Identifier
-
Mp00064:
Permutations
—reverse⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
St001727: Permutations ⟶ ℤ
Values
[1] => [1] => [1] => 0
[1,2] => [2,1] => [2,1] => 0
[2,1] => [1,2] => [1,2] => 0
[1,2,3] => [3,2,1] => [2,3,1] => 0
[1,3,2] => [2,3,1] => [3,2,1] => 1
[2,1,3] => [3,1,2] => [3,1,2] => 1
[2,3,1] => [1,3,2] => [1,3,2] => 0
[3,1,2] => [2,1,3] => [2,1,3] => 0
[3,2,1] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [4,3,2,1] => [2,3,4,1] => 0
[1,2,4,3] => [3,4,2,1] => [2,4,3,1] => 1
[1,3,2,4] => [4,2,3,1] => [3,4,2,1] => 1
[1,3,4,2] => [2,4,3,1] => [3,2,4,1] => 1
[1,4,2,3] => [3,2,4,1] => [4,3,2,1] => 2
[1,4,3,2] => [2,3,4,1] => [4,2,3,1] => 2
[2,1,3,4] => [4,3,1,2] => [3,1,4,2] => 1
[2,1,4,3] => [3,4,1,2] => [4,1,3,2] => 2
[2,3,1,4] => [4,1,3,2] => [4,3,1,2] => 2
[2,3,4,1] => [1,4,3,2] => [1,3,4,2] => 0
[2,4,1,3] => [3,1,4,2] => [3,4,1,2] => 1
[2,4,3,1] => [1,3,4,2] => [1,4,3,2] => 1
[3,1,2,4] => [4,2,1,3] => [2,4,1,3] => 1
[3,1,4,2] => [2,4,1,3] => [4,2,1,3] => 2
[3,2,1,4] => [4,1,2,3] => [4,1,2,3] => 2
[3,2,4,1] => [1,4,2,3] => [1,4,2,3] => 1
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 0
[3,4,2,1] => [1,2,4,3] => [1,2,4,3] => 0
[4,1,2,3] => [3,2,1,4] => [2,3,1,4] => 0
[4,1,3,2] => [2,3,1,4] => [3,2,1,4] => 1
[4,2,1,3] => [3,1,2,4] => [3,1,2,4] => 1
[4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 0
[4,3,1,2] => [2,1,3,4] => [2,1,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [5,4,3,2,1] => [2,3,4,5,1] => 0
[1,2,3,5,4] => [4,5,3,2,1] => [2,3,5,4,1] => 1
[1,2,4,3,5] => [5,3,4,2,1] => [2,4,5,3,1] => 1
[1,2,4,5,3] => [3,5,4,2,1] => [2,4,3,5,1] => 1
[1,2,5,3,4] => [4,3,5,2,1] => [2,5,4,3,1] => 2
[1,2,5,4,3] => [3,4,5,2,1] => [2,5,3,4,1] => 2
[1,3,2,4,5] => [5,4,2,3,1] => [3,4,2,5,1] => 1
[1,3,2,5,4] => [4,5,2,3,1] => [3,5,2,4,1] => 2
[1,3,4,2,5] => [5,2,4,3,1] => [3,4,5,1,2] => 1
[1,3,4,5,2] => [2,5,4,3,1] => [3,2,4,5,1] => 1
[1,3,5,2,4] => [4,2,5,3,1] => [3,5,4,1,2] => 2
[1,3,5,4,2] => [2,4,5,3,1] => [3,2,5,4,1] => 2
[1,4,2,3,5] => [5,3,2,4,1] => [4,3,5,2,1] => 2
[1,4,2,5,3] => [3,5,2,4,1] => [4,5,3,2,1] => 3
[1,4,3,2,5] => [5,2,3,4,1] => [4,5,2,3,1] => 3
[1,4,3,5,2] => [2,5,3,4,1] => [4,2,5,3,1] => 2
[1,4,5,2,3] => [3,2,5,4,1] => [4,3,2,5,1] => 2
[1,4,5,3,2] => [2,3,5,4,1] => [4,2,3,5,1] => 2
[1,5,2,3,4] => [4,3,2,5,1] => [5,3,4,2,1] => 3
[1,5,2,4,3] => [3,4,2,5,1] => [5,4,3,2,1] => 4
[1,5,3,2,4] => [4,2,3,5,1] => [5,4,2,3,1] => 4
[1,5,3,4,2] => [2,4,3,5,1] => [5,2,4,3,1] => 3
[1,5,4,2,3] => [3,2,4,5,1] => [5,3,2,4,1] => 3
[1,5,4,3,2] => [2,3,4,5,1] => [5,2,3,4,1] => 3
[2,1,3,4,5] => [5,4,3,1,2] => [3,1,4,5,2] => 1
[2,1,3,5,4] => [4,5,3,1,2] => [3,1,5,4,2] => 2
[2,1,4,3,5] => [5,3,4,1,2] => [4,1,5,3,2] => 2
[2,1,4,5,3] => [3,5,4,1,2] => [4,1,3,5,2] => 2
[2,1,5,3,4] => [4,3,5,1,2] => [5,1,4,3,2] => 3
[2,1,5,4,3] => [3,4,5,1,2] => [5,1,3,4,2] => 3
[2,3,1,4,5] => [5,4,1,3,2] => [4,3,1,5,2] => 2
[2,3,1,5,4] => [4,5,1,3,2] => [5,3,1,4,2] => 3
[2,3,4,1,5] => [5,1,4,3,2] => [5,3,4,1,2] => 3
[2,3,4,5,1] => [1,5,4,3,2] => [1,3,4,5,2] => 0
[2,3,5,1,4] => [4,1,5,3,2] => [4,3,5,1,2] => 2
[2,3,5,4,1] => [1,4,5,3,2] => [1,3,5,4,2] => 1
[2,4,1,3,5] => [5,3,1,4,2] => [3,5,4,2,1] => 2
[2,4,1,5,3] => [3,5,1,4,2] => [5,4,3,1,2] => 4
[2,4,3,1,5] => [5,1,3,4,2] => [5,4,1,3,2] => 4
[2,4,3,5,1] => [1,5,3,4,2] => [1,4,5,3,2] => 1
[2,4,5,1,3] => [3,1,5,4,2] => [3,4,1,5,2] => 1
[2,4,5,3,1] => [1,3,5,4,2] => [1,4,3,5,2] => 1
[2,5,1,3,4] => [4,3,1,5,2] => [3,4,5,2,1] => 1
[2,5,1,4,3] => [3,4,1,5,2] => [4,5,3,1,2] => 3
[2,5,3,1,4] => [4,1,3,5,2] => [4,5,1,3,2] => 3
[2,5,3,4,1] => [1,4,3,5,2] => [1,5,4,3,2] => 2
[2,5,4,1,3] => [3,1,4,5,2] => [3,5,1,4,2] => 2
[2,5,4,3,1] => [1,3,4,5,2] => [1,5,3,4,2] => 2
[3,1,2,4,5] => [5,4,2,1,3] => [2,4,1,5,3] => 1
[3,1,2,5,4] => [4,5,2,1,3] => [2,5,1,4,3] => 2
[3,1,4,2,5] => [5,2,4,1,3] => [4,5,1,2,3] => 3
[3,1,4,5,2] => [2,5,4,1,3] => [4,2,1,5,3] => 2
[3,1,5,2,4] => [4,2,5,1,3] => [5,4,1,2,3] => 4
[3,1,5,4,2] => [2,4,5,1,3] => [5,2,1,4,3] => 3
[3,2,1,4,5] => [5,4,1,2,3] => [4,1,2,5,3] => 2
[3,2,1,5,4] => [4,5,1,2,3] => [5,1,2,4,3] => 3
[3,2,4,1,5] => [5,1,4,2,3] => [5,4,2,1,3] => 4
[3,2,4,5,1] => [1,5,4,2,3] => [1,4,2,5,3] => 1
[3,2,5,1,4] => [4,1,5,2,3] => [4,5,2,1,3] => 3
[3,2,5,4,1] => [1,4,5,2,3] => [1,5,2,4,3] => 2
[3,4,1,2,5] => [5,2,1,4,3] => [2,5,4,1,3] => 2
[3,4,1,5,2] => [2,5,1,4,3] => [5,2,4,1,3] => 3
[3,4,2,1,5] => [5,1,2,4,3] => [5,1,4,2,3] => 3
[3,4,2,5,1] => [1,5,2,4,3] => [1,5,4,2,3] => 2
[3,4,5,1,2] => [2,1,5,4,3] => [2,1,4,5,3] => 0
[3,4,5,2,1] => [1,2,5,4,3] => [1,2,4,5,3] => 0
[3,5,1,2,4] => [4,2,1,5,3] => [2,4,5,1,3] => 1
[3,5,1,4,2] => [2,4,1,5,3] => [4,2,5,1,3] => 2
>>> Load all 1200 entries. <<<[3,5,2,1,4] => [4,1,2,5,3] => [4,1,5,2,3] => 2
[3,5,2,4,1] => [1,4,2,5,3] => [1,4,5,2,3] => 1
[3,5,4,1,2] => [2,1,4,5,3] => [2,1,5,4,3] => 1
[3,5,4,2,1] => [1,2,4,5,3] => [1,2,5,4,3] => 1
[4,1,2,3,5] => [5,3,2,1,4] => [2,3,5,1,4] => 1
[4,1,2,5,3] => [3,5,2,1,4] => [2,5,3,1,4] => 2
[4,1,3,2,5] => [5,2,3,1,4] => [3,5,2,1,4] => 2
[4,1,3,5,2] => [2,5,3,1,4] => [3,2,5,1,4] => 2
[4,1,5,2,3] => [3,2,5,1,4] => [5,3,2,1,4] => 3
[4,1,5,3,2] => [2,3,5,1,4] => [5,2,3,1,4] => 3
[4,2,1,3,5] => [5,3,1,2,4] => [3,1,5,2,4] => 2
[4,2,1,5,3] => [3,5,1,2,4] => [5,1,3,2,4] => 3
[4,2,3,1,5] => [5,1,3,2,4] => [5,3,1,2,4] => 3
[4,2,3,5,1] => [1,5,3,2,4] => [1,3,5,2,4] => 1
[4,2,5,1,3] => [3,1,5,2,4] => [3,5,1,2,4] => 2
[4,2,5,3,1] => [1,3,5,2,4] => [1,5,3,2,4] => 2
[4,3,1,2,5] => [5,2,1,3,4] => [2,5,1,3,4] => 2
[4,3,1,5,2] => [2,5,1,3,4] => [5,2,1,3,4] => 3
[4,3,2,1,5] => [5,1,2,3,4] => [5,1,2,3,4] => 3
[4,3,2,5,1] => [1,5,2,3,4] => [1,5,2,3,4] => 2
[4,3,5,1,2] => [2,1,5,3,4] => [2,1,5,3,4] => 1
[4,3,5,2,1] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[4,5,1,2,3] => [3,2,1,5,4] => [2,3,1,5,4] => 0
[4,5,1,3,2] => [2,3,1,5,4] => [3,2,1,5,4] => 1
[4,5,2,1,3] => [3,1,2,5,4] => [3,1,2,5,4] => 1
[4,5,2,3,1] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[4,5,3,1,2] => [2,1,3,5,4] => [2,1,3,5,4] => 0
[4,5,3,2,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[5,1,2,3,4] => [4,3,2,1,5] => [2,3,4,1,5] => 0
[5,1,2,4,3] => [3,4,2,1,5] => [2,4,3,1,5] => 1
[5,1,3,2,4] => [4,2,3,1,5] => [3,4,2,1,5] => 1
[5,1,3,4,2] => [2,4,3,1,5] => [3,2,4,1,5] => 1
[5,1,4,2,3] => [3,2,4,1,5] => [4,3,2,1,5] => 2
[5,1,4,3,2] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[5,2,1,3,4] => [4,3,1,2,5] => [3,1,4,2,5] => 1
[5,2,1,4,3] => [3,4,1,2,5] => [4,1,3,2,5] => 2
[5,2,3,1,4] => [4,1,3,2,5] => [4,3,1,2,5] => 2
[5,2,3,4,1] => [1,4,3,2,5] => [1,3,4,2,5] => 0
[5,2,4,1,3] => [3,1,4,2,5] => [3,4,1,2,5] => 1
[5,2,4,3,1] => [1,3,4,2,5] => [1,4,3,2,5] => 1
[5,3,1,2,4] => [4,2,1,3,5] => [2,4,1,3,5] => 1
[5,3,1,4,2] => [2,4,1,3,5] => [4,2,1,3,5] => 2
[5,3,2,1,4] => [4,1,2,3,5] => [4,1,2,3,5] => 2
[5,3,2,4,1] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[5,3,4,1,2] => [2,1,4,3,5] => [2,1,4,3,5] => 0
[5,3,4,2,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[5,4,1,2,3] => [3,2,1,4,5] => [2,3,1,4,5] => 0
[5,4,1,3,2] => [2,3,1,4,5] => [3,2,1,4,5] => 1
[5,4,2,1,3] => [3,1,2,4,5] => [3,1,2,4,5] => 1
[5,4,2,3,1] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[5,4,3,1,2] => [2,1,3,4,5] => [2,1,3,4,5] => 0
[5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => 0
[1,2,3,4,6,5] => [5,6,4,3,2,1] => [2,3,4,6,5,1] => 1
[1,2,3,5,4,6] => [6,4,5,3,2,1] => [2,3,5,6,4,1] => 1
[1,2,3,5,6,4] => [4,6,5,3,2,1] => [2,3,5,4,6,1] => 1
[1,2,3,6,4,5] => [5,4,6,3,2,1] => [2,3,6,5,4,1] => 2
[1,2,3,6,5,4] => [4,5,6,3,2,1] => [2,3,6,4,5,1] => 2
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [2,4,5,3,6,1] => 1
[1,2,4,3,6,5] => [5,6,3,4,2,1] => [2,4,6,3,5,1] => 2
[1,2,4,5,3,6] => [6,3,5,4,2,1] => [2,4,5,6,1,3] => 1
[1,2,4,5,6,3] => [3,6,5,4,2,1] => [2,4,3,5,6,1] => 1
[1,2,4,6,3,5] => [5,3,6,4,2,1] => [2,4,6,5,1,3] => 2
[1,2,4,6,5,3] => [3,5,6,4,2,1] => [2,4,3,6,5,1] => 2
[1,2,5,3,4,6] => [6,4,3,5,2,1] => [2,5,4,6,3,1] => 2
[1,2,5,3,6,4] => [4,6,3,5,2,1] => [2,5,6,4,3,1] => 3
[1,2,5,4,3,6] => [6,3,4,5,2,1] => [2,5,6,3,4,1] => 3
[1,2,5,4,6,3] => [3,6,4,5,2,1] => [2,5,3,6,4,1] => 2
[1,2,5,6,3,4] => [4,3,6,5,2,1] => [2,5,4,3,6,1] => 2
[1,2,5,6,4,3] => [3,4,6,5,2,1] => [2,5,3,4,6,1] => 2
[1,2,6,3,4,5] => [5,4,3,6,2,1] => [2,6,4,5,3,1] => 3
[1,2,6,3,5,4] => [4,5,3,6,2,1] => [2,6,5,4,3,1] => 4
[1,2,6,4,3,5] => [5,3,4,6,2,1] => [2,6,5,3,4,1] => 4
[1,2,6,4,5,3] => [3,5,4,6,2,1] => [2,6,3,5,4,1] => 3
[1,2,6,5,3,4] => [4,3,5,6,2,1] => [2,6,4,3,5,1] => 3
[1,2,6,5,4,3] => [3,4,5,6,2,1] => [2,6,3,4,5,1] => 3
[1,3,2,4,5,6] => [6,5,4,2,3,1] => [3,4,2,5,6,1] => 1
[1,3,2,4,6,5] => [5,6,4,2,3,1] => [3,4,2,6,5,1] => 2
