Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000407: Permutations ⟶ ℤ
Values
[1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => 0
[1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [3,1,2] => 0
[2,1,3] => [2,1,3] => [2,3,1] => 0
[2,3,1] => [3,2,1] => [3,2,1] => 0
[3,1,2] => [3,2,1] => [3,2,1] => 0
[3,2,1] => [3,2,1] => [3,2,1] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [4,1,2,3] => 0
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 0
[1,3,4,2] => [1,4,3,2] => [4,3,1,2] => 0
[1,4,2,3] => [1,4,3,2] => [4,3,1,2] => 0
[1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 0
[2,1,3,4] => [2,1,3,4] => [2,3,4,1] => 0
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1
[2,3,1,4] => [3,2,1,4] => [3,4,2,1] => 0
[2,3,4,1] => [4,2,3,1] => [4,2,3,1] => 0
[2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 0
[2,4,3,1] => [4,3,2,1] => [4,3,2,1] => 0
[3,1,2,4] => [3,2,1,4] => [3,4,2,1] => 0
[3,1,4,2] => [4,2,3,1] => [4,2,3,1] => 0
[3,2,1,4] => [3,2,1,4] => [3,4,2,1] => 0
[3,2,4,1] => [4,2,3,1] => [4,2,3,1] => 0
[3,4,1,2] => [4,3,2,1] => [4,3,2,1] => 0
[3,4,2,1] => [4,3,2,1] => [4,3,2,1] => 0
[4,1,2,3] => [4,2,3,1] => [4,2,3,1] => 0
[4,1,3,2] => [4,2,3,1] => [4,2,3,1] => 0
[4,2,1,3] => [4,3,2,1] => [4,3,2,1] => 0
[4,2,3,1] => [4,3,2,1] => [4,3,2,1] => 0
[4,3,1,2] => [4,3,2,1] => [4,3,2,1] => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => 0
[1,2,4,3,5] => [1,2,4,3,5] => [1,4,2,3,5] => 0
[1,2,4,5,3] => [1,2,5,4,3] => [5,4,1,2,3] => 0
[1,2,5,3,4] => [1,2,5,4,3] => [5,4,1,2,3] => 0
[1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 0
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,4,2,5] => 0
[1,3,2,5,4] => [1,3,2,5,4] => [3,1,5,2,4] => 1
[1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[1,3,4,5,2] => [1,5,3,4,2] => [5,1,3,2,4] => 0
[1,3,5,2,4] => [1,4,5,2,3] => [4,5,1,2,3] => 0
[1,3,5,4,2] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,4,2,3,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[1,4,2,5,3] => [1,5,3,4,2] => [5,1,3,2,4] => 0
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[1,4,3,5,2] => [1,5,3,4,2] => [5,1,3,2,4] => 0
[1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,4,5,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,5,2,3,4] => [1,5,3,4,2] => [5,1,3,2,4] => 0
[1,5,2,4,3] => [1,5,3,4,2] => [5,1,3,2,4] => 0
[1,5,3,2,4] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,5,4,2,3] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 0
[2,1,3,4,5] => [2,1,3,4,5] => [2,3,4,5,1] => 0
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[2,1,4,3,5] => [2,1,4,3,5] => [2,4,1,5,3] => 1
[2,1,4,5,3] => [2,1,5,4,3] => [5,2,1,4,3] => 1
[2,1,5,3,4] => [2,1,5,4,3] => [5,2,1,4,3] => 1
[2,1,5,4,3] => [2,1,5,4,3] => [5,2,1,4,3] => 1
[2,3,1,4,5] => [3,2,1,4,5] => [3,4,5,2,1] => 0
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,5,4,1] => 1
[2,3,4,1,5] => [4,2,3,1,5] => [2,4,3,5,1] => 0
[2,3,4,5,1] => [5,2,3,4,1] => [5,2,3,4,1] => 0
[2,3,5,1,4] => [4,2,5,1,3] => [4,5,2,3,1] => 0
[2,3,5,4,1] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[2,4,1,3,5] => [3,4,1,2,5] => [3,4,5,1,2] => 0
[2,4,1,5,3] => [3,5,1,4,2] => [5,3,4,1,2] => 0
[2,4,3,1,5] => [4,3,2,1,5] => [4,5,3,2,1] => 0
[2,4,3,5,1] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[2,4,5,1,3] => [4,5,3,1,2] => [4,5,3,1,2] => 0
[2,4,5,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[2,5,1,3,4] => [3,5,1,4,2] => [5,3,4,1,2] => 0
[2,5,1,4,3] => [3,5,1,4,2] => [5,3,4,1,2] => 0
[2,5,3,1,4] => [4,5,3,1,2] => [4,5,3,1,2] => 0
[2,5,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[2,5,4,1,3] => [4,5,3,1,2] => [4,5,3,1,2] => 0
[2,5,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[3,1,2,4,5] => [3,2,1,4,5] => [3,4,5,2,1] => 0
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,5,4,1] => 1
[3,1,4,2,5] => [4,2,3,1,5] => [2,4,3,5,1] => 0
[3,1,4,5,2] => [5,2,3,4,1] => [5,2,3,4,1] => 0
[3,1,5,2,4] => [4,2,5,1,3] => [4,5,2,3,1] => 0
[3,1,5,4,2] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[3,2,1,4,5] => [3,2,1,4,5] => [3,4,5,2,1] => 0
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,5,4,1] => 1
[3,2,4,1,5] => [4,2,3,1,5] => [2,4,3,5,1] => 0
[3,2,4,5,1] => [5,2,3,4,1] => [5,2,3,4,1] => 0
[3,2,5,1,4] => [4,2,5,1,3] => [4,5,2,3,1] => 0
[3,2,5,4,1] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[3,4,1,2,5] => [4,3,2,1,5] => [4,5,3,2,1] => 0
[3,4,1,5,2] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[3,4,2,1,5] => [4,3,2,1,5] => [4,5,3,2,1] => 0
[3,4,2,5,1] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[3,4,5,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[3,4,5,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[3,5,1,2,4] => [4,5,3,1,2] => [4,5,3,1,2] => 0
[3,5,1,4,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
>>> Load all 895 entries. <<<[3,5,2,1,4] => [4,5,3,1,2] => [4,5,3,1,2] => 0
[3,5,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[3,5,4,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[3,5,4,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,1,2,3,5] => [4,2,3,1,5] => [2,4,3,5,1] => 0
[4,1,2,5,3] => [5,2,3,4,1] => [5,2,3,4,1] => 0
[4,1,3,2,5] => [4,2,3,1,5] => [2,4,3,5,1] => 0
[4,1,3,5,2] => [5,2,3,4,1] => [5,2,3,4,1] => 0
[4,1,5,2,3] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[4,1,5,3,2] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[4,2,1,3,5] => [4,3,2,1,5] => [4,5,3,2,1] => 0
[4,2,1,5,3] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[4,2,3,1,5] => [4,3,2,1,5] => [4,5,3,2,1] => 0
[4,2,3,5,1] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[4,2,5,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,2,5,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,3,1,2,5] => [4,3,2,1,5] => [4,5,3,2,1] => 0
[4,3,1,5,2] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[4,3,2,1,5] => [4,3,2,1,5] => [4,5,3,2,1] => 0
