Identifier
-
Mp00069:
Permutations
—complement⟶
Permutations
St000646: 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] => 0
[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] => 0
[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] => 1
[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] => 2
[3,2,1,4] => [2,3,4,1] => 0
[3,2,4,1] => [2,3,1,4] => 1
[3,4,1,2] => [2,1,4,3] => 1
[3,4,2,1] => [2,1,3,4] => 1
[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] => 1
[4,3,2,1] => [1,2,3,4] => 0
[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] => 0
[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] => 1
[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] => 2
[1,4,3,2,5] => [5,2,3,4,1] => 0
[1,4,3,5,2] => [5,2,3,1,4] => 1
[1,4,5,2,3] => [5,2,1,4,3] => 1
[1,4,5,3,2] => [5,2,1,3,4] => 1
[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] => 1
[1,5,4,3,2] => [5,1,2,3,4] => 0
[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] => 0
[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] => 1
[2,3,5,4,1] => [4,3,1,2,5] => 1
[2,4,1,3,5] => [4,2,5,3,1] => 1
[2,4,1,5,3] => [4,2,5,1,3] => 2
[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] => 1
[2,4,5,3,1] => [4,2,1,3,5] => 2
[2,5,1,3,4] => [4,1,5,3,2] => 1
[2,5,1,4,3] => [4,1,5,2,3] => 1
[2,5,3,1,4] => [4,1,3,5,2] => 2
[2,5,3,4,1] => [4,1,3,2,5] => 2
[2,5,4,1,3] => [4,1,2,5,3] => 1
[2,5,4,3,1] => [4,1,2,3,5] => 1
[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] => 2
[3,1,4,5,2] => [3,5,2,1,4] => 2
[3,1,5,2,4] => [3,5,1,4,2] => 2
[3,1,5,4,2] => [3,5,1,2,4] => 2
[3,2,1,4,5] => [3,4,5,2,1] => 0
[3,2,1,5,4] => [3,4,5,1,2] => 0
[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] => 1
[3,2,5,4,1] => [3,4,1,2,5] => 1
[3,4,1,2,5] => [3,2,5,4,1] => 1
[3,4,1,5,2] => [3,2,5,1,4] => 2
[3,4,2,1,5] => [3,2,4,5,1] => 1
[3,4,2,5,1] => [3,2,4,1,5] => 2
[3,4,5,1,2] => [3,2,1,5,4] => 1
[3,4,5,2,1] => [3,2,1,4,5] => 1
[3,5,1,2,4] => [3,1,5,4,2] => 1
[3,5,1,4,2] => [3,1,5,2,4] => 2
[3,5,2,1,4] => [3,1,4,5,2] => 1
>>> Load all 1200 entries. <<<[3,5,2,4,1] => [3,1,4,2,5] => 2
[3,5,4,1,2] => [3,1,2,5,4] => 1
[3,5,4,2,1] => [3,1,2,4,5] => 1
[4,1,2,3,5] => [2,5,4,3,1] => 1
[4,1,2,5,3] => [2,5,4,1,3] => 2
[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] => 2
[4,1,5,3,2] => [2,5,1,3,4] => 2
[4,2,1,3,5] => [2,4,5,3,1] => 1
[4,2,1,5,3] => [2,4,5,1,3] => 2
[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] => 3
[4,3,1,2,5] => [2,3,5,4,1] => 1
[4,3,1,5,2] => [2,3,5,1,4] => 2
[4,3,2,1,5] => [2,3,4,5,1] => 0
[4,3,2,5,1] => [2,3,4,1,5] => 1
[4,3,5,1,2] => [2,3,1,5,4] => 1
[4,3,5,2,1] => [2,3,1,4,5] => 1
[4,5,1,2,3] => [2,1,5,4,3] => 1
[4,5,1,3,2] => [2,1,5,3,4] => 1
[4,5,2,1,3] => [2,1,4,5,3] => 1
[4,5,2,3,1] => [2,1,4,3,5] => 2
[4,5,3,1,2] => [2,1,3,5,4] => 2
[4,5,3,2,1] => [2,1,3,4,5] => 1
[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] => 1
[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] => 2
[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] => 3
[5,3,2,1,4] => [1,3,4,5,2] => 1
[5,3,2,4,1] => [1,3,4,2,5] => 2
[5,3,4,1,2] => [1,3,2,5,4] => 2
[5,3,4,2,1] => [1,3,2,4,5] => 2
[5,4,1,2,3] => [1,2,5,4,3] => 1
[5,4,1,3,2] => [1,2,5,3,4] => 1
[5,4,2,1,3] => [1,2,4,5,3] => 1
[5,4,2,3,1] => [1,2,4,3,5] => 2
[5,4,3,1,2] => [1,2,3,5,4] => 1
[5,4,3,2,1] => [1,2,3,4,5] => 0
[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] => 0
[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] => 1
[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] => 2
[1,2,5,4,3,6] => [6,5,2,3,4,1] => 0
[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] => 1
[1,2,5,6,4,3] => [6,5,2,1,3,4] => 1
[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] => 1
[1,2,6,5,4,3] => [6,5,1,2,3,4] => 0
[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] => 0
[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] => 1
[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] => 1
[1,3,5,2,6,4] => [6,4,2,5,1,3] => 2
[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] => 1
[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] => 1
[1,3,6,2,5,4] => [6,4,1,5,2,3] => 1
[1,3,6,4,2,5] => [6,4,1,3,5,2] => 2
[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] => 1
[1,3,6,5,4,2] => [6,4,1,2,3,5] => 1
[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] => 2
[1,4,2,5,6,3] => [6,3,5,2,1,4] => 2
[1,4,2,6,3,5] => [6,3,5,1,4,2] => 2
[1,4,2,6,5,3] => [6,3,5,1,2,4] => 2
