Identifier
-
Mp00069:
Permutations
—complement⟶
Permutations
St000341: Permutations ⟶ ℤ
Values
[1] => [1] => 0
[1,2] => [2,1] => 0
[2,1] => [1,2] => 1
[1,2,3] => [3,2,1] => 0
[1,3,2] => [3,1,2] => 1
[2,1,3] => [2,3,1] => 1
[2,3,1] => [2,1,3] => 3
[3,1,2] => [1,3,2] => 3
[3,2,1] => [1,2,3] => 4
[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] => 3
[1,4,2,3] => [4,1,3,2] => 3
[1,4,3,2] => [4,1,2,3] => 4
[2,1,3,4] => [3,4,2,1] => 1
[2,1,4,3] => [3,4,1,2] => 2
[2,3,1,4] => [3,2,4,1] => 3
[2,3,4,1] => [3,2,1,4] => 6
[2,4,1,3] => [3,1,4,2] => 5
[2,4,3,1] => [3,1,2,4] => 7
[3,1,2,4] => [2,4,3,1] => 3
[3,1,4,2] => [2,4,1,3] => 5
[3,2,1,4] => [2,3,4,1] => 4
[3,2,4,1] => [2,3,1,4] => 7
[3,4,1,2] => [2,1,4,3] => 8
[3,4,2,1] => [2,1,3,4] => 9
[4,1,2,3] => [1,4,3,2] => 6
[4,1,3,2] => [1,4,2,3] => 7
[4,2,1,3] => [1,3,4,2] => 7
[4,2,3,1] => [1,3,2,4] => 9
[4,3,1,2] => [1,2,4,3] => 9
[4,3,2,1] => [1,2,3,4] => 10
[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] => 3
[1,2,5,3,4] => [5,4,1,3,2] => 3
[1,2,5,4,3] => [5,4,1,2,3] => 4
[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] => 3
[1,3,4,5,2] => [5,3,2,1,4] => 6
[1,3,5,2,4] => [5,3,1,4,2] => 5
[1,3,5,4,2] => [5,3,1,2,4] => 7
[1,4,2,3,5] => [5,2,4,3,1] => 3
[1,4,2,5,3] => [5,2,4,1,3] => 5
[1,4,3,2,5] => [5,2,3,4,1] => 4
[1,4,3,5,2] => [5,2,3,1,4] => 7
[1,4,5,2,3] => [5,2,1,4,3] => 8
[1,4,5,3,2] => [5,2,1,3,4] => 9
[1,5,2,3,4] => [5,1,4,3,2] => 6
[1,5,2,4,3] => [5,1,4,2,3] => 7
[1,5,3,2,4] => [5,1,3,4,2] => 7
[1,5,3,4,2] => [5,1,3,2,4] => 9
[1,5,4,2,3] => [5,1,2,4,3] => 9
[1,5,4,3,2] => [5,1,2,3,4] => 10
[2,1,3,4,5] => [4,5,3,2,1] => 1
[2,1,3,5,4] => [4,5,3,1,2] => 2
[2,1,4,3,5] => [4,5,2,3,1] => 2
[2,1,4,5,3] => [4,5,2,1,3] => 4
[2,1,5,3,4] => [4,5,1,3,2] => 4
[2,1,5,4,3] => [4,5,1,2,3] => 5
[2,3,1,4,5] => [4,3,5,2,1] => 3
[2,3,1,5,4] => [4,3,5,1,2] => 4
[2,3,4,1,5] => [4,3,2,5,1] => 6
[2,3,4,5,1] => [4,3,2,1,5] => 10
[2,3,5,1,4] => [4,3,1,5,2] => 8
[2,3,5,4,1] => [4,3,1,2,5] => 11
[2,4,1,3,5] => [4,2,5,3,1] => 5
[2,4,1,5,3] => [4,2,5,1,3] => 7
[2,4,3,1,5] => [4,2,3,5,1] => 7
[2,4,3,5,1] => [4,2,3,1,5] => 11
[2,4,5,1,3] => [4,2,1,5,3] => 11
[2,4,5,3,1] => [4,2,1,3,5] => 13
[2,5,1,3,4] => [4,1,5,3,2] => 8
[2,5,1,4,3] => [4,1,5,2,3] => 9
[2,5,3,1,4] => [4,1,3,5,2] => 10
[2,5,3,4,1] => [4,1,3,2,5] => 13
[2,5,4,1,3] => [4,1,2,5,3] => 12
[2,5,4,3,1] => [4,1,2,3,5] => 14
[3,1,2,4,5] => [3,5,4,2,1] => 3
[3,1,2,5,4] => [3,5,4,1,2] => 4
[3,1,4,2,5] => [3,5,2,4,1] => 5
[3,1,4,5,2] => [3,5,2,1,4] => 8
[3,1,5,2,4] => [3,5,1,4,2] => 7
[3,1,5,4,2] => [3,5,1,2,4] => 9
[3,2,1,4,5] => [3,4,5,2,1] => 4
[3,2,1,5,4] => [3,4,5,1,2] => 5
[3,2,4,1,5] => [3,4,2,5,1] => 7
[3,2,4,5,1] => [3,4,2,1,5] => 11
[3,2,5,1,4] => [3,4,1,5,2] => 9
[3,2,5,4,1] => [3,4,1,2,5] => 12
[3,4,1,2,5] => [3,2,5,4,1] => 8
[3,4,1,5,2] => [3,2,5,1,4] => 11
[3,4,2,1,5] => [3,2,4,5,1] => 9
[3,4,2,5,1] => [3,2,4,1,5] => 13
[3,4,5,1,2] => [3,2,1,5,4] => 15
[3,4,5,2,1] => [3,2,1,4,5] => 16
[3,5,1,2,4] => [3,1,5,4,2] => 11
[3,5,1,4,2] => [3,1,5,2,4] => 13
>>> Load all 1201 entries. <<<[3,5,2,1,4] => [3,1,4,5,2] => 12
[3,5,2,4,1] => [3,1,4,2,5] => 15
[3,5,4,1,2] => [3,1,2,5,4] => 16
[3,5,4,2,1] => [3,1,2,4,5] => 17
[4,1,2,3,5] => [2,5,4,3,1] => 6
[4,1,2,5,3] => [2,5,4,1,3] => 8
[4,1,3,2,5] => [2,5,3,4,1] => 7
[4,1,3,5,2] => [2,5,3,1,4] => 10
[4,1,5,2,3] => [2,5,1,4,3] => 11
[4,1,5,3,2] => [2,5,1,3,4] => 12
[4,2,1,3,5] => [2,4,5,3,1] => 7
[4,2,1,5,3] => [2,4,5,1,3] => 9
[4,2,3,1,5] => [2,4,3,5,1] => 9
[4,2,3,5,1] => [2,4,3,1,5] => 13
[4,2,5,1,3] => [2,4,1,5,3] => 13
[4,2,5,3,1] => [2,4,1,3,5] => 15
[4,3,1,2,5] => [2,3,5,4,1] => 9
[4,3,1,5,2] => [2,3,5,1,4] => 12
[4,3,2,1,5] => [2,3,4,5,1] => 10
[4,3,2,5,1] => [2,3,4,1,5] => 14
[4,3,5,1,2] => [2,3,1,5,4] => 16
[4,3,5,2,1] => [2,3,1,4,5] => 17
[4,5,1,2,3] => [2,1,5,4,3] => 15
[4,5,1,3,2] => [2,1,5,3,4] => 16
[4,5,2,1,3] => [2,1,4,5,3] => 16
[4,5,2,3,1] => [2,1,4,3,5] => 18
[4,5,3,1,2] => [2,1,3,5,4] => 18
[4,5,3,2,1] => [2,1,3,4,5] => 19
[5,1,2,3,4] => [1,5,4,3,2] => 10
[5,1,2,4,3] => [1,5,4,2,3] => 11
[5,1,3,2,4] => [1,5,3,4,2] => 11
[5,1,3,4,2] => [1,5,3,2,4] => 13
[5,1,4,2,3] => [1,5,2,4,3] => 13
[5,1,4,3,2] => [1,5,2,3,4] => 14
[5,2,1,3,4] => [1,4,5,3,2] => 11
[5,2,1,4,3] => [1,4,5,2,3] => 12
[5,2,3,1,4] => [1,4,3,5,2] => 13
[5,2,3,4,1] => [1,4,3,2,5] => 16
[5,2,4,1,3] => [1,4,2,5,3] => 15
[5,2,4,3,1] => [1,4,2,3,5] => 17
[5,3,1,2,4] => [1,3,5,4,2] => 13
[5,3,1,4,2] => [1,3,5,2,4] => 15
[5,3,2,1,4] => [1,3,4,5,2] => 14
[5,3,2,4,1] => [1,3,4,2,5] => 17
[5,3,4,1,2] => [1,3,2,5,4] => 18
[5,3,4,2,1] => [1,3,2,4,5] => 19
[5,4,1,2,3] => [1,2,5,4,3] => 16
[5,4,1,3,2] => [1,2,5,3,4] => 17
[5,4,2,1,3] => [1,2,4,5,3] => 17
[5,4,2,3,1] => [1,2,4,3,5] => 19
[5,4,3,1,2] => [1,2,3,5,4] => 19
[5,4,3,2,1] => [1,2,3,4,5] => 20
[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] => 3
[1,2,3,6,4,5] => [6,5,4,1,3,2] => 3
[1,2,3,6,5,4] => [6,5,4,1,2,3] => 4
[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] => 3
[1,2,4,5,6,3] => [6,5,3,2,1,4] => 6
[1,2,4,6,3,5] => [6,5,3,1,4,2] => 5
[1,2,4,6,5,3] => [6,5,3,1,2,4] => 7
[1,2,5,3,4,6] => [6,5,2,4,3,1] => 3
[1,2,5,3,6,4] => [6,5,2,4,1,3] => 5
[1,2,5,4,3,6] => [6,5,2,3,4,1] => 4
[1,2,5,4,6,3] => [6,5,2,3,1,4] => 7
[1,2,5,6,3,4] => [6,5,2,1,4,3] => 8
[1,2,5,6,4,3] => [6,5,2,1,3,4] => 9
[1,2,6,3,4,5] => [6,5,1,4,3,2] => 6
[1,2,6,3,5,4] => [6,5,1,4,2,3] => 7
[1,2,6,4,3,5] => [6,5,1,3,4,2] => 7
[1,2,6,4,5,3] => [6,5,1,3,2,4] => 9
[1,2,6,5,3,4] => [6,5,1,2,4,3] => 9
[1,2,6,5,4,3] => [6,5,1,2,3,4] => 10
[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] => 4
[1,3,2,6,4,5] => [6,4,5,1,3,2] => 4
[1,3,2,6,5,4] => [6,4,5,1,2,3] => 5
[1,3,4,2,5,6] => [6,4,3,5,2,1] => 3
[1,3,4,2,6,5] => [6,4,3,5,1,2] => 4
[1,3,4,5,2,6] => [6,4,3,2,5,1] => 6
[1,3,4,5,6,2] => [6,4,3,2,1,5] => 10
[1,3,4,6,2,5] => [6,4,3,1,5,2] => 8
[1,3,4,6,5,2] => [6,4,3,1,2,5] => 11