[4,3,2,5,1] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[4,3,5,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,3,5,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,5,1,2,3] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,5,1,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,5,2,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,5,2,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,5,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[4,5,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,1,2,3,4] => [5,2,3,4,1] => [5,2,3,4,1] => 0
[5,1,2,4,3] => [5,2,3,4,1] => [5,2,3,4,1] => 0
[5,1,3,2,4] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[5,1,3,4,2] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[5,1,4,2,3] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[5,1,4,3,2] => [5,2,4,3,1] => [5,4,2,3,1] => 0
[5,2,1,3,4] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[5,2,1,4,3] => [5,3,2,4,1] => [5,3,4,2,1] => 0
[5,2,3,1,4] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,2,4,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,3,1,2,4] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,3,1,4,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,3,2,1,4] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,3,4,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,3,4,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,4,1,2,3] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,4,1,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,4,2,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,4,2,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,4,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 0
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,5,2,3,4,6] => 0
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 0
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 0
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 0
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 0
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,1,6,2,3,5] => 1
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 0
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [6,1,4,2,3,5] => 0
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [5,6,1,2,3,4] => 0
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 0
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 0
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [6,1,4,2,3,5] => 0
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,5,4,2,3,6] => 0
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [6,1,4,2,3,5] => 0
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 0
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 0
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [6,1,4,2,3,5] => 0
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [6,1,4,2,3,5] => 0
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 0
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 0
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 0
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 0
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,4,5,2,6] => 0
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,1,2,6,4,5] => 4
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 1
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 1
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 1
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,1,5,2,4] => 1
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,5,3,2,6] => 0
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 1
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,5,3,4,2,6] => 0
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [6,1,3,4,2,5] => 0
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [5,6,1,3,2,4] => 0
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 0
[1,3,5,2,6,4] => [1,4,6,2,5,3] => [6,4,5,1,2,3] => 0
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,3,5,4,6,2] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [5,6,4,1,2,3] => 0
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,3,6,2,4,5] => [1,4,6,2,5,3] => [6,4,5,1,2,3] => 0
[1,3,6,2,5,4] => [1,4,6,2,5,3] => [6,4,5,1,2,3] => 0
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [5,6,4,1,2,3] => 0
[1,3,6,4,5,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [5,6,4,1,2,3] => 0
[1,3,6,5,4,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,4,5,3,2,6] => 0
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 1
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,5,3,4,2,6] => 0
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [6,1,3,4,2,5] => 0
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [5,6,1,3,2,4] => 0
[1,4,2,6,5,3] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,5,3,2,6] => 0
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,1,6,3,2,5] => 1
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,5,3,4,2,6] => 0
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [6,1,3,4,2,5] => 0
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [5,6,1,3,2,4] => 0
[1,4,3,6,5,2] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,4,5,2,6,3] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,4,5,3,6,2] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,4,6,2,3,5] => [1,5,6,4,2,3] => [5,6,4,1,2,3] => 0
[1,4,6,2,5,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,4,6,3,2,5] => [1,5,6,4,2,3] => [5,6,4,1,2,3] => 0
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,4,6,5,2,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,4,6,5,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [1,5,3,4,2,6] => 0
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [6,1,3,4,2,5] => 0
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [1,5,3,4,2,6] => 0
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [6,1,3,4,2,5] => 0
[1,5,2,6,3,4] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,5,2,6,4,3] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,5,3,2,6,4] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,5,3,4,6,2] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,5,4,2,6,3] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 0
