Identifier
-
Mp00069:
Permutations
—complement⟶
Permutations
St000837: Permutations ⟶ ℤ
Values
[1,2] => [2,1] => 0
[2,1] => [1,2] => 0
[1,2,3] => [3,2,1] => 0
[1,3,2] => [3,1,2] => 0
[2,1,3] => [2,3,1] => 0
[2,3,1] => [2,1,3] => 1
[3,1,2] => [1,3,2] => 1
[3,2,1] => [1,2,3] => 1
[1,2,3,4] => [4,3,2,1] => 0
[1,2,4,3] => [4,3,1,2] => 0
[1,3,2,4] => [4,2,3,1] => 0
[1,3,4,2] => [4,2,1,3] => 1
[1,4,2,3] => [4,1,3,2] => 1
[1,4,3,2] => [4,1,2,3] => 1
[2,1,3,4] => [3,4,2,1] => 0
[2,1,4,3] => [3,4,1,2] => 0
[2,3,1,4] => [3,2,4,1] => 1
[2,3,4,1] => [3,2,1,4] => 1
[2,4,1,3] => [3,1,4,2] => 2
[2,4,3,1] => [3,1,2,4] => 1
[3,1,2,4] => [2,4,3,1] => 1
[3,1,4,2] => [2,4,1,3] => 0
[3,2,1,4] => [2,3,4,1] => 1
[3,2,4,1] => [2,3,1,4] => 1
[3,4,1,2] => [2,1,4,3] => 2
[3,4,2,1] => [2,1,3,4] => 2
[4,1,2,3] => [1,4,3,2] => 1
[4,1,3,2] => [1,4,2,3] => 1
[4,2,1,3] => [1,3,4,2] => 1
[4,2,3,1] => [1,3,2,4] => 2
[4,3,1,2] => [1,2,4,3] => 2
[4,3,2,1] => [1,2,3,4] => 2
[1,2,3,4,5] => [5,4,3,2,1] => 0
[1,2,3,5,4] => [5,4,3,1,2] => 0
[1,2,4,3,5] => [5,4,2,3,1] => 0
[1,2,4,5,3] => [5,4,2,1,3] => 1
[1,2,5,3,4] => [5,4,1,3,2] => 1
[1,2,5,4,3] => [5,4,1,2,3] => 1
[1,3,2,4,5] => [5,3,4,2,1] => 0
[1,3,2,5,4] => [5,3,4,1,2] => 0
[1,3,4,2,5] => [5,3,2,4,1] => 1
[1,3,4,5,2] => [5,3,2,1,4] => 1
[1,3,5,2,4] => [5,3,1,4,2] => 2
[1,3,5,4,2] => [5,3,1,2,4] => 1
[1,4,2,3,5] => [5,2,4,3,1] => 1
[1,4,2,5,3] => [5,2,4,1,3] => 0
[1,4,3,2,5] => [5,2,3,4,1] => 1
[1,4,3,5,2] => [5,2,3,1,4] => 1
[1,4,5,2,3] => [5,2,1,4,3] => 2
[1,4,5,3,2] => [5,2,1,3,4] => 2
[1,5,2,3,4] => [5,1,4,3,2] => 1
[1,5,2,4,3] => [5,1,4,2,3] => 1
[1,5,3,2,4] => [5,1,3,4,2] => 1
[1,5,3,4,2] => [5,1,3,2,4] => 2
[1,5,4,2,3] => [5,1,2,4,3] => 2
[1,5,4,3,2] => [5,1,2,3,4] => 2
[2,1,3,4,5] => [4,5,3,2,1] => 0
[2,1,3,5,4] => [4,5,3,1,2] => 0
[2,1,4,3,5] => [4,5,2,3,1] => 0
[2,1,4,5,3] => [4,5,2,1,3] => 1
[2,1,5,3,4] => [4,5,1,3,2] => 1
[2,1,5,4,3] => [4,5,1,2,3] => 1
[2,3,1,4,5] => [4,3,5,2,1] => 1
[2,3,1,5,4] => [4,3,5,1,2] => 1
[2,3,4,1,5] => [4,3,2,5,1] => 1
[2,3,4,5,1] => [4,3,2,1,5] => 1
[2,3,5,1,4] => [4,3,1,5,2] => 2
[2,3,5,4,1] => [4,3,1,2,5] => 1
[2,4,1,3,5] => [4,2,5,3,1] => 2
[2,4,1,5,3] => [4,2,5,1,3] => 1
[2,4,3,1,5] => [4,2,3,5,1] => 1
[2,4,3,5,1] => [4,2,3,1,5] => 1
[2,4,5,1,3] => [4,2,1,5,3] => 2
[2,4,5,3,1] => [4,2,1,3,5] => 2
[2,5,1,3,4] => [4,1,5,3,2] => 2
[2,5,1,4,3] => [4,1,5,2,3] => 2
[2,5,3,1,4] => [4,1,3,5,2] => 1
[2,5,3,4,1] => [4,1,3,2,5] => 2
[2,5,4,1,3] => [4,1,2,5,3] => 2
[2,5,4,3,1] => [4,1,2,3,5] => 2
[3,1,2,4,5] => [3,5,4,2,1] => 1
[3,1,2,5,4] => [3,5,4,1,2] => 1
[3,1,4,2,5] => [3,5,2,4,1] => 0
[3,1,4,5,2] => [3,5,2,1,4] => 1
[3,1,5,2,4] => [3,5,1,4,2] => 1
[3,1,5,4,2] => [3,5,1,2,4] => 1
[3,2,1,4,5] => [3,4,5,2,1] => 1
[3,2,1,5,4] => [3,4,5,1,2] => 1
[3,2,4,1,5] => [3,4,2,5,1] => 1
[3,2,4,5,1] => [3,4,2,1,5] => 1
[3,2,5,1,4] => [3,4,1,5,2] => 2
[3,2,5,4,1] => [3,4,1,2,5] => 1
[3,4,1,2,5] => [3,2,5,4,1] => 2
[3,4,1,5,2] => [3,2,5,1,4] => 1
[3,4,2,1,5] => [3,2,4,5,1] => 2
[3,4,2,5,1] => [3,2,4,1,5] => 2
[3,4,5,1,2] => [3,2,1,5,4] => 2
[3,4,5,2,1] => [3,2,1,4,5] => 2
[3,5,1,2,4] => [3,1,5,4,2] => 2
[3,5,1,4,2] => [3,1,5,2,4] => 2
[3,5,2,1,4] => [3,1,4,5,2] => 2
>>> Load all 1200 entries. <<<[3,5,2,4,1] => [3,1,4,2,5] => 3
[3,5,4,1,2] => [3,1,2,5,4] => 2
[3,5,4,2,1] => [3,1,2,4,5] => 2
[4,1,2,3,5] => [2,5,4,3,1] => 1
[4,1,2,5,3] => [2,5,4,1,3] => 1
[4,1,3,2,5] => [2,5,3,4,1] => 1
[4,1,3,5,2] => [2,5,3,1,4] => 2
[4,1,5,2,3] => [2,5,1,4,3] => 1
[4,1,5,3,2] => [2,5,1,3,4] => 1
[4,2,1,3,5] => [2,4,5,3,1] => 1
[4,2,1,5,3] => [2,4,5,1,3] => 1
[4,2,3,1,5] => [2,4,3,5,1] => 2
[4,2,3,5,1] => [2,4,3,1,5] => 2
[4,2,5,1,3] => [2,4,1,5,3] => 2
[4,2,5,3,1] => [2,4,1,3,5] => 1
[4,3,1,2,5] => [2,3,5,4,1] => 2
[4,3,1,5,2] => [2,3,5,1,4] => 1
[4,3,2,1,5] => [2,3,4,5,1] => 2
[4,3,2,5,1] => [2,3,4,1,5] => 2
[4,3,5,1,2] => [2,3,1,5,4] => 2
[4,3,5,2,1] => [2,3,1,4,5] => 2
[4,5,1,2,3] => [2,1,5,4,3] => 2
[4,5,1,3,2] => [2,1,5,3,4] => 2
[4,5,2,1,3] => [2,1,4,5,3] => 2
[4,5,2,3,1] => [2,1,4,3,5] => 3
[4,5,3,1,2] => [2,1,3,5,4] => 3
[4,5,3,2,1] => [2,1,3,4,5] => 3
[5,1,2,3,4] => [1,5,4,3,2] => 1
[5,1,2,4,3] => [1,5,4,2,3] => 1
[5,1,3,2,4] => [1,5,3,4,2] => 1
[5,1,3,4,2] => [1,5,3,2,4] => 2
[5,1,4,2,3] => [1,5,2,4,3] => 2
[5,1,4,3,2] => [1,5,2,3,4] => 2
[5,2,1,3,4] => [1,4,5,3,2] => 1
[5,2,1,4,3] => [1,4,5,2,3] => 1
[5,2,3,1,4] => [1,4,3,5,2] => 2
[5,2,3,4,1] => [1,4,3,2,5] => 2
[5,2,4,1,3] => [1,4,2,5,3] => 3
[5,2,4,3,1] => [1,4,2,3,5] => 2
[5,3,1,2,4] => [1,3,5,4,2] => 2
[5,3,1,4,2] => [1,3,5,2,4] => 1
[5,3,2,1,4] => [1,3,4,5,2] => 2
[5,3,2,4,1] => [1,3,4,2,5] => 2
[5,3,4,1,2] => [1,3,2,5,4] => 3
[5,3,4,2,1] => [1,3,2,4,5] => 3
[5,4,1,2,3] => [1,2,5,4,3] => 2
[5,4,1,3,2] => [1,2,5,3,4] => 2
[5,4,2,1,3] => [1,2,4,5,3] => 2
[5,4,2,3,1] => [1,2,4,3,5] => 3
[5,4,3,1,2] => [1,2,3,5,4] => 3
[5,4,3,2,1] => [1,2,3,4,5] => 3
[1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,2,3,4,6,5] => [6,5,4,3,1,2] => 0
[1,2,3,5,4,6] => [6,5,4,2,3,1] => 0
[1,2,3,5,6,4] => [6,5,4,2,1,3] => 1
[1,2,3,6,4,5] => [6,5,4,1,3,2] => 1
[1,2,3,6,5,4] => [6,5,4,1,2,3] => 1
[1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,2,4,3,6,5] => [6,5,3,4,1,2] => 0
[1,2,4,5,3,6] => [6,5,3,2,4,1] => 1
[1,2,4,5,6,3] => [6,5,3,2,1,4] => 1
[1,2,4,6,3,5] => [6,5,3,1,4,2] => 2
[1,2,4,6,5,3] => [6,5,3,1,2,4] => 1
[1,2,5,3,4,6] => [6,5,2,4,3,1] => 1
[1,2,5,3,6,4] => [6,5,2,4,1,3] => 0
[1,2,5,4,3,6] => [6,5,2,3,4,1] => 1
[1,2,5,4,6,3] => [6,5,2,3,1,4] => 1
[1,2,5,6,3,4] => [6,5,2,1,4,3] => 2
[1,2,5,6,4,3] => [6,5,2,1,3,4] => 2
[1,2,6,3,4,5] => [6,5,1,4,3,2] => 1
[1,2,6,3,5,4] => [6,5,1,4,2,3] => 1
[1,2,6,4,3,5] => [6,5,1,3,4,2] => 1
[1,2,6,4,5,3] => [6,5,1,3,2,4] => 2