[1,3,5,2,4,6] => [6,4,2,5,3,1] => 5
[1,3,5,2,6,4] => [6,4,2,5,1,3] => 7
[1,3,5,4,2,6] => [6,4,2,3,5,1] => 7
[1,3,5,4,6,2] => [6,4,2,3,1,5] => 11
[1,3,5,6,2,4] => [6,4,2,1,5,3] => 11
[1,3,5,6,4,2] => [6,4,2,1,3,5] => 13
[1,3,6,2,4,5] => [6,4,1,5,3,2] => 8
[1,3,6,2,5,4] => [6,4,1,5,2,3] => 9
[1,3,6,4,2,5] => [6,4,1,3,5,2] => 10
[1,3,6,4,5,2] => [6,4,1,3,2,5] => 13
[1,3,6,5,2,4] => [6,4,1,2,5,3] => 12
[1,3,6,5,4,2] => [6,4,1,2,3,5] => 14
[1,4,2,3,5,6] => [6,3,5,4,2,1] => 3
[1,4,2,3,6,5] => [6,3,5,4,1,2] => 4
[1,4,2,5,3,6] => [6,3,5,2,4,1] => 5
[1,4,2,5,6,3] => [6,3,5,2,1,4] => 8
[1,4,2,6,3,5] => [6,3,5,1,4,2] => 7
[1,4,2,6,5,3] => [6,3,5,1,2,4] => 9
[1,4,3,2,5,6] => [6,3,4,5,2,1] => 4
[1,4,3,2,6,5] => [6,3,4,5,1,2] => 5
[1,4,3,5,2,6] => [6,3,4,2,5,1] => 7
[1,4,3,5,6,2] => [6,3,4,2,1,5] => 11
[1,4,3,6,2,5] => [6,3,4,1,5,2] => 9
[1,4,3,6,5,2] => [6,3,4,1,2,5] => 12
[1,4,5,2,3,6] => [6,3,2,5,4,1] => 8
[1,4,5,2,6,3] => [6,3,2,5,1,4] => 11
[1,4,5,3,2,6] => [6,3,2,4,5,1] => 9
[1,4,5,3,6,2] => [6,3,2,4,1,5] => 13
[1,4,5,6,2,3] => [6,3,2,1,5,4] => 15
[1,4,5,6,3,2] => [6,3,2,1,4,5] => 16
[1,4,6,2,3,5] => [6,3,1,5,4,2] => 11
[1,4,6,2,5,3] => [6,3,1,5,2,4] => 13
[1,4,6,3,2,5] => [6,3,1,4,5,2] => 12
[1,4,6,3,5,2] => [6,3,1,4,2,5] => 15
[1,4,6,5,2,3] => [6,3,1,2,5,4] => 16
[1,4,6,5,3,2] => [6,3,1,2,4,5] => 17
[1,5,2,3,4,6] => [6,2,5,4,3,1] => 6
[1,5,2,3,6,4] => [6,2,5,4,1,3] => 8
[1,5,2,4,3,6] => [6,2,5,3,4,1] => 7
[1,5,2,4,6,3] => [6,2,5,3,1,4] => 10
[1,5,2,6,3,4] => [6,2,5,1,4,3] => 11
[1,5,2,6,4,3] => [6,2,5,1,3,4] => 12
[1,5,3,2,4,6] => [6,2,4,5,3,1] => 7
[1,5,3,2,6,4] => [6,2,4,5,1,3] => 9
[1,5,3,4,2,6] => [6,2,4,3,5,1] => 9
[1,5,3,4,6,2] => [6,2,4,3,1,5] => 13
[1,5,3,6,2,4] => [6,2,4,1,5,3] => 13
[1,5,3,6,4,2] => [6,2,4,1,3,5] => 15
[1,5,4,2,3,6] => [6,2,3,5,4,1] => 9
[1,5,4,2,6,3] => [6,2,3,5,1,4] => 12
[1,5,4,3,2,6] => [6,2,3,4,5,1] => 10
[1,5,4,3,6,2] => [6,2,3,4,1,5] => 14
[1,5,4,6,2,3] => [6,2,3,1,5,4] => 16
[1,5,4,6,3,2] => [6,2,3,1,4,5] => 17
[1,5,6,2,3,4] => [6,2,1,5,4,3] => 15
[1,5,6,2,4,3] => [6,2,1,5,3,4] => 16
[1,5,6,3,2,4] => [6,2,1,4,5,3] => 16
[1,5,6,3,4,2] => [6,2,1,4,3,5] => 18
[1,5,6,4,2,3] => [6,2,1,3,5,4] => 18
[1,5,6,4,3,2] => [6,2,1,3,4,5] => 19
[1,6,2,3,4,5] => [6,1,5,4,3,2] => 10
[1,6,2,3,5,4] => [6,1,5,4,2,3] => 11
[1,6,2,4,3,5] => [6,1,5,3,4,2] => 11
[1,6,2,4,5,3] => [6,1,5,3,2,4] => 13
[1,6,2,5,3,4] => [6,1,5,2,4,3] => 13
[1,6,2,5,4,3] => [6,1,5,2,3,4] => 14
[1,6,3,2,4,5] => [6,1,4,5,3,2] => 11
[1,6,3,2,5,4] => [6,1,4,5,2,3] => 12
[1,6,3,4,2,5] => [6,1,4,3,5,2] => 13
[1,6,3,4,5,2] => [6,1,4,3,2,5] => 16
[1,6,3,5,2,4] => [6,1,4,2,5,3] => 15
[1,6,3,5,4,2] => [6,1,4,2,3,5] => 17
[1,6,4,2,3,5] => [6,1,3,5,4,2] => 13
[1,6,4,2,5,3] => [6,1,3,5,2,4] => 15
[1,6,4,3,2,5] => [6,1,3,4,5,2] => 14
[1,6,4,3,5,2] => [6,1,3,4,2,5] => 17
[1,6,4,5,2,3] => [6,1,3,2,5,4] => 18
[1,6,4,5,3,2] => [6,1,3,2,4,5] => 19
[1,6,5,2,3,4] => [6,1,2,5,4,3] => 16
[1,6,5,2,4,3] => [6,1,2,5,3,4] => 17
[1,6,5,3,2,4] => [6,1,2,4,5,3] => 17
[1,6,5,3,4,2] => [6,1,2,4,3,5] => 19
[1,6,5,4,2,3] => [6,1,2,3,5,4] => 19
[1,6,5,4,3,2] => [6,1,2,3,4,5] => 20
[2,1,3,4,5,6] => [5,6,4,3,2,1] => 1
[2,1,3,4,6,5] => [5,6,4,3,1,2] => 2
[2,1,3,5,4,6] => [5,6,4,2,3,1] => 2
[2,1,3,5,6,4] => [5,6,4,2,1,3] => 4
[2,1,3,6,4,5] => [5,6,4,1,3,2] => 4
[2,1,3,6,5,4] => [5,6,4,1,2,3] => 5
[2,1,4,3,5,6] => [5,6,3,4,2,1] => 2
[2,1,4,3,6,5] => [5,6,3,4,1,2] => 3
[2,1,4,5,3,6] => [5,6,3,2,4,1] => 4
[2,1,4,5,6,3] => [5,6,3,2,1,4] => 7
[2,1,4,6,3,5] => [5,6,3,1,4,2] => 6
[2,1,4,6,5,3] => [5,6,3,1,2,4] => 8
[2,1,5,3,4,6] => [5,6,2,4,3,1] => 4
[2,1,5,3,6,4] => [5,6,2,4,1,3] => 6
[2,1,5,4,3,6] => [5,6,2,3,4,1] => 5
[2,1,5,4,6,3] => [5,6,2,3,1,4] => 8
[2,1,5,6,3,4] => [5,6,2,1,4,3] => 9
[2,1,5,6,4,3] => [5,6,2,1,3,4] => 10
[2,1,6,3,4,5] => [5,6,1,4,3,2] => 7
[2,1,6,3,5,4] => [5,6,1,4,2,3] => 8
[2,1,6,4,3,5] => [5,6,1,3,4,2] => 8
[2,1,6,4,5,3] => [5,6,1,3,2,4] => 10
[2,1,6,5,3,4] => [5,6,1,2,4,3] => 10
[2,1,6,5,4,3] => [5,6,1,2,3,4] => 11
[2,3,1,4,5,6] => [5,4,6,3,2,1] => 3
[2,3,1,4,6,5] => [5,4,6,3,1,2] => 4
[2,3,1,5,4,6] => [5,4,6,2,3,1] => 4
[2,3,1,5,6,4] => [5,4,6,2,1,3] => 6
[2,3,1,6,4,5] => [5,4,6,1,3,2] => 6
[2,3,1,6,5,4] => [5,4,6,1,2,3] => 7
[2,3,4,1,5,6] => [5,4,3,6,2,1] => 6
[2,3,4,1,6,5] => [5,4,3,6,1,2] => 7
[2,3,4,5,1,6] => [5,4,3,2,6,1] => 10
[2,3,4,5,6,1] => [5,4,3,2,1,6] => 15
[2,3,4,6,1,5] => [5,4,3,1,6,2] => 12
[2,3,4,6,5,1] => [5,4,3,1,2,6] => 16
[2,3,5,1,4,6] => [5,4,2,6,3,1] => 8
[2,3,5,1,6,4] => [5,4,2,6,1,3] => 10
[2,3,5,4,1,6] => [5,4,2,3,6,1] => 11
[2,3,5,4,6,1] => [5,4,2,3,1,6] => 16
[2,3,5,6,1,4] => [5,4,2,1,6,3] => 15
[2,3,5,6,4,1] => [5,4,2,1,3,6] => 18
[2,3,6,1,4,5] => [5,4,1,6,3,2] => 11
[2,3,6,1,5,4] => [5,4,1,6,2,3] => 12
[2,3,6,4,1,5] => [5,4,1,3,6,2] => 14
[2,3,6,4,5,1] => [5,4,1,3,2,6] => 18
[2,3,6,5,1,4] => [5,4,1,2,6,3] => 16
[2,3,6,5,4,1] => [5,4,1,2,3,6] => 19
[2,4,1,3,5,6] => [5,3,6,4,2,1] => 5
[2,4,1,3,6,5] => [5,3,6,4,1,2] => 6
[2,4,1,5,3,6] => [5,3,6,2,4,1] => 7
[2,4,1,5,6,3] => [5,3,6,2,1,4] => 10
[2,4,1,6,3,5] => [5,3,6,1,4,2] => 9
[2,4,1,6,5,3] => [5,3,6,1,2,4] => 11
[2,4,3,1,5,6] => [5,3,4,6,2,1] => 7
[2,4,3,1,6,5] => [5,3,4,6,1,2] => 8
[2,4,3,5,1,6] => [5,3,4,2,6,1] => 11
[2,4,3,5,6,1] => [5,3,4,2,1,6] => 16
[2,4,3,6,1,5] => [5,3,4,1,6,2] => 13
[2,4,3,6,5,1] => [5,3,4,1,2,6] => 17
[2,4,5,1,3,6] => [5,3,2,6,4,1] => 11
[2,4,5,1,6,3] => [5,3,2,6,1,4] => 14
[2,4,5,3,1,6] => [5,3,2,4,6,1] => 13
[2,4,5,3,6,1] => [5,3,2,4,1,6] => 18
[2,4,5,6,1,3] => [5,3,2,1,6,4] => 19
[2,4,5,6,3,1] => [5,3,2,1,4,6] => 21
[2,4,6,1,3,5] => [5,3,1,6,4,2] => 14
[2,4,6,1,5,3] => [5,3,1,6,2,4] => 16
[2,4,6,3,1,5] => [5,3,1,4,6,2] => 16
[2,4,6,3,5,1] => [5,3,1,4,2,6] => 20
[2,4,6,5,1,3] => [5,3,1,2,6,4] => 20
[2,4,6,5,3,1] => [5,3,1,2,4,6] => 22
[2,5,1,3,4,6] => [5,2,6,4,3,1] => 8
[2,5,1,3,6,4] => [5,2,6,4,1,3] => 10
[2,5,1,4,3,6] => [5,2,6,3,4,1] => 9
