Identifier
Identifier
Values
[1] => 0
[1,2] => 1
[2,1] => 0
[1,2,3] => 2
[1,3,2] => 2
[2,1,3] => 0
[2,3,1] => 2
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 3
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 2
[2,1,3,4] => 1
[2,1,4,3] => 0
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 3
[2,4,3,1] => 2
[3,1,2,4] => 1
[3,1,4,2] => 0
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 3
[3,4,2,1] => 2
[4,1,2,3] => 1
[4,1,3,2] => 0
[4,2,1,3] => 0
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 4
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 4
[1,3,5,2,4] => 4
[1,3,5,4,2] => 4
[1,4,2,3,5] => 4
[1,4,2,5,3] => 4
[1,4,3,2,5] => 2
[1,4,3,5,2] => 4
[1,4,5,2,3] => 4
[1,4,5,3,2] => 4
[1,5,2,3,4] => 4
[1,5,2,4,3] => 4
[1,5,3,2,4] => 2
[1,5,3,4,2] => 4
[1,5,4,2,3] => 2
[1,5,4,3,2] => 2
[2,1,3,4,5] => 2
[2,1,3,5,4] => 2
[2,1,4,3,5] => 0
[2,1,4,5,3] => 2
[2,1,5,3,4] => 0
[2,1,5,4,3] => 0
[2,3,1,4,5] => 4
[2,3,1,5,4] => 4
[2,3,4,1,5] => 4
[2,3,4,5,1] => 4
[2,3,5,1,4] => 4
[2,3,5,4,1] => 4
[2,4,1,3,5] => 4
[2,4,1,5,3] => 4
[2,4,3,1,5] => 2
[2,4,3,5,1] => 4
[2,4,5,1,3] => 4
[2,4,5,3,1] => 4
[2,5,1,3,4] => 4
[2,5,1,4,3] => 4
[2,5,3,1,4] => 2
[2,5,3,4,1] => 4
[2,5,4,1,3] => 2
[2,5,4,3,1] => 2
[3,1,2,4,5] => 2
[3,1,2,5,4] => 2
[3,1,4,2,5] => 0
[3,1,4,5,2] => 2
[3,1,5,2,4] => 0
[3,1,5,4,2] => 0
[3,2,1,4,5] => 0
[3,2,1,5,4] => 0
[3,2,4,1,5] => 0
[3,2,4,5,1] => 2
[3,2,5,1,4] => 0
[3,2,5,4,1] => 0
[3,4,1,2,5] => 4
[3,4,1,5,2] => 4
[3,4,2,1,5] => 2
[3,4,2,5,1] => 4
[3,4,5,1,2] => 4
[3,4,5,2,1] => 4
[3,5,1,2,4] => 4
[3,5,1,4,2] => 4
[3,5,2,1,4] => 2
[3,5,2,4,1] => 4
[3,5,4,1,2] => 2
[3,5,4,2,1] => 2
[4,1,2,3,5] => 2
[4,1,2,5,3] => 2
[4,1,3,2,5] => 0
[4,1,3,5,2] => 2
[4,1,5,2,3] => 0
[4,1,5,3,2] => 0
[4,2,1,3,5] => 0
[4,2,1,5,3] => 0
[4,2,3,1,5] => 0
[4,2,3,5,1] => 2
[4,2,5,1,3] => 0
[4,2,5,3,1] => 0
[4,3,1,2,5] => 0
[4,3,1,5,2] => 0
[4,3,2,1,5] => 0
[4,3,2,5,1] => 0
[4,3,5,1,2] => 0
[4,3,5,2,1] => 0
[4,5,1,2,3] => 4
[4,5,1,3,2] => 4
[4,5,2,1,3] => 2
[4,5,2,3,1] => 4
[4,5,3,1,2] => 2
[4,5,3,2,1] => 2
[5,1,2,3,4] => 2
[5,1,2,4,3] => 2
[5,1,3,2,4] => 0
[5,1,3,4,2] => 2
[5,1,4,2,3] => 0
[5,1,4,3,2] => 0
[5,2,1,3,4] => 0
[5,2,1,4,3] => 0
[5,2,3,1,4] => 0
[5,2,3,4,1] => 2
[5,2,4,1,3] => 0
[5,2,4,3,1] => 0
[5,3,1,2,4] => 0
[5,3,1,4,2] => 0
[5,3,2,1,4] => 0
[5,3,2,4,1] => 0
[5,3,4,1,2] => 0
[5,3,4,2,1] => 0
[5,4,1,2,3] => 0
[5,4,1,3,2] => 0
[5,4,2,1,3] => 0
[5,4,2,3,1] => 0
[5,4,3,1,2] => 0
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 5
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 5
[1,2,3,5,6,4] => 5
[1,2,3,6,4,5] => 5
[1,2,3,6,5,4] => 5
[1,2,4,3,5,6] => 5
[1,2,4,3,6,5] => 5
[1,2,4,5,3,6] => 5
[1,2,4,5,6,3] => 5
[1,2,4,6,3,5] => 5
[1,2,4,6,5,3] => 5
[1,2,5,3,4,6] => 5
[1,2,5,3,6,4] => 5
[1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => 5
[1,2,5,6,3,4] => 5
[1,2,5,6,4,3] => 5
[1,2,6,3,4,5] => 5
[1,2,6,3,5,4] => 5
[1,2,6,4,3,5] => 5
[1,2,6,4,5,3] => 5
[1,2,6,5,3,4] => 5
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 5
[1,3,2,4,6,5] => 5
[1,3,2,5,4,6] => 5
[1,3,2,5,6,4] => 5
