Identifier
-
Mp00086:
Permutations
—first fundamental transformation⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000241: Permutations ⟶ ℤ
Values
[1] => [1] => [1] => 1
[1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => 1
[2,1,3] => [2,1,3] => [2,1,3] => 1
[2,3,1] => [3,2,1] => [3,2,1] => 1
[3,1,2] => [2,3,1] => [3,1,2] => 0
[3,2,1] => [3,1,2] => [2,3,1] => 3
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 0
[1,4,2,3] => [1,3,4,2] => [1,4,2,3] => 0
[1,4,3,2] => [1,4,2,3] => [1,3,4,2] => 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
[2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[2,3,4,1] => [4,2,3,1] => [4,2,3,1] => 1
[2,4,1,3] => [3,2,4,1] => [4,2,1,3] => 0
[2,4,3,1] => [4,2,1,3] => [3,2,4,1] => 2
[3,1,2,4] => [2,3,1,4] => [3,1,2,4] => 0
[3,1,4,2] => [3,4,1,2] => [3,4,1,2] => 0
[3,2,1,4] => [3,1,2,4] => [2,3,1,4] => 2
[3,2,4,1] => [4,3,2,1] => [4,3,2,1] => 2
[3,4,1,2] => [2,4,3,1] => [4,1,3,2] => 0
[3,4,2,1] => [4,1,3,2] => [2,4,3,1] => 2
[4,1,2,3] => [2,3,4,1] => [4,1,2,3] => 0
[4,1,3,2] => [3,4,2,1] => [4,3,1,2] => 1
[4,2,1,3] => [3,1,4,2] => [2,4,1,3] => 1
[4,2,3,1] => [4,3,1,2] => [3,4,2,1] => 1
[4,3,1,2] => [2,4,1,3] => [3,1,4,2] => 1
[4,3,2,1] => [4,1,2,3] => [2,3,4,1] => 4
[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] => [1,2,3,5,4] => 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[1,2,5,3,4] => [1,2,4,5,3] => [1,2,5,3,4] => 0
[1,2,5,4,3] => [1,2,5,3,4] => [1,2,4,5,3] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[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] => [1,5,3,4,2] => 0
[1,3,5,2,4] => [1,4,3,5,2] => [1,5,3,2,4] => 0
[1,3,5,4,2] => [1,5,3,2,4] => [1,4,3,5,2] => 1
[1,4,2,3,5] => [1,3,4,2,5] => [1,4,2,3,5] => 0
[1,4,2,5,3] => [1,4,5,2,3] => [1,4,5,2,3] => 0
[1,4,3,2,5] => [1,4,2,3,5] => [1,3,4,2,5] => 2
[1,4,3,5,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1
[1,4,5,2,3] => [1,3,5,4,2] => [1,5,2,4,3] => 0
[1,4,5,3,2] => [1,5,2,4,3] => [1,3,5,4,2] => 1
[1,5,2,3,4] => [1,3,4,5,2] => [1,5,2,3,4] => 0
[1,5,2,4,3] => [1,4,5,3,2] => [1,5,4,2,3] => 1
[1,5,3,2,4] => [1,4,2,5,3] => [1,3,5,2,4] => 1
[1,5,3,4,2] => [1,5,4,2,3] => [1,4,5,3,2] => 0
[1,5,4,2,3] => [1,3,5,2,4] => [1,4,2,5,3] => 1
[1,5,4,3,2] => [1,5,2,3,4] => [1,3,4,5,2] => 3
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 2
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 2
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => 1
[2,1,5,3,4] => [2,1,4,5,3] => [2,1,5,3,4] => 1
[2,1,5,4,3] => [2,1,5,3,4] => [2,1,4,5,3] => 3
[2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 0
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 1
[2,3,4,1,5] => [4,2,3,1,5] => [4,2,3,1,5] => 0
[2,3,4,5,1] => [5,2,3,4,1] => [5,2,3,4,1] => 1
[2,3,5,1,4] => [4,2,3,5,1] => [5,2,3,1,4] => 0
[2,3,5,4,1] => [5,2,3,1,4] => [4,2,3,5,1] => 2
[2,4,1,3,5] => [3,2,4,1,5] => [4,2,1,3,5] => 0
[2,4,1,5,3] => [4,2,5,1,3] => [4,2,5,1,3] => 0
[2,4,3,1,5] => [4,2,1,3,5] => [3,2,4,1,5] => 1
[2,4,3,5,1] => [5,2,4,3,1] => [5,2,4,3,1] => 2
[2,4,5,1,3] => [3,2,5,4,1] => [5,2,1,4,3] => 0
[2,4,5,3,1] => [5,2,1,4,3] => [3,2,5,4,1] => 1
[2,5,1,3,4] => [3,2,4,5,1] => [5,2,1,3,4] => 0
[2,5,1,4,3] => [4,2,5,3,1] => [5,2,4,1,3] => 1
[2,5,3,1,4] => [4,2,1,5,3] => [3,2,5,1,4] => 0
[2,5,3,4,1] => [5,2,4,1,3] => [4,2,5,3,1] => 1
[2,5,4,1,3] => [3,2,5,1,4] => [4,2,1,5,3] => 1
[2,5,4,3,1] => [5,2,1,3,4] => [3,2,4,5,1] => 3
[3,1,2,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => 0
[3,1,2,5,4] => [2,3,1,5,4] => [3,1,2,5,4] => 1
[3,1,4,2,5] => [3,4,1,2,5] => [3,4,1,2,5] => 0
[3,1,4,5,2] => [3,5,1,4,2] => [3,5,1,4,2] => 0
[3,1,5,2,4] => [3,4,1,5,2] => [3,5,1,2,4] => 0
[3,1,5,4,2] => [3,5,1,2,4] => [3,4,1,5,2] => 1
[3,2,1,4,5] => [3,1,2,4,5] => [2,3,1,4,5] => 2
[3,2,1,5,4] => [3,1,2,5,4] => [2,3,1,5,4] => 3
[3,2,4,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1
[3,2,4,5,1] => [5,3,2,4,1] => [5,3,2,4,1] => 2
[3,2,5,1,4] => [4,3,2,5,1] => [5,3,2,1,4] => 1
[3,2,5,4,1] => [5,3,2,1,4] => [4,3,2,5,1] => 3
[3,4,1,2,5] => [2,4,3,1,5] => [4,1,3,2,5] => 0
[3,4,1,5,2] => [4,5,3,1,2] => [4,5,3,1,2] => 0
[3,4,2,1,5] => [4,1,3,2,5] => [2,4,3,1,5] => 1
[3,4,2,5,1] => [5,4,3,2,1] => [5,4,3,2,1] => 1
[3,4,5,1,2] => [2,5,3,4,1] => [5,1,3,4,2] => 0
[3,4,5,2,1] => [5,1,3,4,2] => [2,5,3,4,1] => 2
[3,5,1,2,4] => [2,4,3,5,1] => [5,1,3,2,4] => 0
[3,5,1,4,2] => [4,5,3,2,1] => [5,4,3,1,2] => 0
>>> Load all 873 entries. <<<[3,5,2,1,4] => [4,1,3,5,2] => [2,5,3,1,4] => 1
[3,5,2,4,1] => [5,4,3,1,2] => [4,5,3,2,1] => 1
[3,5,4,1,2] => [2,5,3,1,4] => [4,1,3,5,2] => 1
[3,5,4,2,1] => [5,1,3,2,4] => [2,4,3,5,1] => 3
[4,1,2,3,5] => [2,3,4,1,5] => [4,1,2,3,5] => 0
[4,1,2,5,3] => [2,4,5,1,3] => [4,1,5,2,3] => 0
[4,1,3,2,5] => [3,4,2,1,5] => [4,3,1,2,5] => 1
[4,1,3,5,2] => [3,5,4,1,2] => [4,5,1,3,2] => 0
[4,1,5,2,3] => [4,3,5,1,2] => [4,5,2,1,3] => 0
[4,1,5,3,2] => [4,5,2,1,3] => [4,3,5,1,2] => 1
[4,2,1,3,5] => [3,1,4,2,5] => [2,4,1,3,5] => 1
[4,2,1,5,3] => [4,1,5,2,3] => [2,4,5,1,3] => 1
[4,2,3,1,5] => [4,3,1,2,5] => [3,4,2,1,5] => 0
[4,2,3,5,1] => [5,3,4,2,1] => [5,4,2,3,1] => 1
[4,2,5,1,3] => [3,4,5,2,1] => [5,4,1,2,3] => 0
[4,2,5,3,1] => [5,4,1,2,3] => [3,4,5,2,1] => 1
[4,3,1,2,5] => [2,4,1,3,5] => [3,1,4,2,5] => 1
[4,3,1,5,2] => [4,5,1,3,2] => [3,5,4,1,2] => 1
[4,3,2,1,5] => [4,1,2,3,5] => [2,3,4,1,5] => 3
[4,3,2,5,1] => [5,4,2,3,1] => [5,3,4,2,1] => 3
[4,3,5,1,2] => [2,5,4,3,1] => [5,1,4,3,2] => 1
[4,3,5,2,1] => [5,1,4,3,2] => [2,5,4,3,1] => 3
[4,5,1,2,3] => [2,3,5,4,1] => [5,1,2,4,3] => 0
[4,5,1,3,2] => [3,5,2,4,1] => [5,3,1,4,2] => 1
[4,5,2,1,3] => [3,1,5,4,2] => [2,5,1,4,3] => 1
[4,5,2,3,1] => [5,3,1,4,2] => [3,5,2,4,1] => 1
[4,5,3,1,2] => [2,5,1,4,3] => [3,1,5,4,2] => 0
[4,5,3,2,1] => [5,1,2,4,3] => [2,3,5,4,1] => 3
[5,1,2,3,4] => [2,3,4,5,1] => [5,1,2,3,4] => 0
[5,1,2,4,3] => [2,4,5,3,1] => [5,1,4,2,3] => 1
[5,1,3,2,4] => [3,4,2,5,1] => [5,3,1,2,4] => 1
[5,1,3,4,2] => [3,5,4,2,1] => [5,4,1,3,2] => 0
