Identifier
-
Mp00069:
Permutations
—complement⟶
Permutations
Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
St000076: Alternating sign matrices ⟶ ℤ
Values
[1] => [1] => [[1]] => 0
[1,2] => [2,1] => [[0,1],[1,0]] => 1
[2,1] => [1,2] => [[1,0],[0,1]] => 0
[1,2,3] => [3,2,1] => [[0,0,1],[0,1,0],[1,0,0]] => 4
[1,3,2] => [3,1,2] => [[0,1,0],[0,0,1],[1,0,0]] => 3
[2,1,3] => [2,3,1] => [[0,0,1],[1,0,0],[0,1,0]] => 3
[2,3,1] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]] => 1
[3,1,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]] => 1
[3,2,1] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]] => 0
[1,2,3,4] => [4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => 10
[1,2,4,3] => [4,3,1,2] => [[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]] => 9
[1,3,2,4] => [4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]] => 9
[1,3,4,2] => [4,2,1,3] => [[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]] => 7
[1,4,2,3] => [4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]] => 7
[1,4,3,2] => [4,1,2,3] => [[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]] => 6
[2,1,3,4] => [3,4,2,1] => [[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]] => 9
[2,1,4,3] => [3,4,1,2] => [[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]] => 8
[2,3,1,4] => [3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]] => 7
[2,3,4,1] => [3,2,1,4] => [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]] => 4
[2,4,1,3] => [3,1,4,2] => [[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]] => 5
[2,4,3,1] => [3,1,2,4] => [[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]] => 3
[3,1,2,4] => [2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]] => 7
[3,1,4,2] => [2,4,1,3] => [[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]] => 5
[3,2,1,4] => [2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]] => 6
[3,2,4,1] => [2,3,1,4] => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]] => 3
[3,4,1,2] => [2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]] => 2
[3,4,2,1] => [2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]] => 1
[4,1,2,3] => [1,4,3,2] => [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]] => 4
[4,1,3,2] => [1,4,2,3] => [[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]] => 3
[4,2,1,3] => [1,3,4,2] => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]] => 3
[4,2,3,1] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]] => 1
[4,3,1,2] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]] => 1
[4,3,2,1] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] => 0
[1,2,3,4,5] => [5,4,3,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]] => 20
[1,2,3,5,4] => [5,4,3,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]] => 19
[1,2,4,3,5] => [5,4,2,3,1] => [[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0]] => 19
[1,2,4,5,3] => [5,4,2,1,3] => [[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0]] => 17
[1,2,5,3,4] => [5,4,1,3,2] => [[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0]] => 17
[1,2,5,4,3] => [5,4,1,2,3] => [[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0]] => 16
[1,3,2,4,5] => [5,3,4,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0]] => 19
[1,3,2,5,4] => [5,3,4,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0]] => 18
[1,3,4,2,5] => [5,3,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]] => 17
[1,3,4,5,2] => [5,3,2,1,4] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0]] => 14
[1,3,5,2,4] => [5,3,1,4,2] => [[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]] => 15
[1,3,5,4,2] => [5,3,1,2,4] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0]] => 13
[1,4,2,3,5] => [5,2,4,3,1] => [[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]] => 17
[1,4,2,5,3] => [5,2,4,1,3] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]] => 15
[1,4,3,2,5] => [5,2,3,4,1] => [[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]] => 16
[1,4,3,5,2] => [5,2,3,1,4] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]] => 13
[1,4,5,2,3] => [5,2,1,4,3] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0]] => 12
[1,4,5,3,2] => [5,2,1,3,4] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]] => 11
[1,5,2,3,4] => [5,1,4,3,2] => [[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]] => 14
[1,5,2,4,3] => [5,1,4,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]] => 13
[1,5,3,2,4] => [5,1,3,4,2] => [[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]] => 13
[1,5,3,4,2] => [5,1,3,2,4] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]] => 11
[1,5,4,2,3] => [5,1,2,4,3] => [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0]] => 11
[1,5,4,3,2] => [5,1,2,3,4] => [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]] => 10
[2,1,3,4,5] => [4,5,3,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]] => 19
[2,1,3,5,4] => [4,5,3,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]] => 18
[2,1,4,3,5] => [4,5,2,3,1] => [[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]] => 18
[2,1,4,5,3] => [4,5,2,1,3] => [[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0]] => 16
[2,1,5,3,4] => [4,5,1,3,2] => [[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]] => 16
[2,1,5,4,3] => [4,5,1,2,3] => [[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0]] => 15
[2,3,1,4,5] => [4,3,5,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]] => 17
[2,3,1,5,4] => [4,3,5,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]] => 16
[2,3,4,1,5] => [4,3,2,5,1] => [[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]] => 14
[2,3,4,5,1] => [4,3,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 10
[2,3,5,1,4] => [4,3,1,5,2] => [[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]] => 12
[2,3,5,4,1] => [4,3,1,2,5] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 9
[2,4,1,3,5] => [4,2,5,3,1] => [[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]] => 15
[2,4,1,5,3] => [4,2,5,1,3] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]] => 13
[2,4,3,1,5] => [4,2,3,5,1] => [[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]] => 13
[2,4,3,5,1] => [4,2,3,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 9
[2,4,5,1,3] => [4,2,1,5,3] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]] => 9
[2,4,5,3,1] => [4,2,1,3,5] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]] => 7
[2,5,1,3,4] => [4,1,5,3,2] => [[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]] => 12
[2,5,1,4,3] => [4,1,5,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]] => 11
[2,5,3,1,4] => [4,1,3,5,2] => [[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]] => 10
[2,5,3,4,1] => [4,1,3,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 7
[2,5,4,1,3] => [4,1,2,5,3] => [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]] => 8
[2,5,4,3,1] => [4,1,2,3,5] => [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]] => 6
[3,1,2,4,5] => [3,5,4,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]] => 17
[3,1,2,5,4] => [3,5,4,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]] => 16
[3,1,4,2,5] => [3,5,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]] => 15
[3,1,4,5,2] => [3,5,2,1,4] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]] => 12
[3,1,5,2,4] => [3,5,1,4,2] => [[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]] => 13
[3,1,5,4,2] => [3,5,1,2,4] => [[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]] => 11
[3,2,1,4,5] => [3,4,5,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0]] => 16
[3,2,1,5,4] => [3,4,5,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0]] => 15
[3,2,4,1,5] => [3,4,2,5,1] => [[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]] => 13
