Identifier
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 2
[1,3,4,2] => 0
[1,4,2,3] => 1
[1,4,3,2] => 1
[2,1,3,4] => 0
[2,1,4,3] => 1
[2,3,1,4] => 1
[2,3,4,1] => 0
[2,4,1,3] => 2
[2,4,3,1] => 1
[3,1,2,4] => 0
[3,1,4,2] => 1
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 1
[1,2,4,5,3] => 0
[1,2,5,3,4] => 0
[1,2,5,4,3] => 0
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 1
[1,3,4,5,2] => 0
[1,3,5,2,4] => 3
[1,3,5,4,2] => 2
[1,4,2,3,5] => 1
[1,4,2,5,3] => 2
[1,4,3,2,5] => 2
[1,4,3,5,2] => 2
[1,4,5,2,3] => 0
[1,4,5,3,2] => 0
[1,5,2,3,4] => 1
[1,5,2,4,3] => 2
[1,5,3,2,4] => 2
[1,5,3,4,2] => 1
[1,5,4,2,3] => 1
[1,5,4,3,2] => 1
[2,1,3,4,5] => 0
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 0
[2,1,5,3,4] => 1
[2,1,5,4,3] => 1
[2,3,1,4,5] => 0
[2,3,1,5,4] => 1
[2,3,4,1,5] => 1
[2,3,4,5,1] => 0
[2,3,5,1,4] => 1
[2,3,5,4,1] => 0
[2,4,1,3,5] => 3
[2,4,1,5,3] => 2
[2,4,3,1,5] => 2
[2,4,3,5,1] => 2
[2,4,5,1,3] => 1
[2,4,5,3,1] => 0
[2,5,1,3,4] => 1
[2,5,1,4,3] => 2
[2,5,3,1,4] => 2
[2,5,3,4,1] => 1
[2,5,4,1,3] => 2
[2,5,4,3,1] => 1
[3,1,2,4,5] => 0
[3,1,2,5,4] => 0
[3,1,4,2,5] => 2
[3,1,4,5,2] => 0
[3,1,5,2,4] => 2
[3,1,5,4,2] => 1
[3,2,1,4,5] => 0
[3,2,1,5,4] => 1
[3,2,4,1,5] => 2
[3,2,4,5,1] => 0
[3,2,5,1,4] => 2
[3,2,5,4,1] => 1
[3,4,1,2,5] => 0
[3,4,1,5,2] => 1
[3,4,2,1,5] => 1
[3,4,2,5,1] => 1
[3,4,5,1,2] => 0
[3,4,5,2,1] => 0
[3,5,1,2,4] => 1
[3,5,1,4,2] => 2
[3,5,2,1,4] => 2
[3,5,2,4,1] => 2
[3,5,4,1,2] => 1
[3,5,4,2,1] => 1
[4,1,2,3,5] => 0
[4,1,2,5,3] => 0
[4,1,3,2,5] => 2
[4,1,3,5,2] => 2
[4,1,5,2,3] => 1
[4,1,5,3,2] => 1
[4,2,1,3,5] => 2
[4,2,1,5,3] => 1
[4,2,3,1,5] => 1
[4,2,3,5,1] => 0
[4,2,5,1,3] => 2
[4,2,5,3,1] => 1
[4,3,1,2,5] => 0
[4,3,1,5,2] => 1
[4,3,2,1,5] => 1
[4,3,2,5,1] => 1
[4,3,5,1,2] => 1
[4,3,5,2,1] => 1
[4,5,1,2,3] => 0
[4,5,1,3,2] => 1
[4,5,2,1,3] => 1
[4,5,2,3,1] => 0
[4,5,3,1,2] => 0
[4,5,3,2,1] => 0
[5,1,2,3,4] => 0
[5,1,2,4,3] => 0
[5,1,3,2,4] => 2
[5,1,3,4,2] => 0
[5,1,4,2,3] => 1
[5,1,4,3,2] => 1
[5,2,1,3,4] => 0
[5,2,1,4,3] => 1
[5,2,3,1,4] => 1
[5,2,3,4,1] => 0
[5,2,4,1,3] => 2
[5,2,4,3,1] => 1
[5,3,1,2,4] => 0
[5,3,1,4,2] => 1
[5,3,2,1,4] => 1
[5,3,2,4,1] => 1
[5,3,4,1,2] => 0
[5,3,4,2,1] => 0
[5,4,1,2,3] => 0
[5,4,1,3,2] => 1
[5,4,2,1,3] => 1
[5,4,2,3,1] => 0
[5,4,3,1,2] => 0
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 0
[1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => 0
[1,2,3,6,4,5] => 0
[1,2,3,6,5,4] => 0
[1,2,4,3,5,6] => 0
[1,2,4,3,6,5] => 1
[1,2,4,5,3,6] => 1
[1,2,4,5,6,3] => 0
[1,2,4,6,3,5] => 2
[1,2,4,6,5,3] => 1
[1,2,5,3,4,6] => 0
[1,2,5,3,6,4] => 1
[1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => 1
[1,2,5,6,3,4] => 0
[1,2,5,6,4,3] => 0
[1,2,6,3,4,5] => 0
[1,2,6,3,5,4] => 1
[1,2,6,4,3,5] => 1
[1,2,6,4,5,3] => 0
[1,2,6,5,3,4] => 0
[1,2,6,5,4,3] => 0
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 3
[1,3,2,5,4,6] => 3
[1,3,2,5,6,4] => 1
[1,3,2,6,4,5] => 2
[1,3,2,6,5,4] => 2
[1,3,4,2,5,6] => 0
[1,3,4,2,6,5] => 1
[1,3,4,5,2,6] => 1
[1,3,4,5,6,2] => 0
[1,3,4,6,2,5] => 1
[1,3,4,6,5,2] => 0