[2,5,1,4,6,3] => [5,2,6,3,1,4] => 12
[2,5,1,6,3,4] => [5,2,6,1,4,3] => 13
[2,5,1,6,4,3] => [5,2,6,1,3,4] => 14
[2,5,3,1,4,6] => [5,2,4,6,3,1] => 10
[2,5,3,1,6,4] => [5,2,4,6,1,3] => 12
[2,5,3,4,1,6] => [5,2,4,3,6,1] => 13
[2,5,3,4,6,1] => [5,2,4,3,1,6] => 18
[2,5,3,6,1,4] => [5,2,4,1,6,3] => 17
[2,5,3,6,4,1] => [5,2,4,1,3,6] => 20
[2,5,4,1,3,6] => [5,2,3,6,4,1] => 12
[2,5,4,1,6,3] => [5,2,3,6,1,4] => 15
[2,5,4,3,1,6] => [5,2,3,4,6,1] => 14
[2,5,4,3,6,1] => [5,2,3,4,1,6] => 19
[2,5,4,6,1,3] => [5,2,3,1,6,4] => 20
[2,5,4,6,3,1] => [5,2,3,1,4,6] => 22
[2,5,6,1,3,4] => [5,2,1,6,4,3] => 18
[2,5,6,1,4,3] => [5,2,1,6,3,4] => 19
[2,5,6,3,1,4] => [5,2,1,4,6,3] => 20
[2,5,6,3,4,1] => [5,2,1,4,3,6] => 23
[2,5,6,4,1,3] => [5,2,1,3,6,4] => 22
[2,5,6,4,3,1] => [5,2,1,3,4,6] => 24
[2,6,1,3,4,5] => [5,1,6,4,3,2] => 12
[2,6,1,3,5,4] => [5,1,6,4,2,3] => 13
[2,6,1,4,3,5] => [5,1,6,3,4,2] => 13
[2,6,1,4,5,3] => [5,1,6,3,2,4] => 15
[2,6,1,5,3,4] => [5,1,6,2,4,3] => 15
[2,6,1,5,4,3] => [5,1,6,2,3,4] => 16
[2,6,3,1,4,5] => [5,1,4,6,3,2] => 14
[2,6,3,1,5,4] => [5,1,4,6,2,3] => 15
[2,6,3,4,1,5] => [5,1,4,3,6,2] => 17
[2,6,3,4,5,1] => [5,1,4,3,2,6] => 21
[2,6,3,5,1,4] => [5,1,4,2,6,3] => 19
[2,6,3,5,4,1] => [5,1,4,2,3,6] => 22
[2,6,4,1,3,5] => [5,1,3,6,4,2] => 16
[2,6,4,1,5,3] => [5,1,3,6,2,4] => 18
[2,6,4,3,1,5] => [5,1,3,4,6,2] => 18
[2,6,4,3,5,1] => [5,1,3,4,2,6] => 22
[2,6,4,5,1,3] => [5,1,3,2,6,4] => 22
[2,6,4,5,3,1] => [5,1,3,2,4,6] => 24
[2,6,5,1,3,4] => [5,1,2,6,4,3] => 19
[2,6,5,1,4,3] => [5,1,2,6,3,4] => 20
[2,6,5,3,1,4] => [5,1,2,4,6,3] => 21
[2,6,5,3,4,1] => [5,1,2,4,3,6] => 24
[2,6,5,4,1,3] => [5,1,2,3,6,4] => 23
[2,6,5,4,3,1] => [5,1,2,3,4,6] => 25
[3,1,2,4,5,6] => [4,6,5,3,2,1] => 3
[3,1,2,4,6,5] => [4,6,5,3,1,2] => 4
[3,1,2,5,4,6] => [4,6,5,2,3,1] => 4
[3,1,2,5,6,4] => [4,6,5,2,1,3] => 6
[3,1,2,6,4,5] => [4,6,5,1,3,2] => 6
[3,1,2,6,5,4] => [4,6,5,1,2,3] => 7
[3,1,4,2,5,6] => [4,6,3,5,2,1] => 5
[3,1,4,2,6,5] => [4,6,3,5,1,2] => 6
[3,1,4,5,2,6] => [4,6,3,2,5,1] => 8
[3,1,4,5,6,2] => [4,6,3,2,1,5] => 12
[3,1,4,6,2,5] => [4,6,3,1,5,2] => 10
[3,1,4,6,5,2] => [4,6,3,1,2,5] => 13
[3,1,5,2,4,6] => [4,6,2,5,3,1] => 7
[3,1,5,2,6,4] => [4,6,2,5,1,3] => 9
[3,1,5,4,2,6] => [4,6,2,3,5,1] => 9
[3,1,5,4,6,2] => [4,6,2,3,1,5] => 13
[3,1,5,6,2,4] => [4,6,2,1,5,3] => 13
[3,1,5,6,4,2] => [4,6,2,1,3,5] => 15
[3,1,6,2,4,5] => [4,6,1,5,3,2] => 10
[3,1,6,2,5,4] => [4,6,1,5,2,3] => 11
[3,1,6,4,2,5] => [4,6,1,3,5,2] => 12
[3,1,6,4,5,2] => [4,6,1,3,2,5] => 15
[3,1,6,5,2,4] => [4,6,1,2,5,3] => 14
[3,1,6,5,4,2] => [4,6,1,2,3,5] => 16
[3,2,1,4,5,6] => [4,5,6,3,2,1] => 4
[3,2,1,4,6,5] => [4,5,6,3,1,2] => 5
[3,2,1,5,4,6] => [4,5,6,2,3,1] => 5
[3,2,1,5,6,4] => [4,5,6,2,1,3] => 7
[3,2,1,6,4,5] => [4,5,6,1,3,2] => 7
[3,2,1,6,5,4] => [4,5,6,1,2,3] => 8
[3,2,4,1,5,6] => [4,5,3,6,2,1] => 7
[3,2,4,1,6,5] => [4,5,3,6,1,2] => 8
[3,2,4,5,1,6] => [4,5,3,2,6,1] => 11
[3,2,4,5,6,1] => [4,5,3,2,1,6] => 16
[3,2,4,6,1,5] => [4,5,3,1,6,2] => 13
[3,2,4,6,5,1] => [4,5,3,1,2,6] => 17
[3,2,5,1,4,6] => [4,5,2,6,3,1] => 9
[3,2,5,1,6,4] => [4,5,2,6,1,3] => 11
[3,2,5,4,1,6] => [4,5,2,3,6,1] => 12
[3,2,5,4,6,1] => [4,5,2,3,1,6] => 17
[3,2,5,6,1,4] => [4,5,2,1,6,3] => 16
[3,2,5,6,4,1] => [4,5,2,1,3,6] => 19
[3,2,6,1,4,5] => [4,5,1,6,3,2] => 12
[3,2,6,1,5,4] => [4,5,1,6,2,3] => 13
[3,2,6,4,1,5] => [4,5,1,3,6,2] => 15
[3,2,6,4,5,1] => [4,5,1,3,2,6] => 19
[3,2,6,5,1,4] => [4,5,1,2,6,3] => 17
[3,2,6,5,4,1] => [4,5,1,2,3,6] => 20
[3,4,1,2,5,6] => [4,3,6,5,2,1] => 8
[3,4,1,2,6,5] => [4,3,6,5,1,2] => 9
[3,4,1,5,2,6] => [4,3,6,2,5,1] => 11
[3,4,1,5,6,2] => [4,3,6,2,1,5] => 15
[3,4,1,6,2,5] => [4,3,6,1,5,2] => 13
[3,4,1,6,5,2] => [4,3,6,1,2,5] => 16
[3,4,2,1,5,6] => [4,3,5,6,2,1] => 9
[3,4,2,1,6,5] => [4,3,5,6,1,2] => 10
[3,4,2,5,1,6] => [4,3,5,2,6,1] => 13
[3,4,2,5,6,1] => [4,3,5,2,1,6] => 18
[3,4,2,6,1,5] => [4,3,5,1,6,2] => 15
[3,4,2,6,5,1] => [4,3,5,1,2,6] => 19
[3,4,5,1,2,6] => [4,3,2,6,5,1] => 15
[3,4,5,1,6,2] => [4,3,2,6,1,5] => 19
[3,4,5,2,1,6] => [4,3,2,5,6,1] => 16
[3,4,5,2,6,1] => [4,3,2,5,1,6] => 21
[3,4,5,6,1,2] => [4,3,2,1,6,5] => 24
[3,4,5,6,2,1] => [4,3,2,1,5,6] => 25
[3,4,6,1,2,5] => [4,3,1,6,5,2] => 18
[3,4,6,1,5,2] => [4,3,1,6,2,5] => 21
[3,4,6,2,1,5] => [4,3,1,5,6,2] => 19
[3,4,6,2,5,1] => [4,3,1,5,2,6] => 23
[3,4,6,5,1,2] => [4,3,1,2,6,5] => 25
[3,4,6,5,2,1] => [4,3,1,2,5,6] => 26
[3,5,1,2,4,6] => [4,2,6,5,3,1] => 11
[3,5,1,2,6,4] => [4,2,6,5,1,3] => 13
[3,5,1,4,2,6] => [4,2,6,3,5,1] => 13
[3,5,1,4,6,2] => [4,2,6,3,1,5] => 17
[3,5,1,6,2,4] => [4,2,6,1,5,3] => 17
[3,5,1,6,4,2] => [4,2,6,1,3,5] => 19
[3,5,2,1,4,6] => [4,2,5,6,3,1] => 12
[3,5,2,1,6,4] => [4,2,5,6,1,3] => 14
[3,5,2,4,1,6] => [4,2,5,3,6,1] => 15
[3,5,2,4,6,1] => [4,2,5,3,1,6] => 20
[3,5,2,6,1,4] => [4,2,5,1,6,3] => 19
[3,5,2,6,4,1] => [4,2,5,1,3,6] => 22
[3,5,4,1,2,6] => [4,2,3,6,5,1] => 16
[3,5,4,1,6,2] => [4,2,3,6,1,5] => 20
[3,5,4,2,1,6] => [4,2,3,5,6,1] => 17
[3,5,4,2,6,1] => [4,2,3,5,1,6] => 22
[3,5,4,6,1,2] => [4,2,3,1,6,5] => 25
[3,5,4,6,2,1] => [4,2,3,1,5,6] => 26
[3,5,6,1,2,4] => [4,2,1,6,5,3] => 22
[3,5,6,1,4,2] => [4,2,1,6,3,5] => 24
[3,5,6,2,1,4] => [4,2,1,5,6,3] => 23
[3,5,6,2,4,1] => [4,2,1,5,3,6] => 26
[3,5,6,4,1,2] => [4,2,1,3,6,5] => 27
[3,5,6,4,2,1] => [4,2,1,3,5,6] => 28
[3,6,1,2,4,5] => [4,1,6,5,3,2] => 15
[3,6,1,2,5,4] => [4,1,6,5,2,3] => 16
[3,6,1,4,2,5] => [4,1,6,3,5,2] => 17
[3,6,1,4,5,2] => [4,1,6,3,2,5] => 20
[3,6,1,5,2,4] => [4,1,6,2,5,3] => 19
[3,6,1,5,4,2] => [4,1,6,2,3,5] => 21
[3,6,2,1,4,5] => [4,1,5,6,3,2] => 16
[3,6,2,1,5,4] => [4,1,5,6,2,3] => 17
[3,6,2,4,1,5] => [4,1,5,3,6,2] => 19
[3,6,2,4,5,1] => [4,1,5,3,2,6] => 23
[3,6,2,5,1,4] => [4,1,5,2,6,3] => 21
[3,6,2,5,4,1] => [4,1,5,2,3,6] => 24
[3,6,4,1,2,5] => [4,1,3,6,5,2] => 20
[3,6,4,1,5,2] => [4,1,3,6,2,5] => 23
[3,6,4,2,1,5] => [4,1,3,5,6,2] => 21
[3,6,4,2,5,1] => [4,1,3,5,2,6] => 25
[3,6,4,5,1,2] => [4,1,3,2,6,5] => 27
