Identifier
Identifier
Values
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 2
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 2
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 3
[2,4,1,3] => 3
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 3
[3,2,1,4] => 2
[3,2,4,1] => 3
[3,4,1,2] => 4
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 4
[4,3,1,2] => 3
[4,3,2,1] => 3
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 2
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 3
[1,3,5,2,4] => 3
[1,3,5,4,2] => 3
[1,4,2,3,5] => 2
[1,4,2,5,3] => 3
[1,4,3,2,5] => 2
[1,4,3,5,2] => 3
[1,4,5,2,3] => 4
[1,4,5,3,2] => 3
[1,5,2,3,4] => 3
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 4
[1,5,4,2,3] => 3
[1,5,4,3,2] => 3
[2,1,3,4,5] => 1
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 3
[2,1,5,3,4] => 3
[2,1,5,4,3] => 3
[2,3,1,4,5] => 2
[2,3,1,5,4] => 3
[2,3,4,1,5] => 3
[2,3,4,5,1] => 4
[2,3,5,1,4] => 4
[2,3,5,4,1] => 4
[2,4,1,3,5] => 3
[2,4,1,5,3] => 4
[2,4,3,1,5] => 3
[2,4,3,5,1] => 4
[2,4,5,1,3] => 5
[2,4,5,3,1] => 4
[2,5,1,3,4] => 4
[2,5,1,4,3] => 4
[2,5,3,1,4] => 4
[2,5,3,4,1] => 5
[2,5,4,1,3] => 4
[2,5,4,3,1] => 4
[3,1,2,4,5] => 2
[3,1,2,5,4] => 3
[3,1,4,2,5] => 3
[3,1,4,5,2] => 4
[3,1,5,2,4] => 4
[3,1,5,4,2] => 4
[3,2,1,4,5] => 2
[3,2,1,5,4] => 3
[3,2,4,1,5] => 3
[3,2,4,5,1] => 4
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 5
[3,4,2,1,5] => 3
[3,4,2,5,1] => 4
[3,4,5,1,2] => 6
[3,4,5,2,1] => 4
[3,5,1,2,4] => 5
[3,5,1,4,2] => 5
[3,5,2,1,4] => 4
[3,5,2,4,1] => 5
[3,5,4,1,2] => 5
[3,5,4,2,1] => 4
[4,1,2,3,5] => 3
[4,1,2,5,3] => 4
[4,1,3,2,5] => 3
[4,1,3,5,2] => 4
[4,1,5,2,3] => 5
[4,1,5,3,2] => 4
[4,2,1,3,5] => 3
[4,2,1,5,3] => 4
[4,2,3,1,5] => 4
[4,2,3,5,1] => 5
[4,2,5,1,3] => 5
[4,2,5,3,1] => 5
[4,3,1,2,5] => 3
[4,3,1,5,2] => 4
[4,3,2,1,5] => 3
[4,3,2,5,1] => 4
[4,3,5,1,2] => 5
[4,3,5,2,1] => 4
[4,5,1,2,3] => 6
[4,5,1,3,2] => 5
[4,5,2,1,3] => 5
[4,5,2,3,1] => 6
[4,5,3,1,2] => 4
[4,5,3,2,1] => 4
[5,1,2,3,4] => 4
[5,1,2,4,3] => 4
[5,1,3,2,4] => 4
[5,1,3,4,2] => 5
[5,1,4,2,3] => 4
[5,1,4,3,2] => 4
[5,2,1,3,4] => 4
[5,2,1,4,3] => 4
[5,2,3,1,4] => 5
[5,2,3,4,1] => 6
[5,2,4,1,3] => 5
[5,2,4,3,1] => 5
[5,3,1,2,4] => 4
[5,3,1,4,2] => 5
[5,3,2,1,4] => 4
[5,3,2,4,1] => 5
[5,3,4,1,2] => 6
[5,3,4,2,1] => 5
[5,4,1,2,3] => 4
[5,4,1,3,2] => 4
[5,4,2,1,3] => 4
[5,4,2,3,1] => 5
[5,4,3,1,2] => 4
[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] => 1
[1,2,3,5,6,4] => 2
[1,2,3,6,4,5] => 2
[1,2,3,6,5,4] => 2
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => 2
[1,2,4,5,6,3] => 3
[1,2,4,6,3,5] => 3
[1,2,4,6,5,3] => 3
[1,2,5,3,4,6] => 2
[1,2,5,3,6,4] => 3
[1,2,5,4,3,6] => 2
[1,2,5,4,6,3] => 3
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 3
[1,2,6,3,4,5] => 3
[1,2,6,3,5,4] => 3
[1,2,6,4,3,5] => 3
[1,2,6,4,5,3] => 4
[1,2,6,5,3,4] => 3
[1,2,6,5,4,3] => 3
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 3
[1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => 2
[1,3,4,2,6,5] => 3