[1,3,5,2,4,6] => 4
[1,3,5,2,6,4] => 3
[1,3,5,4,2,6] => 3
[1,3,5,4,6,2] => 3
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 1
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 3
[1,3,6,4,2,5] => 3
[1,3,6,4,5,2] => 2
[1,3,6,5,2,4] => 3
[1,3,6,5,4,2] => 2
[1,4,2,3,5,6] => 1
[1,4,2,3,6,5] => 1
[1,4,2,5,3,6] => 3
[1,4,2,5,6,3] => 1
[1,4,2,6,3,5] => 3
[1,4,2,6,5,3] => 2
[1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => 3
[1,4,3,6,5,2] => 2
[1,4,5,2,3,6] => 0
[1,4,5,2,6,3] => 1
[1,4,5,3,2,6] => 1
[1,4,5,3,6,2] => 1
[1,4,5,6,2,3] => 0
[1,4,5,6,3,2] => 0
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 3
[1,4,6,3,2,5] => 3
[1,4,6,3,5,2] => 3
[1,4,6,5,2,3] => 2
[1,4,6,5,3,2] => 2
[1,5,2,3,4,6] => 1
[1,5,2,3,6,4] => 1
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 3
[1,5,2,6,3,4] => 2
[1,5,2,6,4,3] => 2
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 2
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 1
[1,5,3,6,2,4] => 3
[1,5,3,6,4,2] => 2
[1,5,4,2,3,6] => 1
[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] => 2
[1,5,4,6,3,2] => 2
[1,5,6,2,3,4] => 0
[1,5,6,2,4,3] => 1
[1,5,6,3,2,4] => 1
[1,5,6,3,4,2] => 0
[1,5,6,4,2,3] => 0
[1,5,6,4,3,2] => 0
[1,6,2,3,4,5] => 1
[1,6,2,3,5,4] => 1
[1,6,2,4,3,5] => 3
[1,6,2,4,5,3] => 1
[1,6,2,5,3,4] => 2
[1,6,2,5,4,3] => 2
[1,6,3,2,4,5] => 1
[1,6,3,2,5,4] => 2
[1,6,3,4,2,5] => 2
[1,6,3,4,5,2] => 1
[1,6,3,5,2,4] => 3
[1,6,3,5,4,2] => 2
[1,6,4,2,3,5] => 1
[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] => 1
[1,6,4,5,3,2] => 1
[1,6,5,2,3,4] => 1
[1,6,5,2,4,3] => 2
[1,6,5,3,2,4] => 2
[1,6,5,3,4,2] => 1
[1,6,5,4,2,3] => 1
[1,6,5,4,3,2] => 1
[2,1,3,4,5,6] => 0
[2,1,3,4,6,5] => 0
[2,1,3,5,4,6] => 3
[2,1,3,5,6,4] => 1
[2,1,3,6,4,5] => 2
[2,1,3,6,5,4] => 2
[2,1,4,3,5,6] => 1
[2,1,4,3,6,5] => 2
[2,1,4,5,3,6] => 1
[2,1,4,5,6,3] => 0
[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] => 2
[2,1,5,4,3,6] => 2
[2,1,5,4,6,3] => 2
[2,1,5,6,3,4] => 0
[2,1,5,6,4,3] => 0
[2,1,6,3,4,5] => 1
[2,1,6,3,5,4] => 2
[2,1,6,4,3,5] => 2
[2,1,6,4,5,3] => 1
[2,1,6,5,3,4] => 1
[2,1,6,5,4,3] => 1
[2,3,1,4,5,6] => 0
[2,3,1,4,6,5] => 2
[2,3,1,5,4,6] => 2
[2,3,1,5,6,4] => 0
[2,3,1,6,4,5] => 1
[2,3,1,6,5,4] => 1
[2,3,4,1,5,6] => 0
[2,3,4,1,6,5] => 1
[2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => 0
[2,3,4,6,1,5] => 1
[2,3,4,6,5,1] => 0
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 1
[2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => 1
[2,3,5,6,1,4] => 1
[2,3,5,6,4,1] => 0
[2,3,6,1,4,5] => 0
[2,3,6,1,5,4] => 1
[2,3,6,4,1,5] => 1
[2,3,6,4,5,1] => 0
[2,3,6,5,1,4] => 1
[2,3,6,5,4,1] => 0
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 3
[2,4,1,5,3,6] => 3
[2,4,1,5,6,3] => 1
[2,4,1,6,3,5] => 3
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 1
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => 3
[2,4,3,6,5,1] => 2
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 1
[2,4,5,3,1,6] => 1
[2,4,5,3,6,1] => 1
[2,4,5,6,1,3] => 1
[2,4,5,6,3,1] => 0
[2,4,6,1,3,5] => 4
[2,4,6,1,5,3] => 3
[2,4,6,3,1,5] => 3