[1,3,2,5,4,6] => [6,4,5,2,3,1] => [3,5,2,6,4,1] => 2
[1,3,2,5,6,4] => [4,6,5,2,3,1] => [3,5,2,4,6,1] => 2
[1,3,2,6,4,5] => [5,4,6,2,3,1] => [3,6,2,5,4,1] => 3
[1,3,2,6,5,4] => [4,5,6,2,3,1] => [3,6,2,4,5,1] => 3
[1,3,4,2,5,6] => [6,5,2,4,3,1] => [3,4,5,1,6,2] => 1
[1,3,4,2,6,5] => [5,6,2,4,3,1] => [3,4,6,1,5,2] => 2
[1,3,4,5,2,6] => [6,2,5,4,3,1] => [3,4,5,6,2,1] => 1
[1,3,4,5,6,2] => [2,6,5,4,3,1] => [3,2,4,5,6,1] => 1
[1,3,4,6,2,5] => [5,2,6,4,3,1] => [3,4,6,5,2,1] => 2
[1,3,4,6,5,2] => [2,5,6,4,3,1] => [3,2,4,6,5,1] => 2
[1,3,5,2,4,6] => [6,4,2,5,3,1] => [3,5,4,6,1,2] => 2
[1,3,5,2,6,4] => [4,6,2,5,3,1] => [3,5,6,4,1,2] => 3
[1,3,5,4,2,6] => [6,2,4,5,3,1] => [3,5,6,1,4,2] => 3
[1,3,5,4,6,2] => [2,6,4,5,3,1] => [3,2,5,6,4,1] => 2
[1,3,5,6,2,4] => [4,2,6,5,3,1] => [3,5,4,1,6,2] => 2
[1,3,5,6,4,2] => [2,4,6,5,3,1] => [3,2,5,4,6,1] => 2
[1,3,6,2,4,5] => [5,4,2,6,3,1] => [3,6,4,5,1,2] => 3
[1,3,6,2,5,4] => [4,5,2,6,3,1] => [3,6,5,4,1,2] => 4
[1,3,6,4,2,5] => [5,2,4,6,3,1] => [3,6,5,1,4,2] => 4
[1,3,6,4,5,2] => [2,5,4,6,3,1] => [3,2,6,5,4,1] => 3
[1,3,6,5,2,4] => [4,2,5,6,3,1] => [3,6,4,1,5,2] => 3
[1,3,6,5,4,2] => [2,4,5,6,3,1] => [3,2,6,4,5,1] => 3
[1,4,2,3,5,6] => [6,5,3,2,4,1] => [4,3,5,2,6,1] => 2
[1,4,2,3,6,5] => [5,6,3,2,4,1] => [4,3,6,2,5,1] => 3
[1,4,2,5,3,6] => [6,3,5,2,4,1] => [4,5,6,2,3,1] => 3
[1,4,2,5,6,3] => [3,6,5,2,4,1] => [4,5,3,2,6,1] => 3
[1,4,2,6,3,5] => [5,3,6,2,4,1] => [4,6,5,2,3,1] => 4
[1,4,2,6,5,3] => [3,5,6,2,4,1] => [4,6,3,2,5,1] => 4
[1,4,3,2,5,6] => [6,5,2,3,4,1] => [4,5,2,3,6,1] => 3
[1,4,3,2,6,5] => [5,6,2,3,4,1] => [4,6,2,3,5,1] => 4
[1,4,3,5,2,6] => [6,2,5,3,4,1] => [4,6,5,3,2,1] => 4
[1,4,3,5,6,2] => [2,6,5,3,4,1] => [4,2,5,3,6,1] => 2
[1,4,3,6,2,5] => [5,2,6,3,4,1] => [4,5,6,3,2,1] => 3
[1,4,3,6,5,2] => [2,5,6,3,4,1] => [4,2,6,3,5,1] => 3
[1,4,5,2,3,6] => [6,3,2,5,4,1] => [4,3,5,6,1,2] => 2
[1,4,5,2,6,3] => [3,6,2,5,4,1] => [4,5,3,6,1,2] => 3
[1,4,5,3,2,6] => [6,2,3,5,4,1] => [4,5,1,6,3,2] => 3
[1,4,5,3,6,2] => [2,6,3,5,4,1] => [4,2,5,6,1,3] => 2
[1,4,5,6,2,3] => [3,2,6,5,4,1] => [4,3,2,5,6,1] => 2
[1,4,5,6,3,2] => [2,3,6,5,4,1] => [4,2,3,5,6,1] => 2
[1,4,6,2,3,5] => [5,3,2,6,4,1] => [4,3,6,5,1,2] => 3
[1,4,6,2,5,3] => [3,5,2,6,4,1] => [4,6,3,5,1,2] => 4
[1,4,6,3,2,5] => [5,2,3,6,4,1] => [4,6,1,5,3,2] => 4
[1,4,6,3,5,2] => [2,5,3,6,4,1] => [4,2,6,5,1,3] => 3
[1,4,6,5,2,3] => [3,2,5,6,4,1] => [4,3,2,6,5,1] => 3
[1,4,6,5,3,2] => [2,3,5,6,4,1] => [4,2,3,6,5,1] => 3
[1,5,2,3,4,6] => [6,4,3,2,5,1] => [5,3,4,6,2,1] => 3
[1,5,2,3,6,4] => [4,6,3,2,5,1] => [5,3,6,4,2,1] => 4
[1,5,2,4,3,6] => [6,3,4,2,5,1] => [5,4,6,3,2,1] => 4
[1,5,2,4,6,3] => [3,6,4,2,5,1] => [5,4,3,6,2,1] => 4
[1,5,2,6,3,4] => [4,3,6,2,5,1] => [5,6,4,3,2,1] => 5
[1,5,2,6,4,3] => [3,4,6,2,5,1] => [5,6,3,4,2,1] => 5
[1,5,3,2,4,6] => [6,4,2,3,5,1] => [5,4,2,6,3,1] => 4
[1,5,3,2,6,4] => [4,6,2,3,5,1] => [5,6,2,4,3,1] => 5
[1,5,3,4,2,6] => [6,2,4,3,5,1] => [5,6,4,2,3,1] => 5
[1,5,3,4,6,2] => [2,6,4,3,5,1] => [5,2,4,6,3,1] => 3
[1,5,3,6,2,4] => [4,2,6,3,5,1] => [5,4,6,2,3,1] => 4
[1,5,3,6,4,2] => [2,4,6,3,5,1] => [5,2,6,4,3,1] => 4
[1,5,4,2,3,6] => [6,3,2,4,5,1] => [5,3,6,2,4,1] => 4
[1,5,4,2,6,3] => [3,6,2,4,5,1] => [5,6,3,2,4,1] => 5
[1,5,4,3,2,6] => [6,2,3,4,5,1] => [5,6,2,3,4,1] => 5
[1,5,4,3,6,2] => [2,6,3,4,5,1] => [5,2,6,3,4,1] => 4
[1,5,4,6,2,3] => [3,2,6,4,5,1] => [5,3,2,6,4,1] => 3
[1,5,4,6,3,2] => [2,3,6,4,5,1] => [5,2,3,6,4,1] => 3
[1,5,6,2,3,4] => [4,3,2,6,5,1] => [5,3,4,2,6,1] => 3
[1,5,6,2,4,3] => [3,4,2,6,5,1] => [5,4,3,2,6,1] => 4
[1,5,6,3,2,4] => [4,2,3,6,5,1] => [5,4,2,3,6,1] => 4
[1,5,6,3,4,2] => [2,4,3,6,5,1] => [5,2,4,3,6,1] => 3
[1,5,6,4,2,3] => [3,2,4,6,5,1] => [5,3,2,4,6,1] => 3
[1,5,6,4,3,2] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => 3
[1,6,2,3,4,5] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => 4
[1,6,2,3,5,4] => [4,5,3,2,6,1] => [6,3,5,4,2,1] => 5
[1,6,2,4,3,5] => [5,3,4,2,6,1] => [6,4,5,3,2,1] => 5
[1,6,2,4,5,3] => [3,5,4,2,6,1] => [6,4,3,5,2,1] => 5
[1,6,2,5,3,4] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => 6
[1,6,2,5,4,3] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => 6
[1,6,3,2,4,5] => [5,4,2,3,6,1] => [6,4,2,5,3,1] => 5
[1,6,3,2,5,4] => [4,5,2,3,6,1] => [6,5,2,4,3,1] => 6
[1,6,3,4,2,5] => [5,2,4,3,6,1] => [6,5,4,2,3,1] => 6
[1,6,3,4,5,2] => [2,5,4,3,6,1] => [6,2,4,5,3,1] => 4
[1,6,3,5,2,4] => [4,2,5,3,6,1] => [6,4,5,2,3,1] => 5
[1,6,3,5,4,2] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => 5
[1,6,4,2,3,5] => [5,3,2,4,6,1] => [6,3,5,2,4,1] => 5
[1,6,4,2,5,3] => [3,5,2,4,6,1] => [6,5,3,2,4,1] => 6
[1,6,4,3,2,5] => [5,2,3,4,6,1] => [6,5,2,3,4,1] => 6
[1,6,4,3,5,2] => [2,5,3,4,6,1] => [6,2,5,3,4,1] => 5
[1,6,4,5,2,3] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => 4
[1,6,4,5,3,2] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => 4
[1,6,5,2,3,4] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => 4
[1,6,5,2,4,3] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => 5
[1,6,5,3,2,4] => [4,2,3,5,6,1] => [6,4,2,3,5,1] => 5
[1,6,5,3,4,2] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => 4
[1,6,5,4,2,3] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => 4
[1,6,5,4,3,2] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 4
[2,1,3,4,5,6] => [6,5,4,3,1,2] => [3,1,4,5,6,2] => 1
[2,1,3,4,6,5] => [5,6,4,3,1,2] => [3,1,4,6,5,2] => 2
[2,1,3,5,4,6] => [6,4,5,3,1,2] => [3,1,5,6,4,2] => 2
[2,1,3,5,6,4] => [4,6,5,3,1,2] => [3,1,5,4,6,2] => 2
[2,1,3,6,4,5] => [5,4,6,3,1,2] => [3,1,6,5,4,2] => 3
[2,1,3,6,5,4] => [4,5,6,3,1,2] => [3,1,6,4,5,2] => 3
[2,1,4,3,5,6] => [6,5,3,4,1,2] => [4,1,5,3,6,2] => 2
[2,1,4,3,6,5] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => 3
[2,1,4,5,3,6] => [6,3,5,4,1,2] => [4,1,5,6,2,3] => 2
[2,1,4,5,6,3] => [3,6,5,4,1,2] => [4,1,3,5,6,2] => 2
[2,1,4,6,3,5] => [5,3,6,4,1,2] => [4,1,6,5,2,3] => 3
[2,1,4,6,5,3] => [3,5,6,4,1,2] => [4,1,3,6,5,2] => 3
[2,1,5,3,4,6] => [6,4,3,5,1,2] => [5,1,4,6,3,2] => 3
[2,1,5,3,6,4] => [4,6,3,5,1,2] => [5,1,6,4,3,2] => 4
[2,1,5,4,3,6] => [6,3,4,5,1,2] => [5,1,6,3,4,2] => 4
[2,1,5,4,6,3] => [3,6,4,5,1,2] => [5,1,3,6,4,2] => 3
[2,1,5,6,3,4] => [4,3,6,5,1,2] => [5,1,4,3,6,2] => 3
[2,1,5,6,4,3] => [3,4,6,5,1,2] => [5,1,3,4,6,2] => 3
[2,1,6,3,4,5] => [5,4,3,6,1,2] => [6,1,4,5,3,2] => 4
[2,1,6,3,5,4] => [4,5,3,6,1,2] => [6,1,5,4,3,2] => 5
[2,1,6,4,3,5] => [5,3,4,6,1,2] => [6,1,5,3,4,2] => 5
[2,1,6,4,5,3] => [3,5,4,6,1,2] => [6,1,3,5,4,2] => 4
[2,1,6,5,3,4] => [4,3,5,6,1,2] => [6,1,4,3,5,2] => 4
[2,1,6,5,4,3] => [3,4,5,6,1,2] => [6,1,3,4,5,2] => 4
[2,3,1,4,5,6] => [6,5,4,1,3,2] => [4,3,1,5,6,2] => 2
[2,3,1,4,6,5] => [5,6,4,1,3,2] => [4,3,1,6,5,2] => 3
[2,3,1,5,4,6] => [6,4,5,1,3,2] => [5,3,1,6,4,2] => 3
[2,3,1,5,6,4] => [4,6,5,1,3,2] => [5,3,1,4,6,2] => 3
[2,3,1,6,4,5] => [5,4,6,1,3,2] => [6,3,1,5,4,2] => 4
[2,3,1,6,5,4] => [4,5,6,1,3,2] => [6,3,1,4,5,2] => 4
[2,3,4,1,5,6] => [6,5,1,4,3,2] => [5,3,4,1,6,2] => 3
[2,3,4,1,6,5] => [5,6,1,4,3,2] => [6,3,4,1,5,2] => 4
[2,3,4,5,1,6] => [6,1,5,4,3,2] => [6,3,4,5,1,2] => 4
[2,3,4,5,6,1] => [1,6,5,4,3,2] => [1,3,4,5,6,2] => 0
[2,3,4,6,1,5] => [5,1,6,4,3,2] => [5,3,4,6,1,2] => 3
[2,3,4,6,5,1] => [1,5,6,4,3,2] => [1,3,4,6,5,2] => 1
[2,3,5,1,4,6] => [6,4,1,5,3,2] => [4,3,6,5,2,1] => 3
[2,3,5,1,6,4] => [4,6,1,5,3,2] => [6,3,5,4,1,2] => 5
[2,3,5,4,1,6] => [6,1,4,5,3,2] => [6,3,5,1,4,2] => 5
[2,3,5,4,6,1] => [1,6,4,5,3,2] => [1,3,5,6,4,2] => 1
[2,3,5,6,1,4] => [4,1,6,5,3,2] => [4,3,5,1,6,2] => 2
[2,3,5,6,4,1] => [1,4,6,5,3,2] => [1,3,5,4,6,2] => 1
[2,3,6,1,4,5] => [5,4,1,6,3,2] => [4,3,5,6,2,1] => 2
[2,3,6,1,5,4] => [4,5,1,6,3,2] => [5,3,6,4,1,2] => 4
[2,3,6,4,1,5] => [5,1,4,6,3,2] => [5,3,6,1,4,2] => 4
[2,3,6,4,5,1] => [1,5,4,6,3,2] => [1,3,6,5,4,2] => 2
[2,3,6,5,1,4] => [4,1,5,6,3,2] => [4,3,6,1,5,2] => 3
[2,3,6,5,4,1] => [1,4,5,6,3,2] => [1,3,6,4,5,2] => 2
[2,4,1,3,5,6] => [6,5,3,1,4,2] => [3,5,4,2,6,1] => 2
[2,4,1,3,6,5] => [5,6,3,1,4,2] => [3,6,4,2,5,1] => 3
[2,4,1,5,3,6] => [6,3,5,1,4,2] => [5,4,6,1,3,2] => 4
[2,4,1,5,6,3] => [3,6,5,1,4,2] => [5,4,3,1,6,2] => 4
[2,4,1,6,3,5] => [5,3,6,1,4,2] => [6,4,5,1,3,2] => 5
[2,4,1,6,5,3] => [3,5,6,1,4,2] => [6,4,3,1,5,2] => 5
[2,4,3,1,5,6] => [6,5,1,3,4,2] => [5,4,1,3,6,2] => 4
[2,4,3,1,6,5] => [5,6,1,3,4,2] => [6,4,1,3,5,2] => 5
[2,4,3,5,1,6] => [6,1,5,3,4,2] => [6,4,5,3,1,2] => 5
[2,4,3,5,6,1] => [1,6,5,3,4,2] => [1,4,5,3,6,2] => 1
[2,4,3,6,1,5] => [5,1,6,3,4,2] => [5,4,6,3,1,2] => 4
[2,4,3,6,5,1] => [1,5,6,3,4,2] => [1,4,6,3,5,2] => 2
[2,4,5,1,3,6] => [6,3,1,5,4,2] => [3,6,4,5,2,1] => 3
[2,4,5,1,6,3] => [3,6,1,5,4,2] => [6,4,3,5,1,2] => 5
[2,4,5,3,1,6] => [6,1,3,5,4,2] => [6,4,1,5,3,2] => 5
[2,4,5,3,6,1] => [1,6,3,5,4,2] => [1,4,5,6,2,3] => 1
