Identifier
Identifier
Values
[1] => 0
[1,1] => 0
[2] => 0
[1,1,1] => 0
[1,2] => 0
[2,1] => 1
[3] => 0
[1,1,1,1] => 0
[1,1,2] => 0
[1,2,1] => 1
[1,3] => 0
[2,1,1] => 2
[2,2] => 0
[3,1] => 1
[4] => 0
[1,1,1,1,1] => 0
[1,1,1,2] => 0
[1,1,2,1] => 1
[1,1,3] => 0
[1,2,1,1] => 2
[1,2,2] => 0
[1,3,1] => 1
[1,4] => 0
[2,1,1,1] => 3
[2,1,2] => 1
[2,2,1] => 2
[2,3] => 0
[3,1,1] => 2
[3,2] => 1
[4,1] => 1
[5] => 0
[1,1,1,1,1,1] => 0
[1,1,1,1,2] => 0
[1,1,1,2,1] => 1
[1,1,1,3] => 0
[1,1,2,1,1] => 2
[1,1,2,2] => 0
[1,1,3,1] => 1
[1,1,4] => 0
[1,2,1,1,1] => 3
[1,2,1,2] => 1
[1,2,2,1] => 2
[1,2,3] => 0
[1,3,1,1] => 2
[1,3,2] => 1
[1,4,1] => 1
[1,5] => 0
[2,1,1,1,1] => 4
[2,1,1,2] => 2
[2,1,2,1] => 3
[2,1,3] => 1
[2,2,1,1] => 4
[2,2,2] => 0
[2,3,1] => 2
[2,4] => 0
[3,1,1,1] => 3
[3,1,2] => 2
[3,2,1] => 3
[3,3] => 0
[4,1,1] => 2
[4,2] => 1
[5,1] => 1
[6] => 0
[1,1,1,1,1,1,1] => 0
[1,1,1,1,1,2] => 0
[1,1,1,1,2,1] => 1
[1,1,1,1,3] => 0
[1,1,1,2,1,1] => 2
[1,1,1,2,2] => 0
[1,1,1,3,1] => 1
[1,1,1,4] => 0
[1,1,2,1,1,1] => 3
[1,1,2,1,2] => 1
[1,1,2,2,1] => 2
[1,1,2,3] => 0
[1,1,3,1,1] => 2
[1,1,3,2] => 1
[1,1,4,1] => 1
[1,1,5] => 0
[1,2,1,1,1,1] => 4
[1,2,1,1,2] => 2
[1,2,1,2,1] => 3
[1,2,1,3] => 1
[1,2,2,1,1] => 4
[1,2,2,2] => 0
[1,2,3,1] => 2
[1,2,4] => 0
[1,3,1,1,1] => 3
[1,3,1,2] => 2
[1,3,2,1] => 3
[1,3,3] => 0
[1,4,1,1] => 2
[1,4,2] => 1
[1,5,1] => 1
[1,6] => 0
[2,1,1,1,1,1] => 5
[2,1,1,1,2] => 3
[2,1,1,2,1] => 4
[2,1,1,3] => 2
[2,1,2,1,1] => 5
[2,1,2,2] => 1
[2,1,3,1] => 3
[2,1,4] => 1
[2,2,1,1,1] => 6
[2,2,1,2] => 2
[2,2,2,1] => 3
[2,2,3] => 0
[2,3,1,1] => 4
[2,3,2] => 1
[2,4,1] => 2
[2,5] => 0
[3,1,1,1,1] => 4
[3,1,1,2] => 3
[3,1,2,1] => 4
[3,1,3] => 1
[3,2,1,1] => 5
[3,2,2] => 2
[3,3,1] => 2
[3,4] => 0
[4,1,1,1] => 3
[4,1,2] => 2
[4,2,1] => 3
[4,3] => 1
[5,1,1] => 2
[5,2] => 1
[6,1] => 1
[7] => 0
[1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,2] => 0