[1,3,4,5,2,6] => 3
[1,3,4,5,6,2] => 4
[1,3,4,6,2,5] => 4
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 3
[1,3,5,2,6,4] => 4
[1,3,5,4,2,6] => 3
[1,3,5,4,6,2] => 4
[1,3,5,6,2,4] => 5
[1,3,5,6,4,2] => 4
[1,3,6,2,4,5] => 4
[1,3,6,2,5,4] => 4
[1,3,6,4,2,5] => 4
[1,3,6,4,5,2] => 5
[1,3,6,5,2,4] => 4
[1,3,6,5,4,2] => 4
[1,4,2,3,5,6] => 2
[1,4,2,3,6,5] => 3
[1,4,2,5,3,6] => 3
[1,4,2,5,6,3] => 4
[1,4,2,6,3,5] => 4
[1,4,2,6,5,3] => 4
[1,4,3,2,5,6] => 2
[1,4,3,2,6,5] => 3
[1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => 4
[1,4,3,6,2,5] => 4
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 4
[1,4,5,2,6,3] => 5
[1,4,5,3,2,6] => 3
[1,4,5,3,6,2] => 4
[1,4,5,6,2,3] => 6
[1,4,5,6,3,2] => 4
[1,4,6,2,3,5] => 5
[1,4,6,2,5,3] => 5
[1,4,6,3,2,5] => 4
[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] => 3
[1,5,2,3,6,4] => 4
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 4
[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] => 4
[1,5,3,4,2,6] => 4
[1,5,3,4,6,2] => 5
[1,5,3,6,2,4] => 5
[1,5,3,6,4,2] => 5
[1,5,4,2,3,6] => 3
[1,5,4,2,6,3] => 4
[1,5,4,3,2,6] => 3
[1,5,4,3,6,2] => 4
[1,5,4,6,2,3] => 5
[1,5,4,6,3,2] => 4
[1,5,6,2,3,4] => 6
[1,5,6,2,4,3] => 5
[1,5,6,3,2,4] => 5
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 4
[1,6,2,3,4,5] => 4
[1,6,2,3,5,4] => 4
[1,6,2,4,3,5] => 4
[1,6,2,4,5,3] => 5
[1,6,2,5,3,4] => 4
[1,6,2,5,4,3] => 4
[1,6,3,2,4,5] => 4
[1,6,3,2,5,4] => 4
[1,6,3,4,2,5] => 5
[1,6,3,4,5,2] => 6
[1,6,3,5,2,4] => 5
[1,6,3,5,4,2] => 5
[1,6,4,2,3,5] => 4
[1,6,4,2,5,3] => 5
[1,6,4,3,2,5] => 4
[1,6,4,3,5,2] => 5
[1,6,4,5,2,3] => 6
[1,6,4,5,3,2] => 5
[1,6,5,2,3,4] => 4
[1,6,5,2,4,3] => 4
[1,6,5,3,2,4] => 4
[1,6,5,3,4,2] => 5
[1,6,5,4,2,3] => 4
[1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => 3
[2,1,3,6,4,5] => 3
[2,1,3,6,5,4] => 3
[2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => 4
[2,1,4,6,3,5] => 4
[2,1,4,6,5,3] => 4
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 4
[2,1,5,4,3,6] => 3
[2,1,5,4,6,3] => 4
[2,1,5,6,3,4] => 5
[2,1,5,6,4,3] => 4
[2,1,6,3,4,5] => 4
[2,1,6,3,5,4] => 4
[2,1,6,4,3,5] => 4
[2,1,6,4,5,3] => 5
[2,1,6,5,3,4] => 4
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 2
[2,3,1,4,6,5] => 3
[2,3,1,5,4,6] => 3
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 4
[2,3,1,6,5,4] => 4
[2,3,4,1,5,6] => 3
[2,3,4,1,6,5] => 4
[2,3,4,5,1,6] => 4
[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] => 4
[2,3,5,1,6,4] => 5
[2,3,5,4,1,6] => 4
[2,3,5,4,6,1] => 5
[2,3,5,6,1,4] => 6
[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] => 6
[2,3,6,5,1,4] => 5
[2,3,6,5,4,1] => 5
[2,4,1,3,5,6] => 3
[2,4,1,3,6,5] => 4
[2,4,1,5,3,6] => 4
[2,4,1,5,6,3] => 5
[2,4,1,6,3,5] => 5
[2,4,1,6,5,3] => 5
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 4
[2,4,3,5,1,6] => 4
[2,4,3,5,6,1] => 5
[2,4,3,6,1,5] => 5
[2,4,3,6,5,1] => 5
[2,4,5,1,3,6] => 5
[2,4,5,1,6,3] => 6
[2,4,5,3,1,6] => 4
[2,4,5,3,6,1] => 5
[2,4,5,6,1,3] => 7
[2,4,5,6,3,1] => 5
[2,4,6,1,3,5] => 6
