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] => 1
[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] => 1
[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] => 2
[3,1,2,4] => 2
[3,1,4,2] => 3
[3,2,1,4] => 1
[3,2,4,1] => 2
[3,4,1,2] => 4
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 1
[4,3,1,2] => 3
[4,3,2,1] => 2
[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] => 1
[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] => 2
[1,4,2,3,5] => 2
[1,4,2,5,3] => 3
[1,4,3,2,5] => 1
[1,4,3,5,2] => 2
[1,4,5,2,3] => 4
[1,4,5,3,2] => 3
[1,5,2,3,4] => 3
[1,5,2,4,3] => 2
[1,5,3,2,4] => 2
[1,5,3,4,2] => 1
[1,5,4,2,3] => 3
[1,5,4,3,2] => 2
[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] => 2
[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] => 3
[2,4,1,3,5] => 3
[2,4,1,5,3] => 4
[2,4,3,1,5] => 2
[2,4,3,5,1] => 3
[2,4,5,1,3] => 5
[2,4,5,3,1] => 4
[2,5,1,3,4] => 4
[2,5,1,4,3] => 3
[2,5,3,1,4] => 3
[2,5,3,4,1] => 2
[2,5,4,1,3] => 4
[2,5,4,3,1] => 3
[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] => 3
[3,2,1,4,5] => 1
[3,2,1,5,4] => 2
[3,2,4,1,5] => 2
[3,2,4,5,1] => 3
[3,2,5,1,4] => 3
[3,2,5,4,1] => 2
[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] => 5
[3,5,1,2,4] => 5
[3,5,1,4,2] => 4
[3,5,2,1,4] => 4
[3,5,2,4,1] => 3
[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] => 2
[4,1,3,5,2] => 3
[4,1,5,2,3] => 5
[4,1,5,3,2] => 4
[4,2,1,3,5] => 2
[4,2,1,5,3] => 3
[4,2,3,1,5] => 1
[4,2,3,5,1] => 2
[4,2,5,1,3] => 4
[4,2,5,3,1] => 3
[4,3,1,2,5] => 3
[4,3,1,5,2] => 4
[4,3,2,1,5] => 2
[4,3,2,5,1] => 3
[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] => 4
[4,5,3,1,2] => 4
[4,5,3,2,1] => 3
[5,1,2,3,4] => 4
[5,1,2,4,3] => 3
[5,1,3,2,4] => 3
[5,1,3,4,2] => 2
[5,1,4,2,3] => 4
[5,1,4,3,2] => 3
[5,2,1,3,4] => 3
[5,2,1,4,3] => 2
[5,2,3,1,4] => 2
[5,2,3,4,1] => 1
[5,2,4,1,3] => 3
[5,2,4,3,1] => 2
[5,3,1,2,4] => 4
[5,3,1,4,2] => 3
[5,3,2,1,4] => 3
[5,3,2,4,1] => 2
[5,3,4,1,2] => 4
[5,3,4,2,1] => 3
[5,4,1,2,3] => 5
[5,4,1,3,2] => 4
[5,4,2,1,3] => 4
[5,4,2,3,1] => 3
[5,4,3,1,2] => 3
[5,4,3,2,1] => 2
[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] => 1
[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] => 2
[1,2,5,3,4,6] => 2
[1,2,5,3,6,4] => 3
[1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => 2
[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] => 2
[1,2,6,4,3,5] => 2
[1,2,6,4,5,3] => 1
[1,2,6,5,3,4] => 3
[1,2,6,5,4,3] => 2
[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] => 2
[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] => 3
[1,3,5,2,4,6] => 3
[1,3,5,2,6,4] => 4