[5,1,4,2,3] => [4,3,5,2,1] => [5,4,2,1,3] => 0
[5,1,4,3,2] => [4,5,2,3,1] => [5,3,4,1,2] => 2
[5,2,1,3,4] => [3,1,4,5,2] => [2,5,1,3,4] => 1
[5,2,1,4,3] => [4,1,5,3,2] => [2,5,4,1,3] => 2
[5,2,3,1,4] => [4,3,1,5,2] => [3,5,2,1,4] => 0
[5,2,3,4,1] => [5,3,4,1,2] => [4,5,2,3,1] => 1
[5,2,4,1,3] => [3,4,5,1,2] => [4,5,1,2,3] => 0
[5,2,4,3,1] => [5,4,1,3,2] => [3,5,4,2,1] => 2
[5,3,1,2,4] => [2,4,1,5,3] => [3,1,5,2,4] => 0
[5,3,1,4,2] => [4,5,1,2,3] => [3,4,5,1,2] => 0
[5,3,2,1,4] => [4,1,2,5,3] => [2,3,5,1,4] => 2
[5,3,2,4,1] => [5,4,2,1,3] => [4,3,5,2,1] => 2
[5,3,4,1,2] => [2,5,4,1,3] => [4,1,5,3,2] => 0
[5,3,4,2,1] => [5,1,4,2,3] => [2,4,5,3,1] => 2
[5,4,1,2,3] => [2,3,5,1,4] => [4,1,2,5,3] => 1
[5,4,1,3,2] => [3,5,2,1,4] => [4,3,1,5,2] => 2
[5,4,2,1,3] => [3,1,5,2,4] => [2,4,1,5,3] => 2
[5,4,2,3,1] => [5,3,1,2,4] => [3,4,2,5,1] => 2
[5,4,3,1,2] => [2,5,1,3,4] => [3,1,4,5,2] => 2
[5,4,3,2,1] => [5,1,2,3,4] => [2,3,4,5,1] => 5
[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] => [1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 0
[1,2,3,6,4,5] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 0
[1,2,3,6,5,4] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 0
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,6,4,5,3] => 0
[1,2,4,6,3,5] => [1,2,5,4,6,3] => [1,2,6,4,3,5] => 0
[1,2,4,6,5,3] => [1,2,6,4,3,5] => [1,2,5,4,6,3] => 1
[1,2,5,3,4,6] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 0
[1,2,5,3,6,4] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 0
[1,2,5,4,3,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
[1,2,5,4,6,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 1
[1,2,5,6,3,4] => [1,2,4,6,5,3] => [1,2,6,3,5,4] => 0
[1,2,5,6,4,3] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => 1
[1,2,6,3,4,5] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 0
[1,2,6,3,5,4] => [1,2,5,6,4,3] => [1,2,6,5,3,4] => 1
[1,2,6,4,3,5] => [1,2,5,3,6,4] => [1,2,4,6,3,5] => 1
[1,2,6,4,5,3] => [1,2,6,5,3,4] => [1,2,5,6,4,3] => 0
[1,2,6,5,3,4] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 1
[1,2,6,5,4,3] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 3
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 1
[1,3,2,6,4,5] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => 1
[1,3,2,6,5,4] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => 3
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 0
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 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] => [1,6,3,4,5,2] => 0
[1,3,4,6,2,5] => [1,5,3,4,6,2] => [1,6,3,4,2,5] => 0
[1,3,4,6,5,2] => [1,6,3,4,2,5] => [1,5,3,4,6,2] => 1
[1,3,5,2,4,6] => [1,4,3,5,2,6] => [1,5,3,2,4,6] => 0
[1,3,5,2,6,4] => [1,5,3,6,2,4] => [1,5,3,6,2,4] => 0
[1,3,5,4,2,6] => [1,5,3,2,4,6] => [1,4,3,5,2,6] => 1
[1,3,5,4,6,2] => [1,6,3,5,4,2] => [1,6,3,5,4,2] => 1
[1,3,5,6,2,4] => [1,4,3,6,5,2] => [1,6,3,2,5,4] => 0
[1,3,5,6,4,2] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => 0
[1,3,6,2,4,5] => [1,4,3,5,6,2] => [1,6,3,2,4,5] => 0
[1,3,6,2,5,4] => [1,5,3,6,4,2] => [1,6,3,5,2,4] => 1
[1,3,6,4,2,5] => [1,5,3,2,6,4] => [1,4,3,6,2,5] => 0
[1,3,6,4,5,2] => [1,6,3,5,2,4] => [1,5,3,6,4,2] => 0
[1,3,6,5,2,4] => [1,4,3,6,2,5] => [1,5,3,2,6,4] => 1
[1,3,6,5,4,2] => [1,6,3,2,4,5] => [1,4,3,5,6,2] => 2
[1,4,2,3,5,6] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 0
[1,4,2,3,6,5] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => 1
[1,4,2,5,3,6] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 0
[1,4,2,5,6,3] => [1,4,6,2,5,3] => [1,4,6,2,5,3] => 0
[1,4,2,6,3,5] => [1,4,5,2,6,3] => [1,4,6,2,3,5] => 0
[1,4,2,6,5,3] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 1
[1,4,3,2,5,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
[1,4,3,2,6,5] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 3
[1,4,3,5,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 1
[1,4,3,5,6,2] => [1,6,4,3,5,2] => [1,6,4,3,5,2] => 1
[1,4,3,6,2,5] => [1,5,4,3,6,2] => [1,6,4,3,2,5] => 1
[1,4,3,6,5,2] => [1,6,4,3,2,5] => [1,5,4,3,6,2] => 2
[1,4,5,2,3,6] => [1,3,5,4,2,6] => [1,5,2,4,3,6] => 0
[1,4,5,2,6,3] => [1,5,6,4,2,3] => [1,5,6,4,2,3] => 0
[1,4,5,3,2,6] => [1,5,2,4,3,6] => [1,3,5,4,2,6] => 1
[1,4,5,3,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 0
[1,4,5,6,2,3] => [1,3,6,4,5,2] => [1,6,2,4,5,3] => 0
[1,4,5,6,3,2] => [1,6,2,4,5,3] => [1,3,6,4,5,2] => 1
[1,4,6,2,3,5] => [1,3,5,4,6,2] => [1,6,2,4,3,5] => 0
[1,4,6,2,5,3] => [1,5,6,4,3,2] => [1,6,5,4,2,3] => 0
[1,4,6,3,2,5] => [1,5,2,4,6,3] => [1,3,6,4,2,5] => 1
[1,4,6,3,5,2] => [1,6,5,4,2,3] => [1,5,6,4,3,2] => 0
[1,4,6,5,2,3] => [1,3,6,4,2,5] => [1,5,2,4,6,3] => 1
[1,4,6,5,3,2] => [1,6,2,4,3,5] => [1,3,5,4,6,2] => 2
[1,5,2,3,4,6] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 0
[1,5,2,3,6,4] => [1,3,5,6,2,4] => [1,5,2,6,3,4] => 0
[1,5,2,4,3,6] => [1,4,5,3,2,6] => [1,5,4,2,3,6] => 1
[1,5,2,4,6,3] => [1,4,6,5,2,3] => [1,5,6,2,4,3] => 0
[1,5,2,6,3,4] => [1,5,4,6,2,3] => [1,5,6,3,2,4] => 0
[1,5,2,6,4,3] => [1,5,6,3,2,4] => [1,5,4,6,2,3] => 1
[1,5,3,2,4,6] => [1,4,2,5,3,6] => [1,3,5,2,4,6] => 1
[1,5,3,2,6,4] => [1,5,2,6,3,4] => [1,3,5,6,2,4] => 1
[1,5,3,4,2,6] => [1,5,4,2,3,6] => [1,4,5,3,2,6] => 0
[1,5,3,4,6,2] => [1,6,4,5,3,2] => [1,6,5,3,4,2] => 0
[1,5,3,6,2,4] => [1,4,5,6,3,2] => [1,6,5,2,3,4] => 0
[1,5,3,6,4,2] => [1,6,5,2,3,4] => [1,4,5,6,3,2] => 0
[1,5,4,2,3,6] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => 1
[1,5,4,2,6,3] => [1,5,6,2,4,3] => [1,4,6,5,2,3] => 1
[1,5,4,3,2,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 3
[1,5,4,3,6,2] => [1,6,5,3,4,2] => [1,6,4,5,3,2] => 2
[1,5,4,6,2,3] => [1,3,6,5,4,2] => [1,6,2,5,4,3] => 1
[1,5,4,6,3,2] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => 2
[1,5,6,2,3,4] => [1,3,4,6,5,2] => [1,6,2,3,5,4] => 0
[1,5,6,2,4,3] => [1,4,6,3,5,2] => [1,6,4,2,5,3] => 1
[1,5,6,3,2,4] => [1,4,2,6,5,3] => [1,3,6,2,5,4] => 1