[1,4,3,2,5,6] => [6,3,4,5,2,1] => 0
[1,4,3,2,6,5] => [6,3,4,5,1,2] => 0
[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] => 1
[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] => 1
[1,4,5,2,6,3] => [6,3,2,5,1,4] => 2
[1,4,5,3,2,6] => [6,3,2,4,5,1] => 1
[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] => 1
[1,4,5,6,3,2] => [6,3,2,1,4,5] => 1
[1,4,6,2,3,5] => [6,3,1,5,4,2] => 1
[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] => 1
[1,4,6,3,5,2] => [6,3,1,4,2,5] => 2
[1,4,6,5,2,3] => [6,3,1,2,5,4] => 1
[1,4,6,5,3,2] => [6,3,1,2,4,5] => 1
[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] => 2
[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] => 2
[1,5,2,6,4,3] => [6,2,5,1,3,4] => 2
[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] => 2
[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] => 3
[1,5,4,2,3,6] => [6,2,3,5,4,1] => 1
[1,5,4,2,6,3] => [6,2,3,5,1,4] => 2
[1,5,4,3,2,6] => [6,2,3,4,5,1] => 0
[1,5,4,3,6,2] => [6,2,3,4,1,5] => 1
[1,5,4,6,2,3] => [6,2,3,1,5,4] => 1
[1,5,4,6,3,2] => [6,2,3,1,4,5] => 1
[1,5,6,2,3,4] => [6,2,1,5,4,3] => 1
[1,5,6,2,4,3] => [6,2,1,5,3,4] => 1
[1,5,6,3,2,4] => [6,2,1,4,5,3] => 1
[1,5,6,3,4,2] => [6,2,1,4,3,5] => 2
[1,5,6,4,2,3] => [6,2,1,3,5,4] => 2
[1,5,6,4,3,2] => [6,2,1,3,4,5] => 1
[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] => 1
[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] => 2
[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] => 3
[1,6,4,3,2,5] => [6,1,3,4,5,2] => 1
[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] => 2
[1,6,4,5,3,2] => [6,1,3,2,4,5] => 2
[1,6,5,2,3,4] => [6,1,2,5,4,3] => 1
[1,6,5,2,4,3] => [6,1,2,5,3,4] => 1
[1,6,5,3,2,4] => [6,1,2,4,5,3] => 1
[1,6,5,3,4,2] => [6,1,2,4,3,5] => 2
[1,6,5,4,2,3] => [6,1,2,3,5,4] => 1
[1,6,5,4,3,2] => [6,1,2,3,4,5] => 0
[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] => 0
[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] => 1
[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] => 2
[2,1,5,4,3,6] => [5,6,2,3,4,1] => 0
[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] => 1
[2,1,5,6,4,3] => [5,6,2,1,3,4] => 1
[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] => 1
[2,1,6,5,4,3] => [5,6,1,2,3,4] => 0
[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] => 1
[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] => 1
[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] => 1
[2,3,5,1,6,4] => [5,4,2,6,1,3] => 2
[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] => 1
[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] => 1
[2,3,6,1,5,4] => [5,4,1,6,2,3] => 1
[2,3,6,4,1,5] => [5,4,1,3,6,2] => 2
[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] => 1
[2,3,6,5,4,1] => [5,4,1,2,3,6] => 1
[2,4,1,3,5,6] => [5,3,6,4,2,1] => 1
[2,4,1,3,6,5] => [5,3,6,4,1,2] => 1
[2,4,1,5,3,6] => [5,3,6,2,4,1] => 2
[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] => 1
[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] => 1
[2,4,5,1,6,3] => [5,3,2,6,1,4] => 2
[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] => 1
[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] => 1
[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] => 2
[2,4,6,5,1,3] => [5,3,1,2,6,4] => 1
[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] => 1
[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] => 1
[2,5,1,4,6,3] => [5,2,6,3,1,4] => 2
[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] => 2
[2,5,3,1,6,4] => [5,2,4,6,1,3] => 3
[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] => 3
[2,5,4,1,3,6] => [5,2,3,6,4,1] => 1
[2,5,4,1,6,3] => [5,2,3,6,1,4] => 2
[2,5,4,3,1,6] => [5,2,3,4,6,1] => 1
[2,5,4,3,6,1] => [5,2,3,4,1,6] => 1
[2,5,4,6,1,3] => [5,2,3,1,6,4] => 1
[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] => 1
[2,5,6,1,4,3] => [5,2,1,6,3,4] => 1
[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] => 2
[2,5,6,4,1,3] => [5,2,1,3,6,4] => 2
[2,5,6,4,3,1] => [5,2,1,3,4,6] => 2
[2,6,1,3,4,5] => [5,1,6,4,3,2] => 1
[2,6,1,3,5,4] => [5,1,6,4,2,3] => 1
[2,6,1,4,3,5] => [5,1,6,3,4,2] => 1
[2,6,1,4,5,3] => [5,1,6,3,2,4] => 2
[2,6,1,5,3,4] => [5,1,6,2,4,3] => 2
[2,6,1,5,4,3] => [5,1,6,2,3,4] => 1
[2,6,3,1,4,5] => [5,1,4,6,3,2] => 2
[2,6,3,1,5,4] => [5,1,4,6,2,3] => 2
[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] => 2
[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] => 3
[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] => 2