[3,2,4,5,1] => [3,4,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 9
[3,2,5,1,4] => [3,4,1,5,2] => [[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]] => 11
[3,2,5,4,1] => [3,4,1,2,5] => [[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 8
[3,4,1,2,5] => [3,2,5,4,1] => [[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => 12
[3,4,1,5,2] => [3,2,5,1,4] => [[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => 9
[3,4,2,1,5] => [3,2,4,5,1] => [[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => 11
[3,4,2,5,1] => [3,2,4,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 7
[3,4,5,1,2] => [3,2,1,5,4] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => 5
[3,4,5,2,1] => [3,2,1,4,5] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => 4
[3,5,1,2,4] => [3,1,5,4,2] => [[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => 9
[3,5,1,4,2] => [3,1,5,2,4] => [[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => 7
>>> Load all 668 entries. <<<[3,5,2,1,4] => [3,1,4,5,2] => [[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => 8
[3,5,2,4,1] => [3,1,4,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 5
[3,5,4,1,2] => [3,1,2,5,4] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => 4
[3,5,4,2,1] => [3,1,2,4,5] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => 3
[4,1,2,3,5] => [2,5,4,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => 14
[4,1,2,5,3] => [2,5,4,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]] => 12
[4,1,3,2,5] => [2,5,3,4,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => 13
[4,1,3,5,2] => [2,5,3,1,4] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]] => 10
[4,1,5,2,3] => [2,5,1,4,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]] => 9
[4,1,5,3,2] => [2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => 8
[4,2,1,3,5] => [2,4,5,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]] => 13
[4,2,1,5,3] => [2,4,5,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]] => 11
[4,2,3,1,5] => [2,4,3,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]] => 11
[4,2,3,5,1] => [2,4,3,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 7
[4,2,5,1,3] => [2,4,1,5,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]] => 7
[4,2,5,3,1] => [2,4,1,3,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => 5
[4,3,1,2,5] => [2,3,5,4,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => 11
[4,3,1,5,2] => [2,3,5,1,4] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => 8
[4,3,2,1,5] => [2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => 10
[4,3,2,5,1] => [2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 6
[4,3,5,1,2] => [2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => 4
[4,3,5,2,1] => [2,3,1,4,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => 3
[4,5,1,2,3] => [2,1,5,4,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => 5
[4,5,1,3,2] => [2,1,5,3,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]] => 4
[4,5,2,1,3] => [2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]] => 4
[4,5,2,3,1] => [2,1,4,3,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => 2
[4,5,3,1,2] => [2,1,3,5,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => 2
[4,5,3,2,1] => [2,1,3,4,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => 1
[5,1,2,3,4] => [1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => 10
[5,1,2,4,3] => [1,5,4,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]] => 9
[5,1,3,2,4] => [1,5,3,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => 9
[5,1,3,4,2] => [1,5,3,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]] => 7
[5,1,4,2,3] => [1,5,2,4,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]] => 7
[5,1,4,3,2] => [1,5,2,3,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => 6
[5,2,1,3,4] => [1,4,5,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]] => 9
[5,2,1,4,3] => [1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]] => 8
[5,2,3,1,4] => [1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]] => 7
[5,2,3,4,1] => [1,4,3,2,5] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 4
[5,2,4,1,3] => [1,4,2,5,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]] => 5
[5,2,4,3,1] => [1,4,2,3,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => 3
[5,3,1,2,4] => [1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => 7
[5,3,1,4,2] => [1,3,5,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => 5
[5,3,2,1,4] => [1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => 6
[5,3,2,4,1] => [1,3,4,2,5] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 3
[5,3,4,1,2] => [1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => 2
[5,3,4,2,1] => [1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => 1
[5,4,1,2,3] => [1,2,5,4,3] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => 4
[5,4,1,3,2] => [1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]] => 3
[5,4,2,1,3] => [1,2,4,5,3] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]] => 3
[5,4,2,3,1] => [1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => 1
[5,4,3,1,2] => [1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => 1
[5,4,3,2,1] => [1,2,3,4,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => 0
[1,2,3,4,5,6] => [6,5,4,3,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 35
[1,2,3,4,6,5] => [6,5,4,3,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 34
[1,2,3,5,4,6] => [6,5,4,2,3,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 34
[1,2,3,5,6,4] => [6,5,4,2,1,3] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 32
[1,2,3,6,4,5] => [6,5,4,1,3,2] => [[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 32
[1,2,3,6,5,4] => [6,5,4,1,2,3] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 31
[1,2,4,3,5,6] => [6,5,3,4,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 34
[1,2,4,3,6,5] => [6,5,3,4,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 33
[1,2,4,5,3,6] => [6,5,3,2,4,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 32
[1,2,4,5,6,3] => [6,5,3,2,1,4] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 29
[1,2,4,6,5,3] => [6,5,3,1,2,4] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 28
[1,2,5,3,4,6] => [6,5,2,4,3,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 32
[1,2,5,3,6,4] => [6,5,2,4,1,3] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 30
[1,2,5,4,3,6] => [6,5,2,3,4,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 31
[1,2,5,4,6,3] => [6,5,2,3,1,4] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 28
[1,2,5,6,4,3] => [6,5,2,1,3,4] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 26
[1,2,6,3,4,5] => [6,5,1,4,3,2] => [[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 29
[1,2,6,5,4,3] => [6,5,1,2,3,4] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0]] => 25
[1,3,2,4,5,6] => [6,4,5,3,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 34
[1,3,2,4,6,5] => [6,4,5,3,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 33
[1,3,2,5,4,6] => [6,4,5,2,3,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 33
[1,3,2,5,6,4] => [6,4,5,2,1,3] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 31
[1,3,2,6,4,5] => [6,4,5,1,3,2] => [[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 31
[1,3,2,6,5,4] => [6,4,5,1,2,3] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 30
[1,3,4,2,5,6] => [6,4,3,5,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 32
[1,3,4,2,6,5] => [6,4,3,5,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 31
[1,3,4,5,2,6] => [6,4,3,2,5,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0]] => 29
[1,3,4,5,6,2] => [6,4,3,2,1,5] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 25
[1,3,4,6,5,2] => [6,4,3,1,2,5] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 24