[1,1,1,1,1,2,1] => 1
[1,1,1,1,1,3] => 0
[1,1,1,1,2,1,1] => 2
[1,1,1,1,2,2] => 0
[1,1,1,1,3,1] => 1
[1,1,1,1,4] => 0
[1,1,1,2,1,1,1] => 3
[1,1,1,2,1,2] => 1
[1,1,1,2,2,1] => 2
[1,1,1,2,3] => 0
[1,1,1,3,1,1] => 2
[1,1,1,3,2] => 1
[1,1,1,4,1] => 1
[1,1,1,5] => 0
[1,1,2,1,1,1,1] => 4
[1,1,2,1,1,2] => 2
[1,1,2,1,2,1] => 3
[1,1,2,1,3] => 1
[1,1,2,2,1,1] => 4
[1,1,2,2,2] => 0
[1,1,2,3,1] => 2
[1,1,2,4] => 0
[1,1,3,1,1,1] => 3
[1,1,3,1,2] => 2
[1,1,3,2,1] => 3
[1,1,3,3] => 0
[1,1,4,1,1] => 2
[1,1,4,2] => 1
[1,1,5,1] => 1
[1,1,6] => 0
[1,2,1,1,1,1,1] => 5
[1,2,1,1,1,2] => 3
[1,2,1,1,2,1] => 4
[1,2,1,1,3] => 2
[1,2,1,2,1,1] => 5
[1,2,1,2,2] => 1
[1,2,1,3,1] => 3
[1,2,1,4] => 1
[1,2,2,1,1,1] => 6
[1,2,2,1,2] => 2
[1,2,2,2,1] => 3
[1,2,2,3] => 0
[1,2,3,1,1] => 4
[1,2,3,2] => 1
[1,2,4,1] => 2
[1,2,5] => 0
[1,3,1,1,1,1] => 4
[1,3,1,1,2] => 3
[1,3,1,2,1] => 4
[1,3,1,3] => 1
[1,3,2,1,1] => 5
[1,3,2,2] => 2
[1,3,3,1] => 2
[1,3,4] => 0
[1,4,1,1,1] => 3
[1,4,1,2] => 2
[1,4,2,1] => 3
[1,4,3] => 1
[1,5,1,1] => 2
[1,5,2] => 1
[1,6,1] => 1
[1,7] => 0
[2,1,1,1,1,1,1] => 6
[2,1,1,1,1,2] => 4
[2,1,1,1,2,1] => 5
[2,1,1,1,3] => 3
[2,1,1,2,1,1] => 6
[2,1,1,2,2] => 2
[2,1,1,3,1] => 4
[2,1,1,4] => 2
[2,1,2,1,1,1] => 7
[2,1,2,1,2] => 3
[2,1,2,2,1] => 4
[2,1,2,3] => 1
[2,1,3,1,1] => 5
[2,1,3,2] => 2
[2,1,4,1] => 3
[2,1,5] => 1
[2,2,1,1,1,1] => 8
[2,2,1,1,2] => 4
[2,2,1,2,1] => 5
[2,2,1,3] => 2
[2,2,2,1,1] => 6
[2,2,2,2] => 0
[2,2,3,1] => 3
[2,2,4] => 0
[2,3,1,1,1] => 6
[2,3,1,2] => 3
[2,3,2,1] => 4
[2,3,3] => 0
[2,4,1,1] => 4
[2,4,2] => 1
[2,5,1] => 2
[2,6] => 0
[3,1,1,1,1,1] => 5
[3,1,1,1,2] => 4
[3,1,1,2,1] => 5
[3,1,1,3] => 2
[3,1,2,1,1] => 6
[3,1,2,2] => 3
[3,1,3,1] => 3
[3,1,4] => 1
[3,2,1,1,1] => 7
[3,2,1,2] => 4
[3,2,2,1] => 5
[3,2,3] => 1
[3,3,1,1] => 4
[3,3,2] => 2
[3,4,1] => 2
[3,5] => 0
[4,1,1,1,1] => 4
[4,1,1,2] => 3
[4,1,2,1] => 4