[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] => 1
[2,6,5,1,4,3] => [5,1,2,6,3,4] => 1
[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] => 2
[2,6,5,4,1,3] => [5,1,2,3,6,4] => 1
[2,6,5,4,3,1] => [5,1,2,3,4,6] => 1
[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] => 1
[3,1,4,2,5,6] => [4,6,3,5,2,1] => 2
[3,1,4,2,6,5] => [4,6,3,5,1,2] => 2
[3,1,4,5,2,6] => [4,6,3,2,5,1] => 2
[3,1,4,5,6,2] => [4,6,3,2,1,5] => 2
[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] => 2
[3,1,5,2,4,6] => [4,6,2,5,3,1] => 2
[3,1,5,2,6,4] => [4,6,2,5,1,3] => 3
[3,1,5,4,2,6] => [4,6,2,3,5,1] => 2
[3,1,5,4,6,2] => [4,6,2,3,1,5] => 2
[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] => 3
[3,1,6,2,4,5] => [4,6,1,5,3,2] => 2
[3,1,6,2,5,4] => [4,6,1,5,2,3] => 2
[3,1,6,4,2,5] => [4,6,1,3,5,2] => 3
[3,1,6,4,5,2] => [4,6,1,3,2,5] => 3
[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] => 0
[3,2,1,4,6,5] => [4,5,6,3,1,2] => 0
[3,2,1,5,4,6] => [4,5,6,2,3,1] => 0
[3,2,1,5,6,4] => [4,5,6,2,1,3] => 1
[3,2,1,6,4,5] => [4,5,6,1,3,2] => 1
[3,2,1,6,5,4] => [4,5,6,1,2,3] => 0
[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] => 1
[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] => 1
[3,2,5,1,6,4] => [4,5,2,6,1,3] => 2
[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] => 1
[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] => 1
[3,2,6,1,5,4] => [4,5,1,6,2,3] => 1
[3,2,6,4,1,5] => [4,5,1,3,6,2] => 2
[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] => 1
[3,2,6,5,4,1] => [4,5,1,2,3,6] => 1
[3,4,1,2,5,6] => [4,3,6,5,2,1] => 1
[3,4,1,2,6,5] => [4,3,6,5,1,2] => 1
[3,4,1,5,2,6] => [4,3,6,2,5,1] => 2
[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] => 1
[3,4,2,1,6,5] => [4,3,5,6,1,2] => 1
[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] => 2
[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] => 1
[3,4,5,1,6,2] => [4,3,2,6,1,5] => 2
[3,4,5,2,1,6] => [4,3,2,5,6,1] => 1
[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] => 1
[3,4,5,6,2,1] => [4,3,2,1,5,6] => 1
[3,4,6,1,2,5] => [4,3,1,6,5,2] => 1
[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] => 1
[3,4,6,2,5,1] => [4,3,1,5,2,6] => 2
[3,4,6,5,1,2] => [4,3,1,2,6,5] => 1
[3,4,6,5,2,1] => [4,3,1,2,5,6] => 1
[3,5,1,2,4,6] => [4,2,6,5,3,1] => 1
[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] => 2
[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] => 3
[3,5,2,1,4,6] => [4,2,5,6,3,1] => 1
[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] => 2
[3,5,2,4,6,1] => [4,2,5,3,1,6] => 2
[3,5,2,6,1,4] => [4,2,5,1,6,3] => 2
[3,5,2,6,4,1] => [4,2,5,1,3,6] => 3
[3,5,4,1,2,6] => [4,2,3,6,5,1] => 1
[3,5,4,1,6,2] => [4,2,3,6,1,5] => 2
[3,5,4,2,1,6] => [4,2,3,5,6,1] => 1
[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] => 1
[3,5,4,6,2,1] => [4,2,3,1,5,6] => 1
[3,5,6,1,2,4] => [4,2,1,6,5,3] => 1
[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] => 1
[3,5,6,2,4,1] => [4,2,1,5,3,6] => 2
[3,5,6,4,1,2] => [4,2,1,3,6,5] => 2
[3,5,6,4,2,1] => [4,2,1,3,5,6] => 2
[3,6,1,2,4,5] => [4,1,6,5,3,2] => 1
[3,6,1,2,5,4] => [4,1,6,5,2,3] => 1
[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] => 2
[3,6,1,5,2,4] => [4,1,6,2,5,3] => 2
[3,6,1,5,4,2] => [4,1,6,2,3,5] => 2
[3,6,2,1,4,5] => [4,1,5,6,3,2] => 1
[3,6,2,1,5,4] => [4,1,5,6,2,3] => 1
[3,6,2,4,1,5] => [4,1,5,3,6,2] => 2
[3,6,2,4,5,1] => [4,1,5,3,2,6] => 2
[3,6,2,5,1,4] => [4,1,5,2,6,3] => 2
[3,6,2,5,4,1] => [4,1,5,2,3,6] => 2
[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] => 3
[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] => 3
[3,6,4,5,1,2] => [4,1,3,2,6,5] => 2
[3,6,4,5,2,1] => [4,1,3,2,5,6] => 2
[3,6,5,1,2,4] => [4,1,2,6,5,3] => 1
[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] => 1
[3,6,5,2,4,1] => [4,1,2,5,3,6] => 2
[3,6,5,4,1,2] => [4,1,2,3,6,5] => 1
[3,6,5,4,2,1] => [4,1,2,3,5,6] => 1
[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] => 2
[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] => 2
[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] => 2
[4,1,5,2,6,3] => [3,6,2,5,1,4] => 3
[4,1,5,3,2,6] => [3,6,2,4,5,1] => 2
[4,1,5,3,6,2] => [3,6,2,4,1,5] => 3
[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] => 2
[4,1,6,2,5,3] => [3,6,1,5,2,4] => 3
[4,1,6,3,2,5] => [3,6,1,4,5,2] => 2
[4,1,6,3,5,2] => [3,6,1,4,2,5] => 3
[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] => 2
[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] => 2