[1,3,5,2,6,4] => [6,4,2,5,1,3] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 28
[1,3,5,4,2,6] => [6,4,2,3,5,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0]] => 28
[1,3,5,4,6,2] => [6,4,2,3,1,5] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 24
[1,3,5,6,4,2] => [6,4,2,1,3,5] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 22
[1,3,6,5,4,2] => [6,4,1,2,3,5] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 21
[1,4,2,3,5,6] => [6,3,5,4,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 32
[1,4,2,3,6,5] => [6,3,5,4,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 31
[1,4,2,6,5,3] => [6,3,5,1,2,4] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 26
[1,4,3,2,5,6] => [6,3,4,5,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 31
[1,4,3,2,6,5] => [6,3,4,5,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 30
[1,4,3,5,2,6] => [6,3,4,2,5,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0]] => 28
[1,4,3,5,6,2] => [6,3,4,2,1,5] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 24
[1,4,3,6,5,2] => [6,3,4,1,2,5] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 23
[1,4,5,2,3,6] => [6,3,2,5,4,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 27
[1,4,5,2,6,3] => [6,3,2,5,1,4] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 24
[1,4,5,3,2,6] => [6,3,2,4,5,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0]] => 26
[1,4,5,3,6,2] => [6,3,2,4,1,5] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 22
[1,4,5,6,3,2] => [6,3,2,1,4,5] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 19
[1,4,6,5,3,2] => [6,3,1,2,4,5] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 18
[1,5,2,3,4,6] => [6,2,5,4,3,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 29
[1,5,2,6,4,3] => [6,2,5,1,3,4] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 23
[1,5,3,2,4,6] => [6,2,4,5,3,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 28
[1,5,3,4,2,6] => [6,2,4,3,5,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0]] => 26
[1,5,3,6,4,2] => [6,2,4,1,3,5] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 20
[1,5,4,2,3,6] => [6,2,3,5,4,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]] => 26
[1,5,4,3,2,6] => [6,2,3,4,5,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0]] => 25
[1,5,4,3,6,2] => [6,2,3,4,1,5] => [[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 21
[1,5,4,6,3,2] => [6,2,3,1,4,5] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 18
[1,5,6,4,3,2] => [6,2,1,3,4,5] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 16
[1,6,2,3,4,5] => [6,1,5,4,3,2] => [[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]] => 25
[1,6,5,4,3,2] => [6,1,2,3,4,5] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0]] => 15
[2,1,3,4,5,6] => [5,6,4,3,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 34
[2,1,3,4,6,5] => [5,6,4,3,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 33
[2,1,3,5,4,6] => [5,6,4,2,3,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 33
[2,1,3,5,6,4] => [5,6,4,2,1,3] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 31
[2,1,3,6,4,5] => [5,6,4,1,3,2] => [[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 31
[2,1,3,6,5,4] => [5,6,4,1,2,3] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 30
[2,1,4,3,5,6] => [5,6,3,4,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 33
[2,1,4,3,6,5] => [5,6,3,4,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 32
[2,1,4,5,3,6] => [5,6,3,2,4,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 31
[2,1,4,5,6,3] => [5,6,3,2,1,4] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 28
[2,1,4,6,5,3] => [5,6,3,1,2,4] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 27
[2,1,5,3,4,6] => [5,6,2,4,3,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 31
[2,1,5,3,6,4] => [5,6,2,4,1,3] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 29
[2,1,5,4,3,6] => [5,6,2,3,4,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 30
[2,1,5,4,6,3] => [5,6,2,3,1,4] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 27
[2,1,5,6,4,3] => [5,6,2,1,3,4] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 25
[2,1,6,3,4,5] => [5,6,1,4,3,2] => [[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 28
[2,1,6,5,4,3] => [5,6,1,2,3,4] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0]] => 24
[2,3,1,4,5,6] => [5,4,6,3,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0]] => 32
[2,3,1,4,6,5] => [5,4,6,3,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0]] => 31
[2,3,1,5,4,6] => [5,4,6,2,3,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0]] => 31
[2,3,1,5,6,4] => [5,4,6,2,1,3] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0]] => 29
[2,3,1,6,5,4] => [5,4,6,1,2,3] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0]] => 28
[2,3,4,1,5,6] => [5,4,3,6,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0]] => 29
[2,3,4,1,6,5] => [5,4,3,6,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0]] => 28
[2,3,4,5,1,6] => [5,4,3,2,6,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]] => 25
[2,3,4,5,6,1] => [5,4,3,2,1,6] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 20
[2,3,4,6,5,1] => [5,4,3,1,2,6] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 19
[2,3,5,1,6,4] => [5,4,2,6,1,3] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0]] => 25
[2,3,5,4,1,6] => [5,4,2,3,6,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]] => 24
[2,3,5,4,6,1] => [5,4,2,3,1,6] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 19
[2,3,5,6,4,1] => [5,4,2,1,3,6] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 17
[2,3,6,5,4,1] => [5,4,1,2,3,6] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 16
[2,4,1,6,5,3] => [5,3,6,1,2,4] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0]] => 24
[2,4,3,1,5,6] => [5,3,4,6,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0]] => 28
[2,4,3,1,6,5] => [5,3,4,6,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0]] => 27
[2,4,3,5,1,6] => [5,3,4,2,6,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]] => 24
[2,4,3,5,6,1] => [5,3,4,2,1,6] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 19
[2,4,3,6,5,1] => [5,3,4,1,2,6] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 18
[2,4,5,1,6,3] => [5,3,2,6,1,4] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0]] => 21
[2,4,5,3,1,6] => [5,3,2,4,6,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]] => 22
[2,4,5,3,6,1] => [5,3,2,4,1,6] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 17
[2,4,5,6,3,1] => [5,3,2,1,4,6] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 14
[2,4,6,5,3,1] => [5,3,1,2,4,6] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 13
[2,5,1,6,4,3] => [5,2,6,1,3,4] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0]] => 21
[2,5,3,4,1,6] => [5,2,4,3,6,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]] => 22
[2,5,3,4,6,1] => [5,2,4,3,1,6] => [[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 17
[2,5,3,6,4,1] => [5,2,4,1,3,6] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 15
[2,5,4,3,1,6] => [5,2,3,4,6,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]] => 21
[2,5,4,3,6,1] => [5,2,3,4,1,6] => [[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 16
[2,5,4,6,3,1] => [5,2,3,1,4,6] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 13
[2,5,6,4,3,1] => [5,2,1,3,4,6] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 11
[2,6,1,5,4,3] => [5,1,6,2,3,4] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0]] => 19
[2,6,5,1,4,3] => [5,1,2,6,3,4] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0]] => 15
[2,6,5,4,1,3] => [5,1,2,3,6,4] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0]] => 12
[2,6,5,4,3,1] => [5,1,2,3,4,6] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 10