[1,2,6,5,3,4] => [6,5,1,2,4,3] => 2
[1,2,6,5,4,3] => [6,5,1,2,3,4] => 2
[1,3,2,4,5,6] => [6,4,5,3,2,1] => 0
[1,3,2,4,6,5] => [6,4,5,3,1,2] => 0
[1,3,2,5,4,6] => [6,4,5,2,3,1] => 0
[1,3,2,5,6,4] => [6,4,5,2,1,3] => 1
[1,3,2,6,4,5] => [6,4,5,1,3,2] => 1
[1,3,2,6,5,4] => [6,4,5,1,2,3] => 1
[1,3,4,2,5,6] => [6,4,3,5,2,1] => 1
[1,3,4,2,6,5] => [6,4,3,5,1,2] => 1
[1,3,4,5,2,6] => [6,4,3,2,5,1] => 1
[1,3,4,5,6,2] => [6,4,3,2,1,5] => 1
[1,3,4,6,2,5] => [6,4,3,1,5,2] => 2
[1,3,4,6,5,2] => [6,4,3,1,2,5] => 1
[1,3,5,2,4,6] => [6,4,2,5,3,1] => 2
[1,3,5,2,6,4] => [6,4,2,5,1,3] => 1
[1,3,5,4,2,6] => [6,4,2,3,5,1] => 1
[1,3,5,4,6,2] => [6,4,2,3,1,5] => 1
[1,3,5,6,2,4] => [6,4,2,1,5,3] => 2
[1,3,5,6,4,2] => [6,4,2,1,3,5] => 2
[1,3,6,2,4,5] => [6,4,1,5,3,2] => 2
[1,3,6,2,5,4] => [6,4,1,5,2,3] => 2
[1,3,6,4,2,5] => [6,4,1,3,5,2] => 1
[1,3,6,4,5,2] => [6,4,1,3,2,5] => 2
[1,3,6,5,2,4] => [6,4,1,2,5,3] => 2
[1,3,6,5,4,2] => [6,4,1,2,3,5] => 2
[1,4,2,3,5,6] => [6,3,5,4,2,1] => 1
[1,4,2,3,6,5] => [6,3,5,4,1,2] => 1
[1,4,2,5,3,6] => [6,3,5,2,4,1] => 0
[1,4,2,5,6,3] => [6,3,5,2,1,4] => 1
[1,4,2,6,3,5] => [6,3,5,1,4,2] => 1
[1,4,2,6,5,3] => [6,3,5,1,2,4] => 1
[1,4,3,2,5,6] => [6,3,4,5,2,1] => 1
[1,4,3,2,6,5] => [6,3,4,5,1,2] => 1
[1,4,3,5,2,6] => [6,3,4,2,5,1] => 1
[1,4,3,5,6,2] => [6,3,4,2,1,5] => 1
[1,4,3,6,2,5] => [6,3,4,1,5,2] => 2
[1,4,3,6,5,2] => [6,3,4,1,2,5] => 1
[1,4,5,2,3,6] => [6,3,2,5,4,1] => 2
[1,4,5,2,6,3] => [6,3,2,5,1,4] => 1
[1,4,5,3,2,6] => [6,3,2,4,5,1] => 2
[1,4,5,3,6,2] => [6,3,2,4,1,5] => 2
[1,4,5,6,2,3] => [6,3,2,1,5,4] => 2
[1,4,5,6,3,2] => [6,3,2,1,4,5] => 2
[1,4,6,2,3,5] => [6,3,1,5,4,2] => 2
[1,4,6,2,5,3] => [6,3,1,5,2,4] => 2
[1,4,6,3,2,5] => [6,3,1,4,5,2] => 2
[1,4,6,3,5,2] => [6,3,1,4,2,5] => 3
[1,4,6,5,2,3] => [6,3,1,2,5,4] => 2
[1,4,6,5,3,2] => [6,3,1,2,4,5] => 2
[1,5,2,3,4,6] => [6,2,5,4,3,1] => 1
[1,5,2,3,6,4] => [6,2,5,4,1,3] => 1
[1,5,2,4,3,6] => [6,2,5,3,4,1] => 1
[1,5,2,4,6,3] => [6,2,5,3,1,4] => 2
[1,5,2,6,3,4] => [6,2,5,1,4,3] => 1
[1,5,2,6,4,3] => [6,2,5,1,3,4] => 1
[1,5,3,2,4,6] => [6,2,4,5,3,1] => 1
[1,5,3,2,6,4] => [6,2,4,5,1,3] => 1
[1,5,3,4,2,6] => [6,2,4,3,5,1] => 2
[1,5,3,4,6,2] => [6,2,4,3,1,5] => 2
[1,5,3,6,2,4] => [6,2,4,1,5,3] => 2
[1,5,3,6,4,2] => [6,2,4,1,3,5] => 1
[1,5,4,2,3,6] => [6,2,3,5,4,1] => 2
[1,5,4,2,6,3] => [6,2,3,5,1,4] => 1
[1,5,4,3,2,6] => [6,2,3,4,5,1] => 2
[1,5,4,3,6,2] => [6,2,3,4,1,5] => 2
[1,5,4,6,2,3] => [6,2,3,1,5,4] => 2
[1,5,4,6,3,2] => [6,2,3,1,4,5] => 2
[1,5,6,2,3,4] => [6,2,1,5,4,3] => 2
[1,5,6,2,4,3] => [6,2,1,5,3,4] => 2
[1,5,6,3,2,4] => [6,2,1,4,5,3] => 2
[1,5,6,3,4,2] => [6,2,1,4,3,5] => 3
[1,5,6,4,2,3] => [6,2,1,3,5,4] => 3
[1,5,6,4,3,2] => [6,2,1,3,4,5] => 3
[1,6,2,3,4,5] => [6,1,5,4,3,2] => 1
[1,6,2,3,5,4] => [6,1,5,4,2,3] => 1
[1,6,2,4,3,5] => [6,1,5,3,4,2] => 1
[1,6,2,4,5,3] => [6,1,5,3,2,4] => 2
[1,6,2,5,3,4] => [6,1,5,2,4,3] => 2
[1,6,2,5,4,3] => [6,1,5,2,3,4] => 2
[1,6,3,2,4,5] => [6,1,4,5,3,2] => 1
[1,6,3,2,5,4] => [6,1,4,5,2,3] => 1
[1,6,3,4,2,5] => [6,1,4,3,5,2] => 2
[1,6,3,4,5,2] => [6,1,4,3,2,5] => 2
[1,6,3,5,2,4] => [6,1,4,2,5,3] => 3
[1,6,3,5,4,2] => [6,1,4,2,3,5] => 2
[1,6,4,2,3,5] => [6,1,3,5,4,2] => 2
[1,6,4,2,5,3] => [6,1,3,5,2,4] => 1
[1,6,4,3,2,5] => [6,1,3,4,5,2] => 2
[1,6,4,3,5,2] => [6,1,3,4,2,5] => 2
[1,6,4,5,2,3] => [6,1,3,2,5,4] => 3
[1,6,4,5,3,2] => [6,1,3,2,4,5] => 3
[1,6,5,2,3,4] => [6,1,2,5,4,3] => 2
[1,6,5,2,4,3] => [6,1,2,5,3,4] => 2
[1,6,5,3,2,4] => [6,1,2,4,5,3] => 2
[1,6,5,3,4,2] => [6,1,2,4,3,5] => 3
[1,6,5,4,2,3] => [6,1,2,3,5,4] => 3
[1,6,5,4,3,2] => [6,1,2,3,4,5] => 3
[2,1,3,4,5,6] => [5,6,4,3,2,1] => 0
[2,1,3,4,6,5] => [5,6,4,3,1,2] => 0
[2,1,3,5,4,6] => [5,6,4,2,3,1] => 0
[2,1,3,5,6,4] => [5,6,4,2,1,3] => 1
[2,1,3,6,4,5] => [5,6,4,1,3,2] => 1
[2,1,3,6,5,4] => [5,6,4,1,2,3] => 1
[2,1,4,3,5,6] => [5,6,3,4,2,1] => 0
[2,1,4,3,6,5] => [5,6,3,4,1,2] => 0
[2,1,4,5,3,6] => [5,6,3,2,4,1] => 1
[2,1,4,5,6,3] => [5,6,3,2,1,4] => 1
[2,1,4,6,3,5] => [5,6,3,1,4,2] => 2
[2,1,4,6,5,3] => [5,6,3,1,2,4] => 1
[2,1,5,3,4,6] => [5,6,2,4,3,1] => 1
[2,1,5,3,6,4] => [5,6,2,4,1,3] => 0
[2,1,5,4,3,6] => [5,6,2,3,4,1] => 1
[2,1,5,4,6,3] => [5,6,2,3,1,4] => 1
[2,1,5,6,3,4] => [5,6,2,1,4,3] => 2
[2,1,5,6,4,3] => [5,6,2,1,3,4] => 2
[2,1,6,3,4,5] => [5,6,1,4,3,2] => 1
[2,1,6,3,5,4] => [5,6,1,4,2,3] => 1
[2,1,6,4,3,5] => [5,6,1,3,4,2] => 1
[2,1,6,4,5,3] => [5,6,1,3,2,4] => 2
[2,1,6,5,3,4] => [5,6,1,2,4,3] => 2
[2,1,6,5,4,3] => [5,6,1,2,3,4] => 2
[2,3,1,4,5,6] => [5,4,6,3,2,1] => 1
[2,3,1,4,6,5] => [5,4,6,3,1,2] => 1
[2,3,1,5,4,6] => [5,4,6,2,3,1] => 1
[2,3,1,5,6,4] => [5,4,6,2,1,3] => 2
[2,3,1,6,4,5] => [5,4,6,1,3,2] => 2
[2,3,1,6,5,4] => [5,4,6,1,2,3] => 2
[2,3,4,1,5,6] => [5,4,3,6,2,1] => 1
[2,3,4,1,6,5] => [5,4,3,6,1,2] => 1
[2,3,4,5,1,6] => [5,4,3,2,6,1] => 1
[2,3,4,5,6,1] => [5,4,3,2,1,6] => 1
[2,3,4,6,1,5] => [5,4,3,1,6,2] => 2
[2,3,4,6,5,1] => [5,4,3,1,2,6] => 1
[2,3,5,1,4,6] => [5,4,2,6,3,1] => 2
[2,3,5,1,6,4] => [5,4,2,6,1,3] => 1
[2,3,5,4,1,6] => [5,4,2,3,6,1] => 1
[2,3,5,4,6,1] => [5,4,2,3,1,6] => 1
[2,3,5,6,1,4] => [5,4,2,1,6,3] => 2
[2,3,5,6,4,1] => [5,4,2,1,3,6] => 2
[2,3,6,1,4,5] => [5,4,1,6,3,2] => 2
[2,3,6,1,5,4] => [5,4,1,6,2,3] => 2
[2,3,6,4,1,5] => [5,4,1,3,6,2] => 1
[2,3,6,4,5,1] => [5,4,1,3,2,6] => 2
[2,3,6,5,1,4] => [5,4,1,2,6,3] => 2
[2,3,6,5,4,1] => [5,4,1,2,3,6] => 2
[2,4,1,3,5,6] => [5,3,6,4,2,1] => 2
[2,4,1,3,6,5] => [5,3,6,4,1,2] => 2
[2,4,1,5,3,6] => [5,3,6,2,4,1] => 1
[2,4,1,5,6,3] => [5,3,6,2,1,4] => 2
[2,4,1,6,3,5] => [5,3,6,1,4,2] => 2
[2,4,1,6,5,3] => [5,3,6,1,2,4] => 2
[2,4,3,1,5,6] => [5,3,4,6,2,1] => 1
[2,4,3,1,6,5] => [5,3,4,6,1,2] => 1
[2,4,3,5,1,6] => [5,3,4,2,6,1] => 1
[2,4,3,5,6,1] => [5,3,4,2,1,6] => 1
[2,4,3,6,1,5] => [5,3,4,1,6,2] => 2