[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] => 3
[4,2,5,3,1,6] => [3,5,2,4,6,1] => 3
[4,2,5,3,6,1] => [3,5,2,4,1,6] => 3
[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] => 3
[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] => 3
[4,2,6,3,1,5] => [3,5,1,4,6,2] => 3
[4,2,6,3,5,1] => [3,5,1,4,2,6] => 3
[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] => 3
[4,3,1,2,5,6] => [3,4,6,5,2,1] => 1
[4,3,1,2,6,5] => [3,4,6,5,1,2] => 1
[4,3,1,5,2,6] => [3,4,6,2,5,1] => 2
[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] => 0
[4,3,2,1,6,5] => [3,4,5,6,1,2] => 0
[4,3,2,5,1,6] => [3,4,5,2,6,1] => 1
[4,3,2,5,6,1] => [3,4,5,2,1,6] => 1
[4,3,2,6,1,5] => [3,4,5,1,6,2] => 1
[4,3,2,6,5,1] => [3,4,5,1,2,6] => 1
[4,3,5,1,2,6] => [3,4,2,6,5,1] => 1
[4,3,5,1,6,2] => [3,4,2,6,1,5] => 2
[4,3,5,2,1,6] => [3,4,2,5,6,1] => 1
[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] => 1
[4,3,5,6,2,1] => [3,4,2,1,5,6] => 1
[4,3,6,1,2,5] => [3,4,1,6,5,2] => 1
[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] => 1
[4,3,6,2,5,1] => [3,4,1,5,2,6] => 2
[4,3,6,5,1,2] => [3,4,1,2,6,5] => 1
[4,3,6,5,2,1] => [3,4,1,2,5,6] => 1
[4,5,1,2,3,6] => [3,2,6,5,4,1] => 1
[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] => 1
[4,5,1,3,6,2] => [3,2,6,4,1,5] => 2
[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] => 1
[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] => 2
[4,5,2,3,6,1] => [3,2,5,4,1,6] => 2
[4,5,2,6,1,3] => [3,2,5,1,6,4] => 2
[4,5,2,6,3,1] => [3,2,5,1,4,6] => 3
[4,5,3,1,2,6] => [3,2,4,6,5,1] => 2
[4,5,3,1,6,2] => [3,2,4,6,1,5] => 3
[4,5,3,2,1,6] => [3,2,4,5,6,1] => 1
[4,5,3,2,6,1] => [3,2,4,5,1,6] => 2
[4,5,3,6,1,2] => [3,2,4,1,6,5] => 2
[4,5,3,6,2,1] => [3,2,4,1,5,6] => 2
[4,5,6,1,2,3] => [3,2,1,6,5,4] => 1
[4,5,6,1,3,2] => [3,2,1,6,4,5] => 1
[4,5,6,2,1,3] => [3,2,1,5,6,4] => 1
[4,5,6,2,3,1] => [3,2,1,5,4,6] => 2
[4,5,6,3,1,2] => [3,2,1,4,6,5] => 2
[4,5,6,3,2,1] => [3,2,1,4,5,6] => 1
[4,6,1,2,3,5] => [3,1,6,5,4,2] => 1
[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] => 1
[4,6,1,3,5,2] => [3,1,6,4,2,5] => 2
[4,6,1,5,2,3] => [3,1,6,2,5,4] => 2
[4,6,1,5,3,2] => [3,1,6,2,4,5] => 2
[4,6,2,1,3,5] => [3,1,5,6,4,2] => 1
[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] => 2
[4,6,2,3,5,1] => [3,1,5,4,2,6] => 2
[4,6,2,5,1,3] => [3,1,5,2,6,4] => 2
[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] => 2
[4,6,3,1,5,2] => [3,1,4,6,2,5] => 3
[4,6,3,2,1,5] => [3,1,4,5,6,2] => 1
[4,6,3,2,5,1] => [3,1,4,5,2,6] => 2
[4,6,3,5,1,2] => [3,1,4,2,6,5] => 2
[4,6,3,5,2,1] => [3,1,4,2,5,6] => 2
[4,6,5,1,2,3] => [3,1,2,6,5,4] => 1
[4,6,5,1,3,2] => [3,1,2,6,4,5] => 1
[4,6,5,2,1,3] => [3,1,2,5,6,4] => 1
[4,6,5,2,3,1] => [3,1,2,5,4,6] => 2
[4,6,5,3,1,2] => [3,1,2,4,6,5] => 2
[4,6,5,3,2,1] => [3,1,2,4,5,6] => 1
[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] => 2
[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] => 2
[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] => 2
[5,1,3,6,4,2] => [2,6,4,1,3,5] => 3
[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] => 3
[5,1,4,3,2,6] => [2,6,3,4,5,1] => 1
[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] => 2
[5,1,4,6,3,2] => [2,6,3,1,4,5] => 2
[5,1,6,2,3,4] => [2,6,1,5,4,3] => 2
[5,1,6,2,4,3] => [2,6,1,5,3,4] => 2
[5,1,6,3,2,4] => [2,6,1,4,5,3] => 2
[5,1,6,3,4,2] => [2,6,1,4,3,5] => 3
[5,1,6,4,2,3] => [2,6,1,3,5,4] => 3
[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] => 2
[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] => 3
[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] => 2
[5,2,3,6,4,1] => [2,5,4,1,3,6] => 3
[5,2,4,1,3,6] => [2,5,3,6,4,1] => 2
[5,2,4,1,6,3] => [2,5,3,6,1,4] => 3
[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] => 2
[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] => 3
[5,2,6,3,4,1] => [2,5,1,4,3,6] => 3
[5,2,6,4,1,3] => [2,5,1,3,6,4] => 3
[5,2,6,4,3,1] => [2,5,1,3,4,6] => 3
[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] => 3
[5,3,1,4,2,6] => [2,4,6,3,5,1] => 3
[5,3,1,4,6,2] => [2,4,6,3,1,5] => 3
[5,3,1,6,2,4] => [2,4,6,1,5,3] => 3
[5,3,1,6,4,2] => [2,4,6,1,3,5] => 4
[5,3,2,1,4,6] => [2,4,5,6,3,1] => 1
[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] => 2
[5,3,2,6,4,1] => [2,4,5,1,3,6] => 3
[5,3,4,1,2,6] => [2,4,3,6,5,1] => 2
[5,3,4,1,6,2] => [2,4,3,6,1,5] => 3
[5,3,4,2,1,6] => [2,4,3,5,6,1] => 2
[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] => 2
[5,3,4,6,2,1] => [2,4,3,1,5,6] => 2