[4,1,3] => 2
[4,2,1,1] => 5
[4,2,2] => 2
[4,3,1] => 3
[4,4] => 0
[5,1,1,1] => 3
[5,1,2] => 2
[5,2,1] => 3
[5,3] => 1
[6,1,1] => 2
[6,2] => 1
[7,1] => 1
[8] => 0
[1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,2] => 0
[1,1,1,1,1,1,2,1] => 1
[1,1,1,1,1,1,3] => 0
[1,1,1,1,1,2,1,1] => 2
[1,1,1,1,1,2,2] => 0
[1,1,1,1,1,3,1] => 1
[1,1,1,1,1,4] => 0
[1,1,1,1,2,1,1,1] => 3
[1,1,1,1,2,1,2] => 1
[1,1,1,1,2,2,1] => 2
[1,1,1,1,2,3] => 0
[1,1,1,1,3,1,1] => 2
[1,1,1,1,3,2] => 1
[1,1,1,1,4,1] => 1
[1,1,1,1,5] => 0
[1,1,1,2,1,1,1,1] => 4
[1,1,1,2,1,1,2] => 2
[1,1,1,2,1,2,1] => 3
[1,1,1,2,1,3] => 1
[1,1,1,2,2,1,1] => 4
[1,1,1,2,2,2] => 0
[1,1,1,2,3,1] => 2
[1,1,1,2,4] => 0
[1,1,1,3,1,1,1] => 3
[1,1,1,3,1,2] => 2
[1,1,1,3,2,1] => 3
[1,1,1,3,3] => 0
[1,1,1,4,1,1] => 2
[1,1,1,4,2] => 1
[1,1,1,5,1] => 1
[1,1,1,6] => 0
[1,1,2,1,1,1,1,1] => 5
[1,1,2,1,1,1,2] => 3
[1,1,2,1,1,2,1] => 4
[1,1,2,1,1,3] => 2
[1,1,2,1,2,1,1] => 5
[1,1,2,1,2,2] => 1
[1,1,2,1,3,1] => 3
[1,1,2,1,4] => 1
[1,1,2,2,1,1,1] => 6
[1,1,2,2,1,2] => 2
[1,1,2,2,2,1] => 3
[1,1,2,2,3] => 0
[1,1,2,3,1,1] => 4
[1,1,2,3,2] => 1
[1,1,2,4,1] => 2
[1,1,2,5] => 0
[1,1,3,1,1,1,1] => 4
[1,1,3,1,1,2] => 3
[1,1,3,1,2,1] => 4
[1,1,3,1,3] => 1
[1,1,3,2,1,1] => 5
[1,1,3,2,2] => 2
[1,1,3,3,1] => 2
[1,1,3,4] => 0
[1,1,4,1,1,1] => 3
[1,1,4,1,2] => 2
[1,1,4,2,1] => 3
[1,1,4,3] => 1
[1,1,5,1,1] => 2
[1,1,5,2] => 1
[1,1,6,1] => 1
[1,1,7] => 0
[1,2,1,1,1,1,1,1] => 6
[1,2,1,1,1,1,2] => 4
[1,2,1,1,1,2,1] => 5
[1,2,1,1,1,3] => 3
[1,2,1,1,2,1,1] => 6
[1,2,1,1,2,2] => 2
[1,2,1,1,3,1] => 4
[1,2,1,1,4] => 2
[1,2,1,2,1,1,1] => 7
[1,2,1,2,1,2] => 3
[1,2,1,2,2,1] => 4
[1,2,1,2,3] => 1
[1,2,1,3,1,1] => 5
[1,2,1,3,2] => 2
[1,2,1,4,1] => 3
[1,2,1,5] => 1
[1,2,2,1,1,1,1] => 8
[1,2,2,1,1,2] => 4
[1,2,2,1,2,1] => 5
[1,2,2,1,3] => 2
[1,2,2,2,1,1] => 6
[1,2,2,2,2] => 0
[1,2,2,3,1] => 3
[1,2,2,4] => 0
[1,2,3,1,1,1] => 6