[2,4,6,1,5,3] => 6
[2,4,6,3,1,5] => 5
[2,4,6,3,5,1] => 6
[2,4,6,5,1,3] => 6
[2,4,6,5,3,1] => 5
[2,5,1,3,4,6] => 4
[2,5,1,3,6,4] => 5
[2,5,1,4,3,6] => 4
[2,5,1,4,6,3] => 5
[2,5,1,6,3,4] => 6
[2,5,1,6,4,3] => 5
[2,5,3,1,4,6] => 4
[2,5,3,1,6,4] => 5
[2,5,3,4,1,6] => 5
[2,5,3,4,6,1] => 6
[2,5,3,6,1,4] => 6
[2,5,3,6,4,1] => 6
[2,5,4,1,3,6] => 4
[2,5,4,1,6,3] => 5
[2,5,4,3,1,6] => 4
[2,5,4,3,6,1] => 5
[2,5,4,6,1,3] => 6
[2,5,4,6,3,1] => 5
[2,5,6,1,3,4] => 7
[2,5,6,1,4,3] => 6
[2,5,6,3,1,4] => 6
[2,5,6,3,4,1] => 7
[2,5,6,4,1,3] => 5
[2,5,6,4,3,1] => 5
[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] => 6
[2,6,1,5,3,4] => 5
[2,6,1,5,4,3] => 5
[2,6,3,1,4,5] => 5
[2,6,3,1,5,4] => 5
[2,6,3,4,1,5] => 6
[2,6,3,4,5,1] => 7
[2,6,3,5,1,4] => 6
[2,6,3,5,4,1] => 6
[2,6,4,1,3,5] => 5
[2,6,4,1,5,3] => 6
[2,6,4,3,1,5] => 5
[2,6,4,3,5,1] => 6
[2,6,4,5,1,3] => 7
[2,6,4,5,3,1] => 6
[2,6,5,1,3,4] => 5
[2,6,5,1,4,3] => 5
[2,6,5,3,1,4] => 5
[2,6,5,3,4,1] => 6
[2,6,5,4,1,3] => 5
[2,6,5,4,3,1] => 5
[3,1,2,4,5,6] => 2
[3,1,2,4,6,5] => 3
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 4
[3,1,4,2,5,6] => 3
[3,1,4,2,6,5] => 4
[3,1,4,5,2,6] => 4
[3,1,4,5,6,2] => 5
[3,1,4,6,2,5] => 5
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 4
[3,1,5,2,6,4] => 5
[3,1,5,4,2,6] => 4
[3,1,5,4,6,2] => 5
[3,1,5,6,2,4] => 6
[3,1,5,6,4,2] => 5
[3,1,6,2,4,5] => 5
[3,1,6,2,5,4] => 5
[3,1,6,4,2,5] => 5
[3,1,6,4,5,2] => 6
[3,1,6,5,2,4] => 5
[3,1,6,5,4,2] => 5
[3,2,1,4,5,6] => 2
[3,2,1,4,6,5] => 3
[3,2,1,5,4,6] => 3
[3,2,1,5,6,4] => 4
[3,2,1,6,4,5] => 4
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 4
[3,2,4,5,1,6] => 4
[3,2,4,5,6,1] => 5
[3,2,4,6,1,5] => 5
[3,2,4,6,5,1] => 5
[3,2,5,1,4,6] => 4
[3,2,5,1,6,4] => 5
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 5
[3,2,5,6,1,4] => 6
[3,2,5,6,4,1] => 5
[3,2,6,1,4,5] => 5
[3,2,6,1,5,4] => 5
[3,2,6,4,1,5] => 5
[3,2,6,4,5,1] => 6
[3,2,6,5,1,4] => 5
[3,2,6,5,4,1] => 5
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 5
[3,4,1,5,2,6] => 5
[3,4,1,5,6,2] => 6
[3,4,1,6,2,5] => 6
[3,4,1,6,5,2] => 6
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 4
[3,4,2,5,1,6] => 4
[3,4,2,5,6,1] => 5
[3,4,2,6,1,5] => 5
[3,4,2,6,5,1] => 5
[3,4,5,1,2,6] => 6
[3,4,5,1,6,2] => 7
[3,4,5,2,1,6] => 4
[3,4,5,2,6,1] => 5
[3,4,5,6,1,2] => 8
[3,4,5,6,2,1] => 5
[3,4,6,1,2,5] => 7
[3,4,6,1,5,2] => 7
[3,4,6,2,1,5] => 5
[3,4,6,2,5,1] => 6
[3,4,6,5,1,2] => 7
[3,4,6,5,2,1] => 5
[3,5,1,2,4,6] => 5
[3,5,1,2,6,4] => 6
[3,5,1,4,2,6] => 5
[3,5,1,4,6,2] => 6
[3,5,1,6,2,4] => 7
[3,5,1,6,4,2] => 6
[3,5,2,1,4,6] => 4
[3,5,2,1,6,4] => 5
[3,5,2,4,1,6] => 5
[3,5,2,4,6,1] => 6
[3,5,2,6,1,4] => 6
[3,5,2,6,4,1] => 6
[3,5,4,1,2,6] => 5
[3,5,4,1,6,2] => 6
[3,5,4,2,1,6] => 4
[3,5,4,2,6,1] => 5
[3,5,4,6,1,2] => 7
[3,5,4,6,2,1] => 5
[3,5,6,1,2,4] => 8
[3,5,6,1,4,2] => 7
[3,5,6,2,1,4] => 6
[3,5,6,2,4,1] => 7
[3,5,6,4,1,2] => 6
[3,5,6,4,2,1] => 5
[3,6,1,2,4,5] => 6
[3,6,1,2,5,4] => 6
[3,6,1,4,2,5] => 6
[3,6,1,4,5,2] => 7
[3,6,1,5,2,4] => 6