[1,3,2,6,4,5] => 5
[1,3,2,6,5,4] => 4
[1,3,4,2,5,6] => 5
[1,3,4,2,6,5] => 5
[1,3,4,5,2,6] => 5
[1,3,4,5,6,2] => 5
[1,3,4,6,2,5] => 5
[1,3,4,6,5,2] => 5
[1,3,5,2,4,6] => 5
[1,3,5,2,6,4] => 5
[1,3,5,4,2,6] => 5
[1,3,5,4,6,2] => 5
[1,3,5,6,2,4] => 5
[1,3,5,6,4,2] => 5
[1,3,6,2,4,5] => 5
[1,3,6,2,5,4] => 5
[1,3,6,4,2,5] => 5
[1,3,6,4,5,2] => 5
[1,3,6,5,2,4] => 5
[1,3,6,5,4,2] => 4
[1,4,2,3,5,6] => 5
[1,4,2,3,6,5] => 5
[1,4,2,5,3,6] => 5
[1,4,2,5,6,3] => 5
[1,4,2,6,3,5] => 5
[1,4,2,6,5,3] => 4
[1,4,3,2,5,6] => 3
[1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => 5
[1,4,3,5,6,2] => 5
[1,4,3,6,2,5] => 5
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 5
[1,4,5,2,6,3] => 5
[1,4,5,3,2,6] => 5
[1,4,5,3,6,2] => 5
[1,4,5,6,2,3] => 5
[1,4,5,6,3,2] => 5
[1,4,6,2,3,5] => 5
[1,4,6,2,5,3] => 5
[1,4,6,3,2,5] => 5
[1,4,6,3,5,2] => 5
[1,4,6,5,2,3] => 5
[1,4,6,5,3,2] => 4
[1,5,2,3,4,6] => 5
[1,5,2,3,6,4] => 5
[1,5,2,4,3,6] => 5
[1,5,2,4,6,3] => 5
[1,5,2,6,3,4] => 5
[1,5,2,6,4,3] => 4
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 2
[1,5,3,4,2,6] => 5
[1,5,3,4,6,2] => 5
[1,5,3,6,2,4] => 5
[1,5,3,6,4,2] => 4
[1,5,4,2,3,6] => 3
[1,5,4,2,6,3] => 2
[1,5,4,3,2,6] => 2
[1,5,4,3,6,2] => 2
[1,5,4,6,2,3] => 5
[1,5,4,6,3,2] => 4
[1,5,6,2,3,4] => 5
[1,5,6,2,4,3] => 5
[1,5,6,3,2,4] => 5
[1,5,6,3,4,2] => 5
[1,5,6,4,2,3] => 5
[1,5,6,4,3,2] => 4
[1,6,2,3,4,5] => 5
[1,6,2,3,5,4] => 5
[1,6,2,4,3,5] => 5
[1,6,2,4,5,3] => 5
[1,6,2,5,3,4] => 5
[1,6,2,5,4,3] => 4
[1,6,3,2,4,5] => 3
[1,6,3,2,5,4] => 2
[1,6,3,4,2,5] => 5
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 5
[1,6,3,5,4,2] => 4
[1,6,4,2,3,5] => 3
[1,6,4,2,5,3] => 2
[1,6,4,3,2,5] => 2
[1,6,4,3,5,2] => 2
[1,6,4,5,2,3] => 5
[1,6,4,5,3,2] => 4
[1,6,5,2,3,4] => 3
[1,6,5,2,4,3] => 2
[1,6,5,3,2,4] => 2
[1,6,5,3,4,2] => 2
[1,6,5,4,2,3] => 2
[1,6,5,4,3,2] => 2
[2,1,3,4,5,6] => 3
[2,1,3,4,6,5] => 3
[2,1,3,5,4,6] => 3
[2,1,3,5,6,4] => 3
[2,1,3,6,4,5] => 3
[2,1,3,6,5,4] => 2
[2,1,4,3,5,6] => 1
[2,1,4,3,6,5] => 0
[2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => 3
[2,1,4,6,3,5] => 3
[2,1,4,6,5,3] => 2
[2,1,5,3,4,6] => 1
[2,1,5,3,6,4] => 0
[2,1,5,4,3,6] => 0
[2,1,5,4,6,3] => 0
[2,1,5,6,3,4] => 3
[2,1,5,6,4,3] => 2
[2,1,6,3,4,5] => 1
[2,1,6,3,5,4] => 0
[2,1,6,4,3,5] => 0
[2,1,6,4,5,3] => 0
[2,1,6,5,3,4] => 0
[2,1,6,5,4,3] => 0
[2,3,1,4,5,6] => 5
[2,3,1,4,6,5] => 5
[2,3,1,5,4,6] => 5
[2,3,1,5,6,4] => 5
[2,3,1,6,4,5] => 5
[2,3,1,6,5,4] => 4
[2,3,4,1,5,6] => 5
[2,3,4,1,6,5] => 5
[2,3,4,5,1,6] => 5
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 5
[2,3,4,6,5,1] => 5
[2,3,5,1,4,6] => 5
[2,3,5,1,6,4] => 5
[2,3,5,4,1,6] => 5
[2,3,5,4,6,1] => 5
[2,3,5,6,1,4] => 5
[2,3,5,6,4,1] => 5
[2,3,6,1,4,5] => 5
[2,3,6,1,5,4] => 5
[2,3,6,4,1,5] => 5
[2,3,6,4,5,1] => 5
[2,3,6,5,1,4] => 5
[2,3,6,5,4,1] => 4
[2,4,1,3,5,6] => 5
[2,4,1,3,6,5] => 5
[2,4,1,5,3,6] => 5
[2,4,1,5,6,3] => 5
[2,4,1,6,3,5] => 5
[2,4,1,6,5,3] => 4
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 5
[2,4,3,5,6,1] => 5
[2,4,3,6,1,5] => 5
[2,4,3,6,5,1] => 4
[2,4,5,1,3,6] => 5
[2,4,5,1,6,3] => 5
[2,4,5,3,1,6] => 5