[1,3,5,4,2,6] => 2
[1,3,5,4,6,2] => 3
[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] => 3
[1,3,6,4,2,5] => 3
[1,3,6,4,5,2] => 2
[1,3,6,5,2,4] => 4
[1,3,6,5,4,2] => 3
[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] => 3
[1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => 2
[1,4,3,5,6,2] => 3
[1,4,3,6,2,5] => 3
[1,4,3,6,5,2] => 2
[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] => 5
[1,4,6,2,3,5] => 5
[1,4,6,2,5,3] => 4
[1,4,6,3,2,5] => 4
[1,4,6,3,5,2] => 3
[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] => 2
[1,5,2,4,6,3] => 3
[1,5,2,6,3,4] => 5
[1,5,2,6,4,3] => 4
[1,5,3,2,4,6] => 2
[1,5,3,2,6,4] => 3
[1,5,3,4,2,6] => 1
[1,5,3,4,6,2] => 2
[1,5,3,6,2,4] => 4
[1,5,3,6,4,2] => 3
[1,5,4,2,3,6] => 3
[1,5,4,2,6,3] => 4
[1,5,4,3,2,6] => 2
[1,5,4,3,6,2] => 3
[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] => 4
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 3
[1,6,2,3,4,5] => 4
[1,6,2,3,5,4] => 3
[1,6,2,4,3,5] => 3
[1,6,2,4,5,3] => 2
[1,6,2,5,3,4] => 4
[1,6,2,5,4,3] => 3
[1,6,3,2,4,5] => 3
[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] => 4
[1,6,4,2,5,3] => 3
[1,6,4,3,2,5] => 3
[1,6,4,3,5,2] => 2
[1,6,4,5,2,3] => 4
[1,6,4,5,3,2] => 3
[1,6,5,2,3,4] => 5
[1,6,5,2,4,3] => 4
[1,6,5,3,2,4] => 4
[1,6,5,3,4,2] => 3
[1,6,5,4,2,3] => 3
[1,6,5,4,3,2] => 2
[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] => 2
[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] => 3
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 4
[2,1,5,4,3,6] => 2
[2,1,5,4,6,3] => 3
[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] => 3
[2,1,6,4,3,5] => 3
[2,1,6,4,5,3] => 2
[2,1,6,5,3,4] => 4
[2,1,6,5,4,3] => 3
[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] => 3
[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] => 4
[2,3,5,1,4,6] => 4
[2,3,5,1,6,4] => 5
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 4
[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] => 4
[2,3,6,4,1,5] => 4
[2,3,6,4,5,1] => 3
[2,3,6,5,1,4] => 5
[2,3,6,5,4,1] => 4
[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] => 4
[2,4,3,1,5,6] => 2
[2,4,3,1,6,5] => 3
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 4
[2,4,3,6,1,5] => 4
[2,4,3,6,5,1] => 3
[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] => 6
[2,4,6,1,3,5] => 6
[2,4,6,1,5,3] => 5
[2,4,6,3,1,5] => 5
[2,4,6,3,5,1] => 4
[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] => 3
[2,5,1,4,6,3] => 4
[2,5,1,6,3,4] => 6
[2,5,1,6,4,3] => 5
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 4
[2,5,3,4,1,6] => 2
[2,5,3,4,6,1] => 3
[2,5,3,6,1,4] => 5
