Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St000732: Permutations ⟶ ℤ
Values
[1,2] => [1,2] => [1,2] => [2,1] => 0
[2,1] => [2,1] => [1,2] => [2,1] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [3,2,1] => 0
[1,3,2] => [1,3,2] => [1,2,3] => [3,2,1] => 0
[2,1,3] => [2,1,3] => [1,2,3] => [3,2,1] => 0
[2,3,1] => [3,2,1] => [1,3,2] => [2,3,1] => 0
[3,1,2] => [3,2,1] => [1,3,2] => [2,3,1] => 0
[3,2,1] => [3,2,1] => [1,3,2] => [2,3,1] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,3,4] => [4,3,2,1] => 0
[1,3,2,4] => [1,3,2,4] => [1,2,3,4] => [4,3,2,1] => 0
[1,3,4,2] => [1,4,3,2] => [1,2,4,3] => [3,4,2,1] => 0
[1,4,2,3] => [1,4,3,2] => [1,2,4,3] => [3,4,2,1] => 0
[1,4,3,2] => [1,4,3,2] => [1,2,4,3] => [3,4,2,1] => 0
[2,1,3,4] => [2,1,3,4] => [1,2,3,4] => [4,3,2,1] => 0
[2,1,4,3] => [2,1,4,3] => [1,2,3,4] => [4,3,2,1] => 0
[2,3,1,4] => [3,2,1,4] => [1,3,2,4] => [4,2,3,1] => 0
[2,3,4,1] => [4,2,3,1] => [1,4,2,3] => [3,2,4,1] => 0
[2,4,1,3] => [3,4,1,2] => [1,3,2,4] => [4,2,3,1] => 0
[2,4,3,1] => [4,3,2,1] => [1,4,2,3] => [3,2,4,1] => 0
[3,1,2,4] => [3,2,1,4] => [1,3,2,4] => [4,2,3,1] => 0
[3,1,4,2] => [4,2,3,1] => [1,4,2,3] => [3,2,4,1] => 0
[3,2,1,4] => [3,2,1,4] => [1,3,2,4] => [4,2,3,1] => 0
[3,2,4,1] => [4,2,3,1] => [1,4,2,3] => [3,2,4,1] => 0
[3,4,1,2] => [4,3,2,1] => [1,4,2,3] => [3,2,4,1] => 0
[3,4,2,1] => [4,3,2,1] => [1,4,2,3] => [3,2,4,1] => 0
[4,1,2,3] => [4,2,3,1] => [1,4,2,3] => [3,2,4,1] => 0
[4,1,3,2] => [4,2,3,1] => [1,4,2,3] => [3,2,4,1] => 0
[4,2,1,3] => [4,3,2,1] => [1,4,2,3] => [3,2,4,1] => 0
[4,2,3,1] => [4,3,2,1] => [1,4,2,3] => [3,2,4,1] => 0
[4,3,1,2] => [4,3,2,1] => [1,4,2,3] => [3,2,4,1] => 0
[4,3,2,1] => [4,3,2,1] => [1,4,2,3] => [3,2,4,1] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,3,2,4,5] => [1,3,2,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[1,3,2,5,4] => [1,3,2,5,4] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[1,3,4,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => [5,3,4,2,1] => 0
[1,3,4,5,2] => [1,5,3,4,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,3,5,2,4] => [1,4,5,2,3] => [1,2,4,3,5] => [5,3,4,2,1] => 0
[1,3,5,4,2] => [1,5,4,3,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,4,2,3,5] => [1,4,3,2,5] => [1,2,4,3,5] => [5,3,4,2,1] => 0
[1,4,2,5,3] => [1,5,3,4,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,4,3,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => [5,3,4,2,1] => 0
[1,4,3,5,2] => [1,5,3,4,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,4,5,2,3] => [1,5,4,3,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,4,5,3,2] => [1,5,4,3,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,5,2,3,4] => [1,5,3,4,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,5,2,4,3] => [1,5,3,4,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,5,3,2,4] => [1,5,4,3,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,5,3,4,2] => [1,5,4,3,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,5,4,2,3] => [1,5,4,3,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,5,4,3,2] => [1,5,4,3,2] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[2,1,3,4,5] => [2,1,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[2,1,3,5,4] => [2,1,3,5,4] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[2,1,4,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[2,1,4,5,3] => [2,1,5,4,3] => [1,2,3,5,4] => [4,5,3,2,1] => 0
[2,1,5,3,4] => [2,1,5,4,3] => [1,2,3,5,4] => [4,5,3,2,1] => 0
[2,1,5,4,3] => [2,1,5,4,3] => [1,2,3,5,4] => [4,5,3,2,1] => 0
[2,3,1,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => [5,4,2,3,1] => 1
[2,3,1,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => [5,4,2,3,1] => 1
[2,3,4,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[2,3,4,5,1] => [5,2,3,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[2,3,5,1,4] => [4,2,5,1,3] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[2,3,5,4,1] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[2,4,1,3,5] => [3,4,1,2,5] => [1,3,2,4,5] => [5,4,2,3,1] => 1
[2,4,1,5,3] => [3,5,1,4,2] => [1,3,2,5,4] => [4,5,2,3,1] => 1
[2,4,3,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[2,4,3,5,1] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[2,4,5,1,3] => [4,5,3,1,2] => [1,4,2,5,3] => [3,5,2,4,1] => 0
[2,4,5,3,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[2,5,1,3,4] => [3,5,1,4,2] => [1,3,2,5,4] => [4,5,2,3,1] => 1
[2,5,1,4,3] => [3,5,1,4,2] => [1,3,2,5,4] => [4,5,2,3,1] => 1
[2,5,3,1,4] => [4,5,3,1,2] => [1,4,2,5,3] => [3,5,2,4,1] => 0
[2,5,3,4,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[2,5,4,1,3] => [4,5,3,1,2] => [1,4,2,5,3] => [3,5,2,4,1] => 0
[2,5,4,3,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[3,1,2,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => [5,4,2,3,1] => 1
[3,1,2,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => [5,4,2,3,1] => 1
[3,1,4,2,5] => [4,2,3,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[3,1,4,5,2] => [5,2,3,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[3,1,5,2,4] => [4,2,5,1,3] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[3,1,5,4,2] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[3,2,1,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => [5,4,2,3,1] => 1
[3,2,1,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => [5,4,2,3,1] => 1
[3,2,4,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[3,2,4,5,1] => [5,2,3,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[3,2,5,1,4] => [4,2,5,1,3] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[3,2,5,4,1] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[3,4,1,2,5] => [4,3,2,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[3,4,1,5,2] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[3,4,2,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[3,4,2,5,1] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[3,4,5,1,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[3,4,5,2,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[3,5,1,2,4] => [4,5,3,1,2] => [1,4,2,5,3] => [3,5,2,4,1] => 0
[3,5,1,4,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[3,5,2,1,4] => [4,5,3,1,2] => [1,4,2,5,3] => [3,5,2,4,1] => 0
>>> Load all 872 entries. <<<[3,5,2,4,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[3,5,4,1,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[3,5,4,2,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,1,2,3,5] => [4,2,3,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[4,1,2,5,3] => [5,2,3,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[4,1,3,2,5] => [4,2,3,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[4,1,3,5,2] => [5,2,3,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[4,1,5,2,3] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[4,1,5,3,2] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[4,2,1,3,5] => [4,3,2,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[4,2,1,5,3] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[4,2,3,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[4,2,3,5,1] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[4,2,5,1,3] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,2,5,3,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,3,1,2,5] => [4,3,2,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[4,3,1,5,2] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[4,3,2,1,5] => [4,3,2,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => 0