[2,4,5,3,6,1] => 5
[2,4,5,6,1,3] => 5
[2,4,5,6,3,1] => 5
[2,4,6,1,3,5] => 5
[2,4,6,1,5,3] => 5
[2,4,6,3,1,5] => 5
[2,4,6,3,5,1] => 5
[2,4,6,5,1,3] => 5
[2,4,6,5,3,1] => 4
[2,5,1,3,4,6] => 5
[2,5,1,3,6,4] => 5
[2,5,1,4,3,6] => 5
[2,5,1,4,6,3] => 5
[2,5,1,6,3,4] => 5
[2,5,1,6,4,3] => 4
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 5
[2,5,3,4,6,1] => 5
[2,5,3,6,1,4] => 5
[2,5,3,6,4,1] => 4
[2,5,4,1,3,6] => 3
[2,5,4,1,6,3] => 2
[2,5,4,3,1,6] => 2
[2,5,4,3,6,1] => 2
[2,5,4,6,1,3] => 5
[2,5,4,6,3,1] => 4
[2,5,6,1,3,4] => 5
[2,5,6,1,4,3] => 5
[2,5,6,3,1,4] => 5
[2,5,6,3,4,1] => 5
[2,5,6,4,1,3] => 5
[2,5,6,4,3,1] => 4
[2,6,1,3,4,5] => 5
[2,6,1,3,5,4] => 5
[2,6,1,4,3,5] => 5
[2,6,1,4,5,3] => 5
[2,6,1,5,3,4] => 5
[2,6,1,5,4,3] => 4
[2,6,3,1,4,5] => 3
[2,6,3,1,5,4] => 2
[2,6,3,4,1,5] => 5
[2,6,3,4,5,1] => 5
[2,6,3,5,1,4] => 5
[2,6,3,5,4,1] => 4
[2,6,4,1,3,5] => 3
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 2
[2,6,4,3,5,1] => 2
[2,6,4,5,1,3] => 5
[2,6,4,5,3,1] => 4
[2,6,5,1,3,4] => 3
[2,6,5,1,4,3] => 2
[2,6,5,3,1,4] => 2
[2,6,5,3,4,1] => 2
[2,6,5,4,1,3] => 2
[2,6,5,4,3,1] => 2
[3,1,2,4,5,6] => 3
[3,1,2,4,6,5] => 3
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 3
[3,1,2,6,4,5] => 3
[3,1,2,6,5,4] => 2
[3,1,4,2,5,6] => 1
[3,1,4,2,6,5] => 0
[3,1,4,5,2,6] => 3
[3,1,4,5,6,2] => 3
[3,1,4,6,2,5] => 3
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 1
[3,1,5,2,6,4] => 0
[3,1,5,4,2,6] => 0
[3,1,5,4,6,2] => 0
[3,1,5,6,2,4] => 3
[3,1,5,6,4,2] => 2
[3,1,6,2,4,5] => 1
[3,1,6,2,5,4] => 0
[3,1,6,4,2,5] => 0
[3,1,6,4,5,2] => 0
[3,1,6,5,2,4] => 0
[3,1,6,5,4,2] => 0
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 0
[3,2,1,5,4,6] => 0
[3,2,1,5,6,4] => 0
[3,2,1,6,4,5] => 0
[3,2,1,6,5,4] => 0
[3,2,4,1,5,6] => 1
[3,2,4,1,6,5] => 0
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 3
[3,2,4,6,1,5] => 3
[3,2,4,6,5,1] => 2
[3,2,5,1,4,6] => 1
[3,2,5,1,6,4] => 0
[3,2,5,4,1,6] => 0
[3,2,5,4,6,1] => 0
[3,2,5,6,1,4] => 3
[3,2,5,6,4,1] => 2
[3,2,6,1,4,5] => 1
[3,2,6,1,5,4] => 0
[3,2,6,4,1,5] => 0
[3,2,6,4,5,1] => 0
[3,2,6,5,1,4] => 0
[3,2,6,5,4,1] => 0
[3,4,1,2,5,6] => 5
[3,4,1,2,6,5] => 5
[3,4,1,5,2,6] => 5
[3,4,1,5,6,2] => 5
[3,4,1,6,2,5] => 5
[3,4,1,6,5,2] => 4
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => 5
[3,4,2,5,6,1] => 5
[3,4,2,6,1,5] => 5
[3,4,2,6,5,1] => 4
[3,4,5,1,2,6] => 5
[3,4,5,1,6,2] => 5
[3,4,5,2,1,6] => 5
[3,4,5,2,6,1] => 5
[3,4,5,6,1,2] => 5
[3,4,5,6,2,1] => 5
[3,4,6,1,2,5] => 5
[3,4,6,1,5,2] => 5
[3,4,6,2,1,5] => 5
[3,4,6,2,5,1] => 5
[3,4,6,5,1,2] => 5
[3,4,6,5,2,1] => 4
[3,5,1,2,4,6] => 5
[3,5,1,2,6,4] => 5
[3,5,1,4,2,6] => 5
[3,5,1,4,6,2] => 5
[3,5,1,6,2,4] => 5
[3,5,1,6,4,2] => 4
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 5
[3,5,2,4,6,1] => 5
[3,5,2,6,1,4] => 5
[3,5,2,6,4,1] => 4
[3,5,4,1,2,6] => 3
[3,5,4,1,6,2] => 2
[3,5,4,2,1,6] => 2
[3,5,4,2,6,1] => 2
[3,5,4,6,1,2] => 5
[3,5,4,6,2,1] => 4
[3,5,6,1,2,4] => 5
[3,5,6,1,4,2] => 5
[3,5,6,2,1,4] => 5
[3,5,6,2,4,1] => 5
[3,5,6,4,1,2] => 5
[3,5,6,4,2,1] => 4
[3,6,1,2,4,5] => 5
[3,6,1,2,5,4] => 5
[3,6,1,4,2,5] => 5
[3,6,1,4,5,2] => 5