[2,5,3,6,4,1] => 4
[2,5,4,1,3,6] => 4
[2,5,4,1,6,3] => 5
[2,5,4,3,1,6] => 3
[2,5,4,3,6,1] => 4
[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] => 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] => 4
[2,6,1,4,3,5] => 4
[2,6,1,4,5,3] => 3
[2,6,1,5,3,4] => 5
[2,6,1,5,4,3] => 4
[2,6,3,1,4,5] => 4
[2,6,3,1,5,4] => 3
[2,6,3,4,1,5] => 3
[2,6,3,4,5,1] => 2
[2,6,3,5,1,4] => 4
[2,6,3,5,4,1] => 3
[2,6,4,1,3,5] => 5
[2,6,4,1,5,3] => 4
[2,6,4,3,1,5] => 4
[2,6,4,3,5,1] => 3
[2,6,4,5,1,3] => 5
[2,6,4,5,3,1] => 4
[2,6,5,1,3,4] => 6
[2,6,5,1,4,3] => 5
[2,6,5,3,1,4] => 5
[2,6,5,3,4,1] => 4
[2,6,5,4,1,3] => 4
[2,6,5,4,3,1] => 3
[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] => 3
[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] => 4
[3,1,5,2,4,6] => 4
[3,1,5,2,6,4] => 5
[3,1,5,4,2,6] => 3
[3,1,5,4,6,2] => 4
[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] => 4
[3,1,6,4,2,5] => 4
[3,1,6,4,5,2] => 3
[3,1,6,5,2,4] => 5
[3,1,6,5,4,2] => 4
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => 2
[3,2,4,1,6,5] => 3
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 4
[3,2,4,6,1,5] => 4
[3,2,4,6,5,1] => 3
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 4
[3,2,5,4,1,6] => 2
[3,2,5,4,6,1] => 3
[3,2,5,6,1,4] => 5
[3,2,5,6,4,1] => 4
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 3
[3,2,6,4,1,5] => 3
[3,2,6,4,5,1] => 2
[3,2,6,5,1,4] => 4
[3,2,6,5,4,1] => 3
[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] => 5
[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] => 4
[3,4,5,1,2,6] => 6
[3,4,5,1,6,2] => 7
[3,4,5,2,1,6] => 5
[3,4,5,2,6,1] => 6
[3,4,5,6,1,2] => 8
[3,4,5,6,2,1] => 7
[3,4,6,1,2,5] => 7
[3,4,6,1,5,2] => 6
[3,4,6,2,1,5] => 6
[3,4,6,2,5,1] => 5
[3,4,6,5,1,2] => 7
[3,4,6,5,2,1] => 6
[3,5,1,2,4,6] => 5
[3,5,1,2,6,4] => 6
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 5
[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] => 3
[3,5,2,4,6,1] => 4
[3,5,2,6,1,4] => 6
[3,5,2,6,4,1] => 5
[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] => 6
[3,5,6,1,2,4] => 8
[3,5,6,1,4,2] => 7
[3,5,6,2,1,4] => 7
[3,5,6,2,4,1] => 6
[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] => 5
[3,6,1,4,2,5] => 5
[3,6,1,4,5,2] => 4
[3,6,1,5,2,4] => 6
[3,6,1,5,4,2] => 5
[3,6,2,1,4,5] => 5
[3,6,2,1,5,4] => 4
[3,6,2,4,1,5] => 4
[3,6,2,4,5,1] => 3
[3,6,2,5,1,4] => 5
[3,6,2,5,4,1] => 4
[3,6,4,1,2,5] => 6
[3,6,4,1,5,2] => 5
[3,6,4,2,1,5] => 5
[3,6,4,2,5,1] => 4
[3,6,4,5,1,2] => 6
[3,6,4,5,2,1] => 5
[3,6,5,1,2,4] => 7
[3,6,5,1,4,2] => 6
[3,6,5,2,1,4] => 6
[3,6,5,2,4,1] => 5
[3,6,5,4,1,2] => 5
[3,6,5,4,2,1] => 4
