Identifier
Identifier
Values
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 0
[2,3,1] => 1
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 0
[1,3,4,2] => 1
[1,4,2,3] => 0
[1,4,3,2] => 0
[2,1,3,4] => 0
[2,1,4,3] => 0
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 1
[3,1,2,4] => 0
[3,1,4,2] => 1
[3,2,1,4] => 0
[3,2,4,1] => 1
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 0
[4,1,3,2] => 0
[4,2,1,3] => 0
[4,2,3,1] => 1
[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] => 0
[1,2,4,5,3] => 1
[1,2,5,3,4] => 0
[1,2,5,4,3] => 0
[1,3,2,4,5] => 0
[1,3,2,5,4] => 0
[1,3,4,2,5] => 1
[1,3,4,5,2] => 1
[1,3,5,2,4] => 1
[1,3,5,4,2] => 1
[1,4,2,3,5] => 0
[1,4,2,5,3] => 1
[1,4,3,2,5] => 0
[1,4,3,5,2] => 1
[1,4,5,2,3] => 1
[1,4,5,3,2] => 1
[1,5,2,3,4] => 0
[1,5,2,4,3] => 0
[1,5,3,2,4] => 0
[1,5,3,4,2] => 1
[1,5,4,2,3] => 0
[1,5,4,3,2] => 0
[2,1,3,4,5] => 0
[2,1,3,5,4] => 0
[2,1,4,3,5] => 0
[2,1,4,5,3] => 1
[2,1,5,3,4] => 0
[2,1,5,4,3] => 0
[2,3,1,4,5] => 1
[2,3,1,5,4] => 1
[2,3,4,1,5] => 1
[2,3,4,5,1] => 1
[2,3,5,1,4] => 1
[2,3,5,4,1] => 1
[2,4,1,3,5] => 1
[2,4,1,5,3] => 2
[2,4,3,1,5] => 1
[2,4,3,5,1] => 1
[2,4,5,1,3] => 2
[2,4,5,3,1] => 2
[2,5,1,3,4] => 1
[2,5,1,4,3] => 1
[2,5,3,1,4] => 1
[2,5,3,4,1] => 1
[2,5,4,1,3] => 1
[2,5,4,3,1] => 1
[3,1,2,4,5] => 0
[3,1,2,5,4] => 0
[3,1,4,2,5] => 1
[3,1,4,5,2] => 1
[3,1,5,2,4] => 1
[3,1,5,4,2] => 1
[3,2,1,4,5] => 0
[3,2,1,5,4] => 0
[3,2,4,1,5] => 1
[3,2,4,5,1] => 1
[3,2,5,1,4] => 1
[3,2,5,4,1] => 1
[3,4,1,2,5] => 1
[3,4,1,5,2] => 1
[3,4,2,1,5] => 1
[3,4,2,5,1] => 2
[3,4,5,1,2] => 1
[3,4,5,2,1] => 1
[3,5,1,2,4] => 1
[3,5,1,4,2] => 1
[3,5,2,1,4] => 1
[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] => 1
[4,1,3,2,5] => 0
[4,1,3,5,2] => 1
[4,1,5,2,3] => 1
[4,1,5,3,2] => 1
[4,2,1,3,5] => 0
[4,2,1,5,3] => 1
[4,2,3,1,5] => 1
[4,2,3,5,1] => 1
[4,2,5,1,3] => 2
[4,2,5,3,1] => 2
[4,3,1,2,5] => 0
[4,3,1,5,2] => 1
[4,3,2,1,5] => 0
[4,3,2,5,1] => 1
[4,3,5,1,2] => 1
[4,3,5,2,1] => 1
[4,5,1,2,3] => 1
[4,5,1,3,2] => 1
[4,5,2,1,3] => 1
[4,5,2,3,1] => 2
[4,5,3,1,2] => 1
[4,5,3,2,1] => 1
[5,1,2,3,4] => 0
[5,1,2,4,3] => 0
[5,1,3,2,4] => 0
[5,1,3,4,2] => 1
[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] => 1
[5,2,3,4,1] => 1
[5,2,4,1,3] => 1
[5,2,4,3,1] => 1
[5,3,1,2,4] => 0
[5,3,1,4,2] => 1
[5,3,2,1,4] => 0
[5,3,2,4,1] => 1
[5,3,4,1,2] => 1
[5,3,4,2,1] => 1
[5,4,1,2,3] => 0
[5,4,1,3,2] => 0
[5,4,2,1,3] => 0
[5,4,2,3,1] => 1
[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] => 0
[1,2,3,5,6,4] => 1
[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] => 0
[1,2,4,5,3,6] => 1
[1,2,4,5,6,3] => 1
[1,2,4,6,3,5] => 1
[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] => 0
[1,2,5,4,6,3] => 1
[1,2,5,6,3,4] => 1
[1,2,5,6,4,3] => 1
[1,2,6,3,4,5] => 0
[1,2,6,3,5,4] => 0
[1,2,6,4,3,5] => 0
[1,2,6,4,5,3] => 1
[1,2,6,5,3,4] => 0
[1,2,6,5,4,3] => 0
[1,3,2,4,5,6] => 0
[1,3,2,4,6,5] => 0
[1,3,2,5,4,6] => 0
[1,3,2,5,6,4] => 1
[1,3,2,6,4,5] => 0