[2,4,3,6,5,1] => [5,3,4,1,2,6] => 1
[2,4,5,1,3,6] => [5,3,2,6,4,1] => 2
[2,4,5,1,6,3] => [5,3,2,6,1,4] => 1
[2,4,5,3,1,6] => [5,3,2,4,6,1] => 2
[2,4,5,3,6,1] => [5,3,2,4,1,6] => 2
[2,4,5,6,1,3] => [5,3,2,1,6,4] => 2
[2,4,5,6,3,1] => [5,3,2,1,4,6] => 2
[2,4,6,1,3,5] => [5,3,1,6,4,2] => 2
[2,4,6,1,5,3] => [5,3,1,6,2,4] => 2
[2,4,6,3,1,5] => [5,3,1,4,6,2] => 2
[2,4,6,3,5,1] => [5,3,1,4,2,6] => 3
[2,4,6,5,1,3] => [5,3,1,2,6,4] => 2
[2,4,6,5,3,1] => [5,3,1,2,4,6] => 2
[2,5,1,3,4,6] => [5,2,6,4,3,1] => 2
[2,5,1,3,6,4] => [5,2,6,4,1,3] => 2
[2,5,1,4,3,6] => [5,2,6,3,4,1] => 2
[2,5,1,4,6,3] => [5,2,6,3,1,4] => 3
[2,5,1,6,3,4] => [5,2,6,1,4,3] => 2
[2,5,1,6,4,3] => [5,2,6,1,3,4] => 2
[2,5,3,1,4,6] => [5,2,4,6,3,1] => 1
[2,5,3,1,6,4] => [5,2,4,6,1,3] => 1
[2,5,3,4,1,6] => [5,2,4,3,6,1] => 2
[2,5,3,4,6,1] => [5,2,4,3,1,6] => 2
[2,5,3,6,1,4] => [5,2,4,1,6,3] => 2
[2,5,3,6,4,1] => [5,2,4,1,3,6] => 1
[2,5,4,1,3,6] => [5,2,3,6,4,1] => 2
[2,5,4,1,6,3] => [5,2,3,6,1,4] => 1
[2,5,4,3,1,6] => [5,2,3,4,6,1] => 2
[2,5,4,3,6,1] => [5,2,3,4,1,6] => 2
[2,5,4,6,1,3] => [5,2,3,1,6,4] => 2
[2,5,4,6,3,1] => [5,2,3,1,4,6] => 2
[2,5,6,1,3,4] => [5,2,1,6,4,3] => 2
[2,5,6,1,4,3] => [5,2,1,6,3,4] => 2
[2,5,6,3,1,4] => [5,2,1,4,6,3] => 2
[2,5,6,3,4,1] => [5,2,1,4,3,6] => 3
[2,5,6,4,1,3] => [5,2,1,3,6,4] => 3
[2,5,6,4,3,1] => [5,2,1,3,4,6] => 3
[2,6,1,3,4,5] => [5,1,6,4,3,2] => 2
[2,6,1,3,5,4] => [5,1,6,4,2,3] => 2
[2,6,1,4,3,5] => [5,1,6,3,4,2] => 2
[2,6,1,4,5,3] => [5,1,6,3,2,4] => 3
[2,6,1,5,3,4] => [5,1,6,2,4,3] => 3
[2,6,1,5,4,3] => [5,1,6,2,3,4] => 3
[2,6,3,1,4,5] => [5,1,4,6,3,2] => 1
[2,6,3,1,5,4] => [5,1,4,6,2,3] => 1
[2,6,3,4,1,5] => [5,1,4,3,6,2] => 2
[2,6,3,4,5,1] => [5,1,4,3,2,6] => 2
[2,6,3,5,1,4] => [5,1,4,2,6,3] => 3
[2,6,3,5,4,1] => [5,1,4,2,3,6] => 2
[2,6,4,1,3,5] => [5,1,3,6,4,2] => 2
[2,6,4,1,5,3] => [5,1,3,6,2,4] => 1
[2,6,4,3,1,5] => [5,1,3,4,6,2] => 2
[2,6,4,3,5,1] => [5,1,3,4,2,6] => 2
[2,6,4,5,1,3] => [5,1,3,2,6,4] => 3
[2,6,4,5,3,1] => [5,1,3,2,4,6] => 3
[2,6,5,1,3,4] => [5,1,2,6,4,3] => 2
[2,6,5,1,4,3] => [5,1,2,6,3,4] => 2
[2,6,5,3,1,4] => [5,1,2,4,6,3] => 2
[2,6,5,3,4,1] => [5,1,2,4,3,6] => 3
[2,6,5,4,1,3] => [5,1,2,3,6,4] => 3
[2,6,5,4,3,1] => [5,1,2,3,4,6] => 3
[3,1,2,4,5,6] => [4,6,5,3,2,1] => 1
[3,1,2,4,6,5] => [4,6,5,3,1,2] => 1
[3,1,2,5,4,6] => [4,6,5,2,3,1] => 1
[3,1,2,5,6,4] => [4,6,5,2,1,3] => 2
[3,1,2,6,4,5] => [4,6,5,1,3,2] => 2
[3,1,2,6,5,4] => [4,6,5,1,2,3] => 2
[3,1,4,2,5,6] => [4,6,3,5,2,1] => 0
[3,1,4,2,6,5] => [4,6,3,5,1,2] => 0
[3,1,4,5,2,6] => [4,6,3,2,5,1] => 1
[3,1,4,5,6,2] => [4,6,3,2,1,5] => 1
[3,1,4,6,2,5] => [4,6,3,1,5,2] => 2
[3,1,4,6,5,2] => [4,6,3,1,2,5] => 1
[3,1,5,2,4,6] => [4,6,2,5,3,1] => 1
[3,1,5,2,6,4] => [4,6,2,5,1,3] => 0
[3,1,5,4,2,6] => [4,6,2,3,5,1] => 1
[3,1,5,4,6,2] => [4,6,2,3,1,5] => 1
[3,1,5,6,2,4] => [4,6,2,1,5,3] => 2
[3,1,5,6,4,2] => [4,6,2,1,3,5] => 2
[3,1,6,2,4,5] => [4,6,1,5,3,2] => 1
[3,1,6,2,5,4] => [4,6,1,5,2,3] => 1
[3,1,6,4,2,5] => [4,6,1,3,5,2] => 1
[3,1,6,4,5,2] => [4,6,1,3,2,5] => 2
[3,1,6,5,2,4] => [4,6,1,2,5,3] => 2
[3,1,6,5,4,2] => [4,6,1,2,3,5] => 2
[3,2,1,4,5,6] => [4,5,6,3,2,1] => 1
[3,2,1,4,6,5] => [4,5,6,3,1,2] => 1
[3,2,1,5,4,6] => [4,5,6,2,3,1] => 1
[3,2,1,5,6,4] => [4,5,6,2,1,3] => 2
[3,2,1,6,4,5] => [4,5,6,1,3,2] => 2
[3,2,1,6,5,4] => [4,5,6,1,2,3] => 2
[3,2,4,1,5,6] => [4,5,3,6,2,1] => 1
[3,2,4,1,6,5] => [4,5,3,6,1,2] => 1
[3,2,4,5,1,6] => [4,5,3,2,6,1] => 1
[3,2,4,5,6,1] => [4,5,3,2,1,6] => 1
[3,2,4,6,1,5] => [4,5,3,1,6,2] => 2
[3,2,4,6,5,1] => [4,5,3,1,2,6] => 1
[3,2,5,1,4,6] => [4,5,2,6,3,1] => 2
[3,2,5,1,6,4] => [4,5,2,6,1,3] => 1
[3,2,5,4,1,6] => [4,5,2,3,6,1] => 1
[3,2,5,4,6,1] => [4,5,2,3,1,6] => 1
[3,2,5,6,1,4] => [4,5,2,1,6,3] => 2
[3,2,5,6,4,1] => [4,5,2,1,3,6] => 2
[3,2,6,1,4,5] => [4,5,1,6,3,2] => 2
[3,2,6,1,5,4] => [4,5,1,6,2,3] => 2
[3,2,6,4,1,5] => [4,5,1,3,6,2] => 1
[3,2,6,4,5,1] => [4,5,1,3,2,6] => 2
[3,2,6,5,1,4] => [4,5,1,2,6,3] => 2
[3,2,6,5,4,1] => [4,5,1,2,3,6] => 2
[3,4,1,2,5,6] => [4,3,6,5,2,1] => 2
[3,4,1,2,6,5] => [4,3,6,5,1,2] => 2
[3,4,1,5,2,6] => [4,3,6,2,5,1] => 1
[3,4,1,5,6,2] => [4,3,6,2,1,5] => 2
[3,4,1,6,2,5] => [4,3,6,1,5,2] => 2
[3,4,1,6,5,2] => [4,3,6,1,2,5] => 2
[3,4,2,1,5,6] => [4,3,5,6,2,1] => 2
[3,4,2,1,6,5] => [4,3,5,6,1,2] => 2
[3,4,2,5,1,6] => [4,3,5,2,6,1] => 2
[3,4,2,5,6,1] => [4,3,5,2,1,6] => 2
[3,4,2,6,1,5] => [4,3,5,1,6,2] => 3
[3,4,2,6,5,1] => [4,3,5,1,2,6] => 2
[3,4,5,1,2,6] => [4,3,2,6,5,1] => 2
[3,4,5,1,6,2] => [4,3,2,6,1,5] => 1
[3,4,5,2,1,6] => [4,3,2,5,6,1] => 2
[3,4,5,2,6,1] => [4,3,2,5,1,6] => 2
[3,4,5,6,1,2] => [4,3,2,1,6,5] => 2
[3,4,5,6,2,1] => [4,3,2,1,5,6] => 2
[3,4,6,1,2,5] => [4,3,1,6,5,2] => 2
[3,4,6,1,5,2] => [4,3,1,6,2,5] => 2
[3,4,6,2,1,5] => [4,3,1,5,6,2] => 2
[3,4,6,2,5,1] => [4,3,1,5,2,6] => 3
[3,4,6,5,1,2] => [4,3,1,2,6,5] => 2
[3,4,6,5,2,1] => [4,3,1,2,5,6] => 2
[3,5,1,2,4,6] => [4,2,6,5,3,1] => 2
[3,5,1,2,6,4] => [4,2,6,5,1,3] => 2
[3,5,1,4,2,6] => [4,2,6,3,5,1] => 2
[3,5,1,4,6,2] => [4,2,6,3,1,5] => 3
[3,5,1,6,2,4] => [4,2,6,1,5,3] => 2
[3,5,1,6,4,2] => [4,2,6,1,3,5] => 2
[3,5,2,1,4,6] => [4,2,5,6,3,1] => 2
[3,5,2,1,6,4] => [4,2,5,6,1,3] => 2
[3,5,2,4,1,6] => [4,2,5,3,6,1] => 3
[3,5,2,4,6,1] => [4,2,5,3,1,6] => 3
[3,5,2,6,1,4] => [4,2,5,1,6,3] => 3
[3,5,2,6,4,1] => [4,2,5,1,3,6] => 2
[3,5,4,1,2,6] => [4,2,3,6,5,1] => 2
[3,5,4,1,6,2] => [4,2,3,6,1,5] => 1
[3,5,4,2,1,6] => [4,2,3,5,6,1] => 2
[3,5,4,2,6,1] => [4,2,3,5,1,6] => 2
[3,5,4,6,1,2] => [4,2,3,1,6,5] => 2
[3,5,4,6,2,1] => [4,2,3,1,5,6] => 2
[3,5,6,1,2,4] => [4,2,1,6,5,3] => 2
[3,5,6,1,4,2] => [4,2,1,6,3,5] => 2
[3,5,6,2,1,4] => [4,2,1,5,6,3] => 2
[3,5,6,2,4,1] => [4,2,1,5,3,6] => 3
[3,5,6,4,1,2] => [4,2,1,3,6,5] => 3
[3,5,6,4,2,1] => [4,2,1,3,5,6] => 3