[3,6,4,5,2,1] => [4,1,3,2,5,6] => 28
[3,6,5,1,2,4] => [4,1,2,6,5,3] => 23
[3,6,5,1,4,2] => [4,1,2,6,3,5] => 25
[3,6,5,2,1,4] => [4,1,2,5,6,3] => 24
[3,6,5,2,4,1] => [4,1,2,5,3,6] => 27
[3,6,5,4,1,2] => [4,1,2,3,6,5] => 28
[3,6,5,4,2,1] => [4,1,2,3,5,6] => 29
[4,1,2,3,5,6] => [3,6,5,4,2,1] => 6
[4,1,2,3,6,5] => [3,6,5,4,1,2] => 7
[4,1,2,5,3,6] => [3,6,5,2,4,1] => 8
[4,1,2,5,6,3] => [3,6,5,2,1,4] => 11
[4,1,2,6,3,5] => [3,6,5,1,4,2] => 10
[4,1,2,6,5,3] => [3,6,5,1,2,4] => 12
[4,1,3,2,5,6] => [3,6,4,5,2,1] => 7
[4,1,3,2,6,5] => [3,6,4,5,1,2] => 8
[4,1,3,5,2,6] => [3,6,4,2,5,1] => 10
[4,1,3,5,6,2] => [3,6,4,2,1,5] => 14
[4,1,3,6,2,5] => [3,6,4,1,5,2] => 12
[4,1,3,6,5,2] => [3,6,4,1,2,5] => 15
[4,1,5,2,3,6] => [3,6,2,5,4,1] => 11
[4,1,5,2,6,3] => [3,6,2,5,1,4] => 14
[4,1,5,3,2,6] => [3,6,2,4,5,1] => 12
[4,1,5,3,6,2] => [3,6,2,4,1,5] => 16
[4,1,5,6,2,3] => [3,6,2,1,5,4] => 18
[4,1,5,6,3,2] => [3,6,2,1,4,5] => 19
[4,1,6,2,3,5] => [3,6,1,5,4,2] => 14
[4,1,6,2,5,3] => [3,6,1,5,2,4] => 16
[4,1,6,3,2,5] => [3,6,1,4,5,2] => 15
[4,1,6,3,5,2] => [3,6,1,4,2,5] => 18
[4,1,6,5,2,3] => [3,6,1,2,5,4] => 19
[4,1,6,5,3,2] => [3,6,1,2,4,5] => 20
[4,2,1,3,5,6] => [3,5,6,4,2,1] => 7
[4,2,1,3,6,5] => [3,5,6,4,1,2] => 8
[4,2,1,5,3,6] => [3,5,6,2,4,1] => 9
[4,2,1,5,6,3] => [3,5,6,2,1,4] => 12
[4,2,1,6,3,5] => [3,5,6,1,4,2] => 11
[4,2,1,6,5,3] => [3,5,6,1,2,4] => 13
[4,2,3,1,5,6] => [3,5,4,6,2,1] => 9
[4,2,3,1,6,5] => [3,5,4,6,1,2] => 10
[4,2,3,5,1,6] => [3,5,4,2,6,1] => 13
[4,2,3,5,6,1] => [3,5,4,2,1,6] => 18
[4,2,3,6,1,5] => [3,5,4,1,6,2] => 15
[4,2,3,6,5,1] => [3,5,4,1,2,6] => 19
[4,2,5,1,3,6] => [3,5,2,6,4,1] => 13
[4,2,5,1,6,3] => [3,5,2,6,1,4] => 16
[4,2,5,3,1,6] => [3,5,2,4,6,1] => 15
[4,2,5,3,6,1] => [3,5,2,4,1,6] => 20
[4,2,5,6,1,3] => [3,5,2,1,6,4] => 21
[4,2,5,6,3,1] => [3,5,2,1,4,6] => 23
[4,2,6,1,3,5] => [3,5,1,6,4,2] => 16
[4,2,6,1,5,3] => [3,5,1,6,2,4] => 18
[4,2,6,3,1,5] => [3,5,1,4,6,2] => 18
[4,2,6,3,5,1] => [3,5,1,4,2,6] => 22
[4,2,6,5,1,3] => [3,5,1,2,6,4] => 22
[4,2,6,5,3,1] => [3,5,1,2,4,6] => 24
[4,3,1,2,5,6] => [3,4,6,5,2,1] => 9
[4,3,1,2,6,5] => [3,4,6,5,1,2] => 10
[4,3,1,5,2,6] => [3,4,6,2,5,1] => 12
[4,3,1,5,6,2] => [3,4,6,2,1,5] => 16
[4,3,1,6,2,5] => [3,4,6,1,5,2] => 14
[4,3,1,6,5,2] => [3,4,6,1,2,5] => 17
[4,3,2,1,5,6] => [3,4,5,6,2,1] => 10
[4,3,2,1,6,5] => [3,4,5,6,1,2] => 11
[4,3,2,5,1,6] => [3,4,5,2,6,1] => 14
[4,3,2,5,6,1] => [3,4,5,2,1,6] => 19
[4,3,2,6,1,5] => [3,4,5,1,6,2] => 16
[4,3,2,6,5,1] => [3,4,5,1,2,6] => 20
[4,3,5,1,2,6] => [3,4,2,6,5,1] => 16
[4,3,5,1,6,2] => [3,4,2,6,1,5] => 20
[4,3,5,2,1,6] => [3,4,2,5,6,1] => 17
[4,3,5,2,6,1] => [3,4,2,5,1,6] => 22
[4,3,5,6,1,2] => [3,4,2,1,6,5] => 25
[4,3,5,6,2,1] => [3,4,2,1,5,6] => 26
[4,3,6,1,2,5] => [3,4,1,6,5,2] => 19
[4,3,6,1,5,2] => [3,4,1,6,2,5] => 22
[4,3,6,2,1,5] => [3,4,1,5,6,2] => 20
[4,3,6,2,5,1] => [3,4,1,5,2,6] => 24
[4,3,6,5,1,2] => [3,4,1,2,6,5] => 26
[4,3,6,5,2,1] => [3,4,1,2,5,6] => 27
[4,5,1,2,3,6] => [3,2,6,5,4,1] => 15
[4,5,1,2,6,3] => [3,2,6,5,1,4] => 18
[4,5,1,3,2,6] => [3,2,6,4,5,1] => 16
[4,5,1,3,6,2] => [3,2,6,4,1,5] => 20
[4,5,1,6,2,3] => [3,2,6,1,5,4] => 22
[4,5,1,6,3,2] => [3,2,6,1,4,5] => 23
[4,5,2,1,3,6] => [3,2,5,6,4,1] => 16
[4,5,2,1,6,3] => [3,2,5,6,1,4] => 19
[4,5,2,3,1,6] => [3,2,5,4,6,1] => 18
[4,5,2,3,6,1] => [3,2,5,4,1,6] => 23
[4,5,2,6,1,3] => [3,2,5,1,6,4] => 24
[4,5,2,6,3,1] => [3,2,5,1,4,6] => 26
[4,5,3,1,2,6] => [3,2,4,6,5,1] => 18
[4,5,3,1,6,2] => [3,2,4,6,1,5] => 22
[4,5,3,2,1,6] => [3,2,4,5,6,1] => 19
[4,5,3,2,6,1] => [3,2,4,5,1,6] => 24
[4,5,3,6,1,2] => [3,2,4,1,6,5] => 27
[4,5,3,6,2,1] => [3,2,4,1,5,6] => 28
[4,5,6,1,2,3] => [3,2,1,6,5,4] => 27
[4,5,6,1,3,2] => [3,2,1,6,4,5] => 28
[4,5,6,2,1,3] => [3,2,1,5,6,4] => 28
[4,5,6,2,3,1] => [3,2,1,5,4,6] => 30
[4,5,6,3,1,2] => [3,2,1,4,6,5] => 30
[4,5,6,3,2,1] => [3,2,1,4,5,6] => 31
[4,6,1,2,3,5] => [3,1,6,5,4,2] => 19
[4,6,1,2,5,3] => [3,1,6,5,2,4] => 21
[4,6,1,3,2,5] => [3,1,6,4,5,2] => 20
[4,6,1,3,5,2] => [3,1,6,4,2,5] => 23
[4,6,1,5,2,3] => [3,1,6,2,5,4] => 24
[4,6,1,5,3,2] => [3,1,6,2,4,5] => 25
[4,6,2,1,3,5] => [3,1,5,6,4,2] => 20
[4,6,2,1,5,3] => [3,1,5,6,2,4] => 22
[4,6,2,3,1,5] => [3,1,5,4,6,2] => 22
[4,6,2,3,5,1] => [3,1,5,4,2,6] => 26
[4,6,2,5,1,3] => [3,1,5,2,6,4] => 26
[4,6,2,5,3,1] => [3,1,5,2,4,6] => 28
[4,6,3,1,2,5] => [3,1,4,6,5,2] => 22
[4,6,3,1,5,2] => [3,1,4,6,2,5] => 25
[4,6,3,2,1,5] => [3,1,4,5,6,2] => 23
[4,6,3,2,5,1] => [3,1,4,5,2,6] => 27
[4,6,3,5,1,2] => [3,1,4,2,6,5] => 29
[4,6,3,5,2,1] => [3,1,4,2,5,6] => 30
[4,6,5,1,2,3] => [3,1,2,6,5,4] => 28
[4,6,5,1,3,2] => [3,1,2,6,4,5] => 29
[4,6,5,2,1,3] => [3,1,2,5,6,4] => 29
[4,6,5,2,3,1] => [3,1,2,5,4,6] => 31
[4,6,5,3,1,2] => [3,1,2,4,6,5] => 31
[4,6,5,3,2,1] => [3,1,2,4,5,6] => 32
[5,1,2,3,4,6] => [2,6,5,4,3,1] => 10
[5,1,2,3,6,4] => [2,6,5,4,1,3] => 12
[5,1,2,4,3,6] => [2,6,5,3,4,1] => 11
[5,1,2,4,6,3] => [2,6,5,3,1,4] => 14
[5,1,2,6,3,4] => [2,6,5,1,4,3] => 15
[5,1,2,6,4,3] => [2,6,5,1,3,4] => 16
[5,1,3,2,4,6] => [2,6,4,5,3,1] => 11
[5,1,3,2,6,4] => [2,6,4,5,1,3] => 13
[5,1,3,4,2,6] => [2,6,4,3,5,1] => 13
[5,1,3,4,6,2] => [2,6,4,3,1,5] => 17
[5,1,3,6,2,4] => [2,6,4,1,5,3] => 17
[5,1,3,6,4,2] => [2,6,4,1,3,5] => 19
[5,1,4,2,3,6] => [2,6,3,5,4,1] => 13
[5,1,4,2,6,3] => [2,6,3,5,1,4] => 16
[5,1,4,3,2,6] => [2,6,3,4,5,1] => 14
[5,1,4,3,6,2] => [2,6,3,4,1,5] => 18
[5,1,4,6,2,3] => [2,6,3,1,5,4] => 20
[5,1,4,6,3,2] => [2,6,3,1,4,5] => 21
[5,1,6,2,3,4] => [2,6,1,5,4,3] => 19
[5,1,6,2,4,3] => [2,6,1,5,3,4] => 20
[5,1,6,3,2,4] => [2,6,1,4,5,3] => 20
[5,1,6,3,4,2] => [2,6,1,4,3,5] => 22
[5,1,6,4,2,3] => [2,6,1,3,5,4] => 22
[5,1,6,4,3,2] => [2,6,1,3,4,5] => 23
[5,2,1,3,4,6] => [2,5,6,4,3,1] => 11
[5,2,1,3,6,4] => [2,5,6,4,1,3] => 13
[5,2,1,4,3,6] => [2,5,6,3,4,1] => 12
[5,2,1,4,6,3] => [2,5,6,3,1,4] => 15
[5,2,1,6,3,4] => [2,5,6,1,4,3] => 16
[5,2,1,6,4,3] => [2,5,6,1,3,4] => 17
[5,2,3,1,4,6] => [2,5,4,6,3,1] => 13
