Identifier
-
Mp00277:
Permutations
—catalanization⟶
Permutations
St000036: Permutations ⟶ ℤ
Values
[1] => [1] => 1
[1,2] => [1,2] => 1
[2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => 1
[1,3,2] => [1,3,2] => 1
[2,1,3] => [2,1,3] => 1
[2,3,1] => [2,3,1] => 1
[3,1,2] => [2,3,1] => 1
[3,2,1] => [3,2,1] => 1
[1,2,3,4] => [1,2,3,4] => 1
[1,2,4,3] => [1,2,4,3] => 1
[1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2] => [1,3,4,2] => 1
[1,4,2,3] => [1,3,4,2] => 1
[1,4,3,2] => [1,4,3,2] => 1
[2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => [2,1,4,3] => 1
[2,3,1,4] => [2,3,1,4] => 1
[2,3,4,1] => [2,3,4,1] => 1
[2,4,1,3] => [4,3,1,2] => 1
[2,4,3,1] => [2,4,3,1] => 1
[3,1,2,4] => [2,3,1,4] => 1
[3,1,4,2] => [2,3,4,1] => 1
[3,2,1,4] => [3,2,1,4] => 1
[3,2,4,1] => [3,2,4,1] => 1
[3,4,1,2] => [4,3,2,1] => 1
[3,4,2,1] => [3,4,2,1] => 1
[4,1,2,3] => [2,3,4,1] => 1
[4,1,3,2] => [2,4,3,1] => 1
[4,2,1,3] => [3,2,4,1] => 1
[4,2,3,1] => [3,4,2,1] => 1
[4,3,1,2] => [3,4,2,1] => 1
[4,3,2,1] => [4,3,2,1] => 1
[1,2,3,4,5] => [1,2,3,4,5] => 1
[1,2,3,5,4] => [1,2,3,5,4] => 1
[1,2,4,3,5] => [1,2,4,3,5] => 1
[1,2,4,5,3] => [1,2,4,5,3] => 1
[1,2,5,3,4] => [1,2,4,5,3] => 1
[1,2,5,4,3] => [1,2,5,4,3] => 1
[1,3,2,4,5] => [1,3,2,4,5] => 1
[1,3,2,5,4] => [1,3,2,5,4] => 1
[1,3,4,2,5] => [1,3,4,2,5] => 1
[1,3,4,5,2] => [1,3,4,5,2] => 1
[1,3,5,2,4] => [1,5,4,2,3] => 1
[1,3,5,4,2] => [1,3,5,4,2] => 1
[1,4,2,3,5] => [1,3,4,2,5] => 1
[1,4,2,5,3] => [1,3,4,5,2] => 1
[1,4,3,2,5] => [1,4,3,2,5] => 1
[1,4,3,5,2] => [1,4,3,5,2] => 1
[1,4,5,2,3] => [1,5,4,3,2] => 1
[1,4,5,3,2] => [1,4,5,3,2] => 1
[1,5,2,3,4] => [1,3,4,5,2] => 1
[1,5,2,4,3] => [1,3,5,4,2] => 1
[1,5,3,2,4] => [1,4,3,5,2] => 1
[1,5,3,4,2] => [1,4,5,3,2] => 1
[1,5,4,2,3] => [1,4,5,3,2] => 1
[1,5,4,3,2] => [1,5,4,3,2] => 1
[2,1,3,4,5] => [2,1,3,4,5] => 1
[2,1,3,5,4] => [2,1,3,5,4] => 1
[2,1,4,3,5] => [2,1,4,3,5] => 1
[2,1,4,5,3] => [2,1,4,5,3] => 1
[2,1,5,3,4] => [2,1,4,5,3] => 1
[2,1,5,4,3] => [2,1,5,4,3] => 1
[2,3,1,4,5] => [2,3,1,4,5] => 1
[2,3,1,5,4] => [2,3,1,5,4] => 1
[2,3,4,1,5] => [2,3,4,1,5] => 1
[2,3,4,5,1] => [2,3,4,5,1] => 1
[2,3,5,1,4] => [2,5,4,1,3] => 1
[2,3,5,4,1] => [2,3,5,4,1] => 1
[2,4,1,3,5] => [4,3,1,2,5] => 1
[2,4,1,5,3] => [4,3,1,5,2] => 1
[2,4,3,1,5] => [2,4,3,1,5] => 1
[2,4,3,5,1] => [2,4,3,5,1] => 1
[2,4,5,1,3] => [3,5,4,1,2] => 2
[2,4,5,3,1] => [2,4,5,3,1] => 1
[2,5,1,3,4] => [4,3,1,5,2] => 1
[2,5,1,4,3] => [5,3,1,4,2] => 2
[2,5,3,1,4] => [5,4,3,1,2] => 1
[2,5,3,4,1] => [2,4,5,3,1] => 1
[2,5,4,1,3] => [3,4,5,1,2] => 3
[2,5,4,3,1] => [2,5,4,3,1] => 1
[3,1,2,4,5] => [2,3,1,4,5] => 1
[3,1,2,5,4] => [2,3,1,5,4] => 1
[3,1,4,2,5] => [2,3,4,1,5] => 1
[3,1,4,5,2] => [2,3,4,5,1] => 1
[3,1,5,2,4] => [2,5,4,1,3] => 1
[3,1,5,4,2] => [2,3,5,4,1] => 1
[3,2,1,4,5] => [3,2,1,4,5] => 1
[3,2,1,5,4] => [3,2,1,5,4] => 1
[3,2,4,1,5] => [3,2,4,1,5] => 1
[3,2,4,5,1] => [3,2,4,5,1] => 1
[3,2,5,1,4] => [5,2,4,1,3] => 2
[3,2,5,4,1] => [3,2,5,4,1] => 1
[3,4,1,2,5] => [4,3,2,1,5] => 1
[3,4,1,5,2] => [4,3,2,5,1] => 1
[3,4,2,1,5] => [3,4,2,1,5] => 1
[3,4,2,5,1] => [3,4,2,5,1] => 1
[3,4,5,1,2] => [3,5,4,2,1] => 1
[3,4,5,2,1] => [3,4,5,2,1] => 1
[3,5,1,2,4] => [4,3,5,1,2] => 2
[3,5,1,4,2] => [5,3,2,4,1] => 2
>>> Load all 1428 entries. <<<[3,5,2,1,4] => [3,4,5,1,2] => 3
[3,5,2,4,1] => [5,4,2,3,1] => 2
[3,5,4,1,2] => [3,4,5,2,1] => 1
[3,5,4,2,1] => [3,5,4,2,1] => 1
[4,1,2,3,5] => [2,3,4,1,5] => 1
[4,1,2,5,3] => [2,3,4,5,1] => 1
[4,1,3,2,5] => [2,4,3,1,5] => 1
[4,1,3,5,2] => [2,4,3,5,1] => 1
[4,1,5,2,3] => [2,5,4,3,1] => 1
[4,1,5,3,2] => [2,4,5,3,1] => 1
[4,2,1,3,5] => [3,2,4,1,5] => 1
[4,2,1,5,3] => [3,2,4,5,1] => 1
[4,2,3,1,5] => [3,4,2,1,5] => 1
[4,2,3,5,1] => [3,4,2,5,1] => 1
[4,2,5,1,3] => [5,2,4,3,1] => 2
[4,2,5,3,1] => [3,4,5,2,1] => 1
[4,3,1,2,5] => [3,4,2,1,5] => 1
[4,3,1,5,2] => [3,4,2,5,1] => 1
[4,3,2,1,5] => [4,3,2,1,5] => 1
[4,3,2,5,1] => [4,3,2,5,1] => 1
[4,3,5,1,2] => [5,3,4,2,1] => 2
[4,3,5,2,1] => [4,3,5,2,1] => 1
[4,5,1,2,3] => [4,3,5,2,1] => 1
[4,5,1,3,2] => [5,3,4,2,1] => 2
[4,5,2,1,3] => [3,4,5,2,1] => 1
[4,5,2,3,1] => [5,4,3,2,1] => 1
[4,5,3,1,2] => [5,4,3,2,1] => 1
[4,5,3,2,1] => [4,5,3,2,1] => 1
[5,1,2,3,4] => [2,3,4,5,1] => 1
[5,1,2,4,3] => [2,3,5,4,1] => 1
[5,1,3,2,4] => [2,4,3,5,1] => 1
[5,1,3,4,2] => [2,4,5,3,1] => 1
[5,1,4,2,3] => [2,4,5,3,1] => 1
[5,1,4,3,2] => [2,5,4,3,1] => 1
[5,2,1,3,4] => [3,2,4,5,1] => 1
[5,2,1,4,3] => [3,2,5,4,1] => 1
[5,2,3,1,4] => [3,4,2,5,1] => 1
[5,2,3,4,1] => [3,4,5,2,1] => 1
[5,2,4,1,3] => [5,4,2,3,1] => 2
[5,2,4,3,1] => [3,5,4,2,1] => 1
[5,3,1,2,4] => [3,4,2,5,1] => 1
[5,3,1,4,2] => [3,4,5,2,1] => 1
[5,3,2,1,4] => [4,3,2,5,1] => 1
[5,3,2,4,1] => [4,3,5,2,1] => 1
[5,3,4,1,2] => [5,4,3,2,1] => 1
[5,3,4,2,1] => [4,5,3,2,1] => 1
[5,4,1,2,3] => [3,4,5,2,1] => 1
[5,4,1,3,2] => [3,5,4,2,1] => 1
[5,4,2,1,3] => [4,3,5,2,1] => 1
[5,4,2,3,1] => [4,5,3,2,1] => 1
[5,4,3,1,2] => [4,5,3,2,1] => 1
[5,4,3,2,1] => [5,4,3,2,1] => 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
[1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => [1,2,3,5,6,4] => 1
[1,2,3,6,4,5] => [1,2,3,5,6,4] => 1
[1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => 1
[1,2,4,5,3,6] => [1,2,4,5,3,6] => 1
[1,2,4,5,6,3] => [1,2,4,5,6,3] => 1
[1,2,4,6,3,5] => [1,2,6,5,3,4] => 1
[1,2,4,6,5,3] => [1,2,4,6,5,3] => 1
[1,2,5,3,4,6] => [1,2,4,5,3,6] => 1
[1,2,5,3,6,4] => [1,2,4,5,6,3] => 1
[1,2,5,4,3,6] => [1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => [1,2,5,4,6,3] => 1
[1,2,5,6,3,4] => [1,2,6,5,4,3] => 1
[1,2,5,6,4,3] => [1,2,5,6,4,3] => 1
[1,2,6,3,4,5] => [1,2,4,5,6,3] => 1
[1,2,6,3,5,4] => [1,2,4,6,5,3] => 1
[1,2,6,4,3,5] => [1,2,5,4,6,3] => 1
[1,2,6,4,5,3] => [1,2,5,6,4,3] => 1
[1,2,6,5,3,4] => [1,2,5,6,4,3] => 1
[1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => 1
[1,3,2,5,4,6] => [1,3,2,5,4,6] => 1
[1,3,2,5,6,4] => [1,3,2,5,6,4] => 1
[1,3,2,6,4,5] => [1,3,2,5,6,4] => 1
[1,3,2,6,5,4] => [1,3,2,6,5,4] => 1
[1,3,4,2,5,6] => [1,3,4,2,5,6] => 1
[1,3,4,2,6,5] => [1,3,4,2,6,5] => 1
[1,3,4,5,2,6] => [1,3,4,5,2,6] => 1
[1,3,4,5,6,2] => [1,3,4,5,6,2] => 1
[1,3,4,6,2,5] => [1,3,6,5,2,4] => 1
[1,3,4,6,5,2] => [1,3,4,6,5,2] => 1
[1,3,5,2,4,6] => [1,5,4,2,3,6] => 1
[1,3,5,2,6,4] => [1,5,4,2,6,3] => 1
[1,3,5,4,2,6] => [1,3,5,4,2,6] => 1
[1,3,5,4,6,2] => [1,3,5,4,6,2] => 1
[1,3,5,6,2,4] => [1,4,6,5,2,3] => 2
[1,3,5,6,4,2] => [1,3,5,6,4,2] => 1
[1,3,6,2,4,5] => [1,5,4,2,6,3] => 1
[1,3,6,2,5,4] => [1,6,4,2,5,3] => 2
[1,3,6,4,2,5] => [1,6,5,4,2,3] => 1
[1,3,6,4,5,2] => [1,3,5,6,4,2] => 1
[1,3,6,5,2,4] => [1,4,5,6,2,3] => 3
[1,3,6,5,4,2] => [1,3,6,5,4,2] => 1
[1,4,2,3,5,6] => [1,3,4,2,5,6] => 1
[1,4,2,3,6,5] => [1,3,4,2,6,5] => 1
[1,4,2,5,3,6] => [1,3,4,5,2,6] => 1
[1,4,2,5,6,3] => [1,3,4,5,6,2] => 1
[1,4,2,6,3,5] => [1,3,6,5,2,4] => 1
[1,4,2,6,5,3] => [1,3,4,6,5,2] => 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => [1,4,3,2,6,5] => 1
[1,4,3,5,2,6] => [1,4,3,5,2,6] => 1
[1,4,3,5,6,2] => [1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => [1,6,3,5,2,4] => 2