[2,4,6,3,5,1] => 3
[2,4,6,5,1,3] => 3
[2,4,6,5,3,1] => 2
[2,5,1,3,4,6] => 1
[2,5,1,3,6,4] => 3
[2,5,1,4,3,6] => 3
[2,5,1,4,6,3] => 3
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 2
[2,5,3,4,6,1] => 1
[2,5,3,6,1,4] => 3
[2,5,3,6,4,1] => 2
[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] => 3
[2,5,4,6,3,1] => 2
[2,5,6,1,3,4] => 0
[2,5,6,1,4,3] => 1
[2,5,6,3,1,4] => 1
[2,5,6,3,4,1] => 0
[2,5,6,4,1,3] => 1
[2,5,6,4,3,1] => 0
[2,6,1,3,4,5] => 1
[2,6,1,3,5,4] => 3
[2,6,1,4,3,5] => 3
[2,6,1,4,5,3] => 1
[2,6,1,5,3,4] => 2
[2,6,1,5,4,3] => 2
[2,6,3,1,4,5] => 1
[2,6,3,1,5,4] => 2
[2,6,3,4,1,5] => 2
[2,6,3,4,5,1] => 1
[2,6,3,5,1,4] => 3
[2,6,3,5,4,1] => 2
[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] => 2
[2,6,4,5,3,1] => 1
[2,6,5,1,3,4] => 1
[2,6,5,1,4,3] => 2
[2,6,5,3,1,4] => 2
[2,6,5,3,4,1] => 1
[2,6,5,4,1,3] => 2
[2,6,5,4,3,1] => 1
[3,1,2,4,5,6] => 0
[3,1,2,4,6,5] => 1
[3,1,2,5,4,6] => 1
[3,1,2,5,6,4] => 0
[3,1,2,6,4,5] => 0
[3,1,2,6,5,4] => 0
[3,1,4,2,5,6] => 1
[3,1,4,2,6,5] => 2
[3,1,4,5,2,6] => 1
[3,1,4,5,6,2] => 0
[3,1,4,6,2,5] => 3
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 3
[3,1,5,2,6,4] => 2
[3,1,5,4,2,6] => 2
[3,1,5,4,6,2] => 2
[3,1,5,6,2,4] => 1
[3,1,5,6,4,2] => 0
[3,1,6,2,4,5] => 1
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 2
[3,1,6,4,5,2] => 1
[3,1,6,5,2,4] => 2
[3,1,6,5,4,2] => 1
[3,2,1,4,5,6] => 0
[3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => 0
[3,2,1,6,4,5] => 1
[3,2,1,6,5,4] => 1
[3,2,4,1,5,6] => 1
[3,2,4,1,6,5] => 2
[3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => 0
[3,2,4,6,1,5] => 3
[3,2,4,6,5,1] => 2
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 2
[3,2,5,4,6,1] => 2
[3,2,5,6,1,4] => 1
[3,2,5,6,4,1] => 0
[3,2,6,1,4,5] => 1
[3,2,6,1,5,4] => 2
[3,2,6,4,1,5] => 2
[3,2,6,4,5,1] => 1
[3,2,6,5,1,4] => 2
[3,2,6,5,4,1] => 1
[3,4,1,2,5,6] => 0
[3,4,1,2,6,5] => 0
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 0
[3,4,1,6,2,5] => 2
[3,4,1,6,5,2] => 1
[3,4,2,1,5,6] => 0
[3,4,2,1,6,5] => 1
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 0
[3,4,2,6,1,5] => 2
[3,4,2,6,5,1] => 1
[3,4,5,1,2,6] => 0
[3,4,5,1,6,2] => 1
[3,4,5,2,1,6] => 1
[3,4,5,2,6,1] => 1
[3,4,5,6,1,2] => 0
[3,4,5,6,2,1] => 0
[3,4,6,1,2,5] => 0
[3,4,6,1,5,2] => 1
[3,4,6,2,1,5] => 1
[3,4,6,2,5,1] => 1
[3,4,6,5,1,2] => 0
[3,4,6,5,2,1] => 0
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 1
[3,5,1,4,2,6] => 3
[3,5,1,4,6,2] => 3
[3,5,1,6,2,4] => 3
[3,5,1,6,4,2] => 2
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 3
[3,5,2,4,6,1] => 3
[3,5,2,6,1,4] => 3
[3,5,2,6,4,1] => 2
[3,5,4,1,2,6] => 1
[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] => 2
[3,5,4,6,2,1] => 2
[3,5,6,1,2,4] => 0
[3,5,6,1,4,2] => 1
[3,5,6,2,1,4] => 1
[3,5,6,2,4,1] => 1
[3,5,6,4,1,2] => 0
[3,5,6,4,2,1] => 0
[3,6,1,2,4,5] => 1
[3,6,1,2,5,4] => 1
[3,6,1,4,2,5] => 3
[3,6,1,4,5,2] => 1
[3,6,1,5,2,4] => 3
[3,6,1,5,4,2] => 2
[3,6,2,1,4,5] => 1
[3,6,2,1,5,4] => 2
[3,6,2,4,1,5] => 3
[3,6,2,4,5,1] => 1
[3,6,2,5,1,4] => 3
[3,6,2,5,4,1] => 2
[3,6,4,1,2,5] => 1