[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] => 4
[4,1,3,2,5,6] => 2
[4,1,3,2,6,5] => 3
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 4
[4,1,3,6,2,5] => 4
[4,1,3,6,5,2] => 3
[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] => 6
[4,1,6,2,3,5] => 6
[4,1,6,2,5,3] => 5
[4,1,6,3,2,5] => 5
[4,1,6,3,5,2] => 4
[4,1,6,5,2,3] => 6
[4,1,6,5,3,2] => 5
[4,2,1,3,5,6] => 2
[4,2,1,3,6,5] => 3
[4,2,1,5,3,6] => 3
[4,2,1,5,6,3] => 4
[4,2,1,6,3,5] => 4
[4,2,1,6,5,3] => 3
[4,2,3,1,5,6] => 1
[4,2,3,1,6,5] => 2
[4,2,3,5,1,6] => 2
[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] => 4
[4,2,5,1,6,3] => 5
[4,2,5,3,1,6] => 3
[4,2,5,3,6,1] => 4
[4,2,5,6,1,3] => 6
[4,2,5,6,3,1] => 5
[4,2,6,1,3,5] => 5
[4,2,6,1,5,3] => 4
[4,2,6,3,1,5] => 4
[4,2,6,3,5,1] => 3
[4,2,6,5,1,3] => 5
[4,2,6,5,3,1] => 4
[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] => 4
[4,3,2,1,5,6] => 2
[4,3,2,1,6,5] => 3
[4,3,2,5,1,6] => 3
[4,3,2,5,6,1] => 4
[4,3,2,6,1,5] => 4
[4,3,2,6,5,1] => 3
[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] => 6
[4,3,6,1,2,5] => 6
[4,3,6,1,5,2] => 5
[4,3,6,2,1,5] => 5
[4,3,6,2,5,1] => 4
[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] => 7
[4,5,2,1,3,6] => 5
[4,5,2,1,6,3] => 6
[4,5,2,3,1,6] => 4
[4,5,2,3,6,1] => 5
[4,5,2,6,1,3] => 7
[4,5,2,6,3,1] => 6
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 5
[4,5,3,2,1,6] => 3
[4,5,3,2,6,1] => 4
[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] => 8
[4,5,6,2,1,3] => 8
[4,5,6,2,3,1] => 7
[4,5,6,3,1,2] => 7
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 7
[4,6,1,2,5,3] => 6
[4,6,1,3,2,5] => 6
[4,6,1,3,5,2] => 5
[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] => 5
[4,6,2,3,1,5] => 5
[4,6,2,3,5,1] => 4
[4,6,2,5,1,3] => 6
[4,6,2,5,3,1] => 5
[4,6,3,1,2,5] => 5
[4,6,3,1,5,2] => 4
[4,6,3,2,1,5] => 4
[4,6,3,2,5,1] => 3
[4,6,3,5,1,2] => 5
[4,6,3,5,2,1] => 4
[4,6,5,1,2,3] => 8
[4,6,5,1,3,2] => 7
[4,6,5,2,1,3] => 7
[4,6,5,2,3,1] => 6
[4,6,5,3,1,2] => 6
[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] => 3
[5,1,2,4,6,3] => 4
[5,1,2,6,3,4] => 6
[5,1,2,6,4,3] => 5
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 4
[5,1,3,4,2,6] => 2
[5,1,3,4,6,2] => 3
[5,1,3,6,2,4] => 5
[5,1,3,6,4,2] => 4
[5,1,4,2,3,6] => 4
[5,1,4,2,6,3] => 5
[5,1,4,3,2,6] => 3
[5,1,4,3,6,2] => 4
[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] => 5
[5,1,6,4,2,3] => 5
[5,1,6,4,3,2] => 4
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 4
[5,2,1,4,3,6] => 2
[5,2,1,4,6,3] => 3
[5,2,1,6,3,4] => 5
[5,2,1,6,4,3] => 4
[5,2,3,1,4,6] => 2
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => 2