[3,6,1,5,2,4] => 5
[3,6,1,5,4,2] => 4
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 2
[3,6,2,4,1,5] => 5
[3,6,2,4,5,1] => 5
[3,6,2,5,1,4] => 5
[3,6,2,5,4,1] => 4
[3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => 2
[3,6,4,2,1,5] => 2
[3,6,4,2,5,1] => 2
[3,6,4,5,1,2] => 5
[3,6,4,5,2,1] => 4
[3,6,5,1,2,4] => 3
[3,6,5,1,4,2] => 2
[3,6,5,2,1,4] => 2
[3,6,5,2,4,1] => 2
[3,6,5,4,1,2] => 2
[3,6,5,4,2,1] => 2
[4,1,2,3,5,6] => 3
[4,1,2,3,6,5] => 3
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 3
[4,1,2,6,3,5] => 3
[4,1,2,6,5,3] => 2
[4,1,3,2,5,6] => 1
[4,1,3,2,6,5] => 0
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 3
[4,1,3,6,2,5] => 3
[4,1,3,6,5,2] => 2
[4,1,5,2,3,6] => 1
[4,1,5,2,6,3] => 0
[4,1,5,3,2,6] => 0
[4,1,5,3,6,2] => 0
[4,1,5,6,2,3] => 3
[4,1,5,6,3,2] => 2
[4,1,6,2,3,5] => 1
[4,1,6,2,5,3] => 0
[4,1,6,3,2,5] => 0
[4,1,6,3,5,2] => 0
[4,1,6,5,2,3] => 0
[4,1,6,5,3,2] => 0
[4,2,1,3,5,6] => 1
[4,2,1,3,6,5] => 0
[4,2,1,5,3,6] => 0
[4,2,1,5,6,3] => 0
[4,2,1,6,3,5] => 0
[4,2,1,6,5,3] => 0
[4,2,3,1,5,6] => 1
[4,2,3,1,6,5] => 0
[4,2,3,5,1,6] => 3
[4,2,3,5,6,1] => 3
[4,2,3,6,1,5] => 3
[4,2,3,6,5,1] => 2
[4,2,5,1,3,6] => 1
[4,2,5,1,6,3] => 0
[4,2,5,3,1,6] => 0
[4,2,5,3,6,1] => 0
[4,2,5,6,1,3] => 3
[4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => 1
[4,2,6,1,5,3] => 0
[4,2,6,3,1,5] => 0
[4,2,6,3,5,1] => 0
[4,2,6,5,1,3] => 0
[4,2,6,5,3,1] => 0
[4,3,1,2,5,6] => 1
[4,3,1,2,6,5] => 0
[4,3,1,5,2,6] => 0
[4,3,1,5,6,2] => 0
[4,3,1,6,2,5] => 0
[4,3,1,6,5,2] => 0
[4,3,2,1,5,6] => 0
[4,3,2,1,6,5] => 0
[4,3,2,5,1,6] => 0
[4,3,2,5,6,1] => 0
[4,3,2,6,1,5] => 0
[4,3,2,6,5,1] => 0
[4,3,5,1,2,6] => 1
[4,3,5,1,6,2] => 0
[4,3,5,2,1,6] => 0
[4,3,5,2,6,1] => 0
[4,3,5,6,1,2] => 3
[4,3,5,6,2,1] => 2
[4,3,6,1,2,5] => 1
[4,3,6,1,5,2] => 0
[4,3,6,2,1,5] => 0
[4,3,6,2,5,1] => 0
[4,3,6,5,1,2] => 0
[4,3,6,5,2,1] => 0
[4,5,1,2,3,6] => 5
[4,5,1,2,6,3] => 5
[4,5,1,3,2,6] => 5
[4,5,1,3,6,2] => 5
[4,5,1,6,2,3] => 5
[4,5,1,6,3,2] => 4
[4,5,2,1,3,6] => 3
[4,5,2,1,6,3] => 2
[4,5,2,3,1,6] => 5
[4,5,2,3,6,1] => 5
[4,5,2,6,1,3] => 5
[4,5,2,6,3,1] => 4
[4,5,3,1,2,6] => 3
[4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => 2
[4,5,3,2,6,1] => 2
[4,5,3,6,1,2] => 5
[4,5,3,6,2,1] => 4
[4,5,6,1,2,3] => 5
[4,5,6,1,3,2] => 5
[4,5,6,2,1,3] => 5
[4,5,6,2,3,1] => 5
[4,5,6,3,1,2] => 5
[4,5,6,3,2,1] => 4
[4,6,1,2,3,5] => 5
[4,6,1,2,5,3] => 5
[4,6,1,3,2,5] => 5
[4,6,1,3,5,2] => 5
[4,6,1,5,2,3] => 5
[4,6,1,5,3,2] => 4
[4,6,2,1,3,5] => 3
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 5
[4,6,2,3,5,1] => 5
[4,6,2,5,1,3] => 5
[4,6,2,5,3,1] => 4
[4,6,3,1,2,5] => 3
[4,6,3,1,5,2] => 2
[4,6,3,2,1,5] => 2
[4,6,3,2,5,1] => 2
[4,6,3,5,1,2] => 5
[4,6,3,5,2,1] => 4
[4,6,5,1,2,3] => 3
[4,6,5,1,3,2] => 2
[4,6,5,2,1,3] => 2
[4,6,5,2,3,1] => 2
[4,6,5,3,1,2] => 2
[4,6,5,3,2,1] => 2
[5,1,2,3,4,6] => 3
[5,1,2,3,6,4] => 3
[5,1,2,4,3,6] => 3
[5,1,2,4,6,3] => 3
[5,1,2,6,3,4] => 3
[5,1,2,6,4,3] => 2
[5,1,3,2,4,6] => 1
[5,1,3,2,6,4] => 0
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 3
[5,1,3,6,2,4] => 3
[5,1,3,6,4,2] => 2
[5,1,4,2,3,6] => 1