[3,1,2,4,5,6] => [4,6,5,3,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => 32
[3,1,2,4,6,5] => [4,6,5,3,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => 31
[3,1,2,5,4,6] => [4,6,5,2,3,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => 31
[3,1,2,6,4,5] => [4,6,5,1,3,2] => [[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => 29
[3,1,4,2,6,5] => [4,6,3,5,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]] => 29
[3,1,5,2,6,4] => [4,6,2,5,1,3] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]] => 26
[3,1,6,5,4,2] => [4,6,1,2,3,5] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0]] => 19
[3,2,1,4,5,6] => [4,5,6,3,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 31
[3,2,1,4,6,5] => [4,5,6,3,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 30
[3,2,1,5,4,6] => [4,5,6,2,3,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 30
[3,2,1,5,6,4] => [4,5,6,2,1,3] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 28
[3,2,1,6,5,4] => [4,5,6,1,2,3] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 27
[3,2,4,1,5,6] => [4,5,3,6,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 28
[3,2,4,1,6,5] => [4,5,3,6,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 27
[3,2,4,5,1,6] => [4,5,3,2,6,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 24
[3,2,4,5,6,1] => [4,5,3,2,1,6] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 19
[3,2,4,6,5,1] => [4,5,3,1,2,6] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 18
[3,2,5,4,1,6] => [4,5,2,3,6,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 23
[3,2,5,4,6,1] => [4,5,2,3,1,6] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 18
[3,2,5,6,4,1] => [4,5,2,1,3,6] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 16
[3,2,6,1,5,4] => [4,5,1,6,2,3] => [[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 22
[3,2,6,5,1,4] => [4,5,1,2,6,3] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 18
[3,2,6,5,4,1] => [4,5,1,2,3,6] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 15
[3,4,1,2,5,6] => [4,3,6,5,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 27
[3,4,1,6,5,2] => [4,3,6,1,2,5] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 19
[3,4,2,1,5,6] => [4,3,5,6,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 26
[3,4,2,1,6,5] => [4,3,5,6,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 25
[3,4,2,5,1,6] => [4,3,5,2,6,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 22
[3,4,2,5,6,1] => [4,3,5,2,1,6] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 17
[3,4,2,6,5,1] => [4,3,5,1,2,6] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 16
[3,4,5,1,2,6] => [4,3,2,6,5,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 20
[3,4,5,1,6,2] => [4,3,2,6,1,5] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 16
[3,4,5,2,1,6] => [4,3,2,5,6,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 19
[3,4,5,2,6,1] => [4,3,2,5,1,6] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 14
[3,4,5,6,1,2] => [4,3,2,1,6,5] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 11
[3,4,5,6,2,1] => [4,3,2,1,5,6] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 10
[3,4,6,5,2,1] => [4,3,1,2,5,6] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 9
[3,5,1,6,4,2] => [4,2,6,1,3,5] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 16
[3,5,2,6,4,1] => [4,2,5,1,3,6] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 13
[3,5,4,1,2,6] => [4,2,3,6,5,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 19
[3,5,4,2,1,6] => [4,2,3,5,6,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 18
[3,5,4,2,6,1] => [4,2,3,5,1,6] => [[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 13
[3,5,4,6,1,2] => [4,2,3,1,6,5] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 10
[3,5,4,6,2,1] => [4,2,3,1,5,6] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 9
[3,5,6,4,2,1] => [4,2,1,3,5,6] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 7
[3,6,1,5,4,2] => [4,1,6,2,3,5] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 14
[3,6,2,1,5,4] => [4,1,5,6,2,3] => [[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 18
[3,6,2,5,1,4] => [4,1,5,2,6,3] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 14
[3,6,2,5,4,1] => [4,1,5,2,3,6] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 11
[3,6,5,1,4,2] => [4,1,2,6,3,5] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 10
[3,6,5,2,1,4] => [4,1,2,5,6,3] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 11
[3,6,5,2,4,1] => [4,1,2,5,3,6] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 8
[3,6,5,4,1,2] => [4,1,2,3,6,5] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 7
[3,6,5,4,2,1] => [4,1,2,3,5,6] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 6
[4,1,2,3,5,6] => [3,6,5,4,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => 29
[4,1,2,3,6,5] => [3,6,5,4,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => 28
[4,1,5,2,6,3] => [3,6,2,5,1,4] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0]] => 21
[4,1,6,2,3,5] => [3,6,1,5,4,2] => [[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]] => 21
[4,1,6,5,3,2] => [3,6,1,2,4,5] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0]] => 15
[4,2,1,3,5,6] => [3,5,6,4,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 28
[4,2,1,6,5,3] => [3,5,6,1,2,4] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 22
[4,2,3,1,5,6] => [3,5,4,6,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 26
[4,2,3,5,1,6] => [3,5,4,2,6,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 22
[4,2,3,5,6,1] => [3,5,4,2,1,6] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 17
[4,2,6,1,5,3] => [3,5,1,6,2,4] => [[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 17
[4,2,6,5,1,3] => [3,5,1,2,6,4] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 13
[4,2,6,5,3,1] => [3,5,1,2,4,6] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 11
[4,3,1,2,5,6] => [3,4,6,5,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 26
[4,3,1,6,5,2] => [3,4,6,1,2,5] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 18
[4,3,2,1,5,6] => [3,4,5,6,2,1] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 25
[4,3,2,1,6,5] => [3,4,5,6,1,2] => [[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 24
[4,3,2,5,1,6] => [3,4,5,2,6,1] => [[0,0,0,0,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 21
[4,3,2,5,6,1] => [3,4,5,2,1,6] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 16
[4,3,2,6,1,5] => [3,4,5,1,6,2] => [[0,0,0,1,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 19
[4,3,2,6,5,1] => [3,4,5,1,2,6] => [[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 15
[4,3,5,1,2,6] => [3,4,2,6,5,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 19
[4,3,5,2,1,6] => [3,4,2,5,6,1] => [[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 18
[4,3,5,2,6,1] => [3,4,2,5,1,6] => [[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 13
[4,3,5,6,1,2] => [3,4,2,1,6,5] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 10
[4,3,5,6,2,1] => [3,4,2,1,5,6] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 9
[4,3,6,1,5,2] => [3,4,1,6,2,5] => [[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 13
[4,3,6,2,1,5] => [3,4,1,5,6,2] => [[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 15
[4,3,6,2,5,1] => [3,4,1,5,2,6] => [[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 11
[4,3,6,5,1,2] => [3,4,1,2,6,5] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 9
[4,3,6,5,2,1] => [3,4,1,2,5,6] => [[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 8
[4,5,1,2,3,6] => [3,2,6,5,4,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 20
[4,5,1,3,2,6] => [3,2,6,4,5,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0]] => 19