[3,6,1,2,4,5] => [4,1,6,5,3,2] => 2
[3,6,1,2,5,4] => [4,1,6,5,2,3] => 2
[3,6,1,4,2,5] => [4,1,6,3,5,2] => 2
[3,6,1,4,5,2] => [4,1,6,3,2,5] => 3
[3,6,1,5,2,4] => [4,1,6,2,5,3] => 3
[3,6,1,5,4,2] => [4,1,6,2,3,5] => 3
[3,6,2,1,4,5] => [4,1,5,6,3,2] => 2
[3,6,2,1,5,4] => [4,1,5,6,2,3] => 2
[3,6,2,4,1,5] => [4,1,5,3,6,2] => 3
[3,6,2,4,5,1] => [4,1,5,3,2,6] => 3
[3,6,2,5,1,4] => [4,1,5,2,6,3] => 4
[3,6,2,5,4,1] => [4,1,5,2,3,6] => 3
[3,6,4,1,2,5] => [4,1,3,6,5,2] => 2
[3,6,4,1,5,2] => [4,1,3,6,2,5] => 1
[3,6,4,2,1,5] => [4,1,3,5,6,2] => 2
[3,6,4,2,5,1] => [4,1,3,5,2,6] => 2
[3,6,4,5,1,2] => [4,1,3,2,6,5] => 3
[3,6,4,5,2,1] => [4,1,3,2,5,6] => 3
[3,6,5,1,2,4] => [4,1,2,6,5,3] => 2
[3,6,5,1,4,2] => [4,1,2,6,3,5] => 2
[3,6,5,2,1,4] => [4,1,2,5,6,3] => 2
[3,6,5,2,4,1] => [4,1,2,5,3,6] => 3
[3,6,5,4,1,2] => [4,1,2,3,6,5] => 3
[3,6,5,4,2,1] => [4,1,2,3,5,6] => 3
[4,1,2,3,5,6] => [3,6,5,4,2,1] => 1
[4,1,2,3,6,5] => [3,6,5,4,1,2] => 1
[4,1,2,5,3,6] => [3,6,5,2,4,1] => 1
[4,1,2,5,6,3] => [3,6,5,2,1,4] => 2
[4,1,2,6,3,5] => [3,6,5,1,4,2] => 2
[4,1,2,6,5,3] => [3,6,5,1,2,4] => 2
[4,1,3,2,5,6] => [3,6,4,5,2,1] => 1
[4,1,3,2,6,5] => [3,6,4,5,1,2] => 1
[4,1,3,5,2,6] => [3,6,4,2,5,1] => 2
[4,1,3,5,6,2] => [3,6,4,2,1,5] => 2
[4,1,3,6,2,5] => [3,6,4,1,5,2] => 3
[4,1,3,6,5,2] => [3,6,4,1,2,5] => 2
[4,1,5,2,3,6] => [3,6,2,5,4,1] => 1
[4,1,5,2,6,3] => [3,6,2,5,1,4] => 0
[4,1,5,3,2,6] => [3,6,2,4,5,1] => 1
[4,1,5,3,6,2] => [3,6,2,4,1,5] => 1
[4,1,5,6,2,3] => [3,6,2,1,5,4] => 2
[4,1,5,6,3,2] => [3,6,2,1,4,5] => 2
[4,1,6,2,3,5] => [3,6,1,5,4,2] => 1
[4,1,6,2,5,3] => [3,6,1,5,2,4] => 1
[4,1,6,3,2,5] => [3,6,1,4,5,2] => 1
[4,1,6,3,5,2] => [3,6,1,4,2,5] => 2
[4,1,6,5,2,3] => [3,6,1,2,5,4] => 2
[4,1,6,5,3,2] => [3,6,1,2,4,5] => 2
[4,2,1,3,5,6] => [3,5,6,4,2,1] => 1
[4,2,1,3,6,5] => [3,5,6,4,1,2] => 1
[4,2,1,5,3,6] => [3,5,6,2,4,1] => 1
[4,2,1,5,6,3] => [3,5,6,2,1,4] => 2
[4,2,1,6,3,5] => [3,5,6,1,4,2] => 2
[4,2,1,6,5,3] => [3,5,6,1,2,4] => 2
[4,2,3,1,5,6] => [3,5,4,6,2,1] => 2
[4,2,3,1,6,5] => [3,5,4,6,1,2] => 2
[4,2,3,5,1,6] => [3,5,4,2,6,1] => 2
[4,2,3,5,6,1] => [3,5,4,2,1,6] => 2
[4,2,3,6,1,5] => [3,5,4,1,6,2] => 3
[4,2,3,6,5,1] => [3,5,4,1,2,6] => 2
[4,2,5,1,3,6] => [3,5,2,6,4,1] => 2
[4,2,5,1,6,3] => [3,5,2,6,1,4] => 1
[4,2,5,3,1,6] => [3,5,2,4,6,1] => 1
[4,2,5,3,6,1] => [3,5,2,4,1,6] => 1
[4,2,5,6,1,3] => [3,5,2,1,6,4] => 2
[4,2,5,6,3,1] => [3,5,2,1,4,6] => 2
[4,2,6,1,3,5] => [3,5,1,6,4,2] => 2
[4,2,6,1,5,3] => [3,5,1,6,2,4] => 2
[4,2,6,3,1,5] => [3,5,1,4,6,2] => 1
[4,2,6,3,5,1] => [3,5,1,4,2,6] => 2
[4,2,6,5,1,3] => [3,5,1,2,6,4] => 2
[4,2,6,5,3,1] => [3,5,1,2,4,6] => 2
[4,3,1,2,5,6] => [3,4,6,5,2,1] => 2
[4,3,1,2,6,5] => [3,4,6,5,1,2] => 2
[4,3,1,5,2,6] => [3,4,6,2,5,1] => 1
[4,3,1,5,6,2] => [3,4,6,2,1,5] => 2
[4,3,1,6,2,5] => [3,4,6,1,5,2] => 2
[4,3,1,6,5,2] => [3,4,6,1,2,5] => 2
[4,3,2,1,5,6] => [3,4,5,6,2,1] => 2
[4,3,2,1,6,5] => [3,4,5,6,1,2] => 2
[4,3,2,5,1,6] => [3,4,5,2,6,1] => 2
[4,3,2,5,6,1] => [3,4,5,2,1,6] => 2
[4,3,2,6,1,5] => [3,4,5,1,6,2] => 3
[4,3,2,6,5,1] => [3,4,5,1,2,6] => 2
[4,3,5,1,2,6] => [3,4,2,6,5,1] => 2
[4,3,5,1,6,2] => [3,4,2,6,1,5] => 1
[4,3,5,2,1,6] => [3,4,2,5,6,1] => 2
[4,3,5,2,6,1] => [3,4,2,5,1,6] => 2
[4,3,5,6,1,2] => [3,4,2,1,6,5] => 2
[4,3,5,6,2,1] => [3,4,2,1,5,6] => 2
[4,3,6,1,2,5] => [3,4,1,6,5,2] => 2
[4,3,6,1,5,2] => [3,4,1,6,2,5] => 2
[4,3,6,2,1,5] => [3,4,1,5,6,2] => 2
[4,3,6,2,5,1] => [3,4,1,5,2,6] => 3
[4,3,6,5,1,2] => [3,4,1,2,6,5] => 2
[4,3,6,5,2,1] => [3,4,1,2,5,6] => 2
[4,5,1,2,3,6] => [3,2,6,5,4,1] => 2
[4,5,1,2,6,3] => [3,2,6,5,1,4] => 2
[4,5,1,3,2,6] => [3,2,6,4,5,1] => 2
[4,5,1,3,6,2] => [3,2,6,4,1,5] => 3
[4,5,1,6,2,3] => [3,2,6,1,5,4] => 2
[4,5,1,6,3,2] => [3,2,6,1,4,5] => 2
[4,5,2,1,3,6] => [3,2,5,6,4,1] => 2
[4,5,2,1,6,3] => [3,2,5,6,1,4] => 2
[4,5,2,3,1,6] => [3,2,5,4,6,1] => 3
[4,5,2,3,6,1] => [3,2,5,4,1,6] => 3
[4,5,2,6,1,3] => [3,2,5,1,6,4] => 3
[4,5,2,6,3,1] => [3,2,5,1,4,6] => 2
[4,5,3,1,2,6] => [3,2,4,6,5,1] => 3
[4,5,3,1,6,2] => [3,2,4,6,1,5] => 2
[4,5,3,2,1,6] => [3,2,4,5,6,1] => 3
[4,5,3,2,6,1] => [3,2,4,5,1,6] => 3
[4,5,3,6,1,2] => [3,2,4,1,6,5] => 3
[4,5,3,6,2,1] => [3,2,4,1,5,6] => 3
[4,5,6,1,2,3] => [3,2,1,6,5,4] => 2
[4,5,6,1,3,2] => [3,2,1,6,4,5] => 2
[4,5,6,2,1,3] => [3,2,1,5,6,4] => 2
[4,5,6,2,3,1] => [3,2,1,5,4,6] => 3
[4,5,6,3,1,2] => [3,2,1,4,6,5] => 3
[4,5,6,3,2,1] => [3,2,1,4,5,6] => 3
[4,6,1,2,3,5] => [3,1,6,5,4,2] => 2
[4,6,1,2,5,3] => [3,1,6,5,2,4] => 2
[4,6,1,3,2,5] => [3,1,6,4,5,2] => 2
[4,6,1,3,5,2] => [3,1,6,4,2,5] => 3
[4,6,1,5,2,3] => [3,1,6,2,5,4] => 3
[4,6,1,5,3,2] => [3,1,6,2,4,5] => 3
[4,6,2,1,3,5] => [3,1,5,6,4,2] => 2
[4,6,2,1,5,3] => [3,1,5,6,2,4] => 2
[4,6,2,3,1,5] => [3,1,5,4,6,2] => 3
[4,6,2,3,5,1] => [3,1,5,4,2,6] => 3
[4,6,2,5,1,3] => [3,1,5,2,6,4] => 4
[4,6,2,5,3,1] => [3,1,5,2,4,6] => 3
[4,6,3,1,2,5] => [3,1,4,6,5,2] => 3
[4,6,3,1,5,2] => [3,1,4,6,2,5] => 2
[4,6,3,2,1,5] => [3,1,4,5,6,2] => 3
[4,6,3,2,5,1] => [3,1,4,5,2,6] => 3
[4,6,3,5,1,2] => [3,1,4,2,6,5] => 4
[4,6,3,5,2,1] => [3,1,4,2,5,6] => 4
[4,6,5,1,2,3] => [3,1,2,6,5,4] => 2
[4,6,5,1,3,2] => [3,1,2,6,4,5] => 2
[4,6,5,2,1,3] => [3,1,2,5,6,4] => 2
[4,6,5,2,3,1] => [3,1,2,5,4,6] => 3
[4,6,5,3,1,2] => [3,1,2,4,6,5] => 3
[4,6,5,3,2,1] => [3,1,2,4,5,6] => 3
[5,1,2,3,4,6] => [2,6,5,4,3,1] => 1
[5,1,2,3,6,4] => [2,6,5,4,1,3] => 1
[5,1,2,4,3,6] => [2,6,5,3,4,1] => 1
[5,1,2,4,6,3] => [2,6,5,3,1,4] => 2
[5,1,2,6,3,4] => [2,6,5,1,4,3] => 2
[5,1,2,6,4,3] => [2,6,5,1,3,4] => 2
[5,1,3,2,4,6] => [2,6,4,5,3,1] => 1
[5,1,3,2,6,4] => [2,6,4,5,1,3] => 1
[5,1,3,4,2,6] => [2,6,4,3,5,1] => 2
[5,1,3,4,6,2] => [2,6,4,3,1,5] => 2
[5,1,3,6,2,4] => [2,6,4,1,5,3] => 3
[5,1,3,6,4,2] => [2,6,4,1,3,5] => 2