[1,5,4,3,6,2] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,4,6,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,6,2,3,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,6,2,4,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,6,3,2,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,6,4,2,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,5,6,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,2,3,4,5] => [1,6,3,4,5,2] => [6,1,3,4,2,5] => 0
[1,6,2,3,5,4] => [1,6,3,4,5,2] => [6,1,3,4,2,5] => 0
[1,6,2,4,3,5] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,6,2,4,5,3] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,6,2,5,3,4] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,6,2,5,4,3] => [1,6,3,5,4,2] => [6,5,1,3,2,4] => 0
[1,6,3,2,4,5] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,6,3,2,5,4] => [1,6,4,3,5,2] => [6,1,4,3,2,5] => 0
[1,6,3,4,2,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,3,5,4,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,4,2,3,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,4,3,2,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,4,3,5,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,4,5,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,5,2,3,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,5,2,4,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,5,3,2,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,5,3,4,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,5,4,2,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 0
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,3,4,5,6,1] => 0
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 1
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,3,1,5,6,4] => 4
[2,1,3,5,6,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 1
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 1
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,1,3,5,4] => 1
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,4,5,1,6,3] => 1
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 1
[2,1,4,5,6,3] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => 1
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [2,5,1,3,6,4] => 1
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 1
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 1
[2,1,5,3,6,4] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => 1
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,5,4,1,6,3] => 1
[2,1,5,4,6,3] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => 1
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 1
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 1
[2,1,6,3,4,5] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => 1
[2,1,6,3,5,4] => [2,1,6,4,5,3] => [6,2,4,1,5,3] => 1
[2,1,6,4,3,5] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 1
[2,1,6,4,5,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 1
[2,1,6,5,3,4] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 1
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,1,4,3] => 1
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,4,5,6,2,1] => 0
[2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,4,6,5,1] => 1
[2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,5,2,6,4,1] => 1
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[2,3,1,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[2,3,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[2,3,4,1,5,6] => [4,2,3,1,5,6] => [2,4,5,3,6,1] => 0
[2,3,4,1,6,5] => [4,2,3,1,6,5] => [4,2,6,3,5,1] => 1
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [2,5,3,4,6,1] => 0
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[2,3,4,6,1,5] => [5,2,3,6,1,4] => [5,6,2,3,4,1] => 0
[2,3,4,6,5,1] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[2,3,5,1,4,6] => [4,2,5,1,3,6] => [4,5,6,2,3,1] => 0
[2,3,5,1,6,4] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[2,3,5,4,6,1] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[2,3,5,6,4,1] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[2,3,6,1,4,5] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[2,3,6,1,5,4] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[2,3,6,4,5,1] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[2,3,6,5,4,1] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [3,4,5,6,1,2] => 0
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [3,1,4,6,2,5] => 1
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [3,5,4,6,1,2] => 0
[2,4,1,5,6,3] => [3,6,1,4,5,2] => [6,3,4,5,1,2] => 0
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [3,5,1,6,2,4] => 1
[2,4,1,6,5,3] => [3,6,1,5,4,2] => [6,5,3,4,1,2] => 0
[2,4,3,1,5,6] => [4,3,2,1,5,6] => [4,5,6,3,2,1] => 0
[2,4,3,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 1
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[2,4,3,5,6,1] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[2,4,3,6,1,5] => [5,3,2,6,1,4] => [5,6,3,4,2,1] => 0
[2,4,3,6,5,1] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [4,5,6,3,1,2] => 0
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[2,4,5,3,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[2,4,5,6,1,3] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[2,4,5,6,3,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[2,4,6,1,3,5] => [4,5,6,1,2,3] => [4,5,6,1,2,3] => 0
[2,4,6,1,5,3] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => 0
[2,4,6,3,1,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 0
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[2,4,6,5,1,3] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[2,4,6,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [3,5,4,6,1,2] => 0
[2,5,1,3,6,4] => [3,6,1,4,5,2] => [6,3,4,5,1,2] => 0
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [3,5,4,6,1,2] => 0
[2,5,1,4,6,3] => [3,6,1,4,5,2] => [6,3,4,5,1,2] => 0
[2,5,1,6,3,4] => [3,6,1,5,4,2] => [6,5,3,4,1,2] => 0