[3,6,1,5,4,2] => 6
[3,6,2,1,4,5] => 5
[3,6,2,1,5,4] => 5
[3,6,2,4,1,5] => 6
[3,6,2,4,5,1] => 7
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 6
[3,6,4,1,2,5] => 6
[3,6,4,1,5,2] => 7
[3,6,4,2,1,5] => 5
[3,6,4,2,5,1] => 6
[3,6,4,5,1,2] => 8
[3,6,4,5,2,1] => 6
[3,6,5,1,2,4] => 6
[3,6,5,1,4,2] => 6
[3,6,5,2,1,4] => 5
[3,6,5,2,4,1] => 6
[3,6,5,4,1,2] => 6
[3,6,5,4,2,1] => 5
[4,1,2,3,5,6] => 3
[4,1,2,3,6,5] => 4
[4,1,2,5,3,6] => 4
[4,1,2,5,6,3] => 5
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 5
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 4
[4,1,3,5,2,6] => 4
[4,1,3,5,6,2] => 5
[4,1,3,6,2,5] => 5
[4,1,3,6,5,2] => 5
[4,1,5,2,3,6] => 5
[4,1,5,2,6,3] => 6
[4,1,5,3,2,6] => 4
[4,1,5,3,6,2] => 5
[4,1,5,6,2,3] => 7
[4,1,5,6,3,2] => 5
[4,1,6,2,3,5] => 6
[4,1,6,2,5,3] => 6
[4,1,6,3,2,5] => 5
[4,1,6,3,5,2] => 6
[4,1,6,5,2,3] => 6
[4,1,6,5,3,2] => 5
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 4
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 5
[4,2,1,6,3,5] => 5
[4,2,1,6,5,3] => 5
[4,2,3,1,5,6] => 4
[4,2,3,1,6,5] => 5
[4,2,3,5,1,6] => 5
[4,2,3,5,6,1] => 6
[4,2,3,6,1,5] => 6
[4,2,3,6,5,1] => 6
[4,2,5,1,3,6] => 5
[4,2,5,1,6,3] => 6
[4,2,5,3,1,6] => 5
[4,2,5,3,6,1] => 6
[4,2,5,6,1,3] => 7
[4,2,5,6,3,1] => 6
[4,2,6,1,3,5] => 6
[4,2,6,1,5,3] => 6
[4,2,6,3,1,5] => 6
[4,2,6,3,5,1] => 7
[4,2,6,5,1,3] => 6
[4,2,6,5,3,1] => 6
[4,3,1,2,5,6] => 3
[4,3,1,2,6,5] => 4
[4,3,1,5,2,6] => 4
[4,3,1,5,6,2] => 5
[4,3,1,6,2,5] => 5
[4,3,1,6,5,2] => 5
[4,3,2,1,5,6] => 3
[4,3,2,1,6,5] => 4
[4,3,2,5,1,6] => 4
[4,3,2,5,6,1] => 5
[4,3,2,6,1,5] => 5
[4,3,2,6,5,1] => 5
[4,3,5,1,2,6] => 5
[4,3,5,1,6,2] => 6
[4,3,5,2,1,6] => 4
[4,3,5,2,6,1] => 5
[4,3,5,6,1,2] => 7
[4,3,5,6,2,1] => 5
[4,3,6,1,2,5] => 6
[4,3,6,1,5,2] => 6
[4,3,6,2,1,5] => 5
[4,3,6,2,5,1] => 6
[4,3,6,5,1,2] => 6
[4,3,6,5,2,1] => 5
[4,5,1,2,3,6] => 6
[4,5,1,2,6,3] => 7
[4,5,1,3,2,6] => 5
[4,5,1,3,6,2] => 6
[4,5,1,6,2,3] => 8
[4,5,1,6,3,2] => 6
[4,5,2,1,3,6] => 5
[4,5,2,1,6,3] => 6
[4,5,2,3,1,6] => 6
[4,5,2,3,6,1] => 7
[4,5,2,6,1,3] => 7
[4,5,2,6,3,1] => 7
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 5
[4,5,3,2,1,6] => 4
[4,5,3,2,6,1] => 5
[4,5,3,6,1,2] => 6
[4,5,3,6,2,1] => 5
[4,5,6,1,2,3] => 9
[4,5,6,1,3,2] => 7
[4,5,6,2,1,3] => 7
[4,5,6,2,3,1] => 8
[4,5,6,3,1,2] => 5
[4,5,6,3,2,1] => 5
[4,6,1,2,3,5] => 7
[4,6,1,2,5,3] => 7
[4,6,1,3,2,5] => 6
[4,6,1,3,5,2] => 7
[4,6,1,5,2,3] => 7
[4,6,1,5,3,2] => 6
[4,6,2,1,3,5] => 6
[4,6,2,1,5,3] => 6
[4,6,2,3,1,5] => 7
[4,6,2,3,5,1] => 8
[4,6,2,5,1,3] => 7
[4,6,2,5,3,1] => 7
[4,6,3,1,2,5] => 5
[4,6,3,1,5,2] => 6
[4,6,3,2,1,5] => 5
[4,6,3,2,5,1] => 6
[4,6,3,5,1,2] => 7
[4,6,3,5,2,1] => 6
[4,6,5,1,2,3] => 7
[4,6,5,1,3,2] => 6
[4,6,5,2,1,3] => 6
[4,6,5,2,3,1] => 7
[4,6,5,3,1,2] => 5
[4,6,5,3,2,1] => 5
[5,1,2,3,4,6] => 4
[5,1,2,3,6,4] => 5
[5,1,2,4,3,6] => 4
[5,1,2,4,6,3] => 5
[5,1,2,6,3,4] => 6
[5,1,2,6,4,3] => 5
[5,1,3,2,4,6] => 4
[5,1,3,2,6,4] => 5
[5,1,3,4,2,6] => 5
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 6