[1,3,2,6,5,4] => 0
[1,3,4,2,5,6] => 1
[1,3,4,2,6,5] => 1
[1,3,4,5,2,6] => 1
[1,3,4,5,6,2] => 1
[1,3,4,6,2,5] => 1
[1,3,4,6,5,2] => 1
[1,3,5,2,4,6] => 1
[1,3,5,2,6,4] => 2
[1,3,5,4,2,6] => 1
[1,3,5,4,6,2] => 1
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 2
[1,3,6,2,4,5] => 1
[1,3,6,2,5,4] => 1
[1,3,6,4,2,5] => 1
[1,3,6,4,5,2] => 1
[1,3,6,5,2,4] => 1
[1,3,6,5,4,2] => 1
[1,4,2,3,5,6] => 0
[1,4,2,3,6,5] => 0
[1,4,2,5,3,6] => 1
[1,4,2,5,6,3] => 1
[1,4,2,6,3,5] => 1
[1,4,2,6,5,3] => 1
[1,4,3,2,5,6] => 0
[1,4,3,2,6,5] => 0
[1,4,3,5,2,6] => 1
[1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => 1
[1,4,3,6,5,2] => 1
[1,4,5,2,3,6] => 1
[1,4,5,2,6,3] => 1
[1,4,5,3,2,6] => 1
[1,4,5,3,6,2] => 2
[1,4,5,6,2,3] => 1
[1,4,5,6,3,2] => 1
[1,4,6,2,3,5] => 1
[1,4,6,2,5,3] => 1
[1,4,6,3,2,5] => 1
[1,4,6,3,5,2] => 2
[1,4,6,5,2,3] => 1
[1,4,6,5,3,2] => 1
[1,5,2,3,4,6] => 0
[1,5,2,3,6,4] => 1
[1,5,2,4,3,6] => 0
[1,5,2,4,6,3] => 1
[1,5,2,6,3,4] => 1
[1,5,2,6,4,3] => 1
[1,5,3,2,4,6] => 0
[1,5,3,2,6,4] => 1
[1,5,3,4,2,6] => 1
[1,5,3,4,6,2] => 1
[1,5,3,6,2,4] => 2
[1,5,3,6,4,2] => 2
[1,5,4,2,3,6] => 0
[1,5,4,2,6,3] => 1
[1,5,4,3,2,6] => 0
[1,5,4,3,6,2] => 1
[1,5,4,6,2,3] => 1
[1,5,4,6,3,2] => 1
[1,5,6,2,3,4] => 1
[1,5,6,2,4,3] => 1
[1,5,6,3,2,4] => 1
[1,5,6,3,4,2] => 2
[1,5,6,4,2,3] => 1
[1,5,6,4,3,2] => 1
[1,6,2,3,4,5] => 0
[1,6,2,3,5,4] => 0
[1,6,2,4,3,5] => 0
[1,6,2,4,5,3] => 1
[1,6,2,5,3,4] => 0
[1,6,2,5,4,3] => 0
[1,6,3,2,4,5] => 0
[1,6,3,2,5,4] => 0
[1,6,3,4,2,5] => 1
[1,6,3,4,5,2] => 1
[1,6,3,5,2,4] => 1
[1,6,3,5,4,2] => 1
[1,6,4,2,3,5] => 0
[1,6,4,2,5,3] => 1
[1,6,4,3,2,5] => 0
[1,6,4,3,5,2] => 1
[1,6,4,5,2,3] => 1
[1,6,4,5,3,2] => 1
[1,6,5,2,3,4] => 0
[1,6,5,2,4,3] => 0
[1,6,5,3,2,4] => 0
[1,6,5,3,4,2] => 1
[1,6,5,4,2,3] => 0
[1,6,5,4,3,2] => 0
[2,1,3,4,5,6] => 0
[2,1,3,4,6,5] => 0
[2,1,3,5,4,6] => 0
[2,1,3,5,6,4] => 1
[2,1,3,6,4,5] => 0
[2,1,3,6,5,4] => 0
[2,1,4,3,5,6] => 0
[2,1,4,3,6,5] => 0
[2,1,4,5,3,6] => 1
[2,1,4,5,6,3] => 1
[2,1,4,6,3,5] => 1
[2,1,4,6,5,3] => 1
[2,1,5,3,4,6] => 0
[2,1,5,3,6,4] => 1
[2,1,5,4,3,6] => 0
[2,1,5,4,6,3] => 1
[2,1,5,6,3,4] => 1
[2,1,5,6,4,3] => 1
[2,1,6,3,4,5] => 0
[2,1,6,3,5,4] => 0
[2,1,6,4,3,5] => 0
[2,1,6,4,5,3] => 1
[2,1,6,5,3,4] => 0
[2,1,6,5,4,3] => 0
[2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => 1
[2,3,1,5,4,6] => 1
[2,3,1,5,6,4] => 2
[2,3,1,6,4,5] => 1
[2,3,1,6,5,4] => 1
[2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => 1
[2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => 1
[2,3,4,6,5,1] => 1
[2,3,5,1,4,6] => 1
[2,3,5,1,6,4] => 2
[2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => 1
[2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => 2
[2,3,6,1,4,5] => 1
[2,3,6,1,5,4] => 1
[2,3,6,4,1,5] => 1
[2,3,6,4,5,1] => 1
[2,3,6,5,1,4] => 1
[2,3,6,5,4,1] => 1
[2,4,1,3,5,6] => 1
[2,4,1,3,6,5] => 1
[2,4,1,5,3,6] => 2
[2,4,1,5,6,3] => 2
[2,4,1,6,3,5] => 2
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 1
[2,4,3,1,6,5] => 1
