Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
St000241: Permutations ⟶ ℤ
Values
[1] => [1] => [1] => [1] => 1
[1,2] => [1,2] => [1,2] => [2,1] => 2
[2,1] => [2,1] => [2,1] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [2,3,1] => 3
[1,3,2] => [1,3,2] => [1,3,2] => [3,2,1] => 1
[2,1,3] => [2,1,3] => [2,1,3] => [1,3,2] => 1
[2,3,1] => [3,2,1] => [2,3,1] => [1,2,3] => 0
[3,1,2] => [3,2,1] => [2,3,1] => [1,2,3] => 0
[3,2,1] => [3,2,1] => [2,3,1] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [2,3,4,1] => 4
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [2,4,3,1] => 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [3,2,4,1] => 2
[1,3,4,2] => [1,4,3,2] => [1,3,4,2] => [4,2,3,1] => 1
[1,4,2,3] => [1,4,3,2] => [1,3,4,2] => [4,2,3,1] => 1
[1,4,3,2] => [1,4,3,2] => [1,3,4,2] => [4,2,3,1] => 1
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,3,4,2] => 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [1,4,3,2] => 0
[2,3,1,4] => [3,2,1,4] => [2,3,1,4] => [1,2,4,3] => 1
[2,3,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,3,4] => 0
[2,4,1,3] => [3,4,1,2] => [4,3,2,1] => [3,2,1,4] => 0
[2,4,3,1] => [4,3,2,1] => [3,4,1,2] => [4,1,2,3] => 0
[3,1,2,4] => [3,2,1,4] => [2,3,1,4] => [1,2,4,3] => 1
[3,1,4,2] => [4,2,3,1] => [2,3,4,1] => [1,2,3,4] => 0
[3,2,1,4] => [3,2,1,4] => [2,3,1,4] => [1,2,4,3] => 1
[3,2,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,3,4] => 0
[3,4,1,2] => [4,3,2,1] => [3,4,1,2] => [4,1,2,3] => 0
[3,4,2,1] => [4,3,2,1] => [3,4,1,2] => [4,1,2,3] => 0
[4,1,2,3] => [4,2,3,1] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,3,2] => [4,2,3,1] => [2,3,4,1] => [1,2,3,4] => 0
[4,2,1,3] => [4,3,2,1] => [3,4,1,2] => [4,1,2,3] => 0
[4,2,3,1] => [4,3,2,1] => [3,4,1,2] => [4,1,2,3] => 0
[4,3,1,2] => [4,3,2,1] => [3,4,1,2] => [4,1,2,3] => 0
[4,3,2,1] => [4,3,2,1] => [3,4,1,2] => [4,1,2,3] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => 5
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => 3
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => 3
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => [2,5,3,4,1] => 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,4,5,3] => [2,5,3,4,1] => 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,4,5,3] => [2,5,3,4,1] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => 3
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => 1
[1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [4,2,3,5,1] => 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [5,2,3,4,1] => 1
[1,3,5,2,4] => [1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => 1
[1,3,5,4,2] => [1,5,4,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => 1
[1,4,2,3,5] => [1,4,3,2,5] => [1,3,4,2,5] => [4,2,3,5,1] => 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,3,4,5,2] => [5,2,3,4,1] => 1
[1,4,3,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [4,2,3,5,1] => 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [5,2,3,4,1] => 1
[1,4,5,2,3] => [1,5,4,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => 1
[1,4,5,3,2] => [1,5,4,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => 1
[1,5,2,3,4] => [1,5,3,4,2] => [1,3,4,5,2] => [5,2,3,4,1] => 1
[1,5,2,4,3] => [1,5,3,4,2] => [1,3,4,5,2] => [5,2,3,4,1] => 1
[1,5,3,2,4] => [1,5,4,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => 1
[1,5,3,4,2] => [1,5,4,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => 1
[1,5,4,2,3] => [1,5,4,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => 1
[1,5,4,3,2] => [1,5,4,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => 1
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,3,4,5,2] => 3
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => 1
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => [1,4,3,5,2] => 1
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,5,3] => [1,5,3,4,2] => 0
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,4,5,3] => [1,5,3,4,2] => 0
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,4,5,3] => [1,5,3,4,2] => 0
[2,3,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => [1,2,4,5,3] => 2
[2,3,1,5,4] => [3,2,1,5,4] => [2,3,1,5,4] => [1,2,5,4,3] => 0
[2,3,4,1,5] => [4,2,3,1,5] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[2,3,4,5,1] => [5,2,3,4,1] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[2,3,5,1,4] => [4,2,5,1,3] => [2,5,4,3,1] => [1,4,3,2,5] => 0
[2,3,5,4,1] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[2,4,1,3,5] => [3,4,1,2,5] => [4,3,2,1,5] => [3,2,1,5,4] => 1
[2,4,1,5,3] => [3,5,1,4,2] => [4,3,2,5,1] => [3,2,1,4,5] => 0
[2,4,3,1,5] => [4,3,2,1,5] => [3,4,1,2,5] => [4,1,2,5,3] => 1
[2,4,3,5,1] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[2,4,5,1,3] => [4,5,3,1,2] => [4,3,5,2,1] => [4,2,1,3,5] => 0
[2,4,5,3,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[2,5,1,3,4] => [3,5,1,4,2] => [4,3,2,5,1] => [3,2,1,4,5] => 0
[2,5,1,4,3] => [3,5,1,4,2] => [4,3,2,5,1] => [3,2,1,4,5] => 0
[2,5,3,1,4] => [4,5,3,1,2] => [4,3,5,2,1] => [4,2,1,3,5] => 0
[2,5,3,4,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[2,5,4,1,3] => [4,5,3,1,2] => [4,3,5,2,1] => [4,2,1,3,5] => 0
[2,5,4,3,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[3,1,2,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => [1,2,4,5,3] => 2
[3,1,2,5,4] => [3,2,1,5,4] => [2,3,1,5,4] => [1,2,5,4,3] => 0
[3,1,4,2,5] => [4,2,3,1,5] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[3,1,4,5,2] => [5,2,3,4,1] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[3,1,5,2,4] => [4,2,5,1,3] => [2,5,4,3,1] => [1,4,3,2,5] => 0
[3,1,5,4,2] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[3,2,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => [1,2,4,5,3] => 2
[3,2,1,5,4] => [3,2,1,5,4] => [2,3,1,5,4] => [1,2,5,4,3] => 0
[3,2,4,1,5] => [4,2,3,1,5] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[3,2,4,5,1] => [5,2,3,4,1] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[3,2,5,1,4] => [4,2,5,1,3] => [2,5,4,3,1] => [1,4,3,2,5] => 0
[3,2,5,4,1] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[3,4,1,2,5] => [4,3,2,1,5] => [3,4,1,2,5] => [4,1,2,5,3] => 1
[3,4,1,5,2] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[3,4,2,1,5] => [4,3,2,1,5] => [3,4,1,2,5] => [4,1,2,5,3] => 1
[3,4,2,5,1] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[3,4,5,1,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[3,4,5,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[3,5,1,2,4] => [4,5,3,1,2] => [4,3,5,2,1] => [4,2,1,3,5] => 0
[3,5,1,4,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