[5,2,3,1,6,4] => [2,5,4,6,1,3] => 15
[5,2,3,4,1,6] => [2,5,4,3,6,1] => 16
[5,2,3,4,6,1] => [2,5,4,3,1,6] => 21
[5,2,3,6,1,4] => [2,5,4,1,6,3] => 20
[5,2,3,6,4,1] => [2,5,4,1,3,6] => 23
[5,2,4,1,3,6] => [2,5,3,6,4,1] => 15
[5,2,4,1,6,3] => [2,5,3,6,1,4] => 18
[5,2,4,3,1,6] => [2,5,3,4,6,1] => 17
[5,2,4,3,6,1] => [2,5,3,4,1,6] => 22
[5,2,4,6,1,3] => [2,5,3,1,6,4] => 23
[5,2,4,6,3,1] => [2,5,3,1,4,6] => 25
[5,2,6,1,3,4] => [2,5,1,6,4,3] => 21
[5,2,6,1,4,3] => [2,5,1,6,3,4] => 22
[5,2,6,3,1,4] => [2,5,1,4,6,3] => 23
[5,2,6,3,4,1] => [2,5,1,4,3,6] => 26
[5,2,6,4,1,3] => [2,5,1,3,6,4] => 25
[5,2,6,4,3,1] => [2,5,1,3,4,6] => 27
[5,3,1,2,4,6] => [2,4,6,5,3,1] => 13
[5,3,1,2,6,4] => [2,4,6,5,1,3] => 15
[5,3,1,4,2,6] => [2,4,6,3,5,1] => 15
[5,3,1,4,6,2] => [2,4,6,3,1,5] => 19
[5,3,1,6,2,4] => [2,4,6,1,5,3] => 19
[5,3,1,6,4,2] => [2,4,6,1,3,5] => 21
[5,3,2,1,4,6] => [2,4,5,6,3,1] => 14
[5,3,2,1,6,4] => [2,4,5,6,1,3] => 16
[5,3,2,4,1,6] => [2,4,5,3,6,1] => 17
[5,3,2,4,6,1] => [2,4,5,3,1,6] => 22
[5,3,2,6,1,4] => [2,4,5,1,6,3] => 21
[5,3,2,6,4,1] => [2,4,5,1,3,6] => 24
[5,3,4,1,2,6] => [2,4,3,6,5,1] => 18
[5,3,4,1,6,2] => [2,4,3,6,1,5] => 22
[5,3,4,2,1,6] => [2,4,3,5,6,1] => 19
[5,3,4,2,6,1] => [2,4,3,5,1,6] => 24
[5,3,4,6,1,2] => [2,4,3,1,6,5] => 27
[5,3,4,6,2,1] => [2,4,3,1,5,6] => 28
[5,3,6,1,2,4] => [2,4,1,6,5,3] => 24
[5,3,6,1,4,2] => [2,4,1,6,3,5] => 26
[5,3,6,2,1,4] => [2,4,1,5,6,3] => 25
[5,3,6,2,4,1] => [2,4,1,5,3,6] => 28
[5,3,6,4,1,2] => [2,4,1,3,6,5] => 29
[5,3,6,4,2,1] => [2,4,1,3,5,6] => 30
[5,4,1,2,3,6] => [2,3,6,5,4,1] => 16
[5,4,1,2,6,3] => [2,3,6,5,1,4] => 19
[5,4,1,3,2,6] => [2,3,6,4,5,1] => 17
[5,4,1,3,6,2] => [2,3,6,4,1,5] => 21
[5,4,1,6,2,3] => [2,3,6,1,5,4] => 23
[5,4,1,6,3,2] => [2,3,6,1,4,5] => 24
[5,4,2,1,3,6] => [2,3,5,6,4,1] => 17
[5,4,2,1,6,3] => [2,3,5,6,1,4] => 20
[5,4,2,3,1,6] => [2,3,5,4,6,1] => 19
[5,4,2,3,6,1] => [2,3,5,4,1,6] => 24
[5,4,2,6,1,3] => [2,3,5,1,6,4] => 25
[5,4,2,6,3,1] => [2,3,5,1,4,6] => 27
[5,4,3,1,2,6] => [2,3,4,6,5,1] => 19
[5,4,3,1,6,2] => [2,3,4,6,1,5] => 23
[5,4,3,2,1,6] => [2,3,4,5,6,1] => 20
[5,4,3,2,6,1] => [2,3,4,5,1,6] => 25
[5,4,3,6,1,2] => [2,3,4,1,6,5] => 28
[5,4,3,6,2,1] => [2,3,4,1,5,6] => 29
[5,4,6,1,2,3] => [2,3,1,6,5,4] => 28
[5,4,6,1,3,2] => [2,3,1,6,4,5] => 29
[5,4,6,2,1,3] => [2,3,1,5,6,4] => 29
[5,4,6,2,3,1] => [2,3,1,5,4,6] => 31
[5,4,6,3,1,2] => [2,3,1,4,6,5] => 31
[5,4,6,3,2,1] => [2,3,1,4,5,6] => 32
[5,6,1,2,3,4] => [2,1,6,5,4,3] => 24
[5,6,1,2,4,3] => [2,1,6,5,3,4] => 25
[5,6,1,3,2,4] => [2,1,6,4,5,3] => 25
[5,6,1,3,4,2] => [2,1,6,4,3,5] => 27
[5,6,1,4,2,3] => [2,1,6,3,5,4] => 27
[5,6,1,4,3,2] => [2,1,6,3,4,5] => 28
[5,6,2,1,3,4] => [2,1,5,6,4,3] => 25
[5,6,2,1,4,3] => [2,1,5,6,3,4] => 26
[5,6,2,3,1,4] => [2,1,5,4,6,3] => 27
[5,6,2,3,4,1] => [2,1,5,4,3,6] => 30
[5,6,2,4,1,3] => [2,1,5,3,6,4] => 29
[5,6,2,4,3,1] => [2,1,5,3,4,6] => 31
[5,6,3,1,2,4] => [2,1,4,6,5,3] => 27
[5,6,3,1,4,2] => [2,1,4,6,3,5] => 29
[5,6,3,2,1,4] => [2,1,4,5,6,3] => 28
[5,6,3,2,4,1] => [2,1,4,5,3,6] => 31
[5,6,3,4,1,2] => [2,1,4,3,6,5] => 32
[5,6,3,4,2,1] => [2,1,4,3,5,6] => 33
[5,6,4,1,2,3] => [2,1,3,6,5,4] => 30
[5,6,4,1,3,2] => [2,1,3,6,4,5] => 31
[5,6,4,2,1,3] => [2,1,3,5,6,4] => 31
[5,6,4,2,3,1] => [2,1,3,5,4,6] => 33
[5,6,4,3,1,2] => [2,1,3,4,6,5] => 33
[5,6,4,3,2,1] => [2,1,3,4,5,6] => 34
[6,1,2,3,4,5] => [1,6,5,4,3,2] => 15
[6,1,2,3,5,4] => [1,6,5,4,2,3] => 16
[6,1,2,4,3,5] => [1,6,5,3,4,2] => 16
[6,1,2,4,5,3] => [1,6,5,3,2,4] => 18
[6,1,2,5,3,4] => [1,6,5,2,4,3] => 18
[6,1,2,5,4,3] => [1,6,5,2,3,4] => 19
[6,1,3,2,4,5] => [1,6,4,5,3,2] => 16
[6,1,3,2,5,4] => [1,6,4,5,2,3] => 17
[6,1,3,4,2,5] => [1,6,4,3,5,2] => 18
[6,1,3,4,5,2] => [1,6,4,3,2,5] => 21
[6,1,3,5,2,4] => [1,6,4,2,5,3] => 20
[6,1,3,5,4,2] => [1,6,4,2,3,5] => 22
[6,1,4,2,3,5] => [1,6,3,5,4,2] => 18
[6,1,4,2,5,3] => [1,6,3,5,2,4] => 20
[6,1,4,3,2,5] => [1,6,3,4,5,2] => 19
[6,1,4,3,5,2] => [1,6,3,4,2,5] => 22
[6,1,4,5,2,3] => [1,6,3,2,5,4] => 23
[6,1,4,5,3,2] => [1,6,3,2,4,5] => 24
[6,1,5,2,3,4] => [1,6,2,5,4,3] => 21
[6,1,5,2,4,3] => [1,6,2,5,3,4] => 22
[6,1,5,3,2,4] => [1,6,2,4,5,3] => 22
[6,1,5,3,4,2] => [1,6,2,4,3,5] => 24
[6,1,5,4,2,3] => [1,6,2,3,5,4] => 24
[6,1,5,4,3,2] => [1,6,2,3,4,5] => 25
[6,2,1,3,4,5] => [1,5,6,4,3,2] => 16
[6,2,1,3,5,4] => [1,5,6,4,2,3] => 17
[6,2,1,4,3,5] => [1,5,6,3,4,2] => 17
[6,2,1,4,5,3] => [1,5,6,3,2,4] => 19
[6,2,1,5,3,4] => [1,5,6,2,4,3] => 19
[6,2,1,5,4,3] => [1,5,6,2,3,4] => 20
[6,2,3,1,4,5] => [1,5,4,6,3,2] => 18
[6,2,3,1,5,4] => [1,5,4,6,2,3] => 19
[6,2,3,4,1,5] => [1,5,4,3,6,2] => 21
[6,2,3,4,5,1] => [1,5,4,3,2,6] => 25
[6,2,3,5,1,4] => [1,5,4,2,6,3] => 23
[6,2,3,5,4,1] => [1,5,4,2,3,6] => 26
[6,2,4,1,3,5] => [1,5,3,6,4,2] => 20
[6,2,4,1,5,3] => [1,5,3,6,2,4] => 22
[6,2,4,3,1,5] => [1,5,3,4,6,2] => 22
[6,2,4,3,5,1] => [1,5,3,4,2,6] => 26
[6,2,4,5,1,3] => [1,5,3,2,6,4] => 26
[6,2,4,5,3,1] => [1,5,3,2,4,6] => 28
[6,2,5,1,3,4] => [1,5,2,6,4,3] => 23
[6,2,5,1,4,3] => [1,5,2,6,3,4] => 24
[6,2,5,3,1,4] => [1,5,2,4,6,3] => 25
[6,2,5,3,4,1] => [1,5,2,4,3,6] => 28
[6,2,5,4,1,3] => [1,5,2,3,6,4] => 27
[6,2,5,4,3,1] => [1,5,2,3,4,6] => 29
[6,3,1,2,4,5] => [1,4,6,5,3,2] => 18
[6,3,1,2,5,4] => [1,4,6,5,2,3] => 19
[6,3,1,4,2,5] => [1,4,6,3,5,2] => 20
[6,3,1,4,5,2] => [1,4,6,3,2,5] => 23
[6,3,1,5,2,4] => [1,4,6,2,5,3] => 22
[6,3,1,5,4,2] => [1,4,6,2,3,5] => 24
[6,3,2,1,4,5] => [1,4,5,6,3,2] => 19
[6,3,2,1,5,4] => [1,4,5,6,2,3] => 20
[6,3,2,4,1,5] => [1,4,5,3,6,2] => 22
[6,3,2,4,5,1] => [1,4,5,3,2,6] => 26
[6,3,2,5,1,4] => [1,4,5,2,6,3] => 24
[6,3,2,5,4,1] => [1,4,5,2,3,6] => 27
[6,3,4,1,2,5] => [1,4,3,6,5,2] => 23
[6,3,4,1,5,2] => [1,4,3,6,2,5] => 26
[6,3,4,2,1,5] => [1,4,3,5,6,2] => 24
[6,3,4,2,5,1] => [1,4,3,5,2,6] => 28
[6,3,4,5,1,2] => [1,4,3,2,6,5] => 30
[6,3,4,5,2,1] => [1,4,3,2,5,6] => 31
[6,3,5,1,2,4] => [1,4,2,6,5,3] => 26
[6,3,5,1,4,2] => [1,4,2,6,3,5] => 28
[6,3,5,2,1,4] => [1,4,2,5,6,3] => 27