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 3
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 4
[5,2,4,3,1,6] => 2
[5,2,4,3,6,1] => 3
[5,2,4,6,1,3] => 5
[5,2,4,6,3,1] => 4
[5,2,6,1,3,4] => 6
[5,2,6,1,4,3] => 5
[5,2,6,3,1,4] => 5
[5,2,6,3,4,1] => 4
[5,2,6,4,1,3] => 4
[5,2,6,4,3,1] => 3
[5,3,1,2,4,6] => 4
[5,3,1,2,6,4] => 5
[5,3,1,4,2,6] => 3
[5,3,1,4,6,2] => 4
[5,3,1,6,2,4] => 6
[5,3,1,6,4,2] => 5
[5,3,2,1,4,6] => 3
[5,3,2,1,6,4] => 4
[5,3,2,4,1,6] => 2
[5,3,2,4,6,1] => 3
[5,3,2,6,1,4] => 5
[5,3,2,6,4,1] => 4
[5,3,4,1,2,6] => 4
[5,3,4,1,6,2] => 5
[5,3,4,2,1,6] => 3
[5,3,4,2,6,1] => 4
[5,3,4,6,1,2] => 6
[5,3,4,6,2,1] => 5
[5,3,6,1,2,4] => 7
[5,3,6,1,4,2] => 6
[5,3,6,2,1,4] => 6
[5,3,6,2,4,1] => 5
[5,3,6,4,1,2] => 5
[5,3,6,4,2,1] => 4
[5,4,1,2,3,6] => 5
[5,4,1,2,6,3] => 6
[5,4,1,3,2,6] => 4
[5,4,1,3,6,2] => 5
[5,4,1,6,2,3] => 7
[5,4,1,6,3,2] => 6
[5,4,2,1,3,6] => 4
[5,4,2,1,6,3] => 5
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 4
[5,4,2,6,1,3] => 6
[5,4,2,6,3,1] => 5
[5,4,3,1,2,6] => 3
[5,4,3,1,6,2] => 4
[5,4,3,2,1,6] => 2
[5,4,3,2,6,1] => 3
[5,4,3,6,1,2] => 5
[5,4,3,6,2,1] => 4
[5,4,6,1,2,3] => 8
[5,4,6,1,3,2] => 7
[5,4,6,2,1,3] => 7
[5,4,6,2,3,1] => 6
[5,4,6,3,1,2] => 6
[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] => 6
[5,6,1,4,2,3] => 6
[5,6,1,4,3,2] => 5
[5,6,2,1,3,4] => 7
[5,6,2,1,4,3] => 6
[5,6,2,3,1,4] => 6
[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] => 6
[5,6,3,1,4,2] => 5
[5,6,3,2,1,4] => 5
[5,6,3,2,4,1] => 4
[5,6,3,4,1,2] => 4
[5,6,3,4,2,1] => 3
[5,6,4,1,2,3] => 7
[5,6,4,1,3,2] => 6
[5,6,4,2,1,3] => 6
[5,6,4,2,3,1] => 5
[5,6,4,3,1,2] => 5
[5,6,4,3,2,1] => 4
[6,1,2,3,4,5] => 5
[6,1,2,3,5,4] => 4
[6,1,2,4,3,5] => 4
[6,1,2,4,5,3] => 3
[6,1,2,5,3,4] => 5
[6,1,2,5,4,3] => 4
[6,1,3,2,4,5] => 4
[6,1,3,2,5,4] => 3
[6,1,3,4,2,5] => 3
[6,1,3,4,5,2] => 2
[6,1,3,5,2,4] => 4
[6,1,3,5,4,2] => 3
[6,1,4,2,3,5] => 5
[6,1,4,2,5,3] => 4
[6,1,4,3,2,5] => 4
[6,1,4,3,5,2] => 3
[6,1,4,5,2,3] => 5
[6,1,4,5,3,2] => 4
[6,1,5,2,3,4] => 6
[6,1,5,2,4,3] => 5
[6,1,5,3,2,4] => 5
[6,1,5,3,4,2] => 4
[6,1,5,4,2,3] => 4
[6,1,5,4,3,2] => 3
[6,2,1,3,4,5] => 4
[6,2,1,3,5,4] => 3
[6,2,1,4,3,5] => 3
[6,2,1,4,5,3] => 2
[6,2,1,5,3,4] => 4
[6,2,1,5,4,3] => 3
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 2
[6,2,3,4,1,5] => 2
[6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => 3
[6,2,3,5,4,1] => 2
[6,2,4,1,3,5] => 4
[6,2,4,1,5,3] => 3
[6,2,4,3,1,5] => 3
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 4
[6,2,4,5,3,1] => 3
[6,2,5,1,3,4] => 5
[6,2,5,1,4,3] => 4
[6,2,5,3,1,4] => 4