[1,4,3,6,5,2] => [1,4,3,6,5,2] => 1
[1,4,5,2,3,6] => [1,5,4,3,2,6] => 1
[1,4,5,2,6,3] => [1,5,4,3,6,2] => 1
[1,4,5,3,2,6] => [1,4,5,3,2,6] => 1
[1,4,5,3,6,2] => [1,4,5,3,6,2] => 1
[1,4,5,6,2,3] => [1,4,6,5,3,2] => 1
[1,4,5,6,3,2] => [1,4,5,6,3,2] => 1
[1,4,6,2,3,5] => [1,5,4,6,2,3] => 2
[1,4,6,2,5,3] => [1,6,4,3,5,2] => 2
[1,4,6,3,2,5] => [1,4,5,6,2,3] => 3
[1,4,6,3,5,2] => [1,6,5,3,4,2] => 2
[1,4,6,5,2,3] => [1,4,5,6,3,2] => 1
[1,4,6,5,3,2] => [1,4,6,5,3,2] => 1
[1,5,2,3,4,6] => [1,3,4,5,2,6] => 1
[1,5,2,3,6,4] => [1,3,4,5,6,2] => 1
[1,5,2,4,3,6] => [1,3,5,4,2,6] => 1
[1,5,2,4,6,3] => [1,3,5,4,6,2] => 1
[1,5,2,6,3,4] => [1,3,6,5,4,2] => 1
[1,5,2,6,4,3] => [1,3,5,6,4,2] => 1
[1,5,3,2,4,6] => [1,4,3,5,2,6] => 1
[1,5,3,2,6,4] => [1,4,3,5,6,2] => 1
[1,5,3,4,2,6] => [1,4,5,3,2,6] => 1
[1,5,3,4,6,2] => [1,4,5,3,6,2] => 1
[1,5,3,6,2,4] => [1,6,3,5,4,2] => 2
[1,5,3,6,4,2] => [1,4,5,6,3,2] => 1
[1,5,4,2,3,6] => [1,4,5,3,2,6] => 1
[1,5,4,2,6,3] => [1,4,5,3,6,2] => 1
[1,5,4,3,2,6] => [1,5,4,3,2,6] => 1
[1,5,4,3,6,2] => [1,5,4,3,6,2] => 1
[1,5,4,6,2,3] => [1,6,4,5,3,2] => 2
[1,5,4,6,3,2] => [1,5,4,6,3,2] => 1
[1,5,6,2,3,4] => [1,5,4,6,3,2] => 1
[1,5,6,2,4,3] => [1,6,4,5,3,2] => 2
[1,5,6,3,2,4] => [1,4,5,6,3,2] => 1
[1,5,6,3,4,2] => [1,6,5,4,3,2] => 1
[1,5,6,4,2,3] => [1,6,5,4,3,2] => 1
[1,5,6,4,3,2] => [1,5,6,4,3,2] => 1
[1,6,2,3,4,5] => [1,3,4,5,6,2] => 1
[1,6,2,3,5,4] => [1,3,4,6,5,2] => 1
[1,6,2,4,3,5] => [1,3,5,4,6,2] => 1
[1,6,2,4,5,3] => [1,3,5,6,4,2] => 1
[1,6,2,5,3,4] => [1,3,5,6,4,2] => 1
[1,6,2,5,4,3] => [1,3,6,5,4,2] => 1
[1,6,3,2,4,5] => [1,4,3,5,6,2] => 1
[1,6,3,2,5,4] => [1,4,3,6,5,2] => 1
[1,6,3,4,2,5] => [1,4,5,3,6,2] => 1
[1,6,3,4,5,2] => [1,4,5,6,3,2] => 1
[1,6,3,5,2,4] => [1,6,5,3,4,2] => 2
[1,6,3,5,4,2] => [1,4,6,5,3,2] => 1
[1,6,4,2,3,5] => [1,4,5,3,6,2] => 1
[1,6,4,2,5,3] => [1,4,5,6,3,2] => 1
[1,6,4,3,2,5] => [1,5,4,3,6,2] => 1
[1,6,4,3,5,2] => [1,5,4,6,3,2] => 1
[1,6,4,5,2,3] => [1,6,5,4,3,2] => 1
[1,6,4,5,3,2] => [1,5,6,4,3,2] => 1
[1,6,5,2,3,4] => [1,4,5,6,3,2] => 1
[1,6,5,2,4,3] => [1,4,6,5,3,2] => 1
[1,6,5,3,2,4] => [1,5,4,6,3,2] => 1
[1,6,5,3,4,2] => [1,5,6,4,3,2] => 1
[1,6,5,4,2,3] => [1,5,6,4,3,2] => 1
[1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => 1
[2,1,3,5,4,6] => [2,1,3,5,4,6] => 1
[2,1,3,5,6,4] => [2,1,3,5,6,4] => 1
[2,1,3,6,4,5] => [2,1,3,5,6,4] => 1
[2,1,3,6,5,4] => [2,1,3,6,5,4] => 1
[2,1,4,3,5,6] => [2,1,4,3,5,6] => 1
[2,1,4,3,6,5] => [2,1,4,3,6,5] => 1
[2,1,4,5,3,6] => [2,1,4,5,3,6] => 1
[2,1,4,5,6,3] => [2,1,4,5,6,3] => 1
[2,1,4,6,3,5] => [2,1,6,5,3,4] => 1
[2,1,4,6,5,3] => [2,1,4,6,5,3] => 1
[2,1,5,3,4,6] => [2,1,4,5,3,6] => 1
[2,1,5,3,6,4] => [2,1,4,5,6,3] => 1
[2,1,5,4,3,6] => [2,1,5,4,3,6] => 1
[2,1,5,4,6,3] => [2,1,5,4,6,3] => 1
[2,1,5,6,3,4] => [2,1,6,5,4,3] => 1
[2,1,5,6,4,3] => [2,1,5,6,4,3] => 1
[2,1,6,3,4,5] => [2,1,4,5,6,3] => 1
[2,1,6,3,5,4] => [2,1,4,6,5,3] => 1
[2,1,6,4,3,5] => [2,1,5,4,6,3] => 1
[2,1,6,4,5,3] => [2,1,5,6,4,3] => 1
[2,1,6,5,3,4] => [2,1,5,6,4,3] => 1
[2,1,6,5,4,3] => [2,1,6,5,4,3] => 1
[2,3,1,4,5,6] => [2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => [2,3,1,4,6,5] => 1
[2,3,1,5,4,6] => [2,3,1,5,4,6] => 1
[2,3,1,5,6,4] => [2,3,1,5,6,4] => 1
[2,3,1,6,4,5] => [2,3,1,5,6,4] => 1
[2,3,1,6,5,4] => [2,3,1,6,5,4] => 1
[2,3,4,1,5,6] => [2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => [2,3,4,1,6,5] => 1
[2,3,4,5,1,6] => [2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => [2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => [2,3,6,5,1,4] => 1
[2,3,4,6,5,1] => [2,3,4,6,5,1] => 1
[2,3,5,1,4,6] => [2,5,4,1,3,6] => 1
[2,3,5,1,6,4] => [2,5,4,1,6,3] => 1
[2,3,5,4,1,6] => [2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => [2,3,5,4,6,1] => 1
[2,3,5,6,1,4] => [2,4,6,5,1,3] => 2
[2,3,5,6,4,1] => [2,3,5,6,4,1] => 1
[2,3,6,1,4,5] => [2,5,4,1,6,3] => 1
[2,3,6,1,5,4] => [2,6,4,1,5,3] => 2
[2,3,6,4,1,5] => [2,6,5,4,1,3] => 1
[2,3,6,4,5,1] => [2,3,5,6,4,1] => 1
[2,3,6,5,1,4] => [2,4,5,6,1,3] => 3
[2,3,6,5,4,1] => [2,3,6,5,4,1] => 1
[2,4,1,3,5,6] => [4,3,1,2,5,6] => 1
[2,4,1,3,6,5] => [4,3,1,2,6,5] => 1
[2,4,1,5,3,6] => [4,3,1,5,2,6] => 1
[2,4,1,5,6,3] => [4,3,1,5,6,2] => 1
[2,4,1,6,3,5] => [6,3,1,5,2,4] => 2
[2,4,1,6,5,3] => [4,3,1,6,5,2] => 1
[2,4,3,1,5,6] => [2,4,3,1,5,6] => 1
[2,4,3,1,6,5] => [2,4,3,1,6,5] => 1
[2,4,3,5,1,6] => [2,4,3,5,1,6] => 1
[2,4,3,5,6,1] => [2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => [2,6,3,5,1,4] => 2
[2,4,3,6,5,1] => [2,4,3,6,5,1] => 1
[2,4,5,1,3,6] => [3,5,4,1,2,6] => 2
[2,4,5,1,6,3] => [3,5,4,1,6,2] => 2
[2,4,5,3,1,6] => [2,4,5,3,1,6] => 1
[2,4,5,3,6,1] => [2,4,5,3,6,1] => 1
[2,4,5,6,1,3] => [3,4,6,5,1,2] => 3
[2,4,5,6,3,1] => [2,4,5,6,3,1] => 1
[2,4,6,1,3,5] => [6,5,4,1,2,3] => 1
[2,4,6,1,5,3] => [3,6,4,1,5,2] => 4
[2,4,6,3,1,5] => [2,4,5,6,1,3] => 3
[2,4,6,3,5,1] => [2,6,5,3,4,1] => 2
[2,4,6,5,1,3] => [3,4,5,6,1,2] => 5
[2,4,6,5,3,1] => [2,4,6,5,3,1] => 1
[2,5,1,3,4,6] => [4,3,1,5,2,6] => 1
[2,5,1,3,6,4] => [4,3,1,5,6,2] => 1
[2,5,1,4,3,6] => [5,3,1,4,2,6] => 2
[2,5,1,4,6,3] => [5,3,1,4,6,2] => 2
[2,5,1,6,3,4] => [6,3,1,5,4,2] => 2
[2,5,1,6,4,3] => [5,3,1,6,4,2] => 2
[2,5,3,1,4,6] => [5,4,3,1,2,6] => 1
[2,5,3,1,6,4] => [5,4,3,1,6,2] => 1
[2,5,3,4,1,6] => [2,4,5,3,1,6] => 1
[2,5,3,4,6,1] => [2,4,5,3,6,1] => 1
[2,5,3,6,1,4] => [4,6,3,5,1,2] => 4
[2,5,3,6,4,1] => [2,4,5,6,3,1] => 1
[2,5,4,1,3,6] => [3,4,5,1,2,6] => 3
[2,5,4,1,6,3] => [3,4,5,1,6,2] => 3
[2,5,4,3,1,6] => [2,5,4,3,1,6] => 1
[2,5,4,3,6,1] => [2,5,4,3,6,1] => 1
[2,5,4,6,1,3] => [3,6,4,5,1,2] => 6
[2,5,4,6,3,1] => [2,5,4,6,3,1] => 1
[2,5,6,1,3,4] => [6,5,4,1,3,2] => 1
[2,5,6,1,4,3] => [5,6,4,1,3,2] => 2
[2,5,6,3,1,4] => [3,4,5,6,1,2] => 5
[2,5,6,3,4,1] => [2,6,5,4,3,1] => 1
[2,5,6,4,1,3] => [3,6,5,4,1,2] => 2
[2,5,6,4,3,1] => [2,5,6,4,3,1] => 1
[2,6,1,3,4,5] => [4,3,1,5,6,2] => 1
[2,6,1,3,5,4] => [4,3,1,6,5,2] => 1
[2,6,1,4,3,5] => [5,3,1,4,6,2] => 2
[2,6,1,4,5,3] => [5,3,1,6,4,2] => 2
[2,6,1,5,3,4] => [5,3,1,6,4,2] => 2
[2,6,1,5,4,3] => [6,3,1,5,4,2] => 2
[2,6,3,1,4,5] => [5,4,3,1,6,2] => 1
[2,6,3,1,5,4] => [6,4,3,1,5,2] => 2
[2,6,3,4,1,5] => [6,4,5,3,1,2] => 3
[2,6,3,4,5,1] => [2,4,5,6,3,1] => 1
[2,6,3,5,1,4] => [4,6,5,3,1,2] => 2
[2,6,3,5,4,1] => [2,4,6,5,3,1] => 1
[2,6,4,1,3,5] => [3,4,5,1,6,2] => 3
[2,6,4,1,5,3] => [6,4,5,1,3,2] => 4
[2,6,4,3,1,5] => [6,5,4,3,1,2] => 1
[2,6,4,3,5,1] => [2,5,4,6,3,1] => 1
[2,6,4,5,1,3] => [3,6,5,4,1,2] => 2
[2,6,4,5,3,1] => [2,5,6,4,3,1] => 1
[2,6,5,1,3,4] => [6,4,5,1,3,2] => 4
[2,6,5,1,4,3] => [5,4,6,1,3,2] => 2
[2,6,5,3,1,4] => [3,5,4,6,1,2] => 4
[2,6,5,3,4,1] => [2,5,6,4,3,1] => 1
[2,6,5,4,1,3] => [3,5,6,4,1,2] => 3
[2,6,5,4,3,1] => [2,6,5,4,3,1] => 1
[3,1,2,4,5,6] => [2,3,1,4,5,6] => 1
[3,1,2,4,6,5] => [2,3,1,4,6,5] => 1
[3,1,2,5,4,6] => [2,3,1,5,4,6] => 1
[3,1,2,5,6,4] => [2,3,1,5,6,4] => 1
[3,1,2,6,4,5] => [2,3,1,5,6,4] => 1
[3,1,2,6,5,4] => [2,3,1,6,5,4] => 1
[3,1,4,2,5,6] => [2,3,4,1,5,6] => 1
[3,1,4,2,6,5] => [2,3,4,1,6,5] => 1