[1,2,3,1,2] => 3
[1,2,3,2,1] => 4
[1,2,3,3] => 0
[1,2,4,1,1] => 4
[1,2,4,2] => 1
[1,2,5,1] => 2
[1,2,6] => 0
[1,3,1,1,1,1,1] => 5
[1,3,1,1,1,2] => 4
[1,3,1,1,2,1] => 5
[1,3,1,1,3] => 2
[1,3,1,2,1,1] => 6
[1,3,1,2,2] => 3
[1,3,1,3,1] => 3
[1,3,1,4] => 1
[1,3,2,1,1,1] => 7
[1,3,2,1,2] => 4
[1,3,2,2,1] => 5
[1,3,2,3] => 1
[1,3,3,1,1] => 4
[1,3,3,2] => 2
[1,3,4,1] => 2
[1,3,5] => 0
[1,4,1,1,1,1] => 4
[1,4,1,1,2] => 3
[1,4,1,2,1] => 4
[1,4,1,3] => 2
[1,4,2,1,1] => 5
[1,4,2,2] => 2
[1,4,3,1] => 3
[1,4,4] => 0
[1,5,1,1,1] => 3
[1,5,1,2] => 2
[1,5,2,1] => 3
[1,5,3] => 1
[1,6,1,1] => 2
[1,6,2] => 1
[1,7,1] => 1
[1,8] => 0
[2,1,1,1,1,1,1,1] => 7
[2,1,1,1,1,1,2] => 5
[2,1,1,1,1,2,1] => 6
[2,1,1,1,1,3] => 4
[2,1,1,1,2,1,1] => 7
[2,1,1,1,2,2] => 3
[2,1,1,1,3,1] => 5
[2,1,1,1,4] => 3
[2,1,1,2,1,1,1] => 8
[2,1,1,2,1,2] => 4
[2,1,1,2,2,1] => 5
[2,1,1,2,3] => 2
[2,1,1,3,1,1] => 6
[2,1,1,3,2] => 3
[2,1,1,4,1] => 4
[2,1,1,5] => 2
[2,1,2,1,1,1,1] => 9
[2,1,2,1,1,2] => 5
[2,1,2,1,2,1] => 6
[2,1,2,1,3] => 3
[2,1,2,2,1,1] => 7
[2,1,2,2,2] => 1
[2,1,2,3,1] => 4
[2,1,2,4] => 1
[2,1,3,1,1,1] => 7
[2,1,3,1,2] => 4
[2,1,3,2,1] => 5
[2,1,3,3] => 1
[2,1,4,1,1] => 5
[2,1,4,2] => 2
[2,1,5,1] => 3
[2,1,6] => 1
[2,2,1,1,1,1,1] => 10
[2,2,1,1,1,2] => 6
[2,2,1,1,2,1] => 7
[2,2,1,1,3] => 4
[2,2,1,2,1,1] => 8
[2,2,1,2,2] => 2
[2,2,1,3,1] => 5
[2,2,1,4] => 2
[2,2,2,1,1,1] => 9
[2,2,2,1,2] => 3
[2,2,2,2,1] => 4
[2,2,2,3] => 0
[2,2,3,1,1] => 6
[2,2,3,2] => 1
[2,2,4,1] => 3
[2,2,5] => 0
[2,3,1,1,1,1] => 8
[2,3,1,1,2] => 5
[2,3,1,2,1] => 6
[2,3,1,3] => 2
[2,3,2,1,1] => 7
[2,3,2,2] => 2
[2,3,3,1] => 3
[2,3,4] => 0
[2,4,1,1,1] => 6
[2,4,1,2] => 3
[2,4,2,1] => 4
[2,4,3] => 1
[2,5,1,1] => 4
[2,5,2] => 1
[2,6,1] => 2
[2,7] => 0
[3,1,1,1,1,1,1] => 6
[3,1,1,1,1,2] => 5
[3,1,1,1,2,1] => 6
[3,1,1,1,3] => 3
[3,1,1,2,1,1] => 7
[3,1,1,2,2] => 4
[3,1,1,3,1] => 4
[3,1,1,4] => 2