[5,1,4,2,6,3] => 0
[5,1,4,3,2,6] => 0
[5,1,4,3,6,2] => 0
[5,1,4,6,2,3] => 3
[5,1,4,6,3,2] => 2
[5,1,6,2,3,4] => 1
[5,1,6,2,4,3] => 0
[5,1,6,3,2,4] => 0
[5,1,6,3,4,2] => 0
[5,1,6,4,2,3] => 0
[5,1,6,4,3,2] => 0
[5,2,1,3,4,6] => 1
[5,2,1,3,6,4] => 0
[5,2,1,4,3,6] => 0
[5,2,1,4,6,3] => 0
[5,2,1,6,3,4] => 0
[5,2,1,6,4,3] => 0
[5,2,3,1,4,6] => 1
[5,2,3,1,6,4] => 0
[5,2,3,4,1,6] => 3
[5,2,3,4,6,1] => 3
[5,2,3,6,1,4] => 3
[5,2,3,6,4,1] => 2
[5,2,4,1,3,6] => 1
[5,2,4,1,6,3] => 0
[5,2,4,3,1,6] => 0
[5,2,4,3,6,1] => 0
[5,2,4,6,1,3] => 3
[5,2,4,6,3,1] => 2
[5,2,6,1,3,4] => 1
[5,2,6,1,4,3] => 0
[5,2,6,3,1,4] => 0
[5,2,6,3,4,1] => 0
[5,2,6,4,1,3] => 0
[5,2,6,4,3,1] => 0
[5,3,1,2,4,6] => 1
[5,3,1,2,6,4] => 0
[5,3,1,4,2,6] => 0
[5,3,1,4,6,2] => 0
[5,3,1,6,2,4] => 0
[5,3,1,6,4,2] => 0
[5,3,2,1,4,6] => 0
[5,3,2,1,6,4] => 0
[5,3,2,4,1,6] => 0
[5,3,2,4,6,1] => 0
[5,3,2,6,1,4] => 0
[5,3,2,6,4,1] => 0
[5,3,4,1,2,6] => 1
[5,3,4,1,6,2] => 0
[5,3,4,2,1,6] => 0
[5,3,4,2,6,1] => 0
[5,3,4,6,1,2] => 3
[5,3,4,6,2,1] => 2
[5,3,6,1,2,4] => 1
[5,3,6,1,4,2] => 0
[5,3,6,2,1,4] => 0
[5,3,6,2,4,1] => 0
[5,3,6,4,1,2] => 0
[5,3,6,4,2,1] => 0
[5,4,1,2,3,6] => 1
[5,4,1,2,6,3] => 0
[5,4,1,3,2,6] => 0
[5,4,1,3,6,2] => 0
[5,4,1,6,2,3] => 0
[5,4,1,6,3,2] => 0
[5,4,2,1,3,6] => 0
[5,4,2,1,6,3] => 0
[5,4,2,3,1,6] => 0
[5,4,2,3,6,1] => 0
[5,4,2,6,1,3] => 0
[5,4,2,6,3,1] => 0
[5,4,3,1,2,6] => 0
[5,4,3,1,6,2] => 0
[5,4,3,2,1,6] => 0
[5,4,3,2,6,1] => 0
[5,4,3,6,1,2] => 0
[5,4,3,6,2,1] => 0
[5,4,6,1,2,3] => 1
[5,4,6,1,3,2] => 0
[5,4,6,2,1,3] => 0
[5,4,6,2,3,1] => 0
[5,4,6,3,1,2] => 0
[5,4,6,3,2,1] => 0
[5,6,1,2,3,4] => 5
[5,6,1,2,4,3] => 5
[5,6,1,3,2,4] => 5
[5,6,1,3,4,2] => 5
[5,6,1,4,2,3] => 5
[5,6,1,4,3,2] => 4
[5,6,2,1,3,4] => 3
[5,6,2,1,4,3] => 2
[5,6,2,3,1,4] => 5
[5,6,2,3,4,1] => 5
[5,6,2,4,1,3] => 5
[5,6,2,4,3,1] => 4
[5,6,3,1,2,4] => 3
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 2
[5,6,3,2,4,1] => 2
[5,6,3,4,1,2] => 5
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 3
[5,6,4,1,3,2] => 2
[5,6,4,2,1,3] => 2
[5,6,4,2,3,1] => 2
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 2
[6,1,2,3,4,5] => 3
[6,1,2,3,5,4] => 3
[6,1,2,4,3,5] => 3
[6,1,2,4,5,3] => 3
[6,1,2,5,3,4] => 3
[6,1,2,5,4,3] => 2
[6,1,3,2,4,5] => 1
[6,1,3,2,5,4] => 0
[6,1,3,4,2,5] => 3
[6,1,3,4,5,2] => 3
[6,1,3,5,2,4] => 3
[6,1,3,5,4,2] => 2
[6,1,4,2,3,5] => 1
[6,1,4,2,5,3] => 0
[6,1,4,3,2,5] => 0
[6,1,4,3,5,2] => 0
[6,1,4,5,2,3] => 3
[6,1,4,5,3,2] => 2
[6,1,5,2,3,4] => 1
[6,1,5,2,4,3] => 0
[6,1,5,3,2,4] => 0
[6,1,5,3,4,2] => 0
[6,1,5,4,2,3] => 0
[6,1,5,4,3,2] => 0
[6,2,1,3,4,5] => 1
[6,2,1,3,5,4] => 0
[6,2,1,4,3,5] => 0
[6,2,1,4,5,3] => 0
[6,2,1,5,3,4] => 0
[6,2,1,5,4,3] => 0
[6,2,3,1,4,5] => 1
[6,2,3,1,5,4] => 0
[6,2,3,4,1,5] => 3
[6,2,3,4,5,1] => 3
[6,2,3,5,1,4] => 3
[6,2,3,5,4,1] => 2
[6,2,4,1,3,5] => 1
[6,2,4,1,5,3] => 0
[6,2,4,3,1,5] => 0
[6,2,4,3,5,1] => 0
[6,2,4,5,1,3] => 3
[6,2,4,5,3,1] => 2
[6,2,5,1,3,4] => 1
[6,2,5,1,4,3] => 0
[6,2,5,3,1,4] => 0
[6,2,5,3,4,1] => 0
[6,2,5,4,1,3] => 0
[6,2,5,4,3,1] => 0
[6,3,1,2,4,5] => 1
[6,3,1,2,5,4] => 0
[6,3,1,4,2,5] => 0
[6,3,1,4,5,2] => 0