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 3
[6,2,5,4,3,1] => 2
[6,3,1,2,4,5] => 5
[6,3,1,2,5,4] => 4
[6,3,1,4,2,5] => 4
[6,3,1,4,5,2] => 3
[6,3,1,5,2,4] => 5
[6,3,1,5,4,2] => 4
[6,3,2,1,4,5] => 4
[6,3,2,1,5,4] => 3
[6,3,2,4,1,5] => 3
[6,3,2,4,5,1] => 2
[6,3,2,5,1,4] => 4
[6,3,2,5,4,1] => 3
[6,3,4,1,2,5] => 5
[6,3,4,1,5,2] => 4
[6,3,4,2,1,5] => 4
[6,3,4,2,5,1] => 3
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 4
[6,3,5,1,2,4] => 6
[6,3,5,1,4,2] => 5
[6,3,5,2,1,4] => 5
[6,3,5,2,4,1] => 4
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 3
[6,4,1,2,3,5] => 6
[6,4,1,2,5,3] => 5
[6,4,1,3,2,5] => 5
[6,4,1,3,5,2] => 4
[6,4,1,5,2,3] => 6
[6,4,1,5,3,2] => 5
[6,4,2,1,3,5] => 5
[6,4,2,1,5,3] => 4
[6,4,2,3,1,5] => 4
[6,4,2,3,5,1] => 3
[6,4,2,5,1,3] => 5
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 4
[6,4,3,1,5,2] => 3
[6,4,3,2,1,5] => 3
[6,4,3,2,5,1] => 2
[6,4,3,5,1,2] => 4
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 7
[6,4,5,1,3,2] => 6
[6,4,5,2,1,3] => 6
[6,4,5,2,3,1] => 5
[6,4,5,3,1,2] => 5
[6,4,5,3,2,1] => 4
[6,5,1,2,3,4] => 7
[6,5,1,2,4,3] => 6
[6,5,1,3,2,4] => 6
[6,5,1,3,4,2] => 5
[6,5,1,4,2,3] => 5
[6,5,1,4,3,2] => 4
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 5
[6,5,2,3,1,4] => 5
[6,5,2,3,4,1] => 4
[6,5,2,4,1,3] => 4
[6,5,2,4,3,1] => 3
[6,5,3,1,2,4] => 5
[6,5,3,1,4,2] => 4
[6,5,3,2,1,4] => 4
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 3
[6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 5
[6,5,4,2,1,3] => 5
[6,5,4,2,3,1] => 4
[6,5,4,3,1,2] => 4
[6,5,4,3,2,1] => 3
[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] => 1
[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] => 2
[1,2,3,6,4,5,7] => 2
[1,2,3,6,4,7,5] => 3
[1,2,3,6,5,4,7] => 1
[1,2,3,6,5,7,4] => 2
[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] => 2
[1,2,3,7,5,4,6] => 2
[1,2,3,7,5,6,4] => 1
[1,2,3,7,6,4,5] => 3
[1,2,3,7,6,5,4] => 2
[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] => 2
[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] => 3
[1,2,4,6,3,5,7] => 3
[1,2,4,6,3,7,5] => 4
[1,2,4,6,5,3,7] => 2
[1,2,4,6,5,7,3] => 3
[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] => 3
[1,2,4,7,5,3,6] => 3
[1,2,4,7,5,6,3] => 2
[1,2,4,7,6,3,5] => 4
[1,2,4,7,6,5,3] => 3
[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] => 3
[1,2,5,4,3,6,7] => 1
[1,2,5,4,3,7,6] => 2
[1,2,5,4,6,3,7] => 2
[1,2,5,4,6,7,3] => 3
[1,2,5,4,7,3,6] => 3
[1,2,5,4,7,6,3] => 2
[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] => 5
[1,2,5,7,3,4,6] => 5
[1,2,5,7,3,6,4] => 4
[1,2,5,7,4,3,6] => 4
[1,2,5,7,4,6,3] => 3