[3,1,2,1,1,1] => 8
[3,1,2,1,2] => 5
[3,1,2,2,1] => 6
[3,1,2,3] => 2
[3,1,3,1,1] => 5
[3,1,3,2] => 3
[3,1,4,1] => 3
[3,1,5] => 1
[3,2,1,1,1,1] => 9
[3,2,1,1,2] => 6
[3,2,1,2,1] => 7
[3,2,1,3] => 3
[3,2,2,1,1] => 8
[3,2,2,2] => 3
[3,2,3,1] => 4
[3,2,4] => 1
[3,3,1,1,1] => 6
[3,3,1,2] => 4
[3,3,2,1] => 5
[3,3,3] => 0
[3,4,1,1] => 4
[3,4,2] => 2
[3,5,1] => 2
[3,6] => 0
[4,1,1,1,1,1] => 5
[4,1,1,1,2] => 4
[4,1,1,2,1] => 5
[4,1,1,3] => 3
[4,1,2,1,1] => 6
[4,1,2,2] => 3
[4,1,3,1] => 4
[4,1,4] => 1
[4,2,1,1,1] => 7
[4,2,1,2] => 4
[4,2,2,1] => 5
[4,2,3] => 2
[4,3,1,1] => 5
[4,3,2] => 3
[4,4,1] => 2
[4,5] => 0
[5,1,1,1,1] => 4
[5,1,1,2] => 3
[5,1,2,1] => 4
[5,1,3] => 2
[5,2,1,1] => 5
[5,2,2] => 2
[5,3,1] => 3
[5,4] => 1
[6,1,1,1] => 3
[6,1,2] => 2
[6,2,1] => 3
[6,3] => 1
[7,1,1] => 2
[7,2] => 1
[8,1] => 1
[9] => 0
[1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,2,2] => 0
[1,1,1,1,2,1,1,2] => 2
[1,1,1,1,2,2,1,1] => 4
[1,1,1,1,3,3] => 0
[1,1,1,1,5,1] => 1
[1,1,2,1,1,1,1,2] => 4
[1,1,2,1,1,2,1,1] => 6
[1,1,2,1,2,3] => 1
[1,1,2,2,1,1,1,1] => 8
[1,1,2,2,2,2] => 0
[1,1,3,1,1,3] => 2
[1,1,3,2,1,2] => 4
[1,1,3,3,1,1] => 4
[1,1,4,4] => 0
[1,1,7,1] => 1
[1,2,1,1,4,1] => 4
[1,2,6,1] => 2
[1,3,1,1,3,1] => 4
[1,3,5,1] => 2
[1,4,1,1,2,1] => 5
[1,4,4,1] => 2
[1,5,1,1,1,1] => 4
[1,5,3,1] => 3
[1,6,1,2] => 2
[1,6,2,1] => 3
[1,7,1,1] => 2
[1,8,1] => 1
[1,9] => 0
[2,1,1,1,1,1,1,2] => 6
[2,1,1,1,1,2,1,1] => 8
[2,1,1,1,2,3] => 3
[2,1,1,2,1,1,1,1] => 10
[2,1,1,2,2,2] => 2
[2,1,2,1,1,3] => 5
[2,1,2,2,1,2] => 4
[2,1,2,3,1,1] => 7
[2,1,3,4] => 1
[2,1,6,1] => 3
[2,2,1,1,1,1,1,1] => 12
[2,2,1,1,2,2] => 4
[2,2,2,1,1,2] => 6
[2,2,2,2,1,1] => 8
[2,2,3,3] => 0
[3,1,1,1,1,3] => 4
[3,1,1,2,1,2] => 6
[3,1,1,3,1,1] => 6
[3,1,2,4] => 2
[3,2,1,1,1,2] => 8
[3,2,1,2,1,1] => 10
[3,2,2,3] => 2
[3,3,1,1,1,1] => 8
[3,3,2,2] => 4
[4,1,1,4] => 2
[4,2,1,3] => 4
[4,3,1,2] => 5
