Identifier
-
Mp00069:
Permutations
—complement⟶
Permutations
St000801: Permutations ⟶ ℤ
Values
[1,2] => [2,1] => 0
[2,1] => [1,2] => 0
[1,2,3] => [3,2,1] => 0
[1,3,2] => [3,1,2] => 1
[2,1,3] => [2,3,1] => 0
[2,3,1] => [2,1,3] => 0
[3,1,2] => [1,3,2] => 0
[3,2,1] => [1,2,3] => 0
[1,2,3,4] => [4,3,2,1] => 0
[1,2,4,3] => [4,3,1,2] => 1
[1,3,2,4] => [4,2,3,1] => 1
[1,3,4,2] => [4,2,1,3] => 2
[1,4,2,3] => [4,1,3,2] => 2
[1,4,3,2] => [4,1,2,3] => 3
[2,1,3,4] => [3,4,2,1] => 0
[2,1,4,3] => [3,4,1,2] => 1
[2,3,1,4] => [3,2,4,1] => 0
[2,3,4,1] => [3,2,1,4] => 0
[2,4,1,3] => [3,1,4,2] => 1
[2,4,3,1] => [3,1,2,4] => 1
[3,1,2,4] => [2,4,3,1] => 0
[3,1,4,2] => [2,4,1,3] => 0
[3,2,1,4] => [2,3,4,1] => 0
[3,2,4,1] => [2,3,1,4] => 0
[3,4,1,2] => [2,1,4,3] => 0
[3,4,2,1] => [2,1,3,4] => 0
[4,1,2,3] => [1,4,3,2] => 0
[4,1,3,2] => [1,4,2,3] => 0
[4,2,1,3] => [1,3,4,2] => 0
[4,2,3,1] => [1,3,2,4] => 0
[4,3,1,2] => [1,2,4,3] => 0
[4,3,2,1] => [1,2,3,4] => 0
[1,2,3,4,5] => [5,4,3,2,1] => 0
[1,2,3,5,4] => [5,4,3,1,2] => 1
[1,2,4,3,5] => [5,4,2,3,1] => 1
[1,2,4,5,3] => [5,4,2,1,3] => 2
[1,2,5,3,4] => [5,4,1,3,2] => 2
[1,2,5,4,3] => [5,4,1,2,3] => 3
[1,3,2,4,5] => [5,3,4,2,1] => 1
[1,3,2,5,4] => [5,3,4,1,2] => 2
[1,3,4,2,5] => [5,3,2,4,1] => 2
[1,3,4,5,2] => [5,3,2,1,4] => 3
[1,3,5,2,4] => [5,3,1,4,2] => 3
[1,3,5,4,2] => [5,3,1,2,4] => 4
[1,4,2,3,5] => [5,2,4,3,1] => 2
[1,4,2,5,3] => [5,2,4,1,3] => 3
[1,4,3,2,5] => [5,2,3,4,1] => 3
[1,4,3,5,2] => [5,2,3,1,4] => 4
[1,4,5,2,3] => [5,2,1,4,3] => 4
[1,4,5,3,2] => [5,2,1,3,4] => 5
[1,5,2,3,4] => [5,1,4,3,2] => 3
[1,5,2,4,3] => [5,1,4,2,3] => 4
[1,5,3,2,4] => [5,1,3,4,2] => 4
[1,5,3,4,2] => [5,1,3,2,4] => 5
[1,5,4,2,3] => [5,1,2,4,3] => 5
[1,5,4,3,2] => [5,1,2,3,4] => 6
[2,1,3,4,5] => [4,5,3,2,1] => 0
[2,1,3,5,4] => [4,5,3,1,2] => 1
[2,1,4,3,5] => [4,5,2,3,1] => 1
[2,1,4,5,3] => [4,5,2,1,3] => 2
[2,1,5,3,4] => [4,5,1,3,2] => 2
[2,1,5,4,3] => [4,5,1,2,3] => 3
[2,3,1,4,5] => [4,3,5,2,1] => 0
[2,3,1,5,4] => [4,3,5,1,2] => 1
[2,3,4,1,5] => [4,3,2,5,1] => 0
[2,3,4,5,1] => [4,3,2,1,5] => 0
[2,3,5,1,4] => [4,3,1,5,2] => 1
[2,3,5,4,1] => [4,3,1,2,5] => 1
[2,4,1,3,5] => [4,2,5,3,1] => 1
[2,4,1,5,3] => [4,2,5,1,3] => 2
[2,4,3,1,5] => [4,2,3,5,1] => 1
[2,4,3,5,1] => [4,2,3,1,5] => 1
[2,4,5,1,3] => [4,2,1,5,3] => 2
[2,4,5,3,1] => [4,2,1,3,5] => 2
[2,5,1,3,4] => [4,1,5,3,2] => 2
[2,5,1,4,3] => [4,1,5,2,3] => 3
[2,5,3,1,4] => [4,1,3,5,2] => 2
[2,5,3,4,1] => [4,1,3,2,5] => 2
[2,5,4,1,3] => [4,1,2,5,3] => 3
[2,5,4,3,1] => [4,1,2,3,5] => 3
[3,1,2,4,5] => [3,5,4,2,1] => 0
[3,1,2,5,4] => [3,5,4,1,2] => 1
[3,1,4,2,5] => [3,5,2,4,1] => 0
[3,1,4,5,2] => [3,5,2,1,4] => 0
[3,1,5,2,4] => [3,5,1,4,2] => 1
[3,1,5,4,2] => [3,5,1,2,4] => 1
[3,2,1,4,5] => [3,4,5,2,1] => 0
[3,2,1,5,4] => [3,4,5,1,2] => 1
[3,2,4,1,5] => [3,4,2,5,1] => 0
[3,2,4,5,1] => [3,4,2,1,5] => 0
[3,2,5,1,4] => [3,4,1,5,2] => 1
[3,2,5,4,1] => [3,4,1,2,5] => 1
[3,4,1,2,5] => [3,2,5,4,1] => 0
[3,4,1,5,2] => [3,2,5,1,4] => 0
[3,4,2,1,5] => [3,2,4,5,1] => 0
[3,4,2,5,1] => [3,2,4,1,5] => 0
[3,4,5,1,2] => [3,2,1,5,4] => 0
[3,4,5,2,1] => [3,2,1,4,5] => 0
[3,5,1,2,4] => [3,1,5,4,2] => 1
[3,5,1,4,2] => [3,1,5,2,4] => 1
[3,5,2,1,4] => [3,1,4,5,2] => 1
>>> Load all 1200 entries. <<<[3,5,2,4,1] => [3,1,4,2,5] => 1
[3,5,4,1,2] => [3,1,2,5,4] => 1
[3,5,4,2,1] => [3,1,2,4,5] => 1
[4,1,2,3,5] => [2,5,4,3,1] => 0
[4,1,2,5,3] => [2,5,4,1,3] => 0
[4,1,3,2,5] => [2,5,3,4,1] => 0
[4,1,3,5,2] => [2,5,3,1,4] => 0
[4,1,5,2,3] => [2,5,1,4,3] => 0
[4,1,5,3,2] => [2,5,1,3,4] => 0
[4,2,1,3,5] => [2,4,5,3,1] => 0
[4,2,1,5,3] => [2,4,5,1,3] => 0
[4,2,3,1,5] => [2,4,3,5,1] => 0
[4,2,3,5,1] => [2,4,3,1,5] => 0
[4,2,5,1,3] => [2,4,1,5,3] => 0
[4,2,5,3,1] => [2,4,1,3,5] => 0
[4,3,1,2,5] => [2,3,5,4,1] => 0
[4,3,1,5,2] => [2,3,5,1,4] => 0
[4,3,2,1,5] => [2,3,4,5,1] => 0
[4,3,2,5,1] => [2,3,4,1,5] => 0
[4,3,5,1,2] => [2,3,1,5,4] => 0
[4,3,5,2,1] => [2,3,1,4,5] => 0
[4,5,1,2,3] => [2,1,5,4,3] => 0
[4,5,1,3,2] => [2,1,5,3,4] => 0
[4,5,2,1,3] => [2,1,4,5,3] => 0
[4,5,2,3,1] => [2,1,4,3,5] => 0
[4,5,3,1,2] => [2,1,3,5,4] => 0
[4,5,3,2,1] => [2,1,3,4,5] => 0
[5,1,2,3,4] => [1,5,4,3,2] => 0
[5,1,2,4,3] => [1,5,4,2,3] => 0
[5,1,3,2,4] => [1,5,3,4,2] => 0
[5,1,3,4,2] => [1,5,3,2,4] => 0
[5,1,4,2,3] => [1,5,2,4,3] => 0
[5,1,4,3,2] => [1,5,2,3,4] => 0
[5,2,1,3,4] => [1,4,5,3,2] => 0
[5,2,1,4,3] => [1,4,5,2,3] => 0
[5,2,3,1,4] => [1,4,3,5,2] => 0
[5,2,3,4,1] => [1,4,3,2,5] => 0
[5,2,4,1,3] => [1,4,2,5,3] => 0
[5,2,4,3,1] => [1,4,2,3,5] => 0
[5,3,1,2,4] => [1,3,5,4,2] => 0
[5,3,1,4,2] => [1,3,5,2,4] => 0
[5,3,2,1,4] => [1,3,4,5,2] => 0
[5,3,2,4,1] => [1,3,4,2,5] => 0
[5,3,4,1,2] => [1,3,2,5,4] => 0
[5,3,4,2,1] => [1,3,2,4,5] => 0
[5,4,1,2,3] => [1,2,5,4,3] => 0
[5,4,1,3,2] => [1,2,5,3,4] => 0
[5,4,2,1,3] => [1,2,4,5,3] => 0
[5,4,2,3,1] => [1,2,4,3,5] => 0
[5,4,3,1,2] => [1,2,3,5,4] => 0
[5,4,3,2,1] => [1,2,3,4,5] => 0
[1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,2,3,4,6,5] => [6,5,4,3,1,2] => 1
[1,2,3,5,4,6] => [6,5,4,2,3,1] => 1
[1,2,3,5,6,4] => [6,5,4,2,1,3] => 2
[1,2,3,6,4,5] => [6,5,4,1,3,2] => 2
[1,2,3,6,5,4] => [6,5,4,1,2,3] => 3
[1,2,4,3,5,6] => [6,5,3,4,2,1] => 1
[1,2,4,3,6,5] => [6,5,3,4,1,2] => 2
[1,2,4,5,3,6] => [6,5,3,2,4,1] => 2
[1,2,4,5,6,3] => [6,5,3,2,1,4] => 3
[1,2,4,6,3,5] => [6,5,3,1,4,2] => 3
[1,2,4,6,5,3] => [6,5,3,1,2,4] => 4
[1,2,5,3,4,6] => [6,5,2,4,3,1] => 2
[1,2,5,3,6,4] => [6,5,2,4,1,3] => 3
[1,2,5,4,3,6] => [6,5,2,3,4,1] => 3
[1,2,5,4,6,3] => [6,5,2,3,1,4] => 4
[1,2,5,6,3,4] => [6,5,2,1,4,3] => 4
[1,2,5,6,4,3] => [6,5,2,1,3,4] => 5
[1,2,6,3,4,5] => [6,5,1,4,3,2] => 3
[1,2,6,3,5,4] => [6,5,1,4,2,3] => 4
[1,2,6,4,3,5] => [6,5,1,3,4,2] => 4
[1,2,6,4,5,3] => [6,5,1,3,2,4] => 5
[1,2,6,5,3,4] => [6,5,1,2,4,3] => 5
