,2,-1] => [2] => 0 => 0
[3,4,5,-2,1] => [3] => 1 => 1
[3,4,-5,2,1] => [2] => 0 => 0
[3,4,-5,2,-1] => [3,2] => 10 => 10
[3,4,-5,-2,-1] => [3] => 1 => 1
[3,-4,5,2,1] => [3] => 1 => 1
[3,-4,5,-2,1] => [3,2] => 10 => 10
[3,-4,5,-2,-1] => [2] => 0 => 0
[3,-4,-5,2,-1] => [3] => 1 => 1
[3,-4,-5,-2,1] => [2] => 0 => 0
[3,-4,-5,-2,-1] => [3,2] => 10 => 10
[-3,4,5,2,1] => [2] => 0 => 0
[-3,4,5,2,-1] => [3,2] => 10 => 10
[-3,4,5,-2,-1] => [3] => 1 => 1
[-3,4,-5,2,1] => [3,2] => 10 => 10
[-3,4,-5,2,-1] => [2] => 0 => 0
[-3,4,-5,-2,1] => [3] => 1 => 1
[-3,-4,5,2,-1] => [3] => 1 => 1
[-3,-4,5,-2,1] => [2] => 0 => 0
[-3,-4,5,-2,-1] => [3,2] => 10 => 10
[-3,-4,-5,2,1] => [3] => 1 => 1
[-3,-4,-5,-2,1] => [3,2] => 10 => 10
[-3,-4,-5,-2,-1] => [2] => 0 => 0
[3,5,1,2,4] => [3,2] => 10 => 10
[3,5,1,2,-4] => [2] => 0 => 0
[3,5,1,-2,4] => [2] => 0 => 0
[3,5,1,-2,-4] => [3,2] => 10 => 10
[3,5,-1,2,4] => [3] => 1 => 1
[3,5,-1,-2,-4] => [3] => 1 => 1
[3,-5,1,2,4] => [2] => 0 => 0
[3,-5,1,2,-4] => [3,2] => 10 => 10
[3,-5,1,-2,4] => [3,2] => 10 => 10
[3,-5,1,-2,-4] => [2] => 0 => 0
[3,-5,-1,2,-4] => [3] => 1 => 1
[3,-5,-1,-2,4] => [3] => 1 => 1
[-3,5,1,2,4] => [3] => 1 => 1
[-3,5,1,-2,-4] => [3] => 1 => 1
[-3,5,-1,2,4] => [3,2] => 10 => 10
[-3,5,-1,2,-4] => [2] => 0 => 0
[-3,5,-1,-2,4] => [2] => 0 => 0
[-3,5,-1,-2,-4] => [3,2] => 10 => 10
[-3,-5,1,2,-4] => [3] => 1 => 1
[-3,-5,1,-2,4] => [3] => 1 => 1
[-3,-5,-1,2,4] => [2] => 0 => 0
[-3,-5,-1,2,-4] => [3,2] => 10 => 10
[-3,-5,-1,-2,4] => [3,2] => 10 => 10
[-3,-5,-1,-2,-4] => [2] => 0 => 0
[3,5,1,4,2] => [2,2,1] => 001 => 001
[3,5,1,4,-2] => [2,1] => 01 => 01
[3,5,1,-4,2] => [2,2] => 00 => 00
[3,5,1,-4,-2] => [2] => 0 => 0
[3,5,-1,4,2] => [2,1] => 01 => 01
[3,5,-1,4,-2] => [1] => 1 => 1
[3,5,-1,-4,2] => [2] => 0 => 0
[3,-5,1,4,2] => [2,1] => 01 => 01
[3,-5,1,4,-2] => [2,2,1] => 001 => 001
[3,-5,1,-4,2] => [2] => 0 => 0
[3,-5,1,-4,-2] => [2,2] => 00 => 00
[3,-5,-1,4,2] => [1] => 1 => 1
[3,-5,-1,4,-2] => [2,1] => 01 => 01
[3,-5,-1,-4,-2] => [2] => 0 => 0
[-3,5,1,4,2] => [2,1] => 01 => 01
[-3,5,1,4,-2] => [1] => 1 => 1
[-3,5,1,-4,2] => [2] => 0 => 0
[-3,5,-1,4,2] => [2,2,1] => 001 => 001
[-3,5,-1,4,-2] => [2,1] => 01 => 01
[-3,5,-1,-4,2] => [2,2] => 00 => 00
[-3,5,-1,-4,-2] => [2] => 0 => 0
[-3,-5,1,4,2] => [1] => 1 => 1
[-3,-5,1,4,-2] => [2,1] => 01 => 01
[-3,-5,1,-4,-2] => [2] => 0 => 0
[-3,-5,-1,4,2] => [2,1] => 01 => 01
[-3,-5,-1,4,-2] => [2,2,1] => 001 => 001
[-3,-5,-1,-4,2] => [2] => 0 => 0
[-3,-5,-1,-4,-2] => [2,2] => 00 => 00
[3,5,2,1,4] => [5] => 1 => 1
[3,5,2,-1,-4] => [5] => 1 => 1
[3,5,-2,1,-4] => [5] => 1 => 1
[3,5,-2,-1,4] => [5] => 1 => 1
[3,-5,2,1,-4] => [5] => 1 => 1
[3,-5,2,-1,4] => [5] => 1 => 1
[3,-5,-2,1,4] => [5] => 1 => 1
[3,-5,-2,-1,-4] => [5] => 1 => 1
[-3,5,2,1,-4] => [5] => 1 => 1
[-3,5,2,-1,4] => [5] => 1 => 1
[-3,5,-2,1,4] => [5] => 1 => 1
[-3,5,-2,-1,-4] => [5] => 1 => 1
[-3,-5,2,1,4] => [5] => 1 => 1
[-3,-5,2,-1,-4] => [5] => 1 => 1
[-3,-5,-2,1,-4] => [5] => 1 => 1
[-3,-5,-2,-1,4] => [5] => 1 => 1
[3,5,2,4,1] => [4,1] => 01 => 01
[3,5,2,4,-1] => [1] => 1 => 1
[3,5,2,-4,1] => [4] => 0 => 0
[3,5,-2,4,1] => [1] => 1 => 1
[3,5,-2,4,-1] => [4,1] => 01 => 01
[3,5,-2,-4,-1] => [4] => 0 => 0
[3,-5,2,4,1] => [1] => 1 => 1
[3,-5,2,4,-1] => [4,1] => 01 => 01
[3,-5,2,-4,-1] => [4] => 0 => 0
[3,-5,-2,4,1] => [4,1] => 01 => 01
[3,-5,-2,4,-1] => [1] => 1 => 1
[3,-5,-2,-4,1] => [4] => 0 => 0
[-3,5,2,4,1] => [1] => 1 => 1
[-3,5,2,4,-1] => [4,1] => 01 => 01
[-3,5,2,-4,-1] => [4] => 0 => 0
[-3,5,-2,4,1] => [4,1] => 01 => 01
[-3,5,-2,4,-1] => [1] => 1 => 1
[-3,5,-2,-4,1] => [4] => 0 => 0
[-3,-5,2,4,1] => [4,1] => 01 => 01
[-3,-5,2,4,-1] => [1] => 1 => 1
[-3,-5,2,-4,1] => [4] => 0 => 0
[-3,-5,-2,4,1] => [1] => 1 => 1
[-3,-5,-2,4,-1] => [4,1] => 01 => 01
[-3,-5,-2,-4,-1] => [4] => 0 => 0
[3,5,4,1,2] => [3,2] => 10 => 10
[3,5,4,1,-2] => [3] => 1 => 1
[3,5,4,-1,2] => [2] => 0 => 0
[3,5,-4,1,2] => [2] => 0 => 0
[3,5,-4,-1,2] => [3,2] => 10 => 10
[3,5,-4,-1,-2] => [3] => 1 => 1
[3,-5,4,1,2] => [3] => 1 => 1
[3,-5,4,1,-2] => [3,2] => 10 => 10
[3,-5,4,-1,-2] => [2] => 0 => 0
[3,-5,-4,1,-2] => [2] => 0 => 0
[3,-5,-4,-1,2] => [3] => 1 => 1
[3,-5,-4,-1,-2] => [3,2] => 10 => 10
[-3,5,4,1,2] => [2] => 0 => 0
[-3,5,4,-1,2] => [3,2] => 10 => 10
[-3,5,4,-1,-2] => [3] => 1 => 1
[-3,5,-4,1,2] => [3,2] => 10 => 10
[-3,5,-4,1,-2] => [3] => 1 => 1
[-3,5,-4,-1,2] => [2] => 0 => 0
[-3,-5,4,1,-2] => [2] => 0 => 0
[-3,-5,4,-1,2] => [3] => 1 => 1
[-3,-5,4,-1,-2] => [3,2] => 10 => 10
[-3,-5,-4,1,2] => [3] => 1 => 1
[-3,-5,-4,1,-2] => [3,2] => 10 => 10
[-3,-5,-4,-1,-2] => [2] => 0 => 0
[3,5,4,2,1] => [5] => 1 => 1
[3,5,4,-2,-1] => [5] => 1 => 1
[3,5,-4,2,-1] => [5] => 1 => 1
[3,5,-4,-2,1] => [5] => 1 => 1
[3,-5,4,2,-1] => [5] => 1 => 1
[3,-5,4,-2,1] => [5] => 1 => 1
[3,-5,-4,2,1] => [5] => 1 => 1
[3,-5,-4,-2,-1] => [5] => 1 => 1
[-3,5,4,2,-1] => [5] => 1 => 1
[-3,5,4,-2,1] => [5] => 1 => 1
[-3,5,-4,2,1] => [5] => 1 => 1
[-3,5,-4,-2,-1] => [5] => 1 => 1
[-3,-5,4,2,1] => [5] => 1 => 1
[-3,-5,4,-2,-1] => [5] => 1 => 1
[-3,-5,-4,2,-1] => [5] => 1 => 1
[-3,-5,-4,-2,1] => [5] => 1 => 1
[4,1,2,3,5] => [4,1] => 01 => 01
[4,1,2,3,-5] => [4] => 0 => 0
[4,1,2,-3,5] => [1] => 1 => 1
[4,1,-2,3,5] => [1] => 1 => 1
[4,1,-2,-3,5] => [4,1] => 01 => 01
[4,1,-2,-3,-5] => [4] => 0 => 0
[4,-1,2,3,5] => [1] => 1 => 1
[4,-1,2,-3,5] => [4,1] => 01 => 01
[4,-1,2,-3,-5] => [4] => 0 => 0
[4,-1,-2,3,5] => [4,1] => 01 => 01
[4,-1,-2,3,-5] => [4] => 0 => 0
[4,-1,-2,-3,5] => [1] => 1 => 1
[-4,1,2,3,5] => [1] => 1 => 1
[-4,1,2,-3,5] => [4,1] => 01 => 01
[-4,1,2,-3,-5] => [4] => 0 => 0
[-4,1,-2,3,5] => [4,1] => 01 => 01
[-4,1,-2,3,-5] => [4] => 0 => 0
[-4,1,-2,-3,5] => [1] => 1 => 1
[-4,-1,2,3,5] => [4,1] => 01 => 01
[-4,-1,2,3,-5] => [4] => 0 => 0
[-4,-1,2,-3,5] => [1] => 1 => 1
[-4,-1,-2,3,5] => [1] => 1 => 1
[-4,-1,-2,-3,5] => [4,1] => 01 => 01
[-4,-1,-2,-3,-5] => [4] => 0 => 0
[4,1,2,5,3] => [5] => 1 => 1
[4,1,2,-5,-3] => [5] => 1 => 1
[4,1,-2,5,-3] => [5] => 1 => 1
[4,1,-2,-5,3] => [5] => 1 => 1
[4,-1,2,5,-3] => [5] => 1 => 1
[4,-1,2,-5,3] => [5] => 1 => 1
[4,-1,-2,5,3] => [5] => 1 => 1
[4,-1,-2,-5,-3] => [5] => 1 => 1
[-4,1,2,5,-3] => [5] => 1 => 1
[-4,1,2,-5,3] => [5] => 1 => 1
[-4,1,-2,5,3] => [5] => 1 => 1
[-4,1,-2,-5,-3] => [5] => 1 => 1
[-4,-1,2,5,3] => [5] => 1 => 1
[-4,-1,2,-5,-3] => [5] => 1 => 1
[-4,-1,-2,5,-3] => [5] => 1 => 1
[-4,-1,-2,-5,3] => [5] => 1 => 1
[4,1,3,2,5] => [3,1,1] => 111 => 111
[4,1,3,2,-5] => [3,1] => 11 => 11
[4,1,3,-2,5] => [1,1] => 11 => 11
[4,1,3,-2,-5] => [1] => 1 => 1
[4,1,-3,2,5] => [3,1] => 11 => 11
[4,1,-3,2,-5] => [3] => 1 => 1
[4,1,-3,-2,5] => [1] => 1 => 1
[4,-1,3,2,5] => [1,1] => 11 => 11
[4,-1,3,2,-5] => [1] => 1 => 1
[4,-1,3,-2,5] => [3,1,1] => 111 => 111
[4,-1,3,-2,-5] => [3,1] => 11 => 11
[4,-1,-3,2,5] => [1] => 1 => 1
[4,-1,-3,-2,5] => [3,1] => 11 => 11
[4,-1,-3,-2,-5] => [3] => 1 => 1
[-4,1,3,2,5] => [1,1] => 11 => 11
[-4,1,3,2,-5] => [1] => 1 => 1
[-4,1,3,-2,5] => [3,1,1] => 111 => 111
[-4,1,3,-2,-5] => [3,1] => 11 => 11
[-4,1,-3,2,5] => [1] => 1 => 1
[-4,1,-3,-2,5] => [3,1] => 11 => 11
[-4,1,-3,-2,-5] => [3] => 1 => 1
[-4,-1,3,2,5] => [3,1,1] => 111 => 111
[-4,-1,3,2,-5] => [3,1] => 11 => 11
[-4,-1,3,-2,5] => [1,1] => 11 => 11
[-4,-1,3,-2,-5] => [1] => 1 => 1
[-4,-1,-3,2,5] => [3,1] => 11 => 11
[-4,-1,-3,2,-5] => [3] => 1 => 1
[-4,-1,-3,-2,5] => [1] => 1 => 1
[4,1,3,5,2] => [4,1] => 01 => 01
[4,1,3,5,-2] => [1] => 1 => 1
[4,1,3,-5,2] => [1] => 1 => 1
[4,1,3,-5,-2] => [4,1] => 01 => 01
[4,1,-3,5,2] => [4] => 0 => 0
[4,1,-3,-5,-2] => [4] => 0 => 0
[4,-1,3,5,2] => [1] => 1 => 1
[4,-1,3,5,-2] => [4,1] => 01 => 01
[4,-1,3,-5,2] => [4,1] => 01 => 01
[4,-1,3,-5,-2] => [1] => 1 => 1
[4,-1,-3,5,-2] => [4] => 0 => 0
[4,-1,-3,-5,2] => [4] => 0 => 0
[-4,1,3,5,2] => [1] => 1 => 1
[-4,1,3,5,-2] => [4,1] => 01 => 01
[-4,1,3,-5,2] => [4,1] => 01 => 01
[-4,1,3,-5,-2] => [1] => 1 => 1
[-4,1,-3,5,-2] => [4] => 0 => 0
[-4,1,-3,-5,2] => [4] => 0 => 0
[-4,-1,3,5,2] => [4,1] => 01 => 01
[-4,-1,3,5,-2] => [1] => 1 => 1
[-4,-1,3,-5,2] => [1] => 1 => 1
[-4,-1,3,-5,-2] => [4,1] => 01 => 01
[-4,-1,-3,5,2] => [4] => 0 => 0
[-4,-1,-3,-5,-2] => [4] => 0 => 0
[4,1,5,2,3] => [3,2] => 10 => 10
[4,1,5,2,-3] => [3] => 1 => 1
[4,1,5,-2,3] => [2] => 0 => 0
[4,1,-5,2,3] => [3] => 1 => 1
[4,1,-5,2,-3] => [3,2] => 10 => 10
[4,1,-5,-2,-3] => [2] => 0 => 0
[4,-1,5,2,3] => [2] => 0 => 0
[4,-1,5,-2,3] => [3,2] => 10 => 10
[4,-1,5,-2,-3] => [3] => 1 => 1
[4,-1,-5,2,-3] => [2] => 0 => 0
[4,-1,-5,-2,3] => [3] => 1 => 1
[4,-1,-5,-2,-3] => [3,2] => 10 => 10
[-4,1,5,2,3] => [2] => 0 => 0
[-4,1,5,-2,3] => [3,2] => 10 => 10
[-4,1,5,-2,-3] => [3] => 1 => 1
[-4,1,-5,2,-3] => [2] => 0 => 0
[-4,1,-5,-2,3] => [3] => 1 => 1
[-4,1,-5,-2,-3] => [3,2] => 10 => 10
[-4,-1,5,2,3] => [3,2] => 10 => 10
[-4,-1,5,2,-3] => [3] => 1 => 1
[-4,-1,5,-2,3] => [2] => 0 => 0
[-4,-1,-5,2,3] => [3] => 1 => 1
[-4,-1,-5,2,-3] => [3,2] => 10 => 10
[-4,-1,-5,-2,-3] => [2] => 0 => 0
[4,1,5,3,2] => [5] => 1 => 1
[4,1,5,-3,-2] => [5] => 1 => 1
[4,1,-5,3,-2] => [5] => 1 => 1
[4,1,-5,-3,2] => [5] => 1 => 1
[4,-1,5,3,-2] => [5] => 1 => 1
[4,-1,5,-3,2] => [5] => 1 => 1
[4,-1,-5,3,2] => [5] => 1 => 1
[4,-1,-5,-3,-2] => [5] => 1 => 1
[-4,1,5,3,-2] => [5] => 1 => 1
[-4,1,5,-3,2] => [5] => 1 => 1
[-4,1,-5,3,2] => [5] => 1 => 1
[-4,1,-5,-3,-2] => [5] => 1 => 1
[-4,-1,5,3,2] => [5] => 1 => 1
[-4,-1,5,-3,-2] => [5] => 1 => 1
[-4,-1,-5,3,-2] => [5] => 1 => 1
[-4,-1,-5,-3,2] => [5] => 1 => 1
[4,2,1,3,5] => [3,1,1] => 111 => 111
[4,2,1,3,-5] => [3,1] => 11 => 11
[4,2,1,-3,5] => [1,1] => 11 => 11
[4,2,1,-3,-5] => [1] => 1 => 1
[4,2,-1,3,5] => [1,1] => 11 => 11
[4,2,-1,3,-5] => [1] => 1 => 1
[4,2,-1,-3,5] => [3,1,1] => 111 => 111
[4,2,-1,-3,-5] => [3,1] => 11 => 11
[4,-2,1,3,5] => [3,1] => 11 => 11
[4,-2,1,3,-5] => [3] => 1 => 1
[4,-2,1,-3,5] => [1] => 1 => 1
[4,-2,-1,3,5] => [1] => 1 => 1
[4,-2,-1,-3,5] => [3,1] => 11 => 11
[4,-2,-1,-3,-5] => [3] => 1 => 1
[-4,2,1,3,5] => [1,1] => 11 => 11
[-4,2,1,3,-5] => [1] => 1 => 1
[-4,2,1,-3,5] => [3,1,1] => 111 => 111
[-4,2,1,-3,-5] => [3,1] => 11 => 11
[-4,2,-1,3,5] => [3,1,1] => 111 => 111
[-4,2,-1,3,-5] => [3,1] => 11 => 11
[-4,2,-1,-3,5] => [1,1] => 11 => 11
[-4,2,-1,-3,-5] => [1] => 1 => 1
[-4,-2,1,3,5] => [1] => 1 => 1
[-4,-2,1,-3,5] => [3,1] => 11 => 11
[-4,-2,1,-3,-5] => [3] => 1 => 1
[-4,-2,-1,3,5] => [3,1] => 11 => 11
[-4,-2,-1,3,-5] => [3] => 1 => 1
[-4,-2,-1,-3,5] => [1] => 1 => 1
[4,2,1,5,3] => [4,1] => 01 => 01
[4,2,1,5,-3] => [1] => 1 => 1
[4,2,1,-5,3] => [1] => 1 => 1
[4,2,1,-5,-3] => [4,1] => 01 => 01
[4,2,-1,5,3] => [1] => 1 => 1
[4,2,-1,5,-3] => [4,1] => 01 => 01
[4,2,-1,-5,3] => [4,1] => 01 => 01
[4,2,-1,-5,-3] => [1] => 1 => 1
[4,-2,1,5,3] => [4] => 0 => 0
[4,-2,1,-5,-3] => [4] => 0 => 0
[4,-2,-1,5,-3] => [4] => 0 => 0
[4,-2,-1,-5,3] => [4] => 0 => 0
[-4,2,1,5,3] => [1] => 1 => 1
[-4,2,1,5,-3] => [4,1] => 01 => 01
[-4,2,1,-5,3] => [4,1] => 01 => 01
[-4,2,1,-5,-3] => [1] => 1 => 1
[-4,2,-1,5,3] => [4,1] => 01 => 01
[-4,2,-1,5,-3] => [1] => 1 => 1
[-4,2,-1,-5,3] => [1] => 1 => 1
[-4,2,-1,-5,-3] => [4,1] => 01 => 01
[-4,-2,1,5,-3] => [4] => 0 => 0
[-4,-2,1,-5,3] => [4] => 0 => 0
[-4,-2,-1,5,3] => [4] => 0 => 0
[-4,-2,-1,-5,-3] => [4] => 0 => 0
[4,2,3,1,5] => [2,1,1,1] => 0111 => 0111
[4,2,3,1,-5] => [2,1,1] => 011 => 011
[4,2,3,-1,5] => [1,1,1] => 111 => 111
[4,2,3,-1,-5] => [1,1] => 11 => 11
[4,2,-3,1,5] => [2,1,1] => 011 => 011
[4,2,-3,1,-5] => [2,1] => 01 => 01
[4,2,-3,-1,5] => [1,1] => 11 => 11
[4,2,-3,-1,-5] => [1] => 1 => 1
[4,-2,3,1,5] => [2,1,1] => 011 => 011
[4,-2,3,1,-5] => [2,1] => 01 => 01
[4,-2,3,-1,5] => [1,1] => 11 => 11
[4,-2,3,-1,-5] => [1] => 1 => 1
[4,-2,-3,1,5] => [2,1] => 01 => 01
[4,-2,-3,1,-5] => [2] => 0 => 0
[4,-2,-3,-1,5] => [1] => 1 => 1
[-4,2,3,1,5] => [1,1,1] => 111 => 111
[-4,2,3,1,-5] => [1,1] => 11 => 11
[-4,2,3,-1,5] => [2,1,1,1] => 0111 => 0111
[-4,2,3,-1,-5] => [2,1,1] => 011 => 011
[-4,2,-3,1,5] => [1,1] => 11 => 11
[-4,2,-3,1,-5] => [1] => 1 => 1
[-4,2,-3,-1,5] => [2,1,1] => 011 => 011
[-4,2,-3,-1,-5] => [2,1] => 01 => 01
[-4,-2,3,1,5] => [1,1] => 11 => 11
[-4,-2,3,1,-5] => [1] => 1 => 1
[-4,-2,3,-1,5] => [2,1,1] => 011 => 011
[-4,-2,3,-1,-5] => [2,1] => 01 => 01
[-4,-2,-3,1,5] => [1] => 1 => 1
[-4,-2,-3,-1,5] => [2,1] => 01 => 01
[-4,-2,-3,-1,-5] => [2] => 0 => 0
[4,2,3,5,1] => [3,1,1] => 111 => 111
[4,2,3,5,-1] => [1,1] => 11 => 11
[4,2,3,-5,1] => [1,1] => 11 => 11
[4,2,3,-5,-1] => [3,1,1] => 111 => 111
[4,2,-3,5,1] => [3,1] => 11 => 11
[4,2,-3,5,-1] => [1] => 1 => 1
[4,2,-3,-5,1] => [1] => 1 => 1
[4,2,-3,-5,-1] => [3,1] => 11 => 11
[4,-2,3,5,1] => [3,1] => 11 => 11
[4,-2,3,5,-1] => [1] => 1 => 1
[4,-2,3,-5,1] => [1] => 1 => 1
[4,-2,3,-5,-1] => [3,1] => 11 => 11
[4,-2,-3,5,1] => [3] => 1 => 1
[4,-2,-3,-5,-1] => [3] => 1 => 1
[-4,2,3,5,1] => [1,1] => 11 => 11
[-4,2,3,5,-1] => [3,1,1] => 111 => 111
[-4,2,3,-5,1] => [3,1,1] => 111 => 111
[-4,2,3,-5,-1] => [1,1] => 11 => 11
[-4,2,-3,5,1] => [1] => 1 => 1
[-4,2,-3,5,-1] => [3,1] => 11 => 11
[-4,2,-3,-5,1] => [3,1] => 11 => 11
[-4,2,-3,-5,-1] => [1] => 1 => 1
[-4,-2,3,5,1] => [1] => 1 => 1
[-4,-2,3,5,-1] => [3,1] => 11 => 11
[-4,-2,3,-5,1] => [3,1] => 11 => 11