[2,4,5,6,1,3] => [3,1,6,5,4,2] => [3,4,1,5,6,2] => 1
[2,4,5,6,3,1] => [1,3,6,5,4,2] => [1,4,3,5,6,2] => 1
[2,4,6,1,3,5] => [5,3,1,6,4,2] => [3,5,4,6,2,1] => 2
[2,4,6,1,5,3] => [3,5,1,6,4,2] => [5,4,3,6,1,2] => 4
[2,4,6,3,1,5] => [5,1,3,6,4,2] => [5,4,1,6,3,2] => 4
[2,4,6,3,5,1] => [1,5,3,6,4,2] => [1,4,6,5,2,3] => 2
[2,4,6,5,1,3] => [3,1,5,6,4,2] => [3,4,1,6,5,2] => 2
[2,4,6,5,3,1] => [1,3,5,6,4,2] => [1,4,3,6,5,2] => 2
[2,5,1,3,4,6] => [6,4,3,1,5,2] => [3,4,6,5,1,2] => 2
[2,5,1,3,6,4] => [4,6,3,1,5,2] => [3,6,5,4,2,1] => 4
[2,5,1,4,3,6] => [6,3,4,1,5,2] => [4,5,6,3,1,2] => 3
[2,5,1,4,6,3] => [3,6,4,1,5,2] => [4,6,3,5,2,1] => 4
[2,5,1,6,3,4] => [4,3,6,1,5,2] => [6,5,4,3,1,2] => 6
[2,5,1,6,4,3] => [3,4,6,1,5,2] => [6,5,3,4,1,2] => 6
[2,5,3,1,4,6] => [6,4,1,3,5,2] => [4,6,2,5,3,1] => 4
[2,5,3,1,6,4] => [4,6,1,3,5,2] => [6,5,1,4,3,2] => 6
[2,5,3,4,1,6] => [6,1,4,3,5,2] => [6,5,4,1,3,2] => 6
[2,5,3,4,6,1] => [1,6,4,3,5,2] => [1,5,4,6,3,2] => 2
[2,5,3,6,1,4] => [4,1,6,3,5,2] => [4,5,6,1,3,2] => 3
[2,5,3,6,4,1] => [1,4,6,3,5,2] => [1,5,6,4,3,2] => 3
[2,5,4,1,3,6] => [6,3,1,4,5,2] => [3,6,5,2,4,1] => 4
[2,5,4,1,6,3] => [3,6,1,4,5,2] => [6,5,3,1,4,2] => 6
[2,5,4,3,1,6] => [6,1,3,4,5,2] => [6,5,1,3,4,2] => 6
[2,5,4,3,6,1] => [1,6,3,4,5,2] => [1,5,6,3,4,2] => 3
[2,5,4,6,1,3] => [3,1,6,4,5,2] => [3,5,1,6,4,2] => 2
[2,5,4,6,3,1] => [1,3,6,4,5,2] => [1,5,3,6,4,2] => 2
[2,5,6,1,3,4] => [4,3,1,6,5,2] => [3,4,5,2,6,1] => 1
[2,5,6,1,4,3] => [3,4,1,6,5,2] => [4,5,3,1,6,2] => 3
[2,5,6,3,1,4] => [4,1,3,6,5,2] => [4,5,1,3,6,2] => 3
[2,5,6,3,4,1] => [1,4,3,6,5,2] => [1,5,4,3,6,2] => 2
[2,5,6,4,1,3] => [3,1,4,6,5,2] => [3,5,1,4,6,2] => 2
[2,5,6,4,3,1] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => 2
[2,6,1,3,4,5] => [5,4,3,1,6,2] => [3,4,5,6,1,2] => 1
[2,6,1,3,5,4] => [4,5,3,1,6,2] => [3,5,6,4,2,1] => 3
[2,6,1,4,3,5] => [5,3,4,1,6,2] => [4,6,5,3,1,2] => 4
[2,6,1,4,5,3] => [3,5,4,1,6,2] => [4,5,3,6,2,1] => 3
[2,6,1,5,3,4] => [4,3,5,1,6,2] => [5,6,4,3,1,2] => 5
[2,6,1,5,4,3] => [3,4,5,1,6,2] => [5,6,3,4,1,2] => 5
[2,6,3,1,4,5] => [5,4,1,3,6,2] => [4,5,2,6,3,1] => 3
[2,6,3,1,5,4] => [4,5,1,3,6,2] => [5,6,1,4,3,2] => 5
[2,6,3,4,1,5] => [5,1,4,3,6,2] => [5,6,4,1,3,2] => 5
[2,6,3,4,5,1] => [1,5,4,3,6,2] => [1,6,4,5,3,2] => 3
[2,6,3,5,1,4] => [4,1,5,3,6,2] => [4,6,5,1,3,2] => 4
[2,6,3,5,4,1] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => 4
[2,6,4,1,3,5] => [5,3,1,4,6,2] => [3,5,6,2,4,1] => 3
[2,6,4,1,5,3] => [3,5,1,4,6,2] => [5,6,3,1,4,2] => 5
[2,6,4,3,1,5] => [5,1,3,4,6,2] => [5,6,1,3,4,2] => 5
[2,6,4,3,5,1] => [1,5,3,4,6,2] => [1,6,5,3,4,2] => 4
[2,6,4,5,1,3] => [3,1,5,4,6,2] => [3,6,1,5,4,2] => 3
[2,6,4,5,3,1] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => 3
[2,6,5,1,3,4] => [4,3,1,5,6,2] => [3,4,6,2,5,1] => 2
[2,6,5,1,4,3] => [3,4,1,5,6,2] => [4,6,3,1,5,2] => 4
[2,6,5,3,1,4] => [4,1,3,5,6,2] => [4,6,1,3,5,2] => 4
[2,6,5,3,4,1] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => 3
[2,6,5,4,1,3] => [3,1,4,5,6,2] => [3,6,1,4,5,2] => 3
[2,6,5,4,3,1] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => 3
[3,1,2,4,5,6] => [6,5,4,2,1,3] => [2,4,1,5,6,3] => 1
[3,1,2,4,6,5] => [5,6,4,2,1,3] => [2,4,1,6,5,3] => 2
[3,1,2,5,4,6] => [6,4,5,2,1,3] => [2,5,1,6,4,3] => 2
[3,1,2,5,6,4] => [4,6,5,2,1,3] => [2,5,1,4,6,3] => 2
[3,1,2,6,4,5] => [5,4,6,2,1,3] => [2,6,1,5,4,3] => 3
[3,1,2,6,5,4] => [4,5,6,2,1,3] => [2,6,1,4,5,3] => 3
[3,1,4,2,5,6] => [6,5,2,4,1,3] => [4,5,1,2,6,3] => 3
[3,1,4,2,6,5] => [5,6,2,4,1,3] => [4,6,1,2,5,3] => 4
[3,1,4,5,2,6] => [6,2,5,4,1,3] => [4,5,2,6,1,3] => 3
[3,1,4,5,6,2] => [2,6,5,4,1,3] => [4,2,1,5,6,3] => 2
[3,1,4,6,2,5] => [5,2,6,4,1,3] => [4,6,2,5,1,3] => 4
[3,1,4,6,5,2] => [2,5,6,4,1,3] => [4,2,1,6,5,3] => 3
[3,1,5,2,4,6] => [6,4,2,5,1,3] => [5,4,1,6,2,3] => 4
[3,1,5,2,6,4] => [4,6,2,5,1,3] => [5,6,1,4,2,3] => 5
[3,1,5,4,2,6] => [6,2,4,5,1,3] => [5,6,1,2,4,3] => 5
[3,1,5,4,6,2] => [2,6,4,5,1,3] => [5,2,1,6,4,3] => 3
[3,1,5,6,2,4] => [4,2,6,5,1,3] => [5,4,1,2,6,3] => 4
[3,1,5,6,4,2] => [2,4,6,5,1,3] => [5,2,1,4,6,3] => 3
[3,1,6,2,4,5] => [5,4,2,6,1,3] => [6,4,1,5,2,3] => 5
[3,1,6,2,5,4] => [4,5,2,6,1,3] => [6,5,1,4,2,3] => 6
[3,1,6,4,2,5] => [5,2,4,6,1,3] => [6,5,1,2,4,3] => 6
[3,1,6,4,5,2] => [2,5,4,6,1,3] => [6,2,1,5,4,3] => 4
[3,1,6,5,2,4] => [4,2,5,6,1,3] => [6,4,1,2,5,3] => 5
[3,1,6,5,4,2] => [2,4,5,6,1,3] => [6,2,1,4,5,3] => 4
[3,2,1,4,5,6] => [6,5,4,1,2,3] => [4,1,2,5,6,3] => 2
[3,2,1,4,6,5] => [5,6,4,1,2,3] => [4,1,2,6,5,3] => 3
[3,2,1,5,4,6] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => 3
[3,2,1,5,6,4] => [4,6,5,1,2,3] => [5,1,2,4,6,3] => 3
[3,2,1,6,4,5] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => 4
[3,2,1,6,5,4] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => 4
[3,2,4,1,5,6] => [6,5,1,4,2,3] => [5,4,2,1,6,3] => 4
[3,2,4,1,6,5] => [5,6,1,4,2,3] => [6,4,2,1,5,3] => 5
[3,2,4,5,1,6] => [6,1,5,4,2,3] => [6,4,2,5,1,3] => 5
[3,2,4,5,6,1] => [1,6,5,4,2,3] => [1,4,2,5,6,3] => 1
[3,2,4,6,1,5] => [5,1,6,4,2,3] => [5,4,2,6,1,3] => 4
[3,2,4,6,5,1] => [1,5,6,4,2,3] => [1,4,2,6,5,3] => 2
[3,2,5,1,4,6] => [6,4,1,5,2,3] => [4,6,1,5,2,3] => 4
[3,2,5,1,6,4] => [4,6,1,5,2,3] => [6,5,2,4,1,3] => 6
[3,2,5,4,1,6] => [6,1,4,5,2,3] => [6,5,2,1,4,3] => 6
[3,2,5,4,6,1] => [1,6,4,5,2,3] => [1,5,2,6,4,3] => 2
[3,2,5,6,1,4] => [4,1,6,5,2,3] => [4,5,2,1,6,3] => 3
[3,2,5,6,4,1] => [1,4,6,5,2,3] => [1,5,2,4,6,3] => 2
[3,2,6,1,4,5] => [5,4,1,6,2,3] => [4,5,1,6,2,3] => 3
[3,2,6,1,5,4] => [4,5,1,6,2,3] => [5,6,2,4,1,3] => 5
[3,2,6,4,1,5] => [5,1,4,6,2,3] => [5,6,2,1,4,3] => 5
[3,2,6,4,5,1] => [1,5,4,6,2,3] => [1,6,2,5,4,3] => 3
[3,2,6,5,1,4] => [4,1,5,6,2,3] => [4,6,2,1,5,3] => 4
[3,2,6,5,4,1] => [1,4,5,6,2,3] => [1,6,2,4,5,3] => 3
[3,4,1,2,5,6] => [6,5,2,1,4,3] => [2,5,4,1,6,3] => 2
[3,4,1,2,6,5] => [5,6,2,1,4,3] => [2,6,4,1,5,3] => 3
[3,4,1,5,2,6] => [6,2,5,1,4,3] => [5,6,4,1,2,3] => 5
[3,4,1,5,6,2] => [2,6,5,1,4,3] => [5,2,4,1,6,3] => 3
[3,4,1,6,2,5] => [5,2,6,1,4,3] => [6,5,4,1,2,3] => 6
[3,4,1,6,5,2] => [2,5,6,1,4,3] => [6,2,4,1,5,3] => 4
[3,4,2,1,5,6] => [6,5,1,2,4,3] => [5,1,4,2,6,3] => 3
[3,4,2,1,6,5] => [5,6,1,2,4,3] => [6,1,4,2,5,3] => 4
[3,4,2,5,1,6] => [6,1,5,2,4,3] => [6,5,4,2,1,3] => 6
[3,4,2,5,6,1] => [1,6,5,2,4,3] => [1,5,4,2,6,3] => 2
[3,4,2,6,1,5] => [5,1,6,2,4,3] => [5,6,4,2,1,3] => 5
[3,4,2,6,5,1] => [1,5,6,2,4,3] => [1,6,4,2,5,3] => 3
[3,4,5,1,2,6] => [6,2,1,5,4,3] => [2,6,4,5,1,3] => 3
[3,4,5,1,6,2] => [2,6,1,5,4,3] => [6,2,4,5,1,3] => 4
[3,4,5,2,1,6] => [6,1,2,5,4,3] => [6,1,4,5,2,3] => 4
[3,4,5,2,6,1] => [1,6,2,5,4,3] => [1,6,4,5,2,3] => 3
[3,4,5,6,1,2] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => 0
[3,4,5,6,2,1] => [1,2,6,5,4,3] => [1,2,4,5,6,3] => 0
[3,4,6,1,2,5] => [5,2,1,6,4,3] => [2,5,4,6,1,3] => 2
[3,4,6,1,5,2] => [2,5,1,6,4,3] => [5,2,4,6,1,3] => 3
[3,4,6,2,1,5] => [5,1,2,6,4,3] => [5,1,4,6,2,3] => 3
[3,4,6,2,5,1] => [1,5,2,6,4,3] => [1,5,4,6,2,3] => 2
[3,4,6,5,1,2] => [2,1,5,6,4,3] => [2,1,4,6,5,3] => 1
[3,4,6,5,2,1] => [1,2,5,6,4,3] => [1,2,4,6,5,3] => 1
[3,5,1,2,4,6] => [6,4,2,1,5,3] => [2,4,6,5,3,1] => 2
[3,5,1,2,6,4] => [4,6,2,1,5,3] => [2,6,5,4,1,3] => 4
[3,5,1,4,2,6] => [6,2,4,1,5,3] => [4,6,5,2,1,3] => 4
[3,5,1,4,6,2] => [2,6,4,1,5,3] => [4,2,6,5,3,1] => 3
[3,5,1,6,2,4] => [4,2,6,1,5,3] => [6,4,5,2,1,3] => 5
[3,5,1,6,4,2] => [2,4,6,1,5,3] => [6,2,5,4,1,3] => 5
[3,5,2,1,4,6] => [6,4,1,2,5,3] => [4,1,6,5,3,2] => 3
[3,5,2,1,6,4] => [4,6,1,2,5,3] => [6,1,5,4,2,3] => 5
[3,5,2,4,1,6] => [6,1,4,2,5,3] => [6,4,5,1,2,3] => 5
[3,5,2,4,6,1] => [1,6,4,2,5,3] => [1,4,6,5,3,2] => 2
[3,5,2,6,1,4] => [4,1,6,2,5,3] => [4,6,5,1,2,3] => 4
[3,5,2,6,4,1] => [1,4,6,2,5,3] => [1,6,5,4,2,3] => 4
[3,5,4,1,2,6] => [6,2,1,4,5,3] => [2,6,5,1,4,3] => 4
[3,5,4,1,6,2] => [2,6,1,4,5,3] => [6,2,5,1,4,3] => 5
[3,5,4,2,1,6] => [6,1,2,4,5,3] => [6,1,5,2,4,3] => 5
[3,5,4,2,6,1] => [1,6,2,4,5,3] => [1,6,5,2,4,3] => 4
[3,5,4,6,1,2] => [2,1,6,4,5,3] => [2,1,5,6,4,3] => 1
[3,5,4,6,2,1] => [1,2,6,4,5,3] => [1,2,5,6,4,3] => 1
[3,5,6,1,2,4] => [4,2,1,6,5,3] => [2,4,5,1,6,3] => 1
[3,5,6,1,4,2] => [2,4,1,6,5,3] => [4,2,5,1,6,3] => 2
[3,5,6,2,1,4] => [4,1,2,6,5,3] => [4,1,5,2,6,3] => 2
[3,5,6,2,4,1] => [1,4,2,6,5,3] => [1,4,5,2,6,3] => 1
[3,5,6,4,1,2] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => 1
[3,5,6,4,2,1] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => 1
[3,6,1,2,4,5] => [5,4,2,1,6,3] => [2,4,5,6,3,1] => 1
[3,6,1,2,5,4] => [4,5,2,1,6,3] => [2,5,6,4,1,3] => 3
[3,6,1,4,2,5] => [5,2,4,1,6,3] => [4,5,6,2,1,3] => 3
[3,6,1,4,5,2] => [2,5,4,1,6,3] => [4,2,5,6,3,1] => 2
[3,6,1,5,2,4] => [4,2,5,1,6,3] => [5,4,6,2,1,3] => 4
[3,6,1,5,4,2] => [2,4,5,1,6,3] => [5,2,6,4,1,3] => 4