[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] => 2
[1,2,6,3,5,7,4] => 3
[1,2,6,3,7,4,5] => 5
[1,2,6,3,7,5,4] => 4
[1,2,6,4,3,5,7] => 2
[1,2,6,4,3,7,5] => 3
[1,2,6,4,5,3,7] => 1
[1,2,6,4,5,7,3] => 2
[1,2,6,4,7,3,5] => 4
[1,2,6,4,7,5,3] => 3
[1,2,6,5,3,4,7] => 3
[1,2,6,5,3,7,4] => 4
[1,2,6,5,4,3,7] => 2
[1,2,6,5,4,7,3] => 3
[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] => 4
[1,2,6,7,5,3,4] => 4
[1,2,6,7,5,4,3] => 3
[1,2,7,3,4,5,6] => 4
[1,2,7,3,4,6,5] => 3
[1,2,7,3,5,4,6] => 3
[1,2,7,3,5,6,4] => 2
[1,2,7,3,6,4,5] => 4
[1,2,7,3,6,5,4] => 3
[1,2,7,4,3,5,6] => 3
[1,2,7,4,3,6,5] => 2
[1,2,7,4,5,3,6] => 2
[1,2,7,4,5,6,3] => 1
[1,2,7,4,6,3,5] => 3
[1,2,7,4,6,5,3] => 2
[1,2,7,5,3,4,6] => 4
[1,2,7,5,3,6,4] => 3
[1,2,7,5,4,3,6] => 3
[1,2,7,5,4,6,3] => 2
[1,2,7,5,6,3,4] => 4
[1,2,7,5,6,4,3] => 3
[1,2,7,6,3,4,5] => 5
[1,2,7,6,3,5,4] => 4
[1,2,7,6,4,3,5] => 4
[1,2,7,6,4,5,3] => 3
[1,2,7,6,5,3,4] => 3
[1,2,7,6,5,4,3] => 2
[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] => 2
[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] => 3
[1,3,2,6,4,5,7] => 3
[1,3,2,6,4,7,5] => 4
[1,3,2,6,5,4,7] => 2
[1,3,2,6,5,7,4] => 3
[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] => 3
[1,3,2,7,5,4,6] => 3
[1,3,2,7,5,6,4] => 2
[1,3,2,7,6,4,5] => 4
[1,3,2,7,6,5,4] => 3
[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] => 3
[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] => 4
[1,3,4,6,2,5,7] => 4
[1,3,4,6,2,7,5] => 5
[1,3,4,6,5,2,7] => 3
[1,3,4,6,5,7,2] => 4
[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] => 4
[1,3,4,7,5,2,6] => 4
[1,3,4,7,5,6,2] => 3
[1,3,4,7,6,2,5] => 5
[1,3,4,7,6,5,2] => 4
[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] => 4
[1,3,5,4,2,6,7] => 2
[1,3,5,4,2,7,6] => 3
[1,3,5,4,6,2,7] => 3
[1,3,5,4,6,7,2] => 4
[1,3,5,4,7,2,6] => 4
[1,3,5,4,7,6,2] => 3
[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] => 6
[1,3,5,7,2,4,6] => 6
[1,3,5,7,2,6,4] => 5
[1,3,5,7,4,2,6] => 5
[1,3,5,7,4,6,2] => 4
[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] => 3
[1,3,6,2,5,7,4] => 4
[1,3,6,2,7,4,5] => 6
[1,3,6,2,7,5,4] => 5
[1,3,6,4,2,5,7] => 3
[1,3,6,4,2,7,5] => 4
[1,3,6,4,5,2,7] => 2
[1,3,6,4,5,7,2] => 3
[1,3,6,4,7,2,5] => 5
[1,3,6,4,7,5,2] => 4
[1,3,6,5,2,4,7] => 4
[1,3,6,5,2,7,4] => 5
[1,3,6,5,4,2,7] => 3
[1,3,6,5,4,7,2] => 4
[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] => 5
[1,3,6,7,5,2,4] => 5
[1,3,6,7,5,4,2] => 4
[1,3,7,2,4,5,6] => 5
[1,3,7,2,4,6,5] => 4
[1,3,7,2,5,4,6] => 4
[1,3,7,2,5,6,4] => 3
[1,3,7,2,6,4,5] => 5
[1,3,7,2,6,5,4] => 4
[1,3,7,4,2,5,6] => 4
[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] => 5