[5,1,4,2,3,6] => [2,6,3,5,4,1] => 2
[5,1,4,2,6,3] => [2,6,3,5,1,4] => 1
[5,1,4,3,2,6] => [2,6,3,4,5,1] => 2
[5,1,4,3,6,2] => [2,6,3,4,1,5] => 2
[5,1,4,6,2,3] => [2,6,3,1,5,4] => 3
[5,1,4,6,3,2] => [2,6,3,1,4,5] => 3
[5,1,6,2,3,4] => [2,6,1,5,4,3] => 1
[5,1,6,2,4,3] => [2,6,1,5,3,4] => 1
[5,1,6,3,2,4] => [2,6,1,4,5,3] => 1
[5,1,6,3,4,2] => [2,6,1,4,3,5] => 2
[5,1,6,4,2,3] => [2,6,1,3,5,4] => 2
[5,1,6,4,3,2] => [2,6,1,3,4,5] => 2
[5,2,1,3,4,6] => [2,5,6,4,3,1] => 1
[5,2,1,3,6,4] => [2,5,6,4,1,3] => 1
[5,2,1,4,3,6] => [2,5,6,3,4,1] => 1
[5,2,1,4,6,3] => [2,5,6,3,1,4] => 2
[5,2,1,6,3,4] => [2,5,6,1,4,3] => 2
[5,2,1,6,4,3] => [2,5,6,1,3,4] => 2
[5,2,3,1,4,6] => [2,5,4,6,3,1] => 2
[5,2,3,1,6,4] => [2,5,4,6,1,3] => 2
[5,2,3,4,1,6] => [2,5,4,3,6,1] => 2
[5,2,3,4,6,1] => [2,5,4,3,1,6] => 2
[5,2,3,6,1,4] => [2,5,4,1,6,3] => 3
[5,2,3,6,4,1] => [2,5,4,1,3,6] => 2
[5,2,4,1,3,6] => [2,5,3,6,4,1] => 3
[5,2,4,1,6,3] => [2,5,3,6,1,4] => 2
[5,2,4,3,1,6] => [2,5,3,4,6,1] => 2
[5,2,4,3,6,1] => [2,5,3,4,1,6] => 2
[5,2,4,6,1,3] => [2,5,3,1,6,4] => 3
[5,2,4,6,3,1] => [2,5,3,1,4,6] => 3
[5,2,6,1,3,4] => [2,5,1,6,4,3] => 2
[5,2,6,1,4,3] => [2,5,1,6,3,4] => 2
[5,2,6,3,1,4] => [2,5,1,4,6,3] => 1
[5,2,6,3,4,1] => [2,5,1,4,3,6] => 2
[5,2,6,4,1,3] => [2,5,1,3,6,4] => 2
[5,2,6,4,3,1] => [2,5,1,3,4,6] => 2
[5,3,1,2,4,6] => [2,4,6,5,3,1] => 2
[5,3,1,2,6,4] => [2,4,6,5,1,3] => 2
[5,3,1,4,2,6] => [2,4,6,3,5,1] => 1
[5,3,1,4,6,2] => [2,4,6,3,1,5] => 2
[5,3,1,6,2,4] => [2,4,6,1,5,3] => 2
[5,3,1,6,4,2] => [2,4,6,1,3,5] => 2
[5,3,2,1,4,6] => [2,4,5,6,3,1] => 2
[5,3,2,1,6,4] => [2,4,5,6,1,3] => 2
[5,3,2,4,1,6] => [2,4,5,3,6,1] => 2
[5,3,2,4,6,1] => [2,4,5,3,1,6] => 2
[5,3,2,6,1,4] => [2,4,5,1,6,3] => 3
[5,3,2,6,4,1] => [2,4,5,1,3,6] => 2
[5,3,4,1,2,6] => [2,4,3,6,5,1] => 3
[5,3,4,1,6,2] => [2,4,3,6,1,5] => 2
[5,3,4,2,1,6] => [2,4,3,5,6,1] => 3
[5,3,4,2,6,1] => [2,4,3,5,1,6] => 3
[5,3,4,6,1,2] => [2,4,3,1,6,5] => 3
[5,3,4,6,2,1] => [2,4,3,1,5,6] => 3
[5,3,6,1,2,4] => [2,4,1,6,5,3] => 2
[5,3,6,1,4,2] => [2,4,1,6,3,5] => 2
[5,3,6,2,1,4] => [2,4,1,5,6,3] => 2
[5,3,6,2,4,1] => [2,4,1,5,3,6] => 3
[5,3,6,4,1,2] => [2,4,1,3,6,5] => 2
[5,3,6,4,2,1] => [2,4,1,3,5,6] => 2
[5,4,1,2,3,6] => [2,3,6,5,4,1] => 2
[5,4,1,2,6,3] => [2,3,6,5,1,4] => 2
[5,4,1,3,2,6] => [2,3,6,4,5,1] => 2
[5,4,1,3,6,2] => [2,3,6,4,1,5] => 3
[5,4,1,6,2,3] => [2,3,6,1,5,4] => 2
[5,4,1,6,3,2] => [2,3,6,1,4,5] => 2
[5,4,2,1,3,6] => [2,3,5,6,4,1] => 2
[5,4,2,1,6,3] => [2,3,5,6,1,4] => 2
[5,4,2,3,1,6] => [2,3,5,4,6,1] => 3
[5,4,2,3,6,1] => [2,3,5,4,1,6] => 3
[5,4,2,6,1,3] => [2,3,5,1,6,4] => 3
[5,4,2,6,3,1] => [2,3,5,1,4,6] => 2
[5,4,3,1,2,6] => [2,3,4,6,5,1] => 3
[5,4,3,1,6,2] => [2,3,4,6,1,5] => 2
[5,4,3,2,1,6] => [2,3,4,5,6,1] => 3
[5,4,3,2,6,1] => [2,3,4,5,1,6] => 3
[5,4,3,6,1,2] => [2,3,4,1,6,5] => 3
[5,4,3,6,2,1] => [2,3,4,1,5,6] => 3
[5,4,6,1,2,3] => [2,3,1,6,5,4] => 2
[5,4,6,1,3,2] => [2,3,1,6,4,5] => 2
[5,4,6,2,1,3] => [2,3,1,5,6,4] => 2
[5,4,6,2,3,1] => [2,3,1,5,4,6] => 3
[5,4,6,3,1,2] => [2,3,1,4,6,5] => 3
[5,4,6,3,2,1] => [2,3,1,4,5,6] => 3
[5,6,1,2,3,4] => [2,1,6,5,4,3] => 2
[5,6,1,2,4,3] => [2,1,6,5,3,4] => 2
[5,6,1,3,2,4] => [2,1,6,4,5,3] => 2
[5,6,1,3,4,2] => [2,1,6,4,3,5] => 3
[5,6,1,4,2,3] => [2,1,6,3,5,4] => 3
[5,6,1,4,3,2] => [2,1,6,3,4,5] => 3
[5,6,2,1,3,4] => [2,1,5,6,4,3] => 2
[5,6,2,1,4,3] => [2,1,5,6,3,4] => 2
[5,6,2,3,1,4] => [2,1,5,4,6,3] => 3
[5,6,2,3,4,1] => [2,1,5,4,3,6] => 3
[5,6,2,4,1,3] => [2,1,5,3,6,4] => 4
[5,6,2,4,3,1] => [2,1,5,3,4,6] => 3
[5,6,3,1,2,4] => [2,1,4,6,5,3] => 3
[5,6,3,1,4,2] => [2,1,4,6,3,5] => 2
[5,6,3,2,1,4] => [2,1,4,5,6,3] => 3
[5,6,3,2,4,1] => [2,1,4,5,3,6] => 3
[5,6,3,4,1,2] => [2,1,4,3,6,5] => 4
[5,6,3,4,2,1] => [2,1,4,3,5,6] => 4
[5,6,4,1,2,3] => [2,1,3,6,5,4] => 3
[5,6,4,1,3,2] => [2,1,3,6,4,5] => 3
[5,6,4,2,1,3] => [2,1,3,5,6,4] => 3
[5,6,4,2,3,1] => [2,1,3,5,4,6] => 4
[5,6,4,3,1,2] => [2,1,3,4,6,5] => 4
[5,6,4,3,2,1] => [2,1,3,4,5,6] => 4
[6,1,2,3,4,5] => [1,6,5,4,3,2] => 1
[6,1,2,3,5,4] => [1,6,5,4,2,3] => 1
[6,1,2,4,3,5] => [1,6,5,3,4,2] => 1
[6,1,2,4,5,3] => [1,6,5,3,2,4] => 2
[6,1,2,5,3,4] => [1,6,5,2,4,3] => 2
[6,1,2,5,4,3] => [1,6,5,2,3,4] => 2
[6,1,3,2,4,5] => [1,6,4,5,3,2] => 1
[6,1,3,2,5,4] => [1,6,4,5,2,3] => 1
[6,1,3,4,2,5] => [1,6,4,3,5,2] => 2
[6,1,3,4,5,2] => [1,6,4,3,2,5] => 2
[6,1,3,5,2,4] => [1,6,4,2,5,3] => 3
[6,1,3,5,4,2] => [1,6,4,2,3,5] => 2
[6,1,4,2,3,5] => [1,6,3,5,4,2] => 2
[6,1,4,2,5,3] => [1,6,3,5,2,4] => 1
[6,1,4,3,2,5] => [1,6,3,4,5,2] => 2
[6,1,4,3,5,2] => [1,6,3,4,2,5] => 2
[6,1,4,5,2,3] => [1,6,3,2,5,4] => 3
[6,1,4,5,3,2] => [1,6,3,2,4,5] => 3
[6,1,5,2,3,4] => [1,6,2,5,4,3] => 2
[6,1,5,2,4,3] => [1,6,2,5,3,4] => 2
[6,1,5,3,2,4] => [1,6,2,4,5,3] => 2
[6,1,5,3,4,2] => [1,6,2,4,3,5] => 3
[6,1,5,4,2,3] => [1,6,2,3,5,4] => 3
[6,1,5,4,3,2] => [1,6,2,3,4,5] => 3
[6,2,1,3,4,5] => [1,5,6,4,3,2] => 1
[6,2,1,3,5,4] => [1,5,6,4,2,3] => 1
[6,2,1,4,3,5] => [1,5,6,3,4,2] => 1
[6,2,1,4,5,3] => [1,5,6,3,2,4] => 2
[6,2,1,5,3,4] => [1,5,6,2,4,3] => 2
[6,2,1,5,4,3] => [1,5,6,2,3,4] => 2
[6,2,3,1,4,5] => [1,5,4,6,3,2] => 2
[6,2,3,1,5,4] => [1,5,4,6,2,3] => 2
[6,2,3,4,1,5] => [1,5,4,3,6,2] => 2
[6,2,3,4,5,1] => [1,5,4,3,2,6] => 2
[6,2,3,5,1,4] => [1,5,4,2,6,3] => 3
[6,2,3,5,4,1] => [1,5,4,2,3,6] => 2
[6,2,4,1,3,5] => [1,5,3,6,4,2] => 3
[6,2,4,1,5,3] => [1,5,3,6,2,4] => 2
[6,2,4,3,1,5] => [1,5,3,4,6,2] => 2
[6,2,4,3,5,1] => [1,5,3,4,2,6] => 2
[6,2,4,5,1,3] => [1,5,3,2,6,4] => 3
[6,2,4,5,3,1] => [1,5,3,2,4,6] => 3
[6,2,5,1,3,4] => [1,5,2,6,4,3] => 3
[6,2,5,1,4,3] => [1,5,2,6,3,4] => 3
[6,2,5,3,1,4] => [1,5,2,4,6,3] => 2
[6,2,5,3,4,1] => [1,5,2,4,3,6] => 3
[6,2,5,4,1,3] => [1,5,2,3,6,4] => 3
[6,2,5,4,3,1] => [1,5,2,3,4,6] => 3
[6,3,1,2,4,5] => [1,4,6,5,3,2] => 2