[4,5,1,6,3,2] => [3,2,6,1,4,5] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 12
[4,5,2,1,3,6] => [3,2,5,6,4,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 19
[4,5,2,3,1,6] => [3,2,5,4,6,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 17
[4,5,2,3,6,1] => [3,2,5,4,1,6] => [[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 12
[4,5,2,6,3,1] => [3,2,5,1,4,6] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 9
[4,5,3,1,2,6] => [3,2,4,6,5,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 17
[4,5,3,2,1,6] => [3,2,4,5,6,1] => [[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 16
[4,5,3,2,6,1] => [3,2,4,5,1,6] => [[0,0,0,0,1,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 11
[4,5,3,6,1,2] => [3,2,4,1,6,5] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 8
[4,5,3,6,2,1] => [3,2,4,1,5,6] => [[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 7
[4,5,6,1,2,3] => [3,2,1,6,5,4] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 8
[4,5,6,1,3,2] => [3,2,1,6,4,5] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 7
[4,5,6,2,1,3] => [3,2,1,5,6,4] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 7
[4,5,6,2,3,1] => [3,2,1,5,4,6] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 5
[4,5,6,3,1,2] => [3,2,1,4,6,5] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 5
[4,5,6,3,2,1] => [3,2,1,4,5,6] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 4
[4,6,1,5,3,2] => [3,1,6,2,4,5] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 10
[4,6,2,1,5,3] => [3,1,5,6,2,4] => [[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 13
[4,6,2,5,1,3] => [3,1,5,2,6,4] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 9
[4,6,2,5,3,1] => [3,1,5,2,4,6] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 7
[4,6,3,1,5,2] => [3,1,4,6,2,5] => [[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 10
[4,6,3,2,1,5] => [3,1,4,5,6,2] => [[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 12
[4,6,3,2,5,1] => [3,1,4,5,2,6] => [[0,1,0,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 8
[4,6,3,5,1,2] => [3,1,4,2,6,5] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 6
[4,6,3,5,2,1] => [3,1,4,2,5,6] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 5
[4,6,5,1,2,3] => [3,1,2,6,5,4] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 7
[4,6,5,1,3,2] => [3,1,2,6,4,5] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 6
[4,6,5,2,1,3] => [3,1,2,5,6,4] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 6
[4,6,5,2,3,1] => [3,1,2,5,4,6] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 4
[4,6,5,3,1,2] => [3,1,2,4,6,5] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 4
[4,6,5,3,2,1] => [3,1,2,4,5,6] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 3
[5,1,2,3,4,6] => [2,6,5,4,3,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => 25
[5,1,3,2,4,6] => [2,6,4,5,3,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]] => 24
[5,1,3,4,2,6] => [2,6,4,3,5,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0]] => 22
[5,1,4,2,3,6] => [2,6,3,5,4,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]] => 22
[5,1,4,3,2,6] => [2,6,3,4,5,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0]] => 21
[5,1,6,4,3,2] => [2,6,1,3,4,5] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0]] => 12
[5,2,1,3,4,6] => [2,5,6,4,3,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 24
[5,2,1,6,4,3] => [2,5,6,1,3,4] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 18
[5,2,3,1,4,6] => [2,5,4,6,3,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 22
[5,2,3,4,1,6] => [2,5,4,3,6,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 19
[5,2,3,4,6,1] => [2,5,4,3,1,6] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 14
[5,2,4,3,1,6] => [2,5,3,4,6,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 18
[5,2,4,3,6,1] => [2,5,3,4,1,6] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 13
[5,2,6,1,4,3] => [2,5,1,6,3,4] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 13
[5,2,6,4,1,3] => [2,5,1,3,6,4] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 10
[5,2,6,4,3,1] => [2,5,1,3,4,6] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 8
[5,3,1,2,4,6] => [2,4,6,5,3,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 22
[5,3,1,6,4,2] => [2,4,6,1,3,5] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 14
[5,3,2,1,4,6] => [2,4,5,6,3,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 21
[5,3,2,1,6,4] => [2,4,5,6,1,3] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 19
[5,3,2,4,1,6] => [2,4,5,3,6,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 18
[5,3,2,4,6,1] => [2,4,5,3,1,6] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 13
[5,3,2,6,1,4] => [2,4,5,1,6,3] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 14
[5,3,2,6,4,1] => [2,4,5,1,3,6] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 11
[5,3,4,1,2,6] => [2,4,3,6,5,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 17
[5,3,4,2,1,6] => [2,4,3,5,6,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 16
[5,3,4,2,6,1] => [2,4,3,5,1,6] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 11
[5,3,4,6,1,2] => [2,4,3,1,6,5] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 8
[5,3,4,6,2,1] => [2,4,3,1,5,6] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 7
[5,3,6,1,4,2] => [2,4,1,6,3,5] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 9
[5,3,6,2,1,4] => [2,4,1,5,6,3] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 10
[5,3,6,2,4,1] => [2,4,1,5,3,6] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 7
[5,3,6,4,1,2] => [2,4,1,3,6,5] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 6
[5,3,6,4,2,1] => [2,4,1,3,5,6] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 5
[5,4,1,2,3,6] => [2,3,6,5,4,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 19
[5,4,1,3,2,6] => [2,3,6,4,5,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0]] => 18
[5,4,1,6,3,2] => [2,3,6,1,4,5] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 11
[5,4,2,1,3,6] => [2,3,5,6,4,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 18
[5,4,2,1,6,3] => [2,3,5,6,1,4] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 15
[5,4,2,3,1,6] => [2,3,5,4,6,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 16
[5,4,2,3,6,1] => [2,3,5,4,1,6] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 11
[5,4,2,6,1,3] => [2,3,5,1,6,4] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 10
[5,4,2,6,3,1] => [2,3,5,1,4,6] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 8
[5,4,3,1,2,6] => [2,3,4,6,5,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 16
[5,4,3,1,6,2] => [2,3,4,6,1,5] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 12
[5,4,3,2,1,6] => [2,3,4,5,6,1] => [[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 15
[5,4,3,2,6,1] => [2,3,4,5,1,6] => [[0,0,0,0,1,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 10
[5,4,3,6,1,2] => [2,3,4,1,6,5] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 7
[5,4,3,6,2,1] => [2,3,4,1,5,6] => [[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 6
[5,4,6,1,2,3] => [2,3,1,6,5,4] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 7
[5,4,6,1,3,2] => [2,3,1,6,4,5] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 6
[5,4,6,2,1,3] => [2,3,1,5,6,4] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 6
[5,4,6,2,3,1] => [2,3,1,5,4,6] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 4
[5,4,6,3,1,2] => [2,3,1,4,6,5] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 4
[5,4,6,3,2,1] => [2,3,1,4,5,6] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 3
[5,6,1,2,3,4] => [2,1,6,5,4,3] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 11
[5,6,1,3,2,4] => [2,1,6,4,5,3] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0]] => 10