[1,3,7,5,2,6,4] => 4
[1,3,7,5,4,2,6] => 4
[1,3,7,5,4,6,2] => 3
[1,3,7,5,6,2,4] => 5
[1,3,7,5,6,4,2] => 4
[1,3,7,6,2,4,5] => 6
[1,3,7,6,2,5,4] => 5
[1,3,7,6,4,2,5] => 5
[1,3,7,6,4,5,2] => 4
[1,3,7,6,5,2,4] => 4
[1,3,7,6,5,4,2] => 3
[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] => 3
[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] => 4
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 5
[1,4,2,6,5,3,7] => 3
[1,4,2,6,5,7,3] => 4
[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] => 4
[1,4,2,7,5,3,6] => 4
[1,4,2,7,5,6,3] => 3
[1,4,2,7,6,3,5] => 5
[1,4,2,7,6,5,3] => 4
[1,4,3,2,5,6,7] => 1
[1,4,3,2,5,7,6] => 2
[1,4,3,2,6,5,7] => 2
[1,4,3,2,6,7,5] => 3
[1,4,3,2,7,5,6] => 3
[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] => 3
[1,4,3,5,6,7,2] => 4
[1,4,3,5,7,2,6] => 4
[1,4,3,5,7,6,2] => 3
[1,4,3,6,2,5,7] => 3
[1,4,3,6,2,7,5] => 4
[1,4,3,6,5,2,7] => 2
[1,4,3,6,5,7,2] => 3
[1,4,3,6,7,2,5] => 5
[1,4,3,6,7,5,2] => 4
[1,4,3,7,2,5,6] => 4
[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] => 4
[1,4,3,7,6,5,2] => 3
[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] => 5
[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] => 4
[1,4,5,6,2,3,7] => 6
[1,4,5,6,2,7,3] => 7
[1,4,5,6,3,2,7] => 5
[1,4,5,6,3,7,2] => 6
[1,4,5,6,7,2,3] => 8
[1,4,5,6,7,3,2] => 7
[1,4,5,7,2,3,6] => 7
[1,4,5,7,2,6,3] => 6
[1,4,5,7,3,2,6] => 6
[1,4,5,7,3,6,2] => 5
[1,4,5,7,6,2,3] => 7
[1,4,5,7,6,3,2] => 6
[1,4,6,2,3,5,7] => 5
[1,4,6,2,3,7,5] => 6
[1,4,6,2,5,3,7] => 4
[1,4,6,2,5,7,3] => 5
[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] => 3
[1,4,6,3,5,7,2] => 4
[1,4,6,3,7,2,5] => 6
[1,4,6,3,7,5,2] => 5
[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 reduced reflection length of the permutation.
Let $T$ be the set of reflections in a Coxeter group and let $\ell(w)$ be the usual length function. Then the reduced reflection length of $w$ is
$$\min\{r\in\mathbb N \mid w = t_1\cdots t_r,\quad t_1,\dots,t_r \in T,\quad \ell(w)=\sum \ell(t_i)\}.$$
In the case of the symmetric group, this is twice the depth St000029The depth of a permutation. minus the usual length St000018The number of inversions of a permutation..
References
[1] Bagno, E., Biagioli, R., Novick, M., Woo, A. Depth in classical Coexter groups arXiv:1507.01180
[2] Bemte Reference request: Reduced reflection length in Coxeter groups MathOverflow:270174
Code
def statistic(w):
    depth = sum(w[i]-i-1 for i in range(len(w)) if w[i]>i+1)
    return 2*depth-w.length()
Created
May 19, 2017 at 18:36 by Martin Rubey
Updated
May 19, 2017 at 18:36 by Martin Rubey