Identifier
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 3
[3,2,1] => 2
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 2
[1,3,4,2] => 1
[1,4,2,3] => 3
[1,4,3,2] => 2
[2,1,3,4] => 2
[2,1,4,3] => 3
[2,3,1,4] => 3
[2,3,4,1] => 1
[2,4,1,3] => 4
[2,4,3,1] => 2
[3,1,2,4] => 3
[3,1,4,2] => 4
[3,2,1,4] => 4
[3,2,4,1] => 3
[3,4,1,2] => 5
[3,4,2,1] => 2
[4,1,2,3] => 4
[4,1,3,2] => 5
[4,2,1,3] => 5
[4,2,3,1] => 4
[4,3,1,2] => 6
[4,3,2,1] => 3
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 2
[1,2,4,5,3] => 1
[1,2,5,3,4] => 3
[1,2,5,4,3] => 2
[1,3,2,4,5] => 2
[1,3,2,5,4] => 3
[1,3,4,2,5] => 3
[1,3,4,5,2] => 1
[1,3,5,2,4] => 4
[1,3,5,4,2] => 2
[1,4,2,3,5] => 3
[1,4,2,5,3] => 4
[1,4,3,2,5] => 4
[1,4,3,5,2] => 3
[1,4,5,2,3] => 5
[1,4,5,3,2] => 2
[1,5,2,3,4] => 4
[1,5,2,4,3] => 5
[1,5,3,2,4] => 5
[1,5,3,4,2] => 4
[1,5,4,2,3] => 6
[1,5,4,3,2] => 3
[2,1,3,4,5] => 2
[2,1,3,5,4] => 3
[2,1,4,3,5] => 4
[2,1,4,5,3] => 3
[2,1,5,3,4] => 5
[2,1,5,4,3] => 4
[2,3,1,4,5] => 3
[2,3,1,5,4] => 4
[2,3,4,1,5] => 4
[2,3,4,5,1] => 1
[2,3,5,1,4] => 5
[2,3,5,4,1] => 2
[2,4,1,3,5] => 4
[2,4,1,5,3] => 5
[2,4,3,1,5] => 5
[2,4,3,5,1] => 3
[2,4,5,1,3] => 6
[2,4,5,3,1] => 2
[2,5,1,3,4] => 5
[2,5,1,4,3] => 6
[2,5,3,1,4] => 6
[2,5,3,4,1] => 4
[2,5,4,1,3] => 7
[2,5,4,3,1] => 3
[3,1,2,4,5] => 3
[3,1,2,5,4] => 4
[3,1,4,2,5] => 5
[3,1,4,5,2] => 4
[3,1,5,2,4] => 6
[3,1,5,4,2] => 5
[3,2,1,4,5] => 4
[3,2,1,5,4] => 5
[3,2,4,1,5] => 6
[3,2,4,5,1] => 3
[3,2,5,1,4] => 7
[3,2,5,4,1] => 4
[3,4,1,2,5] => 5
[3,4,1,5,2] => 6
[3,4,2,1,5] => 5
[3,4,2,5,1] => 4
[3,4,5,1,2] => 7
[3,4,5,2,1] => 2
[3,5,1,2,4] => 6
[3,5,1,4,2] => 7
[3,5,2,1,4] => 6
[3,5,2,4,1] => 5
[3,5,4,1,2] => 8
[3,5,4,2,1] => 3
[4,1,2,3,5] => 4
[4,1,2,5,3] => 5
[4,1,3,2,5] => 6
[4,1,3,5,2] => 5
[4,1,5,2,3] => 7
[4,1,5,3,2] => 6
[4,2,1,3,5] => 5
[4,2,1,5,3] => 6
[4,2,3,1,5] => 7
[4,2,3,5,1] => 4
[4,2,5,1,3] => 8
[4,2,5,3,1] => 5
[4,3,1,2,5] => 6
[4,3,1,5,2] => 7
[4,3,2,1,5] => 6
[4,3,2,5,1] => 5
[4,3,5,1,2] => 9
[4,3,5,2,1] => 4
[4,5,1,2,3] => 7
[4,5,1,3,2] => 8
[4,5,2,1,3] => 7
[4,5,2,3,1] => 6
[4,5,3,1,2] => 8
[4,5,3,2,1] => 3
[5,1,2,3,4] => 5
[5,1,2,4,3] => 6
[5,1,3,2,4] => 7
[5,1,3,4,2] => 6
[5,1,4,2,3] => 8
[5,1,4,3,2] => 7
[5,2,1,3,4] => 6
[5,2,1,4,3] => 7
[5,2,3,1,4] => 8
[5,2,3,4,1] => 5
[5,2,4,1,3] => 9
[5,2,4,3,1] => 6
[5,3,1,2,4] => 7
[5,3,1,4,2] => 8
[5,3,2,1,4] => 7
[5,3,2,4,1] => 6
[5,3,4,1,2] => 10
[5,3,4,2,1] => 5
[5,4,1,2,3] => 8
[5,4,1,3,2] => 9
[5,4,2,1,3] => 8
[5,4,2,3,1] => 7
[5,4,3,1,2] => 9
[5,4,3,2,1] => 4
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 2
[1,2,3,5,6,4] => 1
[1,2,3,6,4,5] => 3
[1,2,3,6,5,4] => 2
[1,2,4,3,5,6] => 2
[1,2,4,3,6,5] => 3
[1,2,4,5,3,6] => 3
[1,2,4,5,6,3] => 1
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 2
[1,2,5,3,4,6] => 3
[1,2,5,3,6,4] => 4
[1,2,5,4,3,6] => 4
[1,2,5,4,6,3] => 3
[1,2,5,6,3,4] => 5
[1,2,5,6,4,3] => 2
[1,2,6,3,4,5] => 4
[1,2,6,3,5,4] => 5
[1,2,6,4,3,5] => 5
[1,2,6,4,5,3] => 4
[1,2,6,5,3,4] => 6
[1,2,6,5,4,3] => 3
[1,3,2,4,5,6] => 2
[1,3,2,4,6,5] => 3
[1,3,2,5,4,6] => 4
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 5