[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] => 1
[3,6,4,5,2,1] => 1
[3,6,5,1,2,4] => 1
[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] => 1
[3,6,5,4,2,1] => 1
[4,1,2,3,5,6] => 0
[4,1,2,3,6,5] => 0
[4,1,2,5,3,6] => 1
[4,1,2,5,6,3] => 0
[4,1,2,6,3,5] => 1
[4,1,2,6,5,3] => 0
[4,1,3,2,5,6] => 1
[4,1,3,2,6,5] => 2
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 1
[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] => 2
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 2
[4,1,5,6,2,3] => 0
[4,1,5,6,3,2] => 0
[4,1,6,2,3,5] => 1
[4,1,6,2,5,3] => 2
[4,1,6,3,2,5] => 2
[4,1,6,3,5,2] => 2
[4,1,6,5,2,3] => 1
[4,1,6,5,3,2] => 1
[4,2,1,3,5,6] => 1
[4,2,1,3,6,5] => 2
[4,2,1,5,3,6] => 2
[4,2,1,5,6,3] => 0
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 1
[4,2,3,1,5,6] => 0
[4,2,3,1,6,5] => 1
[4,2,3,5,1,6] => 1
[4,2,3,5,6,1] => 0
[4,2,3,6,1,5] => 1
[4,2,3,6,5,1] => 0
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 2
[4,2,5,3,1,6] => 2
[4,2,5,3,6,1] => 2
[4,2,5,6,1,3] => 1
[4,2,5,6,3,1] => 0
[4,2,6,1,3,5] => 3
[4,2,6,1,5,3] => 2
[4,2,6,3,1,5] => 2
[4,2,6,3,5,1] => 2
[4,2,6,5,1,3] => 2
[4,2,6,5,3,1] => 1
[4,3,1,2,5,6] => 0
[4,3,1,2,6,5] => 0
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 0
[4,3,1,6,2,5] => 2
[4,3,1,6,5,2] => 1
[4,3,2,1,5,6] => 0
[4,3,2,1,6,5] => 1
[4,3,2,5,1,6] => 2
[4,3,2,5,6,1] => 0
[4,3,2,6,1,5] => 2
[4,3,2,6,5,1] => 1
[4,3,5,1,2,6] => 1
[4,3,5,1,6,2] => 2
[4,3,5,2,1,6] => 2
[4,3,5,2,6,1] => 2
[4,3,5,6,1,2] => 0
[4,3,5,6,2,1] => 0
[4,3,6,1,2,5] => 1
[4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => 2
[4,3,6,2,5,1] => 2
[4,3,6,5,1,2] => 1
[4,3,6,5,2,1] => 1
[4,5,1,2,3,6] => 0
[4,5,1,2,6,3] => 0
[4,5,1,3,2,6] => 2
[4,5,1,3,6,2] => 2
[4,5,1,6,2,3] => 1
[4,5,1,6,3,2] => 1
[4,5,2,1,3,6] => 2
[4,5,2,1,6,3] => 1
[4,5,2,3,1,6] => 1
[4,5,2,3,6,1] => 0
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 1
[4,5,3,1,2,6] => 0
[4,5,3,1,6,2] => 1
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 1
[4,5,3,6,1,2] => 1
[4,5,3,6,2,1] => 1
[4,5,6,1,2,3] => 0
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 0
[4,5,6,3,1,2] => 0
[4,5,6,3,2,1] => 0
[4,6,1,2,3,5] => 1
[4,6,1,2,5,3] => 1
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 3
[4,6,1,5,2,3] => 2
[4,6,1,5,3,2] => 2
[4,6,2,1,3,5] => 3
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 2
[4,6,2,3,5,1] => 1
[4,6,2,5,1,3] => 3
[4,6,2,5,3,1] => 2
[4,6,3,1,2,5] => 1
[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] => 2
[4,6,3,5,2,1] => 2
[4,6,5,1,2,3] => 1
[4,6,5,1,3,2] => 2
[4,6,5,2,1,3] => 2
[4,6,5,2,3,1] => 1
[4,6,5,3,1,2] => 1
[4,6,5,3,2,1] => 1
[5,1,2,3,4,6] => 0
[5,1,2,3,6,4] => 0
[5,1,2,4,3,6] => 1
[5,1,2,4,6,3] => 1
[5,1,2,6,3,4] => 0
[5,1,2,6,4,3] => 0
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 2
[5,1,3,4,2,6] => 1
[5,1,3,4,6,2] => 0
[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] => 2
[5,1,4,3,2,6] => 2
[5,1,4,3,6,2] => 2
[5,1,4,6,2,3] => 2
[5,1,4,6,3,2] => 2
[5,1,6,2,3,4] => 1
[5,1,6,2,4,3] => 2
[5,1,6,3,2,4] => 2
[5,1,6,3,4,2] => 1
[5,1,6,4,2,3] => 1