[2,5,1,6,4,3] => [3,6,1,5,4,2] => [6,5,3,4,1,2] => 0
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [4,5,6,3,1,2] => 0
[2,5,3,1,6,4] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[2,5,3,4,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[2,5,3,6,1,4] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[2,5,3,6,4,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [4,5,6,3,1,2] => 0
[2,5,4,1,6,3] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[2,5,4,3,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[2,5,4,6,1,3] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[2,5,4,6,3,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[2,5,6,1,3,4] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => 0
[2,5,6,1,4,3] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => 0
[2,5,6,3,1,4] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[2,5,6,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[2,5,6,4,1,3] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[2,5,6,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[2,6,1,3,4,5] => [3,6,1,4,5,2] => [6,3,4,5,1,2] => 0
[2,6,1,3,5,4] => [3,6,1,4,5,2] => [6,3,4,5,1,2] => 0
[2,6,1,4,3,5] => [3,6,1,5,4,2] => [6,5,3,4,1,2] => 0
[2,6,1,4,5,3] => [3,6,1,5,4,2] => [6,5,3,4,1,2] => 0
[2,6,1,5,3,4] => [3,6,1,5,4,2] => [6,5,3,4,1,2] => 0
[2,6,1,5,4,3] => [3,6,1,5,4,2] => [6,5,3,4,1,2] => 0
[2,6,3,1,4,5] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[2,6,3,1,5,4] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[2,6,3,4,1,5] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[2,6,3,4,5,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[2,6,3,5,1,4] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[2,6,3,5,4,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[2,6,4,1,3,5] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => 0
[2,6,4,1,5,3] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => 0
[2,6,4,3,1,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[2,6,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[2,6,4,5,1,3] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[2,6,4,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[2,6,5,1,3,4] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => 0
[2,6,5,1,4,3] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => 0
[2,6,5,3,1,4] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[2,6,5,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[2,6,5,4,1,3] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[2,6,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [3,4,5,6,2,1] => 0
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [3,2,4,6,5,1] => 1
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [3,5,2,6,4,1] => 1
[3,1,2,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[3,1,2,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[3,1,4,2,5,6] => [4,2,3,1,5,6] => [2,4,5,3,6,1] => 0
[3,1,4,2,6,5] => [4,2,3,1,6,5] => [4,2,6,3,5,1] => 1
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [2,5,3,4,6,1] => 0
[3,1,4,5,6,2] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[3,1,4,6,2,5] => [5,2,3,6,1,4] => [5,6,2,3,4,1] => 0
[3,1,4,6,5,2] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[3,1,5,2,4,6] => [4,2,5,1,3,6] => [4,5,6,2,3,1] => 0
[3,1,5,2,6,4] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[3,1,5,4,6,2] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[3,1,5,6,2,4] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[3,1,5,6,4,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[3,1,6,2,4,5] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[3,1,6,2,5,4] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[3,1,6,4,2,5] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[3,1,6,4,5,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[3,1,6,5,2,4] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[3,1,6,5,4,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,4,5,6,2,1] => 0
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,4,6,5,1] => 1
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,5,2,6,4,1] => 1
[3,2,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[3,2,1,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 9
[3,2,4,1,5,6] => [4,2,3,1,5,6] => [2,4,5,3,6,1] => 0
[3,2,4,1,6,5] => [4,2,3,1,6,5] => [4,2,6,3,5,1] => 1
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [2,5,3,4,6,1] => 0
[3,2,4,5,6,1] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[3,2,4,6,1,5] => [5,2,3,6,1,4] => [5,6,2,3,4,1] => 0
[3,2,4,6,5,1] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[3,2,5,1,4,6] => [4,2,5,1,3,6] => [4,5,6,2,3,1] => 0
[3,2,5,1,6,4] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[3,2,5,4,6,1] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[3,2,5,6,1,4] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[3,2,5,6,4,1] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[3,2,6,1,4,5] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[3,2,6,1,5,4] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 2
[3,2,6,4,1,5] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[3,2,6,4,5,1] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[3,2,6,5,1,4] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[3,2,6,5,4,1] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [4,5,6,3,2,1] => 0
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 1
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[3,4,1,5,6,2] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[3,4,1,6,2,5] => [5,3,2,6,1,4] => [5,6,3,4,2,1] => 0
[3,4,1,6,5,2] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[3,4,2,1,5,6] => [4,3,2,1,5,6] => [4,5,6,3,2,1] => 0
[3,4,2,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 1
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[3,4,2,5,6,1] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[3,4,2,6,1,5] => [5,3,2,6,1,4] => [5,6,3,4,2,1] => 0