[4,3,2,5,1] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[4,3,5,1,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,3,5,2,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,5,1,2,3] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,5,1,3,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,5,2,1,3] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,5,2,3,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,5,3,1,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[4,5,3,2,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,1,2,3,4] => [5,2,3,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[5,1,2,4,3] => [5,2,3,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[5,1,3,2,4] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[5,1,3,4,2] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[5,1,4,2,3] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[5,1,4,3,2] => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[5,2,1,3,4] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[5,2,1,4,3] => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[5,2,3,1,4] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,2,3,4,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,2,4,1,3] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,2,4,3,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,3,1,2,4] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,3,1,4,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,3,2,1,4] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,3,2,4,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,3,4,1,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,3,4,2,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,4,1,2,3] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,4,1,3,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,4,2,1,3] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,4,2,3,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,4,3,1,2] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[5,4,3,2,1] => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,3,5,2,6,4] => [1,4,6,2,5,3] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => 0
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,3,5,4,6,2] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [1,2,5,3,6,4] => [4,6,3,5,2,1] => 0
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,3,6,2,4,5] => [1,4,6,2,5,3] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => 0
[1,3,6,2,5,4] => [1,4,6,2,5,3] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => 0
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [1,2,5,3,6,4] => [4,6,3,5,2,1] => 0
[1,3,6,4,5,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [1,2,5,3,6,4] => [4,6,3,5,2,1] => 0
[1,3,6,5,4,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,4,2,6,5,3] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,4,3,6,5,2] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,4,5,2,6,3] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,4,5,3,6,2] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,4,6,2,3,5] => [1,5,6,4,2,3] => [1,2,5,3,6,4] => [4,6,3,5,2,1] => 0
[1,4,6,2,5,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,4,6,3,2,5] => [1,5,6,4,2,3] => [1,2,5,3,6,4] => [4,6,3,5,2,1] => 0
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,4,6,5,2,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,4,6,5,3,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,5,2,6,3,4] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,5,2,6,4,3] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,5,3,2,6,4] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,5,3,4,6,2] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,5,4,2,6,3] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => 0
[1,5,4,3,6,2] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,4,6,3,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,6,2,3,4] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,6,2,4,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,6,3,2,4] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,5,6,4,3,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,2,3,4,5] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,6,2,3,5,4] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,6,2,4,3,5] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,6,2,4,5,3] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,6,2,5,3,4] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,6,2,5,4,3] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,6,3,2,4,5] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,6,3,2,5,4] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => 0
[1,6,3,4,2,5] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,4,2,3,5] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,4,3,2,5] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,4,5,3,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,5,2,3,4] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,5,2,4,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,5,3,2,4] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,5,3,4,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,5,4,2,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [4,5,3,6,2,1] => 0
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[2,1,3,5,6,4] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[2,1,4,5,3,6] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[2,1,4,5,6,3] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[2,1,5,3,6,4] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[2,1,5,4,6,3] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,6,3,4,5] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,6,3,5,4] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,6,4,3,5] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,6,4,5,3] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,6,5,3,4] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => 0
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[2,3,1,4,6,5] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[2,3,1,5,4,6] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[2,3,1,6,4,5] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[2,3,1,6,5,4] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[2,3,4,1,5,6] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[2,3,4,1,6,5] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[2,3,4,6,1,5] => [5,2,3,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[2,3,4,6,5,1] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[2,3,5,1,4,6] => [4,2,5,1,3,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[2,3,5,1,6,4] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[2,3,5,4,6,1] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[2,3,5,6,4,1] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[2,3,6,1,4,5] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[2,3,6,1,5,4] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[2,3,6,4,5,1] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[2,3,6,5,4,1] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 0
[2,4,1,5,6,3] => [3,6,1,4,5,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 0
[2,4,1,6,5,3] => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,4,3,1,5,6] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[2,4,3,1,6,5] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[2,4,3,5,6,1] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[2,4,3,6,1,5] => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[2,4,3,6,5,1] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => 1
