Identifier
Values
[1,0,1,0] => [1,2] => [2,1] => [2,1] => 0
[1,1,0,0] => [2,1] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [1,2,3] => [3,2,1] => [3,2,1] => 0
[1,0,1,1,0,0] => [1,3,2] => [2,3,1] => [1,3,2] => 0
[1,1,0,0,1,0] => [2,1,3] => [3,1,2] => [3,1,2] => 0
[1,1,0,1,0,0] => [2,3,1] => [1,3,2] => [1,3,2] => 0
[1,1,1,0,0,0] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [3,4,2,1] => [1,4,3,2] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [4,2,3,1] => [4,1,3,2] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,3,1] => [1,4,3,2] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,3,4,1] => [1,2,4,3] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [4,3,1,2] => [4,3,1,2] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,4,1,2] => [2,4,1,3] => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [4,1,3,2] => [4,1,3,2] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,4,3,2] => [1,4,3,2] => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,3,4,2] => [1,2,4,3] => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [4,1,2,3] => [4,1,2,3] => 0
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,4,2,3] => [1,4,2,3] => 0
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [1,2,4,3] => [1,2,4,3] => 0
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [4,5,3,2,1] => [1,5,4,3,2] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [5,3,4,2,1] => [5,1,4,3,2] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,5,4,2,1] => [1,5,4,3,2] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,4,5,2,1] => [1,2,5,4,3] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [5,4,2,3,1] => [5,4,1,3,2] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [4,5,2,3,1] => [2,5,1,4,3] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [5,2,4,3,1] => [5,1,4,3,2] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,5,4,3,1] => [1,5,4,3,2] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [2,4,5,3,1] => [1,2,5,4,3] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [5,2,3,4,1] => [5,1,2,4,3] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [2,5,3,4,1] => [1,5,2,4,3] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [2,3,5,4,1] => [1,2,5,4,3] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,3,4,5,1] => [1,2,3,5,4] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [5,4,3,1,2] => [5,4,3,1,2] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [4,5,3,1,2] => [2,5,4,1,3] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [5,3,4,1,2] => [5,2,4,1,3] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,5,4,1,2] => [2,5,4,1,3] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [3,4,5,1,2] => [1,3,5,2,4] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [5,4,1,3,2] => [5,4,1,3,2] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [4,5,1,3,2] => [2,5,1,4,3] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [5,1,4,3,2] => [5,1,4,3,2] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,5,4,3,2] => [1,5,4,3,2] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,4,5,3,2] => [1,2,5,4,3] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [5,1,3,4,2] => [5,1,2,4,3] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,5,3,4,2] => [1,5,2,4,3] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [1,3,5,4,2] => [1,2,5,4,3] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,3,4,5,2] => [1,2,3,5,4] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [5,4,1,2,3] => [5,4,1,2,3] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [4,5,1,2,3] => [3,5,1,2,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [5,1,4,2,3] => [5,1,4,2,3] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,5,4,2,3] => [1,5,4,2,3] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,4,5,2,3] => [1,3,5,2,4] => 1
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [5,1,2,4,3] => [5,1,2,4,3] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [1,5,2,4,3] => [1,5,2,4,3] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [1,2,4,5,3] => [1,2,3,5,4] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [5,1,2,3,4] => [5,1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => [1,6,5,4,3,2] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => [6,1,5,4,3,2] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [4,6,5,3,2,1] => [1,6,5,4,3,2] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [4,5,6,3,2,1] => [1,2,6,5,4,3] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => [6,5,1,4,3,2] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => [2,6,1,5,4,3] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [6,3,5,4,2,1] => [6,1,5,4,3,2] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [3,6,5,4,2,1] => [1,6,5,4,3,2] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,5,6,4,2,1] => [1,2,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [6,3,4,5,2,1] => [6,1,2,5,4,3] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,6,4,5,2,1] => [1,6,2,5,4,3] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [3,4,6,5,2,1] => [1,2,6,5,4,3] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [3,4,5,6,2,1] => [1,2,3,6,5,4] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => [6,5,4,1,3,2] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => [2,6,5,1,4,3] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => [6,2,5,1,4,3] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [4,6,5,2,3,1] => [2,6,5,1,4,3] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [4,5,6,2,3,1] => [1,3,6,2,5,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [6,5,2,4,3,1] => [6,5,1,4,3,2] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [5,6,2,4,3,1] => [2,6,1,5,4,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [6,2,5,4,3,1] => [6,1,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,6,5,4,3,1] => [1,6,5,4,3,2] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [2,5,6,4,3,1] => [1,2,6,5,4,3] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [6,2,4,5,3,1] => [6,1,2,5,4,3] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [2,6,4,5,3,1] => [1,6,2,5,4,3] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [2,4,6,5,3,1] => [1,2,6,5,4,3] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [2,4,5,6,3,1] => [1,2,3,6,5,4] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [6,5,2,3,4,1] => [6,5,1,2,4,3] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [5,6,2,3,4,1] => [3,6,1,2,5,4] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [6,2,5,3,4,1] => [6,1,5,2,4,3] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [2,6,5,3,4,1] => [1,6,5,2,4,3] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [2,5,6,3,4,1] => [1,3,6,2,5,4] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [6,2,3,5,4,1] => [6,1,2,5,4,3] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [2,6,3,5,4,1] => [1,6,2,5,4,3] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [2,3,6,5,4,1] => [1,2,6,5,4,3] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [2,3,5,6,4,1] => [1,2,3,6,5,4] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [6,2,3,4,5,1] => [6,1,2,3,5,4] => 0
>>> Load all 341 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [2,6,3,4,5,1] => [1,6,2,3,5,4] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [2,3,6,4,5,1] => [1,2,6,3,5,4] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [2,3,4,6,5,1] => [1,2,3,6,5,4] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,3,4,5,6,1] => [1,2,3,4,6,5] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => [6,5,4,3,1,2] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => [2,6,5,4,1,3] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => [6,2,5,4,1,3] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [4,6,5,3,1,2] => [2,6,5,4,1,3] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [4,5,6,3,1,2] => [1,3,6,5,2,4] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => [6,5,2,4,1,3] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [3,6,2,5,1,4] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [6,3,5,4,1,2] => [6,2,5,4,1,3] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [3,6,5,4,1,2] => [2,6,5,4,1,3] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,5,6,4,1,2] => [1,3,6,5,2,4] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [6,3,4,5,1,2] => [6,1,3,5,2,4] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,6,4,5,1,2] => [1,6,3,5,2,4] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [3,4,6,5,1,2] => [1,3,6,5,2,4] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => [1,2,4,6,3,5] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => [6,5,4,1,3,2] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [5,6,4,1,3,2] => [2,6,5,1,4,3] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [6,4,5,1,3,2] => [6,2,5,1,4,3] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,6,5,1,3,2] => [2,6,5,1,4,3] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [4,5,6,1,3,2] => [1,3,6,2,5,4] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [5,6,1,4,3,2] => [2,6,1,5,4,3] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => [6,1,5,4,3,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,5,6,4,3,2] => [1,2,6,5,4,3] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [6,1,4,5,3,2] => [6,1,2,5,4,3] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,6,4,5,3,2] => [1,6,2,5,4,3] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [1,4,6,5,3,2] => [1,2,6,5,4,3] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,4,5,6,3,2] => [1,2,3,6,5,4] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [6,5,1,3,4,2] => [6,5,1,2,4,3] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [5,6,1,3,4,2] => [3,6,1,2,5,4] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [6,1,5,3,4,2] => [6,1,5,2,4,3] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,6,5,3,4,2] => [1,6,5,2,4,3] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,5,6,3,4,2] => [1,3,6,2,5,4] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [6,1,3,5,4,2] => [6,1,2,5,4,3] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [1,6,3,5,4,2] => [1,6,2,5,4,3] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [1,3,6,5,4,2] => [1,2,6,5,4,3] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [1,3,5,6,4,2] => [1,2,3,6,5,4] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [6,1,3,4,5,2] => [6,1,2,3,5,4] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,6,3,4,5,2] => [1,6,2,3,5,4] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [1,3,6,4,5,2] => [1,2,6,3,5,4] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [1,3,4,6,5,2] => [1,2,3,6,5,4] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,3,4,5,6,2] => [1,2,3,4,6,5] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => [6,5,4,1,2,3] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [5,6,4,1,2,3] => [3,6,5,1,2,4] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [6,4,5,1,2,3] => [6,3,5,1,2,4] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [4,6,5,1,2,3] => [3,6,5,1,2,4] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [4,5,6,1,2,3] => [2,4,6,1,3,5] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => [6,5,1,4,2,3] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [5,6,1,4,2,3] => [3,6,1,5,2,4] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => [6,1,5,4,2,3] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => [1,6,5,4,2,3] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,5,6,4,2,3] => [1,3,6,5,2,4] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [6,1,4,5,2,3] => [6,1,3,5,2,4] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,6,4,5,2,3] => [1,6,3,5,2,4] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [1,4,6,5,2,3] => [1,3,6,5,2,4] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,4,5,6,2,3] => [1,2,4,6,3,5] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => [6,5,1,2,4,3] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [5,6,1,2,4,3] => [3,6,1,2,5,4] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => [6,1,5,2,4,3] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => [1,6,5,2,4,3] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [1,5,6,2,4,3] => [1,3,6,2,5,4] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => [6,1,2,5,4,3] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => [1,6,2,5,4,3] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [1,2,5,6,4,3] => [1,2,3,6,5,4] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [6,1,2,4,5,3] => [6,1,2,3,5,4] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [1,6,2,4,5,3] => [1,6,2,3,5,4] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [1,2,6,4,5,3] => [1,2,6,3,5,4] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [1,2,4,6,5,3] => [1,2,3,6,5,4] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [1,2,4,5,6,3] => [1,2,3,4,6,5] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => [6,5,1,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [5,6,1,2,3,4] => [4,6,1,2,3,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => [6,1,5,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => [1,6,5,2,3,4] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,5,6,2,3,4] => [1,4,6,2,3,5] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => [6,1,2,5,3,4] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => [1,6,2,5,3,4] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => [1,2,6,5,3,4] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [1,2,5,6,3,4] => [1,2,4,6,3,5] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => [6,1,2,3,5,4] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => [1,6,2,3,5,4] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => [1,2,6,3,5,4] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [1,2,3,5,6,4] => [1,2,3,4,6,5] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [4,6,7,5,3,2,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [4,5,7,6,3,2,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => [1,3,7,2,6,5,4] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [3,6,7,5,4,2,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [3,5,7,6,4,2,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [3,5,6,7,4,2,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [3,6,7,4,5,2,1] => [1,3,7,2,6,5,4] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [3,4,7,6,5,2,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [3,4,6,7,5,2,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [3,4,7,5,6,2,1] => [1,2,7,3,6,5,4] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [3,4,5,7,6,2,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [3,4,5,6,7,2,1] => [1,2,3,4,7,6,5] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [5,6,7,4,2,3,1] => [1,3,7,6,2,5,4] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [4,6,7,5,2,3,1] => [1,3,7,6,2,5,4] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [4,5,7,6,2,3,1] => [1,3,7,6,2,5,4] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [4,5,6,7,2,3,1] => [1,2,4,7,3,6,5] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [5,6,7,2,4,3,1] => [1,3,7,2,6,5,4] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [2,6,7,5,4,3,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [2,5,7,6,4,3,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [2,5,6,7,4,3,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [2,6,7,4,5,3,1] => [1,3,7,2,6,5,4] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [2,4,7,6,5,3,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [2,4,6,7,5,3,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [2,4,7,5,6,3,1] => [1,2,7,3,6,5,4] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [2,4,5,7,6,3,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [2,4,5,6,7,3,1] => [1,2,3,4,7,6,5] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [2,6,7,5,3,4,1] => [1,3,7,6,2,5,4] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [2,5,7,6,3,4,1] => [1,3,7,6,2,5,4] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [2,5,6,7,3,4,1] => [1,2,4,7,3,6,5] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [2,6,7,3,5,4,1] => [1,3,7,2,6,5,4] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [2,3,7,6,5,4,1] => [1,2,7,6,5,4,3] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [2,3,6,7,5,4,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [2,3,7,5,6,4,1] => [1,2,7,3,6,5,4] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [2,3,5,7,6,4,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [2,3,5,6,7,4,1] => [1,2,3,4,7,6,5] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [2,3,7,6,4,5,1] => [1,2,7,6,3,5,4] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [2,3,6,7,4,5,1] => [1,2,4,7,3,6,5] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [2,3,7,4,6,5,1] => [1,2,7,3,6,5,4] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [2,3,4,7,6,5,1] => [1,2,3,7,6,5,4] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [2,3,4,6,7,5,1] => [1,2,3,4,7,6,5] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [2,3,7,4,5,6,1] => [1,2,7,3,4,6,5] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [2,3,4,7,5,6,1] => [1,2,3,7,4,6,5] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [2,3,4,5,7,6,1] => [1,2,3,4,7,6,5] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,3,4,5,6,7,1] => [1,2,3,4,5,7,6] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [5,6,7,4,3,1,2] => [1,3,7,6,5,2,4] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [4,6,7,5,3,1,2] => [1,3,7,6,5,2,4] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [4,5,7,6,3,1,2] => [1,3,7,6,5,2,4] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [4,5,6,7,3,1,2] => [1,2,4,7,6,3,5] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [3,6,7,5,4,1,2] => [1,3,7,6,5,2,4] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [3,5,7,6,4,1,2] => [1,3,7,6,5,2,4] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [3,5,6,7,4,1,2] => [1,2,4,7,6,3,5] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [3,4,7,6,5,1,2] => [1,3,7,6,5,2,4] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [3,4,6,7,5,1,2] => [1,2,4,7,6,3,5] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [3,4,7,5,6,1,2] => [1,2,7,4,6,3,5] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [3,4,5,7,6,1,2] => [1,2,4,7,6,3,5] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [3,4,5,6,7,1,2] => [1,2,3,5,7,4,6] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [5,6,7,4,1,3,2] => [1,3,7,6,2,5,4] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [4,6,7,5,1,3,2] => [1,3,7,6,2,5,4] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [4,5,7,6,1,3,2] => [1,3,7,6,2,5,4] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [4,5,6,7,1,3,2] => [1,2,4,7,3,6,5] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [5,6,7,1,4,3,2] => [1,3,7,2,6,5,4] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [1,6,7,5,4,3,2] => [1,2,7,6,5,4,3] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [1,5,7,6,4,3,2] => [1,2,7,6,5,4,3] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [1,5,6,7,4,3,2] => [1,2,3,7,6,5,4] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [1,6,7,4,5,3,2] => [1,3,7,2,6,5,4] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [1,4,7,6,5,3,2] => [1,2,7,6,5,4,3] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [1,4,6,7,5,3,2] => [1,2,3,7,6,5,4] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [1,4,7,5,6,3,2] => [1,2,7,3,6,5,4] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [1,4,5,7,6,3,2] => [1,2,3,7,6,5,4] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [1,4,5,6,7,3,2] => [1,2,3,4,7,6,5] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [1,6,7,5,3,4,2] => [1,3,7,6,2,5,4] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [1,5,7,6,3,4,2] => [1,3,7,6,2,5,4] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [1,5,6,7,3,4,2] => [1,2,4,7,3,6,5] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [1,6,7,3,5,4,2] => [1,3,7,2,6,5,4] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [1,3,7,6,5,4,2] => [1,2,7,6,5,4,3] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [1,3,6,7,5,4,2] => [1,2,3,7,6,5,4] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [1,3,7,5,6,4,2] => [1,2,7,3,6,5,4] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [1,3,5,7,6,4,2] => [1,2,3,7,6,5,4] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [1,3,5,6,7,4,2] => [1,2,3,4,7,6,5] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [1,3,7,6,4,5,2] => [1,2,7,6,3,5,4] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [1,3,6,7,4,5,2] => [1,2,4,7,3,6,5] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [1,3,7,4,6,5,2] => [