[3,4,2,6,5,1] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[3,4,5,1,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[3,4,5,2,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[3,4,5,6,1,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,4,5,6,2,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,4,6,1,2,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 0
[3,4,6,1,5,2] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[3,4,6,2,1,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 0
[3,4,6,2,5,1] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[3,4,6,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,4,6,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [4,5,6,3,1,2] => 0
[3,5,1,2,6,4] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[3,5,1,4,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[3,5,1,6,2,4] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[3,5,1,6,4,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [4,5,6,3,1,2] => 0
[3,5,2,1,6,4] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[3,5,2,4,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[3,5,2,6,1,4] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[3,5,2,6,4,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[3,5,4,1,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[3,5,4,2,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[3,5,4,6,1,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,5,4,6,2,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,5,6,1,2,4] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[3,5,6,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,5,6,2,1,4] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[3,5,6,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,5,6,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,5,6,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,6,1,2,4,5] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[3,6,1,2,5,4] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[3,6,1,4,2,5] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[3,6,1,4,5,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,6,1,5,2,4] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,6,2,1,4,5] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[3,6,2,1,5,4] => [4,6,3,1,5,2] => [4,3,6,5,1,2] => 1
[3,6,2,4,1,5] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[3,6,2,4,5,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,6,2,5,1,4] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[3,6,2,5,4,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[3,6,4,1,2,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[3,6,4,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,6,4,2,1,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[3,6,4,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,6,4,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,6,4,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,6,5,1,2,4] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[3,6,5,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,6,5,2,1,4] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[3,6,5,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,6,5,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[3,6,5,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,1,2,3,5,6] => [4,2,3,1,5,6] => [2,4,5,3,6,1] => 0
[4,1,2,3,6,5] => [4,2,3,1,6,5] => [4,2,6,3,5,1] => 1
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [2,5,3,4,6,1] => 0
[4,1,2,5,6,3] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[4,1,2,6,3,5] => [5,2,3,6,1,4] => [5,6,2,3,4,1] => 0
[4,1,2,6,5,3] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[4,1,3,2,5,6] => [4,2,3,1,5,6] => [2,4,5,3,6,1] => 0
[4,1,3,2,6,5] => [4,2,3,1,6,5] => [4,2,6,3,5,1] => 1
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [2,5,3,4,6,1] => 0
[4,1,3,5,6,2] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[4,1,3,6,2,5] => [5,2,3,6,1,4] => [5,6,2,3,4,1] => 0
[4,1,3,6,5,2] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[4,1,5,2,6,3] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[4,1,5,3,2,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[4,1,5,3,6,2] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[4,1,5,6,2,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[4,1,5,6,3,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[4,1,6,2,3,5] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[4,1,6,2,5,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[4,1,6,3,2,5] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 1
[4,1,6,3,5,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[4,1,6,5,2,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[4,1,6,5,3,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[4,2,1,3,5,6] => [4,3,2,1,5,6] => [4,5,6,3,2,1] => 0
[4,2,1,3,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 1
[4,2,1,5,3,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[4,2,1,5,6,3] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[4,2,1,6,3,5] => [5,3,2,6,1,4] => [5,6,3,4,2,1] => 0
[4,2,1,6,5,3] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,5,6,3,2,1] => 0
[4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 1
[4,2,3,5,1,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[4,2,3,5,6,1] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[4,2,3,6,1,5] => [5,3,2,6,1,4] => [5,6,3,4,2,1] => 0
[4,2,3,6,5,1] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,2,5,1,6,3] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,2,5,3,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,2,5,6,1,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,2,5,6,3,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,2,6,1,3,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 0
[4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[4,2,6,3,1,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 0
[4,2,6,3,5,1] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[4,2,6,5,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,2,6,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,3,1,2,5,6] => [4,3,2,1,5,6] => [4,5,6,3,2,1] => 0