[-4,-2,3,-5,-1] => [1] => 1 => 1
[-4,-2,-3,5,-1] => [3] => 1 => 1
[-4,-2,-3,-5,1] => [3] => 1 => 1
[4,2,5,1,3] => [2,2,1] => 001 => 001
[4,2,5,1,-3] => [2,1] => 01 => 01
[4,2,5,-1,3] => [2,1] => 01 => 01
[4,2,5,-1,-3] => [1] => 1 => 1
[4,2,-5,1,3] => [2,1] => 01 => 01
[4,2,-5,1,-3] => [2,2,1] => 001 => 001
[4,2,-5,-1,3] => [1] => 1 => 1
[4,2,-5,-1,-3] => [2,1] => 01 => 01
[4,-2,5,1,3] => [2,2] => 00 => 00
[4,-2,5,1,-3] => [2] => 0 => 0
[4,-2,5,-1,3] => [2] => 0 => 0
[4,-2,-5,1,3] => [2] => 0 => 0
[4,-2,-5,1,-3] => [2,2] => 00 => 00
[4,-2,-5,-1,-3] => [2] => 0 => 0
[-4,2,5,1,3] => [2,1] => 01 => 01
[-4,2,5,1,-3] => [1] => 1 => 1
[-4,2,5,-1,3] => [2,2,1] => 001 => 001
[-4,2,5,-1,-3] => [2,1] => 01 => 01
[-4,2,-5,1,3] => [1] => 1 => 1
[-4,2,-5,1,-3] => [2,1] => 01 => 01
[-4,2,-5,-1,3] => [2,1] => 01 => 01
[-4,2,-5,-1,-3] => [2,2,1] => 001 => 001
[-4,-2,5,1,3] => [2] => 0 => 0
[-4,-2,5,-1,3] => [2,2] => 00 => 00
[-4,-2,5,-1,-3] => [2] => 0 => 0
[-4,-2,-5,1,-3] => [2] => 0 => 0
[-4,-2,-5,-1,3] => [2] => 0 => 0
[-4,-2,-5,-1,-3] => [2,2] => 00 => 00
[4,2,5,3,1] => [4,1] => 01 => 01
[4,2,5,3,-1] => [1] => 1 => 1
[4,2,5,-3,1] => [1] => 1 => 1
[4,2,5,-3,-1] => [4,1] => 01 => 01
[4,2,-5,3,1] => [1] => 1 => 1
[4,2,-5,3,-1] => [4,1] => 01 => 01
[4,2,-5,-3,1] => [4,1] => 01 => 01
[4,2,-5,-3,-1] => [1] => 1 => 1
[4,-2,5,3,1] => [4] => 0 => 0
[4,-2,5,-3,-1] => [4] => 0 => 0
[4,-2,-5,3,-1] => [4] => 0 => 0
[4,-2,-5,-3,1] => [4] => 0 => 0
[-4,2,5,3,1] => [1] => 1 => 1
[-4,2,5,3,-1] => [4,1] => 01 => 01
[-4,2,5,-3,1] => [4,1] => 01 => 01
[-4,2,5,-3,-1] => [1] => 1 => 1
[-4,2,-5,3,1] => [4,1] => 01 => 01
[-4,2,-5,3,-1] => [1] => 1 => 1
[-4,2,-5,-3,1] => [1] => 1 => 1
[-4,2,-5,-3,-1] => [4,1] => 01 => 01
[-4,-2,5,3,-1] => [4] => 0 => 0
[-4,-2,5,-3,1] => [4] => 0 => 0
[-4,-2,-5,3,1] => [4] => 0 => 0
[-4,-2,-5,-3,-1] => [4] => 0 => 0
[4,3,1,2,5] => [4,1] => 01 => 01
[4,3,1,2,-5] => [4] => 0 => 0
[4,3,1,-2,5] => [1] => 1 => 1
[4,3,-1,2,5] => [1] => 1 => 1
[4,3,-1,-2,5] => [4,1] => 01 => 01
[4,3,-1,-2,-5] => [4] => 0 => 0
[4,-3,1,2,5] => [1] => 1 => 1
[4,-3,1,-2,5] => [4,1] => 01 => 01
[4,-3,1,-2,-5] => [4] => 0 => 0
[4,-3,-1,2,5] => [4,1] => 01 => 01
[4,-3,-1,2,-5] => [4] => 0 => 0
[4,-3,-1,-2,5] => [1] => 1 => 1
[-4,3,1,2,5] => [1] => 1 => 1
[-4,3,1,-2,5] => [4,1] => 01 => 01
[-4,3,1,-2,-5] => [4] => 0 => 0
[-4,3,-1,2,5] => [4,1] => 01 => 01
[-4,3,-1,2,-5] => [4] => 0 => 0
[-4,3,-1,-2,5] => [1] => 1 => 1
[-4,-3,1,2,5] => [4,1] => 01 => 01
[-4,-3,1,2,-5] => [4] => 0 => 0
[-4,-3,1,-2,5] => [1] => 1 => 1
[-4,-3,-1,2,5] => [1] => 1 => 1
[-4,-3,-1,-2,5] => [4,1] => 01 => 01
[-4,-3,-1,-2,-5] => [4] => 0 => 0
[4,3,1,5,2] => [5] => 1 => 1
[4,3,1,-5,-2] => [5] => 1 => 1
[4,3,-1,5,-2] => [5] => 1 => 1
[4,3,-1,-5,2] => [5] => 1 => 1
[4,-3,1,5,-2] => [5] => 1 => 1
[4,-3,1,-5,2] => [5] => 1 => 1
[4,-3,-1,5,2] => [5] => 1 => 1
[4,-3,-1,-5,-2] => [5] => 1 => 1
[-4,3,1,5,-2] => [5] => 1 => 1
[-4,3,1,-5,2] => [5] => 1 => 1
[-4,3,-1,5,2] => [5] => 1 => 1
[-4,3,-1,-5,-2] => [5] => 1 => 1
[-4,-3,1,5,2] => [5] => 1 => 1
[-4,-3,1,-5,-2] => [5] => 1 => 1
[-4,-3,-1,5,-2] => [5] => 1 => 1
[-4,-3,-1,-5,2] => [5] => 1 => 1
[4,3,2,1,5] => [2,2,1] => 001 => 001
[4,3,2,1,-5] => [2,2] => 00 => 00
[4,3,2,-1,5] => [2,1] => 01 => 01
[4,3,2,-1,-5] => [2] => 0 => 0
[4,3,-2,1,5] => [2,1] => 01 => 01
[4,3,-2,1,-5] => [2] => 0 => 0
[4,3,-2,-1,5] => [1] => 1 => 1
[4,-3,2,1,5] => [2,1] => 01 => 01
[4,-3,2,1,-5] => [2] => 0 => 0
[4,-3,2,-1,5] => [1] => 1 => 1
[4,-3,-2,1,5] => [2,2,1] => 001 => 001
[4,-3,-2,1,-5] => [2,2] => 00 => 00
[4,-3,-2,-1,5] => [2,1] => 01 => 01
[4,-3,-2,-1,-5] => [2] => 0 => 0
[-4,3,2,1,5] => [2,1] => 01 => 01
[-4,3,2,1,-5] => [2] => 0 => 0
[-4,3,2,-1,5] => [2,2,1] => 001 => 001
[-4,3,2,-1,-5] => [2,2] => 00 => 00
[-4,3,-2,1,5] => [1] => 1 => 1
[-4,3,-2,-1,5] => [2,1] => 01 => 01
[-4,3,-2,-1,-5] => [2] => 0 => 0
[-4,-3,2,1,5] => [1] => 1 => 1
[-4,-3,2,-1,5] => [2,1] => 01 => 01
[-4,-3,2,-1,-5] => [2] => 0 => 0
[-4,-3,-2,1,5] => [2,1] => 01 => 01
[-4,-3,-2,1,-5] => [2] => 0 => 0
[-4,-3,-2,-1,5] => [2,2,1] => 001 => 001
[-4,-3,-2,-1,-5] => [2,2] => 00 => 00
[4,3,2,5,1] => [3,2] => 10 => 10
[4,3,2,5,-1] => [2] => 0 => 0
[4,3,2,-5,1] => [2] => 0 => 0
[4,3,2,-5,-1] => [3,2] => 10 => 10
[4,3,-2,5,1] => [3] => 1 => 1
[4,3,-2,-5,-1] => [3] => 1 => 1
[4,-3,2,5,1] => [3] => 1 => 1
[4,-3,2,-5,-1] => [3] => 1 => 1
[4,-3,-2,5,1] => [3,2] => 10 => 10
[4,-3,-2,5,-1] => [2] => 0 => 0
[4,-3,-2,-5,1] => [2] => 0 => 0
[4,-3,-2,-5,-1] => [3,2] => 10 => 10
[-4,3,2,5,1] => [2] => 0 => 0
[-4,3,2,5,-1] => [3,2] => 10 => 10
[-4,3,2,-5,1] => [3,2] => 10 => 10
[-4,3,2,-5,-1] => [2] => 0 => 0
[-4,3,-2,5,-1] => [3] => 1 => 1
[-4,3,-2,-5,1] => [3] => 1 => 1
[-4,-3,2,5,-1] => [3] => 1 => 1
[-4,-3,2,-5,1] => [3] => 1 => 1
[-4,-3,-2,5,1] => [2] => 0 => 0
[-4,-3,-2,5,-1] => [3,2] => 10 => 10
[-4,-3,-2,-5,1] => [3,2] => 10 => 10
[-4,-3,-2,-5,-1] => [2] => 0 => 0
[4,3,5,1,2] => [3,2] => 10 => 10
[4,3,5,1,-2] => [2] => 0 => 0
[4,3,5,-1,2] => [3] => 1 => 1
[4,3,-5,1,2] => [2] => 0 => 0
[4,3,-5,1,-2] => [3,2] => 10 => 10
[4,3,-5,-1,-2] => [3] => 1 => 1
[4,-3,5,1,2] => [2] => 0 => 0
[4,-3,5,1,-2] => [3,2] => 10 => 10
[4,-3,5,-1,-2] => [3] => 1 => 1
[4,-3,-5,1,2] => [3,2] => 10 => 10
[4,-3,-5,1,-2] => [2] => 0 => 0
[4,-3,-5,-1,2] => [3] => 1 => 1
[-4,3,5,1,2] => [3] => 1 => 1
[-4,3,5,-1,2] => [3,2] => 10 => 10
[-4,3,5,-1,-2] => [2] => 0 => 0
[-4,3,-5,1,-2] => [3] => 1 => 1
[-4,3,-5,-1,2] => [2] => 0 => 0
[-4,3,-5,-1,-2] => [3,2] => 10 => 10
[-4,-3,5,1,-2] => [3] => 1 => 1
[-4,-3,5,-1,2] => [2] => 0 => 0
[-4,-3,5,-1,-2] => [3,2] => 10 => 10
[-4,-3,-5,1,2] => [3] => 1 => 1
[-4,-3,-5,-1,2] => [3,2] => 10 => 10
[-4,-3,-5,-1,-2] => [2] => 0 => 0
[4,3,5,2,1] => [5] => 1 => 1
[4,3,5,-2,-1] => [5] => 1 => 1
[4,3,-5,2,-1] => [5] => 1 => 1
[4,3,-5,-2,1] => [5] => 1 => 1
[4,-3,5,2,-1] => [5] => 1 => 1
[4,-3,5,-2,1] => [5] => 1 => 1
[4,-3,-5,2,1] => [5] => 1 => 1
[4,-3,-5,-2,-1] => [5] => 1 => 1
[-4,3,5,2,-1] => [5] => 1 => 1
[-4,3,5,-2,1] => [5] => 1 => 1
[-4,3,-5,2,1] => [5] => 1 => 1
[-4,3,-5,-2,-1] => [5] => 1 => 1
[-4,-3,5,2,1] => [5] => 1 => 1
[-4,-3,5,-2,-1] => [5] => 1 => 1
[-4,-3,-5,2,-1] => [5] => 1 => 1
[-4,-3,-5,-2,1] => [5] => 1 => 1
[4,5,1,2,3] => [5] => 1 => 1
[4,5,1,-2,-3] => [5] => 1 => 1
[4,5,-1,2,-3] => [5] => 1 => 1
[4,5,-1,-2,3] => [5] => 1 => 1
[4,-5,1,2,-3] => [5] => 1 => 1
[4,-5,1,-2,3] => [5] => 1 => 1
[4,-5,-1,2,3] => [5] => 1 => 1
[4,-5,-1,-2,-3] => [5] => 1 => 1
[-4,5,1,2,-3] => [5] => 1 => 1
[-4,5,1,-2,3] => [5] => 1 => 1
[-4,5,-1,2,3] => [5] => 1 => 1
[-4,5,-1,-2,-3] => [5] => 1 => 1
[-4,-5,1,2,3] => [5] => 1 => 1
[-4,-5,1,-2,-3] => [5] => 1 => 1
[-4,-5,-1,2,-3] => [5] => 1 => 1
[-4,-5,-1,-2,3] => [5] => 1 => 1
[4,5,1,3,2] => [3,2] => 10 => 10
[4,5,1,3,-2] => [3] => 1 => 1
[4,5,1,-3,2] => [2] => 0 => 0
[4,5,-1,3,2] => [2] => 0 => 0
[4,5,-1,-3,2] => [3,2] => 10 => 10
[4,5,-1,-3,-2] => [3] => 1 => 1
[4,-5,1,3,2] => [3] => 1 => 1
[4,-5,1,3,-2] => [3,2] => 10 => 10
[4,-5,1,-3,-2] => [2] => 0 => 0
[4,-5,-1,3,-2] => [2] => 0 => 0
[4,-5,-1,-3,2] => [3] => 1 => 1
[4,-5,-1,-3,-2] => [3,2] => 10 => 10
[-4,5,1,3,2] => [2] => 0 => 0
[-4,5,1,-3,2] => [3,2] => 10 => 10
[-4,5,1,-3,-2] => [3] => 1 => 1
[-4,5,-1,3,2] => [3,2] => 10 => 10
[-4,5,-1,3,-2] => [3] => 1 => 1
[-4,5,-1,-3,2] => [2] => 0 => 0
[-4,-5,1,3,-2] => [2] => 0 => 0
[-4,-5,1,-3,2] => [3] => 1 => 1
[-4,-5,1,-3,-2] => [3,2] => 10 => 10
[-4,-5,-1,3,2] => [3] => 1 => 1
[-4,-5,-1,3,-2] => [3,2] => 10 => 10
[-4,-5,-1,-3,-2] => [2] => 0 => 0
[4,5,2,1,3] => [3,2] => 10 => 10
[4,5,2,1,-3] => [2] => 0 => 0
[4,5,2,-1,3] => [3] => 1 => 1
[4,5,-2,1,3] => [2] => 0 => 0
[4,5,-2,1,-3] => [3,2] => 10 => 10
[4,5,-2,-1,-3] => [3] => 1 => 1
[4,-5,2,1,3] => [2] => 0 => 0
[4,-5,2,1,-3] => [3,2] => 10 => 10
[4,-5,2,-1,-3] => [3] => 1 => 1
[4,-5,-2,1,3] => [3,2] => 10 => 10
[4,-5,-2,1,-3] => [2] => 0 => 0
[4,-5,-2,-1,3] => [3] => 1 => 1
[-4,5,2,1,3] => [3] => 1 => 1
[-4,5,2,-1,3] => [3,2] => 10 => 10
[-4,5,2,-1,-3] => [2] => 0 => 0
[-4,5,-2,1,-3] => [3] => 1 => 1
[-4,5,-2,-1,3] => [2] => 0 => 0
[-4,5,-2,-1,-3] => [3,2] => 10 => 10
[-4,-5,2,1,-3] => [3] => 1 => 1
[-4,-5,2,-1,3] => [2] => 0 => 0
[-4,-5,2,-1,-3] => [3,2] => 10 => 10
[-4,-5,-2,1,3] => [3] => 1 => 1
[-4,-5,-2,-1,3] => [3,2] => 10 => 10
[-4,-5,-2,-1,-3] => [2] => 0 => 0
[4,5,2,3,1] => [5] => 1 => 1
[4,5,2,-3,-1] => [5] => 1 => 1
[4,5,-2,3,-1] => [5] => 1 => 1
[4,5,-2,-3,1] => [5] => 1 => 1
[4,-5,2,3,-1] => [5] => 1 => 1
[4,-5,2,-3,1] => [5] => 1 => 1
[4,-5,-2,3,1] => [5] => 1 => 1
[4,-5,-2,-3,-1] => [5] => 1 => 1
[-4,5,2,3,-1] => [5] => 1 => 1
[-4,5,2,-3,1] => [5] => 1 => 1
[-4,5,-2,3,1] => [5] => 1 => 1
[-4,5,-2,-3,-1] => [5] => 1 => 1
[-4,-5,2,3,1] => [5] => 1 => 1
[-4,-5,2,-3,-1] => [5] => 1 => 1
[-4,-5,-2,3,-1] => [5] => 1 => 1
[-4,-5,-2,-3,1] => [5] => 1 => 1
[4,5,3,1,2] => [2,2,1] => 001 => 001
[4,5,3,1,-2] => [2,1] => 01 => 01
[4,5,3,-1,2] => [2,1] => 01 => 01
[4,5,3,-1,-2] => [1] => 1 => 1
[4,5,-3,1,2] => [2,2] => 00 => 00
[4,5,-3,1,-2] => [2] => 0 => 0
[4,5,-3,-1,2] => [2] => 0 => 0
[4,-5,3,1,2] => [2,1] => 01 => 01
[4,-5,3,1,-2] => [2,2,1] => 001 => 001
[4,-5,3,-1,2] => [1] => 1 => 1
[4,-5,3,-1,-2] => [2,1] => 01 => 01
[4,-5,-3,1,2] => [2] => 0 => 0
[4,-5,-3,1,-2] => [2,2] => 00 => 00
[4,-5,-3,-1,-2] => [2] => 0 => 0
[-4,5,3,1,2] => [2,1] => 01 => 01
[-4,5,3,1,-2] => [1] => 1 => 1
[-4,5,3,-1,2] => [2,2,1] => 001 => 001
[-4,5,3,-1,-2] => [2,1] => 01 => 01
[-4,5,-3,1,2] => [2] => 0 => 0
[-4,5,-3,-1,2] => [2,2] => 00 => 00
[-4,5,-3,-1,-2] => [2] => 0 => 0
[-4,-5,3,1,2] => [1] => 1 => 1
[-4,-5,3,1,-2] => [2,1] => 01 => 01
[-4,-5,3,-1,2] => [2,1] => 01 => 01
[-4,-5,3,-1,-2] => [2,2,1] => 001 => 001
[-4,-5,-3,1,-2] => [2] => 0 => 0
[-4,-5,-3,-1,2] => [2] => 0 => 0
[-4,-5,-3,-1,-2] => [2,2] => 00 => 00
[4,5,3,2,1] => [4,1] => 01 => 01
[4,5,3,2,-1] => [1] => 1 => 1
[4,5,3,-2,1] => [1] => 1 => 1
[4,5,3,-2,-1] => [4,1] => 01 => 01
[4,5,-3,2,1] => [4] => 0 => 0
[4,5,-3,-2,-1] => [4] => 0 => 0
[4,-5,3,2,1] => [1] => 1 => 1
[4,-5,3,2,-1] => [4,1] => 01 => 01
[4,-5,3,-2,1] => [4,1] => 01 => 01
[4,-5,3,-2,-1] => [1] => 1 => 1
[4,-5,-3,2,-1] => [4] => 0 => 0
[4,-5,-3,-2,1] => [4] => 0 => 0
[-4,5,3,2,1] => [1] => 1 => 1
[-4,5,3,2,-1] => [4,1] => 01 => 01
[-4,5,3,-2,1] => [4,1] => 01 => 01
[-4,5,3,-2,-1] => [1] => 1 => 1
[-4,5,-3,2,-1] => [4] => 0 => 0
[-4,5,-3,-2,1] => [4] => 0 => 0
[-4,-5,3,2,1] => [4,1] => 01 => 01
[-4,-5,3,2,-1] => [1] => 1 => 1
[-4,-5,3,-2,1] => [1] => 1 => 1
[-4,-5,3,-2,-1] => [4,1] => 01 => 01
[-4,-5,-3,2,1] => [4] => 0 => 0
[-4,-5,-3,-2,-1] => [4] => 0 => 0
[5,1,2,3,4] => [5] => 1 => 1
[5,1,2,-3,-4] => [5] => 1 => 1
[5,1,-2,3,-4] => [5] => 1 => 1
[5,1,-2,-3,4] => [5] => 1 => 1
[5,-1,2,3,-4] => [5] => 1 => 1
[5,-1,2,-3,4] => [5] => 1 => 1
[5,-1,-2,3,4] => [5] => 1 => 1
[5,-1,-2,-3,-4] => [5] => 1 => 1
[-5,1,2,3,-4] => [5] => 1 => 1
[-5,1,2,-3,4] => [5] => 1 => 1
[-5,1,-2,3,4] => [5] => 1 => 1
[-5,1,-2,-3,-4] => [5] => 1 => 1
[-5,-1,2,3,4] => [5] => 1 => 1
[-5,-1,2,-3,-4] => [5] => 1 => 1
[-5,-1,-2,3,-4] => [5] => 1 => 1
[-5,-1,-2,-3,4] => [5] => 1 => 1
[5,1,2,4,3] => [4,1] => 01 => 01
[5,1,2,4,-3] => [1] => 1 => 1
[5,1,2,-4,3] => [4] => 0 => 0
[5,1,-2,4,3] => [1] => 1 => 1
[5,1,-2,4,-3] => [4,1] => 01 => 01
[5,1,-2,-4,-3] => [4] => 0 => 0
[5,-1,2,4,3] => [1] => 1 => 1
[5,-1,2,4,-3] => [4,1] => 01 => 01
[5,-1,2,-4,-3] => [4] => 0 => 0
[5,-1,-2,4,3] => [4,1] => 01 => 01
[5,-1,-2,4,-3] => [1] => 1 => 1
[5,-1,-2,-4,3] => [4] => 0 => 0
[-5,1,2,4,3] => [1] => 1 => 1
[-5,1,2,4,-3] => [4,1] => 01 => 01
[-5,1,2,-4,-3] => [4] => 0 => 0
[-5,1,-2,4,3] => [4,1] => 01 => 01
[-5,1,-2,4,-3] => [1] => 1 => 1
[-5,1,-2,-4,3] => [4] => 0 => 0
[-5,-1,2,4,3] => [4,1] => 01 => 01
[-5,-1,2,4,-3] => [1] => 1 => 1
[-5,-1,2,-4,3] => [4] => 0 => 0
[-5,-1,-2,4,3] => [1] => 1 => 1
[-5,-1,-2,4,-3] => [4,1] => 01 => 01
[-5,-1,-2,-4,-3] => [4] => 0 => 0
[5,1,3,2,4] => [4,1] => 01 => 01
[5,1,3,2,-4] => [1] => 1 => 1
[5,1,3,-2,4] => [1] => 1 => 1
[5,1,3,-2,-4] => [4,1] => 01 => 01
[5,1,-3,2,4] => [4] => 0 => 0
[5,1,-3,-2,-4] => [4] => 0 => 0
[5,-1,3,2,4] => [1] => 1 => 1
[5,-1,3,2,-4] => [4,1] => 01 => 01
[5,-1,3,-2,4] => [4,1] => 01 => 01
[5,-1,3,-2,-4] => [1] => 1 => 1
[5,-1,-3,2,-4] => [4] => 0 => 0
[5,-1,-3,-2,4] => [4] => 0 => 0
[-5,1,3,2,4] => [1] => 1 => 1
[-5,1,3,2,-4] => [4,1] => 01 => 01
[-5,1,3,-2,4] => [4,1] => 01 => 01
[-5,1,3,-2,-4] => [1] => 1 => 1
[-5,1,-3,2,-4] => [4] => 0 => 0
[-5,1,-3,-2,4] => [4] => 0 => 0
[-5,-1,3,2,4] => [4,1] => 01 => 01
[-5,-1,3,2,-4] => [1] => 1 => 1
[-5,-1,3,-2,4] => [1] => 1 => 1
[-5,-1,3,-2,-4] => [4,1] => 01 => 01
[-5,-1,-3,2,4] => [4] => 0 => 0
[-5,-1,-3,-2,-4] => [4] => 0 => 0
[5,1,3,4,2] => [3,1,1] => 111 => 111
[5,1,3,4,-2] => [1,1] => 11 => 11
[5,1,3,-4,2] => [3,1] => 11 => 11
[5,1,3,-4,-2] => [1] => 1 => 1
[5,1,-3,4,2] => [3,1] => 11 => 11
[5,1,-3,4,-2] => [1] => 1 => 1
[5,1,-3,-4,2] => [3] => 1 => 1
[5,-1,3,4,2] => [1,1] => 11 => 11
[5,-1,3,4,-2] => [3,1,1] => 111 => 111
[5,-1,3,-4,2] => [1] => 1 => 1
[5,-1,3,-4,-2] => [3,1] => 11 => 11
[5,-1,-3,4,2] => [1] => 1 => 1
[5,-1,-3,4,-2] => [3,1] => 11 => 11
[5,-1,-3,-4,-2] => [3] => 1 => 1
[-5,1,3,4,2] => [1,1] => 11 => 11
[-5,1,3,4,-2] => [3,1,1] => 111 => 111