[6,3,5,2,4,1] => [1,4,2,5,3,6] => 30
[6,3,5,4,1,2] => [1,4,2,3,6,5] => 31
[6,3,5,4,2,1] => [1,4,2,3,5,6] => 32
[6,4,1,2,3,5] => [1,3,6,5,4,2] => 21
[6,4,1,2,5,3] => [1,3,6,5,2,4] => 23
[6,4,1,3,2,5] => [1,3,6,4,5,2] => 22
[6,4,1,3,5,2] => [1,3,6,4,2,5] => 25
[6,4,1,5,2,3] => [1,3,6,2,5,4] => 26
[6,4,1,5,3,2] => [1,3,6,2,4,5] => 27
[6,4,2,1,3,5] => [1,3,5,6,4,2] => 22
[6,4,2,1,5,3] => [1,3,5,6,2,4] => 24
[6,4,2,3,1,5] => [1,3,5,4,6,2] => 24
[6,4,2,3,5,1] => [1,3,5,4,2,6] => 28
[6,4,2,5,1,3] => [1,3,5,2,6,4] => 28
[6,4,2,5,3,1] => [1,3,5,2,4,6] => 30
[6,4,3,1,2,5] => [1,3,4,6,5,2] => 24
[6,4,3,1,5,2] => [1,3,4,6,2,5] => 27
[6,4,3,2,1,5] => [1,3,4,5,6,2] => 25
[6,4,3,2,5,1] => [1,3,4,5,2,6] => 29
[6,4,3,5,1,2] => [1,3,4,2,6,5] => 31
[6,4,3,5,2,1] => [1,3,4,2,5,6] => 32
[6,4,5,1,2,3] => [1,3,2,6,5,4] => 30
[6,4,5,1,3,2] => [1,3,2,6,4,5] => 31
[6,4,5,2,1,3] => [1,3,2,5,6,4] => 31
[6,4,5,2,3,1] => [1,3,2,5,4,6] => 33
[6,4,5,3,1,2] => [1,3,2,4,6,5] => 33
[6,4,5,3,2,1] => [1,3,2,4,5,6] => 34
[6,5,1,2,3,4] => [1,2,6,5,4,3] => 25
[6,5,1,2,4,3] => [1,2,6,5,3,4] => 26
[6,5,1,3,2,4] => [1,2,6,4,5,3] => 26
[6,5,1,3,4,2] => [1,2,6,4,3,5] => 28
[6,5,1,4,2,3] => [1,2,6,3,5,4] => 28
[6,5,1,4,3,2] => [1,2,6,3,4,5] => 29
[6,5,2,1,3,4] => [1,2,5,6,4,3] => 26
[6,5,2,1,4,3] => [1,2,5,6,3,4] => 27
[6,5,2,3,1,4] => [1,2,5,4,6,3] => 28
[6,5,2,3,4,1] => [1,2,5,4,3,6] => 31
[6,5,2,4,1,3] => [1,2,5,3,6,4] => 30
[6,5,2,4,3,1] => [1,2,5,3,4,6] => 32
[6,5,3,1,2,4] => [1,2,4,6,5,3] => 28
[6,5,3,1,4,2] => [1,2,4,6,3,5] => 30
[6,5,3,2,1,4] => [1,2,4,5,6,3] => 29
[6,5,3,2,4,1] => [1,2,4,5,3,6] => 32
[6,5,3,4,1,2] => [1,2,4,3,6,5] => 33
[6,5,3,4,2,1] => [1,2,4,3,5,6] => 34
[6,5,4,1,2,3] => [1,2,3,6,5,4] => 31
[6,5,4,1,3,2] => [1,2,3,6,4,5] => 32
[6,5,4,2,1,3] => [1,2,3,5,6,4] => 32
[6,5,4,2,3,1] => [1,2,3,5,4,6] => 34
[6,5,4,3,1,2] => [1,2,3,4,6,5] => 34
[6,5,4,3,2,1] => [1,2,3,4,5,6] => 35
[7,4,2,3,5,1,6] => [1,4,6,5,3,7,2] => 34
[7,4,2,3,5,6,1] => [1,4,6,5,3,2,7] => 39
[7,4,2,3,6,1,5] => [1,4,6,5,2,7,3] => 36
[7,4,2,3,6,5,1] => [1,4,6,5,2,3,7] => 40
[7,4,2,5,1,3,6] => [1,4,6,3,7,5,2] => 34
[7,4,2,5,1,6,3] => [1,4,6,3,7,2,5] => 37
[7,4,2,5,3,1,6] => [1,4,6,3,5,7,2] => 36
[7,4,2,5,3,6,1] => [1,4,6,3,5,2,7] => 41
[7,4,2,5,6,1,3] => [1,4,6,3,2,7,5] => 42
[7,4,2,5,6,3,1] => [1,4,6,3,2,5,7] => 44
[7,4,2,6,1,3,5] => [1,4,6,2,7,5,3] => 37
[7,4,2,6,1,5,3] => [1,4,6,2,7,3,5] => 39
[7,4,2,6,3,1,5] => [1,4,6,2,5,7,3] => 39
[7,4,2,6,3,5,1] => [1,4,6,2,5,3,7] => 43
[7,4,2,6,5,1,3] => [1,4,6,2,3,7,5] => 43
[7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => 45
[7,4,3,1,2,5,6] => [1,4,5,7,6,3,2] => 30
[7,4,3,1,2,6,5] => [1,4,5,7,6,2,3] => 31
[7,4,3,1,5,2,6] => [1,4,5,7,3,6,2] => 33
[7,4,3,1,5,6,2] => [1,4,5,7,3,2,6] => 37
[7,4,3,1,6,2,5] => [1,4,5,7,2,6,3] => 35
[7,4,3,1,6,5,2] => [1,4,5,7,2,3,6] => 38
[7,4,3,2,1,5,6] => [1,4,5,6,7,3,2] => 31
[7,4,3,2,1,6,5] => [1,4,5,6,7,2,3] => 32
[7,4,3,2,5,1,6] => [1,4,5,6,3,7,2] => 35
[7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => 40
[7,4,3,2,6,1,5] => [1,4,5,6,2,7,3] => 37
[7,4,3,2,6,5,1] => [1,4,5,6,2,3,7] => 41
[7,4,3,5,1,2,6] => [1,4,5,3,7,6,2] => 37
[7,4,3,5,1,6,2] => [1,4,5,3,7,2,6] => 41
[7,4,3,5,2,1,6] => [1,4,5,3,6,7,2] => 38
[7,4,3,5,2,6,1] => [1,4,5,3,6,2,7] => 43
[7,4,3,5,6,1,2] => [1,4,5,3,2,7,6] => 46
[7,4,3,5,6,2,1] => [1,4,5,3,2,6,7] => 47
[7,4,3,6,1,2,5] => [1,4,5,2,7,6,3] => 40
[7,4,3,6,1,5,2] => [1,4,5,2,7,3,6] => 43
[7,4,3,6,2,1,5] => [1,4,5,2,6,7,3] => 41
[7,4,3,6,2,5,1] => [1,4,5,2,6,3,7] => 45
[7,4,3,6,5,1,2] => [1,4,5,2,3,7,6] => 47
[7,4,3,6,5,2,1] => [1,4,5,2,3,6,7] => 48
[7,4,5,1,2,3,6] => [1,4,3,7,6,5,2] => 36
[7,4,5,1,2,6,3] => [1,4,3,7,6,2,5] => 39
[7,4,5,1,3,2,6] => [1,4,3,7,5,6,2] => 37
[7,4,5,1,3,6,2] => [1,4,3,7,5,2,6] => 41
[7,4,5,1,6,2,3] => [1,4,3,7,2,6,5] => 43
[7,4,5,1,6,3,2] => [1,4,3,7,2,5,6] => 44
[7,4,5,2,1,3,6] => [1,4,3,6,7,5,2] => 37
[7,4,5,2,1,6,3] => [1,4,3,6,7,2,5] => 40
[7,4,5,2,3,1,6] => [1,4,3,6,5,7,2] => 39
[7,4,5,2,3,6,1] => [1,4,3,6,5,2,7] => 44
[7,4,5,2,6,1,3] => [1,4,3,6,2,7,5] => 45
[7,4,5,2,6,3,1] => [1,4,3,6,2,5,7] => 47
[7,4,5,3,1,2,6] => [1,4,3,5,7,6,2] => 39
[7,4,5,3,1,6,2] => [1,4,3,5,7,2,6] => 43
[7,4,5,3,2,1,6] => [1,4,3,5,6,7,2] => 40
[7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => 45
[7,4,5,3,6,1,2] => [1,4,3,5,2,7,6] => 48
[7,4,5,3,6,2,1] => [1,4,3,5,2,6,7] => 49
[7,4,5,6,1,2,3] => [1,4,3,2,7,6,5] => 48
[7,4,5,6,1,3,2] => [1,4,3,2,7,5,6] => 49
[7,4,5,6,2,1,3] => [1,4,3,2,6,7,5] => 49
[7,4,5,6,2,3,1] => [1,4,3,2,6,5,7] => 51
[7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => 51
[7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => 52
[7,4,6,1,2,3,5] => [1,4,2,7,6,5,3] => 40
[7,4,6,1,2,5,3] => [1,4,2,7,6,3,5] => 42
[7,4,6,1,3,2,5] => [1,4,2,7,5,6,3] => 41
[7,4,6,1,3,5,2] => [1,4,2,7,5,3,6] => 44
[7,4,6,1,5,2,3] => [1,4,2,7,3,6,5] => 45
[7,4,6,1,5,3,2] => [1,4,2,7,3,5,6] => 46
[7,4,6,2,1,3,5] => [1,4,2,6,7,5,3] => 41
[7,4,6,2,1,5,3] => [1,4,2,6,7,3,5] => 43
[7,4,6,2,3,1,5] => [1,4,2,6,5,7,3] => 43
[7,4,6,2,3,5,1] => [1,4,2,6,5,3,7] => 47
[7,4,6,2,5,1,3] => [1,4,2,6,3,7,5] => 47
[7,4,6,2,5,3,1] => [1,4,2,6,3,5,7] => 49
[7,4,6,3,1,2,5] => [1,4,2,5,7,6,3] => 43
[7,4,6,3,1,5,2] => [1,4,2,5,7,3,6] => 46
[7,4,6,3,2,1,5] => [1,4,2,5,6,7,3] => 44
[7,4,6,3,2,5,1] => [1,4,2,5,6,3,7] => 48
[7,4,6,3,5,1,2] => [1,4,2,5,3,7,6] => 50
[7,4,6,3,5,2,1] => [1,4,2,5,3,6,7] => 51
[7,4,6,5,1,2,3] => [1,4,2,3,7,6,5] => 49
[7,4,6,5,1,3,2] => [1,4,2,3,7,5,6] => 50
[7,4,6,5,2,1,3] => [1,4,2,3,6,7,5] => 50
[7,4,6,5,2,3,1] => [1,4,2,3,6,5,7] => 52
[7,4,6,5,3,1,2] => [1,4,2,3,5,7,6] => 52
[7,4,6,5,3,2,1] => [1,4,2,3,5,6,7] => 53
[7,5,1,2,3,4,6] => [1,3,7,6,5,4,2] => 31
[7,5,1,2,3,6,4] => [1,3,7,6,5,2,4] => 33
[7,5,1,2,4,3,6] => [1,3,7,6,4,5,2] => 32
[7,5,1,2,4,6,3] => [1,3,7,6,4,2,5] => 35
[7,5,1,2,6,3,4] => [1,3,7,6,2,5,4] => 36
[7,5,1,2,6,4,3] => [1,3,7,6,2,4,5] => 37