>>> Load all 873 entries. <<<[3,5,2,1,4] => [4,5,3,1,2] => [4,3,5,2,1] => [4,2,1,3,5] => 0
[3,5,2,4,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[3,5,4,1,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[3,5,4,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,1,2,3,5] => [4,2,3,1,5] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[4,1,2,5,3] => [5,2,3,4,1] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[4,1,3,2,5] => [4,2,3,1,5] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[4,1,3,5,2] => [5,2,3,4,1] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[4,1,5,2,3] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[4,1,5,3,2] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[4,2,1,3,5] => [4,3,2,1,5] => [3,4,1,2,5] => [4,1,2,5,3] => 1
[4,2,1,5,3] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[4,2,3,1,5] => [4,3,2,1,5] => [3,4,1,2,5] => [4,1,2,5,3] => 1
[4,2,3,5,1] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[4,2,5,1,3] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,2,5,3,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,3,1,2,5] => [4,3,2,1,5] => [3,4,1,2,5] => [4,1,2,5,3] => 1
[4,3,1,5,2] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[4,3,2,1,5] => [4,3,2,1,5] => [3,4,1,2,5] => [4,1,2,5,3] => 1
[4,3,2,5,1] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[4,3,5,1,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,3,5,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,5,1,2,3] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,5,1,3,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,5,2,1,3] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,5,2,3,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,5,3,1,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[4,5,3,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,1,2,3,4] => [5,2,3,4,1] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[5,1,2,4,3] => [5,2,3,4,1] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[5,1,3,2,4] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[5,1,3,4,2] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[5,1,4,2,3] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[5,1,4,3,2] => [5,2,4,3,1] => [2,4,5,1,3] => [1,5,2,3,4] => 0
[5,2,1,3,4] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[5,2,1,4,3] => [5,3,2,4,1] => [3,4,1,5,2] => [5,1,2,4,3] => 0
[5,2,3,1,4] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,2,3,4,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,2,4,1,3] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,2,4,3,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,3,1,2,4] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,3,1,4,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,3,2,1,4] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,3,2,4,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,3,4,1,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,3,4,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,4,1,2,3] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,4,1,3,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,4,2,1,3] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,4,2,3,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,4,3,1,2] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[5,4,3,2,1] => [5,4,3,2,1] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 6
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => 4
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => 4
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => 3
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => 3
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [2,3,6,4,5,1] => 3
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => 4
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => 3
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => 2
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 2
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => 2
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => 3
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => 2
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [2,5,3,4,6,1] => 3
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => 2
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => 2
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => 2
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => 2
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [2,6,3,4,5,1] => 2
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => 2
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => 2
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => 2
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => [2,5,6,3,4,1] => 2
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => 4
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => 2
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [3,2,6,4,5,1] => 1
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [3,2,6,4,5,1] => 1
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [3,2,6,4,5,1] => 1
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => 3
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [4,2,3,6,5,1] => 1
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => 2
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => 1
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [1,3,6,5,4,2] => [6,2,5,4,3,1] => 1
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => 2
[1,3,5,2,6,4] => [1,4,6,2,5,3] => [1,5,4,3,6,2] => [6,4,3,2,5,1] => 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => 2
[1,3,5,4,6,2] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [1,5,4,6,3,2] => [6,5,3,2,4,1] => 1
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,3,6,2,4,5] => [1,4,6,2,5,3] => [1,5,4,3,6,2] => [6,4,3,2,5,1] => 1
[1,3,6,2,5,4] => [1,4,6,2,5,3] => [1,5,4,3,6,2] => [6,4,3,2,5,1] => 1
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [1,5,4,6,3,2] => [6,5,3,2,4,1] => 1
[1,3,6,4,5,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [1,5,4,6,3,2] => [6,5,3,2,4,1] => 1
[1,3,6,5,4,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => 3
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [4,2,3,6,5,1] => 1
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => 2
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => 1
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [1,3,6,5,4,2] => [6,2,5,4,3,1] => 1
[1,4,2,6,5,3] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [4,2,3,5,6,1] => 3