[-5,1,3,-4,2] => [1] => 1 => 1
[-5,1,3,-4,-2] => [3,1] => 11 => 11
[-5,1,-3,4,2] => [1] => 1 => 1
[-5,1,-3,4,-2] => [3,1] => 11 => 11
[-5,1,-3,-4,-2] => [3] => 1 => 1
[-5,-1,3,4,2] => [3,1,1] => 111 => 111
[-5,-1,3,4,-2] => [1,1] => 11 => 11
[-5,-1,3,-4,2] => [3,1] => 11 => 11
[-5,-1,3,-4,-2] => [1] => 1 => 1
[-5,-1,-3,4,2] => [3,1] => 11 => 11
[-5,-1,-3,4,-2] => [1] => 1 => 1
[-5,-1,-3,-4,2] => [3] => 1 => 1
[5,1,4,2,3] => [5] => 1 => 1
[5,1,4,-2,-3] => [5] => 1 => 1
[5,1,-4,2,-3] => [5] => 1 => 1
[5,1,-4,-2,3] => [5] => 1 => 1
[5,-1,4,2,-3] => [5] => 1 => 1
[5,-1,4,-2,3] => [5] => 1 => 1
[5,-1,-4,2,3] => [5] => 1 => 1
[5,-1,-4,-2,-3] => [5] => 1 => 1
[-5,1,4,2,-3] => [5] => 1 => 1
[-5,1,4,-2,3] => [5] => 1 => 1
[-5,1,-4,2,3] => [5] => 1 => 1
[-5,1,-4,-2,-3] => [5] => 1 => 1
[-5,-1,4,2,3] => [5] => 1 => 1
[-5,-1,4,-2,-3] => [5] => 1 => 1
[-5,-1,-4,2,-3] => [5] => 1 => 1
[-5,-1,-4,-2,3] => [5] => 1 => 1
[5,1,4,3,2] => [3,2] => 10 => 10
[5,1,4,3,-2] => [2] => 0 => 0
[5,1,4,-3,2] => [3] => 1 => 1
[5,1,-4,3,2] => [3] => 1 => 1
[5,1,-4,-3,2] => [3,2] => 10 => 10
[5,1,-4,-3,-2] => [2] => 0 => 0
[5,-1,4,3,2] => [2] => 0 => 0
[5,-1,4,3,-2] => [3,2] => 10 => 10
[5,-1,4,-3,-2] => [3] => 1 => 1
[5,-1,-4,3,-2] => [3] => 1 => 1
[5,-1,-4,-3,2] => [2] => 0 => 0
[5,-1,-4,-3,-2] => [3,2] => 10 => 10
[-5,1,4,3,2] => [2] => 0 => 0
[-5,1,4,3,-2] => [3,2] => 10 => 10
[-5,1,4,-3,-2] => [3] => 1 => 1
[-5,1,-4,3,-2] => [3] => 1 => 1
[-5,1,-4,-3,2] => [2] => 0 => 0
[-5,1,-4,-3,-2] => [3,2] => 10 => 10
[-5,-1,4,3,2] => [3,2] => 10 => 10
[-5,-1,4,3,-2] => [2] => 0 => 0
[-5,-1,4,-3,2] => [3] => 1 => 1
[-5,-1,-4,3,2] => [3] => 1 => 1
[-5,-1,-4,-3,2] => [3,2] => 10 => 10
[-5,-1,-4,-3,-2] => [2] => 0 => 0
[5,2,1,3,4] => [4,1] => 01 => 01
[5,2,1,3,-4] => [1] => 1 => 1
[5,2,1,-3,4] => [1] => 1 => 1
[5,2,1,-3,-4] => [4,1] => 01 => 01
[5,2,-1,3,4] => [1] => 1 => 1
[5,2,-1,3,-4] => [4,1] => 01 => 01
[5,2,-1,-3,4] => [4,1] => 01 => 01
[5,2,-1,-3,-4] => [1] => 1 => 1
[5,-2,1,3,4] => [4] => 0 => 0
[5,-2,1,-3,-4] => [4] => 0 => 0
[5,-2,-1,3,-4] => [4] => 0 => 0
[5,-2,-1,-3,4] => [4] => 0 => 0
[-5,2,1,3,4] => [1] => 1 => 1
[-5,2,1,3,-4] => [4,1] => 01 => 01
[-5,2,1,-3,4] => [4,1] => 01 => 01
[-5,2,1,-3,-4] => [1] => 1 => 1
[-5,2,-1,3,4] => [4,1] => 01 => 01
[-5,2,-1,3,-4] => [1] => 1 => 1
[-5,2,-1,-3,4] => [1] => 1 => 1
[-5,2,-1,-3,-4] => [4,1] => 01 => 01
[-5,-2,1,3,-4] => [4] => 0 => 0
[-5,-2,1,-3,4] => [4] => 0 => 0
[-5,-2,-1,3,4] => [4] => 0 => 0
[-5,-2,-1,-3,-4] => [4] => 0 => 0
[5,2,1,4,3] => [3,1,1] => 111 => 111
[5,2,1,4,-3] => [1,1] => 11 => 11
[5,2,1,-4,3] => [3,1] => 11 => 11
[5,2,1,-4,-3] => [1] => 1 => 1
[5,2,-1,4,3] => [1,1] => 11 => 11
[5,2,-1,4,-3] => [3,1,1] => 111 => 111
[5,2,-1,-4,3] => [1] => 1 => 1
[5,2,-1,-4,-3] => [3,1] => 11 => 11
[5,-2,1,4,3] => [3,1] => 11 => 11
[5,-2,1,4,-3] => [1] => 1 => 1
[5,-2,1,-4,3] => [3] => 1 => 1
[5,-2,-1,4,3] => [1] => 1 => 1
[5,-2,-1,4,-3] => [3,1] => 11 => 11
[5,-2,-1,-4,-3] => [3] => 1 => 1
[-5,2,1,4,3] => [1,1] => 11 => 11
[-5,2,1,4,-3] => [3,1,1] => 111 => 111
[-5,2,1,-4,3] => [1] => 1 => 1
[-5,2,1,-4,-3] => [3,1] => 11 => 11
[-5,2,-1,4,3] => [3,1,1] => 111 => 111
[-5,2,-1,4,-3] => [1,1] => 11 => 11
[-5,2,-1,-4,3] => [3,1] => 11 => 11
[-5,2,-1,-4,-3] => [1] => 1 => 1
[-5,-2,1,4,3] => [1] => 1 => 1
[-5,-2,1,4,-3] => [3,1] => 11 => 11
[-5,-2,1,-4,-3] => [3] => 1 => 1
[-5,-2,-1,4,3] => [3,1] => 11 => 11
[-5,-2,-1,4,-3] => [1] => 1 => 1
[-5,-2,-1,-4,3] => [3] => 1 => 1
[5,2,3,1,4] => [3,1,1] => 111 => 111
[5,2,3,1,-4] => [1,1] => 11 => 11
[5,2,3,-1,4] => [1,1] => 11 => 11
[5,2,3,-1,-4] => [3,1,1] => 111 => 111
[5,2,-3,1,4] => [3,1] => 11 => 11
[5,2,-3,1,-4] => [1] => 1 => 1
[5,2,-3,-1,4] => [1] => 1 => 1
[5,2,-3,-1,-4] => [3,1] => 11 => 11
[5,-2,3,1,4] => [3,1] => 11 => 11
[5,-2,3,1,-4] => [1] => 1 => 1
[5,-2,3,-1,4] => [1] => 1 => 1
[5,-2,3,-1,-4] => [3,1] => 11 => 11
[5,-2,-3,1,4] => [3] => 1 => 1
[5,-2,-3,-1,-4] => [3] => 1 => 1
[-5,2,3,1,4] => [1,1] => 11 => 11
[-5,2,3,1,-4] => [3,1,1] => 111 => 111
[-5,2,3,-1,4] => [3,1,1] => 111 => 111
[-5,2,3,-1,-4] => [1,1] => 11 => 11
[-5,2,-3,1,4] => [1] => 1 => 1
[-5,2,-3,1,-4] => [3,1] => 11 => 11
[-5,2,-3,-1,4] => [3,1] => 11 => 11
[-5,2,-3,-1,-4] => [1] => 1 => 1
[-5,-2,3,1,4] => [1] => 1 => 1
[-5,-2,3,1,-4] => [3,1] => 11 => 11
[-5,-2,3,-1,4] => [3,1] => 11 => 11
[-5,-2,3,-1,-4] => [1] => 1 => 1
[-5,-2,-3,1,-4] => [3] => 1 => 1
[-5,-2,-3,-1,4] => [3] => 1 => 1
[5,2,3,4,1] => [2,1,1,1] => 0111 => 0111
[5,2,3,4,-1] => [1,1,1] => 111 => 111
[5,2,3,-4,1] => [2,1,1] => 011 => 011
[5,2,3,-4,-1] => [1,1] => 11 => 11
[5,2,-3,4,1] => [2,1,1] => 011 => 011
[5,2,-3,4,-1] => [1,1] => 11 => 11
[5,2,-3,-4,1] => [2,1] => 01 => 01
[5,2,-3,-4,-1] => [1] => 1 => 1
[5,-2,3,4,1] => [2,1,1] => 011 => 011
[5,-2,3,4,-1] => [1,1] => 11 => 11
[5,-2,3,-4,1] => [2,1] => 01 => 01
[5,-2,3,-4,-1] => [1] => 1 => 1
[5,-2,-3,4,1] => [2,1] => 01 => 01
[5,-2,-3,4,-1] => [1] => 1 => 1
[5,-2,-3,-4,1] => [2] => 0 => 0
[-5,2,3,4,1] => [1,1,1] => 111 => 111
[-5,2,3,4,-1] => [2,1,1,1] => 0111 => 0111
[-5,2,3,-4,1] => [1,1] => 11 => 11
[-5,2,3,-4,-1] => [2,1,1] => 011 => 011
[-5,2,-3,4,1] => [1,1] => 11 => 11
[-5,2,-3,4,-1] => [2,1,1] => 011 => 011
[-5,2,-3,-4,1] => [1] => 1 => 1
[-5,2,-3,-4,-1] => [2,1] => 01 => 01
[-5,-2,3,4,1] => [1,1] => 11 => 11
[-5,-2,3,4,-1] => [2,1,1] => 011 => 011
[-5,-2,3,-4,1] => [1] => 1 => 1
[-5,-2,3,-4,-1] => [2,1] => 01 => 01
[-5,-2,-3,4,1] => [1] => 1 => 1
[-5,-2,-3,4,-1] => [2,1] => 01 => 01
[-5,-2,-3,-4,-1] => [2] => 0 => 0
[5,2,4,1,3] => [4,1] => 01 => 01
[5,2,4,1,-3] => [1] => 1 => 1
[5,2,4,-1,3] => [1] => 1 => 1
[5,2,4,-1,-3] => [4,1] => 01 => 01
[5,2,-4,1,3] => [1] => 1 => 1
[5,2,-4,1,-3] => [4,1] => 01 => 01
[5,2,-4,-1,3] => [4,1] => 01 => 01
[5,2,-4,-1,-3] => [1] => 1 => 1
[5,-2,4,1,3] => [4] => 0 => 0
[5,-2,4,-1,-3] => [4] => 0 => 0
[5,-2,-4,1,-3] => [4] => 0 => 0
[5,-2,-4,-1,3] => [4] => 0 => 0
[-5,2,4,1,3] => [1] => 1 => 1
[-5,2,4,1,-3] => [4,1] => 01 => 01
[-5,2,4,-1,3] => [4,1] => 01 => 01
[-5,2,4,-1,-3] => [1] => 1 => 1
[-5,2,-4,1,3] => [4,1] => 01 => 01
[-5,2,-4,1,-3] => [1] => 1 => 1
[-5,2,-4,-1,3] => [1] => 1 => 1
[-5,2,-4,-1,-3] => [4,1] => 01 => 01
[-5,-2,4,1,-3] => [4] => 0 => 0
[-5,-2,4,-1,3] => [4] => 0 => 0
[-5,-2,-4,1,3] => [4] => 0 => 0
[-5,-2,-4,-1,-3] => [4] => 0 => 0
[5,2,4,3,1] => [2,2,1] => 001 => 001
[5,2,4,3,-1] => [2,1] => 01 => 01
[5,2,4,-3,1] => [2,1] => 01 => 01
[5,2,4,-3,-1] => [1] => 1 => 1
[5,2,-4,3,1] => [2,1] => 01 => 01
[5,2,-4,3,-1] => [1] => 1 => 1
[5,2,-4,-3,1] => [2,2,1] => 001 => 001
[5,2,-4,-3,-1] => [2,1] => 01 => 01
[5,-2,4,3,1] => [2,2] => 00 => 00
[5,-2,4,3,-1] => [2] => 0 => 0
[5,-2,4,-3,1] => [2] => 0 => 0
[5,-2,-4,3,1] => [2] => 0 => 0
[5,-2,-4,-3,1] => [2,2] => 00 => 00
[5,-2,-4,-3,-1] => [2] => 0 => 0
[-5,2,4,3,1] => [2,1] => 01 => 01
[-5,2,4,3,-1] => [2,2,1] => 001 => 001
[-5,2,4,-3,1] => [1] => 1 => 1
[-5,2,4,-3,-1] => [2,1] => 01 => 01
[-5,2,-4,3,1] => [1] => 1 => 1
[-5,2,-4,3,-1] => [2,1] => 01 => 01
[-5,2,-4,-3,1] => [2,1] => 01 => 01
[-5,2,-4,-3,-1] => [2,2,1] => 001 => 001
[-5,-2,4,3,1] => [2] => 0 => 0
[-5,-2,4,3,-1] => [2,2] => 00 => 00
[-5,-2,4,-3,-1] => [2] => 0 => 0
[-5,-2,-4,3,-1] => [2] => 0 => 0
[-5,-2,-4,-3,1] => [2] => 0 => 0
[-5,-2,-4,-3,-1] => [2,2] => 00 => 00
[5,3,1,2,4] => [5] => 1 => 1
[5,3,1,-2,-4] => [5] => 1 => 1
[5,3,-1,2,-4] => [5] => 1 => 1
[5,3,-1,-2,4] => [5] => 1 => 1
[5,-3,1,2,-4] => [5] => 1 => 1
[5,-3,1,-2,4] => [5] => 1 => 1
[5,-3,-1,2,4] => [5] => 1 => 1
[5,-3,-1,-2,-4] => [5] => 1 => 1
[-5,3,1,2,-4] => [5] => 1 => 1
[-5,3,1,-2,4] => [5] => 1 => 1
[-5,3,-1,2,4] => [5] => 1 => 1
[-5,3,-1,-2,-4] => [5] => 1 => 1
[-5,-3,1,2,4] => [5] => 1 => 1
[-5,-3,1,-2,-4] => [5] => 1 => 1
[-5,-3,-1,2,-4] => [5] => 1 => 1
[-5,-3,-1,-2,4] => [5] => 1 => 1
[5,3,1,4,2] => [4,1] => 01 => 01
[5,3,1,4,-2] => [1] => 1 => 1
[5,3,1,-4,2] => [4] => 0 => 0
[5,3,-1,4,2] => [1] => 1 => 1
[5,3,-1,4,-2] => [4,1] => 01 => 01
[5,3,-1,-4,-2] => [4] => 0 => 0
[5,-3,1,4,2] => [1] => 1 => 1
[5,-3,1,4,-2] => [4,1] => 01 => 01
[5,-3,1,-4,-2] => [4] => 0 => 0
[5,-3,-1,4,2] => [4,1] => 01 => 01
[5,-3,-1,4,-2] => [1] => 1 => 1
[5,-3,-1,-4,2] => [4] => 0 => 0
[-5,3,1,4,2] => [1] => 1 => 1
[-5,3,1,4,-2] => [4,1] => 01 => 01
[-5,3,1,-4,-2] => [4] => 0 => 0
[-5,3,-1,4,2] => [4,1] => 01 => 01
[-5,3,-1,4,-2] => [1] => 1 => 1
[-5,3,-1,-4,2] => [4] => 0 => 0
[-5,-3,1,4,2] => [4,1] => 01 => 01
[-5,-3,1,4,-2] => [1] => 1 => 1
[-5,-3,1,-4,2] => [4] => 0 => 0
[-5,-3,-1,4,2] => [1] => 1 => 1
[-5,-3,-1,4,-2] => [4,1] => 01 => 01
[-5,-3,-1,-4,-2] => [4] => 0 => 0
[5,3,2,1,4] => [3,2] => 10 => 10
[5,3,2,1,-4] => [2] => 0 => 0
[5,3,2,-1,4] => [2] => 0 => 0
[5,3,2,-1,-4] => [3,2] => 10 => 10
[5,3,-2,1,4] => [3] => 1 => 1
[5,3,-2,-1,-4] => [3] => 1 => 1
[5,-3,2,1,4] => [3] => 1 => 1
[5,-3,2,-1,-4] => [3] => 1 => 1
[5,-3,-2,1,4] => [3,2] => 10 => 10
[5,-3,-2,1,-4] => [2] => 0 => 0
[5,-3,-2,-1,4] => [2] => 0 => 0
[5,-3,-2,-1,-4] => [3,2] => 10 => 10
[-5,3,2,1,4] => [2] => 0 => 0
[-5,3,2,1,-4] => [3,2] => 10 => 10
[-5,3,2,-1,4] => [3,2] => 10 => 10
[-5,3,2,-1,-4] => [2] => 0 => 0
[-5,3,-2,1,-4] => [3] => 1 => 1
[-5,3,-2,-1,4] => [3] => 1 => 1
[-5,-3,2,1,-4] => [3] => 1 => 1
[-5,-3,2,-1,4] => [3] => 1 => 1
[-5,-3,-2,1,4] => [2] => 0 => 0
[-5,-3,-2,1,-4] => [3,2] => 10 => 10
[-5,-3,-2,-1,4] => [3,2] => 10 => 10
[-5,-3,-2,-1,-4] => [2] => 0 => 0
[5,3,2,4,1] => [2,2,1] => 001 => 001
[5,3,2,4,-1] => [2,1] => 01 => 01
[5,3,2,-4,1] => [2,2] => 00 => 00
[5,3,2,-4,-1] => [2] => 0 => 0
[5,3,-2,4,1] => [2,1] => 01 => 01
[5,3,-2,4,-1] => [1] => 1 => 1
[5,3,-2,-4,1] => [2] => 0 => 0
[5,-3,2,4,1] => [2,1] => 01 => 01
[5,-3,2,4,-1] => [1] => 1 => 1
[5,-3,2,-4,1] => [2] => 0 => 0
[5,-3,-2,4,1] => [2,2,1] => 001 => 001
[5,-3,-2,4,-1] => [2,1] => 01 => 01
[5,-3,-2,-4,1] => [2,2] => 00 => 00
[5,-3,-2,-4,-1] => [2] => 0 => 0
[-5,3,2,4,1] => [2,1] => 01 => 01
[-5,3,2,4,-1] => [2,2,1] => 001 => 001
[-5,3,2,-4,1] => [2] => 0 => 0
[-5,3,2,-4,-1] => [2,2] => 00 => 00
[-5,3,-2,4,1] => [1] => 1 => 1
[-5,3,-2,4,-1] => [2,1] => 01 => 01
[-5,3,-2,-4,-1] => [2] => 0 => 0
[-5,-3,2,4,1] => [1] => 1 => 1
[-5,-3,2,4,-1] => [2,1] => 01 => 01
[-5,-3,2,-4,-1] => [2] => 0 => 0
[-5,-3,-2,4,1] => [2,1] => 01 => 01
[-5,-3,-2,4,-1] => [2,2,1] => 001 => 001
[-5,-3,-2,-4,1] => [2] => 0 => 0
[-5,-3,-2,-4,-1] => [2,2] => 00 => 00
[5,3,4,1,2] => [5] => 1 => 1
[5,3,4,-1,-2] => [5] => 1 => 1
[5,3,-4,1,-2] => [5] => 1 => 1
[5,3,-4,-1,2] => [5] => 1 => 1
[5,-3,4,1,-2] => [5] => 1 => 1
[5,-3,4,-1,2] => [5] => 1 => 1
[5,-3,-4,1,2] => [5] => 1 => 1
[5,-3,-4,-1,-2] => [5] => 1 => 1
[-5,3,4,1,-2] => [5] => 1 => 1
[-5,3,4,-1,2] => [5] => 1 => 1
[-5,3,-4,1,2] => [5] => 1 => 1
[-5,3,-4,-1,-2] => [5] => 1 => 1
[-5,-3,4,1,2] => [5] => 1 => 1
[-5,-3,4,-1,-2] => [5] => 1 => 1
[-5,-3,-4,1,-2] => [5] => 1 => 1
[-5,-3,-4,-1,2] => [5] => 1 => 1
[5,3,4,2,1] => [3,2] => 10 => 10
[5,3,4,2,-1] => [3] => 1 => 1
[5,3,4,-2,1] => [2] => 0 => 0
[5,3,-4,2,1] => [2] => 0 => 0
[5,3,-4,-2,1] => [3,2] => 10 => 10
[5,3,-4,-2,-1] => [3] => 1 => 1
[5,-3,4,2,1] => [2] => 0 => 0
[5,-3,4,-2,1] => [3,2] => 10 => 10
[5,-3,4,-2,-1] => [3] => 1 => 1
[5,-3,-4,2,1] => [3,2] => 10 => 10
[5,-3,-4,2,-1] => [3] => 1 => 1
[5,-3,-4,-2,1] => [2] => 0 => 0
[-5,3,4,2,1] => [3] => 1 => 1
[-5,3,4,2,-1] => [3,2] => 10 => 10
[-5,3,4,-2,-1] => [2] => 0 => 0
[-5,3,-4,2,-1] => [2] => 0 => 0
[-5,3,-4,-2,1] => [3] => 1 => 1
[-5,3,-4,-2,-1] => [3,2] => 10 => 10
[-5,-3,4,2,-1] => [2] => 0 => 0
[-5,-3,4,-2,1] => [3] => 1 => 1
[-5,-3,4,-2,-1] => [3,2] => 10 => 10
[-5,-3,-4,2,1] => [3] => 1 => 1
[-5,-3,-4,2,-1] => [3,2] => 10 => 10
[-5,-3,-4,-2,-1] => [2] => 0 => 0
[5,4,1,2,3] => [3,2] => 10 => 10
[5,4,1,2,-3] => [2] => 0 => 0
[5,4,1,-2,3] => [3] => 1 => 1
[5,4,-1,2,3] => [2] => 0 => 0
[5,4,-1,2,-3] => [3,2] => 10 => 10
[5,4,-1,-2,-3] => [3] => 1 => 1
[5,-4,1,2,3] => [3] => 1 => 1
[5,-4,1,-2,3] => [3,2] => 10 => 10
[5,-4,1,-2,-3] => [2] => 0 => 0
[5,-4,-1,2,-3] => [3] => 1 => 1
[5,-4,-1,-2,3] => [2] => 0 => 0
[5,-4,-1,-2,-3] => [3,2] => 10 => 10
[-5,4,1,2,3] => [2] => 0 => 0
[-5,4,1,2,-3] => [3,2] => 10 => 10
[-5,4,1,-2,-3] => [3] => 1 => 1
[-5,4,-1,2,3] => [3,2] => 10 => 10
[-5,4,-1,2,-3] => [2] => 0 => 0
[-5,4,-1,-2,3] => [3] => 1 => 1
[-5,-4,1,2,-3] => [3] => 1 => 1
[-5,-4,1,-2,3] => [2] => 0 => 0
[-5,-4,1,-2,-3] => [3,2] => 10 => 10
[-5,-4,-1,2,3] => [3] => 1 => 1
[-5,-4,-1,-2,3] => [3,2] => 10 => 10
[-5,-4,-1,-2,-3] => [2] => 0 => 0
[5,4,1,3,2] => [5] => 1 => 1
[5,4,1,-3,-2] => [5] => 1 => 1
[5,4,-1,3,-2] => [5] => 1 => 1
[5,4,-1,-3,2] => [5] => 1 => 1
[5,-4,1,3,-2] => [5] => 1 => 1
[5,-4,1,-3,2] => [5] => 1 => 1
[5,-4,-1,3,2] => [5] => 1 => 1
[5,-4,-1,-3,-2] => [5] => 1 => 1
[-5,4,1,3,-2] => [5] => 1 => 1
[-5,4,1,-3,2] => [5] => 1 => 1
[-5,4,-1,3,2] => [5] => 1 => 1
[-5,4,-1,-3,-2] => [5] => 1 => 1
[-5,-4,1,3,2] => [5] => 1 => 1
[-5,-4,1,-3,-2] => [5] => 1 => 1
[-5,-4,-1,3,-2] => [5] => 1 => 1
[-5,-4,-1,-3,2] => [5] => 1 => 1
[5,4,2,1,3] => [5] => 1 => 1
[5,4,2,-1,-3] => [5] => 1 => 1
[5,4,-2,1,-3] => [5] => 1 => 1
[5,4,-2,-1,3] => [5] => 1 => 1
[5,-4,2,1,-3] => [5] => 1 => 1
[5,-4,2,-1,3] => [5] => 1 => 1
[5,-4,-2,1,3] => [5] => 1 => 1
[5,-4,-2,-1,-3] => [5] => 1 => 1