[1,2,6,5,4,3] => [6,5,1,2,3,4] => 6
[1,3,2,4,5,6] => [6,4,5,3,2,1] => 1
[1,3,2,4,6,5] => [6,4,5,3,1,2] => 2
[1,3,2,5,4,6] => [6,4,5,2,3,1] => 2
[1,3,2,5,6,4] => [6,4,5,2,1,3] => 3
[1,3,2,6,4,5] => [6,4,5,1,3,2] => 3
[1,3,2,6,5,4] => [6,4,5,1,2,3] => 4
[1,3,4,2,5,6] => [6,4,3,5,2,1] => 2
[1,3,4,2,6,5] => [6,4,3,5,1,2] => 3
[1,3,4,5,2,6] => [6,4,3,2,5,1] => 3
[1,3,4,5,6,2] => [6,4,3,2,1,5] => 4
[1,3,4,6,2,5] => [6,4,3,1,5,2] => 4
[1,3,4,6,5,2] => [6,4,3,1,2,5] => 5
[1,3,5,2,4,6] => [6,4,2,5,3,1] => 3
[1,3,5,2,6,4] => [6,4,2,5,1,3] => 4
[1,3,5,4,2,6] => [6,4,2,3,5,1] => 4
[1,3,5,4,6,2] => [6,4,2,3,1,5] => 5
[1,3,5,6,2,4] => [6,4,2,1,5,3] => 5
[1,3,5,6,4,2] => [6,4,2,1,3,5] => 6
[1,3,6,2,4,5] => [6,4,1,5,3,2] => 4
[1,3,6,2,5,4] => [6,4,1,5,2,3] => 5
[1,3,6,4,2,5] => [6,4,1,3,5,2] => 5
[1,3,6,4,5,2] => [6,4,1,3,2,5] => 6
[1,3,6,5,2,4] => [6,4,1,2,5,3] => 6
[1,3,6,5,4,2] => [6,4,1,2,3,5] => 7
[1,4,2,3,5,6] => [6,3,5,4,2,1] => 2
[1,4,2,3,6,5] => [6,3,5,4,1,2] => 3
[1,4,2,5,3,6] => [6,3,5,2,4,1] => 3
[1,4,2,5,6,3] => [6,3,5,2,1,4] => 4
[1,4,2,6,3,5] => [6,3,5,1,4,2] => 4
[1,4,2,6,5,3] => [6,3,5,1,2,4] => 5
[1,4,3,2,5,6] => [6,3,4,5,2,1] => 3
[1,4,3,2,6,5] => [6,3,4,5,1,2] => 4
[1,4,3,5,2,6] => [6,3,4,2,5,1] => 4
[1,4,3,5,6,2] => [6,3,4,2,1,5] => 5
[1,4,3,6,2,5] => [6,3,4,1,5,2] => 5
[1,4,3,6,5,2] => [6,3,4,1,2,5] => 6
[1,4,5,2,3,6] => [6,3,2,5,4,1] => 4
[1,4,5,2,6,3] => [6,3,2,5,1,4] => 5
[1,4,5,3,2,6] => [6,3,2,4,5,1] => 5
[1,4,5,3,6,2] => [6,3,2,4,1,5] => 6
[1,4,5,6,2,3] => [6,3,2,1,5,4] => 6
[1,4,5,6,3,2] => [6,3,2,1,4,5] => 7
[1,4,6,2,3,5] => [6,3,1,5,4,2] => 5
[1,4,6,2,5,3] => [6,3,1,5,2,4] => 6
[1,4,6,3,2,5] => [6,3,1,4,5,2] => 6
[1,4,6,3,5,2] => [6,3,1,4,2,5] => 7
[1,4,6,5,2,3] => [6,3,1,2,5,4] => 7
[1,4,6,5,3,2] => [6,3,1,2,4,5] => 8
[1,5,2,3,4,6] => [6,2,5,4,3,1] => 3
[1,5,2,3,6,4] => [6,2,5,4,1,3] => 4
[1,5,2,4,3,6] => [6,2,5,3,4,1] => 4
[1,5,2,4,6,3] => [6,2,5,3,1,4] => 5
[1,5,2,6,3,4] => [6,2,5,1,4,3] => 5
[1,5,2,6,4,3] => [6,2,5,1,3,4] => 6
[1,5,3,2,4,6] => [6,2,4,5,3,1] => 4
[1,5,3,2,6,4] => [6,2,4,5,1,3] => 5
[1,5,3,4,2,6] => [6,2,4,3,5,1] => 5
[1,5,3,4,6,2] => [6,2,4,3,1,5] => 6
[1,5,3,6,2,4] => [6,2,4,1,5,3] => 6
[1,5,3,6,4,2] => [6,2,4,1,3,5] => 7
[1,5,4,2,3,6] => [6,2,3,5,4,1] => 5
[1,5,4,2,6,3] => [6,2,3,5,1,4] => 6
[1,5,4,3,2,6] => [6,2,3,4,5,1] => 6
[1,5,4,3,6,2] => [6,2,3,4,1,5] => 7
[1,5,4,6,2,3] => [6,2,3,1,5,4] => 7
[1,5,4,6,3,2] => [6,2,3,1,4,5] => 8
[1,5,6,2,3,4] => [6,2,1,5,4,3] => 6
[1,5,6,2,4,3] => [6,2,1,5,3,4] => 7
[1,5,6,3,2,4] => [6,2,1,4,5,3] => 7
[1,5,6,3,4,2] => [6,2,1,4,3,5] => 8
[1,5,6,4,2,3] => [6,2,1,3,5,4] => 8
[1,5,6,4,3,2] => [6,2,1,3,4,5] => 9
[1,6,2,3,4,5] => [6,1,5,4,3,2] => 4
[1,6,2,3,5,4] => [6,1,5,4,2,3] => 5
[1,6,2,4,3,5] => [6,1,5,3,4,2] => 5
[1,6,2,4,5,3] => [6,1,5,3,2,4] => 6
[1,6,2,5,3,4] => [6,1,5,2,4,3] => 6
[1,6,2,5,4,3] => [6,1,5,2,3,4] => 7
[1,6,3,2,4,5] => [6,1,4,5,3,2] => 5
[1,6,3,2,5,4] => [6,1,4,5,2,3] => 6
[1,6,3,4,2,5] => [6,1,4,3,5,2] => 6
[1,6,3,4,5,2] => [6,1,4,3,2,5] => 7
[1,6,3,5,2,4] => [6,1,4,2,5,3] => 7
[1,6,3,5,4,2] => [6,1,4,2,3,5] => 8
[1,6,4,2,3,5] => [6,1,3,5,4,2] => 6
[1,6,4,2,5,3] => [6,1,3,5,2,4] => 7
[1,6,4,3,2,5] => [6,1,3,4,5,2] => 7
[1,6,4,3,5,2] => [6,1,3,4,2,5] => 8
[1,6,4,5,2,3] => [6,1,3,2,5,4] => 8
[1,6,4,5,3,2] => [6,1,3,2,4,5] => 9
[1,6,5,2,3,4] => [6,1,2,5,4,3] => 7
[1,6,5,2,4,3] => [6,1,2,5,3,4] => 8
[1,6,5,3,2,4] => [6,1,2,4,5,3] => 8
[1,6,5,3,4,2] => [6,1,2,4,3,5] => 9
[1,6,5,4,2,3] => [6,1,2,3,5,4] => 9
[1,6,5,4,3,2] => [6,1,2,3,4,5] => 10
[2,1,3,4,5,6] => [5,6,4,3,2,1] => 0
[2,1,3,4,6,5] => [5,6,4,3,1,2] => 1
[2,1,3,5,4,6] => [5,6,4,2,3,1] => 1
[2,1,3,5,6,4] => [5,6,4,2,1,3] => 2
[2,1,3,6,4,5] => [5,6,4,1,3,2] => 2
[2,1,3,6,5,4] => [5,6,4,1,2,3] => 3
[2,1,4,3,5,6] => [5,6,3,4,2,1] => 1
[2,1,4,3,6,5] => [5,6,3,4,1,2] => 2
[2,1,4,5,3,6] => [5,6,3,2,4,1] => 2
[2,1,4,5,6,3] => [5,6,3,2,1,4] => 3
[2,1,4,6,3,5] => [5,6,3,1,4,2] => 3
[2,1,4,6,5,3] => [5,6,3,1,2,4] => 4
[2,1,5,3,4,6] => [5,6,2,4,3,1] => 2
[2,1,5,3,6,4] => [5,6,2,4,1,3] => 3
[2,1,5,4,3,6] => [5,6,2,3,4,1] => 3
[2,1,5,4,6,3] => [5,6,2,3,1,4] => 4
[2,1,5,6,3,4] => [5,6,2,1,4,3] => 4
[2,1,5,6,4,3] => [5,6,2,1,3,4] => 5
[2,1,6,3,4,5] => [5,6,1,4,3,2] => 3
[2,1,6,3,5,4] => [5,6,1,4,2,3] => 4
[2,1,6,4,3,5] => [5,6,1,3,4,2] => 4
[2,1,6,4,5,3] => [5,6,1,3,2,4] => 5
[2,1,6,5,3,4] => [5,6,1,2,4,3] => 5
[2,1,6,5,4,3] => [5,6,1,2,3,4] => 6
[2,3,1,4,5,6] => [5,4,6,3,2,1] => 0
[2,3,1,4,6,5] => [5,4,6,3,1,2] => 1
[2,3,1,5,4,6] => [5,4,6,2,3,1] => 1
[2,3,1,5,6,4] => [5,4,6,2,1,3] => 2
[2,3,1,6,4,5] => [5,4,6,1,3,2] => 2
[2,3,1,6,5,4] => [5,4,6,1,2,3] => 3
[2,3,4,1,5,6] => [5,4,3,6,2,1] => 0
[2,3,4,1,6,5] => [5,4,3,6,1,2] => 1
[2,3,4,5,1,6] => [5,4,3,2,6,1] => 0
[2,3,4,5,6,1] => [5,4,3,2,1,6] => 0
[2,3,4,6,1,5] => [5,4,3,1,6,2] => 1
[2,3,4,6,5,1] => [5,4,3,1,2,6] => 1
[2,3,5,1,4,6] => [5,4,2,6,3,1] => 1
[2,3,5,1,6,4] => [5,4,2,6,1,3] => 2
[2,3,5,4,1,6] => [5,4,2,3,6,1] => 1
[2,3,5,4,6,1] => [5,4,2,3,1,6] => 1
[2,3,5,6,1,4] => [5,4,2,1,6,3] => 2
[2,3,5,6,4,1] => [5,4,2,1,3,6] => 2
[2,3,6,1,4,5] => [5,4,1,6,3,2] => 2
[2,3,6,1,5,4] => [5,4,1,6,2,3] => 3
[2,3,6,4,1,5] => [5,4,1,3,6,2] => 2
[2,3,6,4,5,1] => [5,4,1,3,2,6] => 2
[2,3,6,5,1,4] => [5,4,1,2,6,3] => 3
[2,3,6,5,4,1] => [5,4,1,2,3,6] => 3
[2,4,1,3,5,6] => [5,3,6,4,2,1] => 1
[2,4,1,3,6,5] => [5,3,6,4,1,2] => 2
[2,4,1,5,3,6] => [5,3,6,2,4,1] => 2
[2,4,1,5,6,3] => [5,3,6,2,1,4] => 3
[2,4,1,6,3,5] => [5,3,6,1,4,2] => 3
[2,4,1,6,5,3] => [5,3,6,1,2,4] => 4
[2,4,3,1,5,6] => [5,3,4,6,2,1] => 1
[2,4,3,1,6,5] => [5,3,4,6,1,2] => 2
[2,4,3,5,1,6] => [5,3,4,2,6,1] => 1
[2,4,3,5,6,1] => [5,3,4,2,1,6] => 1
[2,4,3,6,1,5] => [5,3,4,1,6,2] => 2
[2,4,3,6,5,1] => [5,3,4,1,2,6] => 2