[6,3,1,5,2,4] => 0
[6,3,1,5,4,2] => 0
[6,3,2,1,4,5] => 0
[6,3,2,1,5,4] => 0
[6,3,2,4,1,5] => 0
[6,3,2,4,5,1] => 0
[6,3,2,5,1,4] => 0
[6,3,2,5,4,1] => 0
[6,3,4,1,2,5] => 1
[6,3,4,1,5,2] => 0
[6,3,4,2,1,5] => 0
[6,3,4,2,5,1] => 0
[6,3,4,5,1,2] => 3
[6,3,4,5,2,1] => 2
[6,3,5,1,2,4] => 1
[6,3,5,1,4,2] => 0
[6,3,5,2,1,4] => 0
[6,3,5,2,4,1] => 0
[6,3,5,4,1,2] => 0
[6,3,5,4,2,1] => 0
[6,4,1,2,3,5] => 1
[6,4,1,2,5,3] => 0
[6,4,1,3,2,5] => 0
[6,4,1,3,5,2] => 0
[6,4,1,5,2,3] => 0
[6,4,1,5,3,2] => 0
[6,4,2,1,3,5] => 0
[6,4,2,1,5,3] => 0
[6,4,2,3,1,5] => 0
[6,4,2,3,5,1] => 0
[6,4,2,5,1,3] => 0
[6,4,2,5,3,1] => 0
[6,4,3,1,2,5] => 0
[6,4,3,1,5,2] => 0
[6,4,3,2,1,5] => 0
[6,4,3,2,5,1] => 0
[6,4,3,5,1,2] => 0
[6,4,3,5,2,1] => 0
[6,4,5,1,2,3] => 1
[6,4,5,1,3,2] => 0
[6,4,5,2,1,3] => 0
[6,4,5,2,3,1] => 0
[6,4,5,3,1,2] => 0
[6,4,5,3,2,1] => 0
[6,5,1,2,3,4] => 1
[6,5,1,2,4,3] => 0
[6,5,1,3,2,4] => 0
[6,5,1,3,4,2] => 0
[6,5,1,4,2,3] => 0
[6,5,1,4,3,2] => 0
[6,5,2,1,3,4] => 0
[6,5,2,1,4,3] => 0
[6,5,2,3,1,4] => 0
[6,5,2,3,4,1] => 0
[6,5,2,4,1,3] => 0
[6,5,2,4,3,1] => 0
[6,5,3,1,2,4] => 0
[6,5,3,1,4,2] => 0
[6,5,3,2,1,4] => 0
[6,5,3,2,4,1] => 0
[6,5,3,4,1,2] => 0
[6,5,3,4,2,1] => 0
[6,5,4,1,2,3] => 0
[6,5,4,1,3,2] => 0
[6,5,4,2,1,3] => 0
[6,5,4,2,3,1] => 0
[6,5,4,3,1,2] => 0
[6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => 6
[1,2,3,4,5,7,6] => 6
[1,2,3,4,6,5,7] => 6
[1,2,3,4,6,7,5] => 6
[1,2,3,4,7,5,6] => 6
[1,2,3,4,7,6,5] => 6
[1,2,3,5,4,6,7] => 6
[1,2,3,5,4,7,6] => 6
[1,2,3,5,6,4,7] => 6
[1,2,3,5,6,7,4] => 6
[1,2,3,5,7,4,6] => 6
[1,2,3,5,7,6,4] => 6
[1,2,3,6,4,5,7] => 6
[1,2,3,6,4,7,5] => 6
[1,2,3,6,5,4,7] => 6
[1,2,3,6,5,7,4] => 6
[1,2,3,6,7,4,5] => 6
[1,2,3,6,7,5,4] => 6
[1,2,3,7,4,5,6] => 6
[1,2,3,7,4,6,5] => 6
[1,2,3,7,5,4,6] => 6
[1,2,3,7,5,6,4] => 6
[1,2,3,7,6,4,5] => 6
[1,2,3,7,6,5,4] => 6
[1,2,4,3,5,6,7] => 6
[1,2,4,3,5,7,6] => 6
[1,2,4,3,6,5,7] => 6
[1,2,4,3,6,7,5] => 6
[1,2,4,3,7,5,6] => 6
[1,2,4,3,7,6,5] => 6
[1,2,4,5,3,6,7] => 6
[1,2,4,5,3,7,6] => 6
[1,2,4,5,6,3,7] => 6
[1,2,4,5,6,7,3] => 6
[1,2,4,5,7,3,6] => 6
[1,2,4,5,7,6,3] => 6
[1,2,4,6,3,5,7] => 6
[1,2,4,6,3,7,5] => 6
[1,2,4,6,5,3,7] => 6
[1,2,4,6,5,7,3] => 6
[1,2,4,6,7,3,5] => 6
[1,2,4,6,7,5,3] => 6
[1,2,4,7,3,5,6] => 6
[1,2,4,7,3,6,5] => 6
[1,2,4,7,5,3,6] => 6
[1,2,4,7,5,6,3] => 6
[1,2,4,7,6,3,5] => 6
[1,2,4,7,6,5,3] => 6
[1,2,5,3,4,6,7] => 6
[1,2,5,3,4,7,6] => 6
[1,2,5,3,6,4,7] => 6
[1,2,5,3,6,7,4] => 6
[1,2,5,3,7,4,6] => 6
[1,2,5,3,7,6,4] => 6
[1,2,5,4,3,6,7] => 6
[1,2,5,4,3,7,6] => 6
[1,2,5,4,6,3,7] => 6
[1,2,5,4,6,7,3] => 6
[1,2,5,4,7,3,6] => 6
[1,2,5,4,7,6,3] => 6
[1,2,5,6,3,4,7] => 6
[1,2,5,6,3,7,4] => 6
[1,2,5,6,4,3,7] => 6
[1,2,5,6,4,7,3] => 6
[1,2,5,6,7,3,4] => 6
[1,2,5,6,7,4,3] => 6
[1,2,5,7,3,4,6] => 6
[1,2,5,7,3,6,4] => 6
[1,2,5,7,4,3,6] => 6
[1,2,5,7,4,6,3] => 6
[1,2,5,7,6,3,4] => 6
[1,2,5,7,6,4,3] => 6
[1,2,6,3,4,5,7] => 6
[1,2,6,3,4,7,5] => 6
[1,2,6,3,5,4,7] => 6
[1,2,6,3,5,7,4] => 6
[1,2,6,3,7,4,5] => 6
[1,2,6,3,7,5,4] => 6
[1,2,6,4,3,5,7] => 6
[1,2,6,4,3,7,5] => 6
[1,2,6,4,5,3,7] => 6
[1,2,6,4,5,7,3] => 6
[1,2,6,4,7,3,5] => 6