[1,5,6,3,4,2] => [1,6,4,2,5,3] => [1,4,6,3,5,2] => 0
[1,5,6,4,2,3] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => 0
[1,5,6,4,3,2] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => 2
[1,6,2,3,4,5] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 0
[1,6,2,3,5,4] => [1,3,5,6,4,2] => [1,6,2,5,3,4] => 1
[1,6,2,4,3,5] => [1,4,5,3,6,2] => [1,6,4,2,3,5] => 1
[1,6,2,4,5,3] => [1,4,6,5,3,2] => [1,6,5,2,4,3] => 0
[1,6,2,5,3,4] => [1,5,4,6,3,2] => [1,6,5,3,2,4] => 0
[1,6,2,5,4,3] => [1,5,6,3,4,2] => [1,6,4,5,2,3] => 2
[1,6,3,2,4,5] => [1,4,2,5,6,3] => [1,3,6,2,4,5] => 1
[1,6,3,2,5,4] => [1,5,2,6,4,3] => [1,3,6,5,2,4] => 2
[1,6,3,4,2,5] => [1,5,4,2,6,3] => [1,4,6,3,2,5] => 0
[1,6,3,4,5,2] => [1,6,4,5,2,3] => [1,5,6,3,4,2] => 0
[1,6,3,5,2,4] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => 0
[1,6,3,5,4,2] => [1,6,5,2,4,3] => [1,4,6,5,3,2] => 1
[1,6,4,2,3,5] => [1,3,5,2,6,4] => [1,4,2,6,3,5] => 0
[1,6,4,2,5,3] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 0
[1,6,4,3,2,5] => [1,5,2,3,6,4] => [1,3,4,6,2,5] => 2
[1,6,4,3,5,2] => [1,6,5,3,2,4] => [1,5,4,6,3,2] => 1
[1,6,4,5,2,3] => [1,3,6,5,2,4] => [1,5,2,6,4,3] => 0
[1,6,4,5,3,2] => [1,6,2,5,3,4] => [1,3,5,6,4,2] => 1
[1,6,5,2,3,4] => [1,3,4,6,2,5] => [1,5,2,3,6,4] => 1
[1,6,5,2,4,3] => [1,4,6,3,2,5] => [1,5,4,2,6,3] => 2
[1,6,5,3,2,4] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => 2
[1,6,5,3,4,2] => [1,6,4,2,3,5] => [1,4,5,3,6,2] => 1
[1,6,5,4,2,3] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 2
[1,6,5,4,3,2] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 4
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 1
[2,1,3,6,4,5] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => 1
[2,1,3,6,5,4] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => 3
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 2
[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] => [2,1,5,4,3,6] => 1
[2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,6,4,5,3] => 1
[2,1,4,6,3,5] => [2,1,5,4,6,3] => [2,1,6,4,3,5] => 1
[2,1,4,6,5,3] => [2,1,6,4,3,5] => [2,1,5,4,6,3] => 2
[2,1,5,3,4,6] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => 1
[2,1,5,3,6,4] => [2,1,5,6,3,4] => [2,1,5,6,3,4] => 1
[2,1,5,4,3,6] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => 3
[2,1,5,4,6,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[2,1,5,6,3,4] => [2,1,4,6,5,3] => [2,1,6,3,5,4] => 1
[2,1,5,6,4,3] => [2,1,6,3,5,4] => [2,1,4,6,5,3] => 2
[2,1,6,3,4,5] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => 1
[2,1,6,3,5,4] => [2,1,5,6,4,3] => [2,1,6,5,3,4] => 2
[2,1,6,4,3,5] => [2,1,5,3,6,4] => [2,1,4,6,3,5] => 2
[2,1,6,4,5,3] => [2,1,6,5,3,4] => [2,1,5,6,4,3] => 1
[2,1,6,5,3,4] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => 2
[2,1,6,5,4,3] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => 4
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 0
[2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 1
[2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 1
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 0
[2,3,1,6,4,5] => [3,2,1,5,6,4] => [3,2,1,6,4,5] => 0
[2,3,1,6,5,4] => [3,2,1,6,4,5] => [3,2,1,5,6,4] => 2
[2,3,4,1,5,6] => [4,2,3,1,5,6] => [4,2,3,1,5,6] => 0
[2,3,4,1,6,5] => [4,2,3,1,6,5] => [4,2,3,1,6,5] => 1
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [5,2,3,4,1,6] => 0
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 1
[2,3,4,6,1,5] => [5,2,3,4,6,1] => [6,2,3,4,1,5] => 0
[2,3,4,6,5,1] => [6,2,3,4,1,5] => [5,2,3,4,6,1] => 2
[2,3,5,1,4,6] => [4,2,3,5,1,6] => [5,2,3,1,4,6] => 0
[2,3,5,1,6,4] => [5,2,3,6,1,4] => [5,2,3,6,1,4] => 0
[2,3,5,4,1,6] => [5,2,3,1,4,6] => [4,2,3,5,1,6] => 1
[2,3,5,4,6,1] => [6,2,3,5,4,1] => [6,2,3,5,4,1] => 2
[2,3,5,6,1,4] => [4,2,3,6,5,1] => [6,2,3,1,5,4] => 0
[2,3,5,6,4,1] => [6,2,3,1,5,4] => [4,2,3,6,5,1] => 1
[2,3,6,1,4,5] => [4,2,3,5,6,1] => [6,2,3,1,4,5] => 0
[2,3,6,1,5,4] => [5,2,3,6,4,1] => [6,2,3,5,1,4] => 1
[2,3,6,4,1,5] => [5,2,3,1,6,4] => [4,2,3,6,1,5] => 0
[2,3,6,4,5,1] => [6,2,3,5,1,4] => [5,2,3,6,4,1] => 1
[2,3,6,5,1,4] => [4,2,3,6,1,5] => [5,2,3,1,6,4] => 1
[2,3,6,5,4,1] => [6,2,3,1,4,5] => [4,2,3,5,6,1] => 3
[2,4,1,3,5,6] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => 0
[2,4,1,3,6,5] => [3,2,4,1,6,5] => [4,2,1,3,6,5] => 1
[2,4,1,5,3,6] => [4,2,5,1,3,6] => [4,2,5,1,3,6] => 0
[2,4,1,5,6,3] => [4,2,6,1,5,3] => [4,2,6,1,5,3] => 0
[2,4,1,6,3,5] => [4,2,5,1,6,3] => [4,2,6,1,3,5] => 0
[2,4,1,6,5,3] => [4,2,6,1,3,5] => [4,2,5,1,6,3] => 1
[2,4,3,1,5,6] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => 1
[2,4,3,1,6,5] => [4,2,1,3,6,5] => [3,2,4,1,6,5] => 2
[2,4,3,5,1,6] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => 1
[2,4,3,5,6,1] => [6,2,4,3,5,1] => [6,2,4,3,5,1] => 2
[2,4,3,6,1,5] => [5,2,4,3,6,1] => [6,2,4,3,1,5] => 1
[2,4,3,6,5,1] => [6,2,4,3,1,5] => [5,2,4,3,6,1] => 3
[2,4,5,1,3,6] => [3,2,5,4,1,6] => [5,2,1,4,3,6] => 0
[2,4,5,1,6,3] => [5,2,6,4,1,3] => [5,2,6,4,1,3] => 0
[2,4,5,3,1,6] => [5,2,1,4,3,6] => [3,2,5,4,1,6] => 0
[2,4,5,3,6,1] => [6,2,5,4,3,1] => [6,2,5,4,3,1] => 1
[2,4,5,6,1,3] => [3,2,6,4,5,1] => [6,2,1,4,5,3] => 0
[2,4,5,6,3,1] => [6,2,1,4,5,3] => [3,2,6,4,5,1] => 1
[2,4,6,1,3,5] => [3,2,5,4,6,1] => [6,2,1,4,3,5] => 0
[2,4,6,1,5,3] => [5,2,6,4,3,1] => [6,2,5,4,1,3] => 0
[2,4,6,3,1,5] => [5,2,1,4,6,3] => [3,2,6,4,1,5] => 0
[2,4,6,3,5,1] => [6,2,5,4,1,3] => [5,2,6,4,3,1] => 1
[2,4,6,5,1,3] => [3,2,6,4,1,5] => [5,2,1,4,6,3] => 1
[2,4,6,5,3,1] => [6,2,1,4,3,5] => [3,2,5,4,6,1] => 2
[2,5,1,3,4,6] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => 0
[2,5,1,3,6,4] => [3,2,5,6,1,4] => [5,2,1,6,3,4] => 0
[2,5,1,4,3,6] => [4,2,5,3,1,6] => [5,2,4,1,3,6] => 1
[2,5,1,4,6,3] => [4,2,6,5,1,3] => [5,2,6,1,4,3] => 0
[2,5,1,6,3,4] => [5,2,4,6,1,3] => [5,2,6,3,1,4] => 0
[2,5,1,6,4,3] => [5,2,6,3,1,4] => [5,2,4,6,1,3] => 1
[2,5,3,1,4,6] => [4,2,1,5,3,6] => [3,2,5,1,4,6] => 0
[2,5,3,1,6,4] => [5,2,1,6,3,4] => [3,2,5,6,1,4] => 0