[3,1,4,5,2,6] => [2,3,4,5,1,6] => 1
[3,1,4,5,6,2] => [2,3,4,5,6,1] => 1
[3,1,4,6,2,5] => [2,3,6,5,1,4] => 1
[3,1,4,6,5,2] => [2,3,4,6,5,1] => 1
[3,1,5,2,4,6] => [2,5,4,1,3,6] => 1
[3,1,5,2,6,4] => [2,5,4,1,6,3] => 1
[3,1,5,4,2,6] => [2,3,5,4,1,6] => 1
[3,1,5,4,6,2] => [2,3,5,4,6,1] => 1
[3,1,5,6,2,4] => [2,4,6,5,1,3] => 2
[3,1,5,6,4,2] => [2,3,5,6,4,1] => 1
[3,1,6,2,4,5] => [2,5,4,1,6,3] => 1
[3,1,6,2,5,4] => [2,6,4,1,5,3] => 2
[3,1,6,4,2,5] => [2,6,5,4,1,3] => 1
[3,1,6,4,5,2] => [2,3,5,6,4,1] => 1
[3,1,6,5,2,4] => [2,4,5,6,1,3] => 3
[3,1,6,5,4,2] => [2,3,6,5,4,1] => 1
[3,2,1,4,5,6] => [3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => [3,2,1,4,6,5] => 1
[3,2,1,5,4,6] => [3,2,1,5,4,6] => 1
[3,2,1,5,6,4] => [3,2,1,5,6,4] => 1
[3,2,1,6,4,5] => [3,2,1,5,6,4] => 1
[3,2,1,6,5,4] => [3,2,1,6,5,4] => 1
[3,2,4,1,5,6] => [3,2,4,1,5,6] => 1
[3,2,4,1,6,5] => [3,2,4,1,6,5] => 1
[3,2,4,5,1,6] => [3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => [3,2,4,5,6,1] => 1
[3,2,4,6,1,5] => [3,2,6,5,1,4] => 1
[3,2,4,6,5,1] => [3,2,4,6,5,1] => 1
[3,2,5,1,4,6] => [5,2,4,1,3,6] => 2
[3,2,5,1,6,4] => [5,2,4,1,6,3] => 2
[3,2,5,4,1,6] => [3,2,5,4,1,6] => 1
[3,2,5,4,6,1] => [3,2,5,4,6,1] => 1
[3,2,5,6,1,4] => [4,2,6,5,1,3] => 2
[3,2,5,6,4,1] => [3,2,5,6,4,1] => 1
[3,2,6,1,4,5] => [5,2,4,1,6,3] => 2
[3,2,6,1,5,4] => [6,2,4,1,5,3] => 4
[3,2,6,4,1,5] => [6,2,5,4,1,3] => 2
[3,2,6,4,5,1] => [3,2,5,6,4,1] => 1
[3,2,6,5,1,4] => [4,2,5,6,1,3] => 3
[3,2,6,5,4,1] => [3,2,6,5,4,1] => 1
[3,4,1,2,5,6] => [4,3,2,1,5,6] => 1
[3,4,1,2,6,5] => [4,3,2,1,6,5] => 1
[3,4,1,5,2,6] => [4,3,2,5,1,6] => 1
[3,4,1,5,6,2] => [4,3,2,5,6,1] => 1
[3,4,1,6,2,5] => [6,3,2,5,1,4] => 2
[3,4,1,6,5,2] => [4,3,2,6,5,1] => 1
[3,4,2,1,5,6] => [3,4,2,1,5,6] => 1
[3,4,2,1,6,5] => [3,4,2,1,6,5] => 1
[3,4,2,5,1,6] => [3,4,2,5,1,6] => 1
[3,4,2,5,6,1] => [3,4,2,5,6,1] => 1
[3,4,2,6,1,5] => [3,6,2,5,1,4] => 2
[3,4,2,6,5,1] => [3,4,2,6,5,1] => 1
[3,4,5,1,2,6] => [3,5,4,2,1,6] => 1
[3,4,5,1,6,2] => [3,5,4,2,6,1] => 1
[3,4,5,2,1,6] => [3,4,5,2,1,6] => 1
[3,4,5,2,6,1] => [3,4,5,2,6,1] => 1
[3,4,5,6,1,2] => [3,4,6,5,2,1] => 1
[3,4,5,6,2,1] => [3,4,5,6,2,1] => 1
[3,4,6,1,2,5] => [6,5,4,2,1,3] => 1
[3,4,6,1,5,2] => [3,6,4,2,5,1] => 2
[3,4,6,2,1,5] => [6,4,5,2,1,3] => 4
[3,4,6,2,5,1] => [3,6,5,2,4,1] => 2
[3,4,6,5,1,2] => [3,4,5,6,2,1] => 1
[3,4,6,5,2,1] => [3,4,6,5,2,1] => 1
[3,5,1,2,4,6] => [4,3,5,1,2,6] => 2
[3,5,1,2,6,4] => [4,3,5,1,6,2] => 2
[3,5,1,4,2,6] => [5,3,2,4,1,6] => 2
[3,5,1,4,6,2] => [5,3,2,4,6,1] => 2
[3,5,1,6,2,4] => [6,3,4,5,1,2] => 9
[3,5,1,6,4,2] => [5,3,2,6,4,1] => 2
[3,5,2,1,4,6] => [3,4,5,1,2,6] => 3
[3,5,2,1,6,4] => [3,4,5,1,6,2] => 3
[3,5,2,4,1,6] => [5,4,2,3,1,6] => 2
[3,5,2,4,6,1] => [5,4,2,3,6,1] => 2
[3,5,2,6,1,4] => [3,6,4,5,1,2] => 6
[3,5,2,6,4,1] => [5,4,2,6,3,1] => 2
[3,5,4,1,2,6] => [3,4,5,2,1,6] => 1
[3,5,4,1,6,2] => [3,4,5,2,6,1] => 1
[3,5,4,2,1,6] => [3,5,4,2,1,6] => 1
[3,5,4,2,6,1] => [3,5,4,2,6,1] => 1
[3,5,4,6,1,2] => [3,6,4,5,2,1] => 2
[3,5,4,6,2,1] => [3,5,4,6,2,1] => 1
[3,5,6,1,2,4] => [6,5,4,3,1,2] => 1
[3,5,6,1,4,2] => [5,6,4,2,3,1] => 3
[3,5,6,2,1,4] => [6,4,5,3,1,2] => 3
[3,5,6,2,4,1] => [4,6,5,2,3,1] => 4
[3,5,6,4,1,2] => [3,6,5,4,2,1] => 1
[3,5,6,4,2,1] => [3,5,6,4,2,1] => 1
[3,6,1,2,4,5] => [4,3,5,1,6,2] => 2
[3,6,1,2,5,4] => [4,3,6,1,5,2] => 2
[3,6,1,4,2,5] => [5,3,6,4,1,2] => 4
[3,6,1,4,5,2] => [5,3,2,6,4,1] => 2
[3,6,1,5,2,4] => [5,3,4,6,1,2] => 6
[3,6,1,5,4,2] => [6,3,2,5,4,1] => 3
[3,6,2,1,4,5] => [3,4,5,1,6,2] => 3
[3,6,2,1,5,4] => [3,4,6,1,5,2] => 3
[3,6,2,4,1,5] => [5,4,6,3,1,2] => 2
[3,6,2,4,5,1] => [5,4,2,6,3,1] => 2
[3,6,2,5,1,4] => [5,6,4,3,1,2] => 2
[3,6,2,5,4,1] => [6,4,2,5,3,1] => 4
[3,6,4,1,2,5] => [3,4,5,6,1,2] => 5
[3,6,4,1,5,2] => [6,4,5,2,3,1] => 8
[3,6,4,2,1,5] => [3,5,4,6,1,2] => 4
[3,6,4,2,5,1] => [6,5,4,2,3,1] => 2
[3,6,4,5,1,2] => [3,6,5,4,2,1] => 1
[3,6,4,5,2,1] => [3,5,6,4,2,1] => 1
[3,6,5,1,2,4] => [6,4,5,3,1,2] => 3
[3,6,5,1,4,2] => [5,4,6,2,3,1] => 4
[3,6,5,2,1,4] => [6,5,4,3,1,2] => 1
[3,6,5,2,4,1] => [4,5,6,2,3,1] => 6
[3,6,5,4,1,2] => [3,5,6,4,2,1] => 1
[3,6,5,4,2,1] => [3,6,5,4,2,1] => 1
[4,1,2,3,5,6] => [2,3,4,1,5,6] => 1
[4,1,2,3,6,5] => [2,3,4,1,6,5] => 1
[4,1,2,5,3,6] => [2,3,4,5,1,6] => 1
[4,1,2,5,6,3] => [2,3,4,5,6,1] => 1
[4,1,2,6,3,5] => [2,3,6,5,1,4] => 1
[4,1,2,6,5,3] => [2,3,4,6,5,1] => 1
[4,1,3,2,5,6] => [2,4,3,1,5,6] => 1
[4,1,3,2,6,5] => [2,4,3,1,6,5] => 1
[4,1,3,5,2,6] => [2,4,3,5,1,6] => 1
[4,1,3,5,6,2] => [2,4,3,5,6,1] => 1
[4,1,3,6,2,5] => [2,6,3,5,1,4] => 2
[4,1,3,6,5,2] => [2,4,3,6,5,1] => 1
[4,1,5,2,3,6] => [2,5,4,3,1,6] => 1
[4,1,5,2,6,3] => [2,5,4,3,6,1] => 1
[4,1,5,3,2,6] => [2,4,5,3,1,6] => 1
[4,1,5,3,6,2] => [2,4,5,3,6,1] => 1
[4,1,5,6,2,3] => [2,4,6,5,3,1] => 1
[4,1,5,6,3,2] => [2,4,5,6,3,1] => 1
[4,1,6,2,3,5] => [2,5,4,6,1,3] => 2
[4,1,6,2,5,3] => [2,6,4,3,5,1] => 2
[4,1,6,3,2,5] => [2,4,5,6,1,3] => 3
[4,1,6,3,5,2] => [2,6,5,3,4,1] => 2
[4,1,6,5,2,3] => [2,4,5,6,3,1] => 1
[4,1,6,5,3,2] => [2,4,6,5,3,1] => 1
[4,2,1,3,5,6] => [3,2,4,1,5,6] => 1
[4,2,1,3,6,5] => [3,2,4,1,6,5] => 1
[4,2,1,5,3,6] => [3,2,4,5,1,6] => 1
[4,2,1,5,6,3] => [3,2,4,5,6,1] => 1
[4,2,1,6,3,5] => [3,2,6,5,1,4] => 1
[4,2,1,6,5,3] => [3,2,4,6,5,1] => 1
[4,2,3,1,5,6] => [3,4,2,1,5,6] => 1
[4,2,3,1,6,5] => [3,4,2,1,6,5] => 1
[4,2,3,5,1,6] => [3,4,2,5,1,6] => 1
[4,2,3,5,6,1] => [3,4,2,5,6,1] => 1
[4,2,3,6,1,5] => [3,6,2,5,1,4] => 2
[4,2,3,6,5,1] => [3,4,2,6,5,1] => 1
[4,2,5,1,3,6] => [5,2,4,3,1,6] => 2
[4,2,5,1,6,3] => [5,2,4,3,6,1] => 2
[4,2,5,3,1,6] => [3,4,5,2,1,6] => 1
[4,2,5,3,6,1] => [3,4,5,2,6,1] => 1
[4,2,5,6,1,3] => [4,2,6,5,3,1] => 2
[4,2,5,6,3,1] => [3,4,5,6,2,1] => 1
[4,2,6,1,3,5] => [5,2,4,6,1,3] => 4
[4,2,6,1,5,3] => [6,2,4,3,5,1] => 4
[4,2,6,3,1,5] => [6,4,5,2,1,3] => 4
[4,2,6,3,5,1] => [3,6,5,2,4,1] => 2
[4,2,6,5,1,3] => [4,2,5,6,3,1] => 2
[4,2,6,5,3,1] => [3,4,6,5,2,1] => 1
[4,3,1,2,5,6] => [3,4,2,1,5,6] => 1
[4,3,1,2,6,5] => [3,4,2,1,6,5] => 1
[4,3,1,5,2,6] => [3,4,2,5,1,6] => 1
[4,3,1,5,6,2] => [3,4,2,5,6,1] => 1
[4,3,1,6,2,5] => [3,6,2,5,1,4] => 2
[4,3,1,6,5,2] => [3,4,2,6,5,1] => 1
[4,3,2,1,5,6] => [4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => [4,3,2,1,6,5] => 1
[4,3,2,5,1,6] => [4,3,2,5,1,6] => 1
[4,3,2,5,6,1] => [4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => [6,3,2,5,1,4] => 2
[4,3,2,6,5,1] => [4,3,2,6,5,1] => 1
[4,3,5,1,2,6] => [5,3,4,2,1,6] => 2
[4,3,5,1,6,2] => [5,3,4,2,6,1] => 2
[4,3,5,2,1,6] => [4,3,5,2,1,6] => 1
[4,3,5,2,6,1] => [4,3,5,2,6,1] => 1
[4,3,5,6,1,2] => [4,3,6,5,2,1] => 1
[4,3,5,6,2,1] => [4,3,5,6,2,1] => 1
[4,3,6,1,2,5] => [5,6,4,2,1,3] => 2
[4,3,6,1,5,2] => [6,3,4,2,5,1] => 4
[4,3,6,2,1,5] => [4,6,5,2,1,3] => 2
[4,3,6,2,5,1] => [6,3,5,2,4,1] => 4
[4,3,6,5,1,2] => [4,3,5,6,2,1] => 1
[4,3,6,5,2,1] => [4,3,6,5,2,1] => 1
[4,5,1,2,3,6] => [4,3,5,2,1,6] => 1
[4,5,1,2,6,3] => [4,3,5,2,6,1] => 1
[4,5,1,3,2,6] => [5,3,4,2,1,6] => 2
[4,5,1,3,6,2] => [5,3,4,2,6,1] => 2
[4,5,1,6,2,3] => [6,3,4,5,2,1] => 4
[4,5,1,6,3,2] => [5,3,4,6,2,1] => 2