[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] => 3
[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] => 3
[5,3,6,4,2,1] => [2,4,1,3,5,6] => 3
[5,4,1,2,3,6] => [2,3,6,5,4,1] => 1
[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] => 1
[5,4,1,3,6,2] => [2,3,6,4,1,5] => 2
[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] => 1
[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] => 2
[5,4,2,3,6,1] => [2,3,5,4,1,6] => 2
[5,4,2,6,1,3] => [2,3,5,1,6,4] => 2
[5,4,2,6,3,1] => [2,3,5,1,4,6] => 3
[5,4,3,1,2,6] => [2,3,4,6,5,1] => 1
[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] => 0
[5,4,3,2,6,1] => [2,3,4,5,1,6] => 1
[5,4,3,6,1,2] => [2,3,4,1,6,5] => 1
[5,4,3,6,2,1] => [2,3,4,1,5,6] => 1
[5,4,6,1,2,3] => [2,3,1,6,5,4] => 1
[5,4,6,1,3,2] => [2,3,1,6,4,5] => 1
[5,4,6,2,1,3] => [2,3,1,5,6,4] => 1
[5,4,6,2,3,1] => [2,3,1,5,4,6] => 2
[5,4,6,3,1,2] => [2,3,1,4,6,5] => 2
[5,4,6,3,2,1] => [2,3,1,4,5,6] => 1
[5,6,1,2,3,4] => [2,1,6,5,4,3] => 1
[5,6,1,2,4,3] => [2,1,6,5,3,4] => 1
[5,6,1,3,2,4] => [2,1,6,4,5,3] => 1
[5,6,1,3,4,2] => [2,1,6,4,3,5] => 2
[5,6,1,4,2,3] => [2,1,6,3,5,4] => 2
[5,6,1,4,3,2] => [2,1,6,3,4,5] => 1
[5,6,2,1,3,4] => [2,1,5,6,4,3] => 1
[5,6,2,1,4,3] => [2,1,5,6,3,4] => 1
[5,6,2,3,1,4] => [2,1,5,4,6,3] => 2
[5,6,2,3,4,1] => [2,1,5,4,3,6] => 2
[5,6,2,4,1,3] => [2,1,5,3,6,4] => 2
[5,6,2,4,3,1] => [2,1,5,3,4,6] => 2
[5,6,3,1,2,4] => [2,1,4,6,5,3] => 2
[5,6,3,1,4,2] => [2,1,4,6,3,5] => 3
[5,6,3,2,1,4] => [2,1,4,5,6,3] => 1
[5,6,3,2,4,1] => [2,1,4,5,3,6] => 2
[5,6,3,4,1,2] => [2,1,4,3,6,5] => 2
[5,6,3,4,2,1] => [2,1,4,3,5,6] => 2
[5,6,4,1,2,3] => [2,1,3,6,5,4] => 2
[5,6,4,1,3,2] => [2,1,3,6,4,5] => 2
[5,6,4,2,1,3] => [2,1,3,5,6,4] => 2
[5,6,4,2,3,1] => [2,1,3,5,4,6] => 3
[5,6,4,3,1,2] => [2,1,3,4,6,5] => 2
[5,6,4,3,2,1] => [2,1,3,4,5,6] => 1
[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] => 1
[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] => 2
[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] => 3
[6,1,4,3,2,5] => [1,6,3,4,5,2] => 1
[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] => 2
[6,1,4,5,3,2] => [1,6,3,2,4,5] => 2
[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] => 2
[6,1,5,4,3,2] => [1,6,2,3,4,5] => 1
[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] => 1
[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] => 2
[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] => 2
[6,2,4,1,5,3] => [1,5,3,6,2,4] => 3
[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] => 2
[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] => 2
[6,2,5,1,4,3] => [1,5,2,6,3,4] => 2
[6,2,5,3,1,4] => [1,5,2,4,6,3] => 3
[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] => 2
[6,2,5,4,3,1] => [1,5,2,3,4,6] => 2
[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] => 3
[6,3,1,4,5,2] => [1,4,6,3,2,5] => 3
[6,3,1,5,2,4] => [1,4,6,2,5,3] => 3
[6,3,1,5,4,2] => [1,4,6,2,3,5] => 3
[6,3,2,1,4,5] => [1,4,5,6,3,2] => 1
[6,3,2,1,5,4] => [1,4,5,6,2,3] => 1
[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] => 2
[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] => 2
[6,3,4,1,5,2] => [1,4,3,6,2,5] => 3
[6,3,4,2,1,5] => [1,4,3,5,6,2] => 2
[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] => 2
[6,3,4,5,2,1] => [1,4,3,2,5,6] => 2
[6,3,5,1,2,4] => [1,4,2,6,5,3] => 2
[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] => 2
[6,3,5,2,4,1] => [1,4,2,5,3,6] => 3
[6,3,5,4,1,2] => [1,4,2,3,6,5] => 2
[6,3,5,4,2,1] => [1,4,2,3,5,6] => 2
[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] => 3
[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] => 3
[6,4,1,5,3,2] => [1,3,6,2,4,5] => 3
[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] => 3
[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] => 4
[6,4,3,1,2,5] => [1,3,4,6,5,2] => 2
[6,4,3,1,5,2] => [1,3,4,6,2,5] => 3
[6,4,3,2,1,5] => [1,3,4,5,6,2] => 1
[6,4,3,2,5,1] => [1,3,4,5,2,6] => 2
[6,4,3,5,1,2] => [1,3,4,2,6,5] => 2
[6,4,3,5,2,1] => [1,3,4,2,5,6] => 2
[6,4,5,1,2,3] => [1,3,2,6,5,4] => 2
[6,4,5,1,3,2] => [1,3,2,6,4,5] => 2
[6,4,5,2,1,3] => [1,3,2,5,6,4] => 2
[6,4,5,2,3,1] => [1,3,2,5,4,6] => 3
[6,4,5,3,1,2] => [1,3,2,4,6,5] => 3
[6,4,5,3,2,1] => [1,3,2,4,5,6] => 2
[6,5,1,2,3,4] => [1,2,6,5,4,3] => 1
[6,5,1,2,4,3] => [1,2,6,5,3,4] => 1
[6,5,1,3,2,4] => [1,2,6,4,5,3] => 1
[6,5,1,3,4,2] => [1,2,6,4,3,5] => 2
[6,5,1,4,2,3] => [1,2,6,3,5,4] => 2
[6,5,1,4,3,2] => [1,2,6,3,4,5] => 1
[6,5,2,1,3,4] => [1,2,5,6,4,3] => 1