[6,3,1,2,5,4] => [1,4,6,5,2,3] => 2
[6,3,1,4,2,5] => [1,4,6,3,5,2] => 1
[6,3,1,4,5,2] => [1,4,6,3,2,5] => 2
[6,3,1,5,2,4] => [1,4,6,2,5,3] => 2
[6,3,1,5,4,2] => [1,4,6,2,3,5] => 2
[6,3,2,1,4,5] => [1,4,5,6,3,2] => 2
[6,3,2,1,5,4] => [1,4,5,6,2,3] => 2
[6,3,2,4,1,5] => [1,4,5,3,6,2] => 2
[6,3,2,4,5,1] => [1,4,5,3,2,6] => 2
[6,3,2,5,1,4] => [1,4,5,2,6,3] => 3
[6,3,2,5,4,1] => [1,4,5,2,3,6] => 2
[6,3,4,1,2,5] => [1,4,3,6,5,2] => 3
[6,3,4,1,5,2] => [1,4,3,6,2,5] => 2
[6,3,4,2,1,5] => [1,4,3,5,6,2] => 3
[6,3,4,2,5,1] => [1,4,3,5,2,6] => 3
[6,3,4,5,1,2] => [1,4,3,2,6,5] => 3
[6,3,4,5,2,1] => [1,4,3,2,5,6] => 3
[6,3,5,1,2,4] => [1,4,2,6,5,3] => 3
[6,3,5,1,4,2] => [1,4,2,6,3,5] => 3
[6,3,5,2,1,4] => [1,4,2,5,6,3] => 3
[6,3,5,2,4,1] => [1,4,2,5,3,6] => 4
[6,3,5,4,1,2] => [1,4,2,3,6,5] => 3
[6,3,5,4,2,1] => [1,4,2,3,5,6] => 3
[6,4,1,2,3,5] => [1,3,6,5,4,2] => 2
[6,4,1,2,5,3] => [1,3,6,5,2,4] => 2
[6,4,1,3,2,5] => [1,3,6,4,5,2] => 2
[6,4,1,3,5,2] => [1,3,6,4,2,5] => 3
[6,4,1,5,2,3] => [1,3,6,2,5,4] => 2
[6,4,1,5,3,2] => [1,3,6,2,4,5] => 2
[6,4,2,1,3,5] => [1,3,5,6,4,2] => 2
[6,4,2,1,5,3] => [1,3,5,6,2,4] => 2
[6,4,2,3,1,5] => [1,3,5,4,6,2] => 3
[6,4,2,3,5,1] => [1,3,5,4,2,6] => 3
[6,4,2,5,1,3] => [1,3,5,2,6,4] => 3
[6,4,2,5,3,1] => [1,3,5,2,4,6] => 2
[6,4,3,1,2,5] => [1,3,4,6,5,2] => 3
[6,4,3,1,5,2] => [1,3,4,6,2,5] => 2
[6,4,3,2,1,5] => [1,3,4,5,6,2] => 3
[6,4,3,2,5,1] => [1,3,4,5,2,6] => 3
[6,4,3,5,1,2] => [1,3,4,2,6,5] => 3
[6,4,3,5,2,1] => [1,3,4,2,5,6] => 3
[6,4,5,1,2,3] => [1,3,2,6,5,4] => 3
[6,4,5,1,3,2] => [1,3,2,6,4,5] => 3
[6,4,5,2,1,3] => [1,3,2,5,6,4] => 3
[6,4,5,2,3,1] => [1,3,2,5,4,6] => 4
[6,4,5,3,1,2] => [1,3,2,4,6,5] => 4
[6,4,5,3,2,1] => [1,3,2,4,5,6] => 4
[6,5,1,2,3,4] => [1,2,6,5,4,3] => 2
[6,5,1,2,4,3] => [1,2,6,5,3,4] => 2
[6,5,1,3,2,4] => [1,2,6,4,5,3] => 2
[6,5,1,3,4,2] => [1,2,6,4,3,5] => 3
[6,5,1,4,2,3] => [1,2,6,3,5,4] => 3
[6,5,1,4,3,2] => [1,2,6,3,4,5] => 3
[6,5,2,1,3,4] => [1,2,5,6,4,3] => 2
[6,5,2,1,4,3] => [1,2,5,6,3,4] => 2
[6,5,2,3,1,4] => [1,2,5,4,6,3] => 3
[6,5,2,3,4,1] => [1,2,5,4,3,6] => 3
[6,5,2,4,1,3] => [1,2,5,3,6,4] => 4
[6,5,2,4,3,1] => [1,2,5,3,4,6] => 3
[6,5,3,1,2,4] => [1,2,4,6,5,3] => 3
[6,5,3,1,4,2] => [1,2,4,6,3,5] => 2
[6,5,3,2,1,4] => [1,2,4,5,6,3] => 3
[6,5,3,2,4,1] => [1,2,4,5,3,6] => 3
[6,5,3,4,1,2] => [1,2,4,3,6,5] => 4
[6,5,3,4,2,1] => [1,2,4,3,5,6] => 4
[6,5,4,1,2,3] => [1,2,3,6,5,4] => 3
[6,5,4,1,3,2] => [1,2,3,6,4,5] => 3
[6,5,4,2,1,3] => [1,2,3,5,6,4] => 3
[6,5,4,2,3,1] => [1,2,3,5,4,6] => 4
[6,5,4,3,1,2] => [1,2,3,4,6,5] => 4
[6,5,4,3,2,1] => [1,2,3,4,5,6] => 4
[7,4,2,3,5,1,6] => [1,4,6,5,3,7,2] => 3
[7,4,2,3,5,6,1] => [1,4,6,5,3,2,7] => 3
[7,4,2,3,6,1,5] => [1,4,6,5,2,7,3] => 4
[7,4,2,3,6,5,1] => [1,4,6,5,2,3,7] => 3
[7,4,2,5,1,3,6] => [1,4,6,3,7,5,2] => 3
[7,4,2,5,1,6,3] => [1,4,6,3,7,2,5] => 2
[7,4,2,5,3,1,6] => [1,4,6,3,5,7,2] => 2
[7,4,2,5,3,6,1] => [1,4,6,3,5,2,7] => 2
[7,4,2,5,6,1,3] => [1,4,6,3,2,7,5] => 3
[7,4,2,5,6,3,1] => [1,4,6,3,2,5,7] => 3
[7,4,2,6,1,3,5] => [1,4,6,2,7,5,3] => 3
[7,4,2,6,1,5,3] => [1,4,6,2,7,3,5] => 3
[7,4,2,6,3,1,5] => [1,4,6,2,5,7,3] => 2
[7,4,2,6,3,5,1] => [1,4,6,2,5,3,7] => 3
[7,4,2,6,5,1,3] => [1,4,6,2,3,7,5] => 3
[7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => 3
[7,4,3,1,2,5,6] => [1,4,5,7,6,3,2] => 3
[7,4,3,1,2,6,5] => [1,4,5,7,6,2,3] => 3
[7,4,3,1,5,2,6] => [1,4,5,7,3,6,2] => 2
[7,4,3,1,5,6,2] => [1,4,5,7,3,2,6] => 3
[7,4,3,1,6,2,5] => [1,4,5,7,2,6,3] => 3
[7,4,3,1,6,5,2] => [1,4,5,7,2,3,6] => 3
[7,4,3,2,1,5,6] => [1,4,5,6,7,3,2] => 3
[7,4,3,2,1,6,5] => [1,4,5,6,7,2,3] => 3
[7,4,3,2,5,1,6] => [1,4,5,6,3,7,2] => 3
[7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => 3
[7,4,3,2,6,1,5] => [1,4,5,6,2,7,3] => 4
[7,4,3,2,6,5,1] => [1,4,5,6,2,3,7] => 3
[7,4,3,5,1,2,6] => [1,4,5,3,7,6,2] => 3
[7,4,3,5,1,6,2] => [1,4,5,3,7,2,6] => 2
[7,4,3,5,2,1,6] => [1,4,5,3,6,7,2] => 3
[7,4,3,5,2,6,1] => [1,4,5,3,6,2,7] => 3
[7,4,3,5,6,1,2] => [1,4,5,3,2,7,6] => 3
[7,4,3,5,6,2,1] => [1,4,5,3,2,6,7] => 3
[7,4,3,6,1,2,5] => [1,4,5,2,7,6,3] => 3
[7,4,3,6,1,5,2] => [1,4,5,2,7,3,6] => 3
[7,4,3,6,2,1,5] => [1,4,5,2,6,7,3] => 3
[7,4,3,6,2,5,1] => [1,4,5,2,6,3,7] => 4
[7,4,3,6,5,1,2] => [1,4,5,2,3,7,6] => 3
[7,4,3,6,5,2,1] => [1,4,5,2,3,6,7] => 3
[7,4,5,1,2,3,6] => [1,4,3,7,6,5,2] => 3
[7,4,5,1,2,6,3] => [1,4,3,7,6,2,5] => 3
[7,4,5,1,3,2,6] => [1,4,3,7,5,6,2] => 3
[7,4,5,1,3,6,2] => [1,4,3,7,5,2,6] => 4
[7,4,5,1,6,2,3] => [1,4,3,7,2,6,5] => 3
[7,4,5,1,6,3,2] => [1,4,3,7,2,5,6] => 3
[7,4,5,2,1,3,6] => [1,4,3,6,7,5,2] => 3
[7,4,5,2,1,6,3] => [1,4,3,6,7,2,5] => 3
[7,4,5,2,3,1,6] => [1,4,3,6,5,7,2] => 4
[7,4,5,2,3,6,1] => [1,4,3,6,5,2,7] => 4
[7,4,5,2,6,1,3] => [1,4,3,6,2,7,5] => 4
[7,4,5,2,6,3,1] => [1,4,3,6,2,5,7] => 3
[7,4,5,3,1,2,6] => [1,4,3,5,7,6,2] => 4
[7,4,5,3,1,6,2] => [1,4,3,5,7,2,6] => 3
[7,4,5,3,2,1,6] => [1,4,3,5,6,7,2] => 4
[7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => 4
[7,4,5,3,6,1,2] => [1,4,3,5,2,7,6] => 4
[7,4,5,3,6,2,1] => [1,4,3,5,2,6,7] => 4
[7,4,5,6,1,2,3] => [1,4,3,2,7,6,5] => 3
[7,4,5,6,1,3,2] => [1,4,3,2,7,5,6] => 3
[7,4,5,6,2,1,3] => [1,4,3,2,6,7,5] => 3
[7,4,5,6,2,3,1] => [1,4,3,2,6,5,7] => 4
[7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => 4
[7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => 4
[7,4,6,1,2,3,5] => [1,4,2,7,6,5,3] => 3
[7,4,6,1,2,5,3] => [1,4,2,7,6,3,5] => 3
[7,4,6,1,3,2,5] => [1,4,2,7,5,6,3] => 3
[7,4,6,1,3,5,2] => [1,4,2,7,5,3,6] => 4
[7,4,6,1,5,2,3] => [1,4,2,7,3,6,5] => 4
[7,4,6,1,5,3,2] => [1,4,2,7,3,5,6] => 4
[7,4,6,2,1,3,5] => [1,4,2,6,7,5,3] => 3
[7,4,6,2,1,5,3] => [1,4,2,6,7,3,5] => 3
[7,4,6,2,3,1,5] => [1,4,2,6,5,7,3] => 4
[7,4,6,2,3,5,1] => [1,4,2,6,5,3,7] => 4
[7,4,6,2,5,1,3] => [1,4,2,6,3,7,5] => 5