[4,5,2,1,3,6] => [3,4,5,2,1,6] => 1
[4,5,2,1,6,3] => [3,4,5,2,6,1] => 1
[4,5,2,3,1,6] => [5,4,3,2,1,6] => 1
[4,5,2,3,6,1] => [5,4,3,2,6,1] => 1
[4,5,2,6,1,3] => [3,6,4,5,2,1] => 2
[4,5,2,6,3,1] => [5,4,3,6,2,1] => 1
[4,5,3,1,2,6] => [5,4,3,2,1,6] => 1
[4,5,3,1,6,2] => [5,4,3,2,6,1] => 1
[4,5,3,2,1,6] => [4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => [4,5,3,2,6,1] => 1
[4,5,3,6,1,2] => [4,6,3,5,2,1] => 2
[4,5,3,6,2,1] => [4,5,3,6,2,1] => 1
[4,5,6,1,2,3] => [6,5,4,3,2,1] => 1
[4,5,6,1,3,2] => [5,6,4,3,2,1] => 1
[4,5,6,2,1,3] => [6,4,5,3,2,1] => 2
[4,5,6,2,3,1] => [4,6,5,3,2,1] => 1
[4,5,6,3,1,2] => [4,6,5,3,2,1] => 1
[4,5,6,3,2,1] => [4,5,6,3,2,1] => 1
[4,6,1,2,3,5] => [4,3,5,6,1,2] => 3
[4,6,1,2,5,3] => [4,3,6,2,5,1] => 2
[4,6,1,3,2,5] => [5,3,4,6,1,2] => 6
[4,6,1,3,5,2] => [5,3,6,2,4,1] => 3
[4,6,1,5,2,3] => [5,3,4,6,2,1] => 2
[4,6,1,5,3,2] => [6,3,4,5,2,1] => 4
[4,6,2,1,3,5] => [3,4,5,6,1,2] => 5
[4,6,2,1,5,3] => [3,4,6,2,5,1] => 2
[4,6,2,3,1,5] => [5,4,3,6,1,2] => 2
[4,6,2,3,5,1] => [5,4,6,2,3,1] => 4
[4,6,2,5,1,3] => [5,6,4,3,2,1] => 1
[4,6,2,5,3,1] => [6,4,3,5,2,1] => 2
[4,6,3,1,2,5] => [5,4,3,6,1,2] => 2
[4,6,3,1,5,2] => [5,4,6,2,3,1] => 4
[4,6,3,2,1,5] => [4,5,3,6,1,2] => 3
[4,6,3,2,5,1] => [4,5,6,2,3,1] => 6
[4,6,3,5,1,2] => [5,6,3,4,2,1] => 4
[4,6,3,5,2,1] => [6,5,3,4,2,1] => 3
[4,6,5,1,2,3] => [6,4,5,3,2,1] => 2
[4,6,5,1,3,2] => [5,4,6,3,2,1] => 1
[4,6,5,2,1,3] => [6,5,4,3,2,1] => 1
[4,6,5,2,3,1] => [4,5,6,3,2,1] => 1
[4,6,5,3,1,2] => [4,5,6,3,2,1] => 1
[4,6,5,3,2,1] => [4,6,5,3,2,1] => 1
[5,1,2,3,4,6] => [2,3,4,5,1,6] => 1
[5,1,2,3,6,4] => [2,3,4,5,6,1] => 1
[5,1,2,4,3,6] => [2,3,5,4,1,6] => 1
[5,1,2,4,6,3] => [2,3,5,4,6,1] => 1
[5,1,2,6,3,4] => [2,3,6,5,4,1] => 1
[5,1,2,6,4,3] => [2,3,5,6,4,1] => 1
[5,1,3,2,4,6] => [2,4,3,5,1,6] => 1
[5,1,3,2,6,4] => [2,4,3,5,6,1] => 1
[5,1,3,4,2,6] => [2,4,5,3,1,6] => 1
[5,1,3,4,6,2] => [2,4,5,3,6,1] => 1
[5,1,3,6,2,4] => [2,6,3,5,4,1] => 2
[5,1,3,6,4,2] => [2,4,5,6,3,1] => 1
[5,1,4,2,3,6] => [2,4,5,3,1,6] => 1
[5,1,4,2,6,3] => [2,4,5,3,6,1] => 1
[5,1,4,3,2,6] => [2,5,4,3,1,6] => 1
[5,1,4,3,6,2] => [2,5,4,3,6,1] => 1
[5,1,4,6,2,3] => [2,6,4,5,3,1] => 2
[5,1,4,6,3,2] => [2,5,4,6,3,1] => 1
[5,1,6,2,3,4] => [2,5,4,6,3,1] => 1
[5,1,6,2,4,3] => [2,6,4,5,3,1] => 2
[5,1,6,3,2,4] => [2,4,5,6,3,1] => 1
[5,1,6,3,4,2] => [2,6,5,4,3,1] => 1
[5,1,6,4,2,3] => [2,6,5,4,3,1] => 1
[5,1,6,4,3,2] => [2,5,6,4,3,1] => 1
[5,2,1,3,4,6] => [3,2,4,5,1,6] => 1
[5,2,1,3,6,4] => [3,2,4,5,6,1] => 1
[5,2,1,4,3,6] => [3,2,5,4,1,6] => 1
[5,2,1,4,6,3] => [3,2,5,4,6,1] => 1
[5,2,1,6,3,4] => [3,2,6,5,4,1] => 1
[5,2,1,6,4,3] => [3,2,5,6,4,1] => 1
[5,2,3,1,4,6] => [3,4,2,5,1,6] => 1
[5,2,3,1,6,4] => [3,4,2,5,6,1] => 1
[5,2,3,4,1,6] => [3,4,5,2,1,6] => 1
[5,2,3,4,6,1] => [3,4,5,2,6,1] => 1
[5,2,3,6,1,4] => [3,6,2,5,4,1] => 2
[5,2,3,6,4,1] => [3,4,5,6,2,1] => 1
[5,2,4,1,3,6] => [5,4,2,3,1,6] => 2
[5,2,4,1,6,3] => [5,4,2,3,6,1] => 2
[5,2,4,3,1,6] => [3,5,4,2,1,6] => 1
[5,2,4,3,6,1] => [3,5,4,2,6,1] => 1
[5,2,4,6,1,3] => [4,6,2,5,3,1] => 3
[5,2,4,6,3,1] => [3,5,4,6,2,1] => 1
[5,2,6,1,3,4] => [5,2,4,6,3,1] => 2
[5,2,6,1,4,3] => [6,2,4,5,3,1] => 4
[5,2,6,3,1,4] => [6,4,5,2,3,1] => 8
[5,2,6,3,4,1] => [3,6,5,4,2,1] => 1
[5,2,6,4,1,3] => [4,6,5,2,3,1] => 4
[5,2,6,4,3,1] => [3,5,6,4,2,1] => 1
[5,3,1,2,4,6] => [3,4,2,5,1,6] => 1
[5,3,1,2,6,4] => [3,4,2,5,6,1] => 1
[5,3,1,4,2,6] => [3,4,5,2,1,6] => 1
[5,3,1,4,6,2] => [3,4,5,2,6,1] => 1
[5,3,1,6,2,4] => [3,6,2,5,4,1] => 2
[5,3,1,6,4,2] => [3,4,5,6,2,1] => 1
[5,3,2,1,4,6] => [4,3,2,5,1,6] => 1
[5,3,2,1,6,4] => [4,3,2,5,6,1] => 1
[5,3,2,4,1,6] => [4,3,5,2,1,6] => 1
[5,3,2,4,6,1] => [4,3,5,2,6,1] => 1
[5,3,2,6,1,4] => [6,3,2,5,4,1] => 3
[5,3,2,6,4,1] => [4,3,5,6,2,1] => 1
[5,3,4,1,2,6] => [5,4,3,2,1,6] => 1
[5,3,4,1,6,2] => [5,4,3,2,6,1] => 1
[5,3,4,2,1,6] => [4,5,3,2,1,6] => 1
[5,3,4,2,6,1] => [4,5,3,2,6,1] => 1
[5,3,4,6,1,2] => [4,6,3,5,2,1] => 2
[5,3,4,6,2,1] => [4,5,3,6,2,1] => 1
[5,3,6,1,2,4] => [5,6,4,2,3,1] => 3
[5,3,6,1,4,2] => [6,3,4,5,2,1] => 4
[5,3,6,2,1,4] => [4,6,5,2,3,1] => 4
[5,3,6,2,4,1] => [6,3,5,4,2,1] => 2
[5,3,6,4,1,2] => [4,6,5,3,2,1] => 1
[5,3,6,4,2,1] => [4,5,6,3,2,1] => 1
[5,4,1,2,3,6] => [3,4,5,2,1,6] => 1
[5,4,1,2,6,3] => [3,4,5,2,6,1] => 1
[5,4,1,3,2,6] => [3,5,4,2,1,6] => 1
[5,4,1,3,6,2] => [3,5,4,2,6,1] => 1
[5,4,1,6,2,3] => [3,6,4,5,2,1] => 2
[5,4,1,6,3,2] => [3,5,4,6,2,1] => 1
[5,4,2,1,3,6] => [4,3,5,2,1,6] => 1
[5,4,2,1,6,3] => [4,3,5,2,6,1] => 1
[5,4,2,3,1,6] => [4,5,3,2,1,6] => 1
[5,4,2,3,6,1] => [4,5,3,2,6,1] => 1
[5,4,2,6,1,3] => [6,3,4,5,2,1] => 4
[5,4,2,6,3,1] => [4,5,3,6,2,1] => 1
[5,4,3,1,2,6] => [4,5,3,2,1,6] => 1
[5,4,3,1,6,2] => [4,5,3,2,6,1] => 1
[5,4,3,2,1,6] => [5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => [5,4,3,2,6,1] => 1
[5,4,3,6,1,2] => [6,4,3,5,2,1] => 2
[5,4,3,6,2,1] => [5,4,3,6,2,1] => 1
[5,4,6,1,2,3] => [5,6,4,3,2,1] => 1
[5,4,6,1,3,2] => [6,5,4,3,2,1] => 1
[5,4,6,2,1,3] => [4,6,5,3,2,1] => 1
[5,4,6,2,3,1] => [6,4,5,3,2,1] => 2
[5,4,6,3,1,2] => [6,4,5,3,2,1] => 2
[5,4,6,3,2,1] => [5,4,6,3,2,1] => 1
[5,6,1,2,3,4] => [4,3,5,6,2,1] => 1
[5,6,1,2,4,3] => [4,3,6,5,2,1] => 1
[5,6,1,3,2,4] => [5,3,4,6,2,1] => 2
[5,6,1,3,4,2] => [5,3,6,4,2,1] => 2
[5,6,1,4,2,3] => [5,3,6,4,2,1] => 2
[5,6,1,4,3,2] => [6,3,5,4,2,1] => 2
[5,6,2,1,3,4] => [3,4,5,6,2,1] => 1
[5,6,2,1,4,3] => [3,4,6,5,2,1] => 1
[5,6,2,3,1,4] => [5,4,3,6,2,1] => 1
[5,6,2,3,4,1] => [5,4,6,3,2,1] => 1
[5,6,2,4,1,3] => [5,6,3,4,2,1] => 4
[5,6,2,4,3,1] => [6,4,5,3,2,1] => 2
[5,6,3,1,2,4] => [5,4,3,6,2,1] => 1
[5,6,3,1,4,2] => [5,4,6,3,2,1] => 1
[5,6,3,2,1,4] => [4,5,3,6,2,1] => 1
[5,6,3,2,4,1] => [4,5,6,3,2,1] => 1
[5,6,3,4,1,2] => [5,6,4,3,2,1] => 1
[5,6,3,4,2,1] => [6,5,4,3,2,1] => 1
[5,6,4,1,2,3] => [5,4,6,3,2,1] => 1
[5,6,4,1,3,2] => [6,4,5,3,2,1] => 2
[5,6,4,2,1,3] => [4,5,6,3,2,1] => 1
[5,6,4,2,3,1] => [6,5,4,3,2,1] => 1
[5,6,4,3,1,2] => [6,5,4,3,2,1] => 1
[5,6,4,3,2,1] => [5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => [2,3,4,5,6,1] => 1
[6,1,2,3,5,4] => [2,3,4,6,5,1] => 1
[6,1,2,4,3,5] => [2,3,5,4,6,1] => 1
[6,1,2,4,5,3] => [2,3,5,6,4,1] => 1
[6,1,2,5,3,4] => [2,3,5,6,4,1] => 1
[6,1,2,5,4,3] => [2,3,6,5,4,1] => 1
[6,1,3,2,4,5] => [2,4,3,5,6,1] => 1
[6,1,3,2,5,4] => [2,4,3,6,5,1] => 1
[6,1,3,4,2,5] => [2,4,5,3,6,1] => 1
[6,1,3,4,5,2] => [2,4,5,6,3,1] => 1
[6,1,3,5,2,4] => [2,6,5,3,4,1] => 2
[6,1,3,5,4,2] => [2,4,6,5,3,1] => 1
[6,1,4,2,3,5] => [2,4,5,3,6,1] => 1
[6,1,4,2,5,3] => [2,4,5,6,3,1] => 1
[6,1,4,3,2,5] => [2,5,4,3,6,1] => 1
[6,1,4,3,5,2] => [2,5,4,6,3,1] => 1
[6,1,4,5,2,3] => [2,6,5,4,3,1] => 1
[6,1,4,5,3,2] => [2,5,6,4,3,1] => 1
[6,1,5,2,3,4] => [2,4,5,6,3,1] => 1
[6,1,5,2,4,3] => [2,4,6,5,3,1] => 1
[6,1,5,3,2,4] => [2,5,4,6,3,1] => 1
[6,1,5,3,4,2] => [2,5,6,4,3,1] => 1
[6,1,5,4,2,3] => [2,5,6,4,3,1] => 1
[6,1,5,4,3,2] => [2,6,5,4,3,1] => 1
[6,2,1,3,4,5] => [3,2,4,5,6,1] => 1
[6,2,1,3,5,4] => [3,2,4,6,5,1] => 1
[6,2,1,4,3,5] => [3,2,5,4,6,1] => 1
[6,2,1,4,5,3] => [3,2,5,6,4,1] => 1