[1,3,2,6,5,4] => 4
[1,3,4,2,5,6] => 3
[1,3,4,2,6,5] => 4
[1,3,4,5,2,6] => 4
[1,3,4,5,6,2] => 1
[1,3,4,6,2,5] => 5
[1,3,4,6,5,2] => 2
[1,3,5,2,4,6] => 4
[1,3,5,2,6,4] => 5
[1,3,5,4,2,6] => 5
[1,3,5,4,6,2] => 3
[1,3,5,6,2,4] => 6
[1,3,5,6,4,2] => 2
[1,3,6,2,4,5] => 5
[1,3,6,2,5,4] => 6
[1,3,6,4,2,5] => 6
[1,3,6,4,5,2] => 4
[1,3,6,5,2,4] => 7
[1,3,6,5,4,2] => 3
[1,4,2,3,5,6] => 3
[1,4,2,3,6,5] => 4
[1,4,2,5,3,6] => 5
[1,4,2,5,6,3] => 4
[1,4,2,6,3,5] => 6
[1,4,2,6,5,3] => 5
[1,4,3,2,5,6] => 4
[1,4,3,2,6,5] => 5
[1,4,3,5,2,6] => 6
[1,4,3,5,6,2] => 3
[1,4,3,6,2,5] => 7
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 5
[1,4,5,2,6,3] => 6
[1,4,5,3,2,6] => 5
[1,4,5,3,6,2] => 4
[1,4,5,6,2,3] => 7
[1,4,5,6,3,2] => 2
[1,4,6,2,3,5] => 6
[1,4,6,2,5,3] => 7
[1,4,6,3,2,5] => 6
[1,4,6,3,5,2] => 5
[1,4,6,5,2,3] => 8
[1,4,6,5,3,2] => 3
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 5
[1,5,2,4,3,6] => 6
[1,5,2,4,6,3] => 5
[1,5,2,6,3,4] => 7
[1,5,2,6,4,3] => 6
[1,5,3,2,4,6] => 5
[1,5,3,2,6,4] => 6
[1,5,3,4,2,6] => 7
[1,5,3,4,6,2] => 4
[1,5,3,6,2,4] => 8
[1,5,3,6,4,2] => 5
[1,5,4,2,3,6] => 6
[1,5,4,2,6,3] => 7
[1,5,4,3,2,6] => 6
[1,5,4,3,6,2] => 5
[1,5,4,6,2,3] => 9
[1,5,4,6,3,2] => 4
[1,5,6,2,3,4] => 7
[1,5,6,2,4,3] => 8
[1,5,6,3,2,4] => 7
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 8
[1,5,6,4,3,2] => 3
[1,6,2,3,4,5] => 5
[1,6,2,3,5,4] => 6
[1,6,2,4,3,5] => 7
[1,6,2,4,5,3] => 6
[1,6,2,5,3,4] => 8
[1,6,2,5,4,3] => 7
[1,6,3,2,4,5] => 6
[1,6,3,2,5,4] => 7
[1,6,3,4,2,5] => 8
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 9
[1,6,3,5,4,2] => 6
[1,6,4,2,3,5] => 7
[1,6,4,2,5,3] => 8
[1,6,4,3,2,5] => 7
[1,6,4,3,5,2] => 6
[1,6,4,5,2,3] => 10
[1,6,4,5,3,2] => 5
[1,6,5,2,3,4] => 8
[1,6,5,2,4,3] => 9
[1,6,5,3,2,4] => 8
[1,6,5,3,4,2] => 7
[1,6,5,4,2,3] => 9
[1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => 2
[2,1,3,4,6,5] => 3
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 3
[2,1,3,6,4,5] => 5
[2,1,3,6,5,4] => 4
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 5
[2,1,4,5,3,6] => 5
[2,1,4,5,6,3] => 3
[2,1,4,6,3,5] => 6
[2,1,4,6,5,3] => 4
[2,1,5,3,4,6] => 5
[2,1,5,3,6,4] => 6
[2,1,5,4,3,6] => 6
[2,1,5,4,6,3] => 5
[2,1,5,6,3,4] => 7
[2,1,5,6,4,3] => 4
[2,1,6,3,4,5] => 6
[2,1,6,3,5,4] => 7
[2,1,6,4,3,5] => 7
[2,1,6,4,5,3] => 6
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 5
[2,3,1,4,5,6] => 3
[2,3,1,4,6,5] => 4
[2,3,1,5,4,6] => 5
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 6
[2,3,1,6,5,4] => 5
[2,3,4,1,5,6] => 4
[2,3,4,1,6,5] => 5
[2,3,4,5,1,6] => 5
[2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => 6
[2,3,4,6,5,1] => 2
[2,3,5,1,4,6] => 5
[2,3,5,1,6,4] => 6
[2,3,5,4,1,6] => 6
[2,3,5,4,6,1] => 3
[2,3,5,6,1,4] => 7
[2,3,5,6,4,1] => 2
[2,3,6,1,4,5] => 6
[2,3,6,1,5,4] => 7
[2,3,6,4,1,5] => 7
[2,3,6,4,5,1] => 4
[2,3,6,5,1,4] => 8
[2,3,6,5,4,1] => 3
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 5
[2,4,1,5,3,6] => 6
[2,4,1,5,6,3] => 5
[2,4,1,6,3,5] => 7
[2,4,1,6,5,3] => 6
[2,4,3,1,5,6] => 5
[2,4,3,1,6,5] => 6
[2,4,3,5,1,6] => 7
[2,4,3,5,6,1] => 3
[2,4,3,6,1,5] => 8