[2,4,5,1,3,6] => [5,3,2,6,4,1] => 2
[2,4,5,1,6,3] => [5,3,2,6,1,4] => 3
[2,4,5,3,1,6] => [5,3,2,4,6,1] => 2
[2,4,5,3,6,1] => [5,3,2,4,1,6] => 2
[2,4,5,6,1,3] => [5,3,2,1,6,4] => 3
[2,4,5,6,3,1] => [5,3,2,1,4,6] => 3
[2,4,6,1,3,5] => [5,3,1,6,4,2] => 3
[2,4,6,1,5,3] => [5,3,1,6,2,4] => 4
[2,4,6,3,1,5] => [5,3,1,4,6,2] => 3
[2,4,6,3,5,1] => [5,3,1,4,2,6] => 3
[2,4,6,5,1,3] => [5,3,1,2,6,4] => 4
[2,4,6,5,3,1] => [5,3,1,2,4,6] => 4
[2,5,1,3,4,6] => [5,2,6,4,3,1] => 2
[2,5,1,3,6,4] => [5,2,6,4,1,3] => 3
[2,5,1,4,3,6] => [5,2,6,3,4,1] => 3
[2,5,1,4,6,3] => [5,2,6,3,1,4] => 4
[2,5,1,6,3,4] => [5,2,6,1,4,3] => 4
[2,5,1,6,4,3] => [5,2,6,1,3,4] => 5
[2,5,3,1,4,6] => [5,2,4,6,3,1] => 2
[2,5,3,1,6,4] => [5,2,4,6,1,3] => 3
[2,5,3,4,1,6] => [5,2,4,3,6,1] => 2
[2,5,3,4,6,1] => [5,2,4,3,1,6] => 2
[2,5,3,6,1,4] => [5,2,4,1,6,3] => 3
[2,5,3,6,4,1] => [5,2,4,1,3,6] => 3
[2,5,4,1,3,6] => [5,2,3,6,4,1] => 3
[2,5,4,1,6,3] => [5,2,3,6,1,4] => 4
[2,5,4,3,1,6] => [5,2,3,4,6,1] => 3
[2,5,4,3,6,1] => [5,2,3,4,1,6] => 3
[2,5,4,6,1,3] => [5,2,3,1,6,4] => 4
[2,5,4,6,3,1] => [5,2,3,1,4,6] => 4
[2,5,6,1,3,4] => [5,2,1,6,4,3] => 4
[2,5,6,1,4,3] => [5,2,1,6,3,4] => 5
[2,5,6,3,1,4] => [5,2,1,4,6,3] => 4
[2,5,6,3,4,1] => [5,2,1,4,3,6] => 4
[2,5,6,4,1,3] => [5,2,1,3,6,4] => 5
[2,5,6,4,3,1] => [5,2,1,3,4,6] => 5
[2,6,1,3,4,5] => [5,1,6,4,3,2] => 3
[2,6,1,3,5,4] => [5,1,6,4,2,3] => 4
[2,6,1,4,3,5] => [5,1,6,3,4,2] => 4
[2,6,1,4,5,3] => [5,1,6,3,2,4] => 5
[2,6,1,5,3,4] => [5,1,6,2,4,3] => 5
[2,6,1,5,4,3] => [5,1,6,2,3,4] => 6
[2,6,3,1,4,5] => [5,1,4,6,3,2] => 3
[2,6,3,1,5,4] => [5,1,4,6,2,3] => 4
[2,6,3,4,1,5] => [5,1,4,3,6,2] => 3
[2,6,3,4,5,1] => [5,1,4,3,2,6] => 3
[2,6,3,5,1,4] => [5,1,4,2,6,3] => 4
[2,6,3,5,4,1] => [5,1,4,2,3,6] => 4
[2,6,4,1,3,5] => [5,1,3,6,4,2] => 4
[2,6,4,1,5,3] => [5,1,3,6,2,4] => 5
[2,6,4,3,1,5] => [5,1,3,4,6,2] => 4
[2,6,4,3,5,1] => [5,1,3,4,2,6] => 4
[2,6,4,5,1,3] => [5,1,3,2,6,4] => 5
[2,6,4,5,3,1] => [5,1,3,2,4,6] => 5
[2,6,5,1,3,4] => [5,1,2,6,4,3] => 5
[2,6,5,1,4,3] => [5,1,2,6,3,4] => 6
[2,6,5,3,1,4] => [5,1,2,4,6,3] => 5
[2,6,5,3,4,1] => [5,1,2,4,3,6] => 5
[2,6,5,4,1,3] => [5,1,2,3,6,4] => 6
[2,6,5,4,3,1] => [5,1,2,3,4,6] => 6
[3,1,2,4,5,6] => [4,6,5,3,2,1] => 0
[3,1,2,4,6,5] => [4,6,5,3,1,2] => 1
[3,1,2,5,4,6] => [4,6,5,2,3,1] => 1
[3,1,2,5,6,4] => [4,6,5,2,1,3] => 2
[3,1,2,6,4,5] => [4,6,5,1,3,2] => 2
[3,1,2,6,5,4] => [4,6,5,1,2,3] => 3
[3,1,4,2,5,6] => [4,6,3,5,2,1] => 0
[3,1,4,2,6,5] => [4,6,3,5,1,2] => 1
[3,1,4,5,2,6] => [4,6,3,2,5,1] => 0
[3,1,4,5,6,2] => [4,6,3,2,1,5] => 0
[3,1,4,6,2,5] => [4,6,3,1,5,2] => 1
[3,1,4,6,5,2] => [4,6,3,1,2,5] => 1
[3,1,5,2,4,6] => [4,6,2,5,3,1] => 1
[3,1,5,2,6,4] => [4,6,2,5,1,3] => 2
[3,1,5,4,2,6] => [4,6,2,3,5,1] => 1
[3,1,5,4,6,2] => [4,6,2,3,1,5] => 1
[3,1,5,6,2,4] => [4,6,2,1,5,3] => 2
[3,1,5,6,4,2] => [4,6,2,1,3,5] => 2
[3,1,6,2,4,5] => [4,6,1,5,3,2] => 2
[3,1,6,2,5,4] => [4,6,1,5,2,3] => 3
[3,1,6,4,2,5] => [4,6,1,3,5,2] => 2
[3,1,6,4,5,2] => [4,6,1,3,2,5] => 2
[3,1,6,5,2,4] => [4,6,1,2,5,3] => 3
[3,1,6,5,4,2] => [4,6,1,2,3,5] => 3
[3,2,1,4,5,6] => [4,5,6,3,2,1] => 0
[3,2,1,4,6,5] => [4,5,6,3,1,2] => 1
[3,2,1,5,4,6] => [4,5,6,2,3,1] => 1
[3,2,1,5,6,4] => [4,5,6,2,1,3] => 2
[3,2,1,6,4,5] => [4,5,6,1,3,2] => 2
[3,2,1,6,5,4] => [4,5,6,1,2,3] => 3
[3,2,4,1,5,6] => [4,5,3,6,2,1] => 0
[3,2,4,1,6,5] => [4,5,3,6,1,2] => 1
[3,2,4,5,1,6] => [4,5,3,2,6,1] => 0
[3,2,4,5,6,1] => [4,5,3,2,1,6] => 0
[3,2,4,6,1,5] => [4,5,3,1,6,2] => 1
[3,2,4,6,5,1] => [4,5,3,1,2,6] => 1
[3,2,5,1,4,6] => [4,5,2,6,3,1] => 1
[3,2,5,1,6,4] => [4,5,2,6,1,3] => 2
[3,2,5,4,1,6] => [4,5,2,3,6,1] => 1
[3,2,5,4,6,1] => [4,5,2,3,1,6] => 1
[3,2,5,6,1,4] => [4,5,2,1,6,3] => 2
[3,2,5,6,4,1] => [4,5,2,1,3,6] => 2
[3,2,6,1,4,5] => [4,5,1,6,3,2] => 2
[3,2,6,1,5,4] => [4,5,1,6,2,3] => 3
[3,2,6,4,1,5] => [4,5,1,3,6,2] => 2
[3,2,6,4,5,1] => [4,5,1,3,2,6] => 2
[3,2,6,5,1,4] => [4,5,1,2,6,3] => 3
[3,2,6,5,4,1] => [4,5,1,2,3,6] => 3
[3,4,1,2,5,6] => [4,3,6,5,2,1] => 0
[3,4,1,2,6,5] => [4,3,6,5,1,2] => 1
[3,4,1,5,2,6] => [4,3,6,2,5,1] => 0
[3,4,1,5,6,2] => [4,3,6,2,1,5] => 0
[3,4,1,6,2,5] => [4,3,6,1,5,2] => 1
[3,4,1,6,5,2] => [4,3,6,1,2,5] => 1
[3,4,2,1,5,6] => [4,3,5,6,2,1] => 0
[3,4,2,1,6,5] => [4,3,5,6,1,2] => 1
[3,4,2,5,1,6] => [4,3,5,2,6,1] => 0
[3,4,2,5,6,1] => [4,3,5,2,1,6] => 0
[3,4,2,6,1,5] => [4,3,5,1,6,2] => 1
[3,4,2,6,5,1] => [4,3,5,1,2,6] => 1
[3,4,5,1,2,6] => [4,3,2,6,5,1] => 0
[3,4,5,1,6,2] => [4,3,2,6,1,5] => 0
[3,4,5,2,1,6] => [4,3,2,5,6,1] => 0
[3,4,5,2,6,1] => [4,3,2,5,1,6] => 0
[3,4,5,6,1,2] => [4,3,2,1,6,5] => 0
[3,4,5,6,2,1] => [4,3,2,1,5,6] => 0
[3,4,6,1,2,5] => [4,3,1,6,5,2] => 1
[3,4,6,1,5,2] => [4,3,1,6,2,5] => 1
[3,4,6,2,1,5] => [4,3,1,5,6,2] => 1
[3,4,6,2,5,1] => [4,3,1,5,2,6] => 1
[3,4,6,5,1,2] => [4,3,1,2,6,5] => 1
[3,4,6,5,2,1] => [4,3,1,2,5,6] => 1
[3,5,1,2,4,6] => [4,2,6,5,3,1] => 1
[3,5,1,2,6,4] => [4,2,6,5,1,3] => 2
[3,5,1,4,2,6] => [4,2,6,3,5,1] => 1
[3,5,1,4,6,2] => [4,2,6,3,1,5] => 1
[3,5,1,6,2,4] => [4,2,6,1,5,3] => 2
[3,5,1,6,4,2] => [4,2,6,1,3,5] => 2
[3,5,2,1,4,6] => [4,2,5,6,3,1] => 1
[3,5,2,1,6,4] => [4,2,5,6,1,3] => 2
[3,5,2,4,1,6] => [4,2,5,3,6,1] => 1
[3,5,2,4,6,1] => [4,2,5,3,1,6] => 1
[3,5,2,6,1,4] => [4,2,5,1,6,3] => 2
[3,5,2,6,4,1] => [4,2,5,1,3,6] => 2
[3,5,4,1,2,6] => [4,2,3,6,5,1] => 1
[3,5,4,1,6,2] => [4,2,3,6,1,5] => 1
[3,5,4,2,1,6] => [4,2,3,5,6,1] => 1
[3,5,4,2,6,1] => [4,2,3,5,1,6] => 1
[3,5,4,6,1,2] => [4,2,3,1,6,5] => 1
[3,5,4,6,2,1] => [4,2,3,1,5,6] => 1
[3,5,6,1,2,4] => [4,2,1,6,5,3] => 2
[3,5,6,1,4,2] => [4,2,1,6,3,5] => 2
[3,5,6,2,1,4] => [4,2,1,5,6,3] => 2
[3,5,6,2,4,1] => [4,2,1,5,3,6] => 2
[3,5,6,4,1,2] => [4,2,1,3,6,5] => 2
[3,5,6,4,2,1] => [4,2,1,3,5,6] => 2
[3,6,1,2,4,5] => [4,1,6,5,3,2] => 2