[4,3,1,2,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 1
[4,3,1,5,2,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[4,3,1,5,6,2] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[4,3,1,6,2,5] => [5,3,2,6,1,4] => [5,6,3,4,2,1] => 0
[4,3,1,6,5,2] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,5,6,3,2,1] => 0
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,6,5,2,1] => 1
[4,3,2,5,1,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[4,3,2,5,6,1] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[4,3,2,6,1,5] => [5,3,2,6,1,4] => [5,6,3,4,2,1] => 0
[4,3,2,6,5,1] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,3,5,1,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,3,5,2,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,3,5,6,1,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,3,5,6,2,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,3,6,1,2,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 0
[4,3,6,1,5,2] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[4,3,6,2,1,5] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 0
[4,3,6,2,5,1] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[4,3,6,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,3,6,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,5,1,2,6,3] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,5,1,3,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,5,1,6,2,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,5,1,6,3,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,5,2,1,6,3] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,5,2,3,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,5,2,6,1,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,5,2,6,3,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,5,3,1,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[4,5,3,2,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[4,5,3,6,1,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,5,3,6,2,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,5,6,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,5,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,5,6,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,5,6,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,5,6,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,1,2,3,5] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[4,6,1,2,5,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,6,1,3,2,5] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[4,6,1,3,5,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,6,1,5,2,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,6,1,5,3,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[4,6,2,1,3,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[4,6,2,1,5,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,2,3,1,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[4,6,2,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,2,5,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,2,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,3,1,2,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,3,2,1,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[4,6,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,3,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,3,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,5,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,5,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[4,6,5,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,1,2,3,4,6] => [5,2,3,4,1,6] => [2,5,3,4,6,1] => 0
[5,1,2,3,6,4] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[5,1,2,4,3,6] => [5,2,3,4,1,6] => [2,5,3,4,6,1] => 0
[5,1,2,4,6,3] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[5,1,2,6,3,4] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[5,1,2,6,4,3] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[5,1,3,2,4,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[5,1,3,2,6,4] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[5,1,3,4,2,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[5,1,3,4,6,2] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[5,1,3,6,2,4] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,3,6,4,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,4,2,3,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[5,1,4,2,6,3] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[5,1,4,3,2,6] => [5,2,4,3,1,6] => [2,5,4,3,6,1] => 0
[5,1,4,3,6,2] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[5,1,4,6,2,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,4,6,3,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,6,2,3,4] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,6,2,4,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,6,3,2,4] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,6,3,4,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,6,4,2,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,1,6,4,3,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[5,2,1,3,4,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[5,2,1,3,6,4] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[5,2,1,4,3,6] => [5,3,2,4,1,6] => [3,5,4,6,2,1] => 0