1,2,7,3,6,5,4] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [1,3,4,7,6,5,2] => [1,2,3,7,6,5,4] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [1,3,4,6,7,5,2] => [1,2,3,4,7,6,5] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [1,3,7,4,5,6,2] => [1,2,7,3,4,6,5] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [1,3,4,7,5,6,2] => [1,2,3,7,4,6,5] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [1,3,4,5,7,6,2] => [1,2,3,4,7,6,5] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [1,3,4,5,6,7,2] => [1,2,3,4,5,7,6] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [4,5,6,7,1,2,3] => [1,3,5,7,2,4,6] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [1,6,7,5,4,2,3] => [1,3,7,6,5,2,4] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [1,5,7,6,4,2,3] => [1,3,7,6,5,2,4] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [1,5,6,7,4,2,3] => [1,2,4,7,6,3,5] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [1,4,7,6,5,2,3] => [1,3,7,6,5,2,4] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [1,4,6,7,5,2,3] => [1,2,4,7,6,3,5] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [1,4,7,5,6,2,3] => [1,2,7,4,6,3,5] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [1,4,5,7,6,2,3] => [1,2,4,7,6,3,5] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [1,4,5,6,7,2,3] => [1,2,3,5,7,4,6] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [1,6,7,5,2,4,3] => [1,3,7,6,2,5,4] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [1,5,7,6,2,4,3] => [1,3,7,6,2,5,4] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [1,5,6,7,2,4,3] => [1,2,4,7,3,6,5] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [1,6,7,2,5,4,3] => [1,3,7,2,6,5,4] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [1,2,6,7,5,4,3] => [1,2,3,7,6,5,4] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [1,2,7,5,6,4,3] => [1,2,7,3,6,5,4] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [1,2,5,7,6,4,3] => [1,2,3,7,6,5,4] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [1,2,5,6,7,4,3] => [1,2,3,4,7,6,5] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [1,2,7,6,4,5,3] => [1,2,7,6,3,5,4] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [1,2,6,7,4,5,3] => [1,2,4,7,3,6,5] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [1,2,7,4,6,5,3] => [1,2,7,3,6,5,4] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [1,2,4,7,6,5,3] => [1,2,3,7,6,5,4] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [1,2,4,6,7,5,3] => [1,2,3,4,7,6,5] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [1,2,7,4,5,6,3] => [1,2,7,3,4,6,5] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [1,2,4,7,5,6,3] => [1,2,3,7,4,6,5] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [1,2,4,5,7,6,3] => [1,2,3,4,7,6,5] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [1,2,4,5,6,7,3] => [1,2,3,4,5,7,6] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [1,5,6,7,2,3,4] => [1,3,5,7,2,4,6] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => [1,2,7,6,5,3,4] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [1,2,6,7,5,3,4] => [1,2,4,7,6,3,5] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [1,2,7,5,6,3,4] => [1,2,7,4,6,3,5] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [1,2,5,7,6,3,4] => [1,2,4,7,6,3,5] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [1,2,5,6,7,3,4] => [1,2,3,5,7,4,6] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => [1,2,7,6,3,5,4] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [1,2,6,7,3,5,4] => [1,2,4,7,3,6,5] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => [1,2,7,3,6,5,4] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [1,2,3,6,7,5,4] => [1,2,3,4,7,6,5] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [1,2,7,3,5,6,4] => [1,2,7,3,4,6,5] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [1,2,3,7,5,6,4] => [1,2,3,7,4,6,5] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [1,2,3,5,7,6,4] => [1,2,3,4,7,6,5] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [1,2,3,5,6,7,4] => [1,2,3,4,5,7,6] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [1,2,6,7,3,4,5] => [1,2,5,7,3,4,6] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => [1,2,3,7,6,4,5] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [1,2,3,6,7,4,5] => [1,2,3,5,7,4,6] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => [1,2,7,3,4,6,5] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => [1,2,3,7,4,6,5] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [1,2,3,4,6,7,5] => [1,2,3,4,5,7,6] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
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Description
The tier of a permutation.
This is the number of elements $i$ such that $[i+1,k,i]$ is an occurrence of the pattern $[2,3,1]$. For example, $[3,5,6,1,2,4]$ has tier $2$, with witnesses $[3,5,2]$ (or $[3,6,2]$) and $[5,6,4]$.
According to [1], this is the number of passes minus one needed to sort the permutation using a single stack. The generating function for this statistic appears as OEIS:A122890 and OEIS:A158830 in the form of triangles read by rows, see [sec. 4, 1].
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..