[2,4,3,6,5,1] => 4
[2,4,5,1,3,6] => 6
[2,4,5,1,6,3] => 7
[2,4,5,3,1,6] => 6
[2,4,5,3,6,1] => 4
[2,4,5,6,1,3] => 8
[2,4,5,6,3,1] => 2
[2,4,6,1,3,5] => 7
[2,4,6,1,5,3] => 8
[2,4,6,3,1,5] => 7
[2,4,6,3,5,1] => 5
[2,4,6,5,1,3] => 9
[2,4,6,5,3,1] => 3
[2,5,1,3,4,6] => 5
[2,5,1,3,6,4] => 6
[2,5,1,4,3,6] => 7
[2,5,1,4,6,3] => 6
[2,5,1,6,3,4] => 8
[2,5,1,6,4,3] => 7
[2,5,3,1,4,6] => 6
[2,5,3,1,6,4] => 7
[2,5,3,4,1,6] => 8
[2,5,3,4,6,1] => 4
[2,5,3,6,1,4] => 9
[2,5,3,6,4,1] => 5
[2,5,4,1,3,6] => 7
[2,5,4,1,6,3] => 8
[2,5,4,3,1,6] => 7
[2,5,4,3,6,1] => 5
[2,5,4,6,1,3] => 10
[2,5,4,6,3,1] => 4
[2,5,6,1,3,4] => 8
[2,5,6,1,4,3] => 9
[2,5,6,3,1,4] => 8
[2,5,6,3,4,1] => 6
[2,5,6,4,1,3] => 9
[2,5,6,4,3,1] => 3
[2,6,1,3,4,5] => 6
[2,6,1,3,5,4] => 7
[2,6,1,4,3,5] => 8
[2,6,1,4,5,3] => 7
[2,6,1,5,3,4] => 9
[2,6,1,5,4,3] => 8
[2,6,3,1,4,5] => 7
[2,6,3,1,5,4] => 8
[2,6,3,4,1,5] => 9
[2,6,3,4,5,1] => 5
[2,6,3,5,1,4] => 10
[2,6,3,5,4,1] => 6
[2,6,4,1,3,5] => 8
[2,6,4,1,5,3] => 9
[2,6,4,3,1,5] => 8
[2,6,4,3,5,1] => 6
[2,6,4,5,1,3] => 11
[2,6,4,5,3,1] => 5
[2,6,5,1,3,4] => 9
[2,6,5,1,4,3] => 10
[2,6,5,3,1,4] => 9
[2,6,5,3,4,1] => 7
[2,6,5,4,1,3] => 10
[2,6,5,4,3,1] => 4
[3,1,2,4,5,6] => 3
[3,1,2,4,6,5] => 4
[3,1,2,5,4,6] => 5
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 6
[3,1,2,6,5,4] => 5
[3,1,4,2,5,6] => 5
[3,1,4,2,6,5] => 6
[3,1,4,5,2,6] => 6
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 7
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 6
[3,1,5,2,6,4] => 7
[3,1,5,4,2,6] => 7
[3,1,5,4,6,2] => 6
[3,1,5,6,2,4] => 8
[3,1,5,6,4,2] => 5
[3,1,6,2,4,5] => 7
[3,1,6,2,5,4] => 8
[3,1,6,4,2,5] => 8
[3,1,6,4,5,2] => 7
[3,1,6,5,2,4] => 9
[3,1,6,5,4,2] => 6
[3,2,1,4,5,6] => 4
[3,2,1,4,6,5] => 5
[3,2,1,5,4,6] => 6
[3,2,1,5,6,4] => 5
[3,2,1,6,4,5] => 7
[3,2,1,6,5,4] => 6
[3,2,4,1,5,6] => 6
[3,2,4,1,6,5] => 7
[3,2,4,5,1,6] => 7
[3,2,4,5,6,1] => 3
[3,2,4,6,1,5] => 8
[3,2,4,6,5,1] => 4
[3,2,5,1,4,6] => 7
[3,2,5,1,6,4] => 8
[3,2,5,4,1,6] => 8
[3,2,5,4,6,1] => 5
[3,2,5,6,1,4] => 9
[3,2,5,6,4,1] => 4
[3,2,6,1,4,5] => 8
[3,2,6,1,5,4] => 9
[3,2,6,4,1,5] => 9
[3,2,6,4,5,1] => 6
[3,2,6,5,1,4] => 10
[3,2,6,5,4,1] => 5
[3,4,1,2,5,6] => 5
[3,4,1,2,6,5] => 6
[3,4,1,5,2,6] => 7
[3,4,1,5,6,2] => 6
[3,4,1,6,2,5] => 8
[3,4,1,6,5,2] => 7
[3,4,2,1,5,6] => 5
[3,4,2,1,6,5] => 6
[3,4,2,5,1,6] => 8
[3,4,2,5,6,1] => 4
[3,4,2,6,1,5] => 9
[3,4,2,6,5,1] => 5
[3,4,5,1,2,6] => 7
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 6
[3,4,5,2,6,1] => 5
[3,4,5,6,1,2] => 9
[3,4,5,6,2,1] => 2
[3,4,6,1,2,5] => 8
[3,4,6,1,5,2] => 9
[3,4,6,2,1,5] => 7
[3,4,6,2,5,1] => 6
[3,4,6,5,1,2] => 10
[3,4,6,5,2,1] => 3
[3,5,1,2,4,6] => 6
[3,5,1,2,6,4] => 7
[3,5,1,4,2,6] => 8
[3,5,1,4,6,2] => 7
[3,5,1,6,2,4] => 9
[3,5,1,6,4,2] => 8
[3,5,2,1,4,6] => 6
[3,5,2,1,6,4] => 7
[3,5,2,4,1,6] => 9
[3,5,2,4,6,1] => 5
[3,5,2,6,1,4] => 10
[3,5,2,6,4,1] => 6
[3,5,4,1,2,6] => 8
[3,5,4,1,6,2] => 9
[3,5,4,2,1,6] => 7
[3,5,4,2,6,1] => 6
[3,5,4,6,1,2] => 11
[3,5,4,6,2,1] => 4
[3,5,6,1,2,4] => 9
[3,5,6,1,4,2] => 10
[3,5,6,2,1,4] => 8
[3,5,6,2,4,1] => 7
[3,5,6,4,1,2] => 10
[3,5,6,4,2,1] => 3