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[2,4,5,3,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[2,4,5,6,1,3] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,4,5,6,3,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,4,6,1,3,5] => [4,5,6,1,2,3] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => 1
[2,4,6,1,5,3] => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,4,6,3,1,5] => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[2,4,6,5,1,3] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,4,6,5,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 0
[2,5,1,3,6,4] => [3,6,1,4,5,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 0
[2,5,1,4,6,3] => [3,6,1,4,5,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,5,1,6,3,4] => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,5,1,6,4,3] => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => 1
[2,5,3,1,6,4] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[2,5,3,4,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[2,5,3,6,1,4] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,5,3,6,4,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => 1
[2,5,4,1,6,3] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[2,5,4,3,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[2,5,4,6,1,3] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,5,4,6,3,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,5,6,1,3,4] => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,5,6,1,4,3] => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,5,6,3,1,4] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,5,6,3,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,5,6,4,1,3] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,5,6,4,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,6,1,3,4,5] => [3,6,1,4,5,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,6,1,3,5,4] => [3,6,1,4,5,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,6,1,4,3,5] => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,6,1,4,5,3] => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,6,1,5,3,4] => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,6,1,5,4,3] => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => 0
[2,6,3,1,4,5] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,6,3,1,5,4] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,6,3,4,1,5] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,6,3,4,5,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,6,3,5,1,4] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,6,3,5,4,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,6,4,1,3,5] => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,6,4,1,5,3] => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,6,4,3,1,5] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,6,4,3,5,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,6,4,5,1,3] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,6,4,5,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,6,5,1,3,4] => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,6,5,1,4,3] => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[2,6,5,3,1,4] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,6,5,3,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[2,6,5,4,1,3] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[2,6,5,4,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[3,1,2,5,6,4] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[3,1,2,6,5,4] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[3,1,4,2,5,6] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,1,4,2,6,5] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,1,4,5,6,2] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,1,4,6,2,5] => [5,2,3,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,1,4,6,5,2] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,1,5,2,4,6] => [4,2,5,1,3,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,1,5,2,6,4] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,1,5,4,6,2] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,1,5,6,2,4] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[3,1,5,6,4,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[3,1,6,2,4,5] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[3,1,6,2,5,4] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[3,1,6,4,5,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[3,1,6,5,2,4] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[3,1,6,5,4,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[3,2,1,5,6,4] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[3,2,1,6,4,5] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[3,2,4,1,5,6] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,2,4,1,6,5] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,2,4,5,6,1] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,2,4,6,1,5] => [5,2,3,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,2,4,6,5,1] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,2,5,1,4,6] => [4,2,5,1,3,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,2,5,1,6,4] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,2,5,4,6,1] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,2,5,6,1,4] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[3,2,5,6,4,1] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[3,2,6,1,4,5] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[3,2,6,1,5,4] => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => 1
[3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[3,2,6,4,5,1] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[3,2,6,5,4,1] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,4,1,5,6,2] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,4,1,6,2,5] => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,4,1,6,5,2] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,4,2,1,5,6] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,4,2,1,6,5] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,4,2,5,6,1] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,4,2,6,1,5] => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[3,4,2,6,5,1] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[3,4,5,1,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[3,4,5,2,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[3,4,5,6,1,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,4,5,6,2,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,4,6,1,2,5] => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[3,4,6,1,5,2] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[3,4,6,2,1,5] => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[3,4,6,2,5,1] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[3,4,6,5,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,4,6,5,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => 1
[3,5,1,2,6,4] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[3,5,1,4,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[3,5,1,6,2,4] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,5,1,6,4,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => 1