[2,4,3,5,1,6] => 1
[2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => 1
[2,4,3,6,5,1] => 1
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 2
[2,4,5,3,6,1] => 2
[2,4,5,6,1,3] => 2
[2,4,5,6,3,1] => 2
[2,4,6,1,3,5] => 2
[2,4,6,1,5,3] => 2
[2,4,6,3,1,5] => 2
[2,4,6,3,5,1] => 2
[2,4,6,5,1,3] => 2
[2,4,6,5,3,1] => 2
[2,5,1,3,4,6] => 1
[2,5,1,3,6,4] => 2
[2,5,1,4,3,6] => 1
[2,5,1,4,6,3] => 2
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 1
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 1
[2,5,3,4,6,1] => 1
[2,5,3,6,1,4] => 2
[2,5,3,6,4,1] => 2
[2,5,4,1,3,6] => 1
[2,5,4,1,6,3] => 2
[2,5,4,3,1,6] => 1
[2,5,4,3,6,1] => 1
[2,5,4,6,1,3] => 2
[2,5,4,6,3,1] => 2
[2,5,6,1,3,4] => 2
[2,5,6,1,4,3] => 2
[2,5,6,3,1,4] => 2
[2,5,6,3,4,1] => 2
[2,5,6,4,1,3] => 2
[2,5,6,4,3,1] => 2
[2,6,1,3,4,5] => 1
[2,6,1,3,5,4] => 1
[2,6,1,4,3,5] => 1
[2,6,1,4,5,3] => 2
[2,6,1,5,3,4] => 1
[2,6,1,5,4,3] => 1
[2,6,3,1,4,5] => 1
[2,6,3,1,5,4] => 1
[2,6,3,4,1,5] => 1
[2,6,3,4,5,1] => 1
[2,6,3,5,1,4] => 1
[2,6,3,5,4,1] => 1
[2,6,4,1,3,5] => 1
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 1
[2,6,4,3,5,1] => 1
[2,6,4,5,1,3] => 2
[2,6,4,5,3,1] => 2
[2,6,5,1,3,4] => 1
[2,6,5,1,4,3] => 1
[2,6,5,3,1,4] => 1
[2,6,5,3,4,1] => 1
[2,6,5,4,1,3] => 1
[2,6,5,4,3,1] => 1
[3,1,2,4,5,6] => 0
[3,1,2,4,6,5] => 0
[3,1,2,5,4,6] => 0
[3,1,2,5,6,4] => 1
[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] => 1
[3,1,4,5,2,6] => 1
[3,1,4,5,6,2] => 1
[3,1,4,6,2,5] => 1
[3,1,4,6,5,2] => 1
[3,1,5,2,4,6] => 1
[3,1,5,2,6,4] => 2
[3,1,5,4,2,6] => 1
[3,1,5,4,6,2] => 1
[3,1,5,6,2,4] => 2
[3,1,5,6,4,2] => 2
[3,1,6,2,4,5] => 1
[3,1,6,2,5,4] => 1
[3,1,6,4,2,5] => 1
[3,1,6,4,5,2] => 1
[3,1,6,5,2,4] => 1
[3,1,6,5,4,2] => 1
[3,2,1,4,5,6] => 0
[3,2,1,4,6,5] => 0
[3,2,1,5,4,6] => 0
[3,2,1,5,6,4] => 1
[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] => 1
[3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => 1
[3,2,4,6,1,5] => 1
[3,2,4,6,5,1] => 1
[3,2,5,1,4,6] => 1
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 1
[3,2,5,4,6,1] => 1
[3,2,5,6,1,4] => 2
[3,2,5,6,4,1] => 2
[3,2,6,1,4,5] => 1
[3,2,6,1,5,4] => 1
[3,2,6,4,1,5] => 1
[3,2,6,4,5,1] => 1
[3,2,6,5,1,4] => 1
[3,2,6,5,4,1] => 1
[3,4,1,2,5,6] => 1
[3,4,1,2,6,5] => 1
[3,4,1,5,2,6] => 1
[3,4,1,5,6,2] => 1
[3,4,1,6,2,5] => 1
[3,4,1,6,5,2] => 1
[3,4,2,1,5,6] => 1
[3,4,2,1,6,5] => 1
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 2
[3,4,2,6,1,5] => 2
[3,4,2,6,5,1] => 2
[3,4,5,1,2,6] => 1
[3,4,5,1,6,2] => 1
[3,4,5,2,1,6] => 1
[3,4,5,2,6,1] => 2
[3,4,5,6,1,2] => 1
[3,4,5,6,2,1] => 1
[3,4,6,1,2,5] => 1
[3,4,6,1,5,2] => 1
[3,4,6,2,1,5] => 1
[3,4,6,2,5,1] => 2
[3,4,6,5,1,2] => 1
[3,4,6,5,2,1] => 1
[3,5,1,2,4,6] => 1
[3,5,1,2,6,4] => 2
[3,5,1,4,2,6] => 1
[3,5,1,4,6,2] => 1
[3,5,1,6,2,4] => 2
[3,5,1,6,4,2] => 2
[3,5,2,1,4,6] => 1
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 2
[3,5,2,4,6,1] => 2
[3,5,2,6,1,4] => 3
[3,5,2,6,4,1] => 3
[3,5,4,1,2,6] => 1
[3,5,4,1,6,2] => 1