[7,5,1,3,2,4,6] => [1,3,7,5,6,4,2] => 32
[7,5,1,3,2,6,4] => [1,3,7,5,6,2,4] => 34
[7,5,1,3,4,2,6] => [1,3,7,5,4,6,2] => 34
[7,5,1,3,4,6,2] => [1,3,7,5,4,2,6] => 38
[7,5,1,3,6,2,4] => [1,3,7,5,2,6,4] => 38
[7,5,1,3,6,4,2] => [1,3,7,5,2,4,6] => 40
[7,5,1,4,2,3,6] => [1,3,7,4,6,5,2] => 34
[7,5,1,4,2,6,3] => [1,3,7,4,6,2,5] => 37
[7,5,1,4,3,2,6] => [1,3,7,4,5,6,2] => 35
[7,5,1,4,3,6,2] => [1,3,7,4,5,2,6] => 39
[7,5,1,4,6,2,3] => [1,3,7,4,2,6,5] => 41
[7,5,1,4,6,3,2] => [1,3,7,4,2,5,6] => 42
[7,5,1,6,2,3,4] => [1,3,7,2,6,5,4] => 40
[7,5,1,6,2,4,3] => [1,3,7,2,6,4,5] => 41
[7,5,1,6,3,2,4] => [1,3,7,2,5,6,4] => 41
[7,5,1,6,3,4,2] => [1,3,7,2,5,4,6] => 43
[7,5,1,6,4,2,3] => [1,3,7,2,4,6,5] => 43
[7,5,1,6,4,3,2] => [1,3,7,2,4,5,6] => 44
[7,5,2,1,3,4,6] => [1,3,6,7,5,4,2] => 32
[7,5,2,1,3,6,4] => [1,3,6,7,5,2,4] => 34
[7,5,2,1,4,3,6] => [1,3,6,7,4,5,2] => 33
[7,5,2,1,4,6,3] => [1,3,6,7,4,2,5] => 36
[7,5,2,1,6,3,4] => [1,3,6,7,2,5,4] => 37
[7,5,2,1,6,4,3] => [1,3,6,7,2,4,5] => 38
[7,5,2,3,1,4,6] => [1,3,6,5,7,4,2] => 34
[7,5,2,3,1,6,4] => [1,3,6,5,7,2,4] => 36
[7,5,2,3,4,1,6] => [1,3,6,5,4,7,2] => 37
[7,5,2,3,4,6,1] => [1,3,6,5,4,2,7] => 42
[7,5,2,3,6,1,4] => [1,3,6,5,2,7,4] => 41
[7,5,2,3,6,4,1] => [1,3,6,5,2,4,7] => 44
[7,5,2,4,1,3,6] => [1,3,6,4,7,5,2] => 36
[7,5,2,4,1,6,3] => [1,3,6,4,7,2,5] => 39
[7,5,2,4,3,1,6] => [1,3,6,4,5,7,2] => 38
[7,5,2,4,3,6,1] => [1,3,6,4,5,2,7] => 43
[7,5,2,4,6,1,3] => [1,3,6,4,2,7,5] => 44
[7,5,2,4,6,3,1] => [1,3,6,4,2,5,7] => 46
[7,5,2,6,1,3,4] => [1,3,6,2,7,5,4] => 42
[7,5,2,6,1,4,3] => [1,3,6,2,7,4,5] => 43
[7,5,2,6,3,1,4] => [1,3,6,2,5,7,4] => 44
[7,5,2,6,3,4,1] => [1,3,6,2,5,4,7] => 47
[7,5,2,6,4,1,3] => [1,3,6,2,4,7,5] => 46
[7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => 48
[7,5,3,1,2,4,6] => [1,3,5,7,6,4,2] => 34
[7,5,3,1,2,6,4] => [1,3,5,7,6,2,4] => 36
[7,5,3,1,4,2,6] => [1,3,5,7,4,6,2] => 36
[7,5,3,1,4,6,2] => [1,3,5,7,4,2,6] => 40
[7,5,3,1,6,2,4] => [1,3,5,7,2,6,4] => 40
[7,5,3,1,6,4,2] => [1,3,5,7,2,4,6] => 42
[7,5,3,2,1,4,6] => [1,3,5,6,7,4,2] => 35
[7,5,3,2,1,6,4] => [1,3,5,6,7,2,4] => 37
[7,5,3,2,4,1,6] => [1,3,5,6,4,7,2] => 38
[7,5,3,2,4,6,1] => [1,3,5,6,4,2,7] => 43
[7,5,3,2,6,1,4] => [1,3,5,6,2,7,4] => 42
[7,5,3,2,6,4,1] => [1,3,5,6,2,4,7] => 45
[7,5,3,4,1,2,6] => [1,3,5,4,7,6,2] => 39
[7,5,3,4,1,6,2] => [1,3,5,4,7,2,6] => 43
[7,5,3,4,2,1,6] => [1,3,5,4,6,7,2] => 40
[7,5,3,4,2,6,1] => [1,3,5,4,6,2,7] => 45
[7,5,3,4,6,1,2] => [1,3,5,4,2,7,6] => 48
[7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => 49
[7,5,3,6,1,2,4] => [1,3,5,2,7,6,4] => 45
[7,5,3,6,1,4,2] => [1,3,5,2,7,4,6] => 47
[7,5,3,6,2,1,4] => [1,3,5,2,6,7,4] => 46
[7,5,3,6,2,4,1] => [1,3,5,2,6,4,7] => 49
[7,5,3,6,4,1,2] => [1,3,5,2,4,7,6] => 50
[7,5,3,6,4,2,1] => [1,3,5,2,4,6,7] => 51
[7,5,4,1,2,3,6] => [1,3,4,7,6,5,2] => 37
[7,5,4,1,2,6,3] => [1,3,4,7,6,2,5] => 40
[7,5,4,1,3,2,6] => [1,3,4,7,5,6,2] => 38
[7,5,4,1,3,6,2] => [1,3,4,7,5,2,6] => 42
[7,5,4,1,6,2,3] => [1,3,4,7,2,6,5] => 44
[7,5,4,1,6,3,2] => [1,3,4,7,2,5,6] => 45
[7,5,4,2,1,3,6] => [1,3,4,6,7,5,2] => 38
[7,5,4,2,1,6,3] => [1,3,4,6,7,2,5] => 41
[7,5,4,2,3,1,6] => [1,3,4,6,5,7,2] => 40
[7,5,4,2,3,6,1] => [1,3,4,6,5,2,7] => 45
[7,5,4,2,6,1,3] => [1,3,4,6,2,7,5] => 46
[7,5,4,2,6,3,1] => [1,3,4,6,2,5,7] => 48
[7,5,4,3,1,2,6] => [1,3,4,5,7,6,2] => 40
[7,5,4,3,1,6,2] => [1,3,4,5,7,2,6] => 44
[7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => 41
[7,5,4,3,2,6,1] => [1,3,4,5,6,2,7] => 46
[7,5,4,3,6,1,2] => [1,3,4,5,2,7,6] => 49
[7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => 50
[7,5,4,6,1,2,3] => [1,3,4,2,7,6,5] => 49
[7,5,4,6,1,3,2] => [1,3,4,2,7,5,6] => 50
[7,5,4,6,2,1,3] => [1,3,4,2,6,7,5] => 50
[7,5,4,6,2,3,1] => [1,3,4,2,6,5,7] => 52
[7,5,4,6,3,1,2] => [1,3,4,2,5,7,6] => 52
[7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => 53
[7,5,6,1,2,3,4] => [1,3,2,7,6,5,4] => 45
[7,5,6,1,2,4,3] => [1,3,2,7,6,4,5] => 46
[7,5,6,1,3,2,4] => [1,3,2,7,5,6,4] => 46
[7,5,6,1,3,4,2] => [1,3,2,7,5,4,6] => 48
[7,5,6,1,4,2,3] => [1,3,2,7,4,6,5] => 48
[7,5,6,1,4,3,2] => [1,3,2,7,4,5,6] => 49
[7,5,6,2,1,3,4] => [1,3,2,6,7,5,4] => 46
[7,5,6,2,1,4,3] => [1,3,2,6,7,4,5] => 47
[7,5,6,2,3,1,4] => [1,3,2,6,5,7,4] => 48
[7,5,6,2,3,4,1] => [1,3,2,6,5,4,7] => 51
[7,5,6,2,4,1,3] => [1,3,2,6,4,7,5] => 50
[7,5,6,2,4,3,1] => [1,3,2,6,4,5,7] => 52
[7,5,6,3,1,2,4] => [1,3,2,5,7,6,4] => 48
[7,5,6,3,1,4,2] => [1,3,2,5,7,4,6] => 50
[7,5,6,3,2,1,4] => [1,3,2,5,6,7,4] => 49
[7,5,6,3,2,4,1] => [1,3,2,5,6,4,7] => 52
[7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => 53
[7,5,6,3,4,2,1] => [1,3,2,5,4,6,7] => 54
[7,5,6,4,1,2,3] => [1,3,2,4,7,6,5] => 51
[7,5,6,4,1,3,2] => [1,3,2,4,7,5,6] => 52
[7,5,6,4,2,1,3] => [1,3,2,4,6,7,5] => 52
[7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => 54
[7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => 54
[7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => 55
[7,6,1,2,3,4,5] => [1,2,7,6,5,4,3] => 36
[7,6,1,2,3,5,4] => [1,2,7,6,5,3,4] => 37
[7,6,1,2,4,3,5] => [1,2,7,6,4,5,3] => 37
[7,6,1,2,4,5,3] => [1,2,7,6,4,3,5] => 39
[7,6,1,2,5,3,4] => [1,2,7,6,3,5,4] => 39
[7,6,1,2,5,4,3] => [1,2,7,6,3,4,5] => 40
[7,6,1,3,2,4,5] => [1,2,7,5,6,4,3] => 37
[7,6,1,3,2,5,4] => [1,2,7,5,6,3,4] => 38
[7,6,1,3,4,2,5] => [1,2,7,5,4,6,3] => 39
[7,6,1,3,4,5,2] => [1,2,7,5,4,3,6] => 42
[7,6,1,3,5,2,4] => [1,2,7,5,3,6,4] => 41
[7,6,1,3,5,4,2] => [1,2,7,5,3,4,6] => 43
[7,6,1,4,2,3,5] => [1,2,7,4,6,5,3] => 39
[7,6,1,4,2,5,3] => [1,2,7,4,6,3,5] => 41
[7,6,1,4,3,2,5] => [1,2,7,4,5,6,3] => 40
[7,6,1,4,3,5,2] => [1,2,7,4,5,3,6] => 43
[7,6,1,4,5,2,3] => [1,2,7,4,3,6,5] => 44
[7,6,1,4,5,3,2] => [1,2,7,4,3,5,6] => 45
[7,6,1,5,2,3,4] => [1,2,7,3,6,5,4] => 42
[7,6,1,5,2,4,3] => [1,2,7,3,6,4,5] => 43
[7,6,1,5,3,2,4] => [1,2,7,3,5,6,4] => 43
[7,6,1,5,3,4,2] => [1,2,7,3,5,4,6] => 45
[7,6,1,5,4,2,3] => [1,2,7,3,4,6,5] => 45
[7,6,1,5,4,3,2] => [1,2,7,3,4,5,6] => 46