[6,5,2,1,4,3] => [1,2,5,6,3,4] => 1
[6,5,2,3,1,4] => [1,2,5,4,6,3] => 2
[6,5,2,3,4,1] => [1,2,5,4,3,6] => 2
[6,5,2,4,1,3] => [1,2,5,3,6,4] => 2
[6,5,2,4,3,1] => [1,2,5,3,4,6] => 2
[6,5,3,1,2,4] => [1,2,4,6,5,3] => 2
[6,5,3,1,4,2] => [1,2,4,6,3,5] => 3
[6,5,3,2,1,4] => [1,2,4,5,6,3] => 1
[6,5,3,2,4,1] => [1,2,4,5,3,6] => 2
[6,5,3,4,1,2] => [1,2,4,3,6,5] => 2
[6,5,3,4,2,1] => [1,2,4,3,5,6] => 2
[6,5,4,1,2,3] => [1,2,3,6,5,4] => 1
[6,5,4,1,3,2] => [1,2,3,6,4,5] => 1
[6,5,4,2,1,3] => [1,2,3,5,6,4] => 1
[6,5,4,2,3,1] => [1,2,3,5,4,6] => 2
[6,5,4,3,1,2] => [1,2,3,4,6,5] => 1
[6,5,4,3,2,1] => [1,2,3,4,5,6] => 0
[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] => 3
[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] => 4
[7,4,2,5,3,1,6] => [1,4,6,3,5,7,2] => 4
[7,4,2,5,3,6,1] => [1,4,6,3,5,2,7] => 4
[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] => 4
[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] => 4
[7,4,2,6,3,1,5] => [1,4,6,2,5,7,3] => 4
[7,4,2,6,3,5,1] => [1,4,6,2,5,3,7] => 4
[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] => 4
[7,4,3,1,2,5,6] => [1,4,5,7,6,3,2] => 2
[7,4,3,1,2,6,5] => [1,4,5,7,6,2,3] => 2
[7,4,3,1,5,2,6] => [1,4,5,7,3,6,2] => 3
[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] => 1
[7,4,3,2,1,6,5] => [1,4,5,6,7,2,3] => 1
[7,4,3,2,5,1,6] => [1,4,5,6,3,7,2] => 2
[7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => 2
[7,4,3,2,6,1,5] => [1,4,5,6,2,7,3] => 2
[7,4,3,2,6,5,1] => [1,4,5,6,2,3,7] => 2
[7,4,3,5,1,2,6] => [1,4,5,3,7,6,2] => 2
[7,4,3,5,1,6,2] => [1,4,5,3,7,2,6] => 3
[7,4,3,5,2,1,6] => [1,4,5,3,6,7,2] => 2
[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] => 2
[7,4,3,5,6,2,1] => [1,4,5,3,2,6,7] => 2
[7,4,3,6,1,2,5] => [1,4,5,2,7,6,3] => 2
[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] => 2
[7,4,3,6,2,5,1] => [1,4,5,2,6,3,7] => 3
[7,4,3,6,5,1,2] => [1,4,5,2,3,7,6] => 2
[7,4,3,6,5,2,1] => [1,4,5,2,3,6,7] => 2
[7,4,5,1,2,3,6] => [1,4,3,7,6,5,2] => 2
[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] => 2
[7,4,5,1,3,6,2] => [1,4,3,7,5,2,6] => 3
[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] => 2
[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] => 3
[7,4,5,2,3,6,1] => [1,4,3,6,5,2,7] => 3
[7,4,5,2,6,1,3] => [1,4,3,6,2,7,5] => 3
[7,4,5,2,6,3,1] => [1,4,3,6,2,5,7] => 4
[7,4,5,3,1,2,6] => [1,4,3,5,7,6,2] => 3
[7,4,5,3,1,6,2] => [1,4,3,5,7,2,6] => 4
[7,4,5,3,2,1,6] => [1,4,3,5,6,7,2] => 2
[7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => 3
[7,4,5,3,6,1,2] => [1,4,3,5,2,7,6] => 3
[7,4,5,3,6,2,1] => [1,4,3,5,2,6,7] => 3
[7,4,5,6,1,2,3] => [1,4,3,2,7,6,5] => 2
[7,4,5,6,1,3,2] => [1,4,3,2,7,5,6] => 2
[7,4,5,6,2,1,3] => [1,4,3,2,6,7,5] => 2
[7,4,5,6,2,3,1] => [1,4,3,2,6,5,7] => 3
[7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => 3
[7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => 2
[7,4,6,1,2,3,5] => [1,4,2,7,6,5,3] => 2
[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] => 2
[7,4,6,1,3,5,2] => [1,4,2,7,5,3,6] => 3
[7,4,6,1,5,2,3] => [1,4,2,7,3,6,5] => 3
[7,4,6,1,5,3,2] => [1,4,2,7,3,5,6] => 3
[7,4,6,2,1,3,5] => [1,4,2,6,7,5,3] => 2
[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] => 3
[7,4,6,2,3,5,1] => [1,4,2,6,5,3,7] => 3
[7,4,6,2,5,1,3] => [1,4,2,6,3,7,5] => 3
[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] => 3
[7,4,6,3,1,5,2] => [1,4,2,5,7,3,6] => 4
[7,4,6,3,2,1,5] => [1,4,2,5,6,7,3] => 2
[7,4,6,3,2,5,1] => [1,4,2,5,6,3,7] => 3
[7,4,6,3,5,1,2] => [1,4,2,5,3,7,6] => 3
[7,4,6,3,5,2,1] => [1,4,2,5,3,6,7] => 3
[7,4,6,5,1,2,3] => [1,4,2,3,7,6,5] => 2
[7,4,6,5,1,3,2] => [1,4,2,3,7,5,6] => 2
[7,4,6,5,2,1,3] => [1,4,2,3,6,7,5] => 2
[7,4,6,5,2,3,1] => [1,4,2,3,6,5,7] => 3
[7,4,6,5,3,1,2] => [1,4,2,3,5,7,6] => 3
[7,4,6,5,3,2,1] => [1,4,2,3,5,6,7] => 2
[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] => 3
[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] => 3
[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] => 3
[7,5,1,3,6,4,2] => [1,3,7,5,2,4,6] => 4
[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] => 4
[7,5,1,4,3,2,6] => [1,3,7,4,5,6,2] => 2
[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] => 3
[7,5,1,4,6,3,2] => [1,3,7,4,2,5,6] => 3
[7,5,1,6,2,3,4] => [1,3,7,2,6,5,4] => 3
[7,5,1,6,2,4,3] => [1,3,7,2,6,4,5] => 3
[7,5,1,6,3,2,4] => [1,3,7,2,5,6,4] => 3
[7,5,1,6,3,4,2] => [1,3,7,2,5,4,6] => 4
[7,5,1,6,4,2,3] => [1,3,7,2,4,6,5] => 4
[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] => 3