[3,5,4,2,1,6] => 1
[3,5,4,2,6,1] => 2
[3,5,4,6,1,2] => 1
[3,5,4,6,2,1] => 1
[3,5,6,1,2,4] => 2
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 2
[3,5,6,2,4,1] => 3
[3,5,6,4,1,2] => 2
[3,5,6,4,2,1] => 2
[3,6,1,2,4,5] => 1
[3,6,1,2,5,4] => 1
[3,6,1,4,2,5] => 1
[3,6,1,4,5,2] => 1
[3,6,1,5,2,4] => 1
[3,6,1,5,4,2] => 1
[3,6,2,1,4,5] => 1
[3,6,2,1,5,4] => 1
[3,6,2,4,1,5] => 2
[3,6,2,4,5,1] => 2
[3,6,2,5,1,4] => 2
[3,6,2,5,4,1] => 2
[3,6,4,1,2,5] => 1
[3,6,4,1,5,2] => 1
[3,6,4,2,1,5] => 1
[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] => 1
[3,6,5,2,1,4] => 1
[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] => 1
[4,1,2,6,3,5] => 1
[4,1,2,6,5,3] => 1
[4,1,3,2,5,6] => 0
[4,1,3,2,6,5] => 0
[4,1,3,5,2,6] => 1
[4,1,3,5,6,2] => 1
[4,1,3,6,2,5] => 1
[4,1,3,6,5,2] => 1
[4,1,5,2,3,6] => 1
[4,1,5,2,6,3] => 1
[4,1,5,3,2,6] => 1
[4,1,5,3,6,2] => 2
[4,1,5,6,2,3] => 1
[4,1,5,6,3,2] => 1
[4,1,6,2,3,5] => 1
[4,1,6,2,5,3] => 1
[4,1,6,3,2,5] => 1
[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] => 0
[4,2,1,3,6,5] => 0
[4,2,1,5,3,6] => 1
[4,2,1,5,6,3] => 1
[4,2,1,6,3,5] => 1
[4,2,1,6,5,3] => 1
[4,2,3,1,5,6] => 1
[4,2,3,1,6,5] => 1
[4,2,3,5,1,6] => 1
[4,2,3,5,6,1] => 1
[4,2,3,6,1,5] => 1
[4,2,3,6,5,1] => 1
[4,2,5,1,3,6] => 2
[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] => 2
[4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => 2
[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] => 2
[4,3,1,2,5,6] => 0
[4,3,1,2,6,5] => 0
[4,3,1,5,2,6] => 1
[4,3,1,5,6,2] => 1
[4,3,1,6,2,5] => 1
[4,3,1,6,5,2] => 1
[4,3,2,1,5,6] => 0
[4,3,2,1,6,5] => 0
[4,3,2,5,1,6] => 1
[4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => 1
[4,3,2,6,5,1] => 1
[4,3,5,1,2,6] => 1
[4,3,5,1,6,2] => 1
[4,3,5,2,1,6] => 1
[4,3,5,2,6,1] => 2
[4,3,5,6,1,2] => 1
[4,3,5,6,2,1] => 1
[4,3,6,1,2,5] => 1
[4,3,6,1,5,2] => 1
[4,3,6,2,1,5] => 1
[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] => 1
[4,5,1,2,6,3] => 1
[4,5,1,3,2,6] => 1
[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] => 1
[4,5,2,1,6,3] => 1
[4,5,2,3,1,6] => 2
[4,5,2,3,6,1] => 2
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 2
[4,5,3,1,2,6] => 1
[4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 2
[4,5,3,6,1,2] => 2
[4,5,3,6,2,1] => 2
[4,5,6,1,2,3] => 1
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 2
[4,5,6,3,1,2] => 1
[4,5,6,3,2,1] => 1
[4,6,1,2,3,5] => 1
[4,6,1,2,5,3] => 1
[4,6,1,3,2,5] => 1
[4,6,1,3,5,2] => 2
[4,6,1,5,2,3] => 1
[4,6,1,5,3,2] => 1
[4,6,2,1,3,5] => 1
[4,6,2,1,5,3] => 1
[4,6,2,3,1,5] => 2
[4,6,2,3,5,1] => 2
[4,6,2,5,1,3] => 2
[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] => 1
[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] => 1
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 2
[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] => 1
[5,1,2,4,3,6] => 0
[5,1,2,4,6,3] => 1
[5,1,2,6,3,4] => 1
[5,1,2,6,4,3] => 1
[5,1,3,2,4,6] => 0
[5,1,3,2,6,4] => 1
[5,1,3,4,2,6] => 1
[5,1,3,4,6,2] => 1