[3,6,1,2,5,4] => [4,1,6,5,2,3] => 3
[3,6,1,4,2,5] => [4,1,6,3,5,2] => 2
[3,6,1,4,5,2] => [4,1,6,3,2,5] => 2
[3,6,1,5,2,4] => [4,1,6,2,5,3] => 3
[3,6,1,5,4,2] => [4,1,6,2,3,5] => 3
[3,6,2,1,4,5] => [4,1,5,6,3,2] => 2
[3,6,2,1,5,4] => [4,1,5,6,2,3] => 3
[3,6,2,4,1,5] => [4,1,5,3,6,2] => 2
[3,6,2,4,5,1] => [4,1,5,3,2,6] => 2
[3,6,2,5,1,4] => [4,1,5,2,6,3] => 3
[3,6,2,5,4,1] => [4,1,5,2,3,6] => 3
[3,6,4,1,2,5] => [4,1,3,6,5,2] => 2
[3,6,4,1,5,2] => [4,1,3,6,2,5] => 2
[3,6,4,2,1,5] => [4,1,3,5,6,2] => 2
[3,6,4,2,5,1] => [4,1,3,5,2,6] => 2
[3,6,4,5,1,2] => [4,1,3,2,6,5] => 2
[3,6,4,5,2,1] => [4,1,3,2,5,6] => 2
[3,6,5,1,2,4] => [4,1,2,6,5,3] => 3
[3,6,5,1,4,2] => [4,1,2,6,3,5] => 3
[3,6,5,2,1,4] => [4,1,2,5,6,3] => 3
[3,6,5,2,4,1] => [4,1,2,5,3,6] => 3
[3,6,5,4,1,2] => [4,1,2,3,6,5] => 3
[3,6,5,4,2,1] => [4,1,2,3,5,6] => 3
[4,1,2,3,5,6] => [3,6,5,4,2,1] => 0
[4,1,2,3,6,5] => [3,6,5,4,1,2] => 1
[4,1,2,5,3,6] => [3,6,5,2,4,1] => 0
[4,1,2,5,6,3] => [3,6,5,2,1,4] => 0
[4,1,2,6,3,5] => [3,6,5,1,4,2] => 1
[4,1,2,6,5,3] => [3,6,5,1,2,4] => 1
[4,1,3,2,5,6] => [3,6,4,5,2,1] => 0
[4,1,3,2,6,5] => [3,6,4,5,1,2] => 1
[4,1,3,5,2,6] => [3,6,4,2,5,1] => 0
[4,1,3,5,6,2] => [3,6,4,2,1,5] => 0
[4,1,3,6,2,5] => [3,6,4,1,5,2] => 1
[4,1,3,6,5,2] => [3,6,4,1,2,5] => 1
[4,1,5,2,3,6] => [3,6,2,5,4,1] => 0
[4,1,5,2,6,3] => [3,6,2,5,1,4] => 0
[4,1,5,3,2,6] => [3,6,2,4,5,1] => 0
[4,1,5,3,6,2] => [3,6,2,4,1,5] => 0
[4,1,5,6,2,3] => [3,6,2,1,5,4] => 0
[4,1,5,6,3,2] => [3,6,2,1,4,5] => 0
[4,1,6,2,3,5] => [3,6,1,5,4,2] => 1
[4,1,6,2,5,3] => [3,6,1,5,2,4] => 1
[4,1,6,3,2,5] => [3,6,1,4,5,2] => 1
[4,1,6,3,5,2] => [3,6,1,4,2,5] => 1
[4,1,6,5,2,3] => [3,6,1,2,5,4] => 1
[4,1,6,5,3,2] => [3,6,1,2,4,5] => 1
[4,2,1,3,5,6] => [3,5,6,4,2,1] => 0
[4,2,1,3,6,5] => [3,5,6,4,1,2] => 1
[4,2,1,5,3,6] => [3,5,6,2,4,1] => 0
[4,2,1,5,6,3] => [3,5,6,2,1,4] => 0
[4,2,1,6,3,5] => [3,5,6,1,4,2] => 1
[4,2,1,6,5,3] => [3,5,6,1,2,4] => 1
[4,2,3,1,5,6] => [3,5,4,6,2,1] => 0
[4,2,3,1,6,5] => [3,5,4,6,1,2] => 1
[4,2,3,5,1,6] => [3,5,4,2,6,1] => 0
[4,2,3,5,6,1] => [3,5,4,2,1,6] => 0
[4,2,3,6,1,5] => [3,5,4,1,6,2] => 1
[4,2,3,6,5,1] => [3,5,4,1,2,6] => 1
[4,2,5,1,3,6] => [3,5,2,6,4,1] => 0
[4,2,5,1,6,3] => [3,5,2,6,1,4] => 0
[4,2,5,3,1,6] => [3,5,2,4,6,1] => 0
[4,2,5,3,6,1] => [3,5,2,4,1,6] => 0
[4,2,5,6,1,3] => [3,5,2,1,6,4] => 0
[4,2,5,6,3,1] => [3,5,2,1,4,6] => 0
[4,2,6,1,3,5] => [3,5,1,6,4,2] => 1
[4,2,6,1,5,3] => [3,5,1,6,2,4] => 1
[4,2,6,3,1,5] => [3,5,1,4,6,2] => 1
[4,2,6,3,5,1] => [3,5,1,4,2,6] => 1
[4,2,6,5,1,3] => [3,5,1,2,6,4] => 1
[4,2,6,5,3,1] => [3,5,1,2,4,6] => 1
[4,3,1,2,5,6] => [3,4,6,5,2,1] => 0
[4,3,1,2,6,5] => [3,4,6,5,1,2] => 1
[4,3,1,5,2,6] => [3,4,6,2,5,1] => 0
[4,3,1,5,6,2] => [3,4,6,2,1,5] => 0
[4,3,1,6,2,5] => [3,4,6,1,5,2] => 1
[4,3,1,6,5,2] => [3,4,6,1,2,5] => 1
[4,3,2,1,5,6] => [3,4,5,6,2,1] => 0
[4,3,2,1,6,5] => [3,4,5,6,1,2] => 1
[4,3,2,5,1,6] => [3,4,5,2,6,1] => 0
[4,3,2,5,6,1] => [3,4,5,2,1,6] => 0
[4,3,2,6,1,5] => [3,4,5,1,6,2] => 1
[4,3,2,6,5,1] => [3,4,5,1,2,6] => 1
[4,3,5,1,2,6] => [3,4,2,6,5,1] => 0
[4,3,5,1,6,2] => [3,4,2,6,1,5] => 0
[4,3,5,2,1,6] => [3,4,2,5,6,1] => 0
[4,3,5,2,6,1] => [3,4,2,5,1,6] => 0
[4,3,5,6,1,2] => [3,4,2,1,6,5] => 0
[4,3,5,6,2,1] => [3,4,2,1,5,6] => 0
[4,3,6,1,2,5] => [3,4,1,6,5,2] => 1
[4,3,6,1,5,2] => [3,4,1,6,2,5] => 1
[4,3,6,2,1,5] => [3,4,1,5,6,2] => 1
[4,3,6,2,5,1] => [3,4,1,5,2,6] => 1
[4,3,6,5,1,2] => [3,4,1,2,6,5] => 1
[4,3,6,5,2,1] => [3,4,1,2,5,6] => 1
[4,5,1,2,3,6] => [3,2,6,5,4,1] => 0
[4,5,1,2,6,3] => [3,2,6,5,1,4] => 0
[4,5,1,3,2,6] => [3,2,6,4,5,1] => 0
[4,5,1,3,6,2] => [3,2,6,4,1,5] => 0
[4,5,1,6,2,3] => [3,2,6,1,5,4] => 0
[4,5,1,6,3,2] => [3,2,6,1,4,5] => 0
[4,5,2,1,3,6] => [3,2,5,6,4,1] => 0
[4,5,2,1,6,3] => [3,2,5,6,1,4] => 0
[4,5,2,3,1,6] => [3,2,5,4,6,1] => 0
[4,5,2,3,6,1] => [3,2,5,4,1,6] => 0
[4,5,2,6,1,3] => [3,2,5,1,6,4] => 0
[4,5,2,6,3,1] => [3,2,5,1,4,6] => 0
[4,5,3,1,2,6] => [3,2,4,6,5,1] => 0
[4,5,3,1,6,2] => [3,2,4,6,1,5] => 0
[4,5,3,2,1,6] => [3,2,4,5,6,1] => 0
[4,5,3,2,6,1] => [3,2,4,5,1,6] => 0
[4,5,3,6,1,2] => [3,2,4,1,6,5] => 0
[4,5,3,6,2,1] => [3,2,4,1,5,6] => 0
[4,5,6,1,2,3] => [3,2,1,6,5,4] => 0
[4,5,6,1,3,2] => [3,2,1,6,4,5] => 0
[4,5,6,2,1,3] => [3,2,1,5,6,4] => 0
[4,5,6,2,3,1] => [3,2,1,5,4,6] => 0
[4,5,6,3,1,2] => [3,2,1,4,6,5] => 0
[4,5,6,3,2,1] => [3,2,1,4,5,6] => 0
[4,6,1,2,3,5] => [3,1,6,5,4,2] => 1
[4,6,1,2,5,3] => [3,1,6,5,2,4] => 1
[4,6,1,3,2,5] => [3,1,6,4,5,2] => 1
[4,6,1,3,5,2] => [3,1,6,4,2,5] => 1
[4,6,1,5,2,3] => [3,1,6,2,5,4] => 1
[4,6,1,5,3,2] => [3,1,6,2,4,5] => 1
[4,6,2,1,3,5] => [3,1,5,6,4,2] => 1
[4,6,2,1,5,3] => [3,1,5,6,2,4] => 1
[4,6,2,3,1,5] => [3,1,5,4,6,2] => 1
[4,6,2,3,5,1] => [3,1,5,4,2,6] => 1
[4,6,2,5,1,3] => [3,1,5,2,6,4] => 1
[4,6,2,5,3,1] => [3,1,5,2,4,6] => 1
[4,6,3,1,2,5] => [3,1,4,6,5,2] => 1
[4,6,3,1,5,2] => [3,1,4,6,2,5] => 1
[4,6,3,2,1,5] => [3,1,4,5,6,2] => 1
[4,6,3,2,5,1] => [3,1,4,5,2,6] => 1
[4,6,3,5,1,2] => [3,1,4,2,6,5] => 1
[4,6,3,5,2,1] => [3,1,4,2,5,6] => 1
[4,6,5,1,2,3] => [3,1,2,6,5,4] => 1
[4,6,5,1,3,2] => [3,1,2,6,4,5] => 1
[4,6,5,2,1,3] => [3,1,2,5,6,4] => 1
[4,6,5,2,3,1] => [3,1,2,5,4,6] => 1
[4,6,5,3,1,2] => [3,1,2,4,6,5] => 1
[4,6,5,3,2,1] => [3,1,2,4,5,6] => 1
[5,1,2,3,4,6] => [2,6,5,4,3,1] => 0
[5,1,2,3,6,4] => [2,6,5,4,1,3] => 0
[5,1,2,4,3,6] => [2,6,5,3,4,1] => 0
[5,1,2,4,6,3] => [2,6,5,3,1,4] => 0
[5,1,2,6,3,4] => [2,6,5,1,4,3] => 0
[5,1,2,6,4,3] => [2,6,5,1,3,4] => 0
[5,1,3,2,4,6] => [2,6,4,5,3,1] => 0
[5,1,3,2,6,4] => [2,6,4,5,1,3] => 0
[5,1,3,4,2,6] => [2,6,4,3,5,1] => 0
[5,1,3,4,6,2] => [2,6,4,3,1,5] => 0
[5,1,3,6,2,4] => [2,6,4,1,5,3] => 0
[5,1,3,6,4,2] => [2,6,4,1,3,5] => 0
[5,1,4,2,3,6] => [2,6,3,5,4,1] => 0
[5,1,4,2,6,3] => [2,6,3,5,1,4] => 0