[3,5,2,1,6,4] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[3,5,2,4,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[3,5,2,6,1,4] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,5,2,6,4,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[3,5,4,1,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[3,5,4,2,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[3,5,4,6,1,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,5,4,6,2,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,5,6,1,2,4] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,5,6,1,4,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,5,6,2,1,4] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,5,6,2,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,5,6,4,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,5,6,4,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,1,2,4,5] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[3,6,1,2,5,4] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[3,6,1,4,2,5] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,6,1,4,5,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,1,5,2,4] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,6,1,5,4,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,2,1,4,5] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[3,6,2,1,5,4] => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => 1
[3,6,2,4,1,5] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,6,2,4,5,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,2,5,1,4] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,6,2,5,4,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,4,1,2,5] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,6,4,1,5,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,4,2,1,5] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,6,4,2,5,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,4,5,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,4,5,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,5,1,2,4] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,6,5,1,4,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,5,2,1,4] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[3,6,5,2,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,5,4,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[3,6,5,4,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,1,2,3,5,6] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,1,2,3,6,5] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,1,2,5,6,3] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,1,2,6,3,5] => [5,2,3,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,1,2,6,5,3] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,1,3,2,5,6] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,1,3,2,6,5] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,1,3,5,6,2] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,1,3,6,2,5] => [5,2,3,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,1,3,6,5,2] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,1,5,2,6,3] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,1,5,3,2,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,1,5,3,6,2] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,1,5,6,2,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[4,1,5,6,3,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[4,1,6,2,3,5] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[4,1,6,2,5,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[4,1,6,3,2,5] => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [4,6,3,2,5,1] => 0
[4,1,6,3,5,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[4,1,6,5,2,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[4,1,6,5,3,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[4,2,1,3,5,6] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,2,1,3,6,5] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,2,1,5,3,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,2,1,5,6,3] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,2,1,6,3,5] => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,2,1,6,5,3] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,2,3,1,5,6] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,2,3,1,6,5] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,2,3,5,1,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,2,3,5,6,1] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,2,3,6,1,5] => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,2,3,6,5,1] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,2,5,1,6,3] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,2,5,3,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,2,5,6,1,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,2,5,6,3,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,2,6,1,3,5] => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,2,6,1,5,3] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,2,6,3,1,5] => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,2,6,3,5,1] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,2,6,5,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,2,6,5,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,3,1,2,5,6] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,3,1,2,6,5] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,3,1,5,2,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,3,1,5,6,2] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,3,1,6,2,5] => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,3,1,6,5,2] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => 1
[4,3,2,5,1,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,3,2,5,6,1] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,3,2,6,1,5] => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[4,3,2,6,5,1] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,3,5,1,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,3,5,2,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,3,5,6,1,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,3,5,6,2,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,3,6,1,2,5] => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,3,6,1,5,2] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,3,6,2,1,5] => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,3,6,2,5,1] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,3,6,5,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,3,6,5,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,5,1,2,6,3] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,5,1,3,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,5,1,6,2,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,1,6,3,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,5,2,1,6,3] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,5,2,3,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,5,2,6,1,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,2,6,3,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,5,3,1,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[4,5,3,2,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[4,5,3,6,1,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,3,6,2,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,6,1,3,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,6,2,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,6,2,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,6,3,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,5,6,3,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,1,2,3,5] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[4,6,1,2,5,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,1,3,2,5] => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[4,6,1,3,5,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,1,5,2,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,1,5,3,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,2,1,3,5] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[4,6,2,1,5,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,2,3,1,5] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[4,6,2,3,5,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,2,5,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,2,5,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,3,1,2,5] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[4,6,3,1,5,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,3,2,1,5] => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => 0