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [4,2,3,6,5,1] => 1
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => 2
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => 1
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [1,3,6,5,4,2] => [6,2,5,4,3,1] => 1
[1,4,3,6,5,2] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => 2
[1,4,5,2,6,3] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => 2
[1,4,5,3,6,2] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,4,6,2,3,5] => [1,5,6,4,2,3] => [1,5,4,6,3,2] => [6,5,3,2,4,1] => 1
[1,4,6,2,5,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,4,6,3,2,5] => [1,5,6,4,2,3] => [1,5,4,6,3,2] => [6,5,3,2,4,1] => 1
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,4,6,5,2,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,4,6,5,3,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => 2
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [5,2,3,4,6,1] => 2
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => 1
[1,5,2,6,3,4] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,5,2,6,4,3] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => 2
[1,5,3,2,6,4] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => 2
[1,5,3,4,6,2] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => 2
[1,5,4,2,6,3] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => [4,5,2,3,6,1] => 2
[1,5,4,3,6,2] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,4,6,3,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,6,2,3,4] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,6,2,4,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,6,3,2,4] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,5,6,4,3,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,2,3,4,5] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => 1
[1,6,2,3,5,4] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [6,2,3,4,5,1] => 1
[1,6,2,4,3,5] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,6,2,4,5,3] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,6,2,5,3,4] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,6,2,5,4,3] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => [5,2,6,3,4,1] => 1
[1,6,3,2,4,5] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,6,3,2,5,4] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => [4,6,2,3,5,1] => 1
[1,6,3,4,2,5] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,4,2,3,5] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,4,3,2,5] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,4,5,3,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,5,2,3,4] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,5,2,4,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,5,3,2,4] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,5,3,4,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,5,4,2,3] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => [5,6,2,3,4,1] => 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,3,4,6,5,2] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,3,5,4,6,2] => 2
[2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [1,3,6,4,5,2] => 1
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [1,3,6,4,5,2] => 1
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [1,3,6,4,5,2] => 1
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 2
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0
[2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [1,5,3,4,6,2] => 1
[2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => 0
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => 0
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => [1,5,6,3,4,2] => 0
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [1,5,3,4,6,2] => 1
[2,1,5,3,6,4] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => 0
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [1,5,3,4,6,2] => 1
[2,1,5,4,6,3] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => 0
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => [1,5,6,3,4,2] => 0
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => [1,5,6,3,4,2] => 0
[2,1,6,3,4,5] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => 0
[2,1,6,3,5,4] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => 0
[2,1,6,4,3,5] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => [1,5,6,3,4,2] => 0
[2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => [1,5,6,3,4,2] => 0
[2,1,6,5,3,4] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => [1,5,6,3,4,2] => 0
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => [1,5,6,3,4,2] => 0
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[2,3,1,4,6,5] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [1,2,4,6,5,3] => 1
[2,3,1,5,4,6] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [1,2,5,4,6,3] => 1
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[2,3,1,6,4,5] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[2,3,1,6,5,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[2,3,4,1,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[2,3,4,1,6,5] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [1,2,3,6,5,4] => 0
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[2,3,4,6,1,5] => [5,2,3,6,1,4] => [2,3,6,5,4,1] => [1,2,5,4,3,6] => 0
[2,3,4,6,5,1] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[2,3,5,1,4,6] => [4,2,5,1,3,6] => [2,5,4,3,1,6] => [1,4,3,2,6,5] => 1
[2,3,5,1,6,4] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[2,3,5,4,6,1] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[2,3,5,6,4,1] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[2,3,6,1,4,5] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[2,3,6,1,5,4] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[2,3,6,4,5,1] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[2,3,6,5,4,1] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => [3,2,1,5,6,4] => 2
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [4,3,2,1,6,5] => [3,2,1,6,5,4] => 0
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [4,3,2,5,1,6] => [3,2,1,4,6,5] => 1
[2,4,1,5,6,3] => [3,6,1,4,5,2] => [4,3,2,5,6,1] => [3,2,1,4,5,6] => 0
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [6,3,2,5,4,1] => [3,2,5,4,1,6] => 0
[2,4,1,6,5,3] => [3,6,1,5,4,2] => [5,3,2,6,1,4] => [3,2,6,1,4,5] => 0
[2,4,3,1,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 2
[2,4,3,1,6,5] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => [4,1,2,6,5,3] => 0
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[2,4,3,5,6,1] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[2,4,3,6,1,5] => [5,3,2,6,1,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => 0