[5,1,4,3,2,6] => [2,6,3,4,5,1] => 0
[5,1,4,3,6,2] => [2,6,3,4,1,5] => 0
[5,1,4,6,2,3] => [2,6,3,1,5,4] => 0
[5,1,4,6,3,2] => [2,6,3,1,4,5] => 0
[5,1,6,2,3,4] => [2,6,1,5,4,3] => 0
[5,1,6,2,4,3] => [2,6,1,5,3,4] => 0
[5,1,6,3,2,4] => [2,6,1,4,5,3] => 0
[5,1,6,3,4,2] => [2,6,1,4,3,5] => 0
[5,1,6,4,2,3] => [2,6,1,3,5,4] => 0
[5,1,6,4,3,2] => [2,6,1,3,4,5] => 0
[5,2,1,3,4,6] => [2,5,6,4,3,1] => 0
[5,2,1,3,6,4] => [2,5,6,4,1,3] => 0
[5,2,1,4,3,6] => [2,5,6,3,4,1] => 0
[5,2,1,4,6,3] => [2,5,6,3,1,4] => 0
[5,2,1,6,3,4] => [2,5,6,1,4,3] => 0
[5,2,1,6,4,3] => [2,5,6,1,3,4] => 0
[5,2,3,1,4,6] => [2,5,4,6,3,1] => 0
[5,2,3,1,6,4] => [2,5,4,6,1,3] => 0
[5,2,3,4,1,6] => [2,5,4,3,6,1] => 0
[5,2,3,4,6,1] => [2,5,4,3,1,6] => 0
[5,2,3,6,1,4] => [2,5,4,1,6,3] => 0
[5,2,3,6,4,1] => [2,5,4,1,3,6] => 0
[5,2,4,1,3,6] => [2,5,3,6,4,1] => 0
[5,2,4,1,6,3] => [2,5,3,6,1,4] => 0
[5,2,4,3,1,6] => [2,5,3,4,6,1] => 0
[5,2,4,3,6,1] => [2,5,3,4,1,6] => 0
[5,2,4,6,1,3] => [2,5,3,1,6,4] => 0
[5,2,4,6,3,1] => [2,5,3,1,4,6] => 0
[5,2,6,1,3,4] => [2,5,1,6,4,3] => 0
[5,2,6,1,4,3] => [2,5,1,6,3,4] => 0
[5,2,6,3,1,4] => [2,5,1,4,6,3] => 0
[5,2,6,3,4,1] => [2,5,1,4,3,6] => 0
[5,2,6,4,1,3] => [2,5,1,3,6,4] => 0
[5,2,6,4,3,1] => [2,5,1,3,4,6] => 0
[5,3,1,2,4,6] => [2,4,6,5,3,1] => 0
[5,3,1,2,6,4] => [2,4,6,5,1,3] => 0
[5,3,1,4,2,6] => [2,4,6,3,5,1] => 0
[5,3,1,4,6,2] => [2,4,6,3,1,5] => 0
[5,3,1,6,2,4] => [2,4,6,1,5,3] => 0
[5,3,1,6,4,2] => [2,4,6,1,3,5] => 0
[5,3,2,1,4,6] => [2,4,5,6,3,1] => 0
[5,3,2,1,6,4] => [2,4,5,6,1,3] => 0
[5,3,2,4,1,6] => [2,4,5,3,6,1] => 0
[5,3,2,4,6,1] => [2,4,5,3,1,6] => 0
[5,3,2,6,1,4] => [2,4,5,1,6,3] => 0
[5,3,2,6,4,1] => [2,4,5,1,3,6] => 0
[5,3,4,1,2,6] => [2,4,3,6,5,1] => 0
[5,3,4,1,6,2] => [2,4,3,6,1,5] => 0
[5,3,4,2,1,6] => [2,4,3,5,6,1] => 0
[5,3,4,2,6,1] => [2,4,3,5,1,6] => 0
[5,3,4,6,1,2] => [2,4,3,1,6,5] => 0
[5,3,4,6,2,1] => [2,4,3,1,5,6] => 0
[5,3,6,1,2,4] => [2,4,1,6,5,3] => 0
[5,3,6,1,4,2] => [2,4,1,6,3,5] => 0
[5,3,6,2,1,4] => [2,4,1,5,6,3] => 0
[5,3,6,2,4,1] => [2,4,1,5,3,6] => 0
[5,3,6,4,1,2] => [2,4,1,3,6,5] => 0
[5,3,6,4,2,1] => [2,4,1,3,5,6] => 0
[5,4,1,2,3,6] => [2,3,6,5,4,1] => 0
[5,4,1,2,6,3] => [2,3,6,5,1,4] => 0
[5,4,1,3,2,6] => [2,3,6,4,5,1] => 0
[5,4,1,3,6,2] => [2,3,6,4,1,5] => 0
[5,4,1,6,2,3] => [2,3,6,1,5,4] => 0
[5,4,1,6,3,2] => [2,3,6,1,4,5] => 0
[5,4,2,1,3,6] => [2,3,5,6,4,1] => 0
[5,4,2,1,6,3] => [2,3,5,6,1,4] => 0
[5,4,2,3,1,6] => [2,3,5,4,6,1] => 0
[5,4,2,3,6,1] => [2,3,5,4,1,6] => 0
[5,4,2,6,1,3] => [2,3,5,1,6,4] => 0
[5,4,2,6,3,1] => [2,3,5,1,4,6] => 0
[5,4,3,1,2,6] => [2,3,4,6,5,1] => 0
[5,4,3,1,6,2] => [2,3,4,6,1,5] => 0
[5,4,3,2,1,6] => [2,3,4,5,6,1] => 0
[5,4,3,2,6,1] => [2,3,4,5,1,6] => 0
[5,4,3,6,1,2] => [2,3,4,1,6,5] => 0
[5,4,3,6,2,1] => [2,3,4,1,5,6] => 0
[5,4,6,1,2,3] => [2,3,1,6,5,4] => 0
[5,4,6,1,3,2] => [2,3,1,6,4,5] => 0
[5,4,6,2,1,3] => [2,3,1,5,6,4] => 0
[5,4,6,2,3,1] => [2,3,1,5,4,6] => 0
[5,4,6,3,1,2] => [2,3,1,4,6,5] => 0
[5,4,6,3,2,1] => [2,3,1,4,5,6] => 0
[5,6,1,2,3,4] => [2,1,6,5,4,3] => 0
[5,6,1,2,4,3] => [2,1,6,5,3,4] => 0
[5,6,1,3,2,4] => [2,1,6,4,5,3] => 0
[5,6,1,3,4,2] => [2,1,6,4,3,5] => 0
[5,6,1,4,2,3] => [2,1,6,3,5,4] => 0
[5,6,1,4,3,2] => [2,1,6,3,4,5] => 0
[5,6,2,1,3,4] => [2,1,5,6,4,3] => 0
[5,6,2,1,4,3] => [2,1,5,6,3,4] => 0
[5,6,2,3,1,4] => [2,1,5,4,6,3] => 0
[5,6,2,3,4,1] => [2,1,5,4,3,6] => 0
[5,6,2,4,1,3] => [2,1,5,3,6,4] => 0
[5,6,2,4,3,1] => [2,1,5,3,4,6] => 0
[5,6,3,1,2,4] => [2,1,4,6,5,3] => 0
[5,6,3,1,4,2] => [2,1,4,6,3,5] => 0
[5,6,3,2,1,4] => [2,1,4,5,6,3] => 0
[5,6,3,2,4,1] => [2,1,4,5,3,6] => 0
[5,6,3,4,1,2] => [2,1,4,3,6,5] => 0
[5,6,3,4,2,1] => [2,1,4,3,5,6] => 0
[5,6,4,1,2,3] => [2,1,3,6,5,4] => 0
[5,6,4,1,3,2] => [2,1,3,6,4,5] => 0
[5,6,4,2,1,3] => [2,1,3,5,6,4] => 0
[5,6,4,2,3,1] => [2,1,3,5,4,6] => 0
[5,6,4,3,1,2] => [2,1,3,4,6,5] => 0
[5,6,4,3,2,1] => [2,1,3,4,5,6] => 0
[6,1,2,3,4,5] => [1,6,5,4,3,2] => 0
[6,1,2,3,5,4] => [1,6,5,4,2,3] => 0
[6,1,2,4,3,5] => [1,6,5,3,4,2] => 0
[6,1,2,4,5,3] => [1,6,5,3,2,4] => 0
[6,1,2,5,3,4] => [1,6,5,2,4,3] => 0
[6,1,2,5,4,3] => [1,6,5,2,3,4] => 0
[6,1,3,2,4,5] => [1,6,4,5,3,2] => 0
[6,1,3,2,5,4] => [1,6,4,5,2,3] => 0
[6,1,3,4,2,5] => [1,6,4,3,5,2] => 0
[6,1,3,4,5,2] => [1,6,4,3,2,5] => 0
[6,1,3,5,2,4] => [1,6,4,2,5,3] => 0
[6,1,3,5,4,2] => [1,6,4,2,3,5] => 0
[6,1,4,2,3,5] => [1,6,3,5,4,2] => 0
[6,1,4,2,5,3] => [1,6,3,5,2,4] => 0
[6,1,4,3,2,5] => [1,6,3,4,5,2] => 0
[6,1,4,3,5,2] => [1,6,3,4,2,5] => 0
[6,1,4,5,2,3] => [1,6,3,2,5,4] => 0
[6,1,4,5,3,2] => [1,6,3,2,4,5] => 0
[6,1,5,2,3,4] => [1,6,2,5,4,3] => 0
[6,1,5,2,4,3] => [1,6,2,5,3,4] => 0
[6,1,5,3,2,4] => [1,6,2,4,5,3] => 0
[6,1,5,3,4,2] => [1,6,2,4,3,5] => 0
[6,1,5,4,2,3] => [1,6,2,3,5,4] => 0
[6,1,5,4,3,2] => [1,6,2,3,4,5] => 0
[6,2,1,3,4,5] => [1,5,6,4,3,2] => 0
[6,2,1,3,5,4] => [1,5,6,4,2,3] => 0
[6,2,1,4,3,5] => [1,5,6,3,4,2] => 0
[6,2,1,4,5,3] => [1,5,6,3,2,4] => 0
[6,2,1,5,3,4] => [1,5,6,2,4,3] => 0
[6,2,1,5,4,3] => [1,5,6,2,3,4] => 0
[6,2,3,1,4,5] => [1,5,4,6,3,2] => 0
[6,2,3,1,5,4] => [1,5,4,6,2,3] => 0
[6,2,3,4,1,5] => [1,5,4,3,6,2] => 0
[6,2,3,4,5,1] => [1,5,4,3,2,6] => 0
[6,2,3,5,1,4] => [1,5,4,2,6,3] => 0
[6,2,3,5,4,1] => [1,5,4,2,3,6] => 0
[6,2,4,1,3,5] => [1,5,3,6,4,2] => 0
[6,2,4,1,5,3] => [1,5,3,6,2,4] => 0
[6,2,4,3,1,5] => [1,5,3,4,6,2] => 0
[6,2,4,3,5,1] => [1,5,3,4,2,6] => 0
[6,2,4,5,1,3] => [1,5,3,2,6,4] => 0
[6,2,4,5,3,1] => [1,5,3,2,4,6] => 0
[6,2,5,1,3,4] => [1,5,2,6,4,3] => 0
[6,2,5,1,4,3] => [1,5,2,6,3,4] => 0
[6,2,5,3,1,4] => [1,5,2,4,6,3] => 0
[6,2,5,3,4,1] => [1,5,2,4,3,6] => 0
[6,2,5,4,1,3] => [1,5,2,3,6,4] => 0
[6,2,5,4,3,1] => [1,5,2,3,4,6] => 0
[6,3,1,2,4,5] => [1,4,6,5,3,2] => 0
[6,3,1,2,5,4] => [1,4,6,5,2,3] => 0
[6,3,1,4,2,5] => [1,4,6,3,5,2] => 0