[4,6,3,2,5,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,3,5,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,3,5,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,5,1,2,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,5,1,3,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,5,2,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,5,3,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[4,6,5,3,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,1,2,3,4,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[5,1,2,3,6,4] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,1,2,4,3,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[5,1,2,4,6,3] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,1,2,6,3,4] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,1,2,6,4,3] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,1,3,2,4,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[5,1,3,2,6,4] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,1,3,4,2,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[5,1,3,4,6,2] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,1,3,6,2,4] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,3,6,4,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,4,2,3,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[5,1,4,2,6,3] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,1,4,3,2,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[5,1,4,3,6,2] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,1,4,6,2,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,4,6,3,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,6,2,3,4] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,6,2,4,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,6,3,2,4] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,6,3,4,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,6,4,2,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,1,6,4,3,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[5,2,1,3,4,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[5,2,1,3,6,4] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,2,1,4,3,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => 0
[5,2,1,4,6,3] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,2,1,6,3,4] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,2,1,6,4,3] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,2,3,1,6,4] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,2,3,4,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,2,3,6,1,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,2,3,6,4,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,2,4,1,6,3] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,2,4,3,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,2,4,6,1,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,2,4,6,3,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,2,6,1,3,4] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,2,6,1,4,3] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,2,6,3,1,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,2,6,3,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,2,6,4,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,2,6,4,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,3,1,2,6,4] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,3,1,4,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,3,1,6,2,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,1,6,4,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,3,2,1,6,4] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,3,2,4,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,3,2,6,1,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,2,6,4,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,3,4,1,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,3,4,2,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,3,4,6,1,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,4,6,2,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,6,1,2,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,6,1,4,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,6,2,1,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,6,2,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,6,4,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,3,6,4,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,4,1,2,6,3] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,4,1,3,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,4,1,6,2,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,1,6,3,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,4,2,1,6,3] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,4,2,3,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,4,2,6,1,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,2,6,3,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,4,3,1,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [6,3,4,2,5,1] => 0
[5,4,3,2,6,1] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[5,4,3,6,1,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,3,6,2,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,6,1,2,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,6,2,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,6,2,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,6,3,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,4,6,3,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,1,2,3,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,1,2,4,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,1,3,2,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,1,3,4,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,1,4,2,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,1,4,3,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,2,1,3,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,2,1,4,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,2,3,1,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,2,3,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,2,4,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,2,4,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,3,1,2,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,3,1,4,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,3,2,1,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,3,2,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,3,4,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,4,1,2,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,4,1,3,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,4,2,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[5,6,4,3,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,1,2,3,4,5] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,1,2,3,5,4] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,1,2,4,3,5] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,1,2,4,5,3] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,1,2,5,3,4] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,1,2,5,4,3] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,1,3,2,4,5] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,1,3,2,5,4] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,1,3,4,2,5] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,3,4,5,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,3,5,2,4] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,3,5,4,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,4,2,3,5] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,4,2,5,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,4,3,2,5] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,4,3,5,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,4,5,2,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,4,5,3,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,5,2,3,4] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,5,2,4,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,5,3,2,4] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,5,3,4,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,5,4,2,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,1,5,4,3,2] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [4,5,3,2,6,1] => 0