[3,6,1,2,4,5] => 7
[3,6,1,2,5,4] => 8
[3,6,1,4,2,5] => 9
[3,6,1,4,5,2] => 8
[3,6,1,5,2,4] => 10
[3,6,1,5,4,2] => 9
[3,6,2,1,4,5] => 7
[3,6,2,1,5,4] => 8
[3,6,2,4,1,5] => 10
[3,6,2,4,5,1] => 6
[3,6,2,5,1,4] => 11
[3,6,2,5,4,1] => 7
[3,6,4,1,2,5] => 9
[3,6,4,1,5,2] => 10
[3,6,4,2,1,5] => 8
[3,6,4,2,5,1] => 7
[3,6,4,5,1,2] => 12
[3,6,4,5,2,1] => 5
[3,6,5,1,2,4] => 10
[3,6,5,1,4,2] => 11
[3,6,5,2,1,4] => 9
[3,6,5,2,4,1] => 8
[3,6,5,4,1,2] => 11
[3,6,5,4,2,1] => 4
[4,1,2,3,5,6] => 4
[4,1,2,3,6,5] => 5
[4,1,2,5,3,6] => 6
[4,1,2,5,6,3] => 5
[4,1,2,6,3,5] => 7
[4,1,2,6,5,3] => 6
[4,1,3,2,5,6] => 6
[4,1,3,2,6,5] => 7
[4,1,3,5,2,6] => 7
[4,1,3,5,6,2] => 5
[4,1,3,6,2,5] => 8
[4,1,3,6,5,2] => 6
[4,1,5,2,3,6] => 7
[4,1,5,2,6,3] => 8
[4,1,5,3,2,6] => 8
[4,1,5,3,6,2] => 7
[4,1,5,6,2,3] => 9
[4,1,5,6,3,2] => 6
[4,1,6,2,3,5] => 8
[4,1,6,2,5,3] => 9
[4,1,6,3,2,5] => 9
[4,1,6,3,5,2] => 8
[4,1,6,5,2,3] => 10
[4,1,6,5,3,2] => 7
[4,2,1,3,5,6] => 5
[4,2,1,3,6,5] => 6
[4,2,1,5,3,6] => 7
[4,2,1,5,6,3] => 6
[4,2,1,6,3,5] => 8
[4,2,1,6,5,3] => 7
[4,2,3,1,5,6] => 7
[4,2,3,1,6,5] => 8
[4,2,3,5,1,6] => 8
[4,2,3,5,6,1] => 4
[4,2,3,6,1,5] => 9
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 8
[4,2,5,1,6,3] => 9
[4,2,5,3,1,6] => 9
[4,2,5,3,6,1] => 6
[4,2,5,6,1,3] => 10
[4,2,5,6,3,1] => 5
[4,2,6,1,3,5] => 9
[4,2,6,1,5,3] => 10
[4,2,6,3,1,5] => 10
[4,2,6,3,5,1] => 7
[4,2,6,5,1,3] => 11
[4,2,6,5,3,1] => 6
[4,3,1,2,5,6] => 6
[4,3,1,2,6,5] => 7
[4,3,1,5,2,6] => 8
[4,3,1,5,6,2] => 7
[4,3,1,6,2,5] => 9
[4,3,1,6,5,2] => 8
[4,3,2,1,5,6] => 6
[4,3,2,1,6,5] => 7
[4,3,2,5,1,6] => 9
[4,3,2,5,6,1] => 5
[4,3,2,6,1,5] => 10
[4,3,2,6,5,1] => 6
[4,3,5,1,2,6] => 9
[4,3,5,1,6,2] => 10
[4,3,5,2,1,6] => 8
[4,3,5,2,6,1] => 7
[4,3,5,6,1,2] => 11
[4,3,5,6,2,1] => 4
[4,3,6,1,2,5] => 10
[4,3,6,1,5,2] => 11
[4,3,6,2,1,5] => 9
[4,3,6,2,5,1] => 8
[4,3,6,5,1,2] => 12
[4,3,6,5,2,1] => 5
[4,5,1,2,3,6] => 7
[4,5,1,2,6,3] => 8
[4,5,1,3,2,6] => 9
[4,5,1,3,6,2] => 8
[4,5,1,6,2,3] => 10
[4,5,1,6,3,2] => 9
[4,5,2,1,3,6] => 7
[4,5,2,1,6,3] => 8
[4,5,2,3,1,6] => 10
[4,5,2,3,6,1] => 6
[4,5,2,6,1,3] => 11
[4,5,2,6,3,1] => 7
[4,5,3,1,2,6] => 8
[4,5,3,1,6,2] => 9
[4,5,3,2,1,6] => 7
[4,5,3,2,6,1] => 6
[4,5,3,6,1,2] => 12
[4,5,3,6,2,1] => 5
[4,5,6,1,2,3] => 10
[4,5,6,1,3,2] => 11
[4,5,6,2,1,3] => 9
[4,5,6,2,3,1] => 8
[4,5,6,3,1,2] => 10
[4,5,6,3,2,1] => 3
[4,6,1,2,3,5] => 8
[4,6,1,2,5,3] => 9
[4,6,1,3,2,5] => 10
[4,6,1,3,5,2] => 9
[4,6,1,5,2,3] => 11
[4,6,1,5,3,2] => 10
[4,6,2,1,3,5] => 8
[4,6,2,1,5,3] => 9
[4,6,2,3,1,5] => 11
[4,6,2,3,5,1] => 7
[4,6,2,5,1,3] => 12
[4,6,2,5,3,1] => 8
[4,6,3,1,2,5] => 9
[4,6,3,1,5,2] => 10
[4,6,3,2,1,5] => 8
[4,6,3,2,5,1] => 7
[4,6,3,5,1,2] => 13
[4,6,3,5,2,1] => 6
[4,6,5,1,2,3] => 11
[4,6,5,1,3,2] => 12
[4,6,5,2,1,3] => 10
[4,6,5,2,3,1] => 9
[4,6,5,3,1,2] => 11
[4,6,5,3,2,1] => 4
[5,1,2,3,4,6] => 5
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 7
[5,1,2,4,6,3] => 6
[5,1,2,6,3,4] => 8
[5,1,2,6,4,3] => 7
[5,1,3,2,4,6] => 7
[5,1,3,2,6,4] => 8
[5,1,3,4,2,6] => 8
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 9
[5,1,3,6,4,2] => 7