[2,5,3,4,1,6] => [5,2,4,1,3,6] => [4,2,5,3,1,6] => 0
[2,5,3,4,6,1] => [6,2,4,5,3,1] => [6,2,5,3,4,1] => 1
[2,5,3,6,1,4] => [4,2,5,6,3,1] => [6,2,5,1,3,4] => 0
[2,5,3,6,4,1] => [6,2,5,1,3,4] => [4,2,5,6,3,1] => 1
[2,5,4,1,3,6] => [3,2,5,1,4,6] => [4,2,1,5,3,6] => 1
[2,5,4,1,6,3] => [5,2,6,1,4,3] => [4,2,6,5,1,3] => 1
[2,5,4,3,1,6] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => 2
[2,5,4,3,6,1] => [6,2,5,3,4,1] => [6,2,4,5,3,1] => 3
[2,5,4,6,1,3] => [3,2,6,5,4,1] => [6,2,1,5,4,3] => 1
[2,5,4,6,3,1] => [6,2,1,5,4,3] => [3,2,6,5,4,1] => 2
[2,5,6,1,3,4] => [3,2,4,6,5,1] => [6,2,1,3,5,4] => 0
[2,5,6,1,4,3] => [4,2,6,3,5,1] => [6,2,4,1,5,3] => 1
[2,5,6,3,1,4] => [4,2,1,6,5,3] => [3,2,6,1,5,4] => 0
[2,5,6,3,4,1] => [6,2,4,1,5,3] => [4,2,6,3,5,1] => 1
[2,5,6,4,1,3] => [3,2,6,1,5,4] => [4,2,1,6,5,3] => 0
[2,5,6,4,3,1] => [6,2,1,3,5,4] => [3,2,4,6,5,1] => 2
[2,6,1,3,4,5] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => 0
[2,6,1,3,5,4] => [3,2,5,6,4,1] => [6,2,1,5,3,4] => 1
[2,6,1,4,3,5] => [4,2,5,3,6,1] => [6,2,4,1,3,5] => 1
[2,6,1,4,5,3] => [4,2,6,5,3,1] => [6,2,5,1,4,3] => 0
[2,6,1,5,3,4] => [5,2,4,6,3,1] => [6,2,5,3,1,4] => 0
[2,6,1,5,4,3] => [5,2,6,3,4,1] => [6,2,4,5,1,3] => 2
[2,6,3,1,4,5] => [4,2,1,5,6,3] => [3,2,6,1,4,5] => 0
[2,6,3,1,5,4] => [5,2,1,6,4,3] => [3,2,6,5,1,4] => 1
[2,6,3,4,1,5] => [5,2,4,1,6,3] => [4,2,6,3,1,5] => 0
[2,6,3,4,5,1] => [6,2,4,5,1,3] => [5,2,6,3,4,1] => 1
[2,6,3,5,1,4] => [4,2,5,6,1,3] => [5,2,6,1,3,4] => 0
[2,6,3,5,4,1] => [6,2,5,1,4,3] => [4,2,6,5,3,1] => 2
[2,6,4,1,3,5] => [3,2,5,1,6,4] => [4,2,1,6,3,5] => 0
[2,6,4,1,5,3] => [5,2,6,1,3,4] => [4,2,5,6,1,3] => 0
[2,6,4,3,1,5] => [5,2,1,3,6,4] => [3,2,4,6,1,5] => 1
[2,6,4,3,5,1] => [6,2,5,3,1,4] => [5,2,4,6,3,1] => 2
[2,6,4,5,1,3] => [3,2,6,5,1,4] => [5,2,1,6,4,3] => 0
[2,6,4,5,3,1] => [6,2,1,5,3,4] => [3,2,5,6,4,1] => 1
[2,6,5,1,3,4] => [3,2,4,6,1,5] => [5,2,1,3,6,4] => 1
[2,6,5,1,4,3] => [4,2,6,3,1,5] => [5,2,4,1,6,3] => 2
[2,6,5,3,1,4] => [4,2,1,6,3,5] => [3,2,5,1,6,4] => 1
[2,6,5,3,4,1] => [6,2,4,1,3,5] => [4,2,5,3,6,1] => 2
[2,6,5,4,1,3] => [3,2,6,1,4,5] => [4,2,1,5,6,3] => 2
[2,6,5,4,3,1] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => 4
[3,1,2,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 0
[3,1,2,4,6,5] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => 1
[3,1,2,5,4,6] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => 1
[3,1,2,5,6,4] => [2,3,1,6,5,4] => [3,1,2,6,5,4] => 0
[3,1,2,6,4,5] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => 0
[3,1,2,6,5,4] => [2,3,1,6,4,5] => [3,1,2,5,6,4] => 2
[3,1,4,2,5,6] => [3,4,1,2,5,6] => [3,4,1,2,5,6] => 0
[3,1,4,2,6,5] => [3,4,1,2,6,5] => [3,4,1,2,6,5] => 1
[3,1,4,5,2,6] => [3,5,1,4,2,6] => [3,5,1,4,2,6] => 0
[3,1,4,5,6,2] => [3,6,1,4,5,2] => [3,6,1,4,5,2] => 0
[3,1,4,6,2,5] => [3,5,1,4,6,2] => [3,6,1,4,2,5] => 0
[3,1,4,6,5,2] => [3,6,1,4,2,5] => [3,5,1,4,6,2] => 1
[3,1,5,2,4,6] => [3,4,1,5,2,6] => [3,5,1,2,4,6] => 0
[3,1,5,2,6,4] => [3,5,1,6,2,4] => [3,5,1,6,2,4] => 0
[3,1,5,4,2,6] => [3,5,1,2,4,6] => [3,4,1,5,2,6] => 1
[3,1,5,4,6,2] => [3,6,1,5,4,2] => [3,6,1,5,4,2] => 1
[3,1,5,6,2,4] => [3,4,1,6,5,2] => [3,6,1,2,5,4] => 0
[3,1,5,6,4,2] => [3,6,1,2,5,4] => [3,4,1,6,5,2] => 0
[3,1,6,2,4,5] => [3,4,1,5,6,2] => [3,6,1,2,4,5] => 0
[3,1,6,2,5,4] => [3,5,1,6,4,2] => [3,6,1,5,2,4] => 1
[3,1,6,4,2,5] => [3,5,1,2,6,4] => [3,4,1,6,2,5] => 0
[3,1,6,4,5,2] => [3,6,1,5,2,4] => [3,5,1,6,4,2] => 0
[3,1,6,5,2,4] => [3,4,1,6,2,5] => [3,5,1,2,6,4] => 1
[3,1,6,5,4,2] => [3,6,1,2,4,5] => [3,4,1,5,6,2] => 2
[3,2,1,4,5,6] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => 2
[3,2,1,4,6,5] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 3
[3,2,1,5,4,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => 3
[3,2,1,5,6,4] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 2
[3,2,1,6,4,5] => [3,1,2,5,6,4] => [2,3,1,6,4,5] => 2
[3,2,1,6,5,4] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => 4
[3,2,4,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 1
[3,2,4,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 2
[3,2,4,5,1,6] => [5,3,2,4,1,6] => [5,3,2,4,1,6] => 1
[3,2,4,5,6,1] => [6,3,2,4,5,1] => [6,3,2,4,5,1] => 2
[3,2,4,6,1,5] => [5,3,2,4,6,1] => [6,3,2,4,1,5] => 1
[3,2,4,6,5,1] => [6,3,2,4,1,5] => [5,3,2,4,6,1] => 3
[3,2,5,1,4,6] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => 1
[3,2,5,1,6,4] => [5,3,2,6,1,4] => [5,3,2,6,1,4] => 1
[3,2,5,4,1,6] => [5,3,2,1,4,6] => [4,3,2,5,1,6] => 2
[3,2,5,4,6,1] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 3
[3,2,5,6,1,4] => [4,3,2,6,5,1] => [6,3,2,1,5,4] => 1
[3,2,5,6,4,1] => [6,3,2,1,5,4] => [4,3,2,6,5,1] => 2
[3,2,6,1,4,5] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => 1
[3,2,6,1,5,4] => [5,3,2,6,4,1] => [6,3,2,5,1,4] => 2
[3,2,6,4,1,5] => [5,3,2,1,6,4] => [4,3,2,6,1,5] => 1
[3,2,6,4,5,1] => [6,3,2,5,1,4] => [5,3,2,6,4,1] => 2
[3,2,6,5,1,4] => [4,3,2,6,1,5] => [5,3,2,1,6,4] => 2
[3,2,6,5,4,1] => [6,3,2,1,4,5] => [4,3,2,5,6,1] => 4
[3,4,1,2,5,6] => [2,4,3,1,5,6] => [4,1,3,2,5,6] => 0
[3,4,1,2,6,5] => [2,4,3,1,6,5] => [4,1,3,2,6,5] => 1
[3,4,1,5,2,6] => [4,5,3,1,2,6] => [4,5,3,1,2,6] => 0
[3,4,1,5,6,2] => [4,6,3,1,5,2] => [4,6,3,1,5,2] => 0
[3,4,1,6,2,5] => [4,5,3,1,6,2] => [4,6,3,1,2,5] => 0
[3,4,1,6,5,2] => [4,6,3,1,2,5] => [4,5,3,1,6,2] => 1
[3,4,2,1,5,6] => [4,1,3,2,5,6] => [2,4,3,1,5,6] => 1
[3,4,2,1,6,5] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => 2
[3,4,2,5,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 0
[3,4,2,5,6,1] => [6,4,3,2,5,1] => [6,4,3,2,5,1] => 1
[3,4,2,6,1,5] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => 0
[3,4,2,6,5,1] => [6,4,3,2,1,5] => [5,4,3,2,6,1] => 2
[3,4,5,1,2,6] => [2,5,3,4,1,6] => [5,1,3,4,2,6] => 0
[3,4,5,1,6,2] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[3,4,5,2,1,6] => [5,1,3,4,2,6] => [2,5,3,4,1,6] => 1
[3,4,5,2,6,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 1