[4,4,1,1] => 4
[5,5] => 0
[8,1,1] => 2
[9,1] => 1
[10,1] => 1
[1,10] => 0
[1,8,1,1] => 2
[1,7,2,1] => 3
[1,6,3,1] => 3
[1,5,4,1] => 3
[1,4,5,1] => 2
[1,3,6,1] => 2
[1,2,7,1] => 2
[1,1,8,1] => 1
[5,5,1,1] => 4
[1,1,5,5] => 0
[1,1,4,1,1,4] => 2
[4,1,1,4,1,1] => 6
[1,1,3,1,2,4] => 2
[1,1,4,2,1,3] => 4
[3,1,2,4,1,1] => 8
[4,2,1,3,1,1] => 10
[1,1,2,1,3,4] => 1
[1,1,3,1,1,1,1,3] => 4
[1,1,4,3,1,2] => 5
[2,2,4,4] => 0
[2,1,3,4,1,1] => 7
[3,1,1,1,1,3,1,1] => 8
[4,4,2,2] => 4
[4,3,1,2,1,1] => 11
[1,1,1,1,4,4] => 0
[1,1,2,1,2,1,1,3] => 5
[1,1,3,2,2,3] => 2
[1,1,3,1,1,2,1,2] => 6
[1,1,4,4,1,1] => 4
[2,2,3,1,1,3] => 6
[2,1,2,1,1,3,1,1] => 11
[3,3,3,3] => 0
[3,2,2,3,1,1] => 10
[3,1,1,3,2,2] => 6
[3,1,1,2,1,2,1,1] => 12
[4,4,1,1,1,1] => 8
[1,1,1,1,3,1,1,3] => 2
[1,1,2,1,1,1,2,3] => 3
[1,1,2,1,2,2,1,2] => 4
[1,1,3,2,1,1,1,2] => 8
[1,1,3,1,1,3,1,1] => 6
[2,2,2,1,2,3] => 3
[2,2,3,2,1,2] => 6
[2,1,1,2,3,3] => 2
[2,1,1,1,2,3,1,1] => 9
[2,1,2,3,2,2] => 3
[2,1,2,2,1,2,1,1] => 12
[3,3,2,1,1,2] => 10
[3,2,1,2,2,2] => 6
[3,2,1,1,1,2,1,1] => 14
[3,1,1,3,1,1,1,1] => 10
[1,1,1,1,1,1,2,1,1,2] => 2
[1,1,1,1,1,1,1,1,2,2] => 0
[2,2,1,1,2,1,1,2] => 10
[2,2,1,1,1,1,2,2] => 8
[2,1,1,2,2,1,1,2] => 8
[1,1,2,2,2,1,1,2] => 6
[2,1,1,2,1,1,2,2] => 6
[1,1,2,2,1,1,2,2] => 4
[1,1,1,1,3,2,1,2] => 4
[1,1,2,1,1,1,1,1,1,2] => 6
[1,1,2,1,1,2,2,2] => 2
[3,3,1,1,2,2] => 8
[1,1,1,1,2,1,1,1,1,2] => 4
[1,1,1,1,2,2,2,2] => 0
[3,2,2,2,1,2] => 8
[2,1,1,1,2,2,1,2] => 6
[1,1,1,1,2,1,2,3] => 1
[3,2,1,1,1,1,1,2] => 12
[2,1,1,1,1,1,1,1,1,2] => 8
[2,1,1,1,1,2,2,2] => 4
[2,2,2,1,1,1,1,2] => 12
[2,2,2,2,2,2] => 0
[1,1,1,1,1,1,3,3] => 0
[3,1,2,3,1,2] => 7
[2,1,3,3,1,2] => 6
[3,1,1,1,1,2,1,2] => 8
[2,1,2,1,1,2,1,2] => 8
[3,1,1,2,1,1,1,2] => 10
[2,1,2,2,1,1,1,2] => 10
[1,1,3,3,2,2] => 4
[2,2,1,1,3,3] => 4
[3,3,1,1,1,1,1,1] => 12
[2,1,2,3,1,1,1,1] => 13
[1,1,3,3,1,1,1,1] => 8
[2,2,3,3,1,1] => 8