[6,2,1,5,3,4] => [3,2,5,6,4,1] => 1
[6,2,1,5,4,3] => [3,2,6,5,4,1] => 1
[6,2,3,1,4,5] => [3,4,2,5,6,1] => 1
[6,2,3,1,5,4] => [3,4,2,6,5,1] => 1
[6,2,3,4,1,5] => [3,4,5,2,6,1] => 1
[6,2,3,4,5,1] => [3,4,5,6,2,1] => 1
[6,2,3,5,1,4] => [3,6,5,2,4,1] => 2
[6,2,3,5,4,1] => [3,4,6,5,2,1] => 1
[6,2,4,1,3,5] => [5,4,2,3,6,1] => 2
[6,2,4,1,5,3] => [5,4,2,6,3,1] => 2
[6,2,4,3,1,5] => [3,5,4,2,6,1] => 1
[6,2,4,3,5,1] => [3,5,4,6,2,1] => 1
[6,2,4,5,1,3] => [4,6,5,2,3,1] => 4
[6,2,4,5,3,1] => [3,5,6,4,2,1] => 1
[6,2,5,1,3,4] => [5,4,2,6,3,1] => 2
[6,2,5,1,4,3] => [6,4,2,5,3,1] => 4
[6,2,5,3,1,4] => [6,5,4,2,3,1] => 2
[6,2,5,3,4,1] => [3,5,6,4,2,1] => 1
[6,2,5,4,1,3] => [4,5,6,2,3,1] => 6
[6,2,5,4,3,1] => [3,6,5,4,2,1] => 1
[6,3,1,2,4,5] => [3,4,2,5,6,1] => 1
[6,3,1,2,5,4] => [3,4,2,6,5,1] => 1
[6,3,1,4,2,5] => [3,4,5,2,6,1] => 1
[6,3,1,4,5,2] => [3,4,5,6,2,1] => 1
[6,3,1,5,2,4] => [3,6,5,2,4,1] => 2
[6,3,1,5,4,2] => [3,4,6,5,2,1] => 1
[6,3,2,1,4,5] => [4,3,2,5,6,1] => 1
[6,3,2,1,5,4] => [4,3,2,6,5,1] => 1
[6,3,2,4,1,5] => [4,3,5,2,6,1] => 1
[6,3,2,4,5,1] => [4,3,5,6,2,1] => 1
[6,3,2,5,1,4] => [6,3,5,2,4,1] => 4
[6,3,2,5,4,1] => [4,3,6,5,2,1] => 1
[6,3,4,1,2,5] => [5,4,3,2,6,1] => 1
[6,3,4,1,5,2] => [5,4,3,6,2,1] => 1
[6,3,4,2,1,5] => [4,5,3,2,6,1] => 1
[6,3,4,2,5,1] => [4,5,3,6,2,1] => 1
[6,3,4,5,1,2] => [4,6,5,3,2,1] => 1
[6,3,4,5,2,1] => [4,5,6,3,2,1] => 1
[6,3,5,1,2,4] => [5,4,6,2,3,1] => 4
[6,3,5,1,4,2] => [6,4,3,5,2,1] => 2
[6,3,5,2,1,4] => [4,5,6,2,3,1] => 6
[6,3,5,2,4,1] => [6,5,3,4,2,1] => 3
[6,3,5,4,1,2] => [4,5,6,3,2,1] => 1
[6,3,5,4,2,1] => [4,6,5,3,2,1] => 1
[6,4,1,2,3,5] => [3,4,5,2,6,1] => 1
[6,4,1,2,5,3] => [3,4,5,6,2,1] => 1
[6,4,1,3,2,5] => [3,5,4,2,6,1] => 1
[6,4,1,3,5,2] => [3,5,4,6,2,1] => 1
[6,4,1,5,2,3] => [3,6,5,4,2,1] => 1
[6,4,1,5,3,2] => [3,5,6,4,2,1] => 1
[6,4,2,1,3,5] => [4,3,5,2,6,1] => 1
[6,4,2,1,5,3] => [4,3,5,6,2,1] => 1
[6,4,2,3,1,5] => [4,5,3,2,6,1] => 1
[6,4,2,3,5,1] => [4,5,3,6,2,1] => 1
[6,4,2,5,1,3] => [6,3,5,4,2,1] => 2
[6,4,2,5,3,1] => [4,5,6,3,2,1] => 1
[6,4,3,1,2,5] => [4,5,3,2,6,1] => 1
[6,4,3,1,5,2] => [4,5,3,6,2,1] => 1
[6,4,3,2,1,5] => [5,4,3,2,6,1] => 1
[6,4,3,2,5,1] => [5,4,3,6,2,1] => 1
[6,4,3,5,1,2] => [6,4,5,3,2,1] => 2
[6,4,3,5,2,1] => [5,4,6,3,2,1] => 1
[6,4,5,1,2,3] => [5,4,6,3,2,1] => 1
[6,4,5,1,3,2] => [6,4,5,3,2,1] => 2
[6,4,5,2,1,3] => [4,5,6,3,2,1] => 1
[6,4,5,2,3,1] => [6,5,4,3,2,1] => 1
[6,4,5,3,1,2] => [6,5,4,3,2,1] => 1
[6,4,5,3,2,1] => [5,6,4,3,2,1] => 1
[6,5,1,2,3,4] => [3,4,5,6,2,1] => 1
[6,5,1,2,4,3] => [3,4,6,5,2,1] => 1
[6,5,1,3,2,4] => [3,5,4,6,2,1] => 1
[6,5,1,3,4,2] => [3,5,6,4,2,1] => 1
[6,5,1,4,2,3] => [3,5,6,4,2,1] => 1
[6,5,1,4,3,2] => [3,6,5,4,2,1] => 1
[6,5,2,1,3,4] => [4,3,5,6,2,1] => 1
[6,5,2,1,4,3] => [4,3,6,5,2,1] => 1
[6,5,2,3,1,4] => [4,5,3,6,2,1] => 1
[6,5,2,3,4,1] => [4,5,6,3,2,1] => 1
[6,5,2,4,1,3] => [6,5,3,4,2,1] => 3
[6,5,2,4,3,1] => [4,6,5,3,2,1] => 1
[6,5,3,1,2,4] => [4,5,3,6,2,1] => 1
[6,5,3,1,4,2] => [4,5,6,3,2,1] => 1
[6,5,3,2,1,4] => [5,4,3,6,2,1] => 1
[6,5,3,2,4,1] => [5,4,6,3,2,1] => 1
[6,5,3,4,1,2] => [6,5,4,3,2,1] => 1
[6,5,3,4,2,1] => [5,6,4,3,2,1] => 1
[6,5,4,1,2,3] => [4,5,6,3,2,1] => 1
[6,5,4,1,3,2] => [4,6,5,3,2,1] => 1
[6,5,4,2,1,3] => [5,4,6,3,2,1] => 1
[6,5,4,2,3,1] => [5,6,4,3,2,1] => 1
[6,5,4,3,1,2] => [5,6,4,3,2,1] => 1
[6,5,4,3,2,1] => [6,5,4,3,2,1] => 1
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1
[1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[1,3,6,7,4,5,2] => [1,3,7,6,5,4,2] => 1
[1,3,7,6,5,4,2] => [1,3,7,6,5,4,2] => 1
[1,4,6,7,5,2,3] => [1,4,7,6,5,3,2] => 1
[1,4,6,7,5,3,2] => [1,4,6,7,5,3,2] => 1
[1,4,7,2,6,5,3] => [1,7,4,3,6,5,2] => 3
[1,4,7,5,6,2,3] => [1,4,7,6,5,3,2] => 1
[1,4,7,5,6,3,2] => [1,4,6,7,5,3,2] => 1
[1,4,7,6,5,2,3] => [1,4,6,7,5,3,2] => 1
[1,4,7,6,5,3,2] => [1,4,7,6,5,3,2] => 1
[1,5,4,6,7,2,3] => [1,5,4,7,6,3,2] => 1
[1,5,4,7,2,6,3] => [1,7,4,5,3,6,2] => 4
[1,5,4,7,6,3,2] => [1,5,4,7,6,3,2] => 1
[1,5,6,2,7,3,4] => [1,7,4,5,6,3,2] => 4
[1,5,6,3,4,7,2] => [1,6,5,4,3,7,2] => 1
[1,5,6,3,7,4,2] => [1,6,5,4,7,3,2] => 1
[1,5,6,4,2,7,3] => [1,6,5,4,3,7,2] => 1
[1,5,6,4,7,3,2] => [1,5,6,4,7,3,2] => 1
[1,5,6,7,2,3,4] => [1,7,6,5,4,3,2] => 1
[1,5,6,7,2,4,3] => [1,6,7,5,4,3,2] => 1
[1,5,6,7,3,4,2] => [1,5,7,6,4,3,2] => 1
[1,5,6,7,4,2,3] => [1,5,7,6,4,3,2] => 1
[1,5,6,7,4,3,2] => [1,5,6,7,4,3,2] => 1
[1,5,7,2,6,4,3] => [1,7,4,5,6,3,2] => 4
[1,5,7,3,6,2,4] => [1,6,7,5,4,3,2] => 1
[1,5,7,3,6,4,2] => [1,7,5,4,6,3,2] => 2
[1,5,7,4,6,3,2] => [1,7,6,4,5,3,2] => 3
[1,5,7,6,2,4,3] => [1,6,5,7,4,3,2] => 1
[1,5,7,6,3,2,4] => [1,7,6,5,4,3,2] => 1
[1,5,7,6,3,4,2] => [1,5,6,7,4,3,2] => 1
[1,5,7,6,4,2,3] => [1,5,6,7,4,3,2] => 1
[1,5,7,6,4,3,2] => [1,5,7,6,4,3,2] => 1
[1,6,2,7,4,5,3] => [1,3,7,6,5,4,2] => 1
[1,6,2,7,5,3,4] => [1,3,7,6,5,4,2] => 1
[1,6,3,7,2,5,4] => [1,7,3,5,6,4,2] => 4
[1,6,3,7,4,5,2] => [1,4,7,6,5,3,2] => 1
[1,6,3,7,5,4,2] => [1,4,6,7,5,3,2] => 1
[1,6,4,3,7,2,5] => [1,7,4,3,6,5,2] => 3
[1,6,4,5,2,7,3] => [1,6,5,4,3,7,2] => 1
[1,6,4,5,7,3,2] => [1,5,6,4,7,3,2] => 1
[1,6,4,7,2,5,3] => [1,7,4,5,6,3,2] => 4
[1,6,4,7,3,5,2] => [1,7,4,6,5,3,2] => 2
[1,6,4,7,5,2,3] => [1,5,7,6,4,3,2] => 1
[1,6,4,7,5,3,2] => [1,5,6,7,4,3,2] => 1
[1,6,5,3,7,2,4] => [1,7,4,5,6,3,2] => 4
[1,6,5,3,7,4,2] => [1,5,6,4,7,3,2] => 1
[1,6,5,4,3,7,2] => [1,6,5,4,3,7,2] => 1
[1,6,5,4,7,2,3] => [1,7,5,4,6,3,2] => 2
[1,6,5,4,7,3,2] => [1,6,5,4,7,3,2] => 1
[1,6,5,7,2,3,4] => [1,6,7,5,4,3,2] => 1
[1,6,5,7,2,4,3] => [1,7,6,5,4,3,2] => 1
[1,6,5,7,3,2,4] => [1,5,7,6,4,3,2] => 1
[1,6,5,7,4,3,2] => [1,6,5,7,4,3,2] => 1
[1,6,7,2,3,5,4] => [1,5,4,7,6,3,2] => 1
[1,6,7,2,5,4,3] => [1,7,4,6,5,3,2] => 2
[1,6,7,3,4,2,5] => [1,6,5,4,7,3,2] => 1
[1,6,7,3,4,5,2] => [1,6,5,7,4,3,2] => 1
[1,6,7,4,2,3,5] => [1,6,5,4,7,3,2] => 1
[1,6,7,4,2,5,3] => [1,6,5,7,4,3,2] => 1
[1,6,7,4,3,2,5] => [1,5,6,4,7,3,2] => 1
[1,6,7,4,3,5,2] => [1,5,6,7,4,3,2] => 1
[1,6,7,4,5,2,3] => [1,6,7,5,4,3,2] => 1
[1,6,7,4,5,3,2] => [1,7,6,5,4,3,2] => 1
[1,6,7,5,2,3,4] => [1,6,5,7,4,3,2] => 1
[1,6,7,5,3,2,4] => [1,5,6,7,4,3,2] => 1
[1,6,7,5,3,4,2] => [1,7,6,5,4,3,2] => 1
[1,6,7,5,4,2,3] => [1,7,6,5,4,3,2] => 1
[1,6,7,5,4,3,2] => [1,6,7,5,4,3,2] => 1
[1,7,2,5,6,3,4] => [1,3,7,6,5,4,2] => 1
[1,7,2,6,5,4,3] => [1,3,7,6,5,4,2] => 1
[1,7,3,5,6,4,2] => [1,4,6,7,5,3,2] => 1
[1,7,3,6,4,5,2] => [1,4,6,7,5,3,2] => 1
[1,7,3,6,5,4,2] => [1,4,7,6,5,3,2] => 1
[1,7,4,3,6,5,2] => [1,5,4,7,6,3,2] => 1
[1,7,4,5,2,3,6] => [1,6,5,4,3,7,2] => 1
[1,7,4,5,2,6,3] => [1,6,5,4,7,3,2] => 1
[1,7,4,5,3,6,2] => [1,5,6,4,7,3,2] => 1
[1,7,4,5,6,2,3] => [1,5,7,6,4,3,2] => 1
[1,7,4,5,6,3,2] => [1,5,6,7,4,3,2] => 1
[1,7,4,6,2,5,3] => [1,7,5,4,6,3,2] => 2
[1,7,4,6,3,5,2] => [1,7,6,4,5,3,2] => 3
[1,7,4,6,5,2,3] => [1,5,6,7,4,3,2] => 1
[1,7,4,6,5,3,2] => [1,5,7,6,4,3,2] => 1
[1,7,5,2,6,3,4] => [1,4,7,6,5,3,2] => 1
[1,7,5,2,6,4,3] => [1,4,6,7,5,3,2] => 1
[1,7,5,3,4,6,2] => [1,5,6,4,7,3,2] => 1
[1,7,5,3,6,2,4] => [1,7,4,6,5,3,2] => 2
[1,7,5,3,6,4,2] => [1,5,6,7,4,3,2] => 1
[1,7,5,4,2,6,3] => [1,5,6,4,7,3,2] => 1