[7,6,2,1,3,4,5] => [1,2,6,7,5,4,3] => 37
[7,6,2,1,3,5,4] => [1,2,6,7,5,3,4] => 38
[7,6,2,1,4,3,5] => [1,2,6,7,4,5,3] => 38
[7,6,2,1,4,5,3] => [1,2,6,7,4,3,5] => 40
[7,6,2,1,5,3,4] => [1,2,6,7,3,5,4] => 40
[7,6,2,1,5,4,3] => [1,2,6,7,3,4,5] => 41
[7,6,2,3,1,4,5] => [1,2,6,5,7,4,3] => 39
[7,6,2,3,1,5,4] => [1,2,6,5,7,3,4] => 40
[7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => 42
[7,6,2,3,4,5,1] => [1,2,6,5,4,3,7] => 46
[7,6,2,3,5,1,4] => [1,2,6,5,3,7,4] => 44
[7,6,2,3,5,4,1] => [1,2,6,5,3,4,7] => 47
[7,6,2,4,1,3,5] => [1,2,6,4,7,5,3] => 41
[7,6,2,4,1,5,3] => [1,2,6,4,7,3,5] => 43
[7,6,2,4,3,1,5] => [1,2,6,4,5,7,3] => 43
[7,6,2,4,3,5,1] => [1,2,6,4,5,3,7] => 47
[7,6,2,4,5,1,3] => [1,2,6,4,3,7,5] => 47
[7,6,2,4,5,3,1] => [1,2,6,4,3,5,7] => 49
[7,6,2,5,1,3,4] => [1,2,6,3,7,5,4] => 44
[7,6,2,5,1,4,3] => [1,2,6,3,7,4,5] => 45
[7,6,2,5,3,1,4] => [1,2,6,3,5,7,4] => 46
[7,6,2,5,3,4,1] => [1,2,6,3,5,4,7] => 49
[7,6,2,5,4,1,3] => [1,2,6,3,4,7,5] => 48
[7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => 50
[7,6,3,1,2,4,5] => [1,2,5,7,6,4,3] => 39
[7,6,3,1,2,5,4] => [1,2,5,7,6,3,4] => 40
[7,6,3,1,4,2,5] => [1,2,5,7,4,6,3] => 41
[7,6,3,1,4,5,2] => [1,2,5,7,4,3,6] => 44
[7,6,3,1,5,2,4] => [1,2,5,7,3,6,4] => 43
[7,6,3,1,5,4,2] => [1,2,5,7,3,4,6] => 45
[7,6,3,2,1,4,5] => [1,2,5,6,7,4,3] => 40
[7,6,3,2,1,5,4] => [1,2,5,6,7,3,4] => 41
[7,6,3,2,4,1,5] => [1,2,5,6,4,7,3] => 43
[7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => 47
[7,6,3,2,5,1,4] => [1,2,5,6,3,7,4] => 45
[7,6,3,2,5,4,1] => [1,2,5,6,3,4,7] => 48
[7,6,3,4,1,2,5] => [1,2,5,4,7,6,3] => 44
[7,6,3,4,1,5,2] => [1,2,5,4,7,3,6] => 47
[7,6,3,4,2,1,5] => [1,2,5,4,6,7,3] => 45
[7,6,3,4,2,5,1] => [1,2,5,4,6,3,7] => 49
[7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => 51
[7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => 52
[7,6,3,5,1,2,4] => [1,2,5,3,7,6,4] => 47
[7,6,3,5,1,4,2] => [1,2,5,3,7,4,6] => 49
[7,6,3,5,2,1,4] => [1,2,5,3,6,7,4] => 48
[7,6,3,5,2,4,1] => [1,2,5,3,6,4,7] => 51
[7,6,3,5,4,1,2] => [1,2,5,3,4,7,6] => 52
[7,6,3,5,4,2,1] => [1,2,5,3,4,6,7] => 53
[7,6,4,1,2,3,5] => [1,2,4,7,6,5,3] => 42
[7,6,4,1,2,5,3] => [1,2,4,7,6,3,5] => 44
[7,6,4,1,3,2,5] => [1,2,4,7,5,6,3] => 43
[7,6,4,1,3,5,2] => [1,2,4,7,5,3,6] => 46
[7,6,4,1,5,2,3] => [1,2,4,7,3,6,5] => 47
[7,6,4,1,5,3,2] => [1,2,4,7,3,5,6] => 48
[7,6,4,2,1,3,5] => [1,2,4,6,7,5,3] => 43
[7,6,4,2,1,5,3] => [1,2,4,6,7,3,5] => 45
[7,6,4,2,3,1,5] => [1,2,4,6,5,7,3] => 45
[7,6,4,2,3,5,1] => [1,2,4,6,5,3,7] => 49
[7,6,4,2,5,1,3] => [1,2,4,6,3,7,5] => 49
[7,6,4,2,5,3,1] => [1,2,4,6,3,5,7] => 51
[7,6,4,3,1,2,5] => [1,2,4,5,7,6,3] => 45
[7,6,4,3,1,5,2] => [1,2,4,5,7,3,6] => 48
[7,6,4,3,2,1,5] => [1,2,4,5,6,7,3] => 46
[7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => 50
[7,6,4,3,5,1,2] => [1,2,4,5,3,7,6] => 52
[7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => 53
[7,6,4,5,1,2,3] => [1,2,4,3,7,6,5] => 51
[7,6,4,5,1,3,2] => [1,2,4,3,7,5,6] => 52
[7,6,4,5,2,1,3] => [1,2,4,3,6,7,5] => 52
[7,6,4,5,2,3,1] => [1,2,4,3,6,5,7] => 54
[7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => 54
[7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => 55
[7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => 46
[7,6,5,1,2,4,3] => [1,2,3,7,6,4,5] => 47
[7,6,5,1,3,2,4] => [1,2,3,7,5,6,4] => 47
[7,6,5,1,3,4,2] => [1,2,3,7,5,4,6] => 49
[7,6,5,1,4,2,3] => [1,2,3,7,4,6,5] => 49
[7,6,5,1,4,3,2] => [1,2,3,7,4,5,6] => 50
[7,6,5,2,1,3,4] => [1,2,3,6,7,5,4] => 47
[7,6,5,2,1,4,3] => [1,2,3,6,7,4,5] => 48
[7,6,5,2,3,1,4] => [1,2,3,6,5,7,4] => 49
[7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => 52
[7,6,5,2,4,1,3] => [1,2,3,6,4,7,5] => 51
[7,6,5,2,4,3,1] => [1,2,3,6,4,5,7] => 53
[7,6,5,3,1,2,4] => [1,2,3,5,7,6,4] => 49
[7,6,5,3,1,4,2] => [1,2,3,5,7,4,6] => 51
[7,6,5,3,2,1,4] => [1,2,3,5,6,7,4] => 50
[7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => 53
[7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => 54
[7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => 55
[7,6,5,4,1,2,3] => [1,2,3,4,7,6,5] => 52
[7,6,5,4,1,3,2] => [1,2,3,4,7,5,6] => 53
[7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => 53
[7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => 55
[7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => 55
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 56
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,0,2,1 1,3,1,4,2,2,2,4,1,3,1 1,4,3,6,7,6,4,10,6,10,6,10,6,10,4,6,7,6,3,4,1 1,5,6,9,16,12,14,24,20,21,23,28,24,34,20,32,42,29,29,42,32,20,34,24,28,23,21,20,24,14,12,16,9,6,5,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 2\ q^{3} + q^{4}$
$F_{4} = 1 + 3\ q + q^{2} + 4\ q^{3} + 2\ q^{4} + 2\ q^{5} + 2\ q^{6} + 4\ q^{7} + q^{8} + 3\ q^{9} + q^{10}$
$F_{5} = 1 + 4\ q + 3\ q^{2} + 6\ q^{3} + 7\ q^{4} + 6\ q^{5} + 4\ q^{6} + 10\ q^{7} + 6\ q^{8} + 10\ q^{9} + 6\ q^{10} + 10\ q^{11} + 6\ q^{12} + 10\ q^{13} + 4\ q^{14} + 6\ q^{15} + 7\ q^{16} + 6\ q^{17} + 3\ q^{18} + 4\ q^{19} + q^{20}$
$F_{6} = 1 + 5\ q + 6\ q^{2} + 9\ q^{3} + 16\ q^{4} + 12\ q^{5} + 14\ q^{6} + 24\ q^{7} + 20\ q^{8} + 21\ q^{9} + 23\ q^{10} + 28\ q^{11} + 24\ q^{12} + 34\ q^{13} + 20\ q^{14} + 32\ q^{15} + 42\ q^{16} + 29\ q^{17} + 29\ q^{18} + 42\ q^{19} + 32\ q^{20} + 20\ q^{21} + 34\ q^{22} + 24\ q^{23} + 28\ q^{24} + 23\ q^{25} + 21\ q^{26} + 20\ q^{27} + 24\ q^{28} + 14\ q^{29} + 12\ q^{30} + 16\ q^{31} + 9\ q^{32} + 6\ q^{33} + 5\ q^{34} + q^{35}$
Description
The non-inversion sum of a permutation.
A pair $a < b$ is an noninversion of a permutation $\pi$ if $\pi(a) < \pi(b)$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $\pi$.
A pair $a < b$ is an noninversion of a permutation $\pi$ if $\pi(a) < \pi(b)$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $\pi$.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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