[2,4,3,6,5,1] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [4,3,5,2,1,6] => [4,2,1,3,6,5] => 1
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[2,4,5,3,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[2,4,5,6,1,3] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[2,4,5,6,3,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,4,6,1,3,5] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => [5,4,3,2,1,6] => 0
[2,4,6,1,5,3] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => [6,4,2,3,1,5] => 0
[2,4,6,3,1,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => [4,5,3,1,2,6] => 0
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[2,4,6,5,1,3] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[2,4,6,5,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [4,3,2,5,1,6] => [3,2,1,4,6,5] => 1
[2,5,1,3,6,4] => [3,6,1,4,5,2] => [4,3,2,5,6,1] => [3,2,1,4,5,6] => 0
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [4,3,2,5,1,6] => [3,2,1,4,6,5] => 1
[2,5,1,4,6,3] => [3,6,1,4,5,2] => [4,3,2,5,6,1] => [3,2,1,4,5,6] => 0
[2,5,1,6,3,4] => [3,6,1,5,4,2] => [5,3,2,6,1,4] => [3,2,6,1,4,5] => 0
[2,5,1,6,4,3] => [3,6,1,5,4,2] => [5,3,2,6,1,4] => [3,2,6,1,4,5] => 0
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [4,3,5,2,1,6] => [4,2,1,3,6,5] => 1
[2,5,3,1,6,4] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[2,5,3,4,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[2,5,3,6,1,4] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[2,5,3,6,4,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [4,3,5,2,1,6] => [4,2,1,3,6,5] => 1
[2,5,4,1,6,3] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[2,5,4,3,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[2,5,4,6,1,3] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[2,5,4,6,3,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,5,6,1,3,4] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => [6,4,2,3,1,5] => 0
[2,5,6,1,4,3] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => [6,4,2,3,1,5] => 0
[2,5,6,3,1,4] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[2,5,6,3,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[2,5,6,4,1,3] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[2,5,6,4,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[2,6,1,3,4,5] => [3,6,1,4,5,2] => [4,3,2,5,6,1] => [3,2,1,4,5,6] => 0
[2,6,1,3,5,4] => [3,6,1,4,5,2] => [4,3,2,5,6,1] => [3,2,1,4,5,6] => 0
[2,6,1,4,3,5] => [3,6,1,5,4,2] => [5,3,2,6,1,4] => [3,2,6,1,4,5] => 0
[2,6,1,4,5,3] => [3,6,1,5,4,2] => [5,3,2,6,1,4] => [3,2,6,1,4,5] => 0
[2,6,1,5,3,4] => [3,6,1,5,4,2] => [5,3,2,6,1,4] => [3,2,6,1,4,5] => 0
[2,6,1,5,4,3] => [3,6,1,5,4,2] => [5,3,2,6,1,4] => [3,2,6,1,4,5] => 0
[2,6,3,1,4,5] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[2,6,3,1,5,4] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[2,6,3,4,1,5] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[2,6,3,4,5,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,6,3,5,1,4] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[2,6,3,5,4,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,6,4,1,3,5] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => [6,4,2,3,1,5] => 0
[2,6,4,1,5,3] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => [6,4,2,3,1,5] => 0
[2,6,4,3,1,5] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[2,6,4,3,5,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[2,6,4,5,1,3] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[2,6,4,5,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[2,6,5,1,3,4] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => [6,4,2,3,1,5] => 0
[2,6,5,1,4,3] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => [6,4,2,3,1,5] => 0
[2,6,5,3,1,4] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[2,6,5,3,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[2,6,5,4,1,3] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[2,6,5,4,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [1,2,4,6,5,3] => 1
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [1,2,5,4,6,3] => 1
[3,1,2,5,6,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[3,1,2,6,5,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[3,1,4,2,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,1,4,2,6,5] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [1,2,3,6,5,4] => 0
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[3,1,4,5,6,2] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[3,1,4,6,2,5] => [5,2,3,6,1,4] => [2,3,6,5,4,1] => [1,2,5,4,3,6] => 0
[3,1,4,6,5,2] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[3,1,5,2,4,6] => [4,2,5,1,3,6] => [2,5,4,3,1,6] => [1,4,3,2,6,5] => 1
[3,1,5,2,6,4] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[3,1,5,4,6,2] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[3,1,5,6,2,4] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[3,1,5,6,4,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[3,1,6,2,4,5] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[3,1,6,2,5,4] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[3,1,6,4,2,5] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[3,1,6,4,5,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[3,1,6,5,2,4] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[3,1,6,5,4,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [1,2,4,6,5,3] => 1
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [1,2,5,4,6,3] => 1
[3,2,1,5,6,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[3,2,1,6,4,5] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,2,6,4,5,3] => 0
[3,2,4,1,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,2,4,1,6,5] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [1,2,3,6,5,4] => 0
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[3,2,4,5,6,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[3,2,4,6,1,5] => [5,2,3,6,1,4] => [2,3,6,5,4,1] => [1,2,5,4,3,6] => 0
[3,2,4,6,5,1] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[3,2,5,1,4,6] => [4,2,5,1,3,6] => [2,5,4,3,1,6] => [1,4,3,2,6,5] => 1
[3,2,5,1,6,4] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[3,2,5,4,6,1] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[3,2,5,6,1,4] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[3,2,5,6,4,1] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[3,2,6,1,4,5] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[3,2,6,1,5,4] => [4,2,6,1,5,3] => [2,5,4,3,6,1] => [1,4,3,2,5,6] => 0