[5,1,3,6,2,4] => 2
[5,1,3,6,4,2] => 2
[5,1,4,2,3,6] => 0
[5,1,4,2,6,3] => 1
[5,1,4,3,2,6] => 0
[5,1,4,3,6,2] => 1
[5,1,4,6,2,3] => 1
[5,1,4,6,3,2] => 1
[5,1,6,2,3,4] => 1
[5,1,6,2,4,3] => 1
[5,1,6,3,2,4] => 1
[5,1,6,3,4,2] => 2
[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] => 1
[5,2,1,4,3,6] => 0
[5,2,1,4,6,3] => 1
[5,2,1,6,3,4] => 1
[5,2,1,6,4,3] => 1
[5,2,3,1,4,6] => 1
[5,2,3,1,6,4] => 2
[5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => 1
[5,2,3,6,1,4] => 2
[5,2,3,6,4,1] => 2
[5,2,4,1,3,6] => 1
[5,2,4,1,6,3] => 2
[5,2,4,3,1,6] => 1
[5,2,4,3,6,1] => 1
[5,2,4,6,1,3] => 2
[5,2,4,6,3,1] => 2
[5,2,6,1,3,4] => 2
[5,2,6,1,4,3] => 2
[5,2,6,3,1,4] => 2
[5,2,6,3,4,1] => 2
[5,2,6,4,1,3] => 2
[5,2,6,4,3,1] => 2
[5,3,1,2,4,6] => 0
[5,3,1,2,6,4] => 1
[5,3,1,4,2,6] => 1
[5,3,1,4,6,2] => 1
[5,3,1,6,2,4] => 2
[5,3,1,6,4,2] => 2
[5,3,2,1,4,6] => 0
[5,3,2,1,6,4] => 1
[5,3,2,4,1,6] => 1
[5,3,2,4,6,1] => 1
[5,3,2,6,1,4] => 2
[5,3,2,6,4,1] => 2
[5,3,4,1,2,6] => 1
[5,3,4,1,6,2] => 1
[5,3,4,2,1,6] => 1
[5,3,4,2,6,1] => 2
[5,3,4,6,1,2] => 1
[5,3,4,6,2,1] => 1
[5,3,6,1,2,4] => 2
[5,3,6,1,4,2] => 2
[5,3,6,2,1,4] => 2
[5,3,6,2,4,1] => 3
[5,3,6,4,1,2] => 2
[5,3,6,4,2,1] => 2
[5,4,1,2,3,6] => 0
[5,4,1,2,6,3] => 1
[5,4,1,3,2,6] => 0
[5,4,1,3,6,2] => 1
[5,4,1,6,2,3] => 1
[5,4,1,6,3,2] => 1
[5,4,2,1,3,6] => 0
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 1
[5,4,2,3,6,1] => 1
[5,4,2,6,1,3] => 2
[5,4,2,6,3,1] => 2
[5,4,3,1,2,6] => 0
[5,4,3,1,6,2] => 1
[5,4,3,2,1,6] => 0
[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] => 1
[5,4,6,2,1,3] => 1
[5,4,6,2,3,1] => 2
[5,4,6,3,1,2] => 1
[5,4,6,3,2,1] => 1
[5,6,1,2,3,4] => 1
[5,6,1,2,4,3] => 1
[5,6,1,3,2,4] => 1
[5,6,1,3,4,2] => 2
[5,6,1,4,2,3] => 1
[5,6,1,4,3,2] => 1
[5,6,2,1,3,4] => 1
[5,6,2,1,4,3] => 1
[5,6,2,3,1,4] => 2
[5,6,2,3,4,1] => 2
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 2
[5,6,3,1,2,4] => 1
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => 2
[5,6,3,4,1,2] => 2
[5,6,3,4,2,1] => 2
[5,6,4,1,2,3] => 1
[5,6,4,1,3,2] => 1
[5,6,4,2,1,3] => 1
[5,6,4,2,3,1] => 2
[5,6,4,3,1,2] => 1
[5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => 0
[6,1,2,3,5,4] => 0
[6,1,2,4,3,5] => 0
[6,1,2,4,5,3] => 1
[6,1,2,5,3,4] => 0
[6,1,2,5,4,3] => 0
[6,1,3,2,4,5] => 0
[6,1,3,2,5,4] => 0
[6,1,3,4,2,5] => 1
[6,1,3,4,5,2] => 1
[6,1,3,5,2,4] => 1
[6,1,3,5,4,2] => 1
[6,1,4,2,3,5] => 0
[6,1,4,2,5,3] => 1
[6,1,4,3,2,5] => 0
[6,1,4,3,5,2] => 1
[6,1,4,5,2,3] => 1
[6,1,4,5,3,2] => 1
[6,1,5,2,3,4] => 0
[6,1,5,2,4,3] => 0
[6,1,5,3,2,4] => 0
[6,1,5,3,4,2] => 1
[6,1,5,4,2,3] => 0
[6,1,5,4,3,2] => 0
[6,2,1,3,4,5] => 0
[6,2,1,3,5,4] => 0
[6,2,1,4,3,5] => 0
[6,2,1,4,5,3] => 1
[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] => 1
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => 1
[6,2,3,5,4,1] => 1
[6,2,4,1,3,5] => 1
[6,2,4,1,5,3] => 2
[6,2,4,3,1,5] => 1
[6,2,4,3,5,1] => 1
[6,2,4,5,1,3] => 2
[6,2,4,5,3,1] => 2
[6,2,5,1,3,4] => 1