[-5,4,2,1,-3] => [5] => 1 => 1
[-5,4,2,-1,3] => [5] => 1 => 1
[-5,4,-2,1,3] => [5] => 1 => 1
[-5,4,-2,-1,-3] => [5] => 1 => 1
[-5,-4,2,1,3] => [5] => 1 => 1
[-5,-4,2,-1,-3] => [5] => 1 => 1
[-5,-4,-2,1,-3] => [5] => 1 => 1
[-5,-4,-2,-1,3] => [5] => 1 => 1
[5,4,2,3,1] => [3,2] => 10 => 10
[5,4,2,3,-1] => [3] => 1 => 1
[5,4,2,-3,1] => [2] => 0 => 0
[5,4,-2,3,1] => [2] => 0 => 0
[5,4,-2,-3,1] => [3,2] => 10 => 10
[5,4,-2,-3,-1] => [3] => 1 => 1
[5,-4,2,3,1] => [2] => 0 => 0
[5,-4,2,-3,1] => [3,2] => 10 => 10
[5,-4,2,-3,-1] => [3] => 1 => 1
[5,-4,-2,3,1] => [3,2] => 10 => 10
[5,-4,-2,3,-1] => [3] => 1 => 1
[5,-4,-2,-3,1] => [2] => 0 => 0
[-5,4,2,3,1] => [3] => 1 => 1
[-5,4,2,3,-1] => [3,2] => 10 => 10
[-5,4,2,-3,-1] => [2] => 0 => 0
[-5,4,-2,3,-1] => [2] => 0 => 0
[-5,4,-2,-3,1] => [3] => 1 => 1
[-5,4,-2,-3,-1] => [3,2] => 10 => 10
[-5,-4,2,3,-1] => [2] => 0 => 0
[-5,-4,2,-3,1] => [3] => 1 => 1
[-5,-4,2,-3,-1] => [3,2] => 10 => 10
[-5,-4,-2,3,1] => [3] => 1 => 1
[-5,-4,-2,3,-1] => [3,2] => 10 => 10
[-5,-4,-2,-3,-1] => [2] => 0 => 0
[5,4,3,1,2] => [4,1] => 01 => 01
[5,4,3,1,-2] => [1] => 1 => 1
[5,4,3,-1,2] => [1] => 1 => 1
[5,4,3,-1,-2] => [4,1] => 01 => 01
[5,4,-3,1,2] => [4] => 0 => 0
[5,4,-3,-1,-2] => [4] => 0 => 0
[5,-4,3,1,2] => [1] => 1 => 1
[5,-4,3,1,-2] => [4,1] => 01 => 01
[5,-4,3,-1,2] => [4,1] => 01 => 01
[5,-4,3,-1,-2] => [1] => 1 => 1
[5,-4,-3,1,-2] => [4] => 0 => 0
[5,-4,-3,-1,2] => [4] => 0 => 0
[-5,4,3,1,2] => [1] => 1 => 1
[-5,4,3,1,-2] => [4,1] => 01 => 01
[-5,4,3,-1,2] => [4,1] => 01 => 01
[-5,4,3,-1,-2] => [1] => 1 => 1
[-5,4,-3,1,-2] => [4] => 0 => 0
[-5,4,-3,-1,2] => [4] => 0 => 0
[-5,-4,3,1,2] => [4,1] => 01 => 01
[-5,-4,3,1,-2] => [1] => 1 => 1
[-5,-4,3,-1,2] => [1] => 1 => 1
[-5,-4,3,-1,-2] => [4,1] => 01 => 01
[-5,-4,-3,1,2] => [4] => 0 => 0
[-5,-4,-3,-1,-2] => [4] => 0 => 0
[5,4,3,2,1] => [2,2,1] => 001 => 001
[5,4,3,2,-1] => [2,1] => 01 => 01
[5,4,3,-2,1] => [2,1] => 01 => 01
[5,4,3,-2,-1] => [1] => 1 => 1
[5,4,-3,2,1] => [2,2] => 00 => 00
[5,4,-3,2,-1] => [2] => 0 => 0
[5,4,-3,-2,1] => [2] => 0 => 0
[5,-4,3,2,1] => [2,1] => 01 => 01
[5,-4,3,2,-1] => [1] => 1 => 1
[5,-4,3,-2,1] => [2,2,1] => 001 => 001
[5,-4,3,-2,-1] => [2,1] => 01 => 01
[5,-4,-3,2,1] => [2] => 0 => 0
[5,-4,-3,-2,1] => [2,2] => 00 => 00
[5,-4,-3,-2,-1] => [2] => 0 => 0
[-5,4,3,2,1] => [2,1] => 01 => 01
[-5,4,3,2,-1] => [2,2,1] => 001 => 001
[-5,4,3,-2,1] => [1] => 1 => 1
[-5,4,3,-2,-1] => [2,1] => 01 => 01
[-5,4,-3,2,1] => [2] => 0 => 0
[-5,4,-3,2,-1] => [2,2] => 00 => 00
[-5,4,-3,-2,-1] => [2] => 0 => 0
[-5,-4,3,2,1] => [1] => 1 => 1
[-5,-4,3,2,-1] => [2,1] => 01 => 01
[-5,-4,3,-2,1] => [2,1] => 01 => 01
[-5,-4,3,-2,-1] => [2,2,1] => 001 => 001
[-5,-4,-3,2,-1] => [2] => 0 => 0
[-5,-4,-3,-2,1] => [2] => 0 => 0
[-5,-4,-3,-2,-1] => [2,2] => 00 => 00
[1,2,3,4,5,6] => [1,1,1,1,1,1] => 111111 => 111111
[1,2,3,6,4,5] => [3,1,1,1] => 1111 => 1111
[1,2,5,3,4,6] => [3,1,1,1] => 1111 => 1111
[1,2,5,6,3,4] => [2,2,1,1] => 0011 => 0011
[1,4,2,3,5,6] => [3,1,1,1] => 1111 => 1111
[1,4,2,6,3,5] => [5,1] => 11 => 11
[1,4,5,2,3,6] => [2,2,1,1] => 0011 => 0011
[1,4,5,6,2,3] => [5,1] => 11 => 11
[1,5,2,3,4,6] => [4,1,1] => 011 => 011
[1,5,6,2,3,4] => [5,1] => 11 => 11
[1,6,2,3,4,5] => [5,1] => 11 => 11
[1,6,2,5,3,4] => [5,1] => 11 => 11
[1,6,4,2,3,5] => [5,1] => 11 => 11
[1,6,4,5,2,3] => [5,1] => 11 => 11
[3,1,2,4,5,6] => [3,1,1,1] => 1111 => 1111
[3,1,2,6,4,5] => [3,3] => 11 => 11
[3,1,5,2,4,6] => [5,1] => 11 => 11
[3,1,5,6,2,4] => [4,2] => 00 => 00
[3,4,1,2,5,6] => [2,2,1,1] => 0011 => 0011
[3,4,1,6,2,5] => [4,2] => 00 => 00
[3,4,5,1,2,6] => [5,1] => 11 => 11
[3,4,5,6,1,2] => [3,3] => 11 => 11
[3,4,6,1,2,5] => [6] => 0 => 0
[3,5,1,2,4,6] => [3,2,1] => 101 => 101
[3,5,6,1,2,4] => [4,2] => 00 => 00
[3,6,1,2,4,5] => [4,2] => 00 => 00
[3,6,1,5,2,4] => [4,2] => 00 => 00
[3,6,4,1,2,5] => [3,3] => 11 => 11
[3,6,4,5,1,2] => [4,2] => 00 => 00
[4,1,2,3,5,6] => [4,1,1] => 011 => 011
[4,5,1,2,3,6] => [5,1] => 11 => 11
[4,5,6,1,2,3] => [2,2,2] => 000 => 000
[4,6,1,2,3,5] => [6] => 0 => 0
[4,6,5,1,2,3] => [4,2] => 00 => 00
[5,1,2,3,4,6] => [5,1] => 11 => 11
[5,1,2,6,3,4] => [4,2] => 00 => 00
[5,1,4,2,3,6] => [5,1] => 11 => 11
[5,1,4,6,2,3] => [3,3] => 11 => 11
[5,1,6,2,3,4] => [6] => 0 => 0
[5,3,1,2,4,6] => [5,1] => 11 => 11
[5,3,1,6,2,4] => [4,2] => 00 => 00
[5,3,4,1,2,6] => [5,1] => 11 => 11
[5,3,4,6,1,2] => [4,2] => 00 => 00
[5,6,1,2,3,4] => [3,3] => 11 => 11
[5,6,1,4,2,3] => [5,1] => 11 => 11
[5,6,3,1,2,4] => [5,1] => 11 => 11
[5,6,3,4,1,2] => [2,2,1,1] => 0011 => 0011
[6,1,2,3,4,5] => [6] => 0 => 0
[6,2,1,5,3,4] => [5,1] => 11 => 11
[6,2,4,1,3,5] => [5,1] => 11 => 11
[6,3,1,2,4,5] => [6] => 0 => 0
[1,2,3,4,7,5,6] => [3,1,1,1,1] => 11111 => 11111
[1,2,5,3,7,4,6] => [5,1,1] => 111 => 111
[1,2,7,3,4,5,6] => [5,1,1] => 111 => 111
[1,2,7,3,6,4,5] => [5,1,1] => 111 => 111
[1,4,7,2,3,5,6] => [4,2,1] => 001 => 001
[1,5,7,2,3,4,6] => [6,1] => 01 => 01
[1,6,7,2,3,4,5] => [3,3,1] => 111 => 111
[1,6,7,2,5,3,4] => [5,1,1] => 111 => 111
[1,6,7,4,2,3,5] => [5,1,1] => 111 => 111
[3,1,7,2,4,5,6] => [7] => 1 => 1
[3,1,7,5,2,4,6] => [7] => 1 => 1
[3,4,7,1,2,5,6] => [7] => 1 => 1
[3,4,7,1,6,2,5] => [7] => 1 => 1
[3,4,7,5,1,2,6] => [7] => 1 => 1
[3,4,7,5,6,1,2] => [7] => 1 => 1
[3,5,7,1,2,4,6] => [5,2] => 10 => 10
[3,6,1,2,7,4,5] => [3,2,2] => 100 => 010
[3,7,4,1,2,5,6] => [4,3] => 01 => 01
[3,7,4,5,1,2,6] => [4,3] => 01 => 01
[3,7,4,5,6,1,2] => [5,2] => 10 => 10
[3,7,4,6,1,2,5] => [7] => 1 => 1
[3,7,5,1,2,4,6] => [7] => 1 => 1
[3,7,5,6,1,2,4] => [4,3] => 01 => 01
[3,7,6,1,2,4,5] => [4,3] => 01 => 01
[4,7,5,6,1,2,3] => [7] => 1 => 1
[5,3,4,7,1,2,6] => [5,2] => 10 => 10
[5,3,7,1,2,4,6] => [7] => 1 => 1
[5,4,7,1,2,3,6] => [4,3] => 01 => 01
[7,1,2,5,3,4,6] => [7] => 1 => 1
[7,1,3,2,4,5,6] => [6,1] => 01 => 01
[7,1,4,2,3,5,6] => [7] => 1 => 1
[7,1,4,2,6,3,5] => [7] => 1 => 1
[7,1,4,5,2,3,6] => [7] => 1 => 1
[7,1,4,6,2,3,5] => [4,3] => 01 => 01
[7,1,5,2,3,4,6] => [5,2] => 10 => 10
[7,1,5,6,2,3,4] => [7] => 1 => 1
[7,1,6,2,3,4,5] => [7] => 1 => 1
[7,1,6,4,5,2,3] => [5,1,1] => 111 => 111
[7,2,4,1,3,5,6] => [6,1] => 01 => 01
[7,2,5,1,3,4,6] => [4,2,1] => 001 => 001
[7,2,6,1,3,4,5] => [6,1] => 01 => 01
[7,3,1,2,4,5,6] => [7] => 1 => 1
[7,3,5,1,2,4,6] => [4,3] => 01 => 01
[7,3,5,6,1,2,4] => [7] => 1 => 1
[7,3,6,1,2,4,5] => [7] => 1 => 1
[7,5,1,4,2,3,6] => [4,2,1] => 001 => 001
[5,6,7,8,3,4,1,2] => [4,4] => 00 => 00
[5,6,7,8,3,1,2,4] => [6,2] => 00 => 00
[5,6,7,8,4,1,2,3] => [8] => 0 => 0
[5,6,7,8,1,4,2,3] => [6,2] => 00 => 00
[7,8,5,6,3,4,1,2] => [2,2,2,2] => 0000 => 0000
[4,6,-3,1,2,5] => [3,2] => 10 => 10
[-3,2,-6,-4,1,5] => [4,1] => 01 => 01
[3,2,6,-5,1,4] => [1] => 1 => 1
[-5,-3,2,4,-6,1] => [3,1] => 11 => 11
[2,6,-5,1,3,4] => [4] => 0 => 0
[3,6,5,-4,1,2] => [3,2] => 10 => 10
[4,6,-5,3,1,2] => [2] => 0 => 0
[6,8,-4,-3,1,2,5,7] => [6,2] => 00 => 00
[-3,2,-8,-6,-4,1,5,7] => [7,1] => 11 => 11
[3,2,8,-6,-5,1,4,7] => [1] => 1 => 1
[-5,-3,2,4,-8,-6,1,7] => [4,1] => 01 => 01
[5,-3,2,4,8,-7,1,6] => [1] => 1 => 1
[-7,-5,-3,2,4,6,-8,1] => [3,1] => 11 => 11
[5,7,-4,2,3,6,-8,1] => [7,1] => 11 => 11
[-4,5,2,3,8,-7,1,6] => [8] => 0 => 0
[-8,-6,1,-5,-4,2,3,7] => [2] => 0 => 0
[-3,6,8,-5,1,2,4,7] => [6,2] => 00 => 00
[-6,4,3,8,-5,1,2,7] => [4,1] => 01 => 01
[4,3,-5,2,8,-7,1,6] => [8] => 0 => 0
[-4,3,-7,-5,2,6,-8,1] => [7,1] => 11 => 11
[4,3,7,-6,2,5,-8,1] => [8] => 0 => 0
[3,-4,-8,-6,2,-7,1,5] => [8] => 0 => 0
[8,4,-7,-6,3,1,2,5] => [8] => 0 => 0
[5,-3,4,8,-7,1,2,6] => [8] => 0 => 0
[-5,2,4,8,-7,1,3,6] => [7,1] => 11 => 11
[4,-7,-5,6,-8,-3,1,2] => [8] => 0 => 0
[-7,3,-5,6,-8,-4,1,2] => [4] => 0 => 0
[-4,3,6,-7,-8,-5,1,2] => [5,3] => 11 => 11
[4,-8,6,-7,3,5,1,2] => [3] => 1 => 1
[-6,-4,3,5,-7,2,-8,1] => [7,1] => 11 => 11
[5,6,3,4,-7,2,-8,1] => [4,2,1,1] => 0011 => 0011
[3,-8,5,7,4,-6,1,2] => [5] => 1 => 1
[-7,-6,3,-8,4,-5,1,2] => [1] => 1 => 1
[-7,4,-6,5,-8,-3,1,2] => [2] => 0 => 0
[8,-6,2,4,-7,1,3,5] => [7,1] => 11 => 11
[4,-8,-6,-3,-7,1,2,5] => [4,4] => 00 => 00
[-4,3,-8,-6,-7,1,2,5] => [5,3] => 11 => 11
[-7,6,8,1,3,-5,2,4] => [8] => 0 => 0
[-7,-6,5,8,3,1,2,4] => [4,2,2] => 000 => 000
[5,-6,3,8,2,-7,1,4] => [5,2,1] => 101 => 101
[-7,-6,2,-5,3,4,-8,1] => [5,3] => 11 => 11
[-5,2,6,8,3,-7,1,4] => [5,2,1] => 101 => 101
[-5,7,8,-6,2,1,3,4] => [8] => 0 => 0
[5,6,7,1,8,2,3,4] => [4,2,2] => 000 => 000
[-4,-8,-7,1,-6,2,3,5] => [4] => 0 => 0
[8,-7,-6,3,1,2,4,5] => [5,3] => 11 => 11
[2,-7,8,-6,1,3,4,5] => [8] => 0 => 0
[-5,2,8,-7,1,3,4,6] => [3,1] => 11 => 11
[-7,-5,3,8,1,2,4,6] => [7,1] => 11 => 11
[5,-7,-4,8,1,2,3,6] => [6,2] => 00 => 00
[-4,-8,-7,2,-5,1,3,6] => [5] => 1 => 1
[4,2,-7,8,-6,1,3,5] => [1] => 1 => 1
[-6,4,7,2,3,5,-8,1] => [6,2] => 00 => 00
[3,7,-6,2,4,5,-8,1] => [8] => 0 => 0
[6,8,-3,2,4,-7,1,5] => [4] => 0 => 0
[2,-8,-7,-3,-6,1,4,5] => [5,3] => 11 => 11
[-3,2,7,8,-4,1,5,6] => [7,1] => 11 => 11
[3,4,7,8,1,2,5,6] => [4,4] => 00 => 00
[4,8,-7,-2,1,3,5,6] => [8] => 0 => 0
[6,-7,-8,-4,-3,1,2,5] => [3,2] => 10 => 10
[3,7,2,6,-8,-5,1,4] => [4,4] => 00 => 00
[-7,-8,-3,2,5,-6,1,4] => [1] => 1 => 1
[-8,5,-6,-3,2,-7,1,4] => [6,2] => 00 => 00
[-6,5,-7,-3,2,4,-8,1] => [6,2] => 00 => 00
[-8,4,7,2,5,-6,1,3] => [2,1] => 01 => 01
[-7,2,-4,6,-8,-5,1,3] => [1] => 1 => 1
[6,-7,-3,-8,-5,1,2,4] => [2] => 0 => 0
[7,2,6,-8,-5,1,3,4] => [4,1] => 01 => 01
[7,-8,2,5,-6,1,3,4] => [8] => 0 => 0
[7,-8,-5,-3,-6,1,2,4] => [8] => 0 => 0
[-8,6,7,1,4,-5,2,3] => [8] => 0 => 0
[-8,2,5,7,4,-6,1,3] => [1] => 1 => 1
[-8,-6,-5,4,2,-7,1,3] => [7,1] => 11 => 11
[4,7,6,-5,2,3,-8,1] => [6,2] => 00 => 00
[5,7,-6,4,2,3,-8,1] => [1] => 1 => 1
[4,-8,-5,2,-6,-7,1,3] => [8] => 0 => 0
[8,6,-7,-4,5,1,2,3] => [1] => 1 => 1
[-8,6,-7,3,5,1,2,4] => [7,1] => 11 => 11
[5,8,-6,2,-7,1,3,4] => [5,3] => 11 => 11
[-6,5,-7,4,-8,-2,1,3] => [7,1] => 11 => 11
[5,-6,-7,4,-8,-3,1,2] => [7,1] => 11 => 11
[7,-8,6,3,5,-4,1,2] => [2,1] => 01 => 01
[6,-7,-4,-8,3,-5,1,2] => [8] => 0 => 0
[5,7,-8,4,3,-6,1,2] => [1] => 1 => 1
[5,8,-6,4,-7,3,1,2] => [2,1] => 01 => 01
[1,2,3,4,5,-6] => [1,1,1,1,1] => 11111 => 11111
[1,2,3,4,6,-5] => [1,1,1,1] => 1111 => 1111
[1,2,3,6,5,-4] => [1,1,1,1] => 1111 => 1111
[1,2,3,6,4,-5] => [1,1,1] => 111 => 111
[1,2,3,5,6,-4] => [1,1,1] => 111 => 111
[1,2,6,4,5,-3] => [1,1,1,1] => 1111 => 1111
[1,2,5,4,6,-3] => [1,1,1] => 111 => 111
[1,2,6,3,5,-4] => [1,1,1] => 111 => 111
[1,2,6,3,4,-5] => [1,1] => 11 => 11
[1,2,5,3,6,-4] => [1,1] => 11 => 11
[1,2,4,6,5,-3] => [1,1,1] => 111 => 111
[1,2,5,6,4,-3] => [1,1] => 11 => 11
[1,2,5,6,3,-4] => [2,1,1] => 011 => 011
[1,2,4,5,6,-3] => [1,1] => 11 => 11
[1,6,3,4,5,-2] => [1,1,1,1] => 1111 => 1111
[1,5,3,4,6,-2] => [1,1,1] => 111 => 111
[1,4,3,6,5,-2] => [1,1,1] => 111 => 111
[1,5,3,6,4,-2] => [1,1] => 11 => 11
[1,4,3,5,6,-2] => [1,1] => 11 => 11
[1,6,2,4,5,-3] => [1,1,1] => 111 => 111
[1,5,2,4,6,-3] => [1,1] => 11 => 11
[1,6,2,3,5,-4] => [1,1] => 11 => 11
[1,6,2,3,4,-5] => [1] => 1 => 1
[1,5,2,3,6,-4] => [1] => 1 => 1
[1,4,2,6,5,-3] => [1,1] => 11 => 11
[1,5,2,6,4,-3] => [1] => 1 => 1
[1,5,2,6,3,-4] => [3,1] => 11 => 11
[1,4,2,5,6,-3] => [1] => 1 => 1
[1,3,6,4,5,-2] => [1,1,1] => 111 => 111
[1,3,5,4,6,-2] => [1,1] => 11 => 11
[1,4,6,3,5,-2] => [1,1] => 11 => 11
[1,5,6,3,4,-2] => [1] => 1 => 1
[1,4,5,3,6,-2] => [1] => 1 => 1
[1,4,6,2,5,-3] => [2,1,1] => 011 => 011
[1,5,6,2,4,-3] => [3,1] => 11 => 11
[1,5,6,2,3,-4] => [1] => 1 => 1
[1,4,5,2,6,-3] => [2,1] => 01 => 01
[1,3,4,6,5,-2] => [1,1] => 11 => 11
[1,3,5,6,4,-2] => [1] => 1 => 1
[1,4,5,6,3,-2] => [2,1] => 01 => 01
[1,4,5,6,2,-3] => [1] => 1 => 1
[1,3,4,5,6,-2] => [1] => 1 => 1
[6,2,3,4,5,-1] => [1,1,1,1] => 1111 => 1111
[5,2,3,4,6,-1] => [1,1,1] => 111 => 111
[4,2,3,6,5,-1] => [1,1,1] => 111 => 111
[5,2,3,6,4,-1] => [1,1] => 11 => 11
[4,2,3,5,6,-1] => [1,1] => 11 => 11
[3,2,6,4,5,-1] => [1,1,1] => 111 => 111
[3,2,5,4,6,-1] => [1,1] => 11 => 11
[4,2,6,3,5,-1] => [1,1] => 11 => 11
[5,2,6,3,4,-1] => [1] => 1 => 1
[4,2,5,3,6,-1] => [1] => 1 => 1
[3,2,4,6,5,-1] => [1,1] => 11 => 11
[3,2,5,6,4,-1] => [1] => 1 => 1
[4,2,5,6,3,-1] => [2,1] => 01 => 01
[3,2,4,5,6,-1] => [1] => 1 => 1
[6,1,3,4,5,-2] => [1,1,1] => 111 => 111
[5,1,3,4,6,-2] => [1,1] => 11 => 11
[4,1,3,6,5,-2] => [1,1] => 11 => 11
[5,1,3,6,4,-2] => [1] => 1 => 1
[4,1,3,5,6,-2] => [1] => 1 => 1
[6,1,2,4,5,-3] => [1,1] => 11 => 11
[5,1,2,4,6,-3] => [1] => 1 => 1
[6,1,2,3,5,-4] => [1] => 1 => 1
[4,1,2,6,5,-3] => [1] => 1 => 1
[5,1,2,6,3,-4] => [4] => 0 => 0
[3,1,6,4,5,-2] => [1,1] => 11 => 11
[3,1,5,4,6,-2] => [1] => 1 => 1
[4,1,6,3,5,-2] => [1] => 1 => 1
[4,1,6,2,5,-3] => [3,1] => 11 => 11
[5,1,6,2,4,-3] => [4] => 0 => 0
[4,1,5,2,6,-3] => [3] => 1 => 1
[3,1,4,6,5,-2] => [1] => 1 => 1
[4,1,5,6,3,-2] => [2] => 0 => 0
[2,6,3,4,5,-1] => [1,1,1] => 111 => 111
[2,5,3,4,6,-1] => [1,1] => 11 => 11
[2,4,3,6,5,-1] => [1,1] => 11 => 11
[2,5,3,6,4,-1] => [1] => 1 => 1
[2,4,3,5,6,-1] => [1] => 1 => 1
[3,6,2,4,5,-1] => [1,1] => 11 => 11
[3,5,2,4,6,-1] => [1] => 1 => 1
[4,6,2,3,5,-1] => [1] => 1 => 1
[3,4,2,6,5,-1] => [1] => 1 => 1
[4,5,2,6,3,-1] => [3] => 1 => 1
[3,6,1,4,5,-2] => [2,1,1] => 011 => 011
[3,5,1,4,6,-2] => [2,1] => 01 => 01
[4,6,1,3,5,-2] => [3,1] => 11 => 11
[5,6,1,3,4,-2] => [4] => 0 => 0