[5,1,4,2,3,6] => 8
[5,1,4,2,6,3] => 9
[5,1,4,3,2,6] => 9
[5,1,4,3,6,2] => 8
[5,1,4,6,2,3] => 10
[5,1,4,6,3,2] => 7
[5,1,6,2,3,4] => 9
[5,1,6,2,4,3] => 10
[5,1,6,3,2,4] => 10
[5,1,6,3,4,2] => 9
[5,1,6,4,2,3] => 11
[5,1,6,4,3,2] => 8
[5,2,1,3,4,6] => 6
[5,2,1,3,6,4] => 7
[5,2,1,4,3,6] => 8
[5,2,1,4,6,3] => 7
[5,2,1,6,3,4] => 9
[5,2,1,6,4,3] => 8
[5,2,3,1,4,6] => 8
[5,2,3,1,6,4] => 9
[5,2,3,4,1,6] => 9
[5,2,3,4,6,1] => 5
[5,2,3,6,1,4] => 10
[5,2,3,6,4,1] => 6
[5,2,4,1,3,6] => 9
[5,2,4,1,6,3] => 10
[5,2,4,3,1,6] => 10
[5,2,4,3,6,1] => 7
[5,2,4,6,1,3] => 11
[5,2,4,6,3,1] => 6
[5,2,6,1,3,4] => 10
[5,2,6,1,4,3] => 11
[5,2,6,3,1,4] => 11
[5,2,6,3,4,1] => 8
[5,2,6,4,1,3] => 12
[5,2,6,4,3,1] => 7
[5,3,1,2,4,6] => 7
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 9
[5,3,1,4,6,2] => 8
[5,3,1,6,2,4] => 10
[5,3,1,6,4,2] => 9
[5,3,2,1,4,6] => 7
[5,3,2,1,6,4] => 8
[5,3,2,4,1,6] => 10
[5,3,2,4,6,1] => 6
[5,3,2,6,1,4] => 11
[5,3,2,6,4,1] => 7
[5,3,4,1,2,6] => 10
[5,3,4,1,6,2] => 11
[5,3,4,2,1,6] => 9
[5,3,4,2,6,1] => 8
[5,3,4,6,1,2] => 12
[5,3,4,6,2,1] => 5
[5,3,6,1,2,4] => 11
[5,3,6,1,4,2] => 12
[5,3,6,2,1,4] => 10
[5,3,6,2,4,1] => 9
[5,3,6,4,1,2] => 13
[5,3,6,4,2,1] => 6
[5,4,1,2,3,6] => 8
[5,4,1,2,6,3] => 9
[5,4,1,3,2,6] => 10
[5,4,1,3,6,2] => 9
[5,4,1,6,2,3] => 11
[5,4,1,6,3,2] => 10
[5,4,2,1,3,6] => 8
[5,4,2,1,6,3] => 9
[5,4,2,3,1,6] => 11
[5,4,2,3,6,1] => 7
[5,4,2,6,1,3] => 12
[5,4,2,6,3,1] => 8
[5,4,3,1,2,6] => 9
[5,4,3,1,6,2] => 10
[5,4,3,2,1,6] => 8
[5,4,3,2,6,1] => 7
[5,4,3,6,1,2] => 13
[5,4,3,6,2,1] => 6
[5,4,6,1,2,3] => 12
[5,4,6,1,3,2] => 13
[5,4,6,2,1,3] => 11
[5,4,6,2,3,1] => 10
[5,4,6,3,1,2] => 12
[5,4,6,3,2,1] => 5
[5,6,1,2,3,4] => 9
[5,6,1,2,4,3] => 10
[5,6,1,3,2,4] => 11
[5,6,1,3,4,2] => 10
[5,6,1,4,2,3] => 12
[5,6,1,4,3,2] => 11
[5,6,2,1,3,4] => 9
[5,6,2,1,4,3] => 10
[5,6,2,3,1,4] => 12
[5,6,2,3,4,1] => 8
[5,6,2,4,1,3] => 13
[5,6,2,4,3,1] => 9
[5,6,3,1,2,4] => 10
[5,6,3,1,4,2] => 11
[5,6,3,2,1,4] => 9
[5,6,3,2,4,1] => 8
[5,6,3,4,1,2] => 14
[5,6,3,4,2,1] => 7
[5,6,4,1,2,3] => 11
[5,6,4,1,3,2] => 12
[5,6,4,2,1,3] => 10
[5,6,4,2,3,1] => 9
[5,6,4,3,1,2] => 11
[5,6,4,3,2,1] => 4
[6,1,2,3,4,5] => 6
[6,1,2,3,5,4] => 7
[6,1,2,4,3,5] => 8
[6,1,2,4,5,3] => 7
[6,1,2,5,3,4] => 9
[6,1,2,5,4,3] => 8
[6,1,3,2,4,5] => 8
[6,1,3,2,5,4] => 9
[6,1,3,4,2,5] => 9
[6,1,3,4,5,2] => 7
[6,1,3,5,2,4] => 10
[6,1,3,5,4,2] => 8
[6,1,4,2,3,5] => 9
[6,1,4,2,5,3] => 10
[6,1,4,3,2,5] => 10
[6,1,4,3,5,2] => 9
[6,1,4,5,2,3] => 11
[6,1,4,5,3,2] => 8
[6,1,5,2,3,4] => 10
[6,1,5,2,4,3] => 11
[6,1,5,3,2,4] => 11
[6,1,5,3,4,2] => 10
[6,1,5,4,2,3] => 12
[6,1,5,4,3,2] => 9
[6,2,1,3,4,5] => 7
[6,2,1,3,5,4] => 8
[6,2,1,4,3,5] => 9
[6,2,1,4,5,3] => 8
[6,2,1,5,3,4] => 10
[6,2,1,5,4,3] => 9
[6,2,3,1,4,5] => 9
[6,2,3,1,5,4] => 10
[6,2,3,4,1,5] => 10
[6,2,3,4,5,1] => 6
[6,2,3,5,1,4] => 11
[6,2,3,5,4,1] => 7
[6,2,4,1,3,5] => 10
[6,2,4,1,5,3] => 11
[6,2,4,3,1,5] => 11
[6,2,4,3,5,1] => 8
[6,2,4,5,1,3] => 12
[6,2,4,5,3,1] => 7
[6,2,5,1,3,4] => 11
[6,2,5,1,4,3] => 12
[6,2,5,3,1,4] => 12
[6,2,5,3,4,1] => 9
[6,2,5,4,1,3] => 13
[6,2,5,4,3,1] => 8
[6,3,1,2,4,5] => 8