[5,6,1,4,3,2] => [2,1,6,3,4,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 7
[5,6,2,1,3,4] => [2,1,5,6,4,3] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 10
[5,6,2,1,4,3] => [2,1,5,6,3,4] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 9
[5,6,2,3,1,4] => [2,1,5,4,6,3] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 8
[5,6,2,3,4,1] => [2,1,5,4,3,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 5
[5,6,2,4,1,3] => [2,1,5,3,6,4] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 6
[5,6,2,4,3,1] => [2,1,5,3,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 4
[5,6,3,1,2,4] => [2,1,4,6,5,3] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 8
[5,6,3,1,4,2] => [2,1,4,6,3,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 6
[5,6,3,2,1,4] => [2,1,4,5,6,3] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 7
[5,6,3,2,4,1] => [2,1,4,5,3,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 4
[5,6,3,4,1,2] => [2,1,4,3,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 3
[5,6,3,4,2,1] => [2,1,4,3,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 2
[5,6,4,1,2,3] => [2,1,3,6,5,4] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 5
[5,6,4,1,3,2] => [2,1,3,6,4,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 4
[5,6,4,2,1,3] => [2,1,3,5,6,4] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 4
[5,6,4,2,3,1] => [2,1,3,5,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 2
[5,6,4,3,1,2] => [2,1,3,4,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 2
[5,6,4,3,2,1] => [2,1,3,4,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 1
[6,1,2,3,4,5] => [1,6,5,4,3,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => 20
[6,1,3,2,4,5] => [1,6,4,5,3,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0]] => 19
[6,1,3,4,2,5] => [1,6,4,3,5,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0]] => 17
[6,1,4,2,3,5] => [1,6,3,5,4,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]] => 17
[6,1,4,3,2,5] => [1,6,3,4,5,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0]] => 16
[6,1,5,4,3,2] => [1,6,2,3,4,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0]] => 10
[6,2,1,3,4,5] => [1,5,6,4,3,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 19
[6,2,1,5,4,3] => [1,5,6,2,3,4] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0]] => 15
[6,2,3,1,4,5] => [1,5,4,6,3,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 17
[6,2,3,4,1,5] => [1,5,4,3,6,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 14
[6,2,3,4,5,1] => [1,5,4,3,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 10
[6,2,4,3,1,5] => [1,5,3,4,6,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 13
[6,2,4,3,5,1] => [1,5,3,4,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 9
[6,2,5,1,4,3] => [1,5,2,6,3,4] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]] => 11
[6,2,5,4,1,3] => [1,5,2,3,6,4] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]] => 8
[6,2,5,4,3,1] => [1,5,2,3,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 6
[6,3,1,2,4,5] => [1,4,6,5,3,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 17
[6,3,1,5,4,2] => [1,4,6,2,3,5] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 11
[6,3,2,1,4,5] => [1,4,5,6,3,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 16
[6,3,2,1,5,4] => [1,4,5,6,2,3] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 15
[6,3,2,4,1,5] => [1,4,5,3,6,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 13
[6,3,2,4,5,1] => [1,4,5,3,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 9
[6,3,2,5,1,4] => [1,4,5,2,6,3] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 11
[6,3,2,5,4,1] => [1,4,5,2,3,6] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 8
[6,3,4,1,2,5] => [1,4,3,6,5,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 12
[6,3,4,2,1,5] => [1,4,3,5,6,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 11
[6,3,4,2,5,1] => [1,4,3,5,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 7
[6,3,4,5,1,2] => [1,4,3,2,6,5] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 5
[6,3,4,5,2,1] => [1,4,3,2,5,6] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 4
[6,3,5,1,4,2] => [1,4,2,6,3,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 7
[6,3,5,2,1,4] => [1,4,2,5,6,3] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 8
[6,3,5,2,4,1] => [1,4,2,5,3,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 5
[6,3,5,4,1,2] => [1,4,2,3,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 4
[6,3,5,4,2,1] => [1,4,2,3,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 3
[6,4,1,2,3,5] => [1,3,6,5,4,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 14
[6,4,1,3,2,5] => [1,3,6,4,5,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0]] => 13
[6,4,1,5,3,2] => [1,3,6,2,4,5] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 8
[6,4,2,1,3,5] => [1,3,5,6,4,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 13
[6,4,2,1,5,3] => [1,3,5,6,2,4] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 11
[6,4,2,3,1,5] => [1,3,5,4,6,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 11
[6,4,2,3,5,1] => [1,3,5,4,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 7
[6,4,2,5,1,3] => [1,3,5,2,6,4] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 7
[6,4,2,5,3,1] => [1,3,5,2,4,6] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 5
[6,4,3,1,2,5] => [1,3,4,6,5,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 11
[6,4,3,1,5,2] => [1,3,4,6,2,5] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 8
[6,4,3,2,1,5] => [1,3,4,5,6,2] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 10
[6,4,3,2,5,1] => [1,3,4,5,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 6
[6,4,3,5,1,2] => [1,3,4,2,6,5] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 4
[6,4,3,5,2,1] => [1,3,4,2,5,6] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 3
[6,4,5,1,2,3] => [1,3,2,6,5,4] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 5
[6,4,5,1,3,2] => [1,3,2,6,4,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 4
[6,4,5,2,1,3] => [1,3,2,5,6,4] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 4
[6,4,5,2,3,1] => [1,3,2,5,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 2
[6,4,5,3,1,2] => [1,3,2,4,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 2
[6,4,5,3,2,1] => [1,3,2,4,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 1
[6,5,1,2,3,4] => [1,2,6,5,4,3] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => 10
[6,5,1,3,2,4] => [1,2,6,4,5,3] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0]] => 9
[6,5,1,4,3,2] => [1,2,6,3,4,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0]] => 6
[6,5,2,1,3,4] => [1,2,5,6,4,3] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 9
[6,5,2,1,4,3] => [1,2,5,6,3,4] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0]] => 8
[6,5,2,3,1,4] => [1,2,5,4,6,3] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 7
[6,5,2,3,4,1] => [1,2,5,4,3,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 4
[6,5,2,4,1,3] => [1,2,5,3,6,4] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]] => 5
[6,5,2,4,3,1] => [1,2,5,3,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 3
[6,5,3,1,2,4] => [1,2,4,6,5,3] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 7
[6,5,3,1,4,2] => [1,2,4,6,3,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 5
[6,5,3,2,1,4] => [1,2,4,5,6,3] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 6
[6,5,3,2,4,1] => [1,2,4,5,3,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 3
[6,5,3,4,1,2] => [1,2,4,3,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 2
[6,5,3,4,2,1] => [1,2,4,3,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 1