[3,2,6,4,1,5] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[3,2,6,4,5,1] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[3,2,6,5,1,4] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[3,2,6,5,4,1] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 2
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => [4,1,2,6,5,3] => 0
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[3,4,1,5,6,2] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[3,4,1,6,2,5] => [5,3,2,6,1,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => 0
[3,4,1,6,5,2] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[3,4,2,1,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 2
[3,4,2,1,6,5] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => [4,1,2,6,5,3] => 0
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[3,4,2,5,6,1] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[3,4,2,6,1,5] => [5,3,2,6,1,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => 0
[3,4,2,6,5,1] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[3,4,5,1,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[3,4,5,2,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[3,4,5,6,1,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,4,5,6,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,4,6,1,2,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => [4,5,3,1,2,6] => 0
[3,4,6,1,5,2] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[3,4,6,2,1,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => [4,5,3,1,2,6] => 0
[3,4,6,2,5,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[3,4,6,5,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,4,6,5,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [4,3,5,2,1,6] => [4,2,1,3,6,5] => 1
[3,5,1,2,6,4] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[3,5,1,4,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[3,5,1,6,2,4] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[3,5,1,6,4,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [4,3,5,2,1,6] => [4,2,1,3,6,5] => 1
[3,5,2,1,6,4] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[3,5,2,4,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[3,5,2,6,1,4] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[3,5,2,6,4,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[3,5,4,1,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[3,5,4,2,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[3,5,4,6,1,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,5,4,6,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,5,6,1,2,4] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[3,5,6,1,4,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,5,6,2,1,4] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[3,5,6,2,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,5,6,4,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,5,6,4,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,6,1,2,4,5] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[3,6,1,2,5,4] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[3,6,1,4,2,5] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[3,6,1,4,5,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,6,1,5,2,4] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[3,6,1,5,4,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,6,2,1,4,5] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[3,6,2,1,5,4] => [4,6,3,1,5,2] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[3,6,2,4,1,5] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[3,6,2,4,5,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,6,2,5,1,4] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[3,6,2,5,4,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[3,6,4,1,2,5] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[3,6,4,1,5,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,6,4,2,1,5] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[3,6,4,2,5,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,6,4,5,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,6,4,5,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,6,5,1,2,4] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[3,6,5,1,4,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,6,5,2,1,4] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[3,6,5,2,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,6,5,4,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,6,5,4,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,1,2,3,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[4,1,2,3,6,5] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [1,2,3,6,5,4] => 0
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[4,1,2,5,6,3] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[4,1,2,6,3,5] => [5,2,3,6,1,4] => [2,3,6,5,4,1] => [1,2,5,4,3,6] => 0
[4,1,2,6,5,3] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[4,1,3,2,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[4,1,3,2,6,5] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [1,2,3,6,5,4] => 0
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[4,1,3,5,6,2] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[4,1,3,6,2,5] => [5,2,3,6,1,4] => [2,3,6,5,4,1] => [1,2,5,4,3,6] => 0
[4,1,3,6,5,2] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[4,1,5,2,6,3] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[4,1,5,3,2,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[4,1,5,3,6,2] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[4,1,5,6,2,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[4,1,5,6,3,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[4,1,6,2,3,5] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[4,1,6,2,5,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[4,1,6,3,2,5] => [5,2,6,4,1,3] => [2,5,4,6,3,1] => [1,5,3,2,4,6] => 0
[4,1,6,3,5,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[4,1,6,5,2,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[4,1,6,5,3,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[4,2,1,3,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 2
[4,2,1,3,6,5] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => [4,1,2,6,5,3] => 0
[4,2,1,5,3,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[4,2,1,5,6,3] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[4,2,1,6,3,5] => [5,3,2,6,1,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => 0
[4,2,1,6,5,3] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[4,2,3,1,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 2