[6,2,5,1,4,3] => 1
[6,2,5,3,1,4] => 1
[6,2,5,3,4,1] => 1
[6,2,5,4,1,3] => 1
[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] => 1
[6,3,1,4,5,2] => 1
[6,3,1,5,2,4] => 1
[6,3,1,5,4,2] => 1
[6,3,2,1,4,5] => 0
[6,3,2,1,5,4] => 0
[6,3,2,4,1,5] => 1
[6,3,2,4,5,1] => 1
[6,3,2,5,1,4] => 1
[6,3,2,5,4,1] => 1
[6,3,4,1,2,5] => 1
[6,3,4,1,5,2] => 1
[6,3,4,2,1,5] => 1
[6,3,4,2,5,1] => 2
[6,3,4,5,1,2] => 1
[6,3,4,5,2,1] => 1
[6,3,5,1,2,4] => 1
[6,3,5,1,4,2] => 1
[6,3,5,2,1,4] => 1
[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] => 1
[6,4,1,3,2,5] => 0
[6,4,1,3,5,2] => 1
[6,4,1,5,2,3] => 1
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 0
[6,4,2,1,5,3] => 1
[6,4,2,3,1,5] => 1
[6,4,2,3,5,1] => 1
[6,4,2,5,1,3] => 2
[6,4,2,5,3,1] => 2
[6,4,3,1,2,5] => 0
[6,4,3,1,5,2] => 1
[6,4,3,2,1,5] => 0
[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] => 1
[6,4,5,1,3,2] => 1
[6,4,5,2,1,3] => 1
[6,4,5,2,3,1] => 2
[6,4,5,3,1,2] => 1
[6,4,5,3,2,1] => 1
[6,5,1,2,3,4] => 0
[6,5,1,2,4,3] => 0
[6,5,1,3,2,4] => 0
[6,5,1,3,4,2] => 1
[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] => 1
[6,5,2,3,4,1] => 1
[6,5,2,4,1,3] => 1
[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] => 0
[6,5,3,2,4,1] => 1
[6,5,3,4,1,2] => 1
[6,5,3,4,2,1] => 1
[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] => 1
[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] => 0
[1,2,3,4,6,7,5] => 1
[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] => 0
[1,2,3,5,6,4,7] => 1
[1,2,3,5,6,7,4] => 1
[1,2,3,5,7,4,6] => 1
[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] => 0
[1,2,3,6,5,7,4] => 1
[1,2,3,6,7,4,5] => 1
[1,2,3,6,7,5,4] => 1
[1,2,3,7,4,5,6] => 0
[1,2,3,7,4,6,5] => 0
[1,2,3,7,5,4,6] => 0
[1,2,3,7,5,6,4] => 1
[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] => 0
[1,2,4,3,6,5,7] => 0
[1,2,4,3,6,7,5] => 1
[1,2,4,3,7,5,6] => 0
[1,2,4,3,7,6,5] => 0
[1,2,4,5,3,6,7] => 1
[1,2,4,5,3,7,6] => 1
[1,2,4,5,6,3,7] => 1
[1,2,4,5,6,7,3] => 1
[1,2,4,5,7,3,6] => 1
[1,2,4,5,7,6,3] => 1
[1,2,4,6,3,5,7] => 1
[1,2,4,6,3,7,5] => 2
[1,2,4,6,5,3,7] => 1
[1,2,4,6,5,7,3] => 1
[1,2,4,6,7,3,5] => 2
[1,2,4,6,7,5,3] => 2
[1,2,4,7,3,5,6] => 1
[1,2,4,7,3,6,5] => 1
[1,2,4,7,5,3,6] => 1
[1,2,4,7,5,6,3] => 1
[1,2,4,7,6,3,5] => 1
[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] => 1
[1,2,5,3,6,7,4] => 1
[1,2,5,3,7,4,6] => 1
[1,2,5,3,7,6,4] => 1
[1,2,5,4,3,6,7] => 0
[1,2,5,4,3,7,6] => 0
[1,2,5,4,6,3,7] => 1
[1,2,5,4,6,7,3] => 1
[1,2,5,4,7,3,6] => 1
[1,2,5,4,7,6,3] => 1
[1,2,5,6,3,4,7] => 1
[1,2,5,6,3,7,4] => 1
[1,2,5,6,4,3,7] => 1
[1,2,5,6,4,7,3] => 2
[1,2,5,6,7,3,4] => 1
[1,2,5,6,7,4,3] => 1
[1,2,5,7,3,4,6] => 1
[1,2,5,7,3,6,4] => 1
[1,2,5,7,4,3,6] => 1
[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] => 1
[1,2,6,3,5,4,7] => 0
[1,2,6,3,5,7,4] => 1
[1,2,6,3,7,4,5] => 1
[1,2,6,3,7,5,4] => 1
[1,2,6,4,3,5,7] => 0
[1,2,6,4,3,7,5] => 1
[1,2,6,4,5,3,7] => 1
[1,2,6,4,5,7,3] => 1
[1,2,6,4,7,3,5] => 2
[1,2,6,4,7,5,3] => 2
[1,2,6,5,3,4,7] => 0