[7,4,6,2,5,3,1] => [1,4,2,6,3,5,7] => 4
[7,4,6,3,1,2,5] => [1,4,2,5,7,6,3] => 4
[7,4,6,3,1,5,2] => [1,4,2,5,7,3,6] => 3
[7,4,6,3,2,1,5] => [1,4,2,5,6,7,3] => 4
[7,4,6,3,2,5,1] => [1,4,2,5,6,3,7] => 4
[7,4,6,3,5,1,2] => [1,4,2,5,3,7,6] => 5
[7,4,6,3,5,2,1] => [1,4,2,5,3,6,7] => 5
[7,4,6,5,1,2,3] => [1,4,2,3,7,6,5] => 3
[7,4,6,5,1,3,2] => [1,4,2,3,7,5,6] => 3
[7,4,6,5,2,1,3] => [1,4,2,3,6,7,5] => 3
[7,4,6,5,2,3,1] => [1,4,2,3,6,5,7] => 4
[7,4,6,5,3,1,2] => [1,4,2,3,5,7,6] => 4
[7,4,6,5,3,2,1] => [1,4,2,3,5,6,7] => 4
[7,5,1,2,3,4,6] => [1,3,7,6,5,4,2] => 2
[7,5,1,2,3,6,4] => [1,3,7,6,5,2,4] => 2
[7,5,1,2,4,3,6] => [1,3,7,6,4,5,2] => 2
[7,5,1,2,4,6,3] => [1,3,7,6,4,2,5] => 3
[7,5,1,2,6,3,4] => [1,3,7,6,2,5,4] => 3
[7,5,1,2,6,4,3] => [1,3,7,6,2,4,5] => 3
[7,5,1,3,2,4,6] => [1,3,7,5,6,4,2] => 2
[7,5,1,3,2,6,4] => [1,3,7,5,6,2,4] => 2
[7,5,1,3,4,2,6] => [1,3,7,5,4,6,2] => 3
[7,5,1,3,4,6,2] => [1,3,7,5,4,2,6] => 3
[7,5,1,3,6,2,4] => [1,3,7,5,2,6,4] => 4
[7,5,1,3,6,4,2] => [1,3,7,5,2,4,6] => 3
[7,5,1,4,2,3,6] => [1,3,7,4,6,5,2] => 3
[7,5,1,4,2,6,3] => [1,3,7,4,6,2,5] => 2
[7,5,1,4,3,2,6] => [1,3,7,4,5,6,2] => 3
[7,5,1,4,3,6,2] => [1,3,7,4,5,2,6] => 3
[7,5,1,4,6,2,3] => [1,3,7,4,2,6,5] => 4
[7,5,1,4,6,3,2] => [1,3,7,4,2,5,6] => 4
[7,5,1,6,2,3,4] => [1,3,7,2,6,5,4] => 2
[7,5,1,6,2,4,3] => [1,3,7,2,6,4,5] => 2
[7,5,1,6,3,2,4] => [1,3,7,2,5,6,4] => 2
[7,5,1,6,3,4,2] => [1,3,7,2,5,4,6] => 3
[7,5,1,6,4,2,3] => [1,3,7,2,4,6,5] => 3
[7,5,1,6,4,3,2] => [1,3,7,2,4,5,6] => 3
[7,5,2,1,3,4,6] => [1,3,6,7,5,4,2] => 2
[7,5,2,1,3,6,4] => [1,3,6,7,5,2,4] => 2
[7,5,2,1,4,3,6] => [1,3,6,7,4,5,2] => 2
[7,5,2,1,4,6,3] => [1,3,6,7,4,2,5] => 3
[7,5,2,1,6,3,4] => [1,3,6,7,2,5,4] => 3
[7,5,2,1,6,4,3] => [1,3,6,7,2,4,5] => 3
[7,5,2,3,1,4,6] => [1,3,6,5,7,4,2] => 3
[7,5,2,3,1,6,4] => [1,3,6,5,7,2,4] => 3
[7,5,2,3,4,1,6] => [1,3,6,5,4,7,2] => 3
[7,5,2,3,4,6,1] => [1,3,6,5,4,2,7] => 3
[7,5,2,3,6,1,4] => [1,3,6,5,2,7,4] => 4
[7,5,2,3,6,4,1] => [1,3,6,5,2,4,7] => 3
[7,5,2,4,1,3,6] => [1,3,6,4,7,5,2] => 4
[7,5,2,4,1,6,3] => [1,3,6,4,7,2,5] => 3
[7,5,2,4,3,1,6] => [1,3,6,4,5,7,2] => 3
[7,5,2,4,3,6,1] => [1,3,6,4,5,2,7] => 3
[7,5,2,4,6,1,3] => [1,3,6,4,2,7,5] => 4
[7,5,2,4,6,3,1] => [1,3,6,4,2,5,7] => 4
[7,5,2,6,1,3,4] => [1,3,6,2,7,5,4] => 3
[7,5,2,6,1,4,3] => [1,3,6,2,7,4,5] => 3
[7,5,2,6,3,1,4] => [1,3,6,2,5,7,4] => 2
[7,5,2,6,3,4,1] => [1,3,6,2,5,4,7] => 3
[7,5,2,6,4,1,3] => [1,3,6,2,4,7,5] => 3
[7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => 3
[7,5,3,1,2,4,6] => [1,3,5,7,6,4,2] => 3
[7,5,3,1,2,6,4] => [1,3,5,7,6,2,4] => 3
[7,5,3,1,4,2,6] => [1,3,5,7,4,6,2] => 2
[7,5,3,1,4,6,2] => [1,3,5,7,4,2,6] => 3
[7,5,3,1,6,2,4] => [1,3,5,7,2,6,4] => 3
[7,5,3,1,6,4,2] => [1,3,5,7,2,4,6] => 3
[7,5,3,2,1,4,6] => [1,3,5,6,7,4,2] => 3
[7,5,3,2,1,6,4] => [1,3,5,6,7,2,4] => 3
[7,5,3,2,4,1,6] => [1,3,5,6,4,7,2] => 3
[7,5,3,2,4,6,1] => [1,3,5,6,4,2,7] => 3
[7,5,3,2,6,1,4] => [1,3,5,6,2,7,4] => 4
[7,5,3,2,6,4,1] => [1,3,5,6,2,4,7] => 3
[7,5,3,4,1,2,6] => [1,3,5,4,7,6,2] => 4
[7,5,3,4,1,6,2] => [1,3,5,4,7,2,6] => 3
[7,5,3,4,2,1,6] => [1,3,5,4,6,7,2] => 4
[7,5,3,4,2,6,1] => [1,3,5,4,6,2,7] => 4
[7,5,3,4,6,1,2] => [1,3,5,4,2,7,6] => 4
[7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => 4
[7,5,3,6,1,2,4] => [1,3,5,2,7,6,4] => 3
[7,5,3,6,1,4,2] => [1,3,5,2,7,4,6] => 3
[7,5,3,6,2,1,4] => [1,3,5,2,6,7,4] => 3
[7,5,3,6,2,4,1] => [1,3,5,2,6,4,7] => 4
[7,5,3,6,4,1,2] => [1,3,5,2,4,7,6] => 3
[7,5,3,6,4,2,1] => [1,3,5,2,4,6,7] => 3
[7,5,4,1,2,3,6] => [1,3,4,7,6,5,2] => 3
[7,5,4,1,2,6,3] => [1,3,4,7,6,2,5] => 3
[7,5,4,1,3,2,6] => [1,3,4,7,5,6,2] => 3
[7,5,4,1,3,6,2] => [1,3,4,7,5,2,6] => 4
[7,5,4,1,6,2,3] => [1,3,4,7,2,6,5] => 3
[7,5,4,1,6,3,2] => [1,3,4,7,2,5,6] => 3
[7,5,4,2,1,3,6] => [1,3,4,6,7,5,2] => 3
[7,5,4,2,1,6,3] => [1,3,4,6,7,2,5] => 3
[7,5,4,2,3,1,6] => [1,3,4,6,5,7,2] => 4
[7,5,4,2,3,6,1] => [1,3,4,6,5,2,7] => 4
[7,5,4,2,6,1,3] => [1,3,4,6,2,7,5] => 4
[7,5,4,2,6,3,1] => [1,3,4,6,2,5,7] => 3
[7,5,4,3,1,2,6] => [1,3,4,5,7,6,2] => 4
[7,5,4,3,1,6,2] => [1,3,4,5,7,2,6] => 3
[7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => 4
[7,5,4,3,2,6,1] => [1,3,4,5,6,2,7] => 4
[7,5,4,3,6,1,2] => [1,3,4,5,2,7,6] => 4
[7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => 4
[7,5,4,6,1,2,3] => [1,3,4,2,7,6,5] => 3
[7,5,4,6,1,3,2] => [1,3,4,2,7,5,6] => 3
[7,5,4,6,2,1,3] => [1,3,4,2,6,7,5] => 3
[7,5,4,6,2,3,1] => [1,3,4,2,6,5,7] => 4
[7,5,4,6,3,1,2] => [1,3,4,2,5,7,6] => 4
[7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => 4
[7,5,6,1,2,3,4] => [1,3,2,7,6,5,4] => 3
[7,5,6,1,2,4,3] => [1,3,2,7,6,4,5] => 3
[7,5,6,1,3,2,4] => [1,3,2,7,5,6,4] => 3
[7,5,6,1,3,4,2] => [1,3,2,7,5,4,6] => 4
[7,5,6,1,4,2,3] => [1,3,2,7,4,6,5] => 4
[7,5,6,1,4,3,2] => [1,3,2,7,4,5,6] => 4
[7,5,6,2,1,3,4] => [1,3,2,6,7,5,4] => 3
[7,5,6,2,1,4,3] => [1,3,2,6,7,4,5] => 3
[7,5,6,2,3,1,4] => [1,3,2,6,5,7,4] => 4
[7,5,6,2,3,4,1] => [1,3,2,6,5,4,7] => 4
[7,5,6,2,4,1,3] => [1,3,2,6,4,7,5] => 5
[7,5,6,2,4,3,1] => [1,3,2,6,4,5,7] => 4
[7,5,6,3,1,2,4] => [1,3,2,5,7,6,4] => 4
[7,5,6,3,1,4,2] => [1,3,2,5,7,4,6] => 3
[7,5,6,3,2,1,4] => [1,3,2,5,6,7,4] => 4
[7,5,6,3,2,4,1] => [1,3,2,5,6,4,7] => 4
[7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => 5
[7,5,6,3,4,2,1] => [1,3,2,5,4,6,7] => 5
[7,5,6,4,1,2,3] => [1,3,2,4,7,6,5] => 4
[7,5,6,4,1,3,2] => [1,3,2,4,7,5,6] => 4
[7,5,6,4,2,1,3] => [1,3,2,4,6,7,5] => 4
[7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => 5
[7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => 5
[7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => 5
[7,6,1,2,3,4,5] => [1,2,7,6,5,4,3] => 2
[7,6,1,2,3,5,4] => [1,2,7,6,5,3,4] => 2
[7,6,1,2,4,3,5] => [1,2,7,6,4,5,3] => 2
[7,6,1,2,4,5,3] => [1,2,7,6,4,3,5] => 3