[4,5,1,3,6,-2] => [3] => 1 => 1
[4,6,1,2,5,-3] => [1] => 1 => 1
[5,6,1,2,3,-4] => [3] => 1 => 1
[3,4,1,6,5,-2] => [2,1] => 01 => 01
[3,5,1,6,4,-2] => [2] => 0 => 0
[4,5,1,6,2,-3] => [2] => 0 => 0
[3,4,1,5,6,-2] => [2] => 0 => 0
[2,3,6,4,5,-1] => [1,1] => 11 => 11
[2,3,5,4,6,-1] => [1] => 1 => 1
[2,4,6,3,5,-1] => [1] => 1 => 1
[3,4,6,2,5,-1] => [2,1] => 01 => 01
[3,5,6,2,4,-1] => [3] => 1 => 1
[3,4,5,2,6,-1] => [2] => 0 => 0
[3,4,6,1,5,-2] => [1] => 1 => 1
[4,5,6,1,3,-2] => [2] => 0 => 0
[4,5,6,1,2,-3] => [2,2] => 00 => 00
[2,3,4,6,5,-1] => [1] => 1 => 1
[2,4,5,6,3,-1] => [2] => 0 => 0
[3,4,5,6,1,-2] => [3] => 1 => 1
[2,-6,-4,1,3,5] => [6] => 0 => 0
[4,-6,-2,1,3,5] => [4,2] => 00 => 00
[-4,2,-6,1,3,5] => [1] => 1 => 1
[-4,-2,1,3,5,6] => [1,1] => 11 => 11
[2,-4,1,3,5,6] => [1,1] => 11 => 11
[-5,-4,-2,1,3,6] => [1] => 1 => 1
[2,-5,-4,1,3,6] => [5,1] => 11 => 11
[2,5,-4,1,3,6] => [1] => 1 => 1
[-6,-5,-4,-2,1,3] => [6] => 0 => 0
[2,-6,-5,-4,1,3] => [5] => 1 => 1
[2,5,6,-4,1,3] => [3,2] => 10 => 10
[-2,-6,-5,1,3,4] => [4] => 0 => 0
[-6,2,-5,1,3,4] => [1] => 1 => 1
[6,2,-5,1,3,4] => [3,1] => 11 => 11
[2,-5,1,3,4,6] => [1] => 1 => 1
[-2,-5,1,3,4,6] => [5,1] => 11 => 11
[-5,-2,1,3,4,6] => [1] => 1 => 1
[-5,-3,-2,1,4,6] => [2,1] => 01 => 01
[3,-5,-2,1,4,6] => [5,1] => 11 => 11
[-6,-5,-2,1,3,4] => [3] => 1 => 1
[3,-6,-5,-2,1,4] => [3] => 1 => 1
[-2,-6,1,3,4,5] => [6] => 0 => 0
[-6,2,1,3,4,5] => [1] => 1 => 1
[3,-6,-2,1,4,5] => [6] => 0 => 0
[-6,-3,-2,1,4,5] => [2] => 0 => 0
[-6,-4,-3,-2,1,5] => [2] => 0 => 0
[4,-6,-3,-2,1,5] => [5] => 1 => 1
[-2,1,3,4,5,6] => [1,1,1,1] => 1111 => 1111
[-3,-2,1,4,5,6] => [1,1,1] => 111 => 111
[-4,-3,-2,1,5,6] => [2,1,1] => 011 => 011
[-5,-4,-3,-2,1,6] => [2,1] => 01 => 01
[-6,-5,-4,-3,-2,1] => [2,2] => 00 => 00
[4,-3,1,2,5,6] => [1,1] => 11 => 11
[5,-4,-3,1,2,6] => [1] => 1 => 1
[4,5,-3,1,2,6] => [2,2,1] => 001 => 001
[6,-5,-4,-3,1,2] => [2] => 0 => 0
[5,6,-4,-3,1,2] => [2,2,2] => 000 => 000
[5,6,-3,1,2,4] => [5] => 1 => 1
[-3,6,-5,1,2,4] => [6] => 0 => 0
[-6,-5,3,1,2,4] => [1] => 1 => 1
[-5,3,1,2,4,6] => [1] => 1 => 1
[5,-3,1,2,4,6] => [1] => 1 => 1
[-5,-3,1,2,4,6] => [5,1] => 11 => 11
[3,-5,1,2,4,6] => [2,1] => 01 => 01
[6,-5,-3,1,2,4] => [3] => 1 => 1
[3,-6,-5,1,2,4] => [6] => 0 => 0
[3,-6,1,2,4,5] => [2] => 0 => 0
[-6,-3,1,2,4,5] => [6] => 0 => 0
[-6,-4,-3,1,2,5] => [5] => 1 => 1
[4,-6,-3,1,2,5] => [2] => 0 => 0
[-3,1,2,4,5,6] => [1,1,1] => 111 => 111
[-4,-3,1,2,5,6] => [4,1,1] => 011 => 011
[-5,-4,-3,1,2,6] => [4,1] => 01 => 01
[-6,-5,-4,-3,1,2] => [4,2] => 00 => 00
[-5,6,-4,1,2,3] => [6] => 0 => 0
[-6,1,-5,-4,2,3] => [5] => 1 => 1
[-4,5,6,1,2,3] => [2,2] => 00 => 00
[-5,-4,6,1,2,3] => [4,2] => 00 => 00
[-4,5,1,2,3,6] => [1] => 1 => 1
[-5,1,-4,2,3,6] => [5,1] => 11 => 11
[1,-5,-4,2,3,6] => [4,1,1] => 011 => 011
[5,-4,1,2,3,6] => [3,1] => 11 => 11
[1,-6,-5,-4,2,3] => [4,1] => 01 => 01
[-6,1,-4,2,3,5] => [6] => 0 => 0
[4,1,-6,2,3,5] => [3] => 1 => 1
[-6,4,1,2,3,5] => [2] => 0 => 0
[1,-6,-4,2,3,5] => [5,1] => 11 => 11
[6,-4,1,2,3,5] => [4] => 0 => 0
[1,-4,2,3,5,6] => [1,1,1] => 111 => 111
[-4,1,2,3,5,6] => [1,1] => 11 => 11
[-5,-4,1,2,3,6] => [1] => 1 => 1
[-6,-5,-4,1,2,3] => [4] => 0 => 0
[6,1,-5,2,3,4] => [4] => 0 => 0
[-5,6,1,2,3,4] => [3] => 1 => 1
[1,6,-5,2,3,4] => [3,1] => 11 => 11
[1,-6,-5,2,3,4] => [1] => 1 => 1
[1,-5,2,3,4,6] => [1,1] => 11 => 11
[-5,1,2,3,4,6] => [1] => 1 => 1
[-6,-5,1,2,3,4] => [6] => 0 => 0
[1,2,-6,3,4,5] => [1,1] => 11 => 11
[1,-6,2,3,4,5] => [1] => 1 => 1
[2,-3,1,4,5,6] => [1,1,1] => 111 => 111
[-2,-4,1,3,5,6] => [4,1,1] => 011 => 011
[-4,3,1,2,5,6] => [1,1] => 11 => 11
[-5,2,1,3,4,6] => [1,1] => 11 => 11
[4,1,-5,2,3,6] => [3,1] => 11 => 11
[1,-4,-6,2,3,5] => [1] => 1 => 1
[1,-6,5,2,3,4] => [2,1] => 01 => 01
[2,5,-3,1,4,6] => [4,1] => 01 => 01
[-5,2,-4,1,3,6] => [4,1,1] => 011 => 011
[-4,3,5,1,2,6] => [3,1] => 11 => 11
[4,2,-5,1,3,6] => [2,1,1] => 011 => 011
[-3,2,-6,1,4,5] => [5,1] => 11 => 11
[6,2,-4,1,3,5] => [1] => 1 => 1
[-6,-4,3,1,2,5] => [5,1] => 11 => 11
[6,-2,-5,1,3,4] => [3] => 1 => 1
[6,-5,3,1,2,4] => [3,1] => 11 => 11
[6,-4,1,-5,2,3] => [3,3] => 11 => 11
[3,-6,4,1,2,5] => [3] => 1 => 1
[-5,-6,3,1,2,4] => [5,1] => 11 => 11
[4,5,1,-6,2,3] => [2] => 0 => 0
[-3,2,-4,1,5,6] => [3,1,1,1] => 1111 => 1111
[3,2,-5,1,4,6] => [1,1] => 11 => 11
[2,-4,-5,1,3,6] => [1] => 1 => 1
[4,-5,3,1,2,6] => [2,1,1] => 011 => 011
[2,-3,-6,1,4,5] => [6] => 0 => 0
[-2,-4,-6,1,3,5] => [3] => 1 => 1
[-4,-6,3,1,2,5] => [1] => 1 => 1
[-5,-6,2,1,3,4] => [6] => 0 => 0
[-6,5,3,1,2,4] => [2,1] => 01 => 01
[-5,4,1,-6,2,3] => [6] => 0 => 0
[5,-6,2,-4,1,3] => [2] => 0 => 0
[4,-6,3,5,1,2] => [3,1] => 11 => 11
[-4,-6,2,-5,1,3] => [3] => 1 => 1
[-3,2,6,-4,1,5] => [1] => 1 => 1
[6,-4,2,-5,1,3] => [6] => 0 => 0
[4,-5,3,6,1,2] => [1] => 1 => 1
[5,-3,2,-6,1,4] => [2] => 0 => 0
[-4,-6,3,5,1,2] => [1] => 1 => 1
[-6,5,3,4,1,2] => [1,1] => 11 => 11
[3,-4,2,-5,1,6] => [5,1] => 11 => 11
[-5,3,2,-6,1,4] => [2] => 0 => 0
[-4,2,-5,-6,1,3] => [1] => 1 => 1
[3,5,6,4,1,-2] => [1] => 1 => 1
[4,5,3,6,1,-2] => [1] => 1 => 1
[4,6,3,1,5,-2] => [2,1,1] => 011 => 011
[5,1,6,4,3,-2] => [1] => 1 => 1
[5,6,3,4,1,-2] => [2,1,1] => 011 => 011
[1,5,6,4,2,-3] => [2,1,1] => 011 => 011
[4,2,5,6,1,-3] => [1] => 1 => 1
[4,2,6,1,5,-3] => [2,1,1] => 011 => 011
[4,6,2,1,5,-3] => [2,1] => 01 => 01
[5,2,1,6,4,-3] => [1] => 1 => 1
[5,2,6,4,1,-3] => [2,1,1] => 011 => 011
[5,6,2,4,1,-3] => [2,1] => 01 => 01
[6,2,1,4,5,-3] => [1,1,1] => 111 => 111
[1,5,3,6,2,-4] => [2,1,1] => 011 => 011
[1,5,6,3,2,-4] => [2,1] => 01 => 01
[1,6,3,2,5,-4] => [1,1,1] => 111 => 111
[5,2,3,6,1,-4] => [2,1,1] => 011 => 011
[5,2,6,3,1,-4] => [2,1] => 01 => 01
[5,6,3,2,1,-4] => [2,1] => 01 => 01
[6,2,3,1,5,-4] => [1,1,1] => 111 => 111
[1,2,6,4,3,-5] => [1,1,1] => 111 => 111
[1,6,3,4,2,-5] => [1,1,1] => 111 => 111
[6,2,3,4,1,-5] => [1,1,1] => 111 => 111
[3,4,5,7,1,6,-2] => [3,1] => 11 => 11
[3,4,6,7,5,1,-2] => [3,1] => 11 => 11
[3,4,7,1,5,6,-2] => [1,1] => 11 => 11
[3,5,1,6,7,4,-2] => [2,2] => 00 => 00
[3,5,1,7,4,6,-2] => [2,1] => 01 => 01
[3,5,6,4,7,1,-2] => [3,1] => 11 => 11
[3,5,6,7,4,1,-2] => [3] => 1 => 1
[3,5,7,4,1,6,-2] => [1,1] => 11 => 11
[3,6,1,4,7,5,-2] => [2,1] => 01 => 01
[3,6,1,7,5,4,-2] => [2,1] => 01 => 01
[3,6,7,4,5,1,-2] => [1,1] => 11 => 11
[3,7,1,4,5,6,-2] => [2,1,1,1] => 0111 => 0111
[4,1,5,7,3,6,-2] => [2,1] => 01 => 01
[4,1,6,7,5,3,-2] => [2,1] => 01 => 01
[4,1,7,3,5,6,-2] => [1,1] => 11 => 11
[4,5,3,6,7,1,-2] => [3,1] => 11 => 11
[4,5,3,7,1,6,-2] => [1,1] => 11 => 11
[4,5,6,3,7,1,-2] => [4] => 0 => 0
[4,5,6,7,1,3,-2] => [2] => 0 => 0
[4,5,7,3,1,6,-2] => [1] => 1 => 1
[4,6,3,1,7,5,-2] => [2,1] => 01 => 01
[4,6,3,7,5,1,-2] => [1,1] => 11 => 11
[4,6,7,3,5,1,-2] => [1] => 1 => 1
[4,7,3,1,5,6,-2] => [2,1,1,1] => 0111 => 0111
[5,1,3,6,7,4,-2] => [2,1] => 01 => 01
[5,1,3,7,4,6,-2] => [1,1] => 11 => 11
[5,1,6,4,7,3,-2] => [2,1] => 01 => 01
[5,1,6,7,4,3,-2] => [2] => 0 => 0
[5,1,7,4,3,6,-2] => [1,1] => 11 => 11
[5,6,3,4,7,1,-2] => [1,1] => 11 => 11
[5,6,3,7,4,1,-2] => [1] => 1 => 1
[5,6,7,4,3,1,-2] => [1] => 1 => 1
[5,7,3,4,1,6,-2] => [2,1,1,1] => 0111 => 0111
[6,1,3,4,7,5,-2] => [1,1] => 11 => 11
[6,1,3,7,5,4,-2] => [1,1] => 11 => 11
[6,1,7,4,5,3,-2] => [1,1] => 11 => 11
[6,7,3,4,5,1,-2] => [2,1,1,1] => 0111 => 0111
[7,1,3,4,5,6,-2] => [1,1,1,1] => 1111 => 1111
[1,4,5,6,7,2,-3] => [3,1] => 11 => 11
[1,4,5,7,2,6,-3] => [1,1] => 11 => 11
[1,4,6,2,7,5,-3] => [2,1] => 01 => 01
[1,4,6,7,5,2,-3] => [1,1] => 11 => 11
[1,4,7,2,5,6,-3] => [2,1,1,1] => 0111 => 0111
[1,5,2,6,7,4,-3] => [2,1] => 01 => 01
[1,5,2,7,4,6,-3] => [1,1] => 11 => 11
[1,5,6,4,7,2,-3] => [1,1] => 11 => 11
[1,5,6,7,4,2,-3] => [1] => 1 => 1
[1,5,7,4,2,6,-3] => [2,1,1,1] => 0111 => 0111
[1,6,2,4,7,5,-3] => [1,1] => 11 => 11
[1,6,2,7,5,4,-3] => [1,1] => 11 => 11
[1,6,7,4,5,2,-3] => [2,1,1,1] => 0111 => 0111
[1,7,2,4,5,6,-3] => [1,1,1,1] => 1111 => 1111
[4,2,5,6,7,1,-3] => [3,1] => 11 => 11
[4,2,5,7,1,6,-3] => [1,1] => 11 => 11
[4,2,6,1,7,5,-3] => [2,1] => 01 => 01
[4,2,6,7,5,1,-3] => [1,1] => 11 => 11
[4,2,7,1,5,6,-3] => [2,1,1,1] => 0111 => 0111
[4,5,2,6,7,1,-3] => [3] => 1 => 1
[4,5,2,7,1,6,-3] => [1] => 1 => 1
[4,5,6,1,7,2,-3] => [2] => 0 => 0
[4,5,6,7,2,1,-3] => [2] => 0 => 0
[4,5,7,1,2,6,-3] => [2,2,1] => 001 => 001
[4,6,2,1,7,5,-3] => [2] => 0 => 0
[4,6,2,7,5,1,-3] => [1] => 1 => 1
[4,6,7,1,5,2,-3] => [2,2,1] => 001 => 001
[4,7,2,1,5,6,-3] => [2,1,1] => 011 => 011
[5,2,1,6,7,4,-3] => [2,1] => 01 => 01
[5,2,1,7,4,6,-3] => [1,1] => 11 => 11
[5,2,6,4,7,1,-3] => [1,1] => 11 => 11
[5,2,6,7,4,1,-3] => [1] => 1 => 1
[5,2,7,4,1,6,-3] => [2,1,1,1] => 0111 => 0111
[5,6,2,4,7,1,-3] => [1] => 1 => 1
[5,6,7,4,1,2,-3] => [2,2,1] => 001 => 001
[5,7,2,4,1,6,-3] => [2,1,1] => 011 => 011
[6,2,1,4,7,5,-3] => [1,1] => 11 => 11
[6,2,1,7,5,4,-3] => [1,1] => 11 => 11
[6,2,7,4,5,1,-3] => [2,1,1,1] => 0111 => 0111
[6,7,2,4,5,1,-3] => [2,1,1] => 011 => 011
[7,2,1,4,5,6,-3] => [1,1,1,1] => 1111 => 1111
[1,2,5,6,7,3,-4] => [1,1] => 11 => 11
[1,2,5,7,3,6,-4] => [2,1,1,1] => 0111 => 0111
[1,2,6,3,7,5,-4] => [1,1] => 11 => 11
[1,2,6,7,5,3,-4] => [2,1,1,1] => 0111 => 0111
[1,2,7,3,5,6,-4] => [1,1,1,1] => 1111 => 1111
[1,5,3,6,7,2,-4] => [1,1] => 11 => 11
[1,5,3,7,2,6,-4] => [2,1,1,1] => 0111 => 0111
[1,5,6,3,7,2,-4] => [1] => 1 => 1
[1,5,6,7,2,3,-4] => [2,2,1] => 001 => 001
[1,5,7,3,2,6,-4] => [2,1,1] => 011 => 011
[1,6,3,2,7,5,-4] => [1,1] => 11 => 11
[1,6,3,7,5,2,-4] => [2,1,1,1] => 0111 => 0111
[1,6,7,3,5,2,-4] => [2,1,1] => 011 => 011
[1,7,3,2,5,6,-4] => [1,1,1,1] => 1111 => 1111
[5,2,3,6,7,1,-4] => [1,1] => 11 => 11
[5,2,3,7,1,6,-4] => [2,1,1,1] => 0111 => 0111
[5,2,6,3,7,1,-4] => [1] => 1 => 1
[5,2,6,7,1,3,-4] => [2,2,1] => 001 => 001
[5,2,7,3,1,6,-4] => [2,1,1] => 011 => 011
[5,6,3,2,7,1,-4] => [1] => 1 => 1
[5,6,3,7,1,2,-4] => [2,2,1] => 001 => 001
[5,6,7,3,1,2,-4] => [2,2] => 00 => 00
[5,7,3,2,1,6,-4] => [2,1,1] => 011 => 011
[6,2,3,1,7,5,-4] => [1,1] => 11 => 11
[6,2,3,7,5,1,-4] => [2,1,1,1] => 0111 => 0111
[6,2,7,3,5,1,-4] => [2,1,1] => 011 => 011
[6,7,3,2,5,1,-4] => [2,1,1] => 011 => 011
[7,2,3,1,5,6,-4] => [1,1,1,1] => 1111 => 1111
[1,2,3,6,7,4,-5] => [2,1,1,1] => 0111 => 0111
[1,2,3,7,4,6,-5] => [1,1,1,1] => 1111 => 1111
[1,2,6,4,7,3,-5] => [2,1,1,1] => 0111 => 0111
[1,2,6,7,4,3,-5] => [2,1,1] => 011 => 011
[1,2,7,4,3,6,-5] => [1,1,1,1] => 1111 => 1111
[1,6,3,4,7,2,-5] => [2,1,1,1] => 0111 => 0111
[1,6,3,7,4,2,-5] => [2,1,1] => 011 => 011
[1,6,7,4,3,2,-5] => [2,1,1] => 011 => 011
[1,7,3,4,2,6,-5] => [1,1,1,1] => 1111 => 1111
[6,2,3,4,7,1,-5] => [2,1,1,1] => 0111 => 0111
[6,2,3,7,4,1,-5] => [2,1,1] => 011 => 011
[6,2,7,4,3,1,-5] => [2,1,1] => 011 => 011
[6,7,3,4,2,1,-5] => [2,1,1] => 011 => 011
[7,2,3,4,1,6,-5] => [1,1,1,1] => 1111 => 1111
[1,2,3,4,7,5,-6] => [1,1,1,1] => 1111 => 1111
[1,2,3,7,5,4,-6] => [1,1,1,1] => 1111 => 1111
[1,2,7,4,5,3,-6] => [1,1,1,1] => 1111 => 1111
[1,7,3,4,5,2,-6] => [1,1,1,1] => 1111 => 1111
[7,2,3,4,5,1,-6] => [1,1,1,1] => 1111 => 1111
[1,2,3,4,5,6,-7] => [1,1,1,1,1,1] => 111111 => 111111
[2,3,6,5,4,-1] => [2] => 0 => 0
[2,6,3,5,4,-1] => [2,1] => 01 => 01
[2,5,4,3,6,-1] => [2] => 0 => 0
[2,6,4,3,5,-1] => [2,1] => 01 => 01
[2,6,5,3,4,-1] => [3] => 1 => 1
[2,6,5,4,3,-1] => [2,1] => 01 => 01
[3,2,6,5,4,-1] => [2,1] => 01 => 01
[6,2,3,5,4,-1] => [2,1,1] => 011 => 011
[5,2,4,3,6,-1] => [2,1] => 01 => 01
[6,2,4,3,5,-1] => [2,1,1] => 011 => 011
[6,2,5,3,4,-1] => [3,1] => 11 => 11
[6,2,5,4,3,-1] => [2,1,1] => 011 => 011
[4,3,2,5,6,-1] => [2] => 0 => 0
[4,3,2,6,5,-1] => [2,1] => 01 => 01
[5,3,2,4,6,-1] => [2,1] => 01 => 01
[6,3,2,4,5,-1] => [2,1,1] => 011 => 011
[6,3,2,5,4,-1] => [2,2] => 00 => 00
[5,4,2,3,6,-1] => [3] => 1 => 1
[6,4,2,3,5,-1] => [3,1] => 11 => 11
[6,5,2,3,4,-1] => [4] => 0 => 0
[6,5,2,4,3,-1] => [3,1] => 11 => 11
[5,4,3,2,6,-1] => [2,1] => 01 => 01
[6,4,3,2,5,-1] => [2,1,1] => 011 => 011
[6,5,3,2,4,-1] => [3,1] => 11 => 11
[6,5,4,2,3,-1] => [4] => 0 => 0
[6,5,4,3,2,-1] => [2,2] => 00 => 00
[3,2,-5,-4,-6,1] => [4,1] => 01 => 01
[-3,2,-6,-4,-5,1] => [3,1] => 11 => 11
[3,2,-6,-5,-4,1] => [2,1] => 01 => 01
[6,-3,2,-5,-4,1] => [2,2] => 00 => 00
[-2,-5,-6,4,-3,1] => [5,1] => 11 => 11
[-3,-6,2,4,-5,1] => [4,1] => 01 => 01
[2,5,3,4,-6,1] => [1,1] => 11 => 11
[5,6,3,4,-2,1] => [1,1] => 11 => 11
[4,2,3,5,-6,1] => [1,1] => 11 => 11
[4,2,-3,6,-5,1] => [3,1] => 11 => 11
[-5,2,-3,6,-4,1] => [4,1] => 01 => 01
[5,2,-4,6,-3,1] => [5,1] => 11 => 11
[-4,2,3,6,-5,1] => [1,1] => 11 => 11
[5,2,3,6,-4,1] => [1,1] => 11 => 11
[-4,6,-5,3,1,2] => [4,2] => 00 => 00
[5,6,-4,3,1,2] => [2,2] => 00 => 00
[-6,-4,3,5,1,2] => [5,1] => 11 => 11
[-4,-5,3,6,1,2] => [5,1] => 11 => 11
[5,-4,3,6,1,2] => [2,1] => 01 => 01
[-6,5,1,4,2,3] => [2,1] => 01 => 01
[-2,-5,-6,-3,1,4] => [3,3] => 11 => 11
[5,2,-6,3,1,4] => [2,1] => 01 => 01
[4,2,-6,-3,1,5] => [5,1] => 11 => 11
[-4,2,-6,3,1,5] => [5,1] => 11 => 11
[-6,2,3,1,4,5] => [1,1] => 11 => 11
[-2,-3,-4,-5,1,6] => [5,1] => 11 => 11
[2,-3,-5,-4,1,6] => [4,1] => 01 => 01
[4,2,-3,-5,1,6] => [1,1] => 11 => 11
[-5,2,-3,-4,1,6] => [1,1] => 11 => 11
[5,2,-4,-3,1,6] => [2,2,1,1] => 0011 => 0011
[-4,2,3,-5,1,6] => [3,1,1,1] => 1111 => 1111
[5,2,3,-4,1,6] => [2,1,1,1] => 0111 => 0111