[1,2,6,4,7,5,3] => 6
[1,2,6,5,3,4,7] => 6
[1,2,6,5,3,7,4] => 6
[1,2,6,5,4,3,7] => 4
[1,2,6,5,4,7,3] => 6
[1,2,6,5,7,3,4] => 6
[1,2,6,5,7,4,3] => 6
[1,2,6,7,3,4,5] => 6
[1,2,6,7,3,5,4] => 6
[1,2,6,7,4,3,5] => 6
[1,2,6,7,4,5,3] => 6
[1,2,6,7,5,3,4] => 6
[1,2,6,7,5,4,3] => 6
[1,2,7,3,4,5,6] => 6
[1,2,7,3,4,6,5] => 6
[1,2,7,3,5,4,6] => 6
[1,2,7,3,5,6,4] => 6
[1,2,7,3,6,4,5] => 6
[1,2,7,3,6,5,4] => 6
[1,2,7,4,3,5,6] => 6
[1,2,7,4,3,6,5] => 6
[1,2,7,4,5,3,6] => 6
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 6
[1,2,7,4,6,5,3] => 6
[1,2,7,5,3,4,6] => 6
[1,2,7,5,3,6,4] => 6
[1,2,7,5,4,3,6] => 4
[1,2,7,5,4,6,3] => 6
[1,2,7,5,6,3,4] => 6
[1,2,7,5,6,4,3] => 6
[1,2,7,6,3,4,5] => 6
[1,2,7,6,3,5,4] => 6
[1,2,7,6,4,3,5] => 4
[1,2,7,6,4,5,3] => 6
[1,2,7,6,5,3,4] => 4
[1,2,7,6,5,4,3] => 4
[1,3,2,4,5,6,7] => 6
[1,3,2,4,5,7,6] => 6
[1,3,2,4,6,5,7] => 6
[1,3,2,4,6,7,5] => 6
[1,3,2,4,7,5,6] => 6
[1,3,2,4,7,6,5] => 6
[1,3,2,5,4,6,7] => 6
[1,3,2,5,4,7,6] => 6
[1,3,2,5,6,4,7] => 6
[1,3,2,5,6,7,4] => 6
[1,3,2,5,7,4,6] => 6
[1,3,2,5,7,6,4] => 6
[1,3,2,6,4,5,7] => 6
[1,3,2,6,4,7,5] => 6
[1,3,2,6,5,4,7] => 4
[1,3,2,6,5,7,4] => 6
[1,3,2,6,7,4,5] => 6
[1,3,2,6,7,5,4] => 6
[1,3,2,7,4,5,6] => 6
[1,3,2,7,4,6,5] => 6
[1,3,2,7,5,4,6] => 4
[1,3,2,7,5,6,4] => 6
[1,3,2,7,6,4,5] => 4
[1,3,2,7,6,5,4] => 4
[1,3,4,2,5,6,7] => 6
[1,3,4,2,5,7,6] => 6
[1,3,4,2,6,5,7] => 6
[1,3,4,2,6,7,5] => 6
[1,3,4,2,7,5,6] => 6
[1,3,4,2,7,6,5] => 6
[1,3,4,5,2,6,7] => 6
[1,3,4,5,2,7,6] => 6
[1,3,4,5,6,2,7] => 6
[1,3,4,5,6,7,2] => 6
[1,3,4,5,7,2,6] => 6
[1,3,4,5,7,6,2] => 6
[1,3,4,6,2,5,7] => 6
[1,3,4,6,2,7,5] => 6
[1,3,4,6,5,2,7] => 6
[1,3,4,6,5,7,2] => 6
[1,3,4,6,7,2,5] => 6
[1,3,4,6,7,5,2] => 6
[1,3,4,7,2,5,6] => 6
[1,3,4,7,2,6,5] => 6
[1,3,4,7,5,2,6] => 6
[1,3,4,7,5,6,2] => 6
[1,3,4,7,6,2,5] => 6
[1,3,4,7,6,5,2] => 6
[1,3,5,2,4,6,7] => 6
[1,3,5,2,4,7,6] => 6
[1,3,5,2,6,4,7] => 6
[1,3,5,2,6,7,4] => 6
[1,3,5,2,7,4,6] => 6
[1,3,5,2,7,6,4] => 6
[1,3,5,4,2,6,7] => 6
[1,3,5,4,2,7,6] => 6
[1,3,5,4,6,2,7] => 6
[1,3,5,4,6,7,2] => 6
[1,3,5,4,7,2,6] => 6
[1,3,5,4,7,6,2] => 6
[1,3,5,6,2,4,7] => 6
[1,3,5,6,2,7,4] => 6
[1,3,5,6,4,2,7] => 6
[1,3,5,6,4,7,2] => 6
[1,3,5,6,7,2,4] => 6
[1,3,5,6,7,4,2] => 6
[1,3,5,7,2,4,6] => 6
[1,3,5,7,2,6,4] => 6
[1,3,5,7,4,2,6] => 6
[1,3,5,7,4,6,2] => 6
[1,3,5,7,6,2,4] => 6
[1,3,5,7,6,4,2] => 6
[1,3,6,2,4,5,7] => 6
[1,3,6,2,4,7,5] => 6
[1,3,6,2,5,4,7] => 6
[1,3,6,2,5,7,4] => 6
[1,3,6,2,7,4,5] => 6
[1,3,6,2,7,5,4] => 6
[1,3,6,4,2,5,7] => 6
[1,3,6,4,2,7,5] => 6
[1,3,6,4,5,2,7] => 6
[1,3,6,4,5,7,2] => 6
[1,3,6,4,7,2,5] => 6
[1,3,6,4,7,5,2] => 6
[1,3,6,5,2,4,7] => 6
[1,3,6,5,2,7,4] => 6
[1,3,6,5,4,2,7] => 4
[1,3,6,5,4,7,2] => 6
[1,3,6,5,7,2,4] => 6
[1,3,6,5,7,4,2] => 6
[1,3,6,7,2,4,5] => 6
[1,3,6,7,2,5,4] => 6
[1,3,6,7,4,2,5] => 6
[1,3,6,7,4,5,2] => 6
[1,3,6,7,5,2,4] => 6
[1,3,6,7,5,4,2] => 6
[1,3,7,2,4,5,6] => 6
[1,3,7,2,4,6,5] => 6
[1,3,7,2,5,4,6] => 6
[1,3,7,2,5,6,4] => 6
[1,3,7,2,6,4,5] => 6
[1,3,7,2,6,5,4] => 6
[1,3,7,4,2,5,6] => 6
[1,3,7,4,2,6,5] => 6
[1,3,7,4,5,2,6] => 6
[1,3,7,4,5,6,2] => 6
[1,3,7,4,6,2,5] => 6
[1,3,7,4,6,5,2] => 6