[1,7,5,4,3,2,6] => [1,6,5,4,3,7,2] => 1
[1,7,5,4,3,6,2] => [1,6,5,4,7,3,2] => 1
[1,7,5,4,6,3,2] => [1,6,5,7,4,3,2] => 1
[1,7,5,6,2,3,4] => [1,6,5,7,4,3,2] => 1
[1,7,5,6,3,2,4] => [1,5,6,7,4,3,2] => 1
[1,7,5,6,3,4,2] => [1,7,6,5,4,3,2] => 1
[1,7,5,6,4,2,3] => [1,7,6,5,4,3,2] => 1
[1,7,5,6,4,3,2] => [1,6,7,5,4,3,2] => 1
[1,7,6,2,4,5,3] => [1,4,6,7,5,3,2] => 1
[1,7,6,2,5,3,4] => [1,4,6,7,5,3,2] => 1
[1,7,6,2,5,4,3] => [1,4,7,6,5,3,2] => 1
[1,7,6,3,2,5,4] => [1,5,4,7,6,3,2] => 1
[1,7,6,3,4,2,5] => [1,5,6,4,7,3,2] => 1
[1,7,6,3,4,5,2] => [1,5,6,7,4,3,2] => 1
[1,7,6,3,5,2,4] => [1,7,6,4,5,3,2] => 3
[1,7,6,3,5,4,2] => [1,5,7,6,4,3,2] => 1
[1,7,6,4,2,3,5] => [1,5,6,4,7,3,2] => 1
[1,7,6,4,2,5,3] => [1,5,6,7,4,3,2] => 1
[1,7,6,4,3,2,5] => [1,6,5,4,7,3,2] => 1
[1,7,6,4,3,5,2] => [1,6,5,7,4,3,2] => 1
[1,7,6,4,5,2,3] => [1,7,6,5,4,3,2] => 1
[1,7,6,4,5,3,2] => [1,6,7,5,4,3,2] => 1
[1,7,6,5,2,3,4] => [1,5,6,7,4,3,2] => 1
[1,7,6,5,2,4,3] => [1,5,7,6,4,3,2] => 1
[1,7,6,5,3,2,4] => [1,6,5,7,4,3,2] => 1
[1,7,6,5,3,4,2] => [1,6,7,5,4,3,2] => 1
[1,7,6,5,4,2,3] => [1,6,7,5,4,3,2] => 1
[1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[2,1,6,7,4,5,3] => [2,1,7,6,5,4,3] => 1
[2,1,6,7,5,3,4] => [2,1,7,6,5,4,3] => 1
[2,1,7,5,6,3,4] => [2,1,7,6,5,4,3] => 1
[2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1
[2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 1
[2,3,4,1,5,7,6] => [2,3,4,1,5,7,6] => 1
[2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => 1
[2,3,4,5,1,7,6] => [2,3,4,5,1,7,6] => 1
[2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => 1
[2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => 1
[2,3,4,7,6,1,5] => [2,3,5,6,7,1,4] => 3
[2,3,5,7,4,1,6] => [2,3,5,6,7,1,4] => 3
[2,4,5,7,6,1,3] => [3,4,5,6,7,1,2] => 8
[2,4,7,5,1,3,6] => [7,4,5,6,1,2,3] => 31
[2,5,6,3,4,1,7] => [2,6,5,4,3,1,7] => 1
[2,5,7,3,1,4,6] => [7,4,5,6,1,2,3] => 31
[2,5,7,4,1,3,6] => [7,6,5,4,1,2,3] => 1
[2,6,5,4,3,1,7] => [2,6,5,4,3,1,7] => 1
[2,7,5,4,3,1,6] => [7,6,5,4,3,1,2] => 1
[3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[3,1,4,2,5,6,7] => [2,3,4,1,5,6,7] => 1
[3,1,4,2,5,7,6] => [2,3,4,1,5,7,6] => 1
[3,1,4,5,2,6,7] => [2,3,4,5,1,6,7] => 1
[3,1,4,5,2,7,6] => [2,3,4,5,1,7,6] => 1
[3,1,4,5,6,2,7] => [2,3,4,5,6,1,7] => 1
[3,1,4,5,6,7,2] => [2,3,4,5,6,7,1] => 1
[3,1,4,7,6,2,5] => [2,3,5,6,7,1,4] => 3
[3,1,5,7,4,2,6] => [2,3,5,6,7,1,4] => 3
[3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 1
[3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => 1
[3,4,1,2,5,6,7] => [4,3,2,1,5,6,7] => 1
[3,4,1,5,6,7,2] => [4,3,2,5,6,7,1] => 1
[3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => 1
[3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => 1
[3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => 1
[3,4,6,5,1,7,2] => [3,4,5,6,2,7,1] => 1
[3,5,1,4,6,7,2] => [5,3,2,4,6,7,1] => 2
[3,5,4,1,6,7,2] => [3,4,5,2,6,7,1] => 1
[3,5,6,4,1,2,7] => [3,6,5,4,2,1,7] => 1
[3,5,6,4,2,1,7] => [3,5,6,4,2,1,7] => 1
[3,5,7,2,1,4,6] => [6,4,5,7,1,2,3] => 20
[3,6,1,5,4,2,7] => [6,3,2,5,4,1,7] => 3
[3,6,4,5,1,2,7] => [3,6,5,4,2,1,7] => 1
[3,6,4,5,2,1,7] => [3,5,6,4,2,1,7] => 1
[3,6,5,4,1,2,7] => [3,5,6,4,2,1,7] => 1
[3,6,5,4,2,1,7] => [3,6,5,4,2,1,7] => 1
[3,6,7,4,1,2,5] => [7,6,5,4,3,1,2] => 1
[3,7,5,1,6,2,4] => [6,4,7,3,5,1,2] => 8
[3,7,6,4,2,1,5] => [7,6,5,4,3,1,2] => 1
[4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => 1
[4,1,2,5,3,6,7] => [2,3,4,5,1,6,7] => 1
[4,1,2,5,3,7,6] => [2,3,4,5,1,7,6] => 1
[4,1,2,5,6,3,7] => [2,3,4,5,6,1,7] => 1
[4,1,2,5,6,7,3] => [2,3,4,5,6,7,1] => 1
[4,1,2,7,6,3,5] => [2,3,5,6,7,1,4] => 3
[4,2,1,5,6,7,3] => [3,2,4,5,6,7,1] => 1
[4,2,3,5,6,7,1] => [3,4,2,5,6,7,1] => 1
[4,2,5,3,6,7,1] => [3,4,5,2,6,7,1] => 1
[4,2,5,6,3,7,1] => [3,4,5,6,2,7,1] => 1
[4,3,1,5,6,7,2] => [3,4,2,5,6,7,1] => 1
[4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 1
[4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => 1
[4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => 1
[4,3,5,6,1,2,7] => [4,3,6,5,2,1,7] => 1
[4,3,6,1,5,2,7] => [6,3,4,2,5,1,7] => 4
[4,3,6,5,2,1,7] => [4,3,6,5,2,1,7] => 1
[4,5,1,2,6,7,3] => [4,3,5,2,6,7,1] => 1
[4,5,1,6,2,3,7] => [6,3,4,5,2,1,7] => 4
[4,5,2,1,6,7,3] => [3,4,5,2,6,7,1] => 1
[4,5,2,3,1,6,7] => [5,4,3,2,1,6,7] => 1
[4,5,2,3,1,7,6] => [5,4,3,2,1,7,6] => 1
[4,5,2,3,6,1,7] => [5,4,3,2,6,1,7] => 1
[4,5,2,6,3,1,7] => [5,4,3,6,2,1,7] => 1
[4,5,3,1,2,6,7] => [5,4,3,2,1,6,7] => 1
[4,5,3,1,2,7,6] => [5,4,3,2,1,7,6] => 1
[4,5,3,1,6,2,7] => [5,4,3,2,6,1,7] => 1
[4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => 1
[4,5,6,1,2,3,7] => [6,5,4,3,2,1,7] => 1
[4,5,6,1,3,2,7] => [5,6,4,3,2,1,7] => 1
[4,5,6,2,3,1,7] => [4,6,5,3,2,1,7] => 1
[4,5,6,3,1,2,7] => [4,6,5,3,2,1,7] => 1
[4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => 1
[4,6,1,5,3,2,7] => [6,3,4,5,2,1,7] => 4
[4,6,2,5,1,3,7] => [5,6,4,3,2,1,7] => 1
[4,6,2,5,3,1,7] => [6,4,3,5,2,1,7] => 2
[4,6,3,5,2,1,7] => [6,5,3,4,2,1,7] => 3
[4,6,5,1,3,2,7] => [5,4,6,3,2,1,7] => 1
[4,6,5,2,1,3,7] => [6,5,4,3,2,1,7] => 1
[4,6,5,2,3,1,7] => [4,5,6,3,2,1,7] => 1
[4,6,5,3,1,2,7] => [4,5,6,3,2,1,7] => 1
[4,6,5,3,2,1,7] => [4,6,5,3,2,1,7] => 1
[5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => 1
[5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => 1
[5,1,2,3,6,4,7] => [2,3,4,5,6,1,7] => 1
[5,1,2,3,6,7,4] => [2,3,4,5,6,7,1] => 1
[5,1,2,7,4,3,6] => [2,3,5,6,7,1,4] => 3
[5,1,6,3,4,2,7] => [2,6,5,4,3,1,7] => 1
[5,1,6,4,2,3,7] => [2,6,5,4,3,1,7] => 1
[5,2,1,3,6,7,4] => [3,2,4,5,6,7,1] => 1
[5,2,3,1,6,7,4] => [3,4,2,5,6,7,1] => 1
[5,2,3,4,6,7,1] => [3,4,5,2,6,7,1] => 1
[5,2,3,6,4,7,1] => [3,4,5,6,2,7,1] => 1
[5,2,6,1,4,3,7] => [6,2,4,5,3,1,7] => 4
[5,2,6,3,4,1,7] => [3,6,5,4,2,1,7] => 1
[5,2,6,4,3,1,7] => [3,5,6,4,2,1,7] => 1
[5,3,1,2,6,7,4] => [3,4,2,5,6,7,1] => 1
[5,3,1,4,6,7,2] => [3,4,5,2,6,7,1] => 1
[5,3,1,6,4,7,2] => [3,4,5,6,2,7,1] => 1
[5,3,2,1,6,7,4] => [4,3,2,5,6,7,1] => 1
[5,3,2,4,6,7,1] => [4,3,5,2,6,7,1] => 1
[5,3,2,6,1,4,7] => [6,3,2,5,4,1,7] => 3
[5,3,4,1,2,6,7] => [5,4,3,2,1,6,7] => 1
[5,3,4,1,2,7,6] => [5,4,3,2,1,7,6] => 1
[5,3,4,1,6,2,7] => [5,4,3,2,6,1,7] => 1
[5,3,4,6,2,1,7] => [4,5,3,6,2,1,7] => 1
[5,3,6,1,4,2,7] => [6,3,4,5,2,1,7] => 4
[5,3,6,2,4,1,7] => [6,3,5,4,2,1,7] => 2
[5,3,6,4,1,2,7] => [4,6,5,3,2,1,7] => 1
[5,3,6,4,2,1,7] => [4,5,6,3,2,1,7] => 1
[5,4,1,2,6,7,3] => [3,4,5,2,6,7,1] => 1
[5,4,2,1,6,7,3] => [4,3,5,2,6,7,1] => 1
[5,4,2,6,1,3,7] => [6,3,4,5,2,1,7] => 4
[5,4,2,6,3,1,7] => [4,5,3,6,2,1,7] => 1
[5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 1
[5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => 1
[5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => 1
[5,4,3,6,1,2,7] => [6,4,3,5,2,1,7] => 2
[5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => 1
[5,4,6,1,2,3,7] => [5,6,4,3,2,1,7] => 1
[5,4,6,1,3,2,7] => [6,5,4,3,2,1,7] => 1
[5,4,6,2,1,3,7] => [4,6,5,3,2,1,7] => 1
[5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => 1
[5,6,1,2,4,3,7] => [4,3,6,5,2,1,7] => 1