[6,3,1,4,5,2] => [1,4,6,3,2,5] => 0
[6,3,1,5,2,4] => [1,4,6,2,5,3] => 0
[6,3,1,5,4,2] => [1,4,6,2,3,5] => 0
[6,3,2,1,4,5] => [1,4,5,6,3,2] => 0
[6,3,2,1,5,4] => [1,4,5,6,2,3] => 0
[6,3,2,4,1,5] => [1,4,5,3,6,2] => 0
[6,3,2,4,5,1] => [1,4,5,3,2,6] => 0
[6,3,2,5,1,4] => [1,4,5,2,6,3] => 0
[6,3,2,5,4,1] => [1,4,5,2,3,6] => 0
[6,3,4,1,2,5] => [1,4,3,6,5,2] => 0
[6,3,4,1,5,2] => [1,4,3,6,2,5] => 0
[6,3,4,2,1,5] => [1,4,3,5,6,2] => 0
[6,3,4,2,5,1] => [1,4,3,5,2,6] => 0
[6,3,4,5,1,2] => [1,4,3,2,6,5] => 0
[6,3,4,5,2,1] => [1,4,3,2,5,6] => 0
[6,3,5,1,2,4] => [1,4,2,6,5,3] => 0
[6,3,5,1,4,2] => [1,4,2,6,3,5] => 0
[6,3,5,2,1,4] => [1,4,2,5,6,3] => 0
[6,3,5,2,4,1] => [1,4,2,5,3,6] => 0
[6,3,5,4,1,2] => [1,4,2,3,6,5] => 0
[6,3,5,4,2,1] => [1,4,2,3,5,6] => 0
[6,4,1,2,3,5] => [1,3,6,5,4,2] => 0
[6,4,1,2,5,3] => [1,3,6,5,2,4] => 0
[6,4,1,3,2,5] => [1,3,6,4,5,2] => 0
[6,4,1,3,5,2] => [1,3,6,4,2,5] => 0
[6,4,1,5,2,3] => [1,3,6,2,5,4] => 0
[6,4,1,5,3,2] => [1,3,6,2,4,5] => 0
[6,4,2,1,3,5] => [1,3,5,6,4,2] => 0
[6,4,2,1,5,3] => [1,3,5,6,2,4] => 0
[6,4,2,3,1,5] => [1,3,5,4,6,2] => 0
[6,4,2,3,5,1] => [1,3,5,4,2,6] => 0
[6,4,2,5,1,3] => [1,3,5,2,6,4] => 0
[6,4,2,5,3,1] => [1,3,5,2,4,6] => 0
[6,4,3,1,2,5] => [1,3,4,6,5,2] => 0
[6,4,3,1,5,2] => [1,3,4,6,2,5] => 0
[6,4,3,2,1,5] => [1,3,4,5,6,2] => 0
[6,4,3,2,5,1] => [1,3,4,5,2,6] => 0
[6,4,3,5,1,2] => [1,3,4,2,6,5] => 0
[6,4,3,5,2,1] => [1,3,4,2,5,6] => 0
[6,4,5,1,2,3] => [1,3,2,6,5,4] => 0
[6,4,5,1,3,2] => [1,3,2,6,4,5] => 0
[6,4,5,2,1,3] => [1,3,2,5,6,4] => 0
[6,4,5,2,3,1] => [1,3,2,5,4,6] => 0
[6,4,5,3,1,2] => [1,3,2,4,6,5] => 0
[6,4,5,3,2,1] => [1,3,2,4,5,6] => 0
[6,5,1,2,3,4] => [1,2,6,5,4,3] => 0
[6,5,1,2,4,3] => [1,2,6,5,3,4] => 0
[6,5,1,3,2,4] => [1,2,6,4,5,3] => 0
[6,5,1,3,4,2] => [1,2,6,4,3,5] => 0
[6,5,1,4,2,3] => [1,2,6,3,5,4] => 0
[6,5,1,4,3,2] => [1,2,6,3,4,5] => 0
[6,5,2,1,3,4] => [1,2,5,6,4,3] => 0
[6,5,2,1,4,3] => [1,2,5,6,3,4] => 0
[6,5,2,3,1,4] => [1,2,5,4,6,3] => 0
[6,5,2,3,4,1] => [1,2,5,4,3,6] => 0
[6,5,2,4,1,3] => [1,2,5,3,6,4] => 0
[6,5,2,4,3,1] => [1,2,5,3,4,6] => 0
[6,5,3,1,2,4] => [1,2,4,6,5,3] => 0
[6,5,3,1,4,2] => [1,2,4,6,3,5] => 0
[6,5,3,2,1,4] => [1,2,4,5,6,3] => 0
[6,5,3,2,4,1] => [1,2,4,5,3,6] => 0
[6,5,3,4,1,2] => [1,2,4,3,6,5] => 0
[6,5,3,4,2,1] => [1,2,4,3,5,6] => 0
[6,5,4,1,2,3] => [1,2,3,6,5,4] => 0
[6,5,4,1,3,2] => [1,2,3,6,4,5] => 0
[6,5,4,2,1,3] => [1,2,3,5,6,4] => 0
[6,5,4,2,3,1] => [1,2,3,5,4,6] => 0
[6,5,4,3,1,2] => [1,2,3,4,6,5] => 0
[6,5,4,3,2,1] => [1,2,3,4,5,6] => 0
[7,4,2,3,5,1,6] => [1,4,6,5,3,7,2] => 0
[7,4,2,3,5,6,1] => [1,4,6,5,3,2,7] => 0
[7,4,2,3,6,1,5] => [1,4,6,5,2,7,3] => 0
[7,4,2,3,6,5,1] => [1,4,6,5,2,3,7] => 0
[7,4,2,5,1,3,6] => [1,4,6,3,7,5,2] => 0
[7,4,2,5,1,6,3] => [1,4,6,3,7,2,5] => 0
[7,4,2,5,3,1,6] => [1,4,6,3,5,7,2] => 0
[7,4,2,5,3,6,1] => [1,4,6,3,5,2,7] => 0
[7,4,2,5,6,1,3] => [1,4,6,3,2,7,5] => 0
[7,4,2,5,6,3,1] => [1,4,6,3,2,5,7] => 0
[7,4,2,6,1,3,5] => [1,4,6,2,7,5,3] => 0
[7,4,2,6,1,5,3] => [1,4,6,2,7,3,5] => 0
[7,4,2,6,3,1,5] => [1,4,6,2,5,7,3] => 0
[7,4,2,6,3,5,1] => [1,4,6,2,5,3,7] => 0
[7,4,2,6,5,1,3] => [1,4,6,2,3,7,5] => 0
[7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => 0
[7,4,3,1,2,5,6] => [1,4,5,7,6,3,2] => 0
[7,4,3,1,2,6,5] => [1,4,5,7,6,2,3] => 0
[7,4,3,1,5,2,6] => [1,4,5,7,3,6,2] => 0
[7,4,3,1,5,6,2] => [1,4,5,7,3,2,6] => 0
[7,4,3,1,6,2,5] => [1,4,5,7,2,6,3] => 0
[7,4,3,1,6,5,2] => [1,4,5,7,2,3,6] => 0
[7,4,3,2,1,5,6] => [1,4,5,6,7,3,2] => 0
[7,4,3,2,1,6,5] => [1,4,5,6,7,2,3] => 0
[7,4,3,2,5,1,6] => [1,4,5,6,3,7,2] => 0
[7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => 0
[7,4,3,2,6,1,5] => [1,4,5,6,2,7,3] => 0
[7,4,3,2,6,5,1] => [1,4,5,6,2,3,7] => 0
[7,4,3,5,1,2,6] => [1,4,5,3,7,6,2] => 0
[7,4,3,5,1,6,2] => [1,4,5,3,7,2,6] => 0
[7,4,3,5,2,1,6] => [1,4,5,3,6,7,2] => 0
[7,4,3,5,2,6,1] => [1,4,5,3,6,2,7] => 0
[7,4,3,5,6,1,2] => [1,4,5,3,2,7,6] => 0
[7,4,3,5,6,2,1] => [1,4,5,3,2,6,7] => 0
[7,4,3,6,1,2,5] => [1,4,5,2,7,6,3] => 0
[7,4,3,6,1,5,2] => [1,4,5,2,7,3,6] => 0
[7,4,3,6,2,1,5] => [1,4,5,2,6,7,3] => 0
[7,4,3,6,2,5,1] => [1,4,5,2,6,3,7] => 0
[7,4,3,6,5,1,2] => [1,4,5,2,3,7,6] => 0
[7,4,3,6,5,2,1] => [1,4,5,2,3,6,7] => 0
[7,4,5,1,2,3,6] => [1,4,3,7,6,5,2] => 0
[7,4,5,1,2,6,3] => [1,4,3,7,6,2,5] => 0
[7,4,5,1,3,2,6] => [1,4,3,7,5,6,2] => 0
[7,4,5,1,3,6,2] => [1,4,3,7,5,2,6] => 0
[7,4,5,1,6,2,3] => [1,4,3,7,2,6,5] => 0
[7,4,5,1,6,3,2] => [1,4,3,7,2,5,6] => 0
[7,4,5,2,1,3,6] => [1,4,3,6,7,5,2] => 0
[7,4,5,2,1,6,3] => [1,4,3,6,7,2,5] => 0
[7,4,5,2,3,1,6] => [1,4,3,6,5,7,2] => 0
[7,4,5,2,3,6,1] => [1,4,3,6,5,2,7] => 0
[7,4,5,2,6,1,3] => [1,4,3,6,2,7,5] => 0
[7,4,5,2,6,3,1] => [1,4,3,6,2,5,7] => 0
[7,4,5,3,1,2,6] => [1,4,3,5,7,6,2] => 0
[7,4,5,3,1,6,2] => [1,4,3,5,7,2,6] => 0
[7,4,5,3,2,1,6] => [1,4,3,5,6,7,2] => 0
[7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => 0
[7,4,5,3,6,1,2] => [1,4,3,5,2,7,6] => 0
[7,4,5,3,6,2,1] => [1,4,3,5,2,6,7] => 0
[7,4,5,6,1,2,3] => [1,4,3,2,7,6,5] => 0
[7,4,5,6,1,3,2] => [1,4,3,2,7,5,6] => 0
[7,4,5,6,2,1,3] => [1,4,3,2,6,7,5] => 0
[7,4,5,6,2,3,1] => [1,4,3,2,6,5,7] => 0
[7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => 0
[7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => 0
[7,4,6,1,2,3,5] => [1,4,2,7,6,5,3] => 0
[7,4,6,1,2,5,3] => [1,4,2,7,6,3,5] => 0
[7,4,6,1,3,2,5] => [1,4,2,7,5,6,3] => 0
[7,4,6,1,3,5,2] => [1,4,2,7,5,3,6] => 0
[7,4,6,1,5,2,3] => [1,4,2,7,3,6,5] => 0
[7,4,6,1,5,3,2] => [1,4,2,7,3,5,6] => 0
[7,4,6,2,1,3,5] => [1,4,2,6,7,5,3] => 0
[7,4,6,2,1,5,3] => [1,4,2,6,7,3,5] => 0
[7,4,6,2,3,1,5] => [1,4,2,6,5,7,3] => 0
[7,4,6,2,3,5,1] => [1,4,2,6,5,3,7] => 0
[7,4,6,2,5,1,3] => [1,4,2,6,3,7,5] => 0
[7,4,6,2,5,3,1] => [1,4,2,6,3,5,7] => 0
[7,4,6,3,1,2,5] => [1,4,2,5,7,6,3] => 0