[4,2,3,1,6,5] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => [4,1,2,6,5,3] => 0
[4,2,3,5,1,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[4,2,3,5,6,1] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[4,2,3,6,1,5] => [5,3,2,6,1,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => 0
[4,2,3,6,5,1] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,2,5,1,6,3] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,2,5,3,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,2,5,6,1,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,2,5,6,3,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,2,6,1,3,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => [4,5,3,1,2,6] => 0
[4,2,6,1,5,3] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[4,2,6,3,1,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => [4,5,3,1,2,6] => 0
[4,2,6,3,5,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[4,2,6,5,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,2,6,5,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,3,1,2,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 2
[4,3,1,2,6,5] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => [4,1,2,6,5,3] => 0
[4,3,1,5,2,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[4,3,1,5,6,2] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[4,3,1,6,2,5] => [5,3,2,6,1,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => 0
[4,3,1,6,5,2] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 2
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => [4,1,2,6,5,3] => 0
[4,3,2,5,1,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[4,3,2,5,6,1] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[4,3,2,6,1,5] => [5,3,2,6,1,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => 0
[4,3,2,6,5,1] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,3,5,1,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,3,5,2,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,3,5,6,1,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,3,5,6,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,3,6,1,2,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => [4,5,3,1,2,6] => 0
[4,3,6,1,5,2] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[4,3,6,2,1,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => [4,5,3,1,2,6] => 0
[4,3,6,2,5,1] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[4,3,6,5,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,3,6,5,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,5,1,2,6,3] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,5,1,3,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,5,1,6,2,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,5,1,6,3,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,5,2,1,6,3] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,5,2,3,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,5,2,6,1,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,5,2,6,3,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,5,3,1,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[4,5,3,2,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[4,5,3,6,1,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,5,3,6,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,5,6,1,3,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,5,6,2,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,5,6,2,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,5,6,3,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,5,6,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,1,2,3,5] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[4,6,1,2,5,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,6,1,3,2,5] => [5,6,3,4,1,2] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[4,6,1,3,5,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,6,1,5,2,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,6,1,5,3,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[4,6,2,1,3,5] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[4,6,2,1,5,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,2,3,1,5] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[4,6,2,3,5,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,2,5,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,2,5,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,3,1,2,5] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[4,6,3,1,5,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,3,2,1,5] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => [6,5,2,1,3,4] => 0
[4,6,3,2,5,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,3,5,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,3,5,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,5,1,2,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,5,1,3,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,5,2,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,5,3,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[4,6,5,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,1,2,3,4,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[5,1,2,3,6,4] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[5,1,2,4,3,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[5,1,2,4,6,3] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[5,1,2,6,3,4] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[5,1,2,6,4,3] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[5,1,3,2,4,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[5,1,3,2,6,4] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[5,1,3,4,2,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[5,1,3,4,6,2] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[5,1,3,6,2,4] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,3,6,4,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,4,2,3,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[5,1,4,2,6,3] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[5,1,4,3,2,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => [1,5,2,3,6,4] => 1
[5,1,4,3,6,2] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[5,1,4,6,2,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,4,6,3,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,6,2,3,4] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,6,2,4,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,6,3,2,4] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,6,3,4,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,6,4,2,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,1,6,4,3,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[5,2,1,3,4,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[5,2,1,3,6,4] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[5,2,1,4,3,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => [5,1,2,4,6,3] => 1