[6,3,1,2,5,4] => 9
[6,3,1,4,2,5] => 10
[6,3,1,4,5,2] => 9
[6,3,1,5,2,4] => 11
[6,3,1,5,4,2] => 10
[6,3,2,1,4,5] => 8
[6,3,2,1,5,4] => 9
[6,3,2,4,1,5] => 11
[6,3,2,4,5,1] => 7
[6,3,2,5,1,4] => 12
[6,3,2,5,4,1] => 8
[6,3,4,1,2,5] => 11
[6,3,4,1,5,2] => 12
[6,3,4,2,1,5] => 10
[6,3,4,2,5,1] => 9
[6,3,4,5,1,2] => 13
[6,3,4,5,2,1] => 6
[6,3,5,1,2,4] => 12
[6,3,5,1,4,2] => 13
[6,3,5,2,1,4] => 11
[6,3,5,2,4,1] => 10
[6,3,5,4,1,2] => 14
[6,3,5,4,2,1] => 7
[6,4,1,2,3,5] => 9
[6,4,1,2,5,3] => 10
[6,4,1,3,2,5] => 11
[6,4,1,3,5,2] => 10
[6,4,1,5,2,3] => 12
[6,4,1,5,3,2] => 11
[6,4,2,1,3,5] => 9
[6,4,2,1,5,3] => 10
[6,4,2,3,1,5] => 12
[6,4,2,3,5,1] => 8
[6,4,2,5,1,3] => 13
[6,4,2,5,3,1] => 9
[6,4,3,1,2,5] => 10
[6,4,3,1,5,2] => 11
[6,4,3,2,1,5] => 9
[6,4,3,2,5,1] => 8
[6,4,3,5,1,2] => 14
[6,4,3,5,2,1] => 7
[6,4,5,1,2,3] => 13
[6,4,5,1,3,2] => 14
[6,4,5,2,1,3] => 12
[6,4,5,2,3,1] => 11
[6,4,5,3,1,2] => 13
[6,4,5,3,2,1] => 6
[6,5,1,2,3,4] => 10
[6,5,1,2,4,3] => 11
[6,5,1,3,2,4] => 12
[6,5,1,3,4,2] => 11
[6,5,1,4,2,3] => 13
[6,5,1,4,3,2] => 12
[6,5,2,1,3,4] => 10
[6,5,2,1,4,3] => 11
[6,5,2,3,1,4] => 13
[6,5,2,3,4,1] => 9
[6,5,2,4,1,3] => 14
[6,5,2,4,3,1] => 10
[6,5,3,1,2,4] => 11
[6,5,3,1,4,2] => 12
[6,5,3,2,1,4] => 10
[6,5,3,2,4,1] => 9
[6,5,3,4,1,2] => 15
[6,5,3,4,2,1] => 8
[6,5,4,1,2,3] => 12
[6,5,4,1,3,2] => 13
[6,5,4,2,1,3] => 11
[6,5,4,2,3,1] => 10
[6,5,4,3,1,2] => 12
[6,5,4,3,2,1] => 5
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => 2
[1,2,3,4,6,7,5] => 1
[1,2,3,4,7,5,6] => 3
[1,2,3,4,7,6,5] => 2
[1,2,3,5,4,6,7] => 2
[1,2,3,5,4,7,6] => 3
[1,2,3,5,6,4,7] => 3
[1,2,3,5,6,7,4] => 1
[1,2,3,5,7,4,6] => 4
[1,2,3,5,7,6,4] => 2
[1,2,3,6,4,5,7] => 3
[1,2,3,6,4,7,5] => 4
[1,2,3,6,5,4,7] => 4
[1,2,3,6,5,7,4] => 3
[1,2,3,6,7,4,5] => 5
[1,2,3,6,7,5,4] => 2
[1,2,3,7,4,5,6] => 4
[1,2,3,7,4,6,5] => 5
[1,2,3,7,5,4,6] => 5
[1,2,3,7,5,6,4] => 4
[1,2,3,7,6,4,5] => 6
[1,2,3,7,6,5,4] => 3
[1,2,4,3,5,6,7] => 2
[1,2,4,3,5,7,6] => 3
[1,2,4,3,6,5,7] => 4
[1,2,4,3,6,7,5] => 3
[1,2,4,3,7,5,6] => 5
[1,2,4,3,7,6,5] => 4
[1,2,4,5,3,6,7] => 3
[1,2,4,5,3,7,6] => 4
[1,2,4,5,6,3,7] => 4
[1,2,4,5,6,7,3] => 1
[1,2,4,5,7,3,6] => 5
[1,2,4,5,7,6,3] => 2
[1,2,4,6,3,5,7] => 4
[1,2,4,6,3,7,5] => 5
[1,2,4,6,5,3,7] => 5
[1,2,4,6,5,7,3] => 3
[1,2,4,6,7,3,5] => 6
[1,2,4,6,7,5,3] => 2
[1,2,4,7,3,5,6] => 5
[1,2,4,7,3,6,5] => 6
[1,2,4,7,5,3,6] => 6
[1,2,4,7,5,6,3] => 4
[1,2,4,7,6,3,5] => 7
[1,2,4,7,6,5,3] => 3
[1,2,5,3,4,6,7] => 3
[1,2,5,3,4,7,6] => 4
[1,2,5,3,6,4,7] => 5
[1,2,5,3,6,7,4] => 4
[1,2,5,3,7,4,6] => 6
[1,2,5,3,7,6,4] => 5
[1,2,5,4,3,6,7] => 4
[1,2,5,4,3,7,6] => 5
[1,2,5,4,6,3,7] => 6
[1,2,5,4,6,7,3] => 3
[1,2,5,4,7,3,6] => 7
[1,2,5,4,7,6,3] => 4
[1,2,5,6,3,4,7] => 5
[1,2,5,6,3,7,4] => 6
[1,2,5,6,4,3,7] => 5
[1,2,5,6,4,7,3] => 4
[1,2,5,6,7,3,4] => 7
[1,2,5,6,7,4,3] => 2
[1,2,5,7,3,4,6] => 6
[1,2,5,7,3,6,4] => 7
[1,2,5,7,4,3,6] => 6
[1,2,5,7,4,6,3] => 5
[1,2,5,7,6,3,4] => 8
[1,2,5,7,6,4,3] => 3
[1,2,6,3,4,5,7] => 4
[1,2,6,3,4,7,5] => 5
[1,2,6,3,5,4,7] => 6
[1,2,6,3,5,7,4] => 5
[1,2,6,3,7,4,5] => 7
[1,2,6,3,7,5,4] => 6
[1,2,6,4,3,5,7] => 5
[1,2,6,4,3,7,5] => 6