[3,4,5,6,1,2] => [2,6,3,4,5,1] => [6,1,3,4,5,2] => 0
[3,4,5,6,2,1] => [6,1,3,4,5,2] => [2,6,3,4,5,1] => 2
[3,4,6,1,2,5] => [2,5,3,4,6,1] => [6,1,3,4,2,5] => 0
[3,4,6,1,5,2] => [5,6,3,4,2,1] => [6,5,3,4,1,2] => 0
[3,4,6,2,1,5] => [5,1,3,4,6,2] => [2,6,3,4,1,5] => 1
[3,4,6,2,5,1] => [6,5,3,4,1,2] => [5,6,3,4,2,1] => 1
[3,4,6,5,1,2] => [2,6,3,4,1,5] => [5,1,3,4,6,2] => 1
[3,4,6,5,2,1] => [6,1,3,4,2,5] => [2,5,3,4,6,1] => 3
[3,5,1,2,4,6] => [2,4,3,5,1,6] => [5,1,3,2,4,6] => 0
[3,5,1,2,6,4] => [2,5,3,6,1,4] => [5,1,3,6,2,4] => 0
[3,5,1,4,2,6] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => 0
[3,5,1,4,6,2] => [4,6,3,5,1,2] => [5,6,3,1,4,2] => 0
[3,5,1,6,2,4] => [5,4,3,6,1,2] => [5,6,3,2,1,4] => 0
[3,5,1,6,4,2] => [5,6,3,2,1,4] => [5,4,3,6,1,2] => 0
[3,5,2,1,4,6] => [4,1,3,5,2,6] => [2,5,3,1,4,6] => 1
[3,5,2,1,6,4] => [5,1,3,6,2,4] => [2,5,3,6,1,4] => 1
[3,5,2,4,1,6] => [5,4,3,1,2,6] => [4,5,3,2,1,6] => 0
[3,5,2,4,6,1] => [6,4,3,5,2,1] => [6,5,3,2,4,1] => 1
[3,5,2,6,1,4] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => 0
[3,5,2,6,4,1] => [6,5,3,1,2,4] => [4,5,3,6,2,1] => 1
[3,5,4,1,2,6] => [2,5,3,1,4,6] => [4,1,3,5,2,6] => 1
[3,5,4,1,6,2] => [5,6,3,1,4,2] => [4,6,3,5,1,2] => 1
[3,5,4,2,1,6] => [5,1,3,2,4,6] => [2,4,3,5,1,6] => 2
[3,5,4,2,6,1] => [6,5,3,2,4,1] => [6,4,3,5,2,1] => 2
[3,5,4,6,1,2] => [2,6,3,5,4,1] => [6,1,3,5,4,2] => 1
[3,5,4,6,2,1] => [6,1,3,5,4,2] => [2,6,3,5,4,1] => 3
[3,5,6,1,2,4] => [2,4,3,6,5,1] => [6,1,3,2,5,4] => 0
[3,5,6,1,4,2] => [4,6,3,2,5,1] => [6,4,3,1,5,2] => 0
[3,5,6,2,1,4] => [4,1,3,6,5,2] => [2,6,3,1,5,4] => 1
[3,5,6,2,4,1] => [6,4,3,1,5,2] => [4,6,3,2,5,1] => 1
[3,5,6,4,1,2] => [2,6,3,1,5,4] => [4,1,3,6,5,2] => 0
[3,5,6,4,2,1] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => 2
[3,6,1,2,4,5] => [2,4,3,5,6,1] => [6,1,3,2,4,5] => 0
[3,6,1,2,5,4] => [2,5,3,6,4,1] => [6,1,3,5,2,4] => 1
[3,6,1,4,2,5] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => 0
[3,6,1,4,5,2] => [4,6,3,5,2,1] => [6,5,3,1,4,2] => 0
[3,6,1,5,2,4] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => 0
[3,6,1,5,4,2] => [5,6,3,2,4,1] => [6,4,3,5,1,2] => 1
[3,6,2,1,4,5] => [4,1,3,5,6,2] => [2,6,3,1,4,5] => 1
[3,6,2,1,5,4] => [5,1,3,6,4,2] => [2,6,3,5,1,4] => 2
[3,6,2,4,1,5] => [5,4,3,1,6,2] => [4,6,3,2,1,5] => 0
[3,6,2,4,5,1] => [6,4,3,5,1,2] => [5,6,3,2,4,1] => 1
[3,6,2,5,1,4] => [4,5,3,6,1,2] => [5,6,3,1,2,4] => 0
[3,6,2,5,4,1] => [6,5,3,1,4,2] => [4,6,3,5,2,1] => 2
[3,6,4,1,2,5] => [2,5,3,1,6,4] => [4,1,3,6,2,5] => 0
[3,6,4,1,5,2] => [5,6,3,1,2,4] => [4,5,3,6,1,2] => 0
[3,6,4,2,1,5] => [5,1,3,2,6,4] => [2,4,3,6,1,5] => 1
[3,6,4,2,5,1] => [6,5,3,2,1,4] => [5,4,3,6,2,1] => 1
[3,6,4,5,1,2] => [2,6,3,5,1,4] => [5,1,3,6,4,2] => 0
[3,6,4,5,2,1] => [6,1,3,5,2,4] => [2,5,3,6,4,1] => 2
[3,6,5,1,2,4] => [2,4,3,6,1,5] => [5,1,3,2,6,4] => 1
[3,6,5,1,4,2] => [4,6,3,2,1,5] => [5,4,3,1,6,2] => 1
[3,6,5,2,1,4] => [4,1,3,6,2,5] => [2,5,3,1,6,4] => 2
[3,6,5,2,4,1] => [6,4,3,1,2,5] => [4,5,3,2,6,1] => 2
[3,6,5,4,1,2] => [2,6,3,1,4,5] => [4,1,3,5,6,2] => 2
[3,6,5,4,2,1] => [6,1,3,2,4,5] => [2,4,3,5,6,1] => 4
[4,1,2,3,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 0
[4,1,2,3,6,5] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => 1
[4,1,2,5,3,6] => [2,4,5,1,3,6] => [4,1,5,2,3,6] => 0
[4,1,2,5,6,3] => [2,4,6,1,5,3] => [4,1,6,2,5,3] => 0
[4,1,2,6,3,5] => [2,4,5,1,6,3] => [4,1,6,2,3,5] => 0
[4,1,2,6,5,3] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => 1
[4,1,3,2,5,6] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 1
[4,1,3,2,6,5] => [3,4,2,1,6,5] => [4,3,1,2,6,5] => 2
[4,1,3,5,2,6] => [3,5,4,1,2,6] => [4,5,1,3,2,6] => 0
[4,1,3,5,6,2] => [3,6,4,1,5,2] => [4,6,1,3,5,2] => 0
[4,1,3,6,2,5] => [3,5,4,1,6,2] => [4,6,1,3,2,5] => 0
[4,1,3,6,5,2] => [3,6,4,1,2,5] => [4,5,1,3,6,2] => 1
[4,1,5,2,3,6] => [4,3,5,1,2,6] => [4,5,2,1,3,6] => 0
[4,1,5,2,6,3] => [4,5,6,1,2,3] => [4,5,6,1,2,3] => 0
[4,1,5,3,2,6] => [4,5,2,1,3,6] => [4,3,5,1,2,6] => 1
[4,1,5,3,6,2] => [4,6,5,1,3,2] => [4,6,5,1,3,2] => 0
[4,1,5,6,2,3] => [4,3,6,1,5,2] => [4,6,2,1,5,3] => 0
[4,1,5,6,3,2] => [4,6,2,1,5,3] => [4,3,6,1,5,2] => 1
[4,1,6,2,3,5] => [4,3,5,1,6,2] => [4,6,2,1,3,5] => 0
[4,1,6,2,5,3] => [4,5,6,1,3,2] => [4,6,5,1,2,3] => 0
[4,1,6,3,2,5] => [4,5,2,1,6,3] => [4,3,6,1,2,5] => 1
[4,1,6,3,5,2] => [4,6,5,1,2,3] => [4,5,6,1,3,2] => 0
[4,1,6,5,2,3] => [4,3,6,1,2,5] => [4,5,2,1,6,3] => 1
[4,1,6,5,3,2] => [4,6,2,1,3,5] => [4,3,5,1,6,2] => 2
[4,2,1,3,5,6] => [3,1,4,2,5,6] => [2,4,1,3,5,6] => 1
[4,2,1,3,6,5] => [3,1,4,2,6,5] => [2,4,1,3,6,5] => 2
[4,2,1,5,3,6] => [4,1,5,2,3,6] => [2,4,5,1,3,6] => 1
[4,2,1,5,6,3] => [4,1,6,2,5,3] => [2,4,6,1,5,3] => 1
[4,2,1,6,3,5] => [4,1,5,2,6,3] => [2,4,6,1,3,5] => 1
[4,2,1,6,5,3] => [4,1,6,2,3,5] => [2,4,5,1,6,3] => 2
[4,2,3,1,5,6] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => 0
[4,2,3,1,6,5] => [4,3,1,2,6,5] => [3,4,2,1,6,5] => 1
[4,2,3,5,1,6] => [5,3,4,2,1,6] => [5,4,2,3,1,6] => 0
[4,2,3,5,6,1] => [6,3,4,2,5,1] => [6,4,2,3,5,1] => 1
[4,2,3,6,1,5] => [5,3,4,2,6,1] => [6,4,2,3,1,5] => 0
[4,2,3,6,5,1] => [6,3,4,2,1,5] => [5,4,2,3,6,1] => 2
[4,2,5,1,3,6] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => 0
[4,2,5,1,6,3] => [5,4,6,2,1,3] => [5,4,6,2,1,3] => 0
[4,2,5,3,1,6] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => 0
[4,2,5,3,6,1] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 1
[4,2,5,6,1,3] => [3,4,6,2,5,1] => [6,4,1,2,5,3] => 0
[4,2,5,6,3,1] => [6,4,1,2,5,3] => [3,4,6,2,5,1] => 1
[4,2,6,1,3,5] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => 0
[4,2,6,1,5,3] => [5,4,6,2,3,1] => [6,4,5,2,1,3] => 0
[4,2,6,3,1,5] => [5,4,1,2,6,3] => [3,4,6,2,1,5] => 0
[4,2,6,3,5,1] => [6,4,5,2,1,3] => [5,4,6,2,3,1] => 1
[4,2,6,5,1,3] => [3,4,6,2,1,5] => [5,4,1,2,6,3] => 1
[4,2,6,5,3,1] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => 2
[4,3,1,2,5,6] => [2,4,1,3,5,6] => [3,1,4,2,5,6] => 1
[4,3,1,2,6,5] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => 2