[7,4,6,3,1,5,2] => [1,4,2,5,7,3,6] => 0
[7,4,6,3,2,1,5] => [1,4,2,5,6,7,3] => 0
[7,4,6,3,2,5,1] => [1,4,2,5,6,3,7] => 0
[7,4,6,3,5,1,2] => [1,4,2,5,3,7,6] => 0
[7,4,6,3,5,2,1] => [1,4,2,5,3,6,7] => 0
[7,4,6,5,1,2,3] => [1,4,2,3,7,6,5] => 0
[7,4,6,5,1,3,2] => [1,4,2,3,7,5,6] => 0
[7,4,6,5,2,1,3] => [1,4,2,3,6,7,5] => 0
[7,4,6,5,2,3,1] => [1,4,2,3,6,5,7] => 0
[7,4,6,5,3,1,2] => [1,4,2,3,5,7,6] => 0
[7,4,6,5,3,2,1] => [1,4,2,3,5,6,7] => 0
[7,5,1,2,3,4,6] => [1,3,7,6,5,4,2] => 0
[7,5,1,2,3,6,4] => [1,3,7,6,5,2,4] => 0
[7,5,1,2,4,3,6] => [1,3,7,6,4,5,2] => 0
[7,5,1,2,4,6,3] => [1,3,7,6,4,2,5] => 0
[7,5,1,2,6,3,4] => [1,3,7,6,2,5,4] => 0
[7,5,1,2,6,4,3] => [1,3,7,6,2,4,5] => 0
[7,5,1,3,2,4,6] => [1,3,7,5,6,4,2] => 0
[7,5,1,3,2,6,4] => [1,3,7,5,6,2,4] => 0
[7,5,1,3,4,2,6] => [1,3,7,5,4,6,2] => 0
[7,5,1,3,4,6,2] => [1,3,7,5,4,2,6] => 0
[7,5,1,3,6,2,4] => [1,3,7,5,2,6,4] => 0
[7,5,1,3,6,4,2] => [1,3,7,5,2,4,6] => 0
[7,5,1,4,2,3,6] => [1,3,7,4,6,5,2] => 0
[7,5,1,4,2,6,3] => [1,3,7,4,6,2,5] => 0
[7,5,1,4,3,2,6] => [1,3,7,4,5,6,2] => 0
[7,5,1,4,3,6,2] => [1,3,7,4,5,2,6] => 0
[7,5,1,4,6,2,3] => [1,3,7,4,2,6,5] => 0
[7,5,1,4,6,3,2] => [1,3,7,4,2,5,6] => 0
[7,5,1,6,2,3,4] => [1,3,7,2,6,5,4] => 0
[7,5,1,6,2,4,3] => [1,3,7,2,6,4,5] => 0
[7,5,1,6,3,2,4] => [1,3,7,2,5,6,4] => 0
[7,5,1,6,3,4,2] => [1,3,7,2,5,4,6] => 0
[7,5,1,6,4,2,3] => [1,3,7,2,4,6,5] => 0
[7,5,1,6,4,3,2] => [1,3,7,2,4,5,6] => 0
[7,5,2,1,3,4,6] => [1,3,6,7,5,4,2] => 0
[7,5,2,1,3,6,4] => [1,3,6,7,5,2,4] => 0
[7,5,2,1,4,3,6] => [1,3,6,7,4,5,2] => 0
[7,5,2,1,4,6,3] => [1,3,6,7,4,2,5] => 0
[7,5,2,1,6,3,4] => [1,3,6,7,2,5,4] => 0
[7,5,2,1,6,4,3] => [1,3,6,7,2,4,5] => 0
[7,5,2,3,1,4,6] => [1,3,6,5,7,4,2] => 0
[7,5,2,3,1,6,4] => [1,3,6,5,7,2,4] => 0
[7,5,2,3,4,1,6] => [1,3,6,5,4,7,2] => 0
[7,5,2,3,4,6,1] => [1,3,6,5,4,2,7] => 0
[7,5,2,3,6,1,4] => [1,3,6,5,2,7,4] => 0
[7,5,2,3,6,4,1] => [1,3,6,5,2,4,7] => 0
[7,5,2,4,1,3,6] => [1,3,6,4,7,5,2] => 0
[7,5,2,4,1,6,3] => [1,3,6,4,7,2,5] => 0
[7,5,2,4,3,1,6] => [1,3,6,4,5,7,2] => 0
[7,5,2,4,3,6,1] => [1,3,6,4,5,2,7] => 0
[7,5,2,4,6,1,3] => [1,3,6,4,2,7,5] => 0
[7,5,2,4,6,3,1] => [1,3,6,4,2,5,7] => 0
[7,5,2,6,1,3,4] => [1,3,6,2,7,5,4] => 0
[7,5,2,6,1,4,3] => [1,3,6,2,7,4,5] => 0
[7,5,2,6,3,1,4] => [1,3,6,2,5,7,4] => 0
[7,5,2,6,3,4,1] => [1,3,6,2,5,4,7] => 0
[7,5,2,6,4,1,3] => [1,3,6,2,4,7,5] => 0
[7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => 0
[7,5,3,1,2,4,6] => [1,3,5,7,6,4,2] => 0
[7,5,3,1,2,6,4] => [1,3,5,7,6,2,4] => 0
[7,5,3,1,4,2,6] => [1,3,5,7,4,6,2] => 0
[7,5,3,1,4,6,2] => [1,3,5,7,4,2,6] => 0
[7,5,3,1,6,2,4] => [1,3,5,7,2,6,4] => 0
[7,5,3,1,6,4,2] => [1,3,5,7,2,4,6] => 0
[7,5,3,2,1,4,6] => [1,3,5,6,7,4,2] => 0
[7,5,3,2,1,6,4] => [1,3,5,6,7,2,4] => 0
[7,5,3,2,4,1,6] => [1,3,5,6,4,7,2] => 0
[7,5,3,2,4,6,1] => [1,3,5,6,4,2,7] => 0
[7,5,3,2,6,1,4] => [1,3,5,6,2,7,4] => 0
[7,5,3,2,6,4,1] => [1,3,5,6,2,4,7] => 0
[7,5,3,4,1,2,6] => [1,3,5,4,7,6,2] => 0
[7,5,3,4,1,6,2] => [1,3,5,4,7,2,6] => 0
[7,5,3,4,2,1,6] => [1,3,5,4,6,7,2] => 0
[7,5,3,4,2,6,1] => [1,3,5,4,6,2,7] => 0
[7,5,3,4,6,1,2] => [1,3,5,4,2,7,6] => 0
[7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => 0
[7,5,3,6,1,2,4] => [1,3,5,2,7,6,4] => 0
[7,5,3,6,1,4,2] => [1,3,5,2,7,4,6] => 0
[7,5,3,6,2,1,4] => [1,3,5,2,6,7,4] => 0
[7,5,3,6,2,4,1] => [1,3,5,2,6,4,7] => 0
[7,5,3,6,4,1,2] => [1,3,5,2,4,7,6] => 0
[7,5,3,6,4,2,1] => [1,3,5,2,4,6,7] => 0
[7,5,4,1,2,3,6] => [1,3,4,7,6,5,2] => 0
[7,5,4,1,2,6,3] => [1,3,4,7,6,2,5] => 0
[7,5,4,1,3,2,6] => [1,3,4,7,5,6,2] => 0
[7,5,4,1,3,6,2] => [1,3,4,7,5,2,6] => 0
[7,5,4,1,6,2,3] => [1,3,4,7,2,6,5] => 0
[7,5,4,1,6,3,2] => [1,3,4,7,2,5,6] => 0
[7,5,4,2,1,3,6] => [1,3,4,6,7,5,2] => 0
[7,5,4,2,1,6,3] => [1,3,4,6,7,2,5] => 0
[7,5,4,2,3,1,6] => [1,3,4,6,5,7,2] => 0
[7,5,4,2,3,6,1] => [1,3,4,6,5,2,7] => 0
[7,5,4,2,6,1,3] => [1,3,4,6,2,7,5] => 0
[7,5,4,2,6,3,1] => [1,3,4,6,2,5,7] => 0
[7,5,4,3,1,2,6] => [1,3,4,5,7,6,2] => 0
[7,5,4,3,1,6,2] => [1,3,4,5,7,2,6] => 0
[7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => 0
[7,5,4,3,2,6,1] => [1,3,4,5,6,2,7] => 0
[7,5,4,3,6,1,2] => [1,3,4,5,2,7,6] => 0
[7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => 0
[7,5,4,6,1,2,3] => [1,3,4,2,7,6,5] => 0
[7,5,4,6,1,3,2] => [1,3,4,2,7,5,6] => 0
[7,5,4,6,2,1,3] => [1,3,4,2,6,7,5] => 0
[7,5,4,6,2,3,1] => [1,3,4,2,6,5,7] => 0
[7,5,4,6,3,1,2] => [1,3,4,2,5,7,6] => 0
[7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => 0
[7,5,6,1,2,3,4] => [1,3,2,7,6,5,4] => 0
[7,5,6,1,2,4,3] => [1,3,2,7,6,4,5] => 0
[7,5,6,1,3,2,4] => [1,3,2,7,5,6,4] => 0
[7,5,6,1,3,4,2] => [1,3,2,7,5,4,6] => 0
[7,5,6,1,4,2,3] => [1,3,2,7,4,6,5] => 0
[7,5,6,1,4,3,2] => [1,3,2,7,4,5,6] => 0
[7,5,6,2,1,3,4] => [1,3,2,6,7,5,4] => 0
[7,5,6,2,1,4,3] => [1,3,2,6,7,4,5] => 0
[7,5,6,2,3,1,4] => [1,3,2,6,5,7,4] => 0
[7,5,6,2,3,4,1] => [1,3,2,6,5,4,7] => 0
[7,5,6,2,4,1,3] => [1,3,2,6,4,7,5] => 0
[7,5,6,2,4,3,1] => [1,3,2,6,4,5,7] => 0
[7,5,6,3,1,2,4] => [1,3,2,5,7,6,4] => 0
[7,5,6,3,1,4,2] => [1,3,2,5,7,4,6] => 0
[7,5,6,3,2,1,4] => [1,3,2,5,6,7,4] => 0
[7,5,6,3,2,4,1] => [1,3,2,5,6,4,7] => 0
[7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => 0
[7,5,6,3,4,2,1] => [1,3,2,5,4,6,7] => 0
[7,5,6,4,1,2,3] => [1,3,2,4,7,6,5] => 0
[7,5,6,4,1,3,2] => [1,3,2,4,7,5,6] => 0
[7,5,6,4,2,1,3] => [1,3,2,4,6,7,5] => 0
[7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => 0
[7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => 0
[7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => 0
[7,6,1,2,3,4,5] => [1,2,7,6,5,4,3] => 0
[7,6,1,2,3,5,4] => [1,2,7,6,5,3,4] => 0
[7,6,1,2,4,3,5] => [1,2,7,6,4,5,3] => 0
[7,6,1,2,4,5,3] => [1,2,7,6,4,3,5] => 0
[7,6,1,2,5,3,4] => [1,2,7,6,3,5,4] => 0
[7,6,1,2,5,4,3] => [1,2,7,6,3,4,5] => 0