[5,1,6,4,3,2] => 1
[5,2,1,3,4,6] => 0
[5,2,1,3,6,4] => 2
[5,2,1,4,3,6] => 2
[5,2,1,4,6,3] => 2
[5,2,1,6,3,4] => 1
[5,2,1,6,4,3] => 1
[5,2,3,1,4,6] => 2
[5,2,3,1,6,4] => 1
[5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => 0
[5,2,3,6,1,4] => 1
[5,2,3,6,4,1] => 0
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 2
[5,2,4,3,1,6] => 2
[5,2,4,3,6,1] => 2
[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] => 2
[5,2,6,3,1,4] => 2
[5,2,6,3,4,1] => 1
[5,2,6,4,1,3] => 2
[5,2,6,4,3,1] => 1
[5,3,1,2,4,6] => 1
[5,3,1,2,6,4] => 0
[5,3,1,4,2,6] => 2
[5,3,1,4,6,2] => 2
[5,3,1,6,2,4] => 2
[5,3,1,6,4,2] => 1
[5,3,2,1,4,6] => 2
[5,3,2,1,6,4] => 1
[5,3,2,4,1,6] => 2
[5,3,2,4,6,1] => 2
[5,3,2,6,1,4] => 2
[5,3,2,6,4,1] => 1
[5,3,4,1,2,6] => 0
[5,3,4,1,6,2] => 1
[5,3,4,2,1,6] => 1
[5,3,4,2,6,1] => 1
[5,3,4,6,1,2] => 0
[5,3,4,6,2,1] => 0
[5,3,6,1,2,4] => 1
[5,3,6,1,4,2] => 2
[5,3,6,2,1,4] => 2
[5,3,6,2,4,1] => 2
[5,3,6,4,1,2] => 1
[5,3,6,4,2,1] => 1
[5,4,1,2,3,6] => 0
[5,4,1,2,6,3] => 0
[5,4,1,3,2,6] => 2
[5,4,1,3,6,2] => 2
[5,4,1,6,2,3] => 1
[5,4,1,6,3,2] => 1
[5,4,2,1,3,6] => 2
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 1
[5,4,2,3,6,1] => 0
[5,4,2,6,1,3] => 2
[5,4,2,6,3,1] => 1
[5,4,3,1,2,6] => 0
[5,4,3,1,6,2] => 1
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 1
[5,4,3,6,1,2] => 1
[5,4,3,6,2,1] => 1
[5,4,6,1,2,3] => 1
[5,4,6,1,3,2] => 2
[5,4,6,2,1,3] => 2
[5,4,6,2,3,1] => 1
[5,4,6,3,1,2] => 1
[5,4,6,3,2,1] => 1
[5,6,1,2,3,4] => 0
[5,6,1,2,4,3] => 0
[5,6,1,3,2,4] => 2
[5,6,1,3,4,2] => 0
[5,6,1,4,2,3] => 1
[5,6,1,4,3,2] => 1
[5,6,2,1,3,4] => 0
[5,6,2,1,4,3] => 1
[5,6,2,3,1,4] => 1
[5,6,2,3,4,1] => 0
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 1
[5,6,3,1,2,4] => 0
[5,6,3,1,4,2] => 1
[5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => 1
[5,6,3,4,1,2] => 0
[5,6,3,4,2,1] => 0
[5,6,4,1,2,3] => 0
[5,6,4,1,3,2] => 1
[5,6,4,2,1,3] => 1
[5,6,4,2,3,1] => 0
[5,6,4,3,1,2] => 0
[5,6,4,3,2,1] => 0
[6,1,2,3,4,5] => 0
[6,1,2,3,5,4] => 0
[6,1,2,4,3,5] => 1
[6,1,2,4,5,3] => 0
[6,1,2,5,3,4] => 0
[6,1,2,5,4,3] => 0
[6,1,3,2,4,5] => 1
[6,1,3,2,5,4] => 2
[6,1,3,4,2,5] => 1
[6,1,3,4,5,2] => 0
[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] => 2
[6,1,4,3,2,5] => 2
[6,1,4,3,5,2] => 2
[6,1,4,5,2,3] => 0
[6,1,4,5,3,2] => 0
[6,1,5,2,3,4] => 1
[6,1,5,2,4,3] => 2
[6,1,5,3,2,4] => 2
[6,1,5,3,4,2] => 1
[6,1,5,4,2,3] => 1
[6,1,5,4,3,2] => 1
[6,2,1,3,4,5] => 0
[6,2,1,3,5,4] => 2
[6,2,1,4,3,5] => 2
[6,2,1,4,5,3] => 0
[6,2,1,5,3,4] => 1
[6,2,1,5,4,3] => 1
[6,2,3,1,4,5] => 0
[6,2,3,1,5,4] => 1
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 0
[6,2,3,5,1,4] => 1
[6,2,3,5,4,1] => 0
[6,2,4,1,3,5] => 3
[6,2,4,1,5,3] => 2
[6,2,4,3,1,5] => 2
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 1
[6,2,4,5,3,1] => 0
[6,2,5,1,3,4] => 1
[6,2,5,1,4,3] => 2
[6,2,5,3,1,4] => 2
[6,2,5,3,4,1] => 1
[6,2,5,4,1,3] => 2
[6,2,5,4,3,1] => 1
[6,3,1,2,4,5] => 0
[6,3,1,2,5,4] => 0
[6,3,1,4,2,5] => 2
[6,3,1,4,5,2] => 0
[6,3,1,5,2,4] => 2
[6,3,1,5,4,2] => 1
[6,3,2,1,4,5] => 0
[6,3,2,1,5,4] => 1