[-2,-5,4,-3,1,6] => [3,1] => 11 => 11
[5,3,4,-2,1,6] => [2,1] => 01 => 01
[-2,-3,5,-4,1,6] => [4,1] => 01 => 01
[2,-4,5,-3,1,6] => [5,1] => 11 => 11
[2,3,5,-4,1,6] => [4,1] => 01 => 01
[-2,4,5,-3,1,6] => [5,1] => 11 => 11
[3,4,5,-2,1,6] => [3,1] => 11 => 11
[-4,-5,3,1,2,6] => [1,1] => 11 => 11
[5,-4,3,1,2,6] => [1,1] => 11 => 11
[-4,-5,-2,1,3,6] => [3,1] => 11 => 11
[-5,-4,2,1,3,6] => [5,1] => 11 => 11
[-2,-5,-3,1,4,6] => [4,1] => 01 => 01
[2,-5,3,1,4,6] => [1,1] => 11 => 11
[5,-2,1,3,4,6] => [4,1] => 01 => 01
[-2,-3,-4,1,5,6] => [1,1] => 11 => 11
[2,-4,-3,1,5,6] => [1,1] => 11 => 11
[2,3,-4,1,5,6] => [1,1] => 11 => 11
[-2,4,-3,1,5,6] => [1,1] => 11 => 11
[3,4,-2,1,5,6] => [1,1] => 11 => 11
[-2,-3,1,4,5,6] => [3,1,1,1] => 1111 => 1111
[3,-2,1,4,5,6] => [2,1,1,1] => 0111 => 0111
[5,-6,1,2,3,4] => [3] => 1 => 1
[5,-6,-4,1,2,3] => [6] => 0 => 0
[4,-5,1,2,3,6] => [1] => 1 => 1
[4,-6,-5,1,2,3] => [4,2] => 00 => 00
[4,6,-5,1,2,3] => [2] => 0 => 0
[5,-6,-4,-3,1,2] => [2,2] => 00 => 00
[4,-5,-3,1,2,6] => [2,1] => 01 => 01
[4,-6,-5,-3,1,2] => [4] => 0 => 0
[4,6,-5,-3,1,2] => [4,2] => 00 => 00
[-5,4,-6,-3,1,2] => [4] => 0 => 0
[3,-4,1,2,5,6] => [2,1,1] => 011 => 011
[3,-5,-4,1,2,6] => [1] => 1 => 1
[3,5,-4,1,2,6] => [2,1] => 01 => 01
[3,6,-5,-4,1,2] => [2] => 0 => 0
[3,5,6,-4,1,2] => [5] => 1 => 1
[-4,3,-5,1,2,6] => [1] => 1 => 1
[-4,3,-6,-5,1,2] => [3] => 1 => 1
[-4,3,6,-5,1,2] => [3,3] => 11 => 11
[-6,-4,3,-5,1,2] => [1] => 1 => 1
[4,-5,3,-6,1,2] => [5,1] => 11 => 11
[5,-6,-2,1,3,4] => [6] => 0 => 0
[5,-6,-4,-2,1,3] => [2] => 0 => 0
[4,-5,-2,1,3,6] => [3,2,1] => 101 => 101
[4,6,-5,-2,1,3] => [6] => 0 => 0
[5,-6,-3,-2,1,4] => [3,2] => 10 => 10
[5,-6,-4,-3,-2,1] => [4,2] => 00 => 00
[4,-5,-3,-2,1,6] => [4,1] => 01 => 01
[4,-6,-5,-3,-2,1] => [6] => 0 => 0
[-5,4,-6,-3,-2,1] => [6] => 0 => 0
[3,-4,-2,1,5,6] => [4,1,1] => 011 => 011
[3,-5,-4,-2,1,6] => [1] => 1 => 1
[3,5,-4,-2,1,6] => [5,1] => 11 => 11
[3,6,-5,-4,-2,1] => [5] => 1 => 1
[3,5,6,-4,-2,1] => [3] => 1 => 1
[-4,3,-5,-2,1,6] => [1] => 1 => 1
[-4,3,-6,-5,-2,1] => [6] => 0 => 0
[-6,-4,3,-5,-2,1] => [1] => 1 => 1
[4,-5,3,-6,-2,1] => [2,1] => 01 => 01
[2,-5,-3,1,4,6] => [1] => 1 => 1
[2,5,-6,-3,1,4] => [3,3] => 11 => 11
[2,-6,-4,-3,1,5] => [2] => 0 => 0
[2,-5,-4,-3,1,6] => [2,1] => 01 => 01
[2,-6,-5,-4,-3,1] => [2] => 0 => 0
[2,5,-6,-4,-3,1] => [5] => 1 => 1
[2,4,-5,-3,1,6] => [5,1] => 11 => 11
[2,4,6,-5,-3,1] => [6] => 0 => 0
[-5,2,4,-6,-3,1] => [1] => 1 => 1
[2,4,-3,1,5,6] => [3,1,1] => 111 => 111
[2,6,-4,-3,1,5] => [4,2] => 00 => 00
[2,5,-4,-3,1,6] => [3,2,1] => 101 => 101
[2,6,-5,-4,-3,1] => [3,2] => 10 => 10
[-5,2,-6,-4,-3,1] => [1] => 1 => 1
[2,4,5,-3,1,6] => [1] => 1 => 1
[2,4,5,6,-3,1] => [4] => 0 => 0
[-6,2,4,5,-3,1] => [1] => 1 => 1
[-5,2,4,-3,1,6] => [1,1] => 11 => 11
[-4,2,6,-5,-3,1] => [1] => 1 => 1
[-5,2,4,6,-3,1] => [5,1] => 11 => 11
[-6,-5,2,4,-3,1] => [3,1] => 11 => 11
[5,-6,2,4,-3,1] => [5,1] => 11 => 11
[-3,2,-5,-4,1,6] => [3,1,1] => 111 => 111
[-3,2,-6,-5,-4,1] => [3,2,1] => 101 => 101
[-3,2,5,-6,-4,1] => [1] => 1 => 1
[-3,2,5,-4,1,6] => [1,1] => 11 => 11
[-3,2,6,-5,-4,1] => [2,1] => 01 => 01
[-3,2,5,6,-4,1] => [5,1] => 11 => 11
[-5,-3,2,-4,1,6] => [1] => 1 => 1
[-6,-3,2,-5,-4,1] => [2] => 0 => 0
[-5,-3,2,6,-4,1] => [4] => 0 => 0
[-6,-5,-3,2,-4,1] => [3] => 1 => 1
[5,-6,-3,2,-4,1] => [5] => 1 => 1
[3,-4,2,-6,-5,1] => [5] => 1 => 1
[3,-6,-4,2,-5,1] => [5] => 1 => 1
[-6,1,5,2,3,4] => [2] => 0 => 0
[1,-5,-6,2,3,4] => [5,1] => 11 => 11
[-6,3,5,1,2,4] => [3] => 1 => 1
[4,-6,5,1,2,3] => [2] => 0 => 0
[5,2,-6,1,3,4] => [1] => 1 => 1
[-6,-3,-5,1,2,4] => [3] => 1 => 1
[-4,3,6,1,2,5] => [4] => 0 => 0
[-3,6,-5,-4,1,2] => [3,2] => 10 => 10
[4,2,-6,1,3,5] => [2,1] => 01 => 01
[2,-5,-6,1,3,4] => [6] => 0 => 0
[-4,2,-6,-5,1,3] => [3,1] => 11 => 11
[-4,-3,6,-5,1,2] => [3] => 1 => 1
[-5,3,-6,-2,1,4] => [4] => 0 => 0
[-5,-4,2,-6,1,3] => [4] => 0 => 0
[3,-6,4,5,1,2] => [4] => 0 => 0
[1,2,-7,-6,3,4,5] => [1,1] => 11 => 11
[1,7,-6,-5,2,3,4] => [1] => 1 => 1
[-7,1,-4,2,3,5,6] => [7] => 1 => 1
[-6,7,-4,1,2,3,5] => [4,3] => 01 => 01
[1,5,-7,-4,2,3,6] => [2,1] => 01 => 01
[-7,-4,6,1,2,3,5] => [5,2] => 10 => 10
[1,-7,-6,-5,-4,2,3] => [4,2,1] => 001 => 001
[-3,7,-6,1,2,4,5] => [4,3] => 01 => 01
[6,7,-5,-3,1,2,4] => [7] => 1 => 1
[-4,1,7,-6,2,3,5] => [7] => 1 => 1
[5,1,2,-7,3,4,6] => [4] => 0 => 0
[1,-6,7,2,3,4,5] => [3,1] => 11 => 11
[1,-5,-7,-6,2,3,4] => [4,1] => 01 => 01
[-5,7,6,1,2,3,4] => [2] => 0 => 0
[-7,-4,-6,-5,1,2,3] => [7] => 1 => 1
[-4,-7,-6,-3,1,2,5] => [7] => 1 => 1
[6,-7,3,1,2,4,5] => [3,1] => 11 => 11
[6,-7,1,4,2,3,5] => [3,1] => 11 => 11
[6,5,1,-7,2,3,4] => [3,2] => 10 => 10
[5,-4,7,-6,1,2,3] => [3,2,2] => 100 => 010
[-5,-7,-4,-3,1,2,6] => [2] => 0 => 0
[6,4,-7,-3,1,2,5] => [7] => 1 => 1
[7,-6,-5,-4,-3,1,2] => [2] => 0 => 0
[-2,7,-6,1,3,4,5] => [7] => 1 => 1
[-7,2,-5,1,3,4,6] => [1] => 1 => 1
[-4,2,-7,1,3,5,6] => [1] => 1 => 1
[2,7,-6,-4,1,3,5] => [4] => 0 => 0
[-2,-6,-7,1,3,4,5] => [4] => 0 => 0
[5,2,-7,-6,1,3,4] => [4,2,1] => 001 => 001
[2,5,-7,-4,1,3,6] => [3] => 1 => 1
[-7,2,6,-4,1,3,5] => [2,1] => 01 => 01
[2,-7,-6,-5,-4,1,3] => [5,2] => 10 => 10
[-7,-3,-6,-5,1,2,4] => [4,3] => 01 => 01
[1,-7,4,2,3,5,6] => [1] => 1 => 1
[1,-4,-7,-6,2,3,5] => [1] => 1 => 1
[1,-7,5,2,3,4,6] => [2,1] => 01 => 01
[1,6,2,-7,3,4,5] => [1] => 1 => 1
[4,-5,7,1,2,3,6] => [3,2] => 10 => 10
[-4,7,6,1,2,3,5] => [3,2] => 10 => 10
[7,-5,1,6,2,3,4] => [5] => 1 => 1
[-7,-4,3,1,2,5,6] => [6,1] => 01 => 01
[-3,6,7,-4,1,2,5] => [2] => 0 => 0
[3,6,1,-7,2,4,5] => [2] => 0 => 0
[5,-3,7,-6,1,2,4] => [5,2] => 10 => 10
[-4,7,5,1,2,3,6] => [5] => 1 => 1
[-4,6,1,-7,2,3,5] => [7] => 1 => 1
[7,5,1,-6,2,3,4] => [2] => 0 => 0
[-5,-3,-7,-4,1,2,6] => [4] => 0 => 0
[-7,-4,3,6,1,2,5] => [1] => 1 => 1
[4,5,-7,6,1,2,3] => [5] => 1 => 1
[-3,7,-6,-5,-4,1,2] => [3,2,2] => 100 => 010
[-2,3,-7,1,4,5,6] => [7] => 1 => 1
[-6,2,3,-7,1,4,5] => [5,1,1] => 111 => 111
[4,2,-7,-6,1,3,5] => [6,1] => 01 => 01
[2,-5,-7,-6,1,3,4] => [4] => 0 => 0
[-4,2,7,-5,1,3,6] => [3,3,1] => 111 => 111
[6,-4,2,-7,1,3,5] => [7] => 1 => 1
[5,6,2,-7,1,3,4] => [3,2] => 10 => 10
[-4,2,-7,-6,-5,1,3] => [3,1] => 11 => 11
[4,-3,7,-6,1,2,5] => [7] => 1 => 1
[3,5,1,-7,2,4,6] => [2,2] => 00 => 00
[-6,7,3,1,2,4,5] => [3,1] => 11 => 11
[-7,5,3,6,1,2,4] => [1] => 1 => 1
[-5,4,7,6,1,2,3] => [3,2] => 10 => 10
[-4,-3,7,-6,-5,1,2] => [3] => 1 => 1
[4,-7,-6,-3,-2,1,5] => [4,3] => 01 => 01
[-5,2,3,-7,1,4,6] => [1,1] => 11 => 11
[6,2,3,-7,1,4,5] => [1,1] => 11 => 11
[-5,3,-7,-6,-2,1,4] => [7] => 1 => 1
[5,-4,2,-7,1,3,6] => [5,2] => 10 => 10
[-4,-6,2,-7,1,3,5] => [4] => 0 => 0
[-5,2,-6,-7,1,3,4] => [1] => 1 => 1
[-5,-4,2,-7,-6,1,3] => [4,3] => 01 => 01
[3,6,-7,4,1,2,5] => [2,1] => 01 => 01
[6,5,-7,3,1,2,4] => [4] => 0 => 0
[6,4,5,1,-7,2,3] => [4] => 0 => 0
[-5,-4,-3,7,-6,1,2] => [3] => 1 => 1
[5,-7,-4,-3,-2,1,6] => [5,2] => 10 => 10
[-6,-5,3,-7,-2,1,4] => [2,1] => 01 => 01
[-7,-6,-5,-4,-3,-2,1] => [2,2] => 00 => 00
[3,1,2,6,5,-4] => [3,1] => 11 => 11
[3,1,5,2,4,-6] => [5] => 1 => 1
[4,5,1,2,3,-6] => [5] => 1 => 1
[1,6,5,3,4,-2] => [3,1] => 11 => 11
[6,4,1,2,3,-5] => [2] => 0 => 0
[5,4,1,2,3,-6] => [3,2] => 10 => 10
[1,4,3,6,5,8,7,-2] => [1,1,1,1] => 1111 => 1111
[4,1,2,6,5,8,7,-3] => [1,1] => 11 => 11
[3,1,2,6,5,8,7,-4] => [3,1,1] => 111 => 111
[3,1,6,2,4,8,7,-5] => [1] => 1 => 1
[3,1,5,2,4,8,7,-6] => [5,1] => 11 => 11
[3,1,5,2,7,4,6,-8] => [7] => 1 => 1
[4,5,1,2,7,3,6,-8] => [7] => 1 => 1
[4,5,1,2,3,8,7,-6] => [5,1] => 11 => 11
[4,6,1,2,3,8,7,-5] => [1] => 1 => 1
[5,6,1,2,3,8,7,-4] => [3,1] => 11 => 11
[5,1,6,2,4,8,7,-3] => [4,1] => 01 => 01
[1,5,6,3,4,8,7,-2] => [1,1] => 11 => 11
[1,6,5,3,4,8,7,-2] => [3,1,1] => 111 => 111
[6,1,5,2,4,8,7,-3] => [1] => 1 => 1
[6,5,1,2,3,8,7,-4] => [1] => 1 => 1
[6,4,1,2,3,8,7,-5] => [2,1] => 01 => 01
[5,4,1,2,3,8,7,-6] => [3,2,1] => 101 => 101
[5,4,1,2,8,3,6,-7] => [2] => 0 => 0
[5,4,1,2,7,3,6,-8] => [5,2] => 10 => 10
[6,4,1,7,2,3,5,-8] => [4,3] => 01 => 01
[6,4,1,8,2,3,5,-7] => [3] => 1 => 1
[7,4,1,2,8,3,6,-5] => [4,2] => 00 => 00
[7,5,1,2,8,3,6,-4] => [4] => 0 => 0
[7,1,5,2,8,4,6,-3] => [5] => 1 => 1
[1,7,5,3,8,4,6,-2] => [1] => 1 => 1
[1,8,5,3,7,4,6,-2] => [5,1] => 11 => 11
[8,4,1,2,7,3,6,-5] => [2] => 0 => 0
[8,4,1,7,2,3,5,-6] => [4] => 0 => 0
[7,4,1,6,2,3,5,-8] => [7] => 1 => 1
[7,5,6,1,2,3,4,-8] => [3,2,2] => 100 => 010
[8,5,6,1,2,3,4,-7] => [2,2] => 00 => 00
[8,5,7,1,2,3,4,-6] => [2] => 0 => 0
[1,8,6,7,3,4,5,-2] => [5,1] => 11 => 11
[1,7,6,8,3,4,5,-2] => [1] => 1 => 1
[7,1,6,8,2,4,5,-3] => [4] => 0 => 0
[7,6,1,8,2,3,5,-4] => [6] => 0 => 0
[7,6,8,1,2,3,4,-5] => [3] => 1 => 1
[7,5,8,1,2,3,4,-6] => [3,2] => 10 => 10
[6,5,8,1,2,3,4,-7] => [2] => 0 => 0
[6,5,7,1,2,3,4,-8] => [5,2] => 10 => 10
[5,6,7,1,2,3,4,-8] => [7] => 1 => 1
[5,7,8,1,2,3,4,-6] => [5] => 1 => 1
[6,7,1,8,2,3,5,-4] => [3,3] => 11 => 11
[1,6,7,8,3,4,5,-2] => [3,1] => 11 => 11
[1,5,7,3,8,4,6,-2] => [4,1] => 01 => 01
[4,7,1,2,8,3,6,-5] => [6] => 0 => 0
[4,7,1,8,2,3,5,-6] => [3] => 1 => 1
[4,6,1,7,2,3,5,-8] => [7] => 1 => 1
[3,1,6,7,2,4,5,-8] => [7] => 1 => 1
[3,1,7,8,2,4,5,-6] => [5] => 1 => 1
[3,1,7,2,8,4,6,-5] => [6] => 0 => 0
[3,1,2,7,8,5,6,-4] => [3] => 1 => 1
[1,4,3,7,8,5,6,-2] => [1,1] => 11 => 11
[1,4,3,8,7,5,6,-2] => [3,1,1] => 111 => 111
[4,1,2,8,7,5,6,-3] => [3] => 1 => 1
[3,1,2,8,7,5,6,-4] => [3,3] => 11 => 11
[3,1,8,6,2,4,5,-7] => [2] => 0 => 0
[3,1,7,6,2,4,5,-8] => [5,2] => 10 => 10
[4,7,1,6,2,3,5,-8] => [4,3] => 01 => 01
[4,8,1,6,2,3,5,-7] => [4] => 0 => 0
[5,8,1,2,7,3,6,-4] => [5] => 1 => 1
[5,1,8,2,7,4,6,-3] => [6] => 0 => 0
[1,5,8,3,7,4,6,-2] => [1] => 1 => 1
[1,6,8,7,3,4,5,-2] => [1] => 1 => 1
[6,1,8,7,2,4,5,-3] => [6] => 0 => 0
[6,8,1,7,2,3,5,-4] => [3] => 1 => 1
[6,8,7,1,2,3,4,-5] => [5] => 1 => 1
[5,8,6,1,2,3,4,-7] => [2] => 0 => 0
[5,7,6,1,2,3,4,-8] => [5,2] => 10 => 10
[6,7,5,1,2,3,4,-8] => [7] => 1 => 1
[7,8,5,1,2,3,4,-6] => [3] => 1 => 1
[7,8,6,1,2,3,4,-5] => [3,2] => 10 => 10
[7,1,8,6,2,4,5,-3] => [4,2] => 00 => 00
[1,7,8,6,3,4,5,-2] => [2,1] => 01 => 01
[1,8,7,6,3,4,5,-2] => [3,2,1] => 101 => 101
[8,1,7,6,2,4,5,-3] => [2] => 0 => 0
[8,7,1,6,2,3,5,-4] => [3] => 1 => 1
[8,7,6,1,2,3,4,-5] => [2] => 0 => 0
[8,6,5,1,2,3,4,-7] => [4] => 0 => 0
[7,6,5,1,2,3,4,-8] => [4,3] => 01 => 01
[5,4,3,2,1,-6] => [2,2,1] => 001 => 001
[5,4,3,1,2,-6] => [4,1] => 01 => 01
[5,4,1,3,2,-6] => [5] => 1 => 1
[5,4,2,1,3,-6] => [5] => 1 => 1
[5,1,4,3,2,-6] => [3,2] => 10 => 10
[5,1,4,2,3,-6] => [5] => 1 => 1
[5,2,1,4,3,-6] => [3,1,1] => 111 => 111
[5,1,2,4,3,-6] => [4,1] => 01 => 01
[5,3,2,1,4,-6] => [3,2] => 10 => 10
[5,3,1,2,4,-6] => [5] => 1 => 1
[5,1,3,2,4,-6] => [4,1] => 01 => 01
[5,2,1,3,4,-6] => [4,1] => 01 => 01
[5,1,2,3,4,-6] => [5] => 1 => 1
[1,5,4,3,2,-6] => [2,2,1] => 001 => 001
[1,5,4,2,3,-6] => [4,1] => 01 => 01
[1,5,2,4,3,-6] => [3,1,1] => 111 => 111
[1,5,3,2,4,-6] => [3,1,1] => 111 => 111
[1,5,2,3,4,-6] => [4,1] => 01 => 01
[2,1,5,4,3,-6] => [2,2,1] => 001 => 001
[2,1,5,3,4,-6] => [3,2] => 10 => 10
[1,2,5,4,3,-6] => [2,1,1,1] => 0111 => 0111
[1,2,5,3,4,-6] => [3,1,1] => 111 => 111
[3,2,1,5,4,-6] => [2,2,1] => 001 => 001
[3,1,2,5,4,-6] => [3,2] => 10 => 10
[1,3,2,5,4,-6] => [2,2,1] => 001 => 001
[2,1,3,5,4,-6] => [2,2,1] => 001 => 001
[1,2,3,5,4,-6] => [2,1,1,1] => 0111 => 0111
[4,3,2,1,5,-6] => [2,2,1] => 001 => 001
[4,3,1,2,5,-6] => [4,1] => 01 => 01
[4,1,3,2,5,-6] => [3,1,1] => 111 => 111
[4,2,1,3,5,-6] => [3,1,1] => 111 => 111
[4,1,2,3,5,-6] => [4,1] => 01 => 01
[1,4,3,2,5,-6] => [2,1,1,1] => 0111 => 0111
[1,4,2,3,5,-6] => [3,1,1] => 111 => 111
[2,1,4,3,5,-6] => [2,2,1] => 001 => 001
[1,2,4,3,5,-6] => [2,1,1,1] => 0111 => 0111
[3,2,1,4,5,-6] => [2,1,1,1] => 0111 => 0111
[3,1,2,4,5,-6] => [3,1,1] => 111 => 111
[1,3,2,4,5,-6] => [2,1,1,1] => 0111 => 0111
[2,1,3,4,5,-6] => [2,1,1,1] => 0111 => 0111
[1,6,5,4,3,-2] => [2,1,1] => 011 => 011
[1,6,3,5,4,-2] => [2,1,1] => 011 => 011
[1,6,4,3,5,-2] => [2,1,1] => 011 => 011
[2,1,6,5,4,-3] => [2,2] => 00 => 00
[2,1,6,4,5,-3] => [2,1,1] => 011 => 011
[1,2,6,5,4,-3] => [2,1,1] => 011 => 011
[1,3,6,5,4,-2] => [2,1] => 01 => 01
[3,2,1,6,5,-4] => [2,1,1] => 011 => 011
[1,3,2,6,5,-4] => [2,1,1] => 011 => 011
[2,1,3,6,5,-4] => [2,1,1] => 011 => 011
[2,1,4,6,5,-3] => [2,1] => 01 => 01
[4,3,2,1,6,-5] => [2,2] => 00 => 00
[4,3,1,2,6,-5] => [4] => 0 => 0
[4,1,3,2,6,-5] => [3,1] => 11 => 11
[4,2,1,3,6,-5] => [3,1] => 11 => 11
[4,1,2,3,6,-5] => [4] => 0 => 0
[1,4,3,2,6,-5] => [2,1,1] => 011 => 011
[1,4,2,3,6,-5] => [3,1] => 11 => 11
[2,1,4,3,6,-5] => [2,2] => 00 => 00
[1,2,4,3,6,-5] => [2,1,1] => 011 => 011
[3,2,1,4,6,-5] => [2,1,1] => 011 => 011
[3,1,2,4,6,-5] => [3,1] => 11 => 11
[1,3,2,4,6,-5] => [2,1,1] => 011 => 011
[2,1,3,4,6,-5] => [2,1,1] => 011 => 011
[1,5,4,3,6,-2] => [2,1] => 01 => 01
[2,1,5,4,6,-3] => [2,1] => 01 => 01
[3,2,1,5,6,-4] => [2,1] => 01 => 01
[3,1,2,5,6,-4] => [3] => 1 => 1
[1,3,2,5,6,-4] => [2,1] => 01 => 01
[2,1,3,5,6,-4] => [2,1] => 01 => 01
[2,1,4,5,6,-3] => [2] => 0 => 0
[-2,1,-4,3,5,6] => [1,1] => 11 => 11
[-2,4,1,3,5,6] => [1,1] => 11 => 11
[-2,1,5,-4,3,6] => [2,1] => 01 => 01
[5,-2,1,-4,3,6] => [3,1] => 11 => 11
[-2,4,5,1,3,6] => [2,1] => 01 => 01
[-2,-5,1,6,3,4] => [4,2] => 00 => 00
[-2,1,5,6,3,4] => [2,2] => 00 => 00