[6,5,4,1,2,3] => [1,2,3,6,5,4] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => 4
[6,5,4,1,3,2] => [1,2,3,6,4,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0]] => 3
[6,5,4,2,1,3] => [1,2,3,5,6,4] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => 3
[6,5,4,2,3,1] => [1,2,3,5,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 1
[6,5,4,3,1,2] => [1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 1
[6,5,4,3,2,1] => [1,2,3,4,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 0
[2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => [[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1]] => 35
[3,4,5,6,7,1,2] => [5,4,3,2,1,7,6] => [[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]] => 21
[6,5,4,3,2,7,1] => [2,3,4,5,6,1,7] => [[0,0,0,0,0,1,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]] => 15
[6,5,4,3,7,1,2] => [2,3,4,5,1,7,6] => [[0,0,0,0,1,0,0],[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]] => 11
[6,7,1,2,3,4,5] => [2,1,7,6,5,4,3] => [[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]] => 21
[6,7,4,3,2,1,5] => [2,1,4,5,6,7,3] => [[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]] => 11
[7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => [[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0]] => 35
[7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => [[1,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]] => 15
[7,6,5,4,3,2,8,1] => [2,3,4,5,6,7,1,8] => [[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]] => 21
[2,3,4,5,6,7,8,1] => [7,6,5,4,3,2,1,8] => [[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1]] => 56
[7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 4
[5,6,7,8,3,4,1,2] => [4,3,2,1,6,5,8,7] => [[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 12
[7,8,3,4,5,6,1,2] => [2,1,6,5,4,3,8,7] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 12
[3,4,5,6,7,8,1,2] => [6,5,4,3,2,1,8,7] => [[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 36
[7,8,5,6,1,2,3,4] => [2,1,4,3,8,7,6,5] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]] => 12
[5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]] => 20
[7,8,1,2,3,4,5,6] => [2,1,8,7,6,5,4,3] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]] => 36
[8,6,5,4,3,2,1,7] => [1,3,4,5,6,7,8,2] => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]] => 21
[8,1,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]] => 56
[1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]] => 84
[4,3,2,1,8,7,6,5] => [5,6,7,8,1,2,3,4] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 64
[3,4,2,1,7,8,6,5] => [6,5,7,8,2,1,3,4] => [[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 66
[2,4,3,1,7,6,8,5] => [7,5,6,8,2,3,1,4] => [[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 70
[3,2,4,1,6,8,7,5] => [6,7,5,8,3,1,2,4] => [[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 70
[2,3,4,1,6,7,8,5] => [7,6,5,8,3,2,1,4] => [[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 72
[3,2,1,4,5,8,7,6] => [6,7,8,5,4,1,2,3] => [[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0]] => 76
[2,3,1,4,5,7,8,6] => [7,6,8,5,4,2,1,3] => [[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0]] => 78
[2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => [[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]] => 80
[2,1,3,4,5,6,8,7] => [7,8,6,5,4,3,1,2] => [[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]] => 82
[1,4,3,2,7,6,5,8] => [8,5,6,7,2,3,4,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0]] => 76
[1,3,4,2,6,7,5,8] => [8,6,5,7,3,2,4,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0]] => 78
[1,3,2,4,5,7,6,8] => [8,6,7,5,4,2,3,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0]] => 82
[1,2,4,3,6,5,7,8] => [8,7,5,6,3,4,2,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]] => 82
[4,2,3,1,8,6,7,5] => [5,7,6,8,1,3,2,4] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 66
[2,4,1,3,7,5,8,6] => [7,5,8,6,2,4,1,3] => [[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0]] => 74
[2,4,5,6,7,1,8,3] => [7,5,4,3,2,8,1,6] => [[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 50
[2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => [[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]] => 74
[2,5,1,7,3,4,8,6] => [7,4,8,2,6,5,1,3] => [[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0]] => 66
[2,3,5,6,1,7,8,4] => [7,6,4,3,8,2,1,5] => [[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 62
[2,6,7,1,3,4,8,5] => [7,3,2,8,6,5,1,4] => [[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 54
[3,1,4,2,6,8,5,7] => [6,8,5,7,3,1,4,2] => [[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0]] => 74
[3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => [[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]] => 68
[3,1,5,6,2,8,4,7] => [6,8,4,3,7,1,5,2] => [[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0]] => 66
[3,5,1,7,2,8,4,6] => [6,4,8,2,7,1,5,3] => [[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0]] => 58
[1,3,5,6,2,7,4,8] => [8,6,4,3,7,2,5,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0]] => 70
[3,6,7,1,2,8,4,5] => [6,3,2,8,7,1,5,4] => [[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]] => 46
[3,1,2,4,5,8,6,7] => [6,8,7,5,4,1,3,2] => [[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]] => 78
[4,1,5,6,8,2,3,7] => [5,8,4,3,1,7,6,2] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0]] => 54
[4,5,1,7,8,2,3,6] => [5,4,8,2,1,7,6,3] => [[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0]] => 46
[1,4,5,6,7,2,3,8] => [8,5,4,3,2,7,6,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0]] => 60
[4,6,7,1,8,2,3,5] => [5,3,2,8,1,7,6,4] => [[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0]] => 34
[1,4,2,3,7,5,6,8] => [8,5,7,6,2,4,3,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0]] => 78
[4,1,2,3,8,5,6,7] => [5,8,7,6,1,4,3,2] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]] => 72
[1,2,5,6,3,4,7,8] => [8,7,4,3,6,5,2,1] => [[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0]] => 76
[1,5,2,7,3,4,6,8] => [8,4,7,2,6,5,3,1] => [[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0]] => 70
[5,1,2,8,3,4,6,7] => [4,8,7,1,6,5,3,2] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0]] => 62
[1,6,7,2,3,4,5,8] => [8,3,2,7,6,5,4,1] => [[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0]] => 60
[6,1,8,2,3,4,5,7] => [3,8,1,7,6,5,4,2] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0]] => 50
[7,8,4,3,6,5,1,2] => [2,1,5,6,3,4,8,7] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 10
[5,3,2,8,1,7,6,4] => [4,6,7,1,8,2,3,5] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 50
[6,4,8,2,7,1,5,3] => [3,5,1,7,2,8,4,6] => [[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0]] => 26
[6,5,8,7,2,1,4,3] => [3,4,1,2,7,8,5,6] => [[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0]] => 16
[6,3,8,1,2,7,4,5] => [3,6,1,8,7,2,5,4] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]] => 40
[7,8,4,1,6,2,3,5] => [2,1,5,8,3,7,6,4] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0]] => 22
[9,1,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => [[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0]] => 84
[2,3,4,5,6,7,8,9,1] => [8,7,6,5,4,3,2,1,9] => [[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]] => 84
[4,6,7,3,8,5,1,2] => [5,3,2,6,1,4,8,7] => [[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 22
[3,5,2,7,1,8,6,4] => [6,4,7,2,8,1,3,5] => [[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 54
[4,6,7,2,8,1,5,3] => [5,3,2,7,1,8,4,6] => [[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0]] => 30
[5,6,7,8,2,1,4,3] => [4,3,2,1,7,8,5,6] => [[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0]] => 18