[1,1,1,1,3,3,1,1] => 4
[3,1,1,1,1,1,1,3] => 6
[3,1,1,2,2,3] => 4
[3,2,1,1,2,3] => 6
[2,1,1,1,1,1,2,3] => 5
[1,1,2,1,2,3,1,1] => 7
[4,2,1,1,1,3] => 8
[3,2,2,1,1,3] => 8
[4,2,1,2,1,2] => 8
[2,1,2,2,2,3] => 1
[4,3,1,1,1,2] => 9
[1,1,2,2,3,3] => 0
[3,3,2,2,1,1] => 12
[1,1,2,2,2,2,1,1] => 8
[2,2,1,1,1,1,1,1,1,1] => 16
[2,2,1,1,2,2,1,1] => 12
[2,1,1,1,2,1,1,3] => 7
[2,2,2,2,1,1,1,1] => 16
[2,1,1,2,1,1,1,1,1,1] => 14
[2,1,1,1,3,4] => 3
[2,1,1,1,1,1,1,2,1,1] => 10
[2,1,2,1,1,1,1,3] => 9
[2,2,2,1,1,2,1,1] => 14
[2,1,1,1,1,2,1,1,1,1] => 12
[2,1,2,1,2,4] => 3
[2,1,1,2,2,2,1,1] => 10
[2,1,3,2,1,3] => 5
[2,1,3,1,1,4] => 5
[3,1,1,1,2,4] => 4
[1,1,2,1,1,2,1,1,1,1] => 10
[1,1,1,1,2,1,1,2,1,1] => 6
[1,1,2,2,1,1,1,1,1,1] => 12
[1,1,1,1,2,2,1,1,1,1] => 8
[1,1,1,1,1,1,2,2,1,1] => 4
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[5,4,1,2] => 5
[4,1,1,3,1,2] => 7
[4,3,2,3] => 4
[5,3,1,3] => 4
[4,1,1,2,1,3] => 6
[3,2,1,2,1,1,1,1] => 16
[1,1,3,2,1,2,1,1] => 10
[5,2,1,4] => 4
[5,1,1,5] => 2
[3,1,2,2,1,3] => 6
[4,2,2,4] => 2
[3,1,2,1,1,4] => 6
[4,1,1,1,1,4] => 4
[3,1,3,5] => 1
[6,6] => 0
[4,1,2,5] => 2
[2,1,4,5] => 1
[3,2,3,4] => 1
[1,1,2,1,1,1,1,2,1,1] => 8
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Description
The number of inversions of an integer composition.
This is the number of pairs $(i,j)$ such that $i < j$ and $c_i > c_j$.
References
[1] MacMahon, P. A. Two Applications of General Theorems in Combinatory Analysis: (1) To the Theory of Inversions of Permutations; (2) To the Ascertainment of the Numbers of Terms in the Development of a Determinant which has Amongst its Elements an Arbitrary Number of Zeros MathSciNet:1576566
Code
def statistic(w):
    return len([(i,j) for i in range(len(w)) for j in range(i, len(w)) if w[i] > w[j]])

Created
Apr 09, 2017 at 14:37 by Martin Rubey
Updated
Jan 11, 2018 at 09:38 by Martin Rubey