[5,6,1,4,3,2,7] => [6,3,5,4,2,1,7] => 2
[5,6,2,1,3,7,4] => [3,4,5,6,2,7,1] => 1
[5,6,2,3,1,4,7] => [5,4,3,6,2,1,7] => 1
[5,6,2,3,4,1,7] => [5,4,6,3,2,1,7] => 1
[5,6,3,1,2,4,7] => [5,4,3,6,2,1,7] => 1
[5,6,3,1,4,2,7] => [5,4,6,3,2,1,7] => 1
[5,6,3,2,1,4,7] => [4,5,3,6,2,1,7] => 1
[5,6,3,2,4,1,7] => [4,5,6,3,2,1,7] => 1
[5,6,3,4,1,2,7] => [5,6,4,3,2,1,7] => 1
[5,6,3,4,2,1,7] => [6,5,4,3,2,1,7] => 1
[5,6,4,1,2,3,7] => [5,4,6,3,2,1,7] => 1
[5,6,4,2,1,3,7] => [4,5,6,3,2,1,7] => 1
[5,6,4,2,3,1,7] => [6,5,4,3,2,1,7] => 1
[5,6,4,3,1,2,7] => [6,5,4,3,2,1,7] => 1
[5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => 1
[5,6,7,2,3,4,1] => [7,6,5,4,3,2,1] => 1
[5,6,7,3,1,4,2] => [7,6,5,4,3,2,1] => 1
[5,6,7,4,1,2,3] => [7,6,5,4,3,2,1] => 1
[5,7,2,1,3,4,6] => [3,4,5,6,7,1,2] => 8
[5,7,6,3,2,4,1] => [7,6,5,4,3,2,1] => 1
[5,7,6,4,2,1,3] => [7,6,5,4,3,2,1] => 1
[6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => 1
[6,1,2,3,4,7,5] => [2,3,4,5,6,7,1] => 1
[6,1,4,5,2,3,7] => [2,6,5,4,3,1,7] => 1
[6,1,5,4,3,2,7] => [2,6,5,4,3,1,7] => 1
[6,2,1,3,4,7,5] => [3,2,4,5,6,7,1] => 1
[6,2,3,1,4,7,5] => [3,4,2,5,6,7,1] => 1
[6,2,3,4,1,7,5] => [3,4,5,2,6,7,1] => 1
[6,2,3,4,5,7,1] => [3,4,5,6,2,7,1] => 1
[6,2,4,5,3,1,7] => [3,5,6,4,2,1,7] => 1
[6,2,5,3,4,1,7] => [3,5,6,4,2,1,7] => 1
[6,2,5,4,3,1,7] => [3,6,5,4,2,1,7] => 1
[6,3,1,2,4,7,5] => [3,4,2,5,6,7,1] => 1
[6,3,1,4,2,7,5] => [3,4,5,2,6,7,1] => 1
[6,3,1,4,5,7,2] => [3,4,5,6,2,7,1] => 1
[6,3,2,1,4,7,5] => [4,3,2,5,6,7,1] => 1
[6,3,2,4,1,7,5] => [4,3,5,2,6,7,1] => 1
[6,3,2,5,4,1,7] => [4,3,6,5,2,1,7] => 1
[6,3,4,1,2,5,7] => [5,4,3,2,6,1,7] => 1
[6,3,4,1,5,2,7] => [5,4,3,6,2,1,7] => 1
[6,3,4,2,5,1,7] => [4,5,3,6,2,1,7] => 1
[6,3,4,5,1,2,7] => [4,6,5,3,2,1,7] => 1
[6,3,4,5,2,1,7] => [4,5,6,3,2,1,7] => 1
[6,3,5,1,4,2,7] => [6,4,3,5,2,1,7] => 2
[6,3,5,2,4,1,7] => [6,5,3,4,2,1,7] => 3
[6,3,5,4,1,2,7] => [4,5,6,3,2,1,7] => 1
[6,3,5,4,2,1,7] => [4,6,5,3,2,1,7] => 1
[6,4,1,2,3,7,5] => [3,4,5,2,6,7,1] => 1
[6,4,1,2,5,7,3] => [3,4,5,6,2,7,1] => 1
[6,4,1,5,2,3,7] => [3,6,5,4,2,1,7] => 1
[6,4,1,5,3,2,7] => [3,5,6,4,2,1,7] => 1
[6,4,2,1,3,7,5] => [4,3,5,2,6,7,1] => 1
[6,4,2,3,5,1,7] => [4,5,3,6,2,1,7] => 1
[6,4,2,5,1,3,7] => [6,3,5,4,2,1,7] => 2
[6,4,2,5,3,1,7] => [4,5,6,3,2,1,7] => 1
[6,4,3,1,5,2,7] => [4,5,3,6,2,1,7] => 1
[6,4,3,2,1,5,7] => [5,4,3,2,6,1,7] => 1
[6,4,3,2,5,1,7] => [5,4,3,6,2,1,7] => 1
[6,4,3,5,2,1,7] => [5,4,6,3,2,1,7] => 1
[6,4,5,1,2,3,7] => [5,4,6,3,2,1,7] => 1
[6,4,5,2,1,3,7] => [4,5,6,3,2,1,7] => 1
[6,4,5,2,3,1,7] => [6,5,4,3,2,1,7] => 1
[6,4,5,3,1,2,7] => [6,5,4,3,2,1,7] => 1
[6,4,5,3,2,1,7] => [5,6,4,3,2,1,7] => 1
[6,4,7,5,1,2,3] => [7,6,5,4,3,2,1] => 1
[6,5,1,2,3,7,4] => [3,4,5,6,2,7,1] => 1
[6,5,1,3,4,2,7] => [3,5,6,4,2,1,7] => 1
[6,5,1,4,2,3,7] => [3,5,6,4,2,1,7] => 1
[6,5,1,4,3,2,7] => [3,6,5,4,2,1,7] => 1
[6,5,2,1,4,3,7] => [4,3,6,5,2,1,7] => 1
[6,5,2,3,1,4,7] => [4,5,3,6,2,1,7] => 1
[6,5,2,3,4,1,7] => [4,5,6,3,2,1,7] => 1
[6,5,2,4,1,3,7] => [6,5,3,4,2,1,7] => 3
[6,5,2,4,3,1,7] => [4,6,5,3,2,1,7] => 1
[6,5,3,1,2,4,7] => [4,5,3,6,2,1,7] => 1
[6,5,3,1,4,2,7] => [4,5,6,3,2,1,7] => 1
[6,5,3,2,1,4,7] => [5,4,3,6,2,1,7] => 1
[6,5,3,2,4,1,7] => [5,4,6,3,2,1,7] => 1
[6,5,3,4,1,2,7] => [6,5,4,3,2,1,7] => 1
[6,5,3,4,2,1,7] => [5,6,4,3,2,1,7] => 1
[6,5,4,1,2,3,7] => [4,5,6,3,2,1,7] => 1
[6,5,4,1,3,2,7] => [4,6,5,3,2,1,7] => 1
[6,5,4,2,1,3,7] => [5,4,6,3,2,1,7] => 1
[6,5,4,2,3,1,7] => [5,6,4,3,2,1,7] => 1
[6,5,4,3,1,2,7] => [5,6,4,3,2,1,7] => 1
[6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 1
[6,5,7,2,4,3,1] => [7,6,5,4,3,2,1] => 1
[6,5,7,4,1,3,2] => [7,6,5,4,3,2,1] => 1
[6,7,4,5,3,2,1] => [7,6,5,4,3,2,1] => 1
[6,7,5,3,4,2,1] => [7,6,5,4,3,2,1] => 1
[6,7,5,4,2,3,1] => [7,6,5,4,3,2,1] => 1
[6,7,5,4,3,1,2] => [7,6,5,4,3,2,1] => 1
[7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => 1
[7,2,1,3,4,5,6] => [3,2,4,5,6,7,1] => 1
[7,2,3,1,4,5,6] => [3,4,2,5,6,7,1] => 1
[7,2,3,4,1,5,6] => [3,4,5,2,6,7,1] => 1
[7,2,3,4,5,1,6] => [3,4,5,6,2,7,1] => 1
[7,3,1,2,4,5,6] => [3,4,2,5,6,7,1] => 1
[7,3,1,4,2,5,6] => [3,4,5,2,6,7,1] => 1
[7,3,1,4,5,2,6] => [3,4,5,6,2,7,1] => 1
[7,3,2,1,4,5,6] => [4,3,2,5,6,7,1] => 1
[7,3,2,4,1,5,6] => [4,3,5,2,6,7,1] => 1
[7,4,1,2,3,5,6] => [3,4,5,2,6,7,1] => 1
[7,4,1,2,5,3,6] => [3,4,5,6,2,7,1] => 1
[7,4,2,1,3,5,6] => [4,3,5,2,6,7,1] => 1
[7,4,5,6,1,2,3] => [7,6,5,4,3,2,1] => 1
[7,4,6,5,2,1,3] => [7,6,5,4,3,2,1] => 1
[7,5,1,2,3,4,6] => [3,4,5,6,2,7,1] => 1
[7,5,4,6,1,3,2] => [7,6,5,4,3,2,1] => 1
[7,5,6,3,4,2,1] => [7,6,5,4,3,2,1] => 1
[7,5,6,4,2,3,1] => [7,6,5,4,3,2,1] => 1
[7,5,6,4,3,1,2] => [7,6,5,4,3,2,1] => 1
[7,6,4,5,2,3,1] => [7,6,5,4,3,2,1] => 1
[7,6,4,5,3,1,2] => [7,6,5,4,3,2,1] => 1
[7,6,5,3,4,1,2] => [7,6,5,4,3,2,1] => 1
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 1
[8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1
[8,7,5,6,3,4,2,1] => [8,7,6,5,4,3,2,1] => 1
[8,6,7,5,4,2,3,1] => [8,7,6,5,4,3,2,1] => 1
[8,5,6,7,2,3,4,1] => [8,7,6,5,4,3,2,1] => 1
[5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,8,1] => 1
[2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => 1
[7,8,6,5,4,3,1,2] => [8,7,6,5,4,3,2,1] => 1
[7,8,5,6,3,4,1,2] => [8,7,6,5,4,3,2,1] => 1
[7,8,3,4,5,6,1,2] => [6,5,8,7,4,3,2,1] => 1
[8,7,6,5,4,2,1,3] => [7,6,8,5,4,3,2,1] => 1
[6,7,8,5,4,1,2,3] => [8,7,6,5,4,3,2,1] => 1
[7,6,5,8,3,2,1,4] => [6,5,8,7,4,3,2,1] => 1
[6,5,7,8,2,1,3,4] => [7,8,5,6,4,3,2,1] => 4
[6,7,5,8,1,2,3,4] => [7,6,8,5,4,3,2,1] => 1
[7,5,6,8,1,2,3,4] => [7,6,8,5,4,3,2,1] => 1
[5,6,7,8,1,2,3,4] => [8,7,6,5,4,3,2,1] => 1
[8,7,6,4,3,2,1,5] => [7,6,5,4,8,3,2,1] => 1
[8,7,6,4,2,1,3,5] => [6,5,7,4,8,3,2,1] => 1
[8,6,5,4,3,2,1,7] => [7,6,5,4,3,2,8,1] => 1
[8,6,5,4,2,1,3,7] => [6,5,7,4,3,2,8,1] => 1
[8,6,4,3,2,1,5,7] => [6,5,4,3,7,2,8,1] => 1
[8,6,4,2,1,3,5,7] => [5,4,6,3,7,2,8,1] => 1
[8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => 1
[7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 1
[7,5,6,3,4,2,1,8] => [7,6,5,4,3,2,1,8] => 1
[6,7,5,4,2,3,1,8] => [7,6,5,4,3,2,1,8] => 1
[6,5,7,3,2,4,1,8] => [5,7,6,4,3,2,1,8] => 1
[7,6,5,2,3,4,1,8] => [5,6,7,4,3,2,1,8] => 1
[6,7,5,2,3,4,1,8] => [6,5,7,4,3,2,1,8] => 1
[7,5,6,2,3,4,1,8] => [6,5,7,4,3,2,1,8] => 1
[6,5,7,2,3,4,1,8] => [6,7,5,4,3,2,1,8] => 1
[5,6,7,2,3,4,1,8] => [7,6,5,4,3,2,1,8] => 1
[5,6,7,1,2,3,4,8] => [6,5,4,7,3,2,1,8] => 1
[4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 1
[1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 1
[3,5,8,7,6,4,2,1] => [3,5,8,7,6,4,2,1] => 1
[2,6,8,7,5,4,3,1] => [2,6,8,7,5,4,3,1] => 1
[2,3,5,6,8,7,4,1] => [2,3,5,6,8,7,4,1] => 1
[4,3,6,5,7,2,8,1] => [4,3,6,5,7,2,8,1] => 1
[3,2,6,5,7,4,8,1] => [3,2,6,5,7,4,8,1] => 1
[4,3,5,2,7,6,8,1] => [4,3,5,2,7,6,8,1] => 1
[3,2,5,4,7,6,8,1] => [3,2,5,4,7,6,8,1] => 1
[1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 1
[1,7,8,6,5,4,3,2] => [1,7,8,6,5,4,3,2] => 1
[1,3,5,7,8,6,4,2] => [1,3,5,7,8,6,4,2] => 1
[1,4,3,8,7,6,5,2] => [1,4,3,8,7,6,5,2] => 1
[1,6,5,4,3,8,7,2] => [1,6,5,4,3,8,7,2] => 1