[3,6,2,1,4,5] => [5,4,1,2,6,3] => [4,1,5,6,3,2] => 2
[3,6,2,1,5,4] => [4,5,1,2,6,3] => [5,1,6,4,2,3] => 4
[3,6,2,4,1,5] => [5,1,4,2,6,3] => [5,4,6,1,2,3] => 4
[3,6,2,4,5,1] => [1,5,4,2,6,3] => [1,4,5,6,3,2] => 1
[3,6,2,5,1,4] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => 3
[3,6,2,5,4,1] => [1,4,5,2,6,3] => [1,5,6,4,2,3] => 3
[3,6,4,1,2,5] => [5,2,1,4,6,3] => [2,5,6,1,4,3] => 3
[3,6,4,1,5,2] => [2,5,1,4,6,3] => [5,2,6,1,4,3] => 4
[3,6,4,2,1,5] => [5,1,2,4,6,3] => [5,1,6,2,4,3] => 4
[3,6,4,2,5,1] => [1,5,2,4,6,3] => [1,5,6,2,4,3] => 3
[3,6,4,5,1,2] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => 2
[3,6,4,5,2,1] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => 2
[3,6,5,1,2,4] => [4,2,1,5,6,3] => [2,4,6,1,5,3] => 2
[3,6,5,1,4,2] => [2,4,1,5,6,3] => [4,2,6,1,5,3] => 3
[3,6,5,2,1,4] => [4,1,2,5,6,3] => [4,1,6,2,5,3] => 3
[3,6,5,2,4,1] => [1,4,2,5,6,3] => [1,4,6,2,5,3] => 2
[3,6,5,4,1,2] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => 2
[3,6,5,4,2,1] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => 2
[4,1,2,3,5,6] => [6,5,3,2,1,4] => [2,3,5,1,6,4] => 1
[4,1,2,3,6,5] => [5,6,3,2,1,4] => [2,3,6,1,5,4] => 2
[4,1,2,5,3,6] => [6,3,5,2,1,4] => [2,5,6,1,3,4] => 3
[4,1,2,5,6,3] => [3,6,5,2,1,4] => [2,5,3,1,6,4] => 2
[4,1,2,6,3,5] => [5,3,6,2,1,4] => [2,6,5,1,3,4] => 4
[4,1,2,6,5,3] => [3,5,6,2,1,4] => [2,6,3,1,5,4] => 3
[4,1,3,2,5,6] => [6,5,2,3,1,4] => [3,5,2,1,6,4] => 2
[4,1,3,2,6,5] => [5,6,2,3,1,4] => [3,6,2,1,5,4] => 3
[4,1,3,5,2,6] => [6,2,5,3,1,4] => [3,5,6,2,1,4] => 3
[4,1,3,5,6,2] => [2,6,5,3,1,4] => [3,2,5,1,6,4] => 2
[4,1,3,6,2,5] => [5,2,6,3,1,4] => [3,6,5,2,1,4] => 4
[4,1,3,6,5,2] => [2,5,6,3,1,4] => [3,2,6,1,5,4] => 3
[4,1,5,2,3,6] => [6,3,2,5,1,4] => [5,3,6,1,2,4] => 4
[4,1,5,2,6,3] => [3,6,2,5,1,4] => [5,6,3,1,2,4] => 5
[4,1,5,3,2,6] => [6,2,3,5,1,4] => [5,6,2,1,3,4] => 5
[4,1,5,3,6,2] => [2,6,3,5,1,4] => [5,2,6,1,3,4] => 4
[4,1,5,6,2,3] => [3,2,6,5,1,4] => [5,3,2,1,6,4] => 3
[4,1,5,6,3,2] => [2,3,6,5,1,4] => [5,2,3,1,6,4] => 3
[4,1,6,2,3,5] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => 5
[4,1,6,2,5,3] => [3,5,2,6,1,4] => [6,5,3,1,2,4] => 6
[4,1,6,3,2,5] => [5,2,3,6,1,4] => [6,5,2,1,3,4] => 6
[4,1,6,3,5,2] => [2,5,3,6,1,4] => [6,2,5,1,3,4] => 5
[4,1,6,5,2,3] => [3,2,5,6,1,4] => [6,3,2,1,5,4] => 4
[4,1,6,5,3,2] => [2,3,5,6,1,4] => [6,2,3,1,5,4] => 4
[4,2,1,3,5,6] => [6,5,3,1,2,4] => [3,1,5,2,6,4] => 2
[4,2,1,3,6,5] => [5,6,3,1,2,4] => [3,1,6,2,5,4] => 3
[4,2,1,5,3,6] => [6,3,5,1,2,4] => [5,1,6,2,3,4] => 4
[4,2,1,5,6,3] => [3,6,5,1,2,4] => [5,1,3,2,6,4] => 3
[4,2,1,6,3,5] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => 5
[4,2,1,6,5,3] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => 4
[4,2,3,1,5,6] => [6,5,1,3,2,4] => [5,3,1,2,6,4] => 3
[4,2,3,1,6,5] => [5,6,1,3,2,4] => [6,3,1,2,5,4] => 4
[4,2,3,5,1,6] => [6,1,5,3,2,4] => [6,3,5,2,1,4] => 5
[4,2,3,5,6,1] => [1,6,5,3,2,4] => [1,3,5,2,6,4] => 1
[4,2,3,6,1,5] => [5,1,6,3,2,4] => [5,3,6,2,1,4] => 4
[4,2,3,6,5,1] => [1,5,6,3,2,4] => [1,3,6,2,5,4] => 2
[4,2,5,1,3,6] => [6,3,1,5,2,4] => [3,6,5,1,2,4] => 4
[4,2,5,1,6,3] => [3,6,1,5,2,4] => [6,5,3,2,1,4] => 6
[4,2,5,3,1,6] => [6,1,3,5,2,4] => [6,5,1,2,3,4] => 6
[4,2,5,3,6,1] => [1,6,3,5,2,4] => [1,5,6,2,3,4] => 3
[4,2,5,6,1,3] => [3,1,6,5,2,4] => [3,5,1,2,6,4] => 2
[4,2,5,6,3,1] => [1,3,6,5,2,4] => [1,5,3,2,6,4] => 2
[4,2,6,1,3,5] => [5,3,1,6,2,4] => [3,5,6,1,2,4] => 3
[4,2,6,1,5,3] => [3,5,1,6,2,4] => [5,6,3,2,1,4] => 5
[4,2,6,3,1,5] => [5,1,3,6,2,4] => [5,6,1,2,3,4] => 5
[4,2,6,3,5,1] => [1,5,3,6,2,4] => [1,6,5,2,3,4] => 4
[4,2,6,5,1,3] => [3,1,5,6,2,4] => [3,6,1,2,5,4] => 3
[4,2,6,5,3,1] => [1,3,5,6,2,4] => [1,6,3,2,5,4] => 3
[4,3,1,2,5,6] => [6,5,2,1,3,4] => [2,5,1,3,6,4] => 2
[4,3,1,2,6,5] => [5,6,2,1,3,4] => [2,6,1,3,5,4] => 3
[4,3,1,5,2,6] => [6,2,5,1,3,4] => [5,6,1,3,2,4] => 5
[4,3,1,5,6,2] => [2,6,5,1,3,4] => [5,2,1,3,6,4] => 3
[4,3,1,6,2,5] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => 6
[4,3,1,6,5,2] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => 4
[4,3,2,1,5,6] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => 3
[4,3,2,1,6,5] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => 4
[4,3,2,5,1,6] => [6,1,5,2,3,4] => [6,5,2,3,1,4] => 6
[4,3,2,5,6,1] => [1,6,5,2,3,4] => [1,5,2,3,6,4] => 2
[4,3,2,6,1,5] => [5,1,6,2,3,4] => [5,6,2,3,1,4] => 5
[4,3,2,6,5,1] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => 3
[4,3,5,1,2,6] => [6,2,1,5,3,4] => [2,6,5,3,1,4] => 4
[4,3,5,1,6,2] => [2,6,1,5,3,4] => [6,2,5,3,1,4] => 5
[4,3,5,2,1,6] => [6,1,2,5,3,4] => [6,1,5,3,2,4] => 5
[4,3,5,2,6,1] => [1,6,2,5,3,4] => [1,6,5,3,2,4] => 4
[4,3,5,6,1,2] => [2,1,6,5,3,4] => [2,1,5,3,6,4] => 1
[4,3,5,6,2,1] => [1,2,6,5,3,4] => [1,2,5,3,6,4] => 1
[4,3,6,1,2,5] => [5,2,1,6,3,4] => [2,5,6,3,1,4] => 3
[4,3,6,1,5,2] => [2,5,1,6,3,4] => [5,2,6,3,1,4] => 4
[4,3,6,2,1,5] => [5,1,2,6,3,4] => [5,1,6,3,2,4] => 4
[4,3,6,2,5,1] => [1,5,2,6,3,4] => [1,5,6,3,2,4] => 3
[4,3,6,5,1,2] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => 2
[4,3,6,5,2,1] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => 2
[4,5,1,2,3,6] => [6,3,2,1,5,4] => [2,3,6,5,1,4] => 2
[4,5,1,2,6,3] => [3,6,2,1,5,4] => [2,6,3,5,1,4] => 3
[4,5,1,3,2,6] => [6,2,3,1,5,4] => [3,6,2,5,1,4] => 3
[4,5,1,3,6,2] => [2,6,3,1,5,4] => [3,2,6,5,1,4] => 3
[4,5,1,6,2,3] => [3,2,6,1,5,4] => [6,3,2,5,1,4] => 4
[4,5,1,6,3,2] => [2,3,6,1,5,4] => [6,2,3,5,1,4] => 4
[4,5,2,1,3,6] => [6,3,1,2,5,4] => [3,1,6,5,2,4] => 3
[4,5,2,1,6,3] => [3,6,1,2,5,4] => [6,1,3,5,2,4] => 4
[4,5,2,3,1,6] => [6,1,3,2,5,4] => [6,3,1,5,2,4] => 4
[4,5,2,3,6,1] => [1,6,3,2,5,4] => [1,3,6,5,2,4] => 2
[4,5,2,6,1,3] => [3,1,6,2,5,4] => [3,6,1,5,2,4] => 3
[4,5,2,6,3,1] => [1,3,6,2,5,4] => [1,6,3,5,2,4] => 3
[4,5,3,1,2,6] => [6,2,1,3,5,4] => [2,6,1,5,3,4] => 3
[4,5,3,1,6,2] => [2,6,1,3,5,4] => [6,2,1,5,3,4] => 4
[4,5,3,2,1,6] => [6,1,2,3,5,4] => [6,1,2,5,3,4] => 4
[4,5,3,2,6,1] => [1,6,2,3,5,4] => [1,6,2,5,3,4] => 3
[4,5,3,6,1,2] => [2,1,6,3,5,4] => [2,1,6,5,3,4] => 2
[4,5,3,6,2,1] => [1,2,6,3,5,4] => [1,2,6,5,3,4] => 2
[4,5,6,1,2,3] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => 0
[4,5,6,1,3,2] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => 1
[4,5,6,2,1,3] => [3,1,2,6,5,4] => [3,1,2,5,6,4] => 1
[4,5,6,2,3,1] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => 0
[4,5,6,3,1,2] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => 0
[4,5,6,3,2,1] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => 0
[4,6,1,2,3,5] => [5,3,2,1,6,4] => [2,3,5,6,1,4] => 1
[4,6,1,2,5,3] => [3,5,2,1,6,4] => [2,5,3,6,1,4] => 2
[4,6,1,3,2,5] => [5,2,3,1,6,4] => [3,5,2,6,1,4] => 2
[4,6,1,3,5,2] => [2,5,3,1,6,4] => [3,2,5,6,1,4] => 2
[4,6,1,5,2,3] => [3,2,5,1,6,4] => [5,3,2,6,1,4] => 3
[4,6,1,5,3,2] => [2,3,5,1,6,4] => [5,2,3,6,1,4] => 3
[4,6,2,1,3,5] => [5,3,1,2,6,4] => [3,1,5,6,2,4] => 2
[4,6,2,1,5,3] => [3,5,1,2,6,4] => [5,1,3,6,2,4] => 3
[4,6,2,3,1,5] => [5,1,3,2,6,4] => [5,3,1,6,2,4] => 3
[4,6,2,3,5,1] => [1,5,3,2,6,4] => [1,3,5,6,2,4] => 1
[4,6,2,5,1,3] => [3,1,5,2,6,4] => [3,5,1,6,2,4] => 2
[4,6,2,5,3,1] => [1,3,5,2,6,4] => [1,5,3,6,2,4] => 2
[4,6,3,1,2,5] => [5,2,1,3,6,4] => [2,5,1,6,3,4] => 2
[4,6,3,1,5,2] => [2,5,1,3,6,4] => [5,2,1,6,3,4] => 3
[4,6,3,2,1,5] => [5,1,2,3,6,4] => [5,1,2,6,3,4] => 3
[4,6,3,2,5,1] => [1,5,2,3,6,4] => [1,5,2,6,3,4] => 2
[4,6,3,5,1,2] => [2,1,5,3,6,4] => [2,1,5,6,3,4] => 1
[4,6,3,5,2,1] => [1,2,5,3,6,4] => [1,2,5,6,3,4] => 1
[4,6,5,1,2,3] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => 1
[4,6,5,1,3,2] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => 2
[4,6,5,2,1,3] => [3,1,2,5,6,4] => [3,1,2,6,5,4] => 2
[4,6,5,2,3,1] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => 1
[4,6,5,3,1,2] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => 1
[4,6,5,3,2,1] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => 1
[5,1,2,3,4,6] => [6,4,3,2,1,5] => [2,3,4,6,1,5] => 1
[5,1,2,3,6,4] => [4,6,3,2,1,5] => [2,3,6,4,1,5] => 2
[5,1,2,4,3,6] => [6,3,4,2,1,5] => [2,4,6,3,1,5] => 2
[5,1,2,4,6,3] => [3,6,4,2,1,5] => [2,4,3,6,1,5] => 2
[5,1,2,6,3,4] => [4,3,6,2,1,5] => [2,6,4,3,1,5] => 3
[5,1,2,6,4,3] => [3,4,6,2,1,5] => [2,6,3,4,1,5] => 3
[5,1,3,2,4,6] => [6,4,2,3,1,5] => [3,4,2,6,1,5] => 2
[5,1,3,2,6,4] => [4,6,2,3,1,5] => [3,6,2,4,1,5] => 3
[5,1,3,4,2,6] => [6,2,4,3,1,5] => [3,4,6,1,2,5] => 2
[5,1,3,4,6,2] => [2,6,4,3,1,5] => [3,2,4,6,1,5] => 2
[5,1,3,6,2,4] => [4,2,6,3,1,5] => [3,6,4,1,2,5] => 3
[5,1,3,6,4,2] => [2,4,6,3,1,5] => [3,2,6,4,1,5] => 3
[5,1,4,2,3,6] => [6,3,2,4,1,5] => [4,3,6,2,1,5] => 3
[5,1,4,2,6,3] => [3,6,2,4,1,5] => [4,6,3,2,1,5] => 4
[5,1,4,3,2,6] => [6,2,3,4,1,5] => [4,6,2,3,1,5] => 4