[1,2,6,5,3,7,4] => 1
[1,2,6,5,4,3,7] => 0
[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] => 1
[1,2,6,7,3,5,4] => 1
[1,2,6,7,4,3,5] => 1
[1,2,6,7,4,5,3] => 2
[1,2,6,7,5,3,4] => 1
[1,2,6,7,5,4,3] => 1
[1,2,7,3,4,5,6] => 0
[1,2,7,3,4,6,5] => 0
[1,2,7,3,5,4,6] => 0
[1,2,7,3,5,6,4] => 1
[1,2,7,3,6,4,5] => 0
[1,2,7,3,6,5,4] => 0
[1,2,7,4,3,5,6] => 0
[1,2,7,4,3,6,5] => 0
[1,2,7,4,5,3,6] => 1
[1,2,7,4,5,6,3] => 1
[1,2,7,4,6,3,5] => 1
[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] => 0
[1,2,7,5,4,6,3] => 1
[1,2,7,5,6,3,4] => 1
[1,2,7,5,6,4,3] => 1
[1,2,7,6,3,4,5] => 0
[1,2,7,6,3,5,4] => 0
[1,2,7,6,4,3,5] => 0
[1,2,7,6,4,5,3] => 1
[1,2,7,6,5,3,4] => 0
[1,2,7,6,5,4,3] => 0
[1,3,2,4,5,6,7] => 0
[1,3,2,4,5,7,6] => 0
[1,3,2,4,6,5,7] => 0
[1,3,2,4,6,7,5] => 1
[1,3,2,4,7,5,6] => 0
[1,3,2,4,7,6,5] => 0
[1,3,2,5,4,6,7] => 0
[1,3,2,5,4,7,6] => 0
[1,3,2,5,6,4,7] => 1
[1,3,2,5,6,7,4] => 1
[1,3,2,5,7,4,6] => 1
[1,3,2,5,7,6,4] => 1
[1,3,2,6,4,5,7] => 0
[1,3,2,6,4,7,5] => 1
[1,3,2,6,5,4,7] => 0
[1,3,2,6,5,7,4] => 1
[1,3,2,6,7,4,5] => 1
[1,3,2,6,7,5,4] => 1
[1,3,2,7,4,5,6] => 0
[1,3,2,7,4,6,5] => 0
[1,3,2,7,5,4,6] => 0
[1,3,2,7,5,6,4] => 1
[1,3,2,7,6,4,5] => 0
[1,3,2,7,6,5,4] => 0
[1,3,4,2,5,6,7] => 1
[1,3,4,2,5,7,6] => 1
[1,3,4,2,6,5,7] => 1
[1,3,4,2,6,7,5] => 2
[1,3,4,2,7,5,6] => 1
[1,3,4,2,7,6,5] => 1
[1,3,4,5,2,6,7] => 1
[1,3,4,5,2,7,6] => 1
[1,3,4,5,6,2,7] => 1
[1,3,4,5,6,7,2] => 1
[1,3,4,5,7,2,6] => 1
[1,3,4,5,7,6,2] => 1
[1,3,4,6,2,5,7] => 1
[1,3,4,6,2,7,5] => 2
[1,3,4,6,5,2,7] => 1
[1,3,4,6,5,7,2] => 1
[1,3,4,6,7,2,5] => 2
[1,3,4,6,7,5,2] => 2
[1,3,4,7,2,5,6] => 1
[1,3,4,7,2,6,5] => 1
[1,3,4,7,5,2,6] => 1
[1,3,4,7,5,6,2] => 1
[1,3,4,7,6,2,5] => 1
[1,3,4,7,6,5,2] => 1
[1,3,5,2,4,6,7] => 1
[1,3,5,2,4,7,6] => 1
[1,3,5,2,6,4,7] => 2
[1,3,5,2,6,7,4] => 2
[1,3,5,2,7,4,6] => 2
[1,3,5,2,7,6,4] => 2
[1,3,5,4,2,6,7] => 1
[1,3,5,4,2,7,6] => 1
[1,3,5,4,6,2,7] => 1
[1,3,5,4,6,7,2] => 1
[1,3,5,4,7,2,6] => 1
[1,3,5,4,7,6,2] => 1
[1,3,5,6,2,4,7] => 2
[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] => 2
[1,3,5,7,2,4,6] => 2
[1,3,5,7,2,6,4] => 2
[1,3,5,7,4,2,6] => 2
[1,3,5,7,4,6,2] => 2
[1,3,5,7,6,2,4] => 2
[1,3,5,7,6,4,2] => 2
[1,3,6,2,4,5,7] => 1
[1,3,6,2,4,7,5] => 2
[1,3,6,2,5,4,7] => 1
[1,3,6,2,5,7,4] => 2
[1,3,6,2,7,4,5] => 2
[1,3,6,2,7,5,4] => 2
[1,3,6,4,2,5,7] => 1
[1,3,6,4,2,7,5] => 2
[1,3,6,4,5,2,7] => 1
[1,3,6,4,5,7,2] => 1
[1,3,6,4,7,2,5] => 2
[1,3,6,4,7,5,2] => 2
[1,3,6,5,2,4,7] => 1
[1,3,6,5,2,7,4] => 2
[1,3,6,5,4,2,7] => 1
[1,3,6,5,4,7,2] => 1
[1,3,6,5,7,2,4] => 2
[1,3,6,5,7,4,2] => 2
[1,3,6,7,2,4,5] => 2
[1,3,6,7,2,5,4] => 2
[1,3,6,7,4,2,5] => 2
[1,3,6,7,4,5,2] => 2
[1,3,6,7,5,2,4] => 2
[1,3,6,7,5,4,2] => 2
[1,3,7,2,4,5,6] => 1
[1,3,7,2,4,6,5] => 1
[1,3,7,2,5,4,6] => 1
[1,3,7,2,5,6,4] => 2
[1,3,7,2,6,4,5] => 1
[1,3,7,2,6,5,4] => 1
[1,3,7,4,2,5,6] => 1
[1,3,7,4,2,6,5] => 1
[1,3,7,4,5,2,6] => 1
[1,3,7,4,5,6,2] => 1
[1,3,7,4,6,2,5] => 1
[1,3,7,4,6,5,2] => 1
[1,3,7,5,2,4,6] => 1