[-2,1,5,3,4,6] => [3,1] => 11 => 11
[-2,1,3,-5,4,6] => [1,1] => 11 => 11
[3,-2,1,-5,4,6] => [2,1] => 01 => 01
[3,-2,5,1,4,6] => [4,1] => 01 => 01
[-2,1,3,6,-5,4] => [2,1] => 01 => 01
[3,-2,1,6,-5,4] => [2,2] => 00 => 00
[3,-2,5,6,1,4] => [3,2] => 10 => 10
[-2,1,3,6,4,5] => [3,1] => 11 => 11
[3,-2,1,6,4,5] => [3,2] => 10 => 10
[-2,1,3,4,-6,5] => [1,1] => 11 => 11
[3,-2,1,4,-6,5] => [2,1] => 01 => 01
[3,4,1,2,-6,5] => [2,2] => 00 => 00
[-4,6,1,-3,2,5] => [3,3] => 11 => 11
[-4,1,-3,2,5,6] => [1,1] => 11 => 11
[-4,1,5,-3,2,6] => [5,1] => 11 => 11
[5,-4,1,-3,2,6] => [5,1] => 11 => 11
[5,6,-4,1,-3,2] => [4,2] => 00 => 00
[3,6,1,2,-5,4] => [3,2] => 10 => 10
[5,1,-3,6,2,4] => [3,2] => 10 => 10
[5,1,-3,2,4,6] => [4,1] => 01 => 01
[3,1,2,-5,4,6] => [3,1] => 11 => 11
[1,-3,2,-5,4,6] => [1,1] => 11 => 11
[1,-3,5,2,4,6] => [1,1] => 11 => 11
[3,1,2,6,-5,4] => [3,2] => 10 => 10
[1,-3,2,6,-5,4] => [2,1] => 01 => 01
[1,6,-3,2,-5,4] => [3,1] => 11 => 11
[1,-3,5,6,2,4] => [2,1] => 01 => 01
[1,6,-3,2,4,5] => [4,1] => 01 => 01
[1,-3,-6,2,4,5] => [5,1] => 11 => 11
[1,-3,2,6,4,5] => [3,1] => 11 => 11
[3,1,2,4,-6,5] => [3,1] => 11 => 11
[1,-3,2,4,-6,5] => [1,1] => 11 => 11
[1,4,-3,2,-6,5] => [2,1] => 01 => 01
[1,4,-3,6,2,5] => [4,1] => 01 => 01
[1,-3,2,4,5,6] => [1,1,1,1] => 1111 => 1111
[1,4,-3,2,5,6] => [2,1,1,1] => 0111 => 0111
[1,4,5,-3,2,6] => [1,1] => 11 => 11
[1,4,5,6,-3,2] => [3,1] => 11 => 11
[5,1,2,-4,3,6] => [4,1] => 01 => 01
[1,-5,2,-4,3,6] => [1,1] => 11 => 11
[-4,1,5,2,3,6] => [2,1] => 01 => 01
[1,-5,2,6,-4,3] => [5,1] => 11 => 11
[1,6,-5,2,-4,3] => [5,1] => 11 => 11
[1,6,2,-4,3,5] => [4,1] => 01 => 01
[1,4,2,3,-6,5] => [3,1] => 11 => 11
[1,2,-4,3,-6,5] => [1,1] => 11 => 11
[1,2,-4,6,3,5] => [1,1] => 11 => 11
[1,2,-4,3,5,6] => [1,1,1,1] => 1111 => 1111
[1,2,5,-4,3,6] => [2,1,1,1] => 0111 => 0111
[1,2,5,6,-4,3] => [1,1] => 11 => 11
[1,6,2,3,-5,4] => [4,1] => 01 => 01
[1,2,-6,3,-5,4] => [1,1] => 11 => 11
[1,-5,2,6,3,4] => [2,1] => 01 => 01
[1,2,3,-5,4,6] => [1,1,1,1] => 1111 => 1111
[1,2,3,6,-5,4] => [2,1,1,1] => 0111 => 0111
[1,2,3,4,-6,5] => [1,1,1,1] => 1111 => 1111
[1,2,3,-5,-6,4] => [3,1,1,1] => 1111 => 1111
[1,2,5,-4,-6,3] => [1,1] => 11 => 11
[1,2,-4,-5,3,6] => [3,1,1,1] => 1111 => 1111
[1,2,-4,6,-5,3] => [1,1] => 11 => 11
[1,-4,2,5,-6,3] => [5,1] => 11 => 11
[1,2,-4,-5,-6,3] => [1,1] => 11 => 11
[1,-3,2,-5,-6,4] => [3,1] => 11 => 11
[1,4,5,-3,-6,2] => [5,1] => 11 => 11
[1,4,-3,-5,2,6] => [1,1] => 11 => 11
[1,4,-3,6,-5,2] => [3,1] => 11 => 11
[1,-3,4,5,-6,2] => [5,1] => 11 => 11
[1,4,-3,-5,-6,2] => [4,1] => 01 => 01
[1,-3,-4,2,5,6] => [3,1,1,1] => 1111 => 1111
[1,-3,-4,2,-6,5] => [3,1] => 11 => 11
[1,-3,5,-4,2,6] => [1,1] => 11 => 11
[1,-3,5,6,-4,2] => [5,1] => 11 => 11
[1,-3,5,-4,-6,2] => [4,1] => 01 => 01
[-3,1,4,-5,2,6] => [5,1] => 11 => 11
[1,-3,-4,-5,2,6] => [1,1] => 11 => 11
[1,-3,-4,6,-5,2] => [4,1] => 01 => 01
[1,-3,-6,5,-4,2] => [3,1] => 11 => 11
[-5,1,3,-4,-6,2] => [4,1] => 01 => 01
[1,-3,-4,-5,-6,2] => [5,1] => 11 => 11
[-2,1,3,-5,-6,4] => [3,1] => 11 => 11
[-2,1,-4,-5,3,6] => [3,1] => 11 => 11
[3,-2,1,-5,-6,4] => [3,2] => 10 => 10
[3,4,-2,-5,1,6] => [5,1] => 11 => 11
[3,-2,-4,1,5,6] => [1,1] => 11 => 11
[3,-2,5,-4,1,6] => [3,1] => 11 => 11
[-2,3,4,-5,1,6] => [5,1] => 11 => 11
[3,-2,-4,-5,1,6] => [4,1] => 01 => 01
[-2,5,3,-4,-6,1] => [4,1] => 01 => 01
[-2,-3,1,4,-6,5] => [3,1] => 11 => 11
[-2,-3,1,-5,4,6] => [3,1] => 11 => 11
[-2,-3,1,6,-5,4] => [3,2] => 10 => 10
[-2,-3,1,-5,-6,4] => [3,3] => 11 => 11
[-2,4,-3,-5,1,6] => [4,1] => 01 => 01
[2,3,-4,-5,1,6] => [5,1] => 11 => 11
[2,-4,3,5,-6,1] => [5,1] => 11 => 11
[4,5,3,-2,-6,1] => [5,1] => 11 => 11
[4,2,-3,-5,-6,1] => [4,1] => 01 => 01
[3,2,6,1,4,-5] => [1] => 1 => 1
[3,2,5,4,1,-6] => [3,1,1] => 111 => 111
[4,5,2,3,1,-6] => [5] => 1 => 1
[4,6,2,1,3,-5] => [2] => 0 => 0
[6,1,5,4,2,-3] => [1] => 1 => 1
[6,5,1,3,2,-4] => [2] => 0 => 0
[6,4,3,1,2,-5] => [1] => 1 => 1
[3,2,1,6,5,8,7,-4] => [2,1,1,1] => 0111 => 0111
[3,2,6,1,4,8,7,-5] => [1,1] => 11 => 11
[3,2,5,4,1,8,7,-6] => [3,1,1,1] => 1111 => 1111
[3,2,5,4,8,1,6,-7] => [1,1] => 11 => 11
[3,2,5,4,7,6,1,-8] => [4,1,1,1] => 0111 => 0111
[4,5,2,3,7,6,1,-8] => [6,1] => 01 => 01
[4,5,2,3,1,8,7,-6] => [5,1] => 11 => 11
[4,6,2,1,3,8,7,-5] => [2,1] => 01 => 01
[1,6,5,4,3,8,7,-2] => [2,1,1,1] => 0111 => 0111
[6,1,5,4,2,8,7,-3] => [1,1] => 11 => 11
[6,5,1,3,2,8,7,-4] => [2,1] => 01 => 01
[6,4,3,1,2,8,7,-5] => [1,1] => 11 => 11
[5,4,3,2,1,8,7,-6] => [2,2,1,1] => 0011 => 0011
[5,4,3,2,8,1,6,-7] => [2,1] => 01 => 01
[5,4,3,2,7,6,1,-8] => [3,2,1,1] => 1011 => 1011
[6,4,3,7,2,5,1,-8] => [6,1] => 01 => 01
[6,4,3,8,2,1,5,-7] => [2,1] => 01 => 01
[7,4,3,8,1,2,5,-6] => [3,1] => 11 => 11
[7,4,3,1,8,2,6,-5] => [5,1] => 11 => 11
[7,1,5,4,8,2,6,-3] => [4,1] => 01 => 01
[1,7,5,4,8,3,6,-2] => [1,1] => 11 => 11
[1,8,5,4,7,6,3,-2] => [3,1,1,1] => 1111 => 1111
[8,1,5,4,7,6,2,-3] => [1,1] => 11 => 11
[8,5,1,3,7,6,2,-4] => [3,1] => 11 => 11
[8,4,3,1,7,6,2,-5] => [1,1] => 11 => 11
[8,4,3,7,1,5,2,-6] => [3,1] => 11 => 11
[8,4,3,6,5,1,2,-7] => [1,1] => 11 => 11
[7,4,3,6,5,2,1,-8] => [3,2,1,1] => 1011 => 1011
[7,5,6,3,4,2,1,-8] => [5,2] => 10 => 10
[1,8,6,7,4,5,3,-2] => [5,1] => 11 => 11
[1,7,6,8,4,3,5,-2] => [2,1] => 01 => 01
[7,6,1,8,3,2,5,-4] => [4,2] => 00 => 00
[7,6,8,1,3,2,4,-5] => [3,2] => 10 => 10
[6,5,8,3,2,1,4,-7] => [2,2] => 00 => 00
[6,5,7,3,2,4,1,-8] => [5,2] => 10 => 10
[5,6,7,2,3,4,1,-8] => [4,3] => 01 => 01
[5,7,8,2,1,3,4,-6] => [3,2] => 10 => 10
[4,7,2,1,8,3,6,-5] => [4,2] => 00 => 00
[4,6,2,7,3,5,1,-8] => [4,3] => 01 => 01
[3,2,6,7,4,5,1,-8] => [6,1] => 01 => 01
[3,2,6,8,4,1,5,-7] => [3,1] => 11 => 11
[3,2,7,8,1,4,5,-6] => [4,1] => 01 => 01
[3,2,7,1,8,4,6,-5] => [5,1] => 11 => 11
[3,2,1,7,8,5,6,-4] => [2,1] => 01 => 01
[1,4,3,8,7,6,5,-2] => [2,1,1,1] => 0111 => 0111
[4,1,2,8,7,6,5,-3] => [2,1] => 01 => 01
[3,2,1,8,7,6,5,-4] => [2,2,1,1] => 0011 => 0011
[3,2,8,1,7,6,4,-5] => [1,1] => 11 => 11
[3,2,8,7,1,5,4,-6] => [2,1] => 01 => 01
[3,2,8,6,5,1,4,-7] => [1,1] => 11 => 11
[3,2,7,6,5,4,1,-8] => [3,2,1,1] => 1011 => 1011
[4,7,2,6,5,3,1,-8] => [6,1] => 01 => 01
[4,8,2,6,5,1,3,-7] => [3,1] => 11 => 11
[4,8,2,1,7,6,3,-5] => [2,1] => 01 => 01
[5,8,1,2,7,6,3,-4] => [4,1] => 01 => 01
[5,1,8,2,7,6,4,-3] => [5,1] => 11 => 11
[1,5,8,3,7,6,4,-2] => [1,1] => 11 => 11
[1,6,8,7,3,5,4,-2] => [2,1] => 01 => 01
[6,1,8,7,2,5,4,-3] => [4,2] => 00 => 00
[6,8,7,1,2,4,3,-5] => [3,2] => 10 => 10
[5,8,7,2,1,4,3,-6] => [2,2] => 00 => 00
[5,7,6,2,4,3,1,-8] => [5,2] => 10 => 10
[6,7,5,4,2,3,1,-8] => [6,1] => 01 => 01
[6,8,5,4,2,1,3,-7] => [2,1] => 01 => 01
[7,8,5,4,1,2,3,-6] => [4,1] => 01 => 01
[7,8,1,6,5,2,3,-4] => [3,1] => 11 => 11
[7,1,8,6,5,2,4,-3] => [5,1] => 11 => 11
[1,7,8,6,5,3,4,-2] => [1,1] => 11 => 11
[1,8,7,6,5,4,3,-2] => [2,2,1,1] => 0011 => 0011
[8,1,7,6,5,4,2,-3] => [2,1] => 01 => 01
[8,7,1,6,5,3,2,-4] => [2,1] => 01 => 01
[8,7,6,1,4,3,2,-5] => [2,2] => 00 => 00
[8,7,5,4,1,3,2,-6] => [2,1] => 01 => 01
[8,6,5,4,3,1,2,-7] => [2,1] => 01 => 01
[7,6,5,4,3,2,1,-8] => [2,2,2,1] => 0001 => 0001
[5,4,2,3,1,-6] => [3,2] => 10 => 10
[5,3,4,2,1,-6] => [3,2] => 10 => 10
[5,3,4,1,2,-6] => [5] => 1 => 1
[5,3,2,4,1,-6] => [2,2,1] => 001 => 001
[5,2,3,4,1,-6] => [2,1,1,1] => 0111 => 0111
[5,2,3,1,4,-6] => [3,1,1] => 111 => 111
[4,5,3,2,1,-6] => [4,1] => 01 => 01
[4,5,3,1,2,-6] => [2,2,1] => 001 => 001
[4,5,2,1,3,-6] => [3,2] => 10 => 10
[4,3,5,2,1,-6] => [5] => 1 => 1
[4,3,5,1,2,-6] => [3,2] => 10 => 10
[4,3,2,5,1,-6] => [3,2] => 10 => 10
[4,2,3,5,1,-6] => [3,1,1] => 111 => 111
[4,2,3,1,5,-6] => [2,1,1,1] => 0111 => 0111
[3,4,5,2,1,-6] => [3,2] => 10 => 10
[3,4,5,1,2,-6] => [5] => 1 => 1
[3,4,2,5,1,-6] => [5] => 1 => 1
[3,4,2,1,5,-6] => [4,1] => 01 => 01
[3,4,1,2,5,-6] => [2,2,1] => 001 => 001
[3,2,4,5,1,-6] => [4,1] => 01 => 01
[3,2,4,1,5,-6] => [3,1,1] => 111 => 111
[2,3,4,5,1,-6] => [5] => 1 => 1
[2,3,4,1,5,-6] => [4,1] => 01 => 01
[2,3,1,4,5,-6] => [3,1,1] => 111 => 111
[6,4,3,2,1,-5] => [2,1] => 01 => 01
[6,4,2,3,1,-5] => [3] => 1 => 1
[6,3,4,2,1,-5] => [3] => 1 => 1
[6,3,2,4,1,-5] => [2,1] => 01 => 01
[6,3,2,1,4,-5] => [2] => 0 => 0
[6,2,3,1,4,-5] => [1,1] => 11 => 11
[6,2,1,3,4,-5] => [1] => 1 => 1
[4,6,3,2,1,-5] => [1] => 1 => 1
[4,6,3,1,2,-5] => [2,1] => 01 => 01
[4,3,6,1,2,-5] => [2] => 0 => 0
[4,3,2,6,1,-5] => [2] => 0 => 0
[4,2,3,6,1,-5] => [1,1] => 11 => 11
[4,2,3,1,6,-5] => [2,1,1] => 011 => 011
[3,4,6,2,1,-5] => [2] => 0 => 0
[3,4,2,1,6,-5] => [4] => 0 => 0
[3,4,1,2,6,-5] => [2,2] => 00 => 00
[3,2,4,6,1,-5] => [1] => 1 => 1
[3,2,4,1,6,-5] => [3,1] => 11 => 11
[2,3,4,1,6,-5] => [4] => 0 => 0
[2,3,1,4,6,-5] => [3,1] => 11 => 11
[5,6,3,1,2,-4] => [1] => 1 => 1
[5,6,2,3,1,-4] => [2] => 0 => 0
[5,3,6,2,1,-4] => [2] => 0 => 0
[5,3,2,6,1,-4] => [2,2] => 00 => 00
[5,3,2,1,6,-4] => [2] => 0 => 0
[5,2,3,1,6,-4] => [1,1] => 11 => 11
[5,2,1,3,6,-4] => [1] => 1 => 1
[3,5,6,1,2,-4] => [2] => 0 => 0
[3,5,2,6,1,-4] => [4] => 0 => 0
[3,5,1,2,6,-4] => [2] => 0 => 0
[3,2,5,6,1,-4] => [3,1] => 11 => 11
[3,2,5,1,6,-4] => [1] => 1 => 1
[2,3,5,6,1,-4] => [4] => 0 => 0
[2,3,1,5,6,-4] => [3] => 1 => 1
[4,5,6,2,1,-3] => [4] => 0 => 0
[4,5,2,1,6,-3] => [2] => 0 => 0
[4,2,5,1,6,-3] => [2,1] => 01 => 01
[4,2,1,5,6,-3] => [1] => 1 => 1
[2,4,5,1,6,-3] => [3] => 1 => 1
[-3,2,6,-5,1,4] => [5,1] => 11 => 11
[-6,2,4,-5,-3,1] => [3,1] => 11 => 11
[-6,-5,2,3,-4,1] => [4] => 0 => 0
[2,-5,6,-4,1,3] => [2] => 0 => 0
[6,4,-5,-3,1,2] => [6] => 0 => 0
[-6,-5,-4,3,1,2] => [4] => 0 => 0
[2,8,-6,-4,-3,1,5,7] => [7] => 1 => 1
[-3,2,8,-6,-5,1,4,7] => [6,1] => 01 => 01
[-8,2,4,-6,-5,-3,1,7] => [3,1] => 11 => 11
[-8,-7,2,4,-5,-3,1,6] => [1] => 1 => 1
[8,2,4,6,-7,-5,-3,1] => [2,1] => 01 => 01
[5,-7,2,3,8,-4,1,6] => [8] => 0 => 0
[-8,-6,2,3,-5,-4,1,7] => [4] => 0 => 0
[2,-6,8,-5,-4,1,3,7] => [3,2] => 10 => 10
[3,-6,8,-5,-4,1,2,7] => [2] => 0 => 0
[3,-5,6,8,-4,1,2,7] => [5,3] => 11 => 11
[-8,-6,-3,2,-5,-4,1,7] => [3] => 1 => 1
[5,-7,-3,2,8,-4,1,6] => [7] => 1 => 1
[3,8,-6,2,-7,-5,-4,1] => [8] => 0 => 0
[5,8,-7,-3,2,-6,-4,1] => [4] => 0 => 0
[3,8,-7,-4,2,-6,1,5] => [3] => 1 => 1
[5,-7,-4,3,8,1,2,6] => [4] => 0 => 0
[4,-7,8,-5,-3,1,2,6] => [6] => 0 => 0
[-8,6,3,-7,-5,-4,1,2] => [1] => 1 => 1
[3,8,-7,6,-5,-4,1,2] => [2] => 0 => 0
[3,8,-7,-6,5,-4,1,2] => [2,2,1] => 001 => 001
[4,8,-7,-6,3,5,1,2] => [6,2] => 00 => 00
[3,6,7,8,4,-5,1,2] => [3] => 1 => 1
[3,7,8,-6,4,-5,1,2] => [5,3] => 11 => 11
[-5,8,-7,3,-6,-4,1,2] => [6,2] => 00 => 00
[7,8,4,5,-6,-3,1,2] => [4,2,2] => 000 => 000
[-8,-7,4,5,-6,-2,1,3] => [8] => 0 => 0
[-8,-7,2,4,-6,1,3,5] => [4,1] => 01 => 01
[-8,-7,-4,-3,-6,1,2,5] => [4,2] => 00 => 00
[-4,3,-7,8,-6,1,2,5] => [5] => 1 => 1
[6,7,8,1,3,-5,2,4] => [2] => 0 => 0
[3,7,8,-6,2,4,-5,1] => [3] => 1 => 1
[2,7,8,-6,3,-5,1,4] => [5,3] => 11 => 11
[6,7,8,-5,2,1,3,4] => [2] => 0 => 0
[5,-8,-7,2,-4,1,3,6] => [6] => 0 => 0
[-4,2,-7,8,-6,1,3,5] => [5,1] => 11 => 11
[7,8,-4,2,3,-6,1,5] => [2] => 0 => 0
[5,8,-7,2,3,-6,-4,1] => [7] => 1 => 1
[8,-7,2,4,5,-6,-3,1] => [3,2,1,1] => 1011 => 1011
[-8,-7,-3,2,4,-6,1,5] => [6] => 0 => 0
[2,4,7,8,-3,1,5,6] => [5] => 1 => 1
[6,8,-7,-4,-2,1,3,5] => [2] => 0 => 0
[8,6,-7,-4,-3,1,2,5] => [7] => 1 => 1
[-8,2,6,-7,-4,-3,1,5] => [1] => 1 => 1
[-8,-7,-3,2,5,-6,1,4] => [5,1] => 11 => 11
[-8,-7,-5,-3,2,-6,1,4] => [7] => 1 => 1
[5,-8,-7,2,4,-6,-3,1] => [2] => 0 => 0
[6,7,8,2,5,-4,1,3] => [2,1] => 01 => 01
[-5,8,-7,2,-6,-4,1,3] => [8] => 0 => 0
[-6,-8,1,-7,-5,-4,2,3] => [7] => 1 => 1
[-8,2,6,-7,-5,1,3,4] => [6,1] => 01 => 01
[-8,-7,2,5,-6,1,3,4] => [5] => 1 => 1
[-8,-7,-5,-3,-6,1,2,4] => [6] => 0 => 0
[6,7,8,5,-4,1,2,3] => [2,2,2] => 000 => 000
[6,7,8,1,4,-5,2,3] => [2,2] => 00 => 00
[2,7,8,-6,4,-5,1,3] => [3,3,2] => 110 => 110
[-4,7,8,-6,2,-5,1,3] => [2] => 0 => 0
[4,6,7,8,2,3,-5,1] => [3] => 1 => 1
[-6,4,7,8,2,-5,1,3] => [8] => 0 => 0
[-4,7,8,-6,1,-5,2,3] => [2,2] => 00 => 00
[7,8,-6,-4,5,1,2,3] => [1] => 1 => 1
[8,-7,-6,3,5,1,2,4] => [1] => 1 => 1
[-8,-7,-5,2,-6,1,3,4] => [8] => 0 => 0
[-8,-7,-5,4,-6,-2,1,3] => [1] => 1 => 1
[5,8,-7,4,-6,-3,1,2] => [2,1] => 01 => 01
[6,7,8,3,5,-4,1,2] => [1] => 1 => 1
[-6,4,7,8,3,-5,1,2] => [5,3] => 11 => 11
[4,6,7,8,-5,3,1,2] => [7] => 1 => 1
[3,6,7,8,-4,2,-5,1] => [6,2] => 00 => 00
[6,5,3,4,2,-1] => [2,1,1] => 011 => 011
[6,4,3,5,2,-1] => [3,1] => 11 => 11
[6,3,4,5,2,-1] => [4] => 0 => 0
[6,3,4,2,5,-1] => [3,1] => 11 => 11
[5,3,4,2,6,-1] => [3] => 1 => 1
[2,6,4,5,3,-1] => [3] => 1 => 1
[6,2,4,5,3,-1] => [3,1] => 11 => 11
[6,3,5,4,2,-1] => [3,1] => 11 => 11
[1,2,-6,5,3,4] => [1,1] => 11 => 11
[5,1,-6,-3,2,4] => [3,3] => 11 => 11
[-6,5,1,-3,2,4] => [4,2] => 00 => 00
[-6,5,-4,1,2,3] => [4,2] => 00 => 00
[4,6,-3,1,-5,2] => [2,2] => 00 => 00
[1,2,7,3,4,-6,5] => [4,1,1] => 011 => 011
[1,2,7,3,-5,4,6] => [4,1,1] => 011 => 011
[1,2,3,-7,6,4,5] => [1,1,1] => 111 => 111
[1,6,2,3,7,-5,4] => [1] => 1 => 1
[1,2,7,-4,3,5,6] => [4,1,1] => 011 => 011
[7,1,2,-4,3,-6,5] => [5] => 1 => 1
[1,-7,2,5,3,4,6] => [1] => 1 => 1
[1,-7,2,3,6,4,5] => [1] => 1 => 1
[1,7,2,-5,3,-6,4] => [1] => 1 => 1
[5,1,2,-4,7,3,6] => [6] => 0 => 0
[1,6,2,-7,-4,3,5] => [3,3,1] => 111 => 111
[1,-7,2,5,6,3,4] => [1] => 1 => 1
[5,1,2,6,7,-4,3] => [5] => 1 => 1
[1,-3,7,2,4,5,6] => [1] => 1 => 1
[7,1,-3,2,4,-6,5] => [5] => 1 => 1