[5,1,4,3,6,2] => [2,6,3,4,1,5] => [4,2,6,3,1,5] => 3
[5,1,4,6,2,3] => [3,2,6,4,1,5] => [4,3,2,6,1,5] => 3
[5,1,4,6,3,2] => [2,3,6,4,1,5] => [4,2,3,6,1,5] => 3
[5,1,6,2,3,4] => [4,3,2,6,1,5] => [6,3,4,2,1,5] => 4
[5,1,6,2,4,3] => [3,4,2,6,1,5] => [6,4,3,2,1,5] => 5
[5,1,6,3,2,4] => [4,2,3,6,1,5] => [6,4,2,3,1,5] => 5
[5,1,6,3,4,2] => [2,4,3,6,1,5] => [6,2,4,3,1,5] => 4
[5,1,6,4,2,3] => [3,2,4,6,1,5] => [6,3,2,4,1,5] => 4
[5,1,6,4,3,2] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => 4
[5,2,1,3,4,6] => [6,4,3,1,2,5] => [3,1,4,6,2,5] => 2
[5,2,1,3,6,4] => [4,6,3,1,2,5] => [3,1,6,4,2,5] => 3
[5,2,1,4,3,6] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => 3
[5,2,1,4,6,3] => [3,6,4,1,2,5] => [4,1,3,6,2,5] => 3
[5,2,1,6,3,4] => [4,3,6,1,2,5] => [6,1,4,3,2,5] => 4
[5,2,1,6,4,3] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => 4
[5,2,3,1,4,6] => [6,4,1,3,2,5] => [4,3,1,6,2,5] => 3
[5,2,3,1,6,4] => [4,6,1,3,2,5] => [6,3,1,4,2,5] => 4
[5,2,3,4,1,6] => [6,1,4,3,2,5] => [6,3,4,1,2,5] => 4
[5,2,3,4,6,1] => [1,6,4,3,2,5] => [1,3,4,6,2,5] => 1
[5,2,3,6,1,4] => [4,1,6,3,2,5] => [4,3,6,1,2,5] => 3
[5,2,3,6,4,1] => [1,4,6,3,2,5] => [1,3,6,4,2,5] => 2
[5,2,4,1,3,6] => [6,3,1,4,2,5] => [3,6,4,2,1,5] => 3
[5,2,4,1,6,3] => [3,6,1,4,2,5] => [6,4,3,1,2,5] => 5
[5,2,4,3,1,6] => [6,1,3,4,2,5] => [6,4,1,3,2,5] => 5
[5,2,4,3,6,1] => [1,6,3,4,2,5] => [1,4,6,3,2,5] => 2
[5,2,4,6,1,3] => [3,1,6,4,2,5] => [3,4,1,6,2,5] => 2
[5,2,4,6,3,1] => [1,3,6,4,2,5] => [1,4,3,6,2,5] => 2
[5,2,6,1,3,4] => [4,3,1,6,2,5] => [3,4,6,2,1,5] => 2
[5,2,6,1,4,3] => [3,4,1,6,2,5] => [4,6,3,1,2,5] => 4
[5,2,6,3,1,4] => [4,1,3,6,2,5] => [4,6,1,3,2,5] => 4
[5,2,6,3,4,1] => [1,4,3,6,2,5] => [1,6,4,3,2,5] => 3
[5,2,6,4,1,3] => [3,1,4,6,2,5] => [3,6,1,4,2,5] => 3
[5,2,6,4,3,1] => [1,3,4,6,2,5] => [1,6,3,4,2,5] => 3
[5,3,1,2,4,6] => [6,4,2,1,3,5] => [2,4,1,6,3,5] => 2
[5,3,1,2,6,4] => [4,6,2,1,3,5] => [2,6,1,4,3,5] => 3
[5,3,1,4,2,6] => [6,2,4,1,3,5] => [4,6,1,2,3,5] => 4
[5,3,1,4,6,2] => [2,6,4,1,3,5] => [4,2,1,6,3,5] => 3
[5,3,1,6,2,4] => [4,2,6,1,3,5] => [6,4,1,2,3,5] => 5
[5,3,1,6,4,2] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => 4
[5,3,2,1,4,6] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => 3
[5,3,2,1,6,4] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => 4
[5,3,2,4,1,6] => [6,1,4,2,3,5] => [6,4,2,1,3,5] => 5
[5,3,2,4,6,1] => [1,6,4,2,3,5] => [1,4,2,6,3,5] => 2
[5,3,2,6,1,4] => [4,1,6,2,3,5] => [4,6,2,1,3,5] => 4
[5,3,2,6,4,1] => [1,4,6,2,3,5] => [1,6,2,4,3,5] => 3
[5,3,4,1,2,6] => [6,2,1,4,3,5] => [2,6,4,1,3,5] => 3
[5,3,4,1,6,2] => [2,6,1,4,3,5] => [6,2,4,1,3,5] => 4
[5,3,4,2,1,6] => [6,1,2,4,3,5] => [6,1,4,2,3,5] => 4
[5,3,4,2,6,1] => [1,6,2,4,3,5] => [1,6,4,2,3,5] => 3
[5,3,4,6,1,2] => [2,1,6,4,3,5] => [2,1,4,6,3,5] => 1
[5,3,4,6,2,1] => [1,2,6,4,3,5] => [1,2,4,6,3,5] => 1
[5,3,6,1,2,4] => [4,2,1,6,3,5] => [2,4,6,1,3,5] => 2
[5,3,6,1,4,2] => [2,4,1,6,3,5] => [4,2,6,1,3,5] => 3
[5,3,6,2,1,4] => [4,1,2,6,3,5] => [4,1,6,2,3,5] => 3
[5,3,6,2,4,1] => [1,4,2,6,3,5] => [1,4,6,2,3,5] => 2
[5,3,6,4,1,2] => [2,1,4,6,3,5] => [2,1,6,4,3,5] => 2
[5,3,6,4,2,1] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => 2
[5,4,1,2,3,6] => [6,3,2,1,4,5] => [2,3,6,1,4,5] => 2
[5,4,1,2,6,3] => [3,6,2,1,4,5] => [2,6,3,1,4,5] => 3
[5,4,1,3,2,6] => [6,2,3,1,4,5] => [3,6,2,1,4,5] => 3
[5,4,1,3,6,2] => [2,6,3,1,4,5] => [3,2,6,1,4,5] => 3
[5,4,1,6,2,3] => [3,2,6,1,4,5] => [6,3,2,1,4,5] => 4
[5,4,1,6,3,2] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => 4
[5,4,2,1,3,6] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => 3
[5,4,2,1,6,3] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => 4
[5,4,2,3,1,6] => [6,1,3,2,4,5] => [6,3,1,2,4,5] => 4
[5,4,2,3,6,1] => [1,6,3,2,4,5] => [1,3,6,2,4,5] => 2
[5,4,2,6,1,3] => [3,1,6,2,4,5] => [3,6,1,2,4,5] => 3
[5,4,2,6,3,1] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => 3
[5,4,3,1,2,6] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => 3
[5,4,3,1,6,2] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => 4
[5,4,3,2,1,6] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 4
[5,4,3,2,6,1] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 3
[5,4,3,6,1,2] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => 2
[5,4,3,6,2,1] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 2
[5,4,6,1,2,3] => [3,2,1,6,4,5] => [2,3,1,6,4,5] => 1
[5,4,6,1,3,2] => [2,3,1,6,4,5] => [3,2,1,6,4,5] => 2
[5,4,6,2,1,3] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => 2
[5,4,6,2,3,1] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 1
[5,4,6,3,1,2] => [2,1,3,6,4,5] => [2,1,3,6,4,5] => 1
[5,4,6,3,2,1] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 1
[5,6,1,2,3,4] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => 0
[5,6,1,2,4,3] => [3,4,2,1,6,5] => [2,4,3,1,6,5] => 1
[5,6,1,3,2,4] => [4,2,3,1,6,5] => [3,4,2,1,6,5] => 1
[5,6,1,3,4,2] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => 1
[5,6,1,4,2,3] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => 2
[5,6,1,4,3,2] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => 2
[5,6,2,1,3,4] => [4,3,1,2,6,5] => [3,1,4,2,6,5] => 1
[5,6,2,1,4,3] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => 2
[5,6,2,3,1,4] => [4,1,3,2,6,5] => [4,3,1,2,6,5] => 2
[5,6,2,3,4,1] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => 0
[5,6,2,4,1,3] => [3,1,4,2,6,5] => [3,4,1,2,6,5] => 1
[5,6,2,4,3,1] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => 1
[5,6,3,1,2,4] => [4,2,1,3,6,5] => [2,4,1,3,6,5] => 1
[5,6,3,1,4,2] => [2,4,1,3,6,5] => [4,2,1,3,6,5] => 2
[5,6,3,2,1,4] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => 2
[5,6,3,2,4,1] => [1,4,2,3,6,5] => [1,4,2,3,6,5] => 1
[5,6,3,4,1,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 0
[5,6,3,4,2,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 0
[5,6,4,1,2,3] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => 0
[5,6,4,1,3,2] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => 1
[5,6,4,2,1,3] => [3,1,2,4,6,5] => [3,1,2,4,6,5] => 1
[5,6,4,2,3,1] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 0
[5,6,4,3,1,2] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 0
[5,6,4,3,2,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 0
[6,1,2,3,4,5] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => 0
[6,1,2,3,5,4] => [4,5,3,2,1,6] => [2,3,5,4,1,6] => 1
[6,1,2,4,3,5] => [5,3,4,2,1,6] => [2,4,5,3,1,6] => 1
[6,1,2,4,5,3] => [3,5,4,2,1,6] => [2,4,3,5,1,6] => 1
[6,1,2,5,3,4] => [4,3,5,2,1,6] => [2,5,4,3,1,6] => 2
[6,1,2,5,4,3] => [3,4,5,2,1,6] => [2,5,3,4,1,6] => 2
[6,1,3,2,4,5] => [5,4,2,3,1,6] => [3,4,2,5,1,6] => 1
[6,1,3,2,5,4] => [4,5,2,3,1,6] => [3,5,2,4,1,6] => 2
[6,1,3,4,2,5] => [5,2,4,3,1,6] => [3,4,5,1,2,6] => 1
[6,1,3,4,5,2] => [2,5,4,3,1,6] => [3,2,4,5,1,6] => 1
[6,1,3,5,2,4] => [4,2,5,3,1,6] => [3,5,4,1,2,6] => 2
[6,1,3,5,4,2] => [2,4,5,3,1,6] => [3,2,5,4,1,6] => 2
[6,1,4,2,3,5] => [5,3,2,4,1,6] => [4,3,5,2,1,6] => 2
[6,1,4,2,5,3] => [3,5,2,4,1,6] => [4,5,3,2,1,6] => 3
[6,1,4,3,2,5] => [5,2,3,4,1,6] => [4,5,2,3,1,6] => 3
[6,1,4,3,5,2] => [2,5,3,4,1,6] => [4,2,5,3,1,6] => 2
[6,1,4,5,2,3] => [3,2,5,4,1,6] => [4,3,2,5,1,6] => 2
[6,1,4,5,3,2] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => 2
[6,1,5,2,3,4] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => 3
[6,1,5,2,4,3] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => 4
[6,1,5,3,2,4] => [4,2,3,5,1,6] => [5,4,2,3,1,6] => 4
[6,1,5,3,4,2] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => 3
[6,1,5,4,2,3] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => 3
[6,1,5,4,3,2] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => 3
[6,2,1,3,4,5] => [5,4,3,1,2,6] => [3,1,4,5,2,6] => 1
[6,2,1,3,5,4] => [4,5,3,1,2,6] => [3,1,5,4,2,6] => 2
[6,2,1,4,3,5] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => 2
[6,2,1,4,5,3] => [3,5,4,1,2,6] => [4,1,3,5,2,6] => 2
[6,2,1,5,3,4] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => 3
[6,2,1,5,4,3] => [3,4,5,1,2,6] => [5,1,3,4,2,6] => 3
[6,2,3,1,4,5] => [5,4,1,3,2,6] => [4,3,1,5,2,6] => 2
[6,2,3,1,5,4] => [4,5,1,3,2,6] => [5,3,1,4,2,6] => 3
[6,2,3,4,1,5] => [5,1,4,3,2,6] => [5,3,4,1,2,6] => 3
[6,2,3,4,5,1] => [1,5,4,3,2,6] => [1,3,4,5,2,6] => 0
[6,2,3,5,1,4] => [4,1,5,3,2,6] => [4,3,5,1,2,6] => 2
[6,2,3,5,4,1] => [1,4,5,3,2,6] => [1,3,5,4,2,6] => 1
[6,2,4,1,3,5] => [5,3,1,4,2,6] => [3,5,4,2,1,6] => 2
[6,2,4,1,5,3] => [3,5,1,4,2,6] => [5,4,3,1,2,6] => 4
[6,2,4,3,1,5] => [5,1,3,4,2,6] => [5,4,1,3,2,6] => 4
[6,2,4,3,5,1] => [1,5,3,4,2,6] => [1,4,5,3,2,6] => 1
[6,2,4,5,1,3] => [3,1,5,4,2,6] => [3,4,1,5,2,6] => 1
[6,2,4,5,3,1] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => 1