[1,4,3,6,5,8,7,2] => [1,4,3,6,5,8,7,2] => 1
[2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => 1
[2,1,6,5,7,4,8,3] => [2,1,6,5,7,4,8,3] => 1
[2,1,5,4,7,6,8,3] => [2,1,5,4,7,6,8,3] => 1
[1,2,6,7,8,5,4,3] => [1,2,6,7,8,5,4,3] => 1
[3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => 1
[3,2,1,6,5,8,7,4] => [3,2,1,6,5,8,7,4] => 1
[1,2,3,5,6,7,8,4] => [1,2,3,5,6,7,8,4] => 1
[4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => 1
[3,4,2,1,7,8,6,5] => [3,4,2,1,7,8,6,5] => 1
[2,4,3,1,6,8,7,5] => [2,4,3,1,6,8,7,5] => 1
[2,4,3,1,7,6,8,5] => [2,4,3,1,7,6,8,5] => 1
[3,2,4,1,6,8,7,5] => [3,2,4,1,6,8,7,5] => 1
[3,2,4,1,7,6,8,5] => [3,2,4,1,7,6,8,5] => 1
[2,3,4,1,6,7,8,5] => [2,3,4,1,6,7,8,5] => 1
[2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => 1
[2,1,4,3,6,8,7,5] => [2,1,4,3,6,8,7,5] => 1
[2,1,4,3,7,6,8,5] => [2,1,4,3,7,6,8,5] => 1
[5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => 1
[3,2,5,4,1,8,7,6] => [3,2,5,4,1,8,7,6] => 1
[3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6] => 1
[2,3,1,4,5,7,8,6] => [2,3,1,4,5,7,8,6] => 1
[6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[4,3,5,2,6,1,8,7] => [4,3,5,2,6,1,8,7] => 1
[3,2,5,4,6,1,8,7] => [3,2,5,4,6,1,8,7] => 1
[2,3,4,5,6,1,8,7] => [2,3,4,5,6,1,8,7] => 1
[2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => 1
[2,1,4,6,5,3,8,7] => [2,1,4,6,5,3,8,7] => 1
[2,1,5,4,6,3,8,7] => [2,1,5,4,6,3,8,7] => 1
[4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 1
[2,4,3,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => 1
[3,2,4,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => 1
[2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 1
[2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 1
[3,2,7,6,5,4,1,8] => [3,2,7,6,5,4,1,8] => 1
[5,4,3,2,7,6,1,8] => [5,4,3,2,7,6,1,8] => 1
[3,2,5,4,7,6,1,8] => [3,2,5,4,7,6,1,8] => 1
[1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8] => 1
[1,3,4,2,6,7,5,8] => [1,3,4,2,6,7,5,8] => 1
[1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 1
[1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 1
[4,2,3,1,8,6,7,5] => [3,4,2,1,7,8,6,5] => 1
[8,3,2,5,4,7,6,1] => [4,3,6,5,8,7,2,1] => 1
[8,7,4,3,6,5,2,1] => [6,5,8,7,4,3,2,1] => 1
[2,4,6,8,1,3,5,7] => [8,7,6,5,1,2,3,4] => 1
[2,1,4,3,7,8,5,6] => [2,1,4,3,8,7,6,5] => 1
[2,1,5,6,3,4,8,7] => [2,1,6,5,4,3,8,7] => 1
[2,1,6,7,8,3,4,5] => [2,1,8,7,6,5,4,3] => 1
[3,4,1,2,6,5,8,7] => [4,3,2,1,6,5,8,7] => 1
[3,1,4,2,7,5,8,6] => [2,3,4,1,6,7,8,5] => 1
[3,4,1,2,7,8,5,6] => [4,3,2,1,8,7,6,5] => 1
[3,1,2,4,5,8,6,7] => [2,3,1,4,5,7,8,6] => 1
[4,5,6,1,2,3,8,7] => [6,5,4,3,2,1,8,7] => 1
[1,4,2,3,7,5,6,8] => [1,3,4,2,6,7,5,8] => 1
[4,1,2,3,8,5,6,7] => [2,3,4,1,6,7,8,5] => 1
[1,6,7,8,2,3,4,5] => [1,7,6,5,8,4,3,2] => 1
[6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7] => 1
[5,3,2,6,1,4,8,7] => [6,3,2,5,4,1,8,7] => 3
[7,4,5,2,3,8,1,6] => [8,5,4,3,2,7,6,1] => 3
[6,4,5,2,3,1,8,7] => [6,5,4,3,2,1,8,7] => 1
[3,6,1,5,4,2,8,7] => [6,3,2,5,4,1,8,7] => 3
[5,6,4,3,1,2,8,7] => [6,5,4,3,2,1,8,7] => 1
[7,5,4,3,2,8,1,6] => [8,5,4,3,2,7,6,1] => 3
[6,7,4,3,8,1,2,5] => [8,7,4,3,6,5,2,1] => 6
[2,1,7,5,4,8,3,6] => [2,1,8,5,4,7,6,3] => 3
[3,8,1,6,7,4,5,2] => [8,3,2,7,6,5,4,1] => 3
[2,1,8,6,7,4,5,3] => [2,1,8,7,6,5,4,3] => 1
[5,7,6,8,1,3,2,4] => [8,7,6,5,4,3,2,1] => 1
[6,3,2,7,8,1,4,5] => [8,3,2,7,6,5,4,1] => 3
[4,3,2,1,7,8,5,6] => [4,3,2,1,8,7,6,5] => 1
[3,4,1,2,8,7,6,5] => [4,3,2,1,8,7,6,5] => 1
[5,3,2,8,1,7,6,4] => [8,3,2,5,4,7,6,1] => 9
[6,4,8,2,7,1,5,3] => [6,7,8,3,4,5,2,1] => 49
[4,5,8,1,2,7,6,3] => [8,5,4,3,2,7,6,1] => 3
[2,1,5,8,3,7,6,4] => [2,1,8,5,4,7,6,3] => 3
[5,6,8,7,1,2,4,3] => [7,8,5,6,4,3,2,1] => 4
[6,5,8,7,2,1,4,3] => [8,7,6,5,4,3,2,1] => 1
[8,5,7,6,2,4,3,1] => [7,6,8,5,4,3,2,1] => 1
[4,7,8,1,6,5,2,3] => [8,7,4,3,6,5,2,1] => 6
[2,1,7,8,6,5,3,4] => [2,1,8,7,6,5,4,3] => 1
[3,8,1,7,6,5,4,2] => [8,3,2,7,6,5,4,1] => 3
[5,8,7,6,1,4,3,2] => [6,5,8,7,4,3,2,1] => 1
[6,8,7,5,4,1,3,2] => [7,6,8,5,4,3,2,1] => 1
[6,4,7,2,5,1,3,8] => [6,5,7,4,3,2,1,8] => 1
[4,8,3,7,2,6,1,5] => [8,7,5,6,4,3,1,2] => 4
[5,6,7,8,2,1,4,3] => [7,8,5,6,4,3,2,1] => 4
[6,5,8,7,3,4,1,2] => [6,5,8,7,4,3,2,1] => 1
[4,1,3,2,8,6,5,7] => [2,4,3,1,7,6,8,5] => 1
[7,8,5,6,2,1,4,3] => [6,5,8,7,4,3,2,1] => 1
[6,5,8,7,1,2,3,4] => [7,8,5,6,4,3,2,1] => 4
[4,3,1,2,8,7,5,6] => [3,4,2,1,7,8,6,5] => 1
[4,2,1,3,8,5,7,6] => [3,2,4,1,6,8,7,5] => 1
[6,4,7,2,5,1,8,3] => [6,5,7,4,3,2,8,1] => 1
[6,1,8,4,7,2,5,3] => [2,6,8,7,5,4,3,1] => 1
[1,6,8,4,7,2,5,3] => [1,6,8,7,5,4,3,2] => 1
[4,1,3,2,6,5,8,7] => [2,4,3,1,6,5,8,7] => 1
[2,1,6,3,5,4,8,7] => [2,1,4,6,5,3,8,7] => 1
[2,1,4,3,8,5,7,6] => [2,1,4,3,6,8,7,5] => 1
[4,1,3,2,8,5,7,6] => [2,4,3,1,6,8,7,5] => 1
[5,7,3,8,2,4,1,6] => [8,7,5,6,3,4,1,2] => 28
[7,4,5,3,8,2,1,6] => [8,6,4,3,7,2,5,1] => 8
[7,4,5,3,1,8,2,6] => [8,5,4,3,2,7,6,1] => 3
[7,5,8,2,4,6,1,3] => [8,7,6,5,4,3,2,1] => 1
[6,4,7,8,2,1,5,3] => [8,7,5,6,3,4,2,1] => 18
[6,4,7,1,8,2,5,3] => [8,7,4,3,6,5,2,1] => 6
[4,5,2,3,7,6,1,8] => [5,4,3,2,7,6,1,8] => 1
[6,4,3,7,2,5,1,8] => [7,4,3,6,5,2,1,8] => 3
[1,5,6,3,4,8,7,2] => [1,6,5,4,3,8,7,2] => 1
[3,2,6,7,4,5,1,8] => [3,2,7,6,5,4,1,8] => 1
[4,7,2,6,5,3,1,8] => [7,4,3,6,5,2,1,8] => 3
[5,7,6,2,4,3,1,8] => [6,5,7,4,3,2,1,8] => 1
[1,7,5,4,8,3,6,2] => [1,8,5,4,7,6,3,2] => 3
[1,8,6,7,4,5,3,2] => [1,8,7,6,5,4,3,2] => 1
[3,2,1,7,8,5,6,4] => [3,2,1,8,7,6,5,4] => 1
[1,7,6,8,4,3,5,2] => [1,6,8,7,5,4,3,2] => 1
[1,6,7,8,3,4,5,2] => [1,8,7,6,5,4,3,2] => 1
[1,4,3,7,8,5,6,2] => [1,4,3,8,7,6,5,2] => 1
[4,5,2,3,1,8,7,6] => [5,4,3,2,1,8,7,6] => 1
[1,5,8,3,7,6,4,2] => [1,8,5,4,7,6,3,2] => 3
[1,6,8,7,3,5,4,2] => [1,7,6,8,5,4,3,2] => 1
[1,7,8,6,5,3,4,2] => [1,8,7,6,5,4,3,2] => 1
[1,8,6,7,3,4,5,2] => [1,7,6,8,5,4,3,2] => 1
[1,7,6,8,3,4,5,2] => [1,7,8,6,5,4,3,2] => 1
[1,7,8,6,3,4,5,2] => [1,7,6,8,5,4,3,2] => 1
[1,8,7,6,3,4,5,2] => [1,6,7,8,5,4,3,2] => 1
[5,4,6,1,7,3,8,2] => [6,5,4,3,7,2,8,1] => 1
[2,1,7,8,5,6,4,3] => [2,1,8,7,6,5,4,3] => 1
[5,8,7,4,2,6,3,1] => [8,6,7,5,3,4,2,1] => 10
[3,7,8,4,5,1,2,6] => [8,6,7,5,4,3,1,2] => 3
[5,7,3,8,1,4,2,6] => [8,7,6,5,3,4,1,2] => 4
[5,7,8,4,3,6,2,1] => [8,6,7,5,3,4,2,1] => 10
[2,4,3,1,8,5,7,6] => [2,4,3,1,6,8,7,5] => 1
[4,1,3,2,6,8,7,5] => [2,4,3,1,6,8,7,5] => 1
[5,8,2,4,7,6,1,3] => [6,5,7,4,8,3,2,1] => 1
[3,8,7,4,5,2,1,6] => [8,6,7,5,4,3,1,2] => 3
[3,8,6,7,2,4,1,5] => [8,7,6,5,3,4,1,2] => 4
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
108,10,2 525,118,30,32,4,8,0,2,1
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 6\ q$
$F_{4} = 24\ q$
$F_{5} = 108\ q + 10\ q^{2} + 2\ q^{3}$
$F_{6} = 525\ q + 118\ q^{2} + 30\ q^{3} + 32\ q^{4} + 4\ q^{5} + 8\ q^{6} + 2\ q^{8} + q^{9}$
Description
The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation.
These are multiplicities of Verma modules.
These are multiplicities of Verma modules.
Map
catalanization
Description
The catalanization of a permutation.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.
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