[7,1,-3,2,-5,4,6] => [5] => 1 => 1
[1,6,-3,-7,2,4,5] => [1] => 1 => 1
[-6,1,-3,2,7,-5,4] => [6] => 0 => 0
[1,-7,4,2,3,-6,5] => [1] => 1 => 1
[1,-5,7,2,3,-6,4] => [1] => 1 => 1
[1,7,-4,2,-5,3,6] => [1] => 1 => 1
[5,6,1,-7,2,3,4] => [5] => 1 => 1
[6,1,-4,2,7,-5,3] => [7] => 1 => 1
[-4,1,-3,2,7,5,6] => [3] => 1 => 1
[-4,1,7,-3,2,-6,5] => [6] => 0 => 0
[5,-7,1,-3,2,4,6] => [7] => 1 => 1
[1,-7,6,-3,2,4,5] => [1] => 1 => 1
[-7,1,-3,-5,2,-6,4] => [5] => 1 => 1
[-6,-7,1,2,5,3,4] => [1] => 1 => 1
[1,5,7,-4,2,-6,3] => [2,2,1] => 001 => 001
[-4,1,5,-3,7,2,6] => [7] => 1 => 1
[-4,1,-3,-7,6,2,5] => [6] => 0 => 0
[5,-3,-7,1,6,2,4] => [7] => 1 => 1
[-4,1,7,5,6,2,3] => [2] => 0 => 0
[-4,1,5,6,7,-3,2] => [7] => 1 => 1
[-2,1,3,4,7,5,6] => [3,1,1] => 111 => 111
[-2,1,7,3,4,-6,5] => [4] => 0 => 0
[-2,1,7,3,-5,4,6] => [4] => 0 => 0
[-2,1,3,-7,6,4,5] => [1] => 1 => 1
[-2,6,1,3,7,-5,4] => [7] => 1 => 1
[-2,1,7,-4,3,5,6] => [4] => 0 => 0
[7,-2,1,-4,3,-6,5] => [4] => 0 => 0
[-2,-7,1,5,3,4,6] => [7] => 1 => 1
[-2,-7,1,3,6,4,5] => [7] => 1 => 1
[-2,7,1,-5,3,-6,4] => [6] => 0 => 0
[5,-2,1,-4,7,3,6] => [5] => 1 => 1
[-2,6,1,-7,-4,3,5] => [3] => 1 => 1
[-2,-7,1,5,6,3,4] => [7] => 1 => 1
[5,-2,1,6,7,-4,3] => [4] => 0 => 0
[7,3,1,2,4,-6,5] => [6] => 0 => 0
[7,3,1,2,-5,4,6] => [6] => 0 => 0
[-6,3,1,2,7,-5,4] => [7] => 1 => 1
[7,1,4,2,3,-6,5] => [6] => 0 => 0
[1,6,7,2,3,-5,4] => [1] => 1 => 1
[-4,1,7,2,-5,3,6] => [3] => 1 => 1
[4,1,6,-7,2,3,5] => [2] => 0 => 0
[1,7,2,-5,6,3,4] => [1] => 1 => 1
[-4,6,1,2,7,-5,3] => [7] => 1 => 1
[-3,7,1,-4,2,5,6] => [4] => 0 => 0
[-7,-3,1,-4,2,-6,5] => [5] => 1 => 1
[7,5,1,-3,2,4,6] => [2] => 0 => 0
[7,1,6,-3,2,4,5] => [4] => 0 => 0
[-7,-5,1,-3,2,-6,4] => [4] => 0 => 0
[7,5,-4,1,2,3,6] => [2] => 0 => 0
[7,-4,6,1,2,3,5] => [2] => 0 => 0
[-6,1,7,2,5,3,4] => [1] => 1 => 1
[-7,-5,1,-6,2,-4,3] => [2] => 0 => 0
[-5,-3,1,-4,7,2,6] => [6] => 0 => 0
[6,-3,1,-7,-4,2,5] => [3] => 1 => 1
[7,5,1,-3,6,2,4] => [3] => 1 => 1
[7,5,-4,1,6,2,3] => [3] => 1 => 1
[-5,-3,1,6,7,-4,2] => [5] => 1 => 1
[3,-2,1,4,7,5,6] => [3,2,1] => 101 => 101
[3,-2,7,1,4,-6,5] => [5] => 1 => 1
[3,-2,7,1,-5,4,6] => [5] => 1 => 1
[3,-2,1,-7,6,4,5] => [2] => 0 => 0
[3,6,-2,1,7,-5,4] => [7] => 1 => 1
[7,-2,4,1,3,5,6] => [6] => 0 => 0
[-2,-7,4,1,3,-6,5] => [6] => 0 => 0
[7,-2,1,5,3,4,6] => [6] => 0 => 0
[-2,1,3,6,7,4,5] => [2,2,1] => 001 => 001
[-2,-5,7,1,3,-6,4] => [6] => 0 => 0
[-2,7,-4,1,-5,3,6] => [6] => 0 => 0
[-4,6,-2,-7,1,3,5] => [4] => 0 => 0
[5,6,-2,-7,1,3,4] => [2] => 0 => 0
[6,-2,-4,1,7,-5,3] => [6] => 0 => 0
[7,3,4,1,2,-6,5] => [6] => 0 => 0
[5,3,7,1,2,-6,4] => [6] => 0 => 0
[-4,-5,7,1,2,-6,3] => [2] => 0 => 0
[4,-3,7,1,-5,2,6] => [2] => 0 => 0
[4,-3,1,-7,6,2,5] => [7] => 1 => 1
[-3,5,1,-7,6,2,4] => [3] => 1 => 1
[-4,-7,6,-5,1,2,3] => [3] => 1 => 1
[4,6,-3,1,7,-5,2] => [2] => 0 => 0
[3,4,-2,1,7,5,6] => [3] => 1 => 1
[3,4,7,-2,1,-6,5] => [4] => 0 => 0
[3,-7,-2,5,1,4,6] => [7] => 1 => 1
[3,-7,-2,1,6,4,5] => [7] => 1 => 1
[3,7,-2,-5,1,-6,4] => [6] => 0 => 0
[7,-2,4,5,1,3,6] => [6] => 0 => 0
[7,-2,4,1,6,3,5] => [6] => 0 => 0
[-6,-7,-2,1,5,3,4] => [1] => 1 => 1
[-2,5,7,-4,1,-6,3] => [2] => 0 => 0
[3,-7,6,1,5,2,4] => [1] => 1 => 1
[4,5,7,-6,1,-3,2] => [7] => 1 => 1
[3,4,5,-2,7,1,6] => [5] => 1 => 1
[3,4,-2,-7,6,1,5] => [7] => 1 => 1
[3,-7,-2,5,6,1,4] => [7] => 1 => 1
[-7,2,4,5,6,1,3] => [1] => 1 => 1
[3,4,5,6,7,-2,1] => [4] => 0 => 0
[3,5,-4,2,-6,1] => [6] => 0 => 0
[3,4,-5,2,-6,1] => [4,2] => 00 => 00
[-5,-4,-3,2,-6,1] => [3] => 1 => 1
[-5,4,2,3,-6,1] => [3,3] => 11 => 11
[4,6,2,3,-5,1] => [5] => 1 => 1
[6,-4,2,3,-5,1] => [2] => 0 => 0
[-3,-5,2,4,-6,1] => [1] => 1 => 1
[3,-6,2,4,-5,1] => [1] => 1 => 1
[3,-4,2,5,-6,1] => [6] => 0 => 0
[-4,-3,2,5,-6,1] => [4] => 0 => 0
[-4,-3,2,-6,-5,1] => [3] => 1 => 1
[2,-5,3,4,-6,1] => [4,1,1] => 011 => 011
[6,2,3,4,-5,1] => [2,1,1,1] => 0111 => 0111
[4,2,3,-6,-5,1] => [1,1] => 11 => 11
[-6,2,3,-5,-4,1] => [2,1,1] => 011 => 011
[-3,2,4,5,-6,1] => [5,1] => 11 => 11
[-3,2,4,-6,-5,1] => [4,1] => 01 => 01
[2,3,-6,-5,-4,1] => [2] => 0 => 0
[-5,-4,3,6,1,2] => [1] => 1 => 1
[-6,4,2,-5,1,3] => [6] => 0 => 0
[2,5,-4,-6,1,3] => [3,3] => 11 => 11
[-4,-3,2,-5,1,6] => [3,1] => 11 => 11
[2,5,3,-6,1,4] => [3,1] => 11 => 11
[2,-6,3,-5,1,4] => [5,1] => 11 => 11
[2,-4,3,-6,1,5] => [5,1] => 11 => 11
[4,2,3,-5,1,6] => [1,1,1] => 111 => 111
[-5,2,3,-4,1,6] => [1,1,1] => 111 => 111
[3,2,4,-6,1,5] => [1] => 1 => 1
[-3,2,4,-5,1,6] => [4,1,1] => 011 => 011
[-2,3,4,-6,1,5] => [6] => 0 => 0
[2,3,4,-5,1,6] => [1] => 1 => 1
[2,3,-5,-4,1,6] => [1] => 1 => 1
[-5,-4,3,1,2,6] => [4,1,1] => 011 => 011
[6,-5,2,1,3,4] => [3] => 1 => 1
[5,2,-4,1,3,6] => [1,1] => 11 => 11
[-3,-2,-6,1,4,5] => [5] => 1 => 1
[-2,3,-5,1,4,6] => [5,1] => 11 => 11
[4,5,-6,1,2,3] => [2,2] => 00 => 00
[4,5,-6,-3,1,2] => [6] => 0 => 0
[3,4,-5,1,2,6] => [1] => 1 => 1
[3,4,-6,-5,1,2] => [6] => 0 => 0
[3,4,5,-6,1,2] => [3] => 1 => 1
[-4,3,5,-6,1,2] => [6] => 0 => 0
[-5,-4,3,-6,1,2] => [3,1] => 11 => 11
[4,5,-6,-3,-2,1] => [4] => 0 => 0
[3,4,-5,-2,1,6] => [1] => 1 => 1
[3,4,-6,-5,-2,1] => [3] => 1 => 1
[3,4,5,-6,-2,1] => [6] => 0 => 0
[-4,3,5,-6,-2,1] => [3] => 1 => 1
[-5,-4,3,-6,-2,1] => [5,1] => 11 => 11
[2,3,5,-6,-4,1] => [6] => 0 => 0
[-5,2,3,4,-6,1] => [3,1,1,1] => 1111 => 1111
[-4,2,3,-6,-5,1] => [3,1,1] => 111 => 111
[-4,2,3,5,-6,1] => [4,1,1] => 011 => 011
[-5,-4,2,3,-6,1] => [3] => 1 => 1
[4,-5,2,3,-6,1] => [6] => 0 => 0
[4,-5,-3,2,-6,1] => [5] => 1 => 1
[1,2,5,6,7,8,3,4] => [3,3,1,1] => 1111 => 1111
[-5,2,-3,6,1,4] => [2,1] => 01 => 01
[5,6,3,1,-4,2] => [2,1] => 01 => 01
[3,4,1,2,-6,5,-8,7] => [2,2] => 00 => 00
[-5,2,-3,6,1,4,-8,7] => [2,1] => 01 => 01
[-7,2,4,-3,-5,8,1,6] => [2,1] => 01 => 01
[5,2,7,3,-4,8,1,6] => [2,1] => 01 => 01
[1,4,5,6,2,3,-8,7] => [5,1] => 11 => 11
[-2,-5,1,6,3,4,-8,7] => [4,2] => 00 => 00
[5,6,3,1,-4,2,-8,7] => [2,1] => 01 => 01
[5,6,-4,3,1,2,-8,7] => [2,2] => 00 => 00
[3,2,-6,-5,-4,1,-8,7] => [2,1] => 01 => 01
[3,-7,2,-5,-4,8,1,6] => [2,2] => 00 => 00
[3,2,-8,-5,6,-4,-7,1] => [3,1] => 11 => 11
[-7,3,8,-6,2,-4,1,5] => [4,2] => 00 => 00
[5,3,7,1,-4,8,2,6] => [3,2] => 10 => 10
[-7,4,1,-3,-5,8,2,6] => [5,2] => 10 => 10
[-2,1,-7,4,-5,8,3,6] => [2,1] => 01 => 01
[5,8,3,1,6,-4,-7,2] => [2,1] => 01 => 01
[7,-3,8,-6,5,1,-4,2] => [4,1] => 01 => 01
[7,8,-4,3,-6,5,1,2] => [2,2] => 00 => 00
[7,8,3,4,2,-6,-5,1] => [1,1] => 11 => 11
[7,8,-3,-6,4,1,-5,2] => [5,2] => 10 => 10
[1,6,7,8,3,4,-5,2] => [4,1] => 01 => 01
[7,8,3,1,-6,5,-4,2] => [2,1] => 01 => 01
[-7,8,-3,1,4,5,-6,2] => [5,2] => 10 => 10
[7,8,1,4,-6,-3,2,5] => [7,1] => 11 => 11
[3,-7,8,-6,1,-4,2,5] => [4,2] => 00 => 00
[3,6,7,8,-5,1,2,4] => [5,2] => 10 => 10
[2,6,7,8,-5,3,1,4] => [5,2] => 10 => 10
[-6,2,-5,7,1,8,3,4] => [7,1] => 11 => 11
[-4,6,7,8,1,2,3,5] => [2,2] => 00 => 00
[1,6,7,-3,2,8,4,5] => [4,1] => 01 => 01
[5,1,7,8,2,-4,3,6] => [3,2] => 10 => 10
[-6,2,-4,1,7,8,3,5] => [7,1] => 11 => 11
[2,-7,8,-6,3,-4,1,5] => [3,2] => 10 => 10
[-7,2,-3,8,4,5,-6,1] => [6,1] => 01 => 01
[-7,2,4,8,-6,-3,1,5] => [5,1] => 11 => 11
[6,2,-3,1,7,8,4,5] => [6,1] => 01 => 01
[-7,2,-3,8,1,-5,4,6] => [6,1] => 01 => 01
[2,-4,-3,-7,1,8,5,6] => [5,2] => 10 => 10
[3,4,1,-7,2,8,5,6] => [2,2] => 00 => 00
[-2,1,-4,-7,3,8,5,6] => [4,2] => 00 => 00
[3,4,1,2,6,-8,-7,5] => [2,2] => 00 => 00
[-7,2,-3,8,5,1,-6,4] => [3,2,1,1] => 1011 => 1011
[-7,2,-3,8,-6,5,1,4] => [2,1] => 01 => 01
[2,-8,5,4,-3,-7,-6,1] => [2,1] => 01 => 01
[5,2,-8,3,-7,-4,-6,1] => [7,1] => 11 => 11
[2,-7,8,-6,5,1,-4,3] => [2,1] => 01 => 01
[6,2,-8,-5,1,-4,-7,3] => [4,1] => 01 => 01
[-2,-7,1,8,5,3,-6,4] => [2,1] => 01 => 01
[7,8,1,-3,5,2,-6,4] => [7,1] => 11 => 11
[1,6,7,8,4,2,-5,3] => [2,1] => 01 => 01
[1,6,7,8,-5,4,2,3] => [6,1] => 01 => 01
[-2,-7,1,8,-6,5,3,4] => [4,2] => 00 => 00
[-2,1,5,4,-8,-7,-6,3] => [2,1] => 01 => 01
[5,-8,1,4,-3,-7,-6,2] => [2,1] => 01 => 01
[7,8,4,3,1,-6,-5,2] => [2,2] => 00 => 00
[7,8,4,-6,3,1,-5,2] => [6,2] => 00 => 00
[7,8,4,-6,-5,3,1,2] => [2,2] => 00 => 00
[4,3,2,-8,-7,-6,-5,1] => [2,2] => 00 => 00
[4,2,-6,-3,-5,1] => [4,1] => 01 => 01
[-5,2,-3,-4,-6,1] => [3,1] => 11 => 11
[5,2,-4,-3,-6,1] => [2,1] => 01 => 01
[6,-4,2,-3,-5,1] => [3,2] => 10 => 10
[6,-2,3,-4,-5,1] => [2,1] => 01 => 01
[5,6,3,-2,-4,1] => [5,1] => 11 => 11
[1,3,-4,-6,-5,2] => [4,1] => 01 => 01
[1,3,-5,-4,-6,2] => [4,1] => 01 => 01
[1,-6,3,-4,-5,2] => [1,1] => 11 => 11
[1,6,3,-5,-4,2] => [2,2,1,1] => 0011 => 0011
[1,6,4,-3,-5,2] => [2,1] => 01 => 01
[1,3,-5,6,-4,2] => [5,1] => 11 => 11
[1,2,4,-6,-5,3] => [1,1] => 11 => 11
[2,-4,-3,-5,1,6] => [4,1] => 01 => 01
[5,3,-2,-4,1,6] => [2,1] => 01 => 01
[1,3,-5,-4,2,6] => [1,1] => 11 => 11
[-2,-5,-3,6,1,4] => [3,2] => 10 => 10
[5,-4,3,1,-6,2] => [5,1] => 11 => 11
[-2,-5,-3,6,1,4,-8,7] => [3,2] => 10 => 10
[-2,-5,4,-7,-3,8,1,6] => [6,2] => 00 => 00
[-2,-5,-3,4,6,-7,-8,1] => [6,1] => 01 => 01
[4,5,2,-7,3,8,1,6] => [3,2] => 10 => 10
[5,-4,3,1,-6,2,-8,7] => [5,1] => 11 => 11
[-2,-3,-4,-7,-5,8,1,6] => [5,2] => 10 => 10
[-7,-6,4,3,1,8,2,5] => [6,2] => 00 => 00
[5,-4,3,-7,1,8,2,6] => [3,2,2,1] => 1001 => 0101
[-5,4,1,-7,-3,8,2,6] => [3,2] => 10 => 10
[-2,1,-4,-7,-5,8,3,6] => [3,2] => 10 => 10
[-4,5,3,1,6,-7,-8,2] => [5,1] => 11 => 11
[-3,-4,-8,7,5,1,-6,2] => [7,1] => 11 => 11
[-6,-8,4,3,-7,5,1,2] => [4,2] => 00 => 00
[-5,6,3,4,2,-7,-8,1] => [1,1] => 11 => 11
[7,-6,3,1,-8,5,-4,2] => [4,1] => 01 => 01
[6,1,8,4,-7,-3,2,5] => [7,1] => 11 => 11
[-8,-6,3,1,-7,-4,2,5] => [7,1] => 11 => 11
[5,6,3,8,-7,1,2,4] => [2,1] => 01 => 01
[7,-6,5,8,3,1,2,4] => [2,2] => 00 => 00
[2,5,6,8,-7,3,1,4] => [2,2] => 00 => 00
[-4,-6,7,2,1,8,3,5] => [6,2] => 00 => 00
[-6,2,7,-4,3,5,-8,1] => [6,1] => 01 => 01
[-6,2,-3,7,4,5,-8,1] => [6,1] => 01 => 01
[-2,-3,-4,-7,1,8,5,6] => [6,2] => 00 => 00
[3,4,1,2,-6,-7,-8,5] => [2,2] => 00 => 00
[-2,-7,-3,-6,5,1,-8,4] => [6,1] => 01 => 01
[7,-8,-4,2,5,1,-6,3] => [4,1] => 01 => 01
[6,2,-7,-4,1,-5,-8,3] => [3,1] => 11 => 11
[-2,-7,1,-6,5,3,-8,4] => [7,1] => 11 => 11
[8,7,1,5,-6,2,-4,3] => [5,3] => 11 => 11
[5,6,7,1,4,2,-8,3] => [3,2] => 10 => 10
[-8,5,6,-7,2,4,1,3] => [6,2] => 00 => 00
[6,4,-5,2,3,-7,-8,1] => [4,2] => 00 => 00
[-5,-6,3,1,-4,-7,-8,2] => [3,1] => 11 => 11
[-2,-3,5,1,4,6] => [5,1] => 11 => 11
[-4,-2,5,1,3,6] => [2,1] => 01 => 01
[-5,2,4,1,3,6] => [1,1] => 11 => 11
[-2,-3,1,6,4,5] => [3,3] => 11 => 11
[5,-2,1,6,3,4] => [3,2] => 10 => 10
[6,2,-3,5,1,4] => [4,1] => 01 => 01
[-4,6,3,5,1,2] => [2,1] => 01 => 01
[2,-5,6,4,1,3] => [2,1] => 01 => 01
[5,-6,2,4,1,3] => [2,1] => 01 => 01
[2,1,5,3,6,-4] => [2] => 0 => 0
[2,5,3,1,6,-4] => [1] => 1 => 1
[2,1,5,6,3,-4] => [2,2] => 00 => 00
[2,5,1,6,3,-4] => [4] => 0 => 0
[5,2,1,6,3,-4] => [3,1] => 11 => 11
[5,2,6,1,3,-4] => [1] => 1 => 1
[2,5,3,6,1,-4] => [3,1] => 11 => 11
[2,5,6,3,1,-4] => [3] => 1 => 1
[3,1,6,4,2,-5] => [1] => 1 => 1
[3,6,1,4,2,-5] => [2,1] => 01 => 01
[6,3,1,4,2,-5] => [1] => 1 => 1
[3,6,4,1,2,-5] => [3] => 1 => 1
[3,2,1,6,4,-5] => [2,1] => 01 => 01
[3,2,6,4,1,-5] => [1,1] => 11 => 11
[3,6,2,4,1,-5] => [1] => 1 => 1
[1,6,4,5,3,-2] => [3,1] => 11 => 11
[1,2,4,5,3,-6] => [3,1,1] => 111 => 111
[1,3,4,2,6,-5] => [3,1] => 11 => 11
[1,3,4,2,5,-6] => [3,1,1] => 111 => 111
[1,3,4,5,2,-6] => [4,1] => 01 => 01
[1,3,5,4,2,-6] => [3,1,1] => 111 => 111
[1,4,3,5,2,-6] => [3,1,1] => 111 => 111
[1,5,3,4,2,-6] => [2,1,1,1] => 0111 => 0111
[2,1,4,5,3,-6] => [3,2] => 10 => 10
[2,3,1,6,5,-4] => [3,1] => 11 => 11
[2,3,1,5,4,-6] => [3,2] => 10 => 10
[2,3,5,4,1,-6] => [4,1] => 01 => 01
[2,4,3,1,6,-5] => [3,1] => 11 => 11
[2,4,3,1,5,-6] => [3,1,1] => 111 => 111
[2,4,3,5,1,-6] => [4,1] => 01 => 01
[2,5,3,4,1,-6] => [3,1,1] => 111 => 111
[2,5,4,3,1,-6] => [3,2] => 10 => 10
[5,2,4,3,1,-6] => [2,2,1] => 001 => 001
Map
even cycle type
Description
The partition corresponding to the even cycles.
A cycle of length $\ell$ of a signed permutation $\pi$ can be written in two line notation as
$$\begin{array}{cccc} a_1 & a_2 & \dots & a_\ell \\ \pi(a_1) & \pi(a_2) & \dots & \pi(a_\ell) \end{array}$$
where $a_i > 0$ for all $i$, $a_{i+1} = |\pi(a_i)|$ for $i < \ell$ and $a_1 = |\pi(a_\ell)|$.
The cycle is even, if the number of negative elements in the second row is even.
This map records the integer partition given by the lengths of the odd cycles.
The integer partition of even cycles together with the integer partition of the odd cycles determines the conjugacy class of the signed permutation.
A cycle of length $\ell$ of a signed permutation $\pi$ can be written in two line notation as
$$\begin{array}{cccc} a_1 & a_2 & \dots & a_\ell \\ \pi(a_1) & \pi(a_2) & \dots & \pi(a_\ell) \end{array}$$
where $a_i > 0$ for all $i$, $a_{i+1} = |\pi(a_i)|$ for $i < \ell$ and $a_1 = |\pi(a_\ell)|$.
The cycle is even, if the number of negative elements in the second row is even.
This map records the integer partition given by the lengths of the odd cycles.
The integer partition of even cycles together with the integer partition of the odd cycles determines the conjugacy class of the signed permutation.
Map
odd parts
Description
Return the binary word indicating which parts of the partition are odd.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.
See Mp00096Foata bijection.
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