[6,2,1,3,4,5] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,2,1,3,5,4] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,2,1,4,3,5] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,2,1,4,5,3] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,2,1,5,3,4] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,2,1,5,4,3] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => 0
[6,2,3,1,4,5] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,2,3,1,5,4] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,2,3,4,1,5] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,3,4,5,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,3,5,1,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,3,5,4,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,4,1,3,5] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,2,4,1,5,3] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,2,4,3,1,5] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,4,3,5,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,4,5,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,4,5,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,5,1,3,4] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,2,5,1,4,3] => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,2,5,3,1,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,5,3,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,5,4,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,2,5,4,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,1,2,4,5] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,3,1,2,5,4] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,3,1,4,2,5] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,1,4,5,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,1,5,2,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,1,5,4,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,2,1,4,5] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,3,2,1,5,4] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [5,3,4,2,6,1] => 0
[6,3,2,4,1,5] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,2,4,5,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,2,5,1,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,2,5,4,1] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,4,1,2,5] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,4,1,5,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,4,2,1,5] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,4,2,5,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,4,5,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,4,5,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,5,1,2,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,5,1,4,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,5,2,1,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,5,2,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,5,4,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,3,5,4,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,1,2,3,5] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,1,2,5,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,1,3,2,5] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,1,3,5,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,1,5,2,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,1,5,3,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,2,1,3,5] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,2,1,5,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,2,3,1,5] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,2,3,5,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,2,5,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,2,5,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,3,1,2,5] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,3,1,5,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,3,2,1,5] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,3,2,5,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,3,5,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,3,5,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,5,1,2,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,5,1,3,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,5,2,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,5,2,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,5,3,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,4,5,3,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,1,2,3,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,1,2,4,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,1,3,2,4] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,1,3,4,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,1,4,2,3] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,1,4,3,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,2,1,3,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,2,1,4,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,2,3,1,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,2,3,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,2,4,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,2,4,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,3,1,2,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,3,1,4,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,3,2,1,4] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,3,2,4,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,3,4,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,3,4,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,4,1,2,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,4,1,3,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,4,2,1,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,4,2,3,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,4,3,1,2] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 0
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [4,3,5,2,6,1] => 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:
110,10 660,60
$F_{2} = 2$
$F_{3} = 6$
$F_{4} = 24$
$F_{5} = 110 + 10\ q$
$F_{6} = 660 + 60\ q$
Description
The number of double deficiencies of a permutation.
A double deficiency is an index $\sigma(i)$ such that $i > \sigma(i) > \sigma(\sigma(i))$.
A double deficiency is an index $\sigma(i)$ such that $i > \sigma(i) > \sigma(\sigma(i))$.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
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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