[4,3,1,5,2,6] => [4,5,1,3,2,6] => [3,5,4,1,2,6] => 1
[4,3,1,5,6,2] => [4,6,1,3,5,2] => [3,6,4,1,5,2] => 1
[4,3,1,6,2,5] => [4,5,1,3,6,2] => [3,6,4,1,2,5] => 1
[4,3,1,6,5,2] => [4,6,1,3,2,5] => [3,5,4,1,6,2] => 2
[4,3,2,1,5,6] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => 3
[4,3,2,1,6,5] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 4
[4,3,2,5,1,6] => [5,4,2,3,1,6] => [5,3,4,2,1,6] => 2
[4,3,2,5,6,1] => [6,4,2,3,5,1] => [6,3,4,2,5,1] => 3
[4,3,2,6,1,5] => [5,4,2,3,6,1] => [6,3,4,2,1,5] => 2
[4,3,2,6,5,1] => [6,4,2,3,1,5] => [5,3,4,2,6,1] => 4
[4,3,5,1,2,6] => [2,5,4,3,1,6] => [5,1,4,3,2,6] => 1
[4,3,5,1,6,2] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 1
[4,3,5,2,1,6] => [5,1,4,3,2,6] => [2,5,4,3,1,6] => 2
[4,3,5,2,6,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 2
[4,3,5,6,1,2] => [2,6,4,3,5,1] => [6,1,4,3,5,2] => 1
[4,3,5,6,2,1] => [6,1,4,3,5,2] => [2,6,4,3,5,1] => 3
[4,3,6,1,2,5] => [2,5,4,3,6,1] => [6,1,4,3,2,5] => 1
[4,3,6,1,5,2] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => 1
[4,3,6,2,1,5] => [5,1,4,3,6,2] => [2,6,4,3,1,5] => 2
[4,3,6,2,5,1] => [6,5,4,3,1,2] => [5,6,4,3,2,1] => 2
[4,3,6,5,1,2] => [2,6,4,3,1,5] => [5,1,4,3,6,2] => 2
[4,3,6,5,2,1] => [6,1,4,3,2,5] => [2,5,4,3,6,1] => 4
[4,5,1,2,3,6] => [2,3,5,4,1,6] => [5,1,2,4,3,6] => 0
[4,5,1,2,6,3] => [2,5,6,4,1,3] => [5,1,6,4,2,3] => 0
[4,5,1,3,2,6] => [3,5,2,4,1,6] => [5,3,1,4,2,6] => 1
[4,5,1,3,6,2] => [3,6,5,4,1,2] => [5,6,1,4,3,2] => 0
[4,5,1,6,2,3] => [5,3,6,4,1,2] => [5,6,2,4,1,3] => 0
[4,5,1,6,3,2] => [5,6,2,4,1,3] => [5,3,6,4,1,2] => 1
[4,5,2,1,3,6] => [3,1,5,4,2,6] => [2,5,1,4,3,6] => 1
[4,5,2,1,6,3] => [5,1,6,4,2,3] => [2,5,6,4,1,3] => 1
[4,5,2,3,1,6] => [5,3,1,4,2,6] => [3,5,2,4,1,6] => 0
[4,5,2,3,6,1] => [6,3,5,4,2,1] => [6,5,2,4,3,1] => 1
[4,5,2,6,1,3] => [3,5,6,4,2,1] => [6,5,1,4,2,3] => 0
[4,5,2,6,3,1] => [6,5,1,4,2,3] => [3,5,6,4,2,1] => 1
[4,5,3,1,2,6] => [2,5,1,4,3,6] => [3,1,5,4,2,6] => 0
[4,5,3,1,6,2] => [5,6,1,4,3,2] => [3,6,5,4,1,2] => 0
[4,5,3,2,1,6] => [5,1,2,4,3,6] => [2,3,5,4,1,6] => 2
[4,5,3,2,6,1] => [6,5,2,4,3,1] => [6,3,5,4,2,1] => 2
[4,5,3,6,1,2] => [2,6,5,4,3,1] => [6,1,5,4,3,2] => 0
[4,5,3,6,2,1] => [6,1,5,4,3,2] => [2,6,5,4,3,1] => 2
[4,5,6,1,2,3] => [2,3,6,4,5,1] => [6,1,2,4,5,3] => 0
[4,5,6,1,3,2] => [3,6,2,4,5,1] => [6,3,1,4,5,2] => 1
[4,5,6,2,1,3] => [3,1,6,4,5,2] => [2,6,1,4,5,3] => 1
[4,5,6,2,3,1] => [6,3,1,4,5,2] => [3,6,2,4,5,1] => 1
[4,5,6,3,1,2] => [2,6,1,4,5,3] => [3,1,6,4,5,2] => 0
[4,5,6,3,2,1] => [6,1,2,4,5,3] => [2,3,6,4,5,1] => 3
[4,6,1,2,3,5] => [2,3,5,4,6,1] => [6,1,2,4,3,5] => 0
[4,6,1,2,5,3] => [2,5,6,4,3,1] => [6,1,5,4,2,3] => 0
[4,6,1,3,2,5] => [3,5,2,4,6,1] => [6,3,1,4,2,5] => 1
[4,6,1,3,5,2] => [3,6,5,4,2,1] => [6,5,1,4,3,2] => 0
[4,6,1,5,2,3] => [5,3,6,4,2,1] => [6,5,2,4,1,3] => 0
[4,6,1,5,3,2] => [5,6,2,4,3,1] => [6,3,5,4,1,2] => 1
[4,6,2,1,3,5] => [3,1,5,4,6,2] => [2,6,1,4,3,5] => 1
[4,6,2,1,5,3] => [5,1,6,4,3,2] => [2,6,5,4,1,3] => 1
[4,6,2,3,1,5] => [5,3,1,4,6,2] => [3,6,2,4,1,5] => 0
[4,6,2,3,5,1] => [6,3,5,4,1,2] => [5,6,2,4,3,1] => 1
[4,6,2,5,1,3] => [3,5,6,4,1,2] => [5,6,1,4,2,3] => 0
[4,6,2,5,3,1] => [6,5,1,4,3,2] => [3,6,5,4,2,1] => 1
[4,6,3,1,2,5] => [2,5,1,4,6,3] => [3,1,6,4,2,5] => 0
[4,6,3,1,5,2] => [5,6,1,4,2,3] => [3,5,6,4,1,2] => 0
[4,6,3,2,1,5] => [5,1,2,4,6,3] => [2,3,6,4,1,5] => 2
[4,6,3,2,5,1] => [6,5,2,4,1,3] => [5,3,6,4,2,1] => 2
[4,6,3,5,1,2] => [2,6,5,4,1,3] => [5,1,6,4,3,2] => 0
[4,6,3,5,2,1] => [6,1,5,4,2,3] => [2,5,6,4,3,1] => 2
[4,6,5,1,2,3] => [2,3,6,4,1,5] => [5,1,2,4,6,3] => 1
[4,6,5,1,3,2] => [3,6,2,4,1,5] => [5,3,1,4,6,2] => 2
[4,6,5,2,1,3] => [3,1,6,4,2,5] => [2,5,1,4,6,3] => 2
[4,6,5,2,3,1] => [6,3,1,4,2,5] => [3,5,2,4,6,1] => 2
[4,6,5,3,1,2] => [2,6,1,4,3,5] => [3,1,5,4,6,2] => 1
[4,6,5,3,2,1] => [6,1,2,4,3,5] => [2,3,5,4,6,1] => 4
[5,1,2,3,4,6] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 0
[5,1,2,3,6,4] => [2,3,5,6,1,4] => [5,1,2,6,3,4] => 0
[5,1,2,4,3,6] => [2,4,5,3,1,6] => [5,1,4,2,3,6] => 1
[5,1,2,4,6,3] => [2,4,6,5,1,3] => [5,1,6,2,4,3] => 0
[5,1,2,6,3,4] => [2,5,4,6,1,3] => [5,1,6,3,2,4] => 0
[5,1,2,6,4,3] => [2,5,6,3,1,4] => [5,1,4,6,2,3] => 1
[5,1,3,2,4,6] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => 1
[5,1,3,2,6,4] => [3,5,2,6,1,4] => [5,3,1,6,2,4] => 1
[5,1,3,4,2,6] => [3,5,4,2,1,6] => [5,4,1,3,2,6] => 0
[5,1,3,4,6,2] => [3,6,4,5,1,2] => [5,6,1,3,4,2] => 0
[5,1,3,6,2,4] => [3,4,5,6,1,2] => [5,6,1,2,3,4] => 0
[5,1,3,6,4,2] => [3,6,5,2,1,4] => [5,4,1,6,3,2] => 0
[5,1,4,2,3,6] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => 0
[5,1,4,2,6,3] => [4,5,6,2,1,3] => [5,4,6,1,2,3] => 0
[5,1,4,3,2,6] => [4,5,2,3,1,6] => [5,3,4,1,2,6] => 2
[5,1,4,3,6,2] => [4,6,5,3,1,2] => [5,6,4,1,3,2] => 1
[5,1,4,6,2,3] => [4,3,6,5,1,2] => [5,6,2,1,4,3] => 0
[5,1,4,6,3,2] => [4,6,2,5,1,3] => [5,3,6,1,4,2] => 1
[5,1,6,2,3,4] => [5,3,4,6,1,2] => [5,6,2,3,1,4] => 0
[5,1,6,2,4,3] => [5,4,6,3,1,2] => [5,6,4,2,1,3] => 1
[5,1,6,3,2,4] => [5,4,2,6,1,3] => [5,3,6,2,1,4] => 1
[5,1,6,3,4,2] => [5,6,4,2,1,3] => [5,4,6,3,1,2] => 0
[5,1,6,4,2,3] => [5,3,6,2,1,4] => [5,4,2,6,1,3] => 0
[5,1,6,4,3,2] => [5,6,2,3,1,4] => [5,3,4,6,1,2] => 2
[5,2,1,3,4,6] => [3,1,4,5,2,6] => [2,5,1,3,4,6] => 1
[5,2,1,3,6,4] => [3,1,5,6,2,4] => [2,5,1,6,3,4] => 1
[5,2,1,4,3,6] => [4,1,5,3,2,6] => [2,5,4,1,3,6] => 2
[5,2,1,4,6,3] => [4,1,6,5,2,3] => [2,5,6,1,4,3] => 1
[5,2,1,6,3,4] => [5,1,4,6,2,3] => [2,5,6,3,1,4] => 1
[5,2,1,6,4,3] => [5,1,6,3,2,4] => [2,5,4,6,1,3] => 2
[5,2,3,1,4,6] => [4,3,1,5,2,6] => [3,5,2,1,4,6] => 0
[5,2,3,1,6,4] => [5,3,1,6,2,4] => [3,5,2,6,1,4] => 0
[5,2,3,4,1,6] => [5,3,4,1,2,6] => [4,5,2,3,1,6] => 0
[5,2,3,4,6,1] => [6,3,4,5,2,1] => [6,5,2,3,4,1] => 1
[5,2,3,6,1,4] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => 0
[5,2,3,6,4,1] => [6,3,5,1,2,4] => [4,5,2,6,3,1] => 1
[5,2,4,1,3,6] => [3,4,5,1,2,6] => [4,5,1,2,3,6] => 0