[1,2,6,4,5,3,7] => 7
[1,2,6,4,5,7,3] => 4
[1,2,6,4,7,3,5] => 8
[1,2,6,4,7,5,3] => 5
[1,2,6,5,3,4,7] => 6
[1,2,6,5,3,7,4] => 7
[1,2,6,5,4,3,7] => 6
[1,2,6,5,4,7,3] => 5
[1,2,6,5,7,3,4] => 9
[1,2,6,5,7,4,3] => 4
[1,2,6,7,3,4,5] => 7
[1,2,6,7,3,5,4] => 8
[1,2,6,7,4,3,5] => 7
[1,2,6,7,4,5,3] => 6
[1,2,6,7,5,3,4] => 8
[1,2,6,7,5,4,3] => 3
[1,2,7,3,4,5,6] => 5
[1,2,7,3,4,6,5] => 6
[1,2,7,3,5,4,6] => 7
[1,2,7,3,5,6,4] => 6
[1,2,7,3,6,4,5] => 8
[1,2,7,3,6,5,4] => 7
[1,2,7,4,3,5,6] => 6
[1,2,7,4,3,6,5] => 7
[1,2,7,4,5,3,6] => 8
[1,2,7,4,5,6,3] => 5
[1,2,7,4,6,3,5] => 9
[1,2,7,4,6,5,3] => 6
[1,2,7,5,3,4,6] => 7
[1,2,7,5,3,6,4] => 8
[1,2,7,5,4,3,6] => 7
[1,2,7,5,4,6,3] => 6
[1,2,7,5,6,3,4] => 10
[1,2,7,5,6,4,3] => 5
[1,2,7,6,3,4,5] => 8
[1,2,7,6,3,5,4] => 9
[1,2,7,6,4,3,5] => 8
[1,2,7,6,4,5,3] => 7
[1,2,7,6,5,3,4] => 9
[1,2,7,6,5,4,3] => 4
[1,3,2,4,5,6,7] => 2
[1,3,2,4,5,7,6] => 3
[1,3,2,4,6,5,7] => 4
[1,3,2,4,6,7,5] => 3
[1,3,2,4,7,5,6] => 5
[1,3,2,4,7,6,5] => 4
[1,3,2,5,4,6,7] => 4
[1,3,2,5,4,7,6] => 5
[1,3,2,5,6,4,7] => 5
[1,3,2,5,6,7,4] => 3
[1,3,2,5,7,4,6] => 6
[1,3,2,5,7,6,4] => 4
[1,3,2,6,4,5,7] => 5
[1,3,2,6,4,7,5] => 6
[1,3,2,6,5,4,7] => 6
[1,3,2,6,5,7,4] => 5
[1,3,2,6,7,4,5] => 7
[1,3,2,6,7,5,4] => 4
[1,3,2,7,4,5,6] => 6
[1,3,2,7,4,6,5] => 7
[1,3,2,7,5,4,6] => 7
[1,3,2,7,5,6,4] => 6
[1,3,2,7,6,4,5] => 8
[1,3,2,7,6,5,4] => 5
[1,3,4,2,5,6,7] => 3
[1,3,4,2,5,7,6] => 4
[1,3,4,2,6,5,7] => 5
[1,3,4,2,6,7,5] => 4
[1,3,4,2,7,5,6] => 6
[1,3,4,2,7,6,5] => 5
[1,3,4,5,2,6,7] => 4
[1,3,4,5,2,7,6] => 5
[1,3,4,5,6,2,7] => 5
[1,3,4,5,6,7,2] => 1
[1,3,4,5,7,2,6] => 6
[1,3,4,5,7,6,2] => 2
[1,3,4,6,2,5,7] => 5
[1,3,4,6,2,7,5] => 6
[1,3,4,6,5,2,7] => 6
[1,3,4,6,5,7,2] => 3
[1,3,4,6,7,2,5] => 7
[1,3,4,6,7,5,2] => 2
[1,3,4,7,2,5,6] => 6
[1,3,4,7,2,6,5] => 7
[1,3,4,7,5,2,6] => 7
[1,3,4,7,5,6,2] => 4
[1,3,4,7,6,2,5] => 8
[1,3,4,7,6,5,2] => 3
[1,3,5,2,4,6,7] => 4
[1,3,5,2,4,7,6] => 5
[1,3,5,2,6,4,7] => 6
[1,3,5,2,6,7,4] => 5
[1,3,5,2,7,4,6] => 7
[1,3,5,2,7,6,4] => 6
[1,3,5,4,2,6,7] => 5
[1,3,5,4,2,7,6] => 6
[1,3,5,4,6,2,7] => 7
[1,3,5,4,6,7,2] => 3
[1,3,5,4,7,2,6] => 8
[1,3,5,4,7,6,2] => 4
[1,3,5,6,2,4,7] => 6
[1,3,5,6,2,7,4] => 7
[1,3,5,6,4,2,7] => 6
[1,3,5,6,4,7,2] => 4
[1,3,5,6,7,2,4] => 8
[1,3,5,6,7,4,2] => 2
[1,3,5,7,2,4,6] => 7
[1,3,5,7,2,6,4] => 8
[1,3,5,7,4,2,6] => 7
[1,3,5,7,4,6,2] => 5
[1,3,5,7,6,2,4] => 9
[1,3,5,7,6,4,2] => 3
[1,3,6,2,4,5,7] => 5
[1,3,6,2,4,7,5] => 6
[1,3,6,2,5,4,7] => 7
[1,3,6,2,5,7,4] => 6
[1,3,6,2,7,4,5] => 8
[1,3,6,2,7,5,4] => 7
[1,3,6,4,2,5,7] => 6
[1,3,6,4,2,7,5] => 7
[1,3,6,4,5,2,7] => 8
[1,3,6,4,5,7,2] => 4
[1,3,6,4,7,2,5] => 9
[1,3,6,4,7,5,2] => 5
[1,3,6,5,2,4,7] => 7
[1,3,6,5,2,7,4] => 8
[1,3,6,5,4,2,7] => 7
[1,3,6,5,4,7,2] => 5
[1,3,6,5,7,2,4] => 10
[1,3,6,5,7,4,2] => 4
[1,3,6,7,2,4,5] => 8
[1,3,6,7,2,5,4] => 9
[1,3,6,7,4,2,5] => 8
[1,3,6,7,4,5,2] => 6
[1,3,6,7,5,2,4] => 9
[1,3,6,7,5,4,2] => 3
[1,3,7,2,4,5,6] => 6
[1,3,7,2,4,6,5] => 7
[1,3,7,2,5,4,6] => 8
[1,3,7,2,5,6,4] => 7
[1,3,7,2,6,4,5] => 9
[1,3,7,2,6,5,4] => 8
[1,3,7,4,2,5,6] => 7
[1,3,7,4,2,6,5] => 8
[1,3,7,4,5,2,6] => 9
[1,3,7,4,5,6,2] => 5