[5,2,1,4,6,3] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[5,2,1,6,3,4] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[5,2,1,6,4,3] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,2,3,1,6,4] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,2,3,4,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,2,3,6,1,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,2,3,6,4,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,2,4,1,6,3] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,2,4,3,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,2,4,6,1,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,2,4,6,3,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,2,6,1,3,4] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[5,2,6,1,4,3] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[5,2,6,3,1,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,2,6,3,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,2,6,4,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,2,6,4,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,3,1,2,6,4] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,3,1,4,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,3,1,6,2,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,3,1,6,4,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,3,2,1,6,4] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,3,2,4,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,3,2,6,1,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,3,2,6,4,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,3,4,1,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,3,4,2,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,3,4,6,1,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,3,4,6,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,3,6,1,2,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,3,6,1,4,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,3,6,2,1,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,3,6,2,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,3,6,4,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,3,6,4,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,4,1,2,6,3] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,4,1,3,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,4,1,6,2,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,4,1,6,3,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,4,2,1,6,3] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,4,2,3,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,4,2,6,1,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,4,2,6,3,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,4,3,1,6,2] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 1
[5,4,3,2,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[5,4,3,6,1,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,4,3,6,2,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,4,6,1,2,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,4,6,2,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,4,6,2,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,4,6,3,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,4,6,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,1,2,3,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,6,1,2,4,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,6,1,3,2,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,6,1,3,4,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,6,1,4,2,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,6,1,4,3,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[5,6,2,1,3,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,2,1,4,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,2,3,1,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,2,3,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,2,4,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,2,4,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,3,1,2,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,3,1,4,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,3,2,1,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,3,2,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,3,4,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,4,1,2,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,4,1,3,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,4,2,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[5,6,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,1,2,3,4,5] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[6,1,2,3,5,4] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[6,1,2,4,3,5] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[6,1,2,4,5,3] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[6,1,2,5,3,4] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[6,1,2,5,4,3] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => [1,2,6,3,4,5] => 0
[6,1,3,2,4,5] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[6,1,3,2,5,4] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => [1,6,2,3,5,4] => 0
[6,1,3,4,2,5] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,3,4,5,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,3,5,2,4] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,3,5,4,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,4,2,3,5] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,4,2,5,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,4,3,2,5] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,4,3,5,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,4,5,2,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,4,5,3,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,5,2,3,4] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,5,2,4,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,5,3,2,4] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,5,3,4,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,5,4,2,3] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,1,5,4,3,2] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => [1,6,2,3,4,5] => 0
[6,2,1,3,4,5] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[6,2,1,3,5,4] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => [6,1,2,4,5,3] => 0