[6,5,8,7,3,4,1,2] => [3,4,1,2,6,5,8,7] => [[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 10
[3,6,7,4,5,8,1,2] => [6,3,2,5,4,1,8,7] => [[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 28
[2,6,7,4,5,1,8,3] => [7,3,2,5,4,8,1,6] => [[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 42
[1,6,7,4,5,2,3,8] => [8,3,2,5,4,7,6,1] => [[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0]] => 52
[1,5,4,7,6,2,3,8] => [8,4,5,2,3,7,6,1] => [[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0]] => 58
[2,5,4,7,6,1,8,3] => [7,4,5,2,3,8,1,6] => [[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 48
[3,5,4,7,6,8,1,2] => [6,4,5,2,3,1,8,7] => [[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 34
[4,5,3,7,8,6,1,2] => [5,4,6,2,1,3,8,7] => [[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 30
[5,4,3,8,7,6,1,2] => [4,5,6,1,2,3,8,7] => [[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 28
[6,4,8,3,7,5,1,2] => [3,5,1,6,2,4,8,7] => [[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 18
[6,3,8,4,5,7,1,2] => [3,6,1,5,4,2,8,7] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 22
[5,3,4,8,6,7,1,2] => [4,6,5,1,3,2,8,7] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 30
[4,3,5,6,8,7,1,2] => [5,6,4,3,1,2,8,7] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]] => 34
[3,2,5,6,1,8,7,4] => [6,7,4,3,8,1,2,5] => [[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 60
[4,2,5,6,8,1,7,3] => [5,7,4,3,1,8,2,6] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 46
[5,2,4,8,6,1,7,3] => [4,7,5,1,3,8,2,6] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 42
[6,2,8,4,5,1,7,3] => [3,7,1,5,4,8,2,6] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 34
[7,8,2,4,5,1,6,3] => [2,1,7,5,4,8,3,6] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 22
[7,8,1,4,5,2,3,6] => [2,1,8,5,4,7,6,3] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0]] => 28
[6,1,8,4,5,2,3,7] => [3,8,1,5,4,7,6,2] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0]] => 42
[5,1,4,8,6,2,3,7] => [4,8,5,1,3,7,6,2] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0]] => 50
[4,1,3,2,8,6,5,7] => [5,8,6,7,1,3,4,2] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0]] => 70
[5,1,3,8,2,6,4,7] => [4,8,6,1,7,3,5,2] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0]] => 58
[6,1,8,3,2,5,4,7] => [3,8,1,6,7,4,5,2] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0]] => 48
[7,8,1,3,2,5,4,6] => [2,1,8,6,7,4,5,3] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0]] => 34
[7,8,2,3,1,5,6,4] => [2,1,7,6,8,4,3,5] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 30
[6,2,8,3,1,5,7,4] => [3,7,1,6,8,4,2,5] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 42
[5,2,3,8,1,6,7,4] => [4,7,6,1,8,3,2,5] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 52
[6,3,8,2,1,7,5,4] => [3,6,1,7,8,2,4,5] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0]] => 38
[7,8,3,2,1,6,5,4] => [2,1,6,7,8,3,4,5] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0]] => 28
[7,8,4,2,6,1,5,3] => [2,1,5,7,3,8,4,6] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0]] => 18
[5,4,2,8,7,1,6,3] => [4,5,7,1,2,8,3,6] => [[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 38
[4,5,2,7,8,1,6,3] => [5,4,7,2,1,8,3,6] => [[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0]] => 40
[2,5,3,7,1,6,8,4] => [7,4,6,2,8,3,1,5] => [[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 58
[1,5,3,7,2,6,4,8] => [8,4,6,2,7,3,5,1] => [[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0]] => 66
[1,6,7,3,2,5,4,8] => [8,3,2,6,7,4,5,1] => [[0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0]] => 58
[2,6,7,3,1,5,8,4] => [7,3,2,6,8,4,1,5] => [[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0]] => 50
[3,6,7,2,1,8,5,4] => [6,3,2,7,8,1,4,5] => [[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0]] => 44
[7,8,5,6,2,1,4,3] => [2,1,4,3,7,8,5,6] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0]] => 10
[6,5,8,7,1,2,3,4] => [3,4,1,2,8,7,6,5] => [[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0]] => 18
[5,4,1,8,7,2,3,6] => [4,5,8,1,2,7,6,3] => [[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0]] => 44
[6,4,8,1,7,2,3,5] => [3,5,1,8,2,7,6,4] => [[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0]] => 30
[7,8,3,1,2,6,4,5] => [2,1,6,8,7,3,5,4] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0]] => 30
[5,3,1,8,2,7,4,6] => [4,6,8,1,7,2,5,3] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0]] => 54
[4,3,1,2,8,7,5,6] => [5,6,8,7,1,2,4,3] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,0]] => 66
[4,2,1,3,8,5,7,6] => [5,7,8,6,1,4,2,3] => [[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0]] => 70
[5,2,1,8,3,4,7,6] => [4,7,8,1,6,5,2,3] => [[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0]] => 60
[6,2,8,1,3,4,7,5] => [3,7,1,8,6,5,2,4] => [[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 46
[7,8,2,1,3,4,6,5] => [2,1,7,8,6,5,3,4] => [[0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]] => 34
[2,3,4,5,6,7,8,9,10,1] => [9,8,7,6,5,4,3,2,1,10] => [[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]] => 120
[8,7,6,5,4,3,2,9,1] => [2,3,4,5,6,7,8,1,9] => [[0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]] => 28
[9,8,7,6,5,4,3,2,10,1] => [2,3,4,5,6,7,8,9,1,10] => [[0,0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]] => 36
[10,1,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => [[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0]] => 120
[11,1,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => [[1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0]] => 165
[2,3,4,5,6,7,8,9,10,11,1] => [10,9,8,7,6,5,4,3,2,1,11] => [[0,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0],[1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]] => 165
[9,7,6,5,4,3,2,1,8] => [1,3,4,5,6,7,8,9,2] => [[1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0]] => 28
[10,8,7,6,5,4,3,2,1,9] => [1,3,4,5,6,7,8,9,10,2] => [[1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0]] => 36
[11,9,8,7,6,5,4,3,2,1,10] => [1,3,4,5,6,7,8,9,10,11,2] => [[1,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1,0]] => 45
[10,9,8,7,6,5,4,3,2,11,1] => [2,3,4,5,6,7,8,9,10,1,11] => [[0,0,0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]] => 45
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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
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 2\ q^{3} + q^{4}$
$F_{4} = 1 + 3\ q + q^{2} + 4\ q^{3} + 2\ q^{4} + 2\ q^{5} + 2\ q^{6} + 4\ q^{7} + q^{8} + 3\ q^{9} + q^{10}$
$F_{5} = 1 + 4\ q + 3\ q^{2} + 6\ q^{3} + 7\ q^{4} + 6\ q^{5} + 4\ q^{6} + 10\ q^{7} + 6\ q^{8} + 10\ q^{9} + 6\ q^{10} + 10\ q^{11} + 6\ q^{12} + 10\ q^{13} + 4\ q^{14} + 6\ q^{15} + 7\ q^{16} + 6\ q^{17} + 3\ q^{18} + 4\ q^{19} + q^{20}$
Description
The rank of the alternating sign matrix in the alternating sign matrix poset.
This rank is the sum of the entries of the monotone triangle minus $\binom{n+2}{3}$, which is the smallest sum of the entries in the set of all monotone triangles with bottom row $1\dots n$.
Alternatively, $rank(A)=\frac{1}{2} \sum_{i,j=1}^n (i-j)^2 a_{ij}$, see [3, thm.5.1].
This rank is the sum of the entries of the monotone triangle minus $\binom{n+2}{3}$, which is the smallest sum of the entries in the set of all monotone triangles with bottom row $1\dots n$.
Alternatively, $rank(A)=\frac{1}{2} \sum_{i,j=1}^n (i-j)^2 a_{ij}$, see [3, thm.5.1].
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 $\tau(i) = n+1-\sigma(i)$
Map
to alternating sign matrix
Description
Maps a permutation to its permutation matrix as an alternating sign matrix.
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