[6,2,5,1,3,4] => [4,3,1,5,2,6] => [3,4,5,2,1,6] => 1
[6,2,5,1,4,3] => [3,4,1,5,2,6] => [4,5,3,1,2,6] => 3
[6,2,5,3,1,4] => [4,1,3,5,2,6] => [4,5,1,3,2,6] => 3
[6,2,5,3,4,1] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => 2
[6,2,5,4,1,3] => [3,1,4,5,2,6] => [3,5,1,4,2,6] => 2
[6,2,5,4,3,1] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => 2
[6,3,1,2,4,5] => [5,4,2,1,3,6] => [2,4,1,5,3,6] => 1
[6,3,1,2,5,4] => [4,5,2,1,3,6] => [2,5,1,4,3,6] => 2
[6,3,1,4,2,5] => [5,2,4,1,3,6] => [4,5,1,2,3,6] => 3
[6,3,1,4,5,2] => [2,5,4,1,3,6] => [4,2,1,5,3,6] => 2
[6,3,1,5,2,4] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => 4
[6,3,1,5,4,2] => [2,4,5,1,3,6] => [5,2,1,4,3,6] => 3
[6,3,2,1,4,5] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => 2
[6,3,2,1,5,4] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => 3
[6,3,2,4,1,5] => [5,1,4,2,3,6] => [5,4,2,1,3,6] => 4
[6,3,2,4,5,1] => [1,5,4,2,3,6] => [1,4,2,5,3,6] => 1
[6,3,2,5,1,4] => [4,1,5,2,3,6] => [4,5,2,1,3,6] => 3
[6,3,2,5,4,1] => [1,4,5,2,3,6] => [1,5,2,4,3,6] => 2
[6,3,4,1,2,5] => [5,2,1,4,3,6] => [2,5,4,1,3,6] => 2
[6,3,4,1,5,2] => [2,5,1,4,3,6] => [5,2,4,1,3,6] => 3
[6,3,4,2,1,5] => [5,1,2,4,3,6] => [5,1,4,2,3,6] => 3
[6,3,4,2,5,1] => [1,5,2,4,3,6] => [1,5,4,2,3,6] => 2
[6,3,4,5,1,2] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => 0
[6,3,4,5,2,1] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => 0
[6,3,5,1,2,4] => [4,2,1,5,3,6] => [2,4,5,1,3,6] => 1
[6,3,5,1,4,2] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => 2
[6,3,5,2,1,4] => [4,1,2,5,3,6] => [4,1,5,2,3,6] => 2
[6,3,5,2,4,1] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => 1
[6,3,5,4,1,2] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => 1
[6,3,5,4,2,1] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => 1
[6,4,1,2,3,5] => [5,3,2,1,4,6] => [2,3,5,1,4,6] => 1
[6,4,1,2,5,3] => [3,5,2,1,4,6] => [2,5,3,1,4,6] => 2
[6,4,1,3,2,5] => [5,2,3,1,4,6] => [3,5,2,1,4,6] => 2
[6,4,1,3,5,2] => [2,5,3,1,4,6] => [3,2,5,1,4,6] => 2
[6,4,1,5,2,3] => [3,2,5,1,4,6] => [5,3,2,1,4,6] => 3
[6,4,1,5,3,2] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => 3
[6,4,2,1,3,5] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => 2
[6,4,2,1,5,3] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => 3
[6,4,2,3,1,5] => [5,1,3,2,4,6] => [5,3,1,2,4,6] => 3
[6,4,2,3,5,1] => [1,5,3,2,4,6] => [1,3,5,2,4,6] => 1
[6,4,2,5,1,3] => [3,1,5,2,4,6] => [3,5,1,2,4,6] => 2
[6,4,2,5,3,1] => [1,3,5,2,4,6] => [1,5,3,2,4,6] => 2
[6,4,3,1,2,5] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => 2
[6,4,3,1,5,2] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => 3
[6,4,3,2,1,5] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => 3
[6,4,3,2,5,1] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => 2
[6,4,3,5,1,2] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => 1
[6,4,3,5,2,1] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => 1
[6,4,5,1,2,3] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => 0
[6,4,5,1,3,2] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => 1
[6,4,5,2,1,3] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => 1
[6,4,5,2,3,1] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 0
[6,4,5,3,1,2] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 0
[6,4,5,3,2,1] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 0
[6,5,1,2,3,4] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => 0
[6,5,1,2,4,3] => [3,4,2,1,5,6] => [2,4,3,1,5,6] => 1
[6,5,1,3,2,4] => [4,2,3,1,5,6] => [3,4,2,1,5,6] => 1
[6,5,1,3,4,2] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => 1
[6,5,1,4,2,3] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => 2
[6,5,1,4,3,2] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => 2
[6,5,2,1,3,4] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => 1
[6,5,2,1,4,3] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => 2
[6,5,2,3,1,4] => [4,1,3,2,5,6] => [4,3,1,2,5,6] => 2
[6,5,2,3,4,1] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => 0
[6,5,2,4,1,3] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => 1
[6,5,2,4,3,1] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => 1
[6,5,3,1,2,4] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => 1
[6,5,3,1,4,2] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => 2
[6,5,3,2,1,4] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => 2
[6,5,3,2,4,1] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 1
[6,5,3,4,1,2] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 0
[6,5,3,4,2,1] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 0
[6,5,4,1,2,3] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 0
[6,5,4,1,3,2] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => 1
[6,5,4,2,1,3] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => 1
[6,5,4,2,3,1] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 0
[6,5,4,3,1,2] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 0
[6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => [1,3,4,5,6,7,2] => 0
[2,3,4,5,7,6,1] => [1,6,7,5,4,3,2] => [1,3,4,5,7,6,2] => 1
[2,3,4,6,5,7,1] => [1,7,5,6,4,3,2] => [1,3,4,6,7,5,2] => 1
[2,3,4,6,7,5,1] => [1,5,7,6,4,3,2] => [1,3,4,6,5,7,2] => 1
[2,3,4,7,5,6,1] => [1,6,5,7,4,3,2] => [1,3,4,7,6,5,2] => 2
[2,3,4,7,6,5,1] => [1,5,6,7,4,3,2] => [1,3,4,7,5,6,2] => 2
[2,3,5,4,6,7,1] => [1,7,6,4,5,3,2] => [1,3,5,6,4,7,2] => 1
[2,3,5,4,7,6,1] => [1,6,7,4,5,3,2] => [1,3,5,7,4,6,2] => 2
[2,3,5,6,4,7,1] => [1,7,4,6,5,3,2] => [1,3,5,6,7,2,4] => 1
[2,3,5,6,7,4,1] => [1,4,7,6,5,3,2] => [1,3,5,4,6,7,2] => 1
[2,3,5,7,4,6,1] => [1,6,4,7,5,3,2] => [1,3,5,7,6,2,4] => 2
[2,3,5,7,6,4,1] => [1,4,6,7,5,3,2] => [1,3,5,4,7,6,2] => 2
[2,3,6,4,5,7,1] => [1,7,5,4,6,3,2] => [1,3,6,5,7,4,2] => 2
[2,3,6,4,7,5,1] => [1,5,7,4,6,3,2] => [1,3,6,7,5,4,2] => 3
[2,3,6,5,4,7,1] => [1,7,4,5,6,3,2] => [1,3,6,7,4,5,2] => 3
[2,3,6,5,7,4,1] => [1,4,7,5,6,3,2] => [1,3,6,4,7,5,2] => 2
[2,3,6,7,4,5,1] => [1,5,4,7,6,3,2] => [1,3,6,5,4,7,2] => 2
[2,3,6,7,5,4,1] => [1,4,5,7,6,3,2] => [1,3,6,4,5,7,2] => 2
[2,3,7,4,5,6,1] => [1,6,5,4,7,3,2] => [1,3,7,5,6,4,2] => 3
[2,3,7,4,6,5,1] => [1,5,6,4,7,3,2] => [1,3,7,6,5,4,2] => 4
[2,3,7,5,4,6,1] => [1,6,4,5,7,3,2] => [1,3,7,6,4,5,2] => 4
[2,3,7,5,6,4,1] => [1,4,6,5,7,3,2] => [1,3,7,4,6,5,2] => 3
[2,3,7,6,4,5,1] => [1,5,4,6,7,3,2] => [1,3,7,5,4,6,2] => 3
[2,3,7,6,5,4,1] => [1,4,5,6,7,3,2] => [1,3,7,4,5,6,2] => 3
[2,4,3,5,6,7,1] => [1,7,6,5,3,4,2] => [1,4,5,3,6,7,2] => 1
[2,4,3,5,7,6,1] => [1,6,7,5,3,4,2] => [1,4,5,3,7,6,2] => 2
[2,4,3,6,5,7,1] => [1,7,5,6,3,4,2] => [1,4,6,3,7,5,2] => 2
[2,4,3,6,7,5,1] => [1,5,7,6,3,4,2] => [1,4,6,3,5,7,2] => 2
[2,4,5,3,6,7,1] => [1,7,6,3,5,4,2] => [1,4,5,6,2,7,3] => 1
[2,4,5,3,7,6,1] => [1,6,7,3,5,4,2] => [1,4,5,7,2,6,3] => 2
[2,4,5,6,3,7,1] => [1,7,3,6,5,4,2] => [1,4,5,6,7,3,2] => 1
[2,4,5,6,7,3,1] => [1,3,7,6,5,4,2] => [1,4,3,5,6,7,2] => 1
[2,4,5,7,3,6,1] => [1,6,3,7,5,4,2] => [1,4,5,7,6,3,2] => 2
[2,4,5,7,6,3,1] => [1,3,6,7,5,4,2] => [1,4,3,5,7,6,2] => 2
[2,4,6,5,7,3,1] => [1,3,7,5,6,4,2] => [1,4,3,6,7,5,2] => 2
[2,4,6,7,3,5,1] => [1,5,3,7,6,4,2] => [1,4,6,5,2,7,3] => 2
[2,4,6,7,5,3,1] => [1,3,5,7,6,4,2] => [1,4,3,6,5,7,2] => 2
[2,4,7,5,6,3,1] => [1,3,6,5,7,4,2] => [1,4,3,7,6,5,2] => 3
[2,4,7,6,5,3,1] => [1,3,5,6,7,4,2] => [1,4,3,7,5,6,2] => 3
[3,2,4,5,6,7,1] => [1,7,6,5,4,2,3] => [1,4,2,5,6,7,3] => 1
[3,2,4,5,7,6,1] => [1,6,7,5,4,2,3] => [1,4,2,5,7,6,3] => 2
[3,2,4,6,5,7,1] => [1,7,5,6,4,2,3] => [1,4,2,6,7,5,3] => 2
[3,2,4,6,7,5,1] => [1,5,7,6,4,2,3] => [1,4,2,6,5,7,3] => 2
[3,2,4,7,5,6,1] => [1,6,5,7,4,2,3] => [1,4,2,7,6,5,3] => 3
[3,2,4,7,6,5,1] => [1,5,6,7,4,2,3] => [1,4,2,7,5,6,3] => 3
[3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => [1,2,4,5,6,7,3] => 0
[3,4,5,7,6,2,1] => [1,2,6,7,5,4,3] => [1,2,4,5,7,6,3] => 1
[3,4,6,5,7,2,1] => [1,2,7,5,6,4,3] => [1,2,4,6,7,5,3] => 1
[3,4,6,7,5,2,1] => [1,2,5,7,6,4,3] => [1,2,4,6,5,7,3] => 1
[3,4,7,5,6,2,1] => [1,2,6,5,7,4,3] => [1,2,4,7,6,5,3] => 2
[3,4,7,6,5,2,1] => [1,2,5,6,7,4,3] => [1,2,4,7,5,6,3] => 2
[3,5,4,6,7,2,1] => [1,2,7,6,4,5,3] => [1,2,5,6,4,7,3] => 1
[3,5,4,7,6,2,1] => [1,2,6,7,4,5,3] => [1,2,5,7,4,6,3] => 2
[3,5,6,4,7,2,1] => [1,2,7,4,6,5,3] => [1,2,5,6,7,3,4] => 1
[3,5,6,7,2,4,1] => [1,4,2,7,6,5,3] => [1,4,5,2,6,7,3] => 1
[3,5,6,7,4,2,1] => [1,2,4,7,6,5,3] => [1,2,5,4,6,7,3] => 1
[3,5,7,4,6,2,1] => [1,2,6,4,7,5,3] => [1,2,5,7,6,3,4] => 2
[3,5,7,6,2,4,1] => [1,4,2,6,7,5,3] => [1,4,5,2,7,6,3] => 2
[3,5,7,6,4,2,1] => [1,2,4,6,7,5,3] => [1,2,5,4,7,6,3] => 2
[3,6,2,4,5,7,1] => [1,7,5,4,2,6,3] => [1,4,5,7,6,2,3] => 2
[3,6,4,5,7,2,1] => [1,2,7,5,4,6,3] => [1,2,6,5,7,4,3] => 2
[3,6,4,7,5,2,1] => [1,2,5,7,4,6,3] => [1,2,6,7,5,4,3] => 3