[5,2,1,4,6,3] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[5,2,1,6,3,4] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[5,2,1,6,4,3] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,2,3,1,6,4] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,2,3,4,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,2,3,6,1,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,2,3,6,4,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,2,4,1,6,3] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,2,4,3,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,2,4,6,1,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,2,4,6,3,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,2,6,1,3,4] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[5,2,6,1,4,3] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[5,2,6,3,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,2,6,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,2,6,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,3,1,2,6,4] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,3,1,4,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,3,1,6,2,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,3,1,6,4,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,3,2,1,6,4] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,3,2,4,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,3,2,6,4,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,3,4,1,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,3,4,2,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,3,4,6,1,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,3,4,6,2,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,3,6,1,2,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,3,6,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,3,6,2,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,3,6,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,3,6,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,3,6,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,4,1,2,6,3] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,4,1,3,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,4,1,6,2,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,4,1,6,3,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,4,2,1,6,3] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,4,2,3,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,4,2,6,1,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,4,2,6,3,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,4,3,1,6,2] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,6,4,3,2,1] => 0
[5,4,3,2,6,1] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[5,4,3,6,1,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,4,3,6,2,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,4,6,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,4,6,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,4,6,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,4,6,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,1,2,3,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,6,1,2,4,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,6,1,3,2,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,6,1,3,4,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,6,1,4,2,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,6,1,4,3,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[5,6,2,1,3,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,2,1,4,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,2,3,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,2,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,2,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,2,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,3,1,2,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,3,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,3,2,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,3,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,4,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,4,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,4,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,6,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,1,2,3,4,5] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[6,1,2,3,5,4] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 0
[6,1,2,4,3,5] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[6,1,2,4,5,3] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[6,1,2,5,3,4] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[6,1,2,5,4,3] => [6,2,3,5,4,1] => [6,5,2,3,4,1] => 0
[6,1,3,2,4,5] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[6,1,3,2,5,4] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 0
[6,1,3,4,2,5] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,3,4,5,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,3,5,2,4] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,3,5,4,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,4,2,3,5] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,4,2,5,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,4,3,2,5] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,4,3,5,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,4,5,2,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,4,5,3,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,5,2,3,4] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,5,2,4,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,5,3,2,4] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,5,3,4,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,5,4,2,3] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,1,5,4,3,2] => [6,2,5,4,3,1] => [6,5,4,2,3,1] => 0
[6,2,1,3,4,5] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[6,2,1,3,5,4] => [6,3,2,4,5,1] => [6,3,4,5,2,1] => 0
[6,2,1,4,3,5] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[6,2,1,4,5,3] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[6,2,1,5,3,4] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[6,2,1,5,4,3] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 1