[5,1,3,6,4,2] => 6
[5,1,4,2,3,6] => 4
[5,1,4,2,6,3] => 5
[5,1,4,3,2,6] => 4
[5,1,4,3,6,2] => 5
[5,1,4,6,2,3] => 6
[5,1,4,6,3,2] => 5
[5,1,6,2,3,4] => 7
[5,1,6,2,4,3] => 6
[5,1,6,3,2,4] => 6
[5,1,6,3,4,2] => 7
[5,1,6,4,2,3] => 5
[5,1,6,4,3,2] => 5
[5,2,1,3,4,6] => 4
[5,2,1,3,6,4] => 5
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 5
[5,2,1,6,3,4] => 6
[5,2,1,6,4,3] => 5
[5,2,3,1,4,6] => 5
[5,2,3,1,6,4] => 6
[5,2,3,4,1,6] => 6
[5,2,3,4,6,1] => 7
[5,2,3,6,1,4] => 7
[5,2,3,6,4,1] => 7
[5,2,4,1,3,6] => 5
[5,2,4,1,6,3] => 6
[5,2,4,3,1,6] => 5
[5,2,4,3,6,1] => 6
[5,2,4,6,1,3] => 7
[5,2,4,6,3,1] => 6
[5,2,6,1,3,4] => 7
[5,2,6,1,4,3] => 6
[5,2,6,3,1,4] => 7
[5,2,6,3,4,1] => 8
[5,2,6,4,1,3] => 6
[5,2,6,4,3,1] => 6
[5,3,1,2,4,6] => 4
[5,3,1,2,6,4] => 5
[5,3,1,4,2,6] => 5
[5,3,1,4,6,2] => 6
[5,3,1,6,2,4] => 6
[5,3,1,6,4,2] => 6
[5,3,2,1,4,6] => 4
[5,3,2,1,6,4] => 5
[5,3,2,4,1,6] => 5
[5,3,2,4,6,1] => 6
[5,3,2,6,1,4] => 6
[5,3,2,6,4,1] => 6
[5,3,4,1,2,6] => 6
[5,3,4,1,6,2] => 7
[5,3,4,2,1,6] => 5
[5,3,4,2,6,1] => 6
[5,3,4,6,1,2] => 8
[5,3,4,6,2,1] => 6
[5,3,6,1,2,4] => 7
[5,3,6,1,4,2] => 7
[5,3,6,2,1,4] => 6
[5,3,6,2,4,1] => 7
[5,3,6,4,1,2] => 7
[5,3,6,4,2,1] => 6
[5,4,1,2,3,6] => 4
[5,4,1,2,6,3] => 5
[5,4,1,3,2,6] => 4
[5,4,1,3,6,2] => 5
[5,4,1,6,2,3] => 6
[5,4,1,6,3,2] => 5
[5,4,2,1,3,6] => 4
[5,4,2,1,6,3] => 5
[5,4,2,3,1,6] => 5
[5,4,2,3,6,1] => 6
[5,4,2,6,1,3] => 6
[5,4,2,6,3,1] => 6
[5,4,3,1,2,6] => 4
[5,4,3,1,6,2] => 5
[5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => 5
[5,4,3,6,1,2] => 6
[5,4,3,6,2,1] => 5
[5,4,6,1,2,3] => 7
[5,4,6,1,3,2] => 6
[5,4,6,2,1,3] => 6
[5,4,6,2,3,1] => 7
[5,4,6,3,1,2] => 5
[5,4,6,3,2,1] => 5
[5,6,1,2,3,4] => 8
[5,6,1,2,4,3] => 7
[5,6,1,3,2,4] => 7
[5,6,1,3,4,2] => 8
[5,6,1,4,2,3] => 6
[5,6,1,4,3,2] => 6
[5,6,2,1,3,4] => 7
[5,6,2,1,4,3] => 6
[5,6,2,3,1,4] => 8
[5,6,2,3,4,1] => 9
[5,6,2,4,1,3] => 7
[5,6,2,4,3,1] => 7
[5,6,3,1,2,4] => 6
[5,6,3,1,4,2] => 7
[5,6,3,2,1,4] => 6
[5,6,3,2,4,1] => 7
[5,6,3,4,1,2] => 8
[5,6,3,4,2,1] => 7
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 5
[5,6,4,2,1,3] => 5
[5,6,4,2,3,1] => 6
[5,6,4,3,1,2] => 5
[5,6,4,3,2,1] => 5
[6,1,2,3,4,5] => 5
[6,1,2,3,5,4] => 5
[6,1,2,4,3,5] => 5
[6,1,2,4,5,3] => 6
[6,1,2,5,3,4] => 5
[6,1,2,5,4,3] => 5
[6,1,3,2,4,5] => 5
[6,1,3,2,5,4] => 5
[6,1,3,4,2,5] => 6
[6,1,3,4,5,2] => 7
[6,1,3,5,2,4] => 6
[6,1,3,5,4,2] => 6
[6,1,4,2,3,5] => 5
[6,1,4,2,5,3] => 6
[6,1,4,3,2,5] => 5
[6,1,4,3,5,2] => 6
[6,1,4,5,2,3] => 7
[6,1,4,5,3,2] => 6
[6,1,5,2,3,4] => 5
[6,1,5,2,4,3] => 5
[6,1,5,3,2,4] => 5
[6,1,5,3,4,2] => 6
[6,1,5,4,2,3] => 5
[6,1,5,4,3,2] => 5
[6,2,1,3,4,5] => 5
[6,2,1,3,5,4] => 5
[6,2,1,4,3,5] => 5
[6,2,1,4,5,3] => 6
[6,2,1,5,3,4] => 5
[6,2,1,5,4,3] => 5
[6,2,3,1,4,5] => 6
[6,2,3,1,5,4] => 6
[6,2,3,4,1,5] => 7
[6,2,3,4,5,1] => 8
[6,2,3,5,1,4] => 7
[6,2,3,5,4,1] => 7
[6,2,4,1,3,5] => 6
[6,2,4,1,5,3] => 7
[6,2,4,3,1,5] => 6
[6,2,4,3,5,1] => 7
[6,2,4,5,1,3] => 8
[6,2,4,5,3,1] => 7
[6,2,5,1,3,4] => 6
[6,2,5,1,4,3] => 6