[1,3,7,4,6,2,5] => 10
[1,3,7,4,6,5,2] => 6
[1,3,7,5,2,4,6] => 8
[1,3,7,5,2,6,4] => 9
[1,3,7,5,4,2,6] => 8
[1,3,7,5,4,6,2] => 6
[1,3,7,5,6,2,4] => 11
[1,3,7,5,6,4,2] => 5
[1,3,7,6,2,4,5] => 9
[1,3,7,6,2,5,4] => 10
[1,3,7,6,4,2,5] => 9
[1,3,7,6,4,5,2] => 7
[1,3,7,6,5,2,4] => 10
[1,3,7,6,5,4,2] => 4
[1,4,2,3,5,6,7] => 3
[1,4,2,3,5,7,6] => 4
[1,4,2,3,6,5,7] => 5
[1,4,2,3,6,7,5] => 4
[1,4,2,3,7,5,6] => 6
[1,4,2,3,7,6,5] => 5
[1,4,2,5,3,6,7] => 5
[1,4,2,5,3,7,6] => 6
[1,4,2,5,6,3,7] => 6
[1,4,2,5,6,7,3] => 4
[1,4,2,5,7,3,6] => 7
[1,4,2,5,7,6,3] => 5
[1,4,2,6,3,5,7] => 6
[1,4,2,6,3,7,5] => 7
[1,4,2,6,5,3,7] => 7
[1,4,2,6,5,7,3] => 6
[1,4,2,6,7,3,5] => 8
[1,4,2,6,7,5,3] => 5
[1,4,2,7,3,5,6] => 7
[1,4,2,7,3,6,5] => 8
[1,4,2,7,5,3,6] => 8
[1,4,2,7,5,6,3] => 7
[1,4,2,7,6,3,5] => 9
[1,4,2,7,6,5,3] => 6
[1,4,3,2,5,6,7] => 4
[1,4,3,2,5,7,6] => 5
[1,4,3,2,6,5,7] => 6
[1,4,3,2,6,7,5] => 5
[1,4,3,2,7,5,6] => 7
[1,4,3,2,7,6,5] => 6
[1,4,3,5,2,6,7] => 6
[1,4,3,5,2,7,6] => 7
[1,4,3,5,6,2,7] => 7
[1,4,3,5,6,7,2] => 3
[1,4,3,5,7,2,6] => 8
[1,4,3,5,7,6,2] => 4
[1,4,3,6,2,5,7] => 7
[1,4,3,6,2,7,5] => 8
[1,4,3,6,5,2,7] => 8
[1,4,3,6,5,7,2] => 5
[1,4,3,6,7,2,5] => 9
[1,4,3,6,7,5,2] => 4
[1,4,3,7,2,5,6] => 8
[1,4,3,7,2,6,5] => 9
[1,4,3,7,5,2,6] => 9
[1,4,3,7,5,6,2] => 6
[1,4,3,7,6,2,5] => 10
[1,4,3,7,6,5,2] => 5
[1,4,5,2,3,6,7] => 5
[1,4,5,2,3,7,6] => 6
[1,4,5,2,6,3,7] => 7
[1,4,5,2,6,7,3] => 6
[1,4,5,2,7,3,6] => 8
[1,4,5,2,7,6,3] => 7
[1,4,5,3,2,6,7] => 5
[1,4,5,3,2,7,6] => 6
[1,4,5,3,6,2,7] => 8
[1,4,5,3,6,7,2] => 4
[1,4,5,3,7,2,6] => 9
[1,4,5,3,7,6,2] => 5
[1,4,5,6,2,3,7] => 7
[1,4,5,6,2,7,3] => 8
[1,4,5,6,3,2,7] => 6
[1,4,5,6,3,7,2] => 5
[1,4,5,6,7,2,3] => 9
[1,4,5,6,7,3,2] => 2
[1,4,5,7,2,3,6] => 8
[1,4,5,7,2,6,3] => 9
[1,4,5,7,3,2,6] => 7
[1,4,5,7,3,6,2] => 6
[1,4,5,7,6,2,3] => 10
[1,4,5,7,6,3,2] => 3
[1,4,6,2,3,5,7] => 6
[1,4,6,2,3,7,5] => 7
[1,4,6,2,5,3,7] => 8
[1,4,6,2,5,7,3] => 7
[1,4,6,2,7,3,5] => 9
[1,4,6,2,7,5,3] => 8
[1,4,6,3,2,5,7] => 6
[1,4,6,3,2,7,5] => 7
[1,4,6,3,5,2,7] => 9
[1,4,6,3,5,7,2] => 5
[1,4,6,3,7,2,5] => 10
[1,4,6,3,7,5,2] => 6
[1,4,6,5,2,3,7] => 8
[1,4,6,5,2,7,3] => 9
[1,4,6,5,3,2,7] => 7
[1,4,6,5,3,7,2] => 6
click to show generating function       
Description
The aid statistic in the sense of Shareshian-Wachs.
This is the number of admissible inversions St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. plus the number of descents St000021The number of descents of a permutation.. This statistic was introduced by John Shareshian and Michelle L. Wachs in [1]. Theorem 4.1 states that the aid statistic together with the descent statistic is Euler-Mahonian.
References
[1] Shareshian, J., Wachs, M. L. $q$-Eulerian polynomials: excedance number and major index MathSciNet:2300004
Code
def statistic(pi):
    return (sum(1 for i,j in pi.inversions()
                if ((j < len(pi) and pi(j) < pi(j+1)) or
                    (i+1 < j and pi(j) > min(pi(k) for k in range(i+1,j)))))
            + pi.number_of_descents())
Created
Jun 27, 2017 at 08:53 by Christian Stump
Updated
Nov 03, 2017 at 00:15 by Martin Rubey