Identifier
Identifier
Values
[1] generating graphics... => 1
[2] generating graphics... => 2
[1,1] generating graphics... => 1
[3] generating graphics... => 3
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 3
[4] generating graphics... => 4
[3,1] generating graphics... => 1
[2,2] generating graphics... => 4
[2,1,1] generating graphics... => 1
[1,1,1,1] generating graphics... => 2
[5] generating graphics... => 5
[4,1] generating graphics... => 1
[3,2] generating graphics