[6,2,5,3,1,4] => 6
[6,2,5,3,4,1] => 7
[6,2,5,4,1,3] => 6
[6,2,5,4,3,1] => 6
[6,3,1,2,4,5] => 5
[6,3,1,2,5,4] => 5
[6,3,1,4,2,5] => 6
[6,3,1,4,5,2] => 7
[6,3,1,5,2,4] => 6
[6,3,1,5,4,2] => 6
[6,3,2,1,4,5] => 5
[6,3,2,1,5,4] => 5
[6,3,2,4,1,5] => 6
[6,3,2,4,5,1] => 7
[6,3,2,5,1,4] => 6
[6,3,2,5,4,1] => 6
[6,3,4,1,2,5] => 7
[6,3,4,1,5,2] => 8
[6,3,4,2,1,5] => 6
[6,3,4,2,5,1] => 7
[6,3,4,5,1,2] => 9
[6,3,4,5,2,1] => 7
[6,3,5,1,2,4] => 7
[6,3,5,1,4,2] => 7
[6,3,5,2,1,4] => 6
[6,3,5,2,4,1] => 7
[6,3,5,4,1,2] => 7
[6,3,5,4,2,1] => 6
[6,4,1,2,3,5] => 5
[6,4,1,2,5,3] => 6
[6,4,1,3,2,5] => 5
[6,4,1,3,5,2] => 6
[6,4,1,5,2,3] => 7
[6,4,1,5,3,2] => 6
[6,4,2,1,3,5] => 5
[6,4,2,1,5,3] => 6
[6,4,2,3,1,5] => 6
[6,4,2,3,5,1] => 7
[6,4,2,5,1,3] => 7
[6,4,2,5,3,1] => 7
[6,4,3,1,2,5] => 5
[6,4,3,1,5,2] => 6
[6,4,3,2,1,5] => 5
[6,4,3,2,5,1] => 6
[6,4,3,5,1,2] => 7
[6,4,3,5,2,1] => 6
[6,4,5,1,2,3] => 8
[6,4,5,1,3,2] => 7
[6,4,5,2,1,3] => 7
[6,4,5,2,3,1] => 8
[6,4,5,3,1,2] => 6
[6,4,5,3,2,1] => 6
[6,5,1,2,3,4] => 5
[6,5,1,2,4,3] => 5
[6,5,1,3,2,4] => 5
[6,5,1,3,4,2] => 6
[6,5,1,4,2,3] => 5
[6,5,1,4,3,2] => 5
[6,5,2,1,3,4] => 5
[6,5,2,1,4,3] => 5
[6,5,2,3,1,4] => 6
[6,5,2,3,4,1] => 7
[6,5,2,4,1,3] => 6
[6,5,2,4,3,1] => 6
[6,5,3,1,2,4] => 5
[6,5,3,1,4,2] => 6
[6,5,3,2,1,4] => 5
[6,5,3,2,4,1] => 6
[6,5,3,4,1,2] => 7
[6,5,3,4,2,1] => 6
[6,5,4,1,2,3] => 5
[6,5,4,1,3,2] => 5
[6,5,4,2,1,3] => 5
[6,5,4,2,3,1] => 6
[6,5,4,3,1,2] => 5
[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] => 1
[1,2,3,4,6,7,5] => 2
[1,2,3,4,7,5,6] => 2
[1,2,3,4,7,6,5] => 2
[1,2,3,5,4,6,7] => 1
[1,2,3,5,4,7,6] => 2
[1,2,3,5,6,4,7] => 2
[1,2,3,5,6,7,4] => 3
[1,2,3,5,7,4,6] => 3
[1,2,3,5,7,6,4] => 3
[1,2,3,6,4,5,7] => 2
[1,2,3,6,4,7,5] => 3
[1,2,3,6,5,4,7] => 2
[1,2,3,6,5,7,4] => 3
[1,2,3,6,7,4,5] => 4
[1,2,3,6,7,5,4] => 3
[1,2,3,7,4,5,6] => 3
[1,2,3,7,4,6,5] => 3
[1,2,3,7,5,4,6] => 3
[1,2,3,7,5,6,4] => 4
[1,2,3,7,6,4,5] => 3
[1,2,3,7,6,5,4] => 3
[1,2,4,3,5,6,7] => 1
[1,2,4,3,5,7,6] => 2
[1,2,4,3,6,5,7] => 2
[1,2,4,3,6,7,5] => 3
[1,2,4,3,7,5,6] => 3
[1,2,4,3,7,6,5] => 3
[1,2,4,5,3,6,7] => 2
[1,2,4,5,3,7,6] => 3
[1,2,4,5,6,3,7] => 3
[1,2,4,5,6,7,3] => 4
[1,2,4,5,7,3,6] => 4
[1,2,4,5,7,6,3] => 4
[1,2,4,6,3,5,7] => 3
[1,2,4,6,3,7,5] => 4
[1,2,4,6,5,3,7] => 3
[1,2,4,6,5,7,3] => 4
[1,2,4,6,7,3,5] => 5
[1,2,4,6,7,5,3] => 4
[1,2,4,7,3,5,6] => 4
[1,2,4,7,3,6,5] => 4
[1,2,4,7,5,3,6] => 4
[1,2,4,7,5,6,3] => 5
[1,2,4,7,6,3,5] => 4
[1,2,4,7,6,5,3] => 4
[1,2,5,3,4,6,7] => 2
[1,2,5,3,4,7,6] => 3
[1,2,5,3,6,4,7] => 3
[1,2,5,3,6,7,4] => 4
[1,2,5,3,7,4,6] => 4
[1,2,5,3,7,6,4] => 4
[1,2,5,4,3,6,7] => 2
[1,2,5,4,3,7,6] => 3
[1,2,5,4,6,3,7] => 3
[1,2,5,4,6,7,3] => 4
[1,2,5,4,7,3,6] => 4
[1,2,5,4,7,6,3] => 4
[1,2,5,6,3,4,7] => 4
[1,2,5,6,3,7,4] => 5
[1,2,5,6,4,3,7] => 3
[1,2,5,6,4,7,3] => 4
[1,2,5,6,7,3,4] => 6
[1,2,5,6,7,4,3] => 4
[1,2,5,7,3,4,6] => 5
[1,2,5,7,3,6,4] => 5
[1,2,5,7,4,3,6] => 4
[1,2,5,7,4,6,3] => 5
[1,2,5,7,6,3,4] => 5
[1,2,5,7,6,4,3] => 4
[1,2,6,3,4,5,7] => 3
[1,2,6,3,4,7,5] => 4