[3,6,5,4,7,2,1] => [1,2,7,4,5,6,3] => [1,2,6,7,4,5,3] => 3
[3,6,5,7,2,4,1] => [1,4,2,7,5,6,3] => [1,4,6,2,7,5,3] => 2
[3,6,5,7,4,2,1] => [1,2,4,7,5,6,3] => [1,2,6,4,7,5,3] => 2
[3,6,7,2,4,5,1] => [1,5,4,2,7,6,3] => [1,4,5,6,3,7,2] => 1
[3,6,7,4,5,2,1] => [1,2,5,4,7,6,3] => [1,2,6,5,4,7,3] => 2
[3,6,7,5,2,4,1] => [1,4,2,5,7,6,3] => [1,4,6,2,5,7,3] => 2
[3,6,7,5,4,2,1] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3] => 2
[3,7,2,4,5,6,1] => [1,6,5,4,2,7,3] => [1,4,5,6,7,2,3] => 1
[3,7,4,5,6,2,1] => [1,2,6,5,4,7,3] => [1,2,7,5,6,4,3] => 3
[3,7,4,6,5,2,1] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => 4
[3,7,5,4,6,2,1] => [1,2,6,4,5,7,3] => [1,2,7,6,4,5,3] => 4
[3,7,5,6,4,2,1] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => 3
[3,7,6,2,4,5,1] => [1,5,4,2,6,7,3] => [1,4,5,7,3,6,2] => 2
[3,7,6,4,5,2,1] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => 3
[3,7,6,5,4,2,1] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => 3
[4,2,3,5,6,7,1] => [1,7,6,5,3,2,4] => [1,3,5,2,6,7,4] => 1
[4,2,3,5,7,6,1] => [1,6,7,5,3,2,4] => [1,3,5,2,7,6,4] => 2
[4,2,3,6,5,7,1] => [1,7,5,6,3,2,4] => [1,3,6,2,7,5,4] => 2
[4,2,3,6,7,5,1] => [1,5,7,6,3,2,4] => [1,3,6,2,5,7,4] => 2
[4,2,3,7,5,6,1] => [1,6,5,7,3,2,4] => [1,3,7,2,6,5,4] => 3
[4,2,3,7,6,5,1] => [1,5,6,7,3,2,4] => [1,3,7,2,5,6,4] => 3
[4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => [1,2,5,3,6,7,4] => 1
[4,3,5,7,6,2,1] => [1,2,6,7,5,3,4] => [1,2,5,3,7,6,4] => 2
[4,3,6,5,7,2,1] => [1,2,7,5,6,3,4] => [1,2,6,3,7,5,4] => 2
[4,3,6,7,5,2,1] => [1,2,5,7,6,3,4] => [1,2,6,3,5,7,4] => 2
[4,3,7,5,6,2,1] => [1,2,6,5,7,3,4] => [1,2,7,3,6,5,4] => 3
[4,3,7,6,5,2,1] => [1,2,5,6,7,3,4] => [1,2,7,3,5,6,4] => 3
[4,5,2,3,6,7,1] => [1,7,6,3,2,5,4] => [1,3,6,5,2,7,4] => 2
[4,5,2,3,7,6,1] => [1,6,7,3,2,5,4] => [1,3,7,5,2,6,4] => 3
[4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => [1,2,6,5,3,7,4] => 2
[4,5,3,7,6,2,1] => [1,2,6,7,3,5,4] => [1,2,7,5,3,6,4] => 3
[4,5,6,2,3,7,1] => [1,7,3,2,6,5,4] => [1,3,7,5,6,2,4] => 3
[4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => [1,2,7,5,6,3,4] => 3
[4,5,6,7,2,3,1] => [1,3,2,7,6,5,4] => [1,3,2,5,6,7,4] => 0
[4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => [1,2,3,5,6,7,4] => 0
[4,5,7,2,3,6,1] => [1,6,3,2,7,5,4] => [1,3,6,5,7,2,4] => 2
[4,5,7,3,6,2,1] => [1,2,6,3,7,5,4] => [1,2,6,5,7,3,4] => 2
[4,5,7,6,2,3,1] => [1,3,2,6,7,5,4] => [1,3,2,5,7,6,4] => 1
[4,5,7,6,3,2,1] => [1,2,3,6,7,5,4] => [1,2,3,5,7,6,4] => 1
[4,6,2,3,5,7,1] => [1,7,5,3,2,6,4] => [1,3,5,7,6,4,2] => 2
[4,6,2,3,7,5,1] => [1,5,7,3,2,6,4] => [1,3,7,6,5,2,4] => 4
[4,6,3,5,7,2,1] => [1,2,7,5,3,6,4] => [1,2,5,7,6,4,3] => 2
[4,6,3,7,5,2,1] => [1,2,5,7,3,6,4] => [1,2,7,6,5,3,4] => 4
[4,6,5,2,3,7,1] => [1,7,3,2,5,6,4] => [1,3,7,6,2,5,4] => 4
[4,6,5,3,7,2,1] => [1,2,7,3,5,6,4] => [1,2,7,6,3,5,4] => 4
[4,6,5,7,2,3,1] => [1,3,2,7,5,6,4] => [1,3,2,6,7,5,4] => 1
[4,6,5,7,3,2,1] => [1,2,3,7,5,6,4] => [1,2,3,6,7,5,4] => 1
[4,6,7,2,3,5,1] => [1,5,3,2,7,6,4] => [1,3,5,6,2,7,4] => 1
[4,6,7,3,5,2,1] => [1,2,5,3,7,6,4] => [1,2,5,6,3,7,4] => 1
[4,6,7,5,2,3,1] => [1,3,2,5,7,6,4] => [1,3,2,6,5,7,4] => 1
[4,6,7,5,3,2,1] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4] => 1
[4,7,2,3,5,6,1] => [1,6,5,3,2,7,4] => [1,3,5,6,7,4,2] => 1
[4,7,2,3,6,5,1] => [1,5,6,3,2,7,4] => [1,3,6,7,5,2,4] => 3
[4,7,3,5,6,2,1] => [1,2,6,5,3,7,4] => [1,2,5,6,7,4,3] => 1
[4,7,3,6,5,2,1] => [1,2,5,6,3,7,4] => [1,2,6,7,5,3,4] => 3
[4,7,5,2,3,6,1] => [1,6,3,2,5,7,4] => [1,3,6,7,2,5,4] => 3
[4,7,5,3,6,2,1] => [1,2,6,3,5,7,4] => [1,2,6,7,3,5,4] => 3
[4,7,5,6,2,3,1] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => 2
[4,7,5,6,3,2,1] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => 2
[4,7,6,2,3,5,1] => [1,5,3,2,6,7,4] => [1,3,5,7,2,6,4] => 2
[4,7,6,3,5,2,1] => [1,2,5,3,6,7,4] => [1,2,5,7,3,6,4] => 2
[4,7,6,5,2,3,1] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => 2
[4,7,6,5,3,2,1] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => 2
[5,2,3,4,6,7,1] => [1,7,6,4,3,2,5] => [1,3,4,6,2,7,5] => 1
[5,2,3,4,7,6,1] => [1,6,7,4,3,2,5] => [1,3,4,7,2,6,5] => 2
[5,2,3,6,4,7,1] => [1,7,4,6,3,2,5] => [1,3,6,7,2,4,5] => 3
[5,2,3,6,7,4,1] => [1,4,7,6,3,2,5] => [1,3,6,4,2,7,5] => 2
[5,2,3,7,4,6,1] => [1,6,4,7,3,2,5] => [1,3,7,6,2,4,5] => 4
[5,2,3,7,6,4,1] => [1,4,6,7,3,2,5] => [1,3,7,4,2,6,5] => 3
[5,2,4,3,6,7,1] => [1,7,6,3,4,2,5] => [1,4,6,3,2,7,5] => 2
[5,2,4,6,7,3,1] => [1,3,7,6,4,2,5] => [1,4,3,6,2,7,5] => 2
[5,2,4,7,6,3,1] => [1,3,6,7,4,2,5] => [1,4,3,7,2,6,5] => 3
[5,3,2,4,6,7,1] => [1,7,6,4,2,3,5] => [1,4,2,6,3,7,5] => 2
[5,3,2,4,7,6,1] => [1,6,7,4,2,3,5] => [1,4,2,7,3,6,5] => 3
[5,3,4,6,7,2,1] => [1,2,7,6,4,3,5] => [1,2,4,6,3,7,5] => 1
[5,3,4,7,6,2,1] => [1,2,6,7,4,3,5] => [1,2,4,7,3,6,5] => 2
[5,3,6,4,7,2,1] => [1,2,7,4,6,3,5] => [1,2,6,7,3,4,5] => 3
[5,3,6,7,2,4,1] => [1,4,2,7,6,3,5] => [1,4,6,2,3,7,5] => 2
[5,3,6,7,4,2,1] => [1,2,4,7,6,3,5] => [1,2,6,4,3,7,5] => 2
[5,3,7,4,6,2,1] => [1,2,6,4,7,3,5] => [1,2,7,6,3,4,5] => 4
[5,3,7,6,4,2,1] => [1,2,4,6,7,3,5] => [1,2,7,4,3,6,5] => 3
[5,4,2,3,6,7,1] => [1,7,6,3,2,4,5] => [1,3,6,2,4,7,5] => 2
[5,4,2,3,7,6,1] => [1,6,7,3,2,4,5] => [1,3,7,2,4,6,5] => 3
[5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => [1,2,6,3,4,7,5] => 2
[5,4,3,7,6,2,1] => [1,2,6,7,3,4,5] => [1,2,7,3,4,6,5] => 3
[5,4,6,2,3,7,1] => [1,7,3,2,6,4,5] => [1,3,7,6,4,2,5] => 4
[5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => [1,2,7,6,4,3,5] => 4
[5,4,6,7,2,3,1] => [1,3,2,7,6,4,5] => [1,3,2,6,4,7,5] => 1
[5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => [1,2,3,6,4,7,5] => 1
[5,4,7,2,3,6,1] => [1,6,3,2,7,4,5] => [1,3,6,7,4,2,5] => 3
[5,4,7,3,6,2,1] => [1,2,6,3,7,4,5] => [1,2,6,7,4,3,5] => 3
[5,4,7,6,2,3,1] => [1,3,2,6,7,4,5] => [1,3,2,7,4,6,5] => 2
[5,4,7,6,3,2,1] => [1,2,3,6,7,4,5] => [1,2,3,7,4,6,5] => 2
[5,6,2,3,4,7,1] => [1,7,4,3,2,6,5] => [1,3,4,7,6,2,5] => 2
[5,6,2,3,7,4,1] => [1,4,7,3,2,6,5] => [1,3,7,4,6,2,5] => 3
[5,6,2,4,7,3,1] => [1,3,7,4,2,6,5] => [1,4,3,7,6,2,5] => 3
[5,6,3,2,4,7,1] => [1,7,4,2,3,6,5] => [1,4,2,7,6,3,5] => 3
[5,6,3,4,7,2,1] => [1,2,7,4,3,6,5] => [1,2,4,7,6,3,5] => 2
[5,6,3,7,4,2,1] => [1,2,4,7,3,6,5] => [1,2,7,4,6,3,5] => 3
[5,6,4,2,3,7,1] => [1,7,3,2,4,6,5] => [1,3,7,2,6,4,5] => 3
[5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => [1,2,7,3,6,4,5] => 3
[5,6,4,7,2,3,1] => [1,3,2,7,4,6,5] => [1,3,2,7,6,4,5] => 2
[5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => [1,2,3,7,6,4,5] => 2
[5,6,7,2,3,4,1] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => 0
[5,6,7,2,4,3,1] => [1,3,4,2,7,6,5] => [1,4,3,2,6,7,5] => 1
[5,6,7,3,2,4,1] => [1,4,2,3,7,6,5] => [1,4,2,3,6,7,5] => 1
[5,6,7,3,4,2,1] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => 0
[5,6,7,4,2,3,1] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => 0
[5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => 0
[5,7,2,3,4,6,1] => [1,6,4,3,2,7,5] => [1,3,4,6,7,2,5] => 1
[5,7,2,3,6,4,1] => [1,4,6,3,2,7,5] => [1,3,6,4,7,2,5] => 2
[5,7,2,4,3,6,1] => [1,6,3,4,2,7,5] => [1,4,6,3,7,2,5] => 2
[5,7,2,4,6,3,1] => [1,3,6,4,2,7,5] => [1,4,3,6,7,2,5] => 2
[5,7,3,2,4,6,1] => [1,6,4,2,3,7,5] => [1,4,2,6,7,3,5] => 2
[5,7,3,4,6,2,1] => [1,2,6,4,3,7,5] => [1,2,4,6,7,3,5] => 1
[5,7,3,6,2,4,1] => [1,4,2,6,3,7,5] => [1,4,6,2,7,3,5] => 2
[5,7,3,6,4,2,1] => [1,2,4,6,3,7,5] => [1,2,6,4,7,3,5] => 2
[5,7,4,2,3,6,1] => [1,6,3,2,4,7,5] => [1,3,6,2,7,4,5] => 2
[5,7,4,3,6,2,1] => [1,2,6,3,4,7,5] => [1,2,6,3,7,4,5] => 2
[5,7,4,6,2,3,1] => [1,3,2,6,4,7,5] => [1,3,2,6,7,4,5] => 1
[5,7,4,6,3,2,1] => [1,2,3,6,4,7,5] => [1,2,3,6,7,4,5] => 1
[5,7,6,2,3,4,1] => [1,4,3,2,6,7,5] => [1,3,4,2,7,6,5] => 1
[5,7,6,2,4,3,1] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => 2
[5,7,6,3,2,4,1] => [1,4,2,3,6,7,5] => [1,4,2,3,7,6,5] => 2
[5,7,6,3,4,2,1] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => 1
[5,7,6,4,2,3,1] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => 1
[5,7,6,4,3,2,1] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => 1
[6,2,3,4,5,7,1] => [1,7,5,4,3,2,6] => [1,3,4,5,7,2,6] => 1
[6,2,3,4,7,5,1] => [1,5,7,4,3,2,6] => [1,3,4,7,5,2,6] => 2
[6,2,3,5,4,7,1] => [1,7,4,5,3,2,6] => [1,3,5,7,4,2,6] => 2
[6,2,3,5,7,4,1] => [1,4,7,5,3,2,6] => [1,3,5,4,7,2,6] => 2
[6,2,3,7,4,5,1] => [1,5,4,7,3,2,6] => [1,3,7,5,4,2,6] => 3
[6,2,3,7,5,4,1] => [1,4,5,7,3,2,6] => [1,3,7,4,5,2,6] => 3
[6,2,4,3,5,7,1] => [1,7,5,3,4,2,6] => [1,4,5,3,7,2,6] => 2
[6,2,4,5,3,7,1] => [1,7,3,5,4,2,6] => [1,4,5,7,2,3,6] => 2
[6,2,4,5,7,3,1] => [1,3,7,5,4,2,6] => [1,4,3,5,7,2,6] => 2
[6,2,4,7,5,3,1] => [1,3,5,7,4,2,6] => [1,4,3,7,5,2,6] => 3
[6,3,2,4,5,7,1] => [1,7,5,4,2,3,6] => [1,4,2,5,7,3,6] => 2