[5,2,4,1,6,3] => [5,4,6,1,2,3] => [4,5,6,2,1,3] => 0
[5,2,4,3,1,6] => [5,4,1,3,2,6] => [3,5,4,2,1,6] => 1
[5,2,4,3,6,1] => [6,4,5,3,2,1] => [6,5,4,2,3,1] => 2
[5,2,4,6,1,3] => [3,4,6,5,2,1] => [6,5,1,2,4,3] => 0
[5,2,4,6,3,1] => [6,4,1,5,2,3] => [3,5,6,2,4,1] => 1
[5,2,6,1,3,4] => [3,5,4,6,2,1] => [6,5,1,3,2,4] => 0
[5,2,6,1,4,3] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 1
[5,2,6,3,1,4] => [4,5,1,6,2,3] => [3,5,6,1,2,4] => 0
[5,2,6,3,4,1] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 1
[5,2,6,4,1,3] => [3,5,6,1,2,4] => [4,5,1,6,2,3] => 0
[5,2,6,4,3,1] => [6,5,1,3,2,4] => [3,5,4,6,2,1] => 2
[5,3,1,2,4,6] => [2,4,1,5,3,6] => [3,1,5,2,4,6] => 0
[5,3,1,2,6,4] => [2,5,1,6,3,4] => [3,1,5,6,2,4] => 0
[5,3,1,4,2,6] => [4,5,1,2,3,6] => [3,4,5,1,2,6] => 0
[5,3,1,4,6,2] => [4,6,1,5,3,2] => [3,6,5,1,4,2] => 0
[5,3,1,6,2,4] => [5,4,1,6,3,2] => [3,6,5,2,1,4] => 0
[5,3,1,6,4,2] => [5,6,1,2,3,4] => [3,4,5,6,1,2] => 0
[5,3,2,1,4,6] => [4,1,2,5,3,6] => [2,3,5,1,4,6] => 2
[5,3,2,1,6,4] => [5,1,2,6,3,4] => [2,3,5,6,1,4] => 2
[5,3,2,4,1,6] => [5,4,2,1,3,6] => [4,3,5,2,1,6] => 1
[5,3,2,4,6,1] => [6,4,2,5,3,1] => [6,3,5,2,4,1] => 2
[5,3,2,6,1,4] => [4,5,2,6,3,1] => [6,3,5,1,2,4] => 1
[5,3,2,6,4,1] => [6,5,2,1,3,4] => [4,3,5,6,2,1] => 2
[5,3,4,1,2,6] => [2,5,4,1,3,6] => [4,1,5,3,2,6] => 0
[5,3,4,1,6,2] => [5,6,4,1,3,2] => [4,6,5,3,1,2] => 0
[5,3,4,2,1,6] => [5,1,4,2,3,6] => [2,4,5,3,1,6] => 1
[5,3,4,2,6,1] => [6,5,4,2,3,1] => [6,4,5,3,2,1] => 1
[5,3,4,6,1,2] => [2,6,4,5,3,1] => [6,1,5,3,4,2] => 0
[5,3,4,6,2,1] => [6,1,4,5,3,2] => [2,6,5,3,4,1] => 2
[5,3,6,1,2,4] => [2,4,5,6,3,1] => [6,1,5,2,3,4] => 0
[5,3,6,1,4,2] => [4,6,5,2,3,1] => [6,4,5,1,3,2] => 0
[5,3,6,2,1,4] => [4,1,5,6,3,2] => [2,6,5,1,3,4] => 1
[5,3,6,2,4,1] => [6,4,5,1,3,2] => [4,6,5,2,3,1] => 1
[5,3,6,4,1,2] => [2,6,5,1,3,4] => [4,1,5,6,3,2] => 0
[5,3,6,4,2,1] => [6,1,5,2,3,4] => [2,4,5,6,3,1] => 2
[5,4,1,2,3,6] => [2,3,5,1,4,6] => [4,1,2,5,3,6] => 1
[5,4,1,2,6,3] => [2,5,6,1,4,3] => [4,1,6,5,2,3] => 1
[5,4,1,3,2,6] => [3,5,2,1,4,6] => [4,3,1,5,2,6] => 2
[5,4,1,3,6,2] => [3,6,5,1,4,2] => [4,6,1,5,3,2] => 1
[5,4,1,6,2,3] => [5,3,6,1,4,2] => [4,6,2,5,1,3] => 1
[5,4,1,6,3,2] => [5,6,2,1,4,3] => [4,3,6,5,1,2] => 2
[5,4,2,1,3,6] => [3,1,5,2,4,6] => [2,4,1,5,3,6] => 2
[5,4,2,1,6,3] => [5,1,6,2,4,3] => [2,4,6,5,1,3] => 2
[5,4,2,3,1,6] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => 1
[5,4,2,3,6,1] => [6,3,5,2,4,1] => [6,4,2,5,3,1] => 2
[5,4,2,6,1,3] => [3,5,6,2,4,1] => [6,4,1,5,2,3] => 1
[5,4,2,6,3,1] => [6,5,1,2,4,3] => [3,4,6,5,2,1] => 2
[5,4,3,1,2,6] => [2,5,1,3,4,6] => [3,1,4,5,2,6] => 2
[5,4,3,1,6,2] => [5,6,1,3,4,2] => [3,6,4,5,1,2] => 2
[5,4,3,2,1,6] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => 4
[5,4,3,2,6,1] => [6,5,2,3,4,1] => [6,3,4,5,2,1] => 4
[5,4,3,6,1,2] => [2,6,5,3,4,1] => [6,1,4,5,3,2] => 2
[5,4,3,6,2,1] => [6,1,5,3,4,2] => [2,6,4,5,3,1] => 4
[5,4,6,1,2,3] => [2,3,6,5,4,1] => [6,1,2,5,4,3] => 1
[5,4,6,1,3,2] => [3,6,2,5,4,1] => [6,3,1,5,4,2] => 2
[5,4,6,2,1,3] => [3,1,6,5,4,2] => [2,6,1,5,4,3] => 2
[5,4,6,2,3,1] => [6,3,1,5,4,2] => [3,6,2,5,4,1] => 2
[5,4,6,3,1,2] => [2,6,1,5,4,3] => [3,1,6,5,4,2] => 1
[5,4,6,3,2,1] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => 4
[5,6,1,2,3,4] => [2,3,4,6,5,1] => [6,1,2,3,5,4] => 0
[5,6,1,2,4,3] => [2,4,6,3,5,1] => [6,1,4,2,5,3] => 1
[5,6,1,3,2,4] => [3,4,2,6,5,1] => [6,3,1,2,5,4] => 1
[5,6,1,3,4,2] => [3,6,4,2,5,1] => [6,4,1,3,5,2] => 0
[5,6,1,4,2,3] => [4,3,6,2,5,1] => [6,4,2,1,5,3] => 0
[5,6,1,4,3,2] => [4,6,2,3,5,1] => [6,3,4,1,5,2] => 2
[5,6,2,1,3,4] => [3,1,4,6,5,2] => [2,6,1,3,5,4] => 1
[5,6,2,1,4,3] => [4,1,6,3,5,2] => [2,6,4,1,5,3] => 2
[5,6,2,3,1,4] => [4,3,1,6,5,2] => [3,6,2,1,5,4] => 0
[5,6,2,3,4,1] => [6,3,4,1,5,2] => [4,6,2,3,5,1] => 1
[5,6,2,4,1,3] => [3,4,6,1,5,2] => [4,6,1,2,5,3] => 0
[5,6,2,4,3,1] => [6,4,1,3,5,2] => [3,6,4,2,5,1] => 2
[5,6,3,1,2,4] => [2,4,1,6,5,3] => [3,1,6,2,5,4] => 0
[5,6,3,1,4,2] => [4,6,1,2,5,3] => [3,4,6,1,5,2] => 0
[5,6,3,2,1,4] => [4,1,2,6,5,3] => [2,3,6,1,5,4] => 2
[5,6,3,2,4,1] => [6,4,2,1,5,3] => [4,3,6,2,5,1] => 2
[5,6,3,4,1,2] => [2,6,4,1,5,3] => [4,1,6,3,5,2] => 0
[5,6,3,4,2,1] => [6,1,4,2,5,3] => [2,4,6,3,5,1] => 2
[5,6,4,1,2,3] => [2,3,6,1,5,4] => [4,1,2,6,5,3] => 0
[5,6,4,1,3,2] => [3,6,2,1,5,4] => [4,3,1,6,5,2] => 1
[5,6,4,2,1,3] => [3,1,6,2,5,4] => [2,4,1,6,5,3] => 1
[5,6,4,2,3,1] => [6,3,1,2,5,4] => [3,4,2,6,5,1] => 1
[5,6,4,3,1,2] => [2,6,1,3,5,4] => [3,1,4,6,5,2] => 1
[5,6,4,3,2,1] => [6,1,2,3,5,4] => [2,3,4,6,5,1] => 4
[6,1,2,3,4,5] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 0
[6,1,2,3,5,4] => [2,3,5,6,4,1] => [6,1,2,5,3,4] => 1
[6,1,2,4,3,5] => [2,4,5,3,6,1] => [6,1,4,2,3,5] => 1
[6,1,2,4,5,3] => [2,4,6,5,3,1] => [6,1,5,2,4,3] => 0
[6,1,2,5,3,4] => [2,5,4,6,3,1] => [6,1,5,3,2,4] => 0
[6,1,2,5,4,3] => [2,5,6,3,4,1] => [6,1,4,5,2,3] => 2
[6,1,3,2,4,5] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => 1
[6,1,3,2,5,4] => [3,5,2,6,4,1] => [6,3,1,5,2,4] => 2
[6,1,3,4,2,5] => [3,5,4,2,6,1] => [6,4,1,3,2,5] => 0
[6,1,3,4,5,2] => [3,6,4,5,2,1] => [6,5,1,3,4,2] => 0
[6,1,3,5,2,4] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => 0
[6,1,3,5,4,2] => [3,6,5,2,4,1] => [6,4,1,5,3,2] => 1
[6,1,4,2,3,5] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => 0
[6,1,4,2,5,3] => [4,5,6,2,3,1] => [6,4,5,1,2,3] => 0
[6,1,4,3,2,5] => [4,5,2,3,6,1] => [6,3,4,1,2,5] => 2
[6,1,4,3,5,2] => [4,6,5,3,2,1] => [6,5,4,1,3,2] => 1
[6,1,4,5,2,3] => [4,3,6,5,2,1] => [6,5,2,1,4,3] => 0
[6,1,4,5,3,2] => [4,6,2,5,3,1] => [6,3,5,1,4,2] => 1
[6,1,5,2,3,4] => [5,3,4,6,2,1] => [6,5,2,3,1,4] => 0
[6,1,5,2,4,3] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => 1
[6,1,5,3,2,4] => [5,4,2,6,3,1] => [6,3,5,2,1,4] => 1
[6,1,5,3,4,2] => [5,6,4,2,3,1] => [6,4,5,3,1,2] => 0
[6,1,5,4,2,3] => [5,3,6,2,4,1] => [6,4,2,5,1,3] => 1
[6,1,5,4,3,2] => [5,6,2,3,4,1] => [6,3,4,5,1,2] => 3
[6,2,1,3,4,5] => [3,1,4,5,6,2] => [2,6,1,3,4,5] => 1