[1,2,6,3,5,4,7] => 3
[1,2,6,3,5,7,4] => 4
[1,2,6,3,7,4,5] => 5
[1,2,6,3,7,5,4] => 4
[1,2,6,4,3,5,7] => 3
[1,2,6,4,3,7,5] => 4
[1,2,6,4,5,3,7] => 4
[1,2,6,4,5,7,3] => 5
[1,2,6,4,7,3,5] => 5
[1,2,6,4,7,5,3] => 5
[1,2,6,5,3,4,7] => 3
[1,2,6,5,3,7,4] => 4
[1,2,6,5,4,3,7] => 3
[1,2,6,5,4,7,3] => 4
[1,2,6,5,7,3,4] => 5
[1,2,6,5,7,4,3] => 4
[1,2,6,7,3,4,5] => 6
[1,2,6,7,3,5,4] => 5
[1,2,6,7,4,3,5] => 5
[1,2,6,7,4,5,3] => 6
[1,2,6,7,5,3,4] => 4
[1,2,6,7,5,4,3] => 4
[1,2,7,3,4,5,6] => 4
[1,2,7,3,4,6,5] => 4
[1,2,7,3,5,4,6] => 4
[1,2,7,3,5,6,4] => 5
[1,2,7,3,6,4,5] => 4
[1,2,7,3,6,5,4] => 4
[1,2,7,4,3,5,6] => 4
[1,2,7,4,3,6,5] => 4
[1,2,7,4,5,3,6] => 5
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 5
[1,2,7,4,6,5,3] => 5
[1,2,7,5,3,4,6] => 4
[1,2,7,5,3,6,4] => 5
[1,2,7,5,4,3,6] => 4
[1,2,7,5,4,6,3] => 5
[1,2,7,5,6,3,4] => 6
[1,2,7,5,6,4,3] => 5
[1,2,7,6,3,4,5] => 4
[1,2,7,6,3,5,4] => 4
[1,2,7,6,4,3,5] => 4
[1,2,7,6,4,5,3] => 5
[1,2,7,6,5,3,4] => 4
[1,2,7,6,5,4,3] => 4
[1,3,2,4,5,6,7] => 1
[1,3,2,4,5,7,6] => 2
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 3
[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] => 3
[1,3,2,5,6,7,4] => 4
[1,3,2,5,7,4,6] => 4
[1,3,2,5,7,6,4] => 4
[1,3,2,6,4,5,7] => 3
[1,3,2,6,4,7,5] => 4
[1,3,2,6,5,4,7] => 3
[1,3,2,6,5,7,4] => 4
[1,3,2,6,7,4,5] => 5
[1,3,2,6,7,5,4] => 4
[1,3,2,7,4,5,6] => 4
[1,3,2,7,4,6,5] => 4
[1,3,2,7,5,4,6] => 4
[1,3,2,7,5,6,4] => 5
[1,3,2,7,6,4,5] => 4
[1,3,2,7,6,5,4] => 4
[1,3,4,2,5,6,7] => 2
[1,3,4,2,5,7,6] => 3
[1,3,4,2,6,5,7] => 3
[1,3,4,2,6,7,5] => 4
[1,3,4,2,7,5,6] => 4
[1,3,4,2,7,6,5] => 4
[1,3,4,5,2,6,7] => 3
[1,3,4,5,2,7,6] => 4
[1,3,4,5,6,2,7] => 4
[1,3,4,5,6,7,2] => 5
[1,3,4,5,7,2,6] => 5
[1,3,4,5,7,6,2] => 5
[1,3,4,6,2,5,7] => 4
[1,3,4,6,2,7,5] => 5
[1,3,4,6,5,2,7] => 4
[1,3,4,6,5,7,2] => 5
[1,3,4,6,7,2,5] => 6
[1,3,4,6,7,5,2] => 5
[1,3,4,7,2,5,6] => 5
[1,3,4,7,2,6,5] => 5
[1,3,4,7,5,2,6] => 5
[1,3,4,7,5,6,2] => 6
[1,3,4,7,6,2,5] => 5
[1,3,4,7,6,5,2] => 5
[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] => 5
[1,3,5,2,7,4,6] => 5
[1,3,5,2,7,6,4] => 5
[1,3,5,4,2,6,7] => 3
[1,3,5,4,2,7,6] => 4
[1,3,5,4,6,2,7] => 4
[1,3,5,4,6,7,2] => 5
[1,3,5,4,7,2,6] => 5
[1,3,5,4,7,6,2] => 5
[1,3,5,6,2,4,7] => 5
[1,3,5,6,2,7,4] => 6
[1,3,5,6,4,2,7] => 4
[1,3,5,6,4,7,2] => 5
[1,3,5,6,7,2,4] => 7
[1,3,5,6,7,4,2] => 5
[1,3,5,7,2,4,6] => 6
[1,3,5,7,2,6,4] => 6
[1,3,5,7,4,2,6] => 5
[1,3,5,7,4,6,2] => 6
[1,3,5,7,6,2,4] => 6
[1,3,5,7,6,4,2] => 5
[1,3,6,2,4,5,7] => 4
[1,3,6,2,4,7,5] => 5
[1,3,6,2,5,4,7] => 4
[1,3,6,2,5,7,4] => 5
[1,3,6,2,7,4,5] => 6
[1,3,6,2,7,5,4] => 5
[1,3,6,4,2,5,7] => 4
[1,3,6,4,2,7,5] => 5
[1,3,6,4,5,2,7] => 5
[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] => 4
[1,3,6,5,2,7,4] => 5
[1,3,6,5,4,2,7] => 4
[1,3,6,5,4,7,2] => 5
[1,3,6,5,7,2,4] => 6
[1,3,6,5,7,4,2] => 5
[1,3,6,7,2,4,5] => 7
[1,3,6,7,2,5,4] => 6
[1,3,6,7,4,2,5] => 6
[1,3,6,7,4,5,2] => 7
[1,3,6,7,5,2,4] => 5
[1,3,6,7,5,4,2] => 5
[1,3,7,2,4,5,6] => 5
[1,3,7,2,4,6,5] => 5