[6,3,2,4,7,5,1] => [1,5,7,4,2,3,6] => [1,4,2,7,5,3,6] => 3
[6,3,4,5,7,2,1] => [1,2,7,5,4,3,6] => [1,2,4,5,7,3,6] => 1
[6,3,4,7,5,2,1] => [1,2,5,7,4,3,6] => [1,2,4,7,5,3,6] => 2
[6,3,5,4,7,2,1] => [1,2,7,4,5,3,6] => [1,2,5,7,4,3,6] => 2
[6,3,5,7,2,4,1] => [1,4,2,7,5,3,6] => [1,4,5,2,7,3,6] => 2
[6,3,5,7,4,2,1] => [1,2,4,7,5,3,6] => [1,2,5,4,7,3,6] => 2
[6,3,7,2,4,5,1] => [1,5,4,2,7,3,6] => [1,4,5,7,3,2,6] => 2
[6,3,7,4,5,2,1] => [1,2,5,4,7,3,6] => [1,2,7,5,4,3,6] => 3
[6,3,7,5,4,2,1] => [1,2,4,5,7,3,6] => [1,2,7,4,5,3,6] => 3
[6,4,2,3,5,7,1] => [1,7,5,3,2,4,6] => [1,3,5,2,7,4,6] => 2
[6,4,2,3,7,5,1] => [1,5,7,3,2,4,6] => [1,3,7,2,5,4,6] => 3
[6,4,3,5,7,2,1] => [1,2,7,5,3,4,6] => [1,2,5,3,7,4,6] => 2
[6,4,3,7,5,2,1] => [1,2,5,7,3,4,6] => [1,2,7,3,5,4,6] => 3
[6,4,5,2,3,7,1] => [1,7,3,2,5,4,6] => [1,3,7,5,2,4,6] => 3
[6,4,5,3,7,2,1] => [1,2,7,3,5,4,6] => [1,2,7,5,3,4,6] => 3
[6,4,5,7,2,3,1] => [1,3,2,7,5,4,6] => [1,3,2,5,7,4,6] => 1
[6,4,5,7,3,2,1] => [1,2,3,7,5,4,6] => [1,2,3,5,7,4,6] => 1
[6,4,7,2,3,5,1] => [1,5,3,2,7,4,6] => [1,3,5,7,2,4,6] => 2
[6,4,7,3,5,2,1] => [1,2,5,3,7,4,6] => [1,2,5,7,3,4,6] => 2
[6,4,7,5,2,3,1] => [1,3,2,5,7,4,6] => [1,3,2,7,5,4,6] => 2
[6,4,7,5,3,2,1] => [1,2,3,5,7,4,6] => [1,2,3,7,5,4,6] => 2
[6,5,2,3,4,7,1] => [1,7,4,3,2,5,6] => [1,3,4,7,2,5,6] => 2
[6,5,2,3,7,4,1] => [1,4,7,3,2,5,6] => [1,3,7,4,2,5,6] => 3
[6,5,2,4,7,3,1] => [1,3,7,4,2,5,6] => [1,4,3,7,2,5,6] => 3
[6,5,3,2,4,7,1] => [1,7,4,2,3,5,6] => [1,4,2,7,3,5,6] => 3
[6,5,3,4,7,2,1] => [1,2,7,4,3,5,6] => [1,2,4,7,3,5,6] => 2
[6,5,3,7,4,2,1] => [1,2,4,7,3,5,6] => [1,2,7,4,3,5,6] => 3
[6,5,4,2,3,7,1] => [1,7,3,2,4,5,6] => [1,3,7,2,4,5,6] => 3
[6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => 3
[6,5,4,7,2,3,1] => [1,3,2,7,4,5,6] => [1,3,2,7,4,5,6] => 2
[6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => 2
[6,5,7,2,3,4,1] => [1,4,3,2,7,5,6] => [1,3,4,2,7,5,6] => 1
[6,5,7,2,4,3,1] => [1,3,4,2,7,5,6] => [1,4,3,2,7,5,6] => 2
[6,5,7,3,2,4,1] => [1,4,2,3,7,5,6] => [1,4,2,3,7,5,6] => 2
[6,5,7,3,4,2,1] => [1,2,4,3,7,5,6] => [1,2,4,3,7,5,6] => 1
[6,5,7,4,2,3,1] => [1,3,2,4,7,5,6] => [1,3,2,4,7,5,6] => 1
[6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => 1
[6,7,2,3,4,5,1] => [1,5,4,3,2,7,6] => [1,3,4,5,2,7,6] => 0
[6,7,2,3,5,4,1] => [1,4,5,3,2,7,6] => [1,3,5,4,2,7,6] => 1
[6,7,2,4,3,5,1] => [1,5,3,4,2,7,6] => [1,4,5,3,2,7,6] => 1
[6,7,2,4,5,3,1] => [1,3,5,4,2,7,6] => [1,4,3,5,2,7,6] => 1
[6,7,3,2,4,5,1] => [1,5,4,2,3,7,6] => [1,4,2,5,3,7,6] => 1
[6,7,3,4,5,2,1] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => 0
[6,7,3,5,2,4,1] => [1,4,2,5,3,7,6] => [1,4,5,2,3,7,6] => 1
[6,7,3,5,4,2,1] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => 1
[6,7,4,2,3,5,1] => [1,5,3,2,4,7,6] => [1,3,5,2,4,7,6] => 1
[6,7,4,3,5,2,1] => [1,2,5,3,4,7,6] => [1,2,5,3,4,7,6] => 1
[6,7,4,5,2,3,1] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 0
[6,7,4,5,3,2,1] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => 0
[6,7,5,2,3,4,1] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => 0
[6,7,5,2,4,3,1] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => 1
[6,7,5,3,2,4,1] => [1,4,2,3,5,7,6] => [1,4,2,3,5,7,6] => 1
[6,7,5,3,4,2,1] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 0
[6,7,5,4,2,3,1] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 0
[6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => [1,3,4,5,6,2,7] => 0
[7,2,3,4,6,5,1] => [1,5,6,4,3,2,7] => [1,3,4,6,5,2,7] => 1
[7,2,3,5,4,6,1] => [1,6,4,5,3,2,7] => [1,3,5,6,4,2,7] => 1
[7,2,3,5,6,4,1] => [1,4,6,5,3,2,7] => [1,3,5,4,6,2,7] => 1
[7,2,3,6,4,5,1] => [1,5,4,6,3,2,7] => [1,3,6,5,4,2,7] => 2
[7,2,3,6,5,4,1] => [1,4,5,6,3,2,7] => [1,3,6,4,5,2,7] => 2
[7,2,4,3,5,6,1] => [1,6,5,3,4,2,7] => [1,4,5,3,6,2,7] => 1
[7,2,4,3,6,5,1] => [1,5,6,3,4,2,7] => [1,4,6,3,5,2,7] => 2
[7,2,4,5,3,6,1] => [1,6,3,5,4,2,7] => [1,4,5,6,2,3,7] => 1
[7,2,4,5,6,3,1] => [1,3,6,5,4,2,7] => [1,4,3,5,6,2,7] => 1
[7,2,4,6,3,5,1] => [1,5,3,6,4,2,7] => [1,4,6,5,2,3,7] => 2
[7,2,4,6,5,3,1] => [1,3,5,6,4,2,7] => [1,4,3,6,5,2,7] => 2
[7,3,2,4,5,6,1] => [1,6,5,4,2,3,7] => [1,4,2,5,6,3,7] => 1
[7,3,2,4,6,5,1] => [1,5,6,4,2,3,7] => [1,4,2,6,5,3,7] => 2
[7,3,4,5,6,2,1] => [1,2,6,5,4,3,7] => [1,2,4,5,6,3,7] => 0
[7,3,4,6,5,2,1] => [1,2,5,6,4,3,7] => [1,2,4,6,5,3,7] => 1
[7,3,5,2,4,6,1] => [1,6,4,2,5,3,7] => [1,4,6,5,3,2,7] => 2
[7,3,5,4,6,2,1] => [1,2,6,4,5,3,7] => [1,2,5,6,4,3,7] => 1
[7,3,5,6,2,4,1] => [1,4,2,6,5,3,7] => [1,4,5,2,6,3,7] => 1
[7,3,5,6,4,2,1] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7] => 1
[7,3,6,2,4,5,1] => [1,5,4,2,6,3,7] => [1,4,5,6,3,2,7] => 1
[7,3,6,4,5,2,1] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => 2
[7,3,6,5,2,4,1] => [1,4,2,5,6,3,7] => [1,4,6,2,5,3,7] => 2
[7,3,6,5,4,2,1] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => 2
[7,4,2,3,5,6,1] => [1,6,5,3,2,4,7] => [1,3,5,2,6,4,7] => 1
[7,4,2,3,6,5,1] => [1,5,6,3,2,4,7] => [1,3,6,2,5,4,7] => 2
[7,4,3,5,6,2,1] => [1,2,6,5,3,4,7] => [1,2,5,3,6,4,7] => 1
[7,4,3,6,5,2,1] => [1,2,5,6,3,4,7] => [1,2,6,3,5,4,7] => 2
[7,4,5,2,3,6,1] => [1,6,3,2,5,4,7] => [1,3,6,5,2,4,7] => 2
[7,4,5,3,6,2,1] => [1,2,6,3,5,4,7] => [1,2,6,5,3,4,7] => 2
[7,4,5,6,2,3,1] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => 0
[7,4,5,6,3,2,1] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => 0
[7,4,6,2,3,5,1] => [1,5,3,2,6,4,7] => [1,3,5,6,2,4,7] => 1
[7,4,6,3,5,2,1] => [1,2,5,3,6,4,7] => [1,2,5,6,3,4,7] => 1
[7,4,6,5,2,3,1] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => 1
[7,4,6,5,3,2,1] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => 1
[7,5,2,3,4,6,1] => [1,6,4,3,2,5,7] => [1,3,4,6,2,5,7] => 1
[7,5,2,3,6,4,1] => [1,4,6,3,2,5,7] => [1,3,6,4,2,5,7] => 2
[7,5,2,4,3,6,1] => [1,6,3,4,2,5,7] => [1,4,6,3,2,5,7] => 2
[7,5,2,4,6,3,1] => [1,3,6,4,2,5,7] => [1,4,3,6,2,5,7] => 2
[7,5,3,2,4,6,1] => [1,6,4,2,3,5,7] => [1,4,2,6,3,5,7] => 2
[7,5,3,4,6,2,1] => [1,2,6,4,3,5,7] => [1,2,4,6,3,5,7] => 1
[7,5,3,6,2,4,1] => [1,4,2,6,3,5,7] => [1,4,6,2,3,5,7] => 2
[7,5,3,6,4,2,1] => [1,2,4,6,3,5,7] => [1,2,6,4,3,5,7] => 2
[7,5,4,2,3,6,1] => [1,6,3,2,4,5,7] => [1,3,6,2,4,5,7] => 2
[7,5,4,3,6,2,1] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => 2
[7,5,4,6,2,3,1] => [1,3,2,6,4,5,7] => [1,3,2,6,4,5,7] => 1
[7,5,4,6,3,2,1] => [1,2,3,6,4,5,7] => [1,2,3,6,4,5,7] => 1
[7,5,6,2,3,4,1] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => 0
[7,5,6,2,4,3,1] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => 1
[7,5,6,3,2,4,1] => [1,4,2,3,6,5,7] => [1,4,2,3,6,5,7] => 1
[7,5,6,3,4,2,1] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 0
[7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 0
[7,5,6,4,3,2,1] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[7,6,2,3,4,5,1] => [1,5,4,3,2,6,7] => [1,3,4,5,2,6,7] => 0
[7,6,2,3,5,4,1] => [1,4,5,3,2,6,7] => [1,3,5,4,2,6,7] => 1
[7,6,2,4,3,5,1] => [1,5,3,4,2,6,7] => [1,4,5,3,2,6,7] => 1
[7,6,2,4,5,3,1] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => 1
[7,6,3,2,4,5,1] => [1,5,4,2,3,6,7] => [1,4,2,5,3,6,7] => 1
[7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => 0
[7,6,3,5,2,4,1] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => 1
[7,6,3,5,4,2,1] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => 1
[7,6,4,2,3,5,1] => [1,5,3,2,4,6,7] => [1,3,5,2,4,6,7] => 1
[7,6,4,3,5,2,1] => [1,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => 1
[7,6,4,5,2,3,1] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 0
[7,6,4,5,3,2,1] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 0
[7,6,5,2,3,4,1] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => 0
[7,6,5,2,4,3,1] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => 1
[7,6,5,3,2,4,1] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => 1
[7,6,5,3,4,2,1] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 0
[7,6,5,4,2,3,1] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,2 8,10,6 16,34,40,24,6 32,98,170,192,138,66,24
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + 2\ q$
$F_{4} = 8 + 10\ q + 6\ q^{2}$
$F_{5} = 16 + 34\ q + 40\ q^{2} + 24\ q^{3} + 6\ q^{4}$
$F_{6} = 32 + 98\ q + 170\ q^{2} + 192\ q^{3} + 138\ q^{4} + 66\ q^{5} + 24\ q^{6}$
Description
The number of invisible inversions of a permutation.
A visible inversion of a permutation $\pi$ is a pair $i < j$ such that $\pi(j) \leq \min(i, \pi(i))$. Thus, an invisible inversion satisfies $\pi(i) > \pi(j) > i$.
A visible inversion of a permutation $\pi$ is a pair $i < j$ such that $\pi(j) \leq \min(i, \pi(i))$. Thus, an invisible inversion satisfies $\pi(i) > \pi(j) > i$.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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