[6,3,2,4,1,5] => 2
[6,3,2,4,5,1] => 0
[6,3,2,5,1,4] => 2
[6,3,2,5,4,1] => 1
[6,3,4,1,2,5] => 0
[6,3,4,1,5,2] => 1
[6,3,4,2,1,5] => 1
[6,3,4,2,5,1] => 1
[6,3,4,5,1,2] => 0
[6,3,4,5,2,1] => 0
[6,3,5,1,2,4] => 1
[6,3,5,1,4,2] => 2
[6,3,5,2,1,4] => 2
[6,3,5,2,4,1] => 2
[6,3,5,4,1,2] => 1
[6,3,5,4,2,1] => 1
[6,4,1,2,3,5] => 0
[6,4,1,2,5,3] => 0
[6,4,1,3,2,5] => 2
[6,4,1,3,5,2] => 2
[6,4,1,5,2,3] => 1
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 2
[6,4,2,1,5,3] => 1
[6,4,2,3,1,5] => 1
[6,4,2,3,5,1] => 0
[6,4,2,5,1,3] => 2
[6,4,2,5,3,1] => 1
[6,4,3,1,2,5] => 0
[6,4,3,1,5,2] => 1
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 1
[6,4,3,5,1,2] => 1
[6,4,3,5,2,1] => 1
[6,4,5,1,2,3] => 0
[6,4,5,1,3,2] => 1
[6,4,5,2,1,3] => 1
[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] => 0
[6,5,1,2,4,3] => 0
[6,5,1,3,2,4] => 2
[6,5,1,3,4,2] => 0
[6,5,1,4,2,3] => 1
[6,5,1,4,3,2] => 1
[6,5,2,1,3,4] => 0
[6,5,2,1,4,3] => 1
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 0
[6,5,2,4,1,3] => 2
[6,5,2,4,3,1] => 1
[6,5,3,1,2,4] => 0
[6,5,3,1,4,2] => 1
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 1
[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] => 1
[6,5,4,2,1,3] => 1
[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] => 0
[1,2,3,4,5,7,6] => 0
[1,2,3,4,6,5,7] => 1
[1,2,3,4,6,7,5] => 0
[1,2,3,4,7,5,6] => 0
[1,2,3,4,7,6,5] => 0
[1,2,3,5,4,6,7] => 0
[1,2,3,5,4,7,6] => 1
[1,2,3,5,6,4,7] => 1
[1,2,3,5,6,7,4] => 0
[1,2,3,5,7,4,6] => 2
[1,2,3,5,7,6,4] => 1
[1,2,3,6,4,5,7] => 0
[1,2,3,6,4,7,5] => 1
[1,2,3,6,5,4,7] => 1
[1,2,3,6,5,7,4] => 1
[1,2,3,6,7,4,5] => 0
[1,2,3,6,7,5,4] => 0
[1,2,3,7,4,5,6] => 0
[1,2,3,7,4,6,5] => 1
[1,2,3,7,5,4,6] => 1
[1,2,3,7,5,6,4] => 0
[1,2,3,7,6,4,5] => 0
[1,2,3,7,6,5,4] => 0
[1,2,4,3,5,6,7] => 0
[1,2,4,3,5,7,6] => 2
[1,2,4,3,6,5,7] => 2
[1,2,4,3,6,7,5] => 0
[1,2,4,3,7,5,6] => 1
[1,2,4,3,7,6,5] => 1
[1,2,4,5,3,6,7] => 0
[1,2,4,5,3,7,6] => 1
[1,2,4,5,6,3,7] => 1
[1,2,4,5,6,7,3] => 0
[1,2,4,5,7,3,6] => 1
[1,2,4,5,7,6,3] => 0
[1,2,4,6,3,5,7] => 3
[1,2,4,6,3,7,5] => 2
[1,2,4,6,5,3,7] => 2
[1,2,4,6,5,7,3] => 2
[1,2,4,6,7,3,5] => 1
[1,2,4,6,7,5,3] => 0
[1,2,4,7,3,5,6] => 1
[1,2,4,7,3,6,5] => 2
[1,2,4,7,5,3,6] => 2
[1,2,4,7,5,6,3] => 1
[1,2,4,7,6,3,5] => 2
[1,2,4,7,6,5,3] => 1
[1,2,5,3,4,6,7] => 0
[1,2,5,3,4,7,6] => 0
[1,2,5,3,6,4,7] => 2
[1,2,5,3,6,7,4] => 0
[1,2,5,3,7,4,6] => 2
[1,2,5,3,7,6,4] => 1
[1,2,5,4,3,6,7] => 0
[1,2,5,4,3,7,6] => 1
[1,2,5,4,6,3,7] => 2
[1,2,5,4,6,7,3] => 0
[1,2,5,4,7,3,6] => 2
[1,2,5,4,7,6,3] => 1
[1,2,5,6,3,4,7] => 0
[1,2,5,6,3,7,4] => 1
[1,2,5,6,4,3,7] => 1
[1,2,5,6,4,7,3] => 1
[1,2,5,6,7,3,4] => 0
[1,2,5,6,7,4,3] => 0
[1,2,5,7,3,4,6] => 1
[1,2,5,7,3,6,4] => 2
[1,2,5,7,4,3,6] => 2
[1,2,5,7,4,6,3] => 2
[1,2,5,7,6,3,4] => 1
[1,2,5,7,6,4,3] => 1
[1,2,6,3,4,5,7] => 0
[1,2,6,3,4,7,5] => 0
[1,2,6,3,5,4,7] => 2
[1,2,6,3,5,7,4] => 2
[1,2,6,3,7,4,5] => 1
[1,2,6,3,7,5,4] => 1
[1,2,6,4,3,5,7] => 2
[1,2,6,4,3,7,5] => 1
[1,2,6,4,5,3,7] => 1
[1,2,6,4,5,7,3] => 0
[1,2,6,4,7,3,5] => 2
[1,2,6,4,7,5,3] => 1
[1,2,6,5,3,4,7] => 0