[6,2,1,3,5,4] => [3,1,5,6,4,2] => [2,6,1,5,3,4] => 2
[6,2,1,4,3,5] => [4,1,5,3,6,2] => [2,6,4,1,3,5] => 2
[6,2,1,4,5,3] => [4,1,6,5,3,2] => [2,6,5,1,4,3] => 1
[6,2,1,5,3,4] => [5,1,4,6,3,2] => [2,6,5,3,1,4] => 1
[6,2,1,5,4,3] => [5,1,6,3,4,2] => [2,6,4,5,1,3] => 3
[6,2,3,1,4,5] => [4,3,1,5,6,2] => [3,6,2,1,4,5] => 0
[6,2,3,1,5,4] => [5,3,1,6,4,2] => [3,6,2,5,1,4] => 1
[6,2,3,4,1,5] => [5,3,4,1,6,2] => [4,6,2,3,1,5] => 0
[6,2,3,4,5,1] => [6,3,4,5,1,2] => [5,6,2,3,4,1] => 1
[6,2,3,5,1,4] => [4,3,5,6,1,2] => [5,6,2,1,3,4] => 0
[6,2,3,5,4,1] => [6,3,5,1,4,2] => [4,6,2,5,3,1] => 2
[6,2,4,1,3,5] => [3,4,5,1,6,2] => [4,6,1,2,3,5] => 0
[6,2,4,1,5,3] => [5,4,6,1,3,2] => [4,6,5,2,1,3] => 0
[6,2,4,3,1,5] => [5,4,1,3,6,2] => [3,6,4,2,1,5] => 1
[6,2,4,3,5,1] => [6,4,5,3,1,2] => [5,6,4,2,3,1] => 2
[6,2,4,5,1,3] => [3,4,6,5,1,2] => [5,6,1,2,4,3] => 0
[6,2,4,5,3,1] => [6,4,1,5,3,2] => [3,6,5,2,4,1] => 1
[6,2,5,1,3,4] => [3,5,4,6,1,2] => [5,6,1,3,2,4] => 0
[6,2,5,1,4,3] => [4,5,6,3,1,2] => [5,6,4,1,2,3] => 1
[6,2,5,3,1,4] => [4,5,1,6,3,2] => [3,6,5,1,2,4] => 0
[6,2,5,3,4,1] => [6,5,4,1,3,2] => [4,6,5,3,2,1] => 1
[6,2,5,4,1,3] => [3,5,6,1,4,2] => [4,6,1,5,2,3] => 1
[6,2,5,4,3,1] => [6,5,1,3,4,2] => [3,6,4,5,2,1] => 3
[6,3,1,2,4,5] => [2,4,1,5,6,3] => [3,1,6,2,4,5] => 0
[6,3,1,2,5,4] => [2,5,1,6,4,3] => [3,1,6,5,2,4] => 1
[6,3,1,4,2,5] => [4,5,1,2,6,3] => [3,4,6,1,2,5] => 0
[6,3,1,4,5,2] => [4,6,1,5,2,3] => [3,5,6,1,4,2] => 0
[6,3,1,5,2,4] => [5,4,1,6,2,3] => [3,5,6,2,1,4] => 0
[6,3,1,5,4,2] => [5,6,1,2,4,3] => [3,4,6,5,1,2] => 1
[6,3,2,1,4,5] => [4,1,2,5,6,3] => [2,3,6,1,4,5] => 2
[6,3,2,1,5,4] => [5,1,2,6,4,3] => [2,3,6,5,1,4] => 3
[6,3,2,4,1,5] => [5,4,2,1,6,3] => [4,3,6,2,1,5] => 1
[6,3,2,4,5,1] => [6,4,2,5,1,3] => [5,3,6,2,4,1] => 2
[6,3,2,5,1,4] => [4,5,2,6,1,3] => [5,3,6,1,2,4] => 1
[6,3,2,5,4,1] => [6,5,2,1,4,3] => [4,3,6,5,2,1] => 3
[6,3,4,1,2,5] => [2,5,4,1,6,3] => [4,1,6,3,2,5] => 0
[6,3,4,1,5,2] => [5,6,4,1,2,3] => [4,5,6,3,1,2] => 0
[6,3,4,2,1,5] => [5,1,4,2,6,3] => [2,4,6,3,1,5] => 1
[6,3,4,2,5,1] => [6,5,4,2,1,3] => [5,4,6,3,2,1] => 1
[6,3,4,5,1,2] => [2,6,4,5,1,3] => [5,1,6,3,4,2] => 0
[6,3,4,5,2,1] => [6,1,4,5,2,3] => [2,5,6,3,4,1] => 2
[6,3,5,1,2,4] => [2,4,5,6,1,3] => [5,1,6,2,3,4] => 0
[6,3,5,1,4,2] => [4,6,5,2,1,3] => [5,4,6,1,3,2] => 0
[6,3,5,2,1,4] => [4,1,5,6,2,3] => [2,5,6,1,3,4] => 1
[6,3,5,2,4,1] => [6,4,5,1,2,3] => [4,5,6,2,3,1] => 1
[6,3,5,4,1,2] => [2,6,5,1,4,3] => [4,1,6,5,3,2] => 1
[6,3,5,4,2,1] => [6,1,5,2,4,3] => [2,4,6,5,3,1] => 3
[6,4,1,2,3,5] => [2,3,5,1,6,4] => [4,1,2,6,3,5] => 0
[6,4,1,2,5,3] => [2,5,6,1,3,4] => [4,1,5,6,2,3] => 0
[6,4,1,3,2,5] => [3,5,2,1,6,4] => [4,3,1,6,2,5] => 1
[6,4,1,3,5,2] => [3,6,5,1,2,4] => [4,5,1,6,3,2] => 0
[6,4,1,5,2,3] => [5,3,6,1,2,4] => [4,5,2,6,1,3] => 0
[6,4,1,5,3,2] => [5,6,2,1,3,4] => [4,3,5,6,1,2] => 1
[6,4,2,1,3,5] => [3,1,5,2,6,4] => [2,4,1,6,3,5] => 1
[6,4,2,1,5,3] => [5,1,6,2,3,4] => [2,4,5,6,1,3] => 1
[6,4,2,3,1,5] => [5,3,1,2,6,4] => [3,4,2,6,1,5] => 0
[6,4,2,3,5,1] => [6,3,5,2,1,4] => [5,4,2,6,3,1] => 1
[6,4,2,5,1,3] => [3,5,6,2,1,4] => [5,4,1,6,2,3] => 0
[6,4,2,5,3,1] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => 1
[6,4,3,1,2,5] => [2,5,1,3,6,4] => [3,1,4,6,2,5] => 1
[6,4,3,1,5,2] => [5,6,1,3,2,4] => [3,5,4,6,1,2] => 1
[6,4,3,2,1,5] => [5,1,2,3,6,4] => [2,3,4,6,1,5] => 3
[6,4,3,2,5,1] => [6,5,2,3,1,4] => [5,3,4,6,2,1] => 3
[6,4,3,5,1,2] => [2,6,5,3,1,4] => [5,1,4,6,3,2] => 1
[6,4,3,5,2,1] => [6,1,5,3,2,4] => [2,5,4,6,3,1] => 3
[6,4,5,1,2,3] => [2,3,6,5,1,4] => [5,1,2,6,4,3] => 0
[6,4,5,1,3,2] => [3,6,2,5,1,4] => [5,3,1,6,4,2] => 1
[6,4,5,2,1,3] => [3,1,6,5,2,4] => [2,5,1,6,4,3] => 1
[6,4,5,2,3,1] => [6,3,1,5,2,4] => [3,5,2,6,4,1] => 1
[6,4,5,3,1,2] => [2,6,1,5,3,4] => [3,1,5,6,4,2] => 0
[6,4,5,3,2,1] => [6,1,2,5,3,4] => [2,3,5,6,4,1] => 3
[6,5,1,2,3,4] => [2,3,4,6,1,5] => [5,1,2,3,6,4] => 1
[6,5,1,2,4,3] => [2,4,6,3,1,5] => [5,1,4,2,6,3] => 2
[6,5,1,3,2,4] => [3,4,2,6,1,5] => [5,3,1,2,6,4] => 2
[6,5,1,3,4,2] => [3,6,4,2,1,5] => [5,4,1,3,6,2] => 1
[6,5,1,4,2,3] => [4,3,6,2,1,5] => [5,4,2,1,6,3] => 1
[6,5,1,4,3,2] => [4,6,2,3,1,5] => [5,3,4,1,6,2] => 3
[6,5,2,1,3,4] => [3,1,4,6,2,5] => [2,5,1,3,6,4] => 2
[6,5,2,1,4,3] => [4,1,6,3,2,5] => [2,5,4,1,6,3] => 3
[6,5,2,3,1,4] => [4,3,1,6,2,5] => [3,5,2,1,6,4] => 1
[6,5,2,3,4,1] => [6,3,4,1,2,5] => [4,5,2,3,6,1] => 2
[6,5,2,4,1,3] => [3,4,6,1,2,5] => [4,5,1,2,6,3] => 1
[6,5,2,4,3,1] => [6,4,1,3,2,5] => [3,5,4,2,6,1] => 3
[6,5,3,1,2,4] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => 1
[6,5,3,1,4,2] => [4,6,1,2,3,5] => [3,4,5,1,6,2] => 1
[6,5,3,2,1,4] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => 3
[6,5,3,2,4,1] => [6,4,2,1,3,5] => [4,3,5,2,6,1] => 3
[6,5,3,4,1,2] => [2,6,4,1,3,5] => [4,1,5,3,6,2] => 1
[6,5,3,4,2,1] => [6,1,4,2,3,5] => [2,4,5,3,6,1] => 3
[6,5,4,1,2,3] => [2,3,6,1,4,5] => [4,1,2,5,6,3] => 2
[6,5,4,1,3,2] => [3,6,2,1,4,5] => [4,3,1,5,6,2] => 3
[6,5,4,2,1,3] => [3,1,6,2,4,5] => [2,4,1,5,6,3] => 3
[6,5,4,2,3,1] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => 3
[6,5,4,3,1,2] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => 3
[6,5,4,3,2,1] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 6
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,1 2,3,0,1 9,8,6,0,1 44,45,20,10,0,1 265,264,135,40,15,0,1
$F_{1} = q$
$F_{2} = 1 + q^{2}$
$F_{3} = 2 + 3\ q + q^{3}$
$F_{4} = 9 + 8\ q + 6\ q^{2} + q^{4}$
$F_{5} = 44 + 45\ q + 20\ q^{2} + 10\ q^{3} + q^{5}$
$F_{6} = 265 + 264\ q + 135\ q^{2} + 40\ q^{3} + 15\ q^{4} + q^{6}$
Description
The number of cyclical small excedances.
A cyclical small excedance is an index $i$ such that $\pi_i = i+1$ considered cyclically.
A cyclical small excedance is an index $i$ such that $\pi_i = i+1$ considered cyclically.
Map
inverse
Description
Sends a permutation to its inverse.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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