[7,6,1,3,2,4,5] => [1,2,7,5,6,4,3] => 0
[7,6,1,3,2,5,4] => [1,2,7,5,6,3,4] => 0
[7,6,1,3,4,2,5] => [1,2,7,5,4,6,3] => 0
[7,6,1,3,4,5,2] => [1,2,7,5,4,3,6] => 0
[7,6,1,3,5,2,4] => [1,2,7,5,3,6,4] => 0
[7,6,1,3,5,4,2] => [1,2,7,5,3,4,6] => 0
[7,6,1,4,2,3,5] => [1,2,7,4,6,5,3] => 0
[7,6,1,4,2,5,3] => [1,2,7,4,6,3,5] => 0
[7,6,1,4,3,2,5] => [1,2,7,4,5,6,3] => 0
[7,6,1,4,3,5,2] => [1,2,7,4,5,3,6] => 0
[7,6,1,4,5,2,3] => [1,2,7,4,3,6,5] => 0
[7,6,1,4,5,3,2] => [1,2,7,4,3,5,6] => 0
[7,6,1,5,2,3,4] => [1,2,7,3,6,5,4] => 0
[7,6,1,5,2,4,3] => [1,2,7,3,6,4,5] => 0
[7,6,1,5,3,2,4] => [1,2,7,3,5,6,4] => 0
[7,6,1,5,3,4,2] => [1,2,7,3,5,4,6] => 0
[7,6,1,5,4,2,3] => [1,2,7,3,4,6,5] => 0
[7,6,1,5,4,3,2] => [1,2,7,3,4,5,6] => 0
[7,6,2,1,3,4,5] => [1,2,6,7,5,4,3] => 0
[7,6,2,1,3,5,4] => [1,2,6,7,5,3,4] => 0
[7,6,2,1,4,3,5] => [1,2,6,7,4,5,3] => 0
[7,6,2,1,4,5,3] => [1,2,6,7,4,3,5] => 0
[7,6,2,1,5,3,4] => [1,2,6,7,3,5,4] => 0
[7,6,2,1,5,4,3] => [1,2,6,7,3,4,5] => 0
[7,6,2,3,1,4,5] => [1,2,6,5,7,4,3] => 0
[7,6,2,3,1,5,4] => [1,2,6,5,7,3,4] => 0
[7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => 0
[7,6,2,3,4,5,1] => [1,2,6,5,4,3,7] => 0
[7,6,2,3,5,1,4] => [1,2,6,5,3,7,4] => 0
[7,6,2,3,5,4,1] => [1,2,6,5,3,4,7] => 0
[7,6,2,4,1,3,5] => [1,2,6,4,7,5,3] => 0
[7,6,2,4,1,5,3] => [1,2,6,4,7,3,5] => 0
[7,6,2,4,3,1,5] => [1,2,6,4,5,7,3] => 0
[7,6,2,4,3,5,1] => [1,2,6,4,5,3,7] => 0
[7,6,2,4,5,1,3] => [1,2,6,4,3,7,5] => 0
[7,6,2,4,5,3,1] => [1,2,6,4,3,5,7] => 0
[7,6,2,5,1,3,4] => [1,2,6,3,7,5,4] => 0
[7,6,2,5,1,4,3] => [1,2,6,3,7,4,5] => 0
[7,6,2,5,3,1,4] => [1,2,6,3,5,7,4] => 0
[7,6,2,5,3,4,1] => [1,2,6,3,5,4,7] => 0
[7,6,2,5,4,1,3] => [1,2,6,3,4,7,5] => 0
[7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => 0
[7,6,3,1,2,4,5] => [1,2,5,7,6,4,3] => 0
[7,6,3,1,2,5,4] => [1,2,5,7,6,3,4] => 0
[7,6,3,1,4,2,5] => [1,2,5,7,4,6,3] => 0
[7,6,3,1,4,5,2] => [1,2,5,7,4,3,6] => 0
[7,6,3,1,5,2,4] => [1,2,5,7,3,6,4] => 0
[7,6,3,1,5,4,2] => [1,2,5,7,3,4,6] => 0
[7,6,3,2,1,4,5] => [1,2,5,6,7,4,3] => 0
[7,6,3,2,1,5,4] => [1,2,5,6,7,3,4] => 0
[7,6,3,2,4,1,5] => [1,2,5,6,4,7,3] => 0
[7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => 0
[7,6,3,2,5,1,4] => [1,2,5,6,3,7,4] => 0
[7,6,3,2,5,4,1] => [1,2,5,6,3,4,7] => 0
[7,6,3,4,1,2,5] => [1,2,5,4,7,6,3] => 0
[7,6,3,4,1,5,2] => [1,2,5,4,7,3,6] => 0
[7,6,3,4,2,1,5] => [1,2,5,4,6,7,3] => 0
[7,6,3,4,2,5,1] => [1,2,5,4,6,3,7] => 0
[7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => 0
[7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => 0
[7,6,3,5,1,2,4] => [1,2,5,3,7,6,4] => 0
[7,6,3,5,1,4,2] => [1,2,5,3,7,4,6] => 0
[7,6,3,5,2,1,4] => [1,2,5,3,6,7,4] => 0
[7,6,3,5,2,4,1] => [1,2,5,3,6,4,7] => 0
[7,6,3,5,4,1,2] => [1,2,5,3,4,7,6] => 0
[7,6,3,5,4,2,1] => [1,2,5,3,4,6,7] => 0
[7,6,4,1,2,3,5] => [1,2,4,7,6,5,3] => 0
[7,6,4,1,2,5,3] => [1,2,4,7,6,3,5] => 0
[7,6,4,1,3,2,5] => [1,2,4,7,5,6,3] => 0
[7,6,4,1,3,5,2] => [1,2,4,7,5,3,6] => 0
[7,6,4,1,5,2,3] => [1,2,4,7,3,6,5] => 0
[7,6,4,1,5,3,2] => [1,2,4,7,3,5,6] => 0
[7,6,4,2,1,3,5] => [1,2,4,6,7,5,3] => 0
[7,6,4,2,1,5,3] => [1,2,4,6,7,3,5] => 0
[7,6,4,2,3,1,5] => [1,2,4,6,5,7,3] => 0
[7,6,4,2,3,5,1] => [1,2,4,6,5,3,7] => 0
[7,6,4,2,5,1,3] => [1,2,4,6,3,7,5] => 0
[7,6,4,2,5,3,1] => [1,2,4,6,3,5,7] => 0
[7,6,4,3,1,2,5] => [1,2,4,5,7,6,3] => 0
[7,6,4,3,1,5,2] => [1,2,4,5,7,3,6] => 0
[7,6,4,3,2,1,5] => [1,2,4,5,6,7,3] => 0
[7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => 0
[7,6,4,3,5,1,2] => [1,2,4,5,3,7,6] => 0
[7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => 0
[7,6,4,5,1,2,3] => [1,2,4,3,7,6,5] => 0
[7,6,4,5,1,3,2] => [1,2,4,3,7,5,6] => 0
[7,6,4,5,2,1,3] => [1,2,4,3,6,7,5] => 0
[7,6,4,5,2,3,1] => [1,2,4,3,6,5,7] => 0
[7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => 0
[7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => 0
[7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => 0
[7,6,5,1,2,4,3] => [1,2,3,7,6,4,5] => 0
[7,6,5,1,3,2,4] => [1,2,3,7,5,6,4] => 0
[7,6,5,1,3,4,2] => [1,2,3,7,5,4,6] => 0
[7,6,5,1,4,2,3] => [1,2,3,7,4,6,5] => 0
[7,6,5,1,4,3,2] => [1,2,3,7,4,5,6] => 0
[7,6,5,2,1,3,4] => [1,2,3,6,7,5,4] => 0
[7,6,5,2,1,4,3] => [1,2,3,6,7,4,5] => 0
[7,6,5,2,3,1,4] => [1,2,3,6,5,7,4] => 0
[7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => 0
[7,6,5,2,4,1,3] => [1,2,3,6,4,7,5] => 0
[7,6,5,2,4,3,1] => [1,2,3,6,4,5,7] => 0
[7,6,5,3,1,2,4] => [1,2,3,5,7,6,4] => 0
[7,6,5,3,1,4,2] => [1,2,3,5,7,4,6] => 0
[7,6,5,3,2,1,4] => [1,2,3,5,6,7,4] => 0
[7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => 0
[7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => 0
[7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => 0
[7,6,5,4,1,2,3] => [1,2,3,4,7,6,5] => 0
[7,6,5,4,1,3,2] => [1,2,3,4,7,5,6] => 0
[7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => 0
[7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => 0
[7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => 0
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 0
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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:
5,1 16,5,2,1 65,23,13,10,5,3,1 326,119,74,65,45,37,25,15,9,4,1
F2=2
F3=5+q
F4=16+5 q+2 q2+q3
F5=65+23 q+13 q2+10 q3+5 q4+3 q5+q6
F6=326+119 q+74 q2+65 q3+45 q4+37 q5+25 q6+15 q7+9 q8+4 q9+q10
Description
The number of occurrences of the vincular pattern |312 in a permutation.
This is the number of occurrences of the pattern (3,1,2), such that the letter matched by 3 is the first entry of the permutation.
This is the number of occurrences of the pattern (3,1,2), such that the letter matched by 3 is the first entry of the permutation.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
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