[1,2,6,5,3,7,4] => 1
[1,2,6,5,4,3,7] => 1
[1,2,6,5,4,7,3] => 1
[1,2,6,5,7,3,4] => 1
[1,2,6,5,7,4,3] => 1
[1,2,6,7,3,4,5] => 0
[1,2,6,7,3,5,4] => 1
[1,2,6,7,4,3,5] => 1
[1,2,6,7,4,5,3] => 0
[1,2,6,7,5,3,4] => 0
[1,2,6,7,5,4,3] => 0
[1,2,7,3,4,5,6] => 0
[1,2,7,3,4,6,5] => 0
[1,2,7,3,5,4,6] => 2
[1,2,7,3,5,6,4] => 0
[1,2,7,3,6,4,5] => 1
[1,2,7,3,6,5,4] => 1
[1,2,7,4,3,5,6] => 0
[1,2,7,4,3,6,5] => 1
[1,2,7,4,5,3,6] => 1
[1,2,7,4,5,6,3] => 0
[1,2,7,4,6,3,5] => 2
[1,2,7,4,6,5,3] => 1
[1,2,7,5,3,4,6] => 0
[1,2,7,5,3,6,4] => 1
[1,2,7,5,4,3,6] => 1
[1,2,7,5,4,6,3] => 1
[1,2,7,5,6,3,4] => 0
[1,2,7,5,6,4,3] => 0
[1,2,7,6,3,4,5] => 0
[1,2,7,6,3,5,4] => 1
[1,2,7,6,4,3,5] => 1
[1,2,7,6,4,5,3] => 0
[1,2,7,6,5,3,4] => 0
[1,2,7,6,5,4,3] => 0
[1,3,2,4,5,6,7] => 1
[1,3,2,4,5,7,6] => 1
[1,3,2,4,6,5,7] => 4
[1,3,2,4,6,7,5] => 2
[1,3,2,4,7,5,6] => 3
[1,3,2,4,7,6,5] => 3
[1,3,2,5,4,6,7] => 2
[1,3,2,5,4,7,6] => 3
[1,3,2,5,6,4,7] => 2
[1,3,2,5,6,7,4] => 1
[1,3,2,5,7,4,6] => 4
[1,3,2,5,7,6,4] => 3
[1,3,2,6,4,5,7] => 2
[1,3,2,6,4,7,5] => 3
[1,3,2,6,5,4,7] => 3
[1,3,2,6,5,7,4] => 3
[1,3,2,6,7,4,5] => 1
[1,3,2,6,7,5,4] => 1
[1,3,2,7,4,5,6] => 2
[1,3,2,7,4,6,5] => 3
[1,3,2,7,5,4,6] => 3
[1,3,2,7,5,6,4] => 2
[1,3,2,7,6,4,5] => 2
[1,3,2,7,6,5,4] => 2
[1,3,4,2,5,6,7] => 0
[1,3,4,2,5,7,6] => 2
[1,3,4,2,6,5,7] => 2
[1,3,4,2,6,7,5] => 0
[1,3,4,2,7,5,6] => 1
[1,3,4,2,7,6,5] => 1
[1,3,4,5,2,6,7] => 0
[1,3,4,5,2,7,6] => 1
[1,3,4,5,6,2,7] => 1
[1,3,4,5,6,7,2] => 0
[1,3,4,5,7,2,6] => 1
[1,3,4,5,7,6,2] => 0
[1,3,4,6,2,5,7] => 2
[1,3,4,6,2,7,5] => 1
[1,3,4,6,5,2,7] => 1
[1,3,4,6,5,7,2] => 1
[1,3,4,6,7,2,5] => 1
[1,3,4,6,7,5,2] => 0
[1,3,4,7,2,5,6] => 0
[1,3,4,7,2,6,5] => 1
[1,3,4,7,5,2,6] => 1
[1,3,4,7,5,6,2] => 0
[1,3,4,7,6,2,5] => 1
[1,3,4,7,6,5,2] => 0
[1,3,5,2,4,6,7] => 3
[1,3,5,2,4,7,6] => 4
[1,3,5,2,6,4,7] => 4
[1,3,5,2,6,7,4] => 2
[1,3,5,2,7,4,6] => 4
[1,3,5,2,7,6,4] => 3
[1,3,5,4,2,6,7] => 2
[1,3,5,4,2,7,6] => 3
[1,3,5,4,6,2,7] => 4
[1,3,5,4,6,7,2] => 2
[1,3,5,4,7,2,6] => 4
[1,3,5,4,7,6,2] => 3
[1,3,5,6,2,4,7] => 3
[1,3,5,6,2,7,4] => 2
[1,3,5,6,4,2,7] => 2
[1,3,5,6,4,7,2] => 2
[1,3,5,6,7,2,4] => 2
[1,3,5,6,7,4,2] => 1
[1,3,5,7,2,4,6] => 5
[1,3,5,7,2,6,4] => 4
[1,3,5,7,4,2,6] => 4
[1,3,5,7,4,6,2] => 4
[1,3,5,7,6,2,4] => 4
[1,3,5,7,6,4,2] => 3
[1,3,6,2,4,5,7] => 2
[1,3,6,2,4,7,5] => 4
[1,3,6,2,5,4,7] => 4
[1,3,6,2,5,7,4] => 4
[1,3,6,2,7,4,5] => 3
[1,3,6,2,7,5,4] => 3
[1,3,6,4,2,5,7] => 4
[1,3,6,4,2,7,5] => 3
[1,3,6,4,5,2,7] => 3
[1,3,6,4,5,7,2] => 2
[1,3,6,4,7,2,5] => 4
[1,3,6,4,7,5,2] => 3
[1,3,6,5,2,4,7] => 4
[1,3,6,5,2,7,4] => 3
[1,3,6,5,4,2,7] => 3
[1,3,6,5,4,7,2] => 3
[1,3,6,5,7,2,4] => 4
[1,3,6,5,7,4,2] => 3
[1,3,6,7,2,4,5] => 1
[1,3,6,7,2,5,4] => 2
[1,3,6,7,4,2,5] => 2
[1,3,6,7,4,5,2] => 1
[1,3,6,7,5,2,4] => 2
[1,3,6,7,5,4,2] => 1
[1,3,7,2,4,5,6] => 2
[1,3,7,2,4,6,5] => 4
[1,3,7,2,5,4,6] => 4
[1,3,7,2,5,6,4] => 2
[1,3,7,2,6,4,5] => 3
[1,3,7,2,6,5,4] => 3
[1,3,7,4,2,5,6] => 2
[1,3,7,4,2,6,5] => 3
[1,3,7,4,5,2,6] => 3
[1,3,7,4,5,6,2] => 2
[1,3,7,4,6,2,5] => 4
[1,3,7,4,6,5,2] => 3
[1,3,7,5,2,4,6] => 4
[1,3,7,5,2,6,4] => 3