[7,6,1,2,5,3,4] => [1,2,7,6,3,5,4] => 3
[7,6,1,2,5,4,3] => [1,2,7,6,3,4,5] => 3
[7,6,1,3,2,4,5] => [1,2,7,5,6,4,3] => 2
[7,6,1,3,2,5,4] => [1,2,7,5,6,3,4] => 2
[7,6,1,3,4,2,5] => [1,2,7,5,4,6,3] => 3
[7,6,1,3,4,5,2] => [1,2,7,5,4,3,6] => 3
[7,6,1,3,5,2,4] => [1,2,7,5,3,6,4] => 4
[7,6,1,3,5,4,2] => [1,2,7,5,3,4,6] => 3
[7,6,1,4,2,3,5] => [1,2,7,4,6,5,3] => 3
[7,6,1,4,2,5,3] => [1,2,7,4,6,3,5] => 2
[7,6,1,4,3,2,5] => [1,2,7,4,5,6,3] => 3
[7,6,1,4,3,5,2] => [1,2,7,4,5,3,6] => 3
[7,6,1,4,5,2,3] => [1,2,7,4,3,6,5] => 4
[7,6,1,4,5,3,2] => [1,2,7,4,3,5,6] => 4
[7,6,1,5,2,3,4] => [1,2,7,3,6,5,4] => 3
[7,6,1,5,2,4,3] => [1,2,7,3,6,4,5] => 3
[7,6,1,5,3,2,4] => [1,2,7,3,5,6,4] => 3
[7,6,1,5,3,4,2] => [1,2,7,3,5,4,6] => 4
[7,6,1,5,4,2,3] => [1,2,7,3,4,6,5] => 4
[7,6,1,5,4,3,2] => [1,2,7,3,4,5,6] => 4
[7,6,2,1,3,4,5] => [1,2,6,7,5,4,3] => 2
[7,6,2,1,3,5,4] => [1,2,6,7,5,3,4] => 2
[7,6,2,1,4,3,5] => [1,2,6,7,4,5,3] => 2
[7,6,2,1,4,5,3] => [1,2,6,7,4,3,5] => 3
[7,6,2,1,5,3,4] => [1,2,6,7,3,5,4] => 3
[7,6,2,1,5,4,3] => [1,2,6,7,3,4,5] => 3
[7,6,2,3,1,4,5] => [1,2,6,5,7,4,3] => 3
[7,6,2,3,1,5,4] => [1,2,6,5,7,3,4] => 3
[7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => 3
[7,6,2,3,4,5,1] => [1,2,6,5,4,3,7] => 3
[7,6,2,3,5,1,4] => [1,2,6,5,3,7,4] => 4
[7,6,2,3,5,4,1] => [1,2,6,5,3,4,7] => 3
[7,6,2,4,1,3,5] => [1,2,6,4,7,5,3] => 4
[7,6,2,4,1,5,3] => [1,2,6,4,7,3,5] => 3
[7,6,2,4,3,1,5] => [1,2,6,4,5,7,3] => 3
[7,6,2,4,3,5,1] => [1,2,6,4,5,3,7] => 3
[7,6,2,4,5,1,3] => [1,2,6,4,3,7,5] => 4
[7,6,2,4,5,3,1] => [1,2,6,4,3,5,7] => 4
[7,6,2,5,1,3,4] => [1,2,6,3,7,5,4] => 4
[7,6,2,5,1,4,3] => [1,2,6,3,7,4,5] => 4
[7,6,2,5,3,1,4] => [1,2,6,3,5,7,4] => 3
[7,6,2,5,3,4,1] => [1,2,6,3,5,4,7] => 4
[7,6,2,5,4,1,3] => [1,2,6,3,4,7,5] => 4
[7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => 4
[7,6,3,1,2,4,5] => [1,2,5,7,6,4,3] => 3
[7,6,3,1,2,5,4] => [1,2,5,7,6,3,4] => 3
[7,6,3,1,4,2,5] => [1,2,5,7,4,6,3] => 2
[7,6,3,1,4,5,2] => [1,2,5,7,4,3,6] => 3
[7,6,3,1,5,2,4] => [1,2,5,7,3,6,4] => 3
[7,6,3,1,5,4,2] => [1,2,5,7,3,4,6] => 3
[7,6,3,2,1,4,5] => [1,2,5,6,7,4,3] => 3
[7,6,3,2,1,5,4] => [1,2,5,6,7,3,4] => 3
[7,6,3,2,4,1,5] => [1,2,5,6,4,7,3] => 3
[7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => 3
[7,6,3,2,5,1,4] => [1,2,5,6,3,7,4] => 4
[7,6,3,2,5,4,1] => [1,2,5,6,3,4,7] => 3
[7,6,3,4,1,2,5] => [1,2,5,4,7,6,3] => 4
[7,6,3,4,1,5,2] => [1,2,5,4,7,3,6] => 3
[7,6,3,4,2,1,5] => [1,2,5,4,6,7,3] => 4
[7,6,3,4,2,5,1] => [1,2,5,4,6,3,7] => 4
[7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => 4
[7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => 4
[7,6,3,5,1,2,4] => [1,2,5,3,7,6,4] => 4
[7,6,3,5,1,4,2] => [1,2,5,3,7,4,6] => 4
[7,6,3,5,2,1,4] => [1,2,5,3,6,7,4] => 4
[7,6,3,5,2,4,1] => [1,2,5,3,6,4,7] => 5
[7,6,3,5,4,1,2] => [1,2,5,3,4,7,6] => 4
[7,6,3,5,4,2,1] => [1,2,5,3,4,6,7] => 4
[7,6,4,1,2,3,5] => [1,2,4,7,6,5,3] => 3
[7,6,4,1,2,5,3] => [1,2,4,7,6,3,5] => 3
[7,6,4,1,3,2,5] => [1,2,4,7,5,6,3] => 3
[7,6,4,1,3,5,2] => [1,2,4,7,5,3,6] => 4
[7,6,4,1,5,2,3] => [1,2,4,7,3,6,5] => 3
[7,6,4,1,5,3,2] => [1,2,4,7,3,5,6] => 3
[7,6,4,2,1,3,5] => [1,2,4,6,7,5,3] => 3
[7,6,4,2,1,5,3] => [1,2,4,6,7,3,5] => 3
[7,6,4,2,3,1,5] => [1,2,4,6,5,7,3] => 4
[7,6,4,2,3,5,1] => [1,2,4,6,5,3,7] => 4
[7,6,4,2,5,1,3] => [1,2,4,6,3,7,5] => 4
[7,6,4,2,5,3,1] => [1,2,4,6,3,5,7] => 3
[7,6,4,3,1,2,5] => [1,2,4,5,7,6,3] => 4
[7,6,4,3,1,5,2] => [1,2,4,5,7,3,6] => 3
[7,6,4,3,2,1,5] => [1,2,4,5,6,7,3] => 4
[7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => 4
[7,6,4,3,5,1,2] => [1,2,4,5,3,7,6] => 4
[7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => 4
[7,6,4,5,1,2,3] => [1,2,4,3,7,6,5] => 4
[7,6,4,5,1,3,2] => [1,2,4,3,7,5,6] => 4
[7,6,4,5,2,1,3] => [1,2,4,3,6,7,5] => 4
[7,6,4,5,2,3,1] => [1,2,4,3,6,5,7] => 5
[7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => 5
[7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => 5
[7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => 3
[7,6,5,1,2,4,3] => [1,2,3,7,6,4,5] => 3
[7,6,5,1,3,2,4] => [1,2,3,7,5,6,4] => 3
[7,6,5,1,3,4,2] => [1,2,3,7,5,4,6] => 4
[7,6,5,1,4,2,3] => [1,2,3,7,4,6,5] => 4
[7,6,5,1,4,3,2] => [1,2,3,7,4,5,6] => 4
[7,6,5,2,1,3,4] => [1,2,3,6,7,5,4] => 3
[7,6,5,2,1,4,3] => [1,2,3,6,7,4,5] => 3
[7,6,5,2,3,1,4] => [1,2,3,6,5,7,4] => 4
[7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => 4
[7,6,5,2,4,1,3] => [1,2,3,6,4,7,5] => 5
[7,6,5,2,4,3,1] => [1,2,3,6,4,5,7] => 4
[7,6,5,3,1,2,4] => [1,2,3,5,7,6,4] => 4
[7,6,5,3,1,4,2] => [1,2,3,5,7,4,6] => 3
[7,6,5,3,2,1,4] => [1,2,3,5,6,7,4] => 4
[7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => 4
[7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => 5
[7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => 5
[7,6,5,4,1,2,3] => [1,2,3,4,7,6,5] => 4
[7,6,5,4,1,3,2] => [1,2,3,4,7,5,6] => 4
[7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => 4
[7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => 5
[7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => 5
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 5
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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:
3,3 6,12,6 10,50,50,10 20,160,360,160,20
$F_{2} = 2$
$F_{3} = 3 + 3\ q$
$F_{4} = 6 + 12\ q + 6\ q^{2}$
$F_{5} = 10 + 50\ q + 50\ q^{2} + 10\ q^{3}$
$F_{6} = 20 + 160\ q + 360\ q^{2} + 160\ q^{3} + 20\ q^{4}$
Description
The number of ascents of distance 2 of a permutation.
This is, $\operatorname{asc}_2(\pi) = | \{ i : \pi(i) < \pi(i+2) \} |$.
This is, $\operatorname{asc}_2(\pi) = | \{ i : \pi(i) < \pi(i+2) \} |$.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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