[1,3,7,5,2,4,6] => 6
[1,3,7,5,2,6,4] => 6
[1,3,7,5,4,2,6] => 4
[1,3,7,5,4,6,2] => 6
[1,3,7,5,6,2,4] => 6
[1,3,7,5,6,4,2] => 6
[1,3,7,6,2,4,5] => 6
[1,3,7,6,2,5,4] => 6
[1,3,7,6,4,2,5] => 4
[1,3,7,6,4,5,2] => 6
[1,3,7,6,5,2,4] => 4
[1,3,7,6,5,4,2] => 4
[1,4,2,3,5,6,7] => 6
[1,4,2,3,5,7,6] => 6
[1,4,2,3,6,5,7] => 6
[1,4,2,3,6,7,5] => 6
[1,4,2,3,7,5,6] => 6
[1,4,2,3,7,6,5] => 6
[1,4,2,5,3,6,7] => 6
[1,4,2,5,3,7,6] => 6
[1,4,2,5,6,3,7] => 6
[1,4,2,5,6,7,3] => 6
[1,4,2,5,7,3,6] => 6
[1,4,2,5,7,6,3] => 6
[1,4,2,6,3,5,7] => 6
[1,4,2,6,3,7,5] => 6
[1,4,2,6,5,3,7] => 4
[1,4,2,6,5,7,3] => 6
[1,4,2,6,7,3,5] => 6
[1,4,2,6,7,5,3] => 6
[1,4,2,7,3,5,6] => 6
[1,4,2,7,3,6,5] => 6
[1,4,2,7,5,3,6] => 4
[1,4,2,7,5,6,3] => 6
[1,4,2,7,6,3,5] => 4
[1,4,2,7,6,5,3] => 4
[1,4,3,2,5,6,7] => 4
[1,4,3,2,5,7,6] => 4
[1,4,3,2,6,5,7] => 2
[1,4,3,2,6,7,5] => 4
[1,4,3,2,7,5,6] => 2
[1,4,3,2,7,6,5] => 2
[1,4,3,5,2,6,7] => 6
[1,4,3,5,2,7,6] => 6
[1,4,3,5,6,2,7] => 6
[1,4,3,5,6,7,2] => 6
[1,4,3,5,7,2,6] => 6
[1,4,3,5,7,6,2] => 6
[1,4,3,6,2,5,7] => 6
[1,4,3,6,2,7,5] => 6
[1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => 6
[1,4,3,6,7,2,5] => 6
[1,4,3,6,7,5,2] => 6
[1,4,3,7,2,5,6] => 6
[1,4,3,7,2,6,5] => 6
[1,4,3,7,5,2,6] => 4
[1,4,3,7,5,6,2] => 6
[1,4,3,7,6,2,5] => 4
[1,4,3,7,6,5,2] => 4
[1,4,5,2,3,6,7] => 6
[1,4,5,2,3,7,6] => 6
[1,4,5,2,6,3,7] => 6
[1,4,5,2,6,7,3] => 6
[1,4,5,2,7,3,6] => 6
[1,4,5,2,7,6,3] => 6
[1,4,5,3,2,6,7] => 6
[1,4,5,3,2,7,6] => 6
[1,4,5,3,6,2,7] => 6
[1,4,5,3,6,7,2] => 6
[1,4,5,3,7,2,6] => 6
[1,4,5,3,7,6,2] => 6
[1,4,5,6,2,3,7] => 6
[1,4,5,6,2,7,3] => 6
[1,4,5,6,3,2,7] => 6
[1,4,5,6,3,7,2] => 6
[1,4,5,6,7,2,3] => 6
[1,4,5,6,7,3,2] => 6
[1,4,5,7,2,3,6] => 6
[1,4,5,7,2,6,3] => 6
[1,4,5,7,3,2,6] => 6
[1,4,5,7,3,6,2] => 6
[1,4,5,7,6,2,3] => 6
[1,4,5,7,6,3,2] => 6
[1,4,6,2,3,5,7] => 6
[1,4,6,2,3,7,5] => 6
[1,4,6,2,5,3,7] => 6
[1,4,6,2,5,7,3] => 6
[1,4,6,2,7,3,5] => 6
[1,4,6,2,7,5,3] => 6
[1,4,6,3,2,5,7] => 6
[1,4,6,3,2,7,5] => 6
[1,4,6,3,5,2,7] => 6
[1,4,6,3,5,7,2] => 6
[1,4,6,3,7,2,5] => 6
[1,4,6,3,7,5,2] => 6
[1,4,6,5,2,3,7] => 6
[1,4,6,5,2,7,3] => 6
[1,4,6,5,3,2,7] => 4
click to show generating function       
Description
The number of steps on the non-negative side of the walk associated with the permutation.
Consider the walk taking an up step for each ascent, a level step for each fixed point, and a down step for each descent of the permutation. Then this statistic is the number of steps that begin and end at non-negative height.
References
[1] Bernardi, O., Duplantier, B., Nadeau, P. A Bijection between well-labelled positive paths and matchings arXiv:0903.5379
[2] KDD Permutation, up-down signature, and counting positive occupation MathOverflow:319104
Code
def signature(pi):
    return [1 if pi[i] < pi[i+1] else -1 for i in range(len(pi)-1)]

def walk(pi):
    x = signature(pi)
    return [sum(x[:k]) for k in range(len(pi))]

def statistic(pi):
    w = walk(pi)
    return sum(1 for i in range(len(pi)-1) if w[i] >= 0 and w[i+1] >= 0)

Created
Dec 21, 2018 at 18:50 by Martin Rubey
Updated
Dec 21, 2018 at 18:50 by Martin Rubey