[1,3,7,5,4,2,6] => 3
[1,3,7,5,4,6,2] => 3
[1,3,7,5,6,2,4] => 3
[1,3,7,5,6,4,2] => 2
[1,3,7,6,2,4,5] => 2
[1,3,7,6,2,5,4] => 3
[1,3,7,6,4,2,5] => 3
[1,3,7,6,4,5,2] => 2
[1,3,7,6,5,2,4] => 3
[1,3,7,6,5,4,2] => 2
[1,4,2,3,5,6,7] => 1
[1,4,2,3,5,7,6] => 2
[1,4,2,3,6,5,7] => 2
[1,4,2,3,6,7,5] => 1
[1,4,2,3,7,5,6] => 1
[1,4,2,3,7,6,5] => 1
[1,4,2,5,3,6,7] => 2
[1,4,2,5,3,7,6] => 3
[1,4,2,5,6,3,7] => 2
[1,4,2,5,6,7,3] => 1
[1,4,2,5,7,3,6] => 4
[1,4,2,5,7,6,3] => 3
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 3
[1,4,2,6,5,3,7] => 3
[1,4,2,6,5,7,3] => 3
[1,4,2,6,7,3,5] => 2
[1,4,2,6,7,5,3] => 1
[1,4,2,7,3,5,6] => 2
[1,4,2,7,3,6,5] => 3
[1,4,2,7,5,3,6] => 3
[1,4,2,7,5,6,3] => 2
[1,4,2,7,6,3,5] => 3
[1,4,2,7,6,5,3] => 2
[1,4,3,2,5,6,7] => 1
[1,4,3,2,5,7,6] => 3
[1,4,3,2,6,5,7] => 3
[1,4,3,2,6,7,5] => 1
[1,4,3,2,7,5,6] => 2
[1,4,3,2,7,6,5] => 2
[1,4,3,5,2,6,7] => 2
[1,4,3,5,2,7,6] => 3
[1,4,3,5,6,2,7] => 2
[1,4,3,5,6,7,2] => 1
[1,4,3,5,7,2,6] => 4
[1,4,3,5,7,6,2] => 3
[1,4,3,6,2,5,7] => 4
[1,4,3,6,2,7,5] => 3
[1,4,3,6,5,2,7] => 3
[1,4,3,6,5,7,2] => 3
[1,4,3,6,7,2,5] => 2
[1,4,3,6,7,5,2] => 1
[1,4,3,7,2,5,6] => 2
[1,4,3,7,2,6,5] => 3
[1,4,3,7,5,2,6] => 3
[1,4,3,7,5,6,2] => 2
[1,4,3,7,6,2,5] => 3
[1,4,3,7,6,5,2] => 2
[1,4,5,2,3,6,7] => 0
[1,4,5,2,3,7,6] => 0
[1,4,5,2,6,3,7] => 2
[1,4,5,2,6,7,3] => 0
[1,4,5,2,7,3,6] => 2
[1,4,5,2,7,6,3] => 1
[1,4,5,3,2,6,7] => 0
[1,4,5,3,2,7,6] => 1
[1,4,5,3,6,2,7] => 2
[1,4,5,3,6,7,2] => 0
[1,4,5,3,7,2,6] => 2
[1,4,5,3,7,6,2] => 1
[1,4,5,6,2,3,7] => 0
[1,4,5,6,2,7,3] => 1
[1,4,5,6,3,2,7] => 1
[1,4,5,6,3,7,2] => 1
[1,4,5,6,7,2,3] => 0
[1,4,5,6,7,3,2] => 0
[1,4,5,7,2,3,6] => 0
[1,4,5,7,2,6,3] => 1
[1,4,5,7,3,2,6] => 1
[1,4,5,7,3,6,2] => 1
[1,4,5,7,6,2,3] => 0
[1,4,5,7,6,3,2] => 0
[1,4,6,2,3,5,7] => 3
[1,4,6,2,3,7,5] => 2
[1,4,6,2,5,3,7] => 4
[1,4,6,2,5,7,3] => 4
[1,4,6,2,7,3,5] => 4
[1,4,6,2,7,5,3] => 3
[1,4,6,3,2,5,7] => 4
[1,4,6,3,2,7,5] => 3
[1,4,6,3,5,2,7] => 4
[1,4,6,3,5,7,2] => 4
[1,4,6,3,7,2,5] => 4
[1,4,6,3,7,5,2] => 3
[1,4,6,5,2,3,7] => 2
[1,4,6,5,2,7,3] => 3
[1,4,6,5,3,2,7] => 3
[1,4,6,5,3,7,2] => 3
click to show generating function       
Description
The number of right floats of a permutation.
Let $\pi$ be a permutation of length $n$. A raft of $\pi$ is a non-empty maximal sequence of consecutive small ascents, St000441The number of successions of a permutation., and a right float is a large ascent not consecutive to any raft of $\pi$.
See Definition 3.10 and Example 3.11 in [1].
References
[1] Billey, S. C., Konvalinka, M., Petersen, T. K., Slofstra, W., Tenner, B. E. Parabolic double cosets in Coxeter groups arXiv:1612.00736
Code
def statistic(pi):
    rafts = [[]]
    for i in range(len(pi)-1):
        if pi[i+1] == pi[i]+1:
            rafts[-1].append(i)
        else:
            rafts.append([])
    rafts = sum(rafts,[])
    return sum(1 for i in range(len(pi)-1)
               if pi[i+1] > pi[i]+1 and i-1 not in rafts and i+1 not in rafts)

Created
Dec 05, 2016 at 12:37 by Christian Stump
Updated
Nov 03, 2017 at 00:20 by Martin Rubey