[6,2,3,1,4,5] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[6,2,3,1,5,4] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[6,2,3,4,1,5] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,2,3,5,1,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,2,4,1,3,5] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[6,2,4,1,5,3] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[6,2,4,3,1,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,2,4,5,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,2,4,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,2,5,1,3,4] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[6,2,5,1,4,3] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[6,2,5,3,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,2,5,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,2,5,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,1,2,4,5] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[6,3,1,2,5,4] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[6,3,1,4,2,5] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,3,1,4,5,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,3,1,5,2,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,3,1,5,4,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,3,2,1,4,5] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[6,3,2,1,5,4] => [6,4,3,2,5,1] => [6,4,5,3,2,1] => 0
[6,3,2,4,1,5] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,3,2,5,1,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,3,4,1,2,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,4,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,4,2,1,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,4,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,4,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,4,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,5,1,2,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,5,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,5,2,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,5,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,5,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,3,5,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,1,2,3,5] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,4,1,2,5,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,4,1,3,2,5] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,4,1,3,5,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,4,1,5,2,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,4,1,5,3,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,4,2,1,3,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,2,1,5,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,2,3,1,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,2,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,2,5,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,2,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,3,1,2,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,3,2,1,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,3,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,3,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,5,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,5,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,5,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,4,5,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,1,2,3,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,5,1,2,4,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,5,1,3,2,4] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,5,1,3,4,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,5,1,4,2,3] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,5,1,4,3,2] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[6,5,2,1,3,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,2,1,4,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,2,3,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,2,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,2,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,2,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,3,1,2,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,3,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,3,2,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,3,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,4,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,4,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,4,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,4,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => 0
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,5,3,6,7] => 0
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => 1
[1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 0
[1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 0
[1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 0
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => 0
[1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 1
[1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => 1
[1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,5,6,3,2,7] => 0
[1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 1
[1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [1,3,5,4,6,2,7] => 0
[1,3,5,2,4,6,7] => [1,4,5,2,3,6,7] => [1,4,5,6,2,3,7] => 0
[1,4,2,3,5,6,7] => [1,4,3,2,5,6,7] => [1,4,5,6,3,2,7] => 0
[1,4,2,3,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 1
[1,4,2,5,3,6,7] => [1,5,3,4,2,6,7] => [1,3,5,4,6,2,7] => 0
[1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,5,6,3,2,7] => 0
[1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,6,5,2,7] => 1
[1,4,3,5,2,6,7] => [1,5,3,4,2,6,7] => [1,3,5,4,6,2,7] => 0
[1,5,2,3,4,6,7] => [1,5,3,4,2,6,7] => [1,3,5,4,6,2,7] => 0
[1,5,2,4,3,6,7] => [1,5,3,4,2,6,7] => [1,3,5,4,6,2,7] => 0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
23,1 111,9 615,84,9,1,2,0,0,0,0,9
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 6$
$F_{4} = 23 + q$
$F_{5} = 111 + 9\ q$
$F_{6} = 615 + 84\ q + 9\ q^{2} + q^{3} + 2\ q^{4} + 9\ q^{9}$
Description
The number of occurrences of the pattern 2143 in a permutation.
A permutation $\pi$ avoids this pattern if and only if it is vexillary as introduced in [1].
A permutation $\pi$ avoids this pattern if and only if it is vexillary as introduced in [1].
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
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 $\pi = \pi^{-1}$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!