[1,3,7,2,5,4,6] => 5
[1,3,7,2,5,6,4] => 6
[1,3,7,2,6,4,5] => 5
[1,3,7,2,6,5,4] => 5
[1,3,7,4,2,5,6] => 5
[1,3,7,4,2,6,5] => 5
[1,3,7,4,5,2,6] => 6
[1,3,7,4,5,6,2] => 7
[1,3,7,4,6,2,5] => 6
[1,3,7,4,6,5,2] => 6
[1,3,7,5,2,4,6] => 5
[1,3,7,5,2,6,4] => 6
[1,3,7,5,4,2,6] => 5
[1,3,7,5,4,6,2] => 6
[1,3,7,5,6,2,4] => 7
[1,3,7,5,6,4,2] => 6
[1,3,7,6,2,4,5] => 5
[1,3,7,6,2,5,4] => 5
[1,3,7,6,4,2,5] => 5
[1,3,7,6,4,5,2] => 6
[1,3,7,6,5,2,4] => 5
[1,3,7,6,5,4,2] => 5
[1,4,2,3,5,6,7] => 2
[1,4,2,3,5,7,6] => 3
[1,4,2,3,6,5,7] => 3
[1,4,2,3,6,7,5] => 4
[1,4,2,3,7,5,6] => 4
[1,4,2,3,7,6,5] => 4
[1,4,2,5,3,6,7] => 3
[1,4,2,5,3,7,6] => 4
[1,4,2,5,6,3,7] => 4
[1,4,2,5,6,7,3] => 5
[1,4,2,5,7,3,6] => 5
[1,4,2,5,7,6,3] => 5
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 5
[1,4,2,6,5,3,7] => 4
[1,4,2,6,5,7,3] => 5
[1,4,2,6,7,3,5] => 6
[1,4,2,6,7,5,3] => 5
[1,4,2,7,3,5,6] => 5
[1,4,2,7,3,6,5] => 5
[1,4,2,7,5,3,6] => 5
[1,4,2,7,5,6,3] => 6
[1,4,2,7,6,3,5] => 5
[1,4,2,7,6,5,3] => 5
[1,4,3,2,5,6,7] => 2
[1,4,3,2,5,7,6] => 3
[1,4,3,2,6,5,7] => 3
[1,4,3,2,6,7,5] => 4
[1,4,3,2,7,5,6] => 4
[1,4,3,2,7,6,5] => 4
[1,4,3,5,2,6,7] => 3
[1,4,3,5,2,7,6] => 4
[1,4,3,5,6,2,7] => 4
[1,4,3,5,6,7,2] => 5
[1,4,3,5,7,2,6] => 5
[1,4,3,5,7,6,2] => 5
[1,4,3,6,2,5,7] => 4
[1,4,3,6,2,7,5] => 5
[1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => 5
[1,4,3,6,7,2,5] => 6
[1,4,3,6,7,5,2] => 5
[1,4,3,7,2,5,6] => 5
[1,4,3,7,2,6,5] => 5
[1,4,3,7,5,2,6] => 5
[1,4,3,7,5,6,2] => 6
[1,4,3,7,6,2,5] => 5
[1,4,3,7,6,5,2] => 5
[1,4,5,2,3,6,7] => 4
[1,4,5,2,3,7,6] => 5
[1,4,5,2,6,3,7] => 5
[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] => 3
[1,4,5,3,2,7,6] => 4
[1,4,5,3,6,2,7] => 4
[1,4,5,3,6,7,2] => 5
[1,4,5,3,7,2,6] => 5
[1,4,5,3,7,6,2] => 5
[1,4,5,6,2,3,7] => 6
[1,4,5,6,2,7,3] => 7
[1,4,5,6,3,2,7] => 4
[1,4,5,6,3,7,2] => 5
[1,4,5,6,7,2,3] => 8
[1,4,5,6,7,3,2] => 5
[1,4,5,7,2,3,6] => 7
[1,4,5,7,2,6,3] => 7
[1,4,5,7,3,2,6] => 5
[1,4,5,7,3,6,2] => 6
[1,4,5,7,6,2,3] => 7
[1,4,5,7,6,3,2] => 5
[1,4,6,2,3,5,7] => 5
[1,4,6,2,3,7,5] => 6
[1,4,6,2,5,3,7] => 5
[1,4,6,2,5,7,3] => 6
[1,4,6,2,7,3,5] => 7
[1,4,6,2,7,5,3] => 6
[1,4,6,3,2,5,7] => 4
[1,4,6,3,2,7,5] => 5
[1,4,6,3,5,2,7] => 5
[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] => 5
[1,4,6,5,2,7,3] => 6
[1,4,6,5,3,2,7] => 4
[1,4,6,5,3,7,2] => 5
click to show generating function       
Description
The number of Bruhat lower covers of a permutation.
This is, for a permutation $\pi$, the number of permutations $\tau$ with $\operatorname{inv}(\tau) = \operatorname{inv}(\pi) - 1$ such that $\tau*t = \pi$ for a transposition $t$.
This is also the number of occurrences of the boxed pattern $21$: occurrences of the pattern $21$ such that any entry between the two matched entries is either larger or smaller than both of the matched entries.
Code
def statistic(pi):
    return len(PermutationGroupElement(pi).bruhat_lower_covers())

Created
Aug 27, 2017 at 22:50 by Martin Rubey
Updated
Jan 15, 2018 at 08:16 by Martin Rubey