[6,2,1,4,3,5] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[6,2,1,4,5,3] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[6,2,1,5,3,4] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[6,2,1,5,4,3] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[6,2,3,1,4,5] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[6,2,3,1,5,4] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[6,2,3,4,1,5] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,2,3,4,5,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,2,3,5,1,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,2,3,5,4,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,2,4,1,3,5] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[6,2,4,1,5,3] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[6,2,4,3,1,5] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,2,4,3,5,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,2,4,5,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,2,4,5,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,2,5,1,3,4] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[6,2,5,1,4,3] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => [4,6,1,3,2,5] => 0
[6,2,5,3,1,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,2,5,3,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,2,5,4,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,2,5,4,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,1,2,4,5] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[6,3,1,2,5,4] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[6,3,1,4,2,5] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,3,1,4,5,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,3,1,5,2,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,3,1,5,4,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,3,2,1,4,5] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[6,3,2,1,5,4] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => [6,1,2,3,5,4] => 0
[6,3,2,4,1,5] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,3,2,4,5,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,3,2,5,1,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,3,2,5,4,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,3,4,1,2,5] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,4,1,5,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,4,2,1,5] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,4,2,5,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,4,5,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,4,5,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,5,1,2,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,5,1,4,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,5,2,1,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,5,2,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,5,4,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,3,5,4,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,1,2,3,5] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,4,1,2,5,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,4,1,3,2,5] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,4,1,3,5,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,4,1,5,2,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,4,1,5,3,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,4,2,1,3,5] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,2,1,5,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,2,3,1,5] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,2,3,5,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,2,5,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,2,5,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,3,1,2,5] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,3,1,5,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,3,2,1,5] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,3,2,5,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,3,5,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,3,5,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,5,1,2,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,5,1,3,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,5,2,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,5,2,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,5,3,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,4,5,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,1,2,3,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,5,1,2,4,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,5,1,3,2,4] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,5,1,3,4,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,5,1,4,2,3] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,5,1,4,3,2] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[6,5,2,1,3,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,2,1,4,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,2,3,1,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,2,3,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,2,4,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,2,4,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,3,1,2,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,3,1,4,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,3,2,1,4] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,3,2,4,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,3,4,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,3,4,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,4,1,2,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,4,1,3,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,4,2,1,3] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,4,2,3,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,4,3,1,2] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 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:
1,0,1 3,2,0,1 14,6,3,0,1 77,29,9,4,0,1 497,160,45,12,5,0,1
F1=q
F2=1+q2
F3=3+2 q+q3
F4=14+6 q+3 q2+q4
F5=77+29 q+9 q2+4 q3+q5
F6=497+160 q+45 q2+12 q3+5 q4+q6
Description
The number of cyclical small excedances.
A cyclical small excedance is an index i such that πi=i+1 considered cyclically.
A cyclical small excedance is an index i such that πi=i+1 considered cyclically.
Map
Demazure product with inverse
Description
This map sends a permutation π to π−1⋆π where ⋆ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
Map
Inverse Kreweras complement
Description
Sends the permutation π∈Sn to the permutation cπ−1 where c=(1,…,n) is the long cycle.
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