[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] => 4
[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] => 3
[7,5,2,3,6,4,1] => [1,3,6,5,2,4,7] => 4
[7,5,2,4,1,3,6] => [1,3,6,4,7,5,2] => 3
[7,5,2,4,1,6,3] => [1,3,6,4,7,2,5] => 4
[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] => 3
[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] => 4
[7,5,2,6,3,4,1] => [1,3,6,2,5,4,7] => 4
[7,5,2,6,4,1,3] => [1,3,6,2,4,7,5] => 4
[7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => 4
[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] => 4
[7,5,3,1,4,2,6] => [1,3,5,7,4,6,2] => 4
[7,5,3,1,4,6,2] => [1,3,5,7,4,2,6] => 4
[7,5,3,1,6,2,4] => [1,3,5,7,2,6,4] => 4
[7,5,3,1,6,4,2] => [1,3,5,7,2,4,6] => 5
[7,5,3,2,1,4,6] => [1,3,5,6,7,4,2] => 2
[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] => 3
[7,5,3,2,6,4,1] => [1,3,5,6,2,4,7] => 4
[7,5,3,4,1,2,6] => [1,3,5,4,7,6,2] => 3
[7,5,3,4,1,6,2] => [1,3,5,4,7,2,6] => 4
[7,5,3,4,2,1,6] => [1,3,5,4,6,7,2] => 3
[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] => 3
[7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => 3
[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] => 4
[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] => 4
[7,5,3,6,4,2,1] => [1,3,5,2,4,6,7] => 4
[7,5,4,1,2,3,6] => [1,3,4,7,6,5,2] => 2
[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] => 2
[7,5,4,1,3,6,2] => [1,3,4,7,5,2,6] => 3
[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] => 2
[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] => 3
[7,5,4,2,3,6,1] => [1,3,4,6,5,2,7] => 3
[7,5,4,2,6,1,3] => [1,3,4,6,2,7,5] => 3
[7,5,4,2,6,3,1] => [1,3,4,6,2,5,7] => 4
[7,5,4,3,1,2,6] => [1,3,4,5,7,6,2] => 2
[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] => 1
[7,5,4,3,2,6,1] => [1,3,4,5,6,2,7] => 2
[7,5,4,3,6,1,2] => [1,3,4,5,2,7,6] => 2
[7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => 2
[7,5,4,6,1,2,3] => [1,3,4,2,7,6,5] => 2
[7,5,4,6,1,3,2] => [1,3,4,2,7,5,6] => 2
[7,5,4,6,2,1,3] => [1,3,4,2,6,7,5] => 2
[7,5,4,6,2,3,1] => [1,3,4,2,6,5,7] => 3
[7,5,4,6,3,1,2] => [1,3,4,2,5,7,6] => 3
[7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => 2
[7,5,6,1,2,3,4] => [1,3,2,7,6,5,4] => 2
[7,5,6,1,2,4,3] => [1,3,2,7,6,4,5] => 2
[7,5,6,1,3,2,4] => [1,3,2,7,5,6,4] => 2
[7,5,6,1,3,4,2] => [1,3,2,7,5,4,6] => 3
[7,5,6,1,4,2,3] => [1,3,2,7,4,6,5] => 3
[7,5,6,1,4,3,2] => [1,3,2,7,4,5,6] => 2
[7,5,6,2,1,3,4] => [1,3,2,6,7,5,4] => 2
[7,5,6,2,1,4,3] => [1,3,2,6,7,4,5] => 2
[7,5,6,2,3,1,4] => [1,3,2,6,5,7,4] => 3
[7,5,6,2,3,4,1] => [1,3,2,6,5,4,7] => 3
[7,5,6,2,4,1,3] => [1,3,2,6,4,7,5] => 3
[7,5,6,2,4,3,1] => [1,3,2,6,4,5,7] => 3
[7,5,6,3,1,2,4] => [1,3,2,5,7,6,4] => 3
[7,5,6,3,1,4,2] => [1,3,2,5,7,4,6] => 4
[7,5,6,3,2,1,4] => [1,3,2,5,6,7,4] => 2
[7,5,6,3,2,4,1] => [1,3,2,5,6,4,7] => 3
[7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => 3
[7,5,6,3,4,2,1] => [1,3,2,5,4,6,7] => 3
[7,5,6,4,1,2,3] => [1,3,2,4,7,6,5] => 3
[7,5,6,4,1,3,2] => [1,3,2,4,7,5,6] => 3
[7,5,6,4,2,1,3] => [1,3,2,4,6,7,5] => 3
[7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => 4
[7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => 3
[7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => 2
[7,6,1,2,3,4,5] => [1,2,7,6,5,4,3] => 1
[7,6,1,2,3,5,4] => [1,2,7,6,5,3,4] => 1
[7,6,1,2,4,3,5] => [1,2,7,6,4,5,3] => 1
[7,6,1,2,4,5,3] => [1,2,7,6,4,3,5] => 2
[7,6,1,2,5,3,4] => [1,2,7,6,3,5,4] => 2
[7,6,1,2,5,4,3] => [1,2,7,6,3,4,5] => 1
[7,6,1,3,2,4,5] => [1,2,7,5,6,4,3] => 1
[7,6,1,3,2,5,4] => [1,2,7,5,6,3,4] => 1
[7,6,1,3,4,2,5] => [1,2,7,5,4,6,3] => 2
[7,6,1,3,4,5,2] => [1,2,7,5,4,3,6] => 2
[7,6,1,3,5,2,4] => [1,2,7,5,3,6,4] => 2
[7,6,1,3,5,4,2] => [1,2,7,5,3,4,6] => 2
[7,6,1,4,2,3,5] => [1,2,7,4,6,5,3] => 2
[7,6,1,4,2,5,3] => [1,2,7,4,6,3,5] => 3
[7,6,1,4,3,2,5] => [1,2,7,4,5,6,3] => 1
[7,6,1,4,3,5,2] => [1,2,7,4,5,3,6] => 2
[7,6,1,4,5,2,3] => [1,2,7,4,3,6,5] => 2
[7,6,1,4,5,3,2] => [1,2,7,4,3,5,6] => 2
[7,6,1,5,2,3,4] => [1,2,7,3,6,5,4] => 2
[7,6,1,5,2,4,3] => [1,2,7,3,6,4,5] => 2
[7,6,1,5,3,2,4] => [1,2,7,3,5,6,4] => 2
[7,6,1,5,3,4,2] => [1,2,7,3,5,4,6] => 3
[7,6,1,5,4,2,3] => [1,2,7,3,4,6,5] => 2
[7,6,1,5,4,3,2] => [1,2,7,3,4,5,6] => 1
[7,6,2,1,3,4,5] => [1,2,6,7,5,4,3] => 1
[7,6,2,1,3,5,4] => [1,2,6,7,5,3,4] => 1
[7,6,2,1,4,3,5] => [1,2,6,7,4,5,3] => 1
[7,6,2,1,4,5,3] => [1,2,6,7,4,3,5] => 2
[7,6,2,1,5,3,4] => [1,2,6,7,3,5,4] => 2
[7,6,2,1,5,4,3] => [1,2,6,7,3,4,5] => 1