[1,3,7,5,2,6,4] => 2
[1,3,7,5,4,2,6] => 1
[1,3,7,5,4,6,2] => 1
[1,3,7,5,6,2,4] => 2
[1,3,7,5,6,4,2] => 2
[1,3,7,6,2,4,5] => 1
[1,3,7,6,2,5,4] => 1
[1,3,7,6,4,2,5] => 1
[1,3,7,6,4,5,2] => 1
[1,3,7,6,5,2,4] => 1
[1,3,7,6,5,4,2] => 1
[1,4,2,3,5,6,7] => 0
[1,4,2,3,5,7,6] => 0
[1,4,2,3,6,5,7] => 0
[1,4,2,3,6,7,5] => 1
[1,4,2,3,7,5,6] => 0
[1,4,2,3,7,6,5] => 0
[1,4,2,5,3,6,7] => 1
[1,4,2,5,3,7,6] => 1
[1,4,2,5,6,3,7] => 1
[1,4,2,5,6,7,3] => 1
[1,4,2,5,7,3,6] => 1
[1,4,2,5,7,6,3] => 1
[1,4,2,6,3,5,7] => 1
[1,4,2,6,3,7,5] => 2
[1,4,2,6,5,3,7] => 1
[1,4,2,6,5,7,3] => 1
[1,4,2,6,7,3,5] => 2
[1,4,2,6,7,5,3] => 2
[1,4,2,7,3,5,6] => 1
[1,4,2,7,3,6,5] => 1
[1,4,2,7,5,3,6] => 1
[1,4,2,7,5,6,3] => 1
[1,4,2,7,6,3,5] => 1
[1,4,2,7,6,5,3] => 1
[1,4,3,2,5,6,7] => 0
[1,4,3,2,5,7,6] => 0
[1,4,3,2,6,5,7] => 0
[1,4,3,2,6,7,5] => 1
[1,4,3,2,7,5,6] => 0
[1,4,3,2,7,6,5] => 0
[1,4,3,5,2,6,7] => 1
[1,4,3,5,2,7,6] => 1
[1,4,3,5,6,2,7] => 1
[1,4,3,5,6,7,2] => 1
[1,4,3,5,7,2,6] => 1
[1,4,3,5,7,6,2] => 1
[1,4,3,6,2,5,7] => 1
[1,4,3,6,2,7,5] => 2
[1,4,3,6,5,2,7] => 1
[1,4,3,6,5,7,2] => 1
[1,4,3,6,7,2,5] => 2
[1,4,3,6,7,5,2] => 2
[1,4,3,7,2,5,6] => 1
[1,4,3,7,2,6,5] => 1
[1,4,3,7,5,2,6] => 1
[1,4,3,7,5,6,2] => 1
[1,4,3,7,6,2,5] => 1
[1,4,3,7,6,5,2] => 1
[1,4,5,2,3,6,7] => 1
[1,4,5,2,3,7,6] => 1
[1,4,5,2,6,3,7] => 1
[1,4,5,2,6,7,3] => 1
[1,4,5,2,7,3,6] => 1
[1,4,5,2,7,6,3] => 1
[1,4,5,3,2,6,7] => 1
[1,4,5,3,2,7,6] => 1
[1,4,5,3,6,2,7] => 2
[1,4,5,3,6,7,2] => 2
[1,4,5,3,7,2,6] => 2
[1,4,5,3,7,6,2] => 2
[1,4,5,6,2,3,7] => 1
[1,4,5,6,2,7,3] => 1
[1,4,5,6,3,2,7] => 1
[1,4,5,6,3,7,2] => 2
[1,4,5,6,7,2,3] => 1
[1,4,5,6,7,3,2] => 1
[1,4,5,7,2,3,6] => 1
[1,4,5,7,2,6,3] => 1
[1,4,5,7,3,2,6] => 1
[1,4,5,7,3,6,2] => 2
[1,4,5,7,6,2,3] => 1
[1,4,5,7,6,3,2] => 1
[1,4,6,2,3,5,7] => 1
[1,4,6,2,3,7,5] => 2
[1,4,6,2,5,3,7] => 1
[1,4,6,2,5,7,3] => 1
[1,4,6,2,7,3,5] => 2
[1,4,6,2,7,5,3] => 2
[1,4,6,3,2,5,7] => 1
[1,4,6,3,2,7,5] => 2
[1,4,6,3,5,2,7] => 2
[1,4,6,3,5,7,2] => 2
[1,4,6,3,7,2,5] => 3
[1,4,6,3,7,5,2] => 3
[1,4,6,5,2,3,7] => 1
[1,4,6,5,2,7,3] => 1
[1,4,6,5,3,2,7] => 1
[1,4,6,5,3,7,2] => 2
click to show generating function       
Description
The tier of a permutation.
This is the number of elements $i$ such that $[i+1,k,i]$ is an occurrence of the pattern $[2,3,1]$. For example, $[3,5,6,1,2,4]$ has tier $2$, with witnesses $[3,5,2]$ (or $[3,6,2]$) and $[5,6,4]$.
According to [1], this is the number of passes minus one needed to sort the permutation using a single stack. The generating function for this statistic appears as OEIS:A122890 and OEIS:A158830 in the form of triangles read by rows, see [sec. 4, 1].
References
[1] Mansour, T., Skogman, H., Smith, R. Passing through a stack $k$ times arXiv:1704.04288
Code
def statistic(pi):
    pi = Permutation(pi)
    return len(set([p[0] for p in pi.pattern_positions([2,3,1]) if pi[p[0]] == pi[p[2]] +1]))

Created
Apr 17, 2017 at 11:47 by Martin Rubey
Updated
Nov 06, 2017 at 21:24 by Martin Rubey