[7,6,2,3,1,4,5] => [1,2,6,5,7,4,3] => 2
[7,6,2,3,1,5,4] => [1,2,6,5,7,3,4] => 2
[7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => 2
[7,6,2,3,4,5,1] => [1,2,6,5,4,3,7] => 2
[7,6,2,3,5,1,4] => [1,2,6,5,3,7,4] => 2
[7,6,2,3,5,4,1] => [1,2,6,5,3,4,7] => 2
[7,6,2,4,1,3,5] => [1,2,6,4,7,5,3] => 2
[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] => 2
[7,6,2,4,3,5,1] => [1,2,6,4,5,3,7] => 2
[7,6,2,4,5,1,3] => [1,2,6,4,3,7,5] => 2
[7,6,2,4,5,3,1] => [1,2,6,4,3,5,7] => 3
[7,6,2,5,1,3,4] => [1,2,6,3,7,5,4] => 2
[7,6,2,5,1,4,3] => [1,2,6,3,7,4,5] => 2
[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] => 3
[7,6,2,5,4,1,3] => [1,2,6,3,4,7,5] => 2
[7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => 2
[7,6,3,1,2,4,5] => [1,2,5,7,6,4,3] => 2
[7,6,3,1,2,5,4] => [1,2,5,7,6,3,4] => 2
[7,6,3,1,4,2,5] => [1,2,5,7,4,6,3] => 3
[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] => 1
[7,6,3,2,1,5,4] => [1,2,5,6,7,3,4] => 1
[7,6,3,2,4,1,5] => [1,2,5,6,4,7,3] => 2
[7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => 2
[7,6,3,2,5,1,4] => [1,2,5,6,3,7,4] => 2
[7,6,3,2,5,4,1] => [1,2,5,6,3,4,7] => 2
[7,6,3,4,1,2,5] => [1,2,5,4,7,6,3] => 2
[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] => 2
[7,6,3,4,2,5,1] => [1,2,5,4,6,3,7] => 3
[7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => 2
[7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => 2
[7,6,3,5,1,2,4] => [1,2,5,3,7,6,4] => 2
[7,6,3,5,1,4,2] => [1,2,5,3,7,4,6] => 3
[7,6,3,5,2,1,4] => [1,2,5,3,6,7,4] => 2
[7,6,3,5,2,4,1] => [1,2,5,3,6,4,7] => 3
[7,6,3,5,4,1,2] => [1,2,5,3,4,7,6] => 2
[7,6,3,5,4,2,1] => [1,2,5,3,4,6,7] => 2
[7,6,4,1,2,3,5] => [1,2,4,7,6,5,3] => 2
[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] => 2
[7,6,4,1,3,5,2] => [1,2,4,7,5,3,6] => 3
[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] => 2
[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] => 3
[7,6,4,2,3,5,1] => [1,2,4,6,5,3,7] => 3
[7,6,4,2,5,1,3] => [1,2,4,6,3,7,5] => 3
[7,6,4,2,5,3,1] => [1,2,4,6,3,5,7] => 4
[7,6,4,3,1,2,5] => [1,2,4,5,7,6,3] => 2
[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] => 1
[7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => 2
[7,6,4,3,5,1,2] => [1,2,4,5,3,7,6] => 2
[7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => 2
[7,6,4,5,1,2,3] => [1,2,4,3,7,6,5] => 2
[7,6,4,5,1,3,2] => [1,2,4,3,7,5,6] => 2
[7,6,4,5,2,1,3] => [1,2,4,3,6,7,5] => 2
[7,6,4,5,2,3,1] => [1,2,4,3,6,5,7] => 3
[7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => 3
[7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => 2
[7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => 1
[7,6,5,1,2,4,3] => [1,2,3,7,6,4,5] => 1
[7,6,5,1,3,2,4] => [1,2,3,7,5,6,4] => 1
[7,6,5,1,3,4,2] => [1,2,3,7,5,4,6] => 2
[7,6,5,1,4,2,3] => [1,2,3,7,4,6,5] => 2
[7,6,5,1,4,3,2] => [1,2,3,7,4,5,6] => 1
[7,6,5,2,1,3,4] => [1,2,3,6,7,5,4] => 1
[7,6,5,2,1,4,3] => [1,2,3,6,7,4,5] => 1
[7,6,5,2,3,1,4] => [1,2,3,6,5,7,4] => 2
[7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => 2
[7,6,5,2,4,1,3] => [1,2,3,6,4,7,5] => 2
[7,6,5,2,4,3,1] => [1,2,3,6,4,5,7] => 2
[7,6,5,3,1,2,4] => [1,2,3,5,7,6,4] => 2
[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] => 1
[7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => 2
[7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => 2
[7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => 2
[7,6,5,4,1,2,3] => [1,2,3,4,7,6,5] => 1
[7,6,5,4,1,3,2] => [1,2,3,4,7,5,6] => 1
[7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => 1
[7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => 2
[7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => 1
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,2 8,14,2 16,66,36,2 32,262,342,82,2
$F_{2} = 2$
$F_{3} = 4 + 2\ q$
$F_{4} = 8 + 14\ q + 2\ q^{2}$
$F_{5} = 16 + 66\ q + 36\ q^{2} + 2\ q^{3}$
$F_{6} = 32 + 262\ q + 342\ q^{2} + 82\ q^{3} + 2\ q^{4}$
Description
The number of big ascents of a permutation.
For a permutation $\pi$, this is the number of indices $i$ such that $\pi(i+1)−\pi(i) > 1$.
For the number of small ascents, see St000441The number of successions of a permutation..
For a permutation $\pi$, this is the number of indices $i$ such that $\pi(i+1)−\pi(i) > 1$.
For the number of small ascents, see St000441The number of successions of a permutation..
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 $\tau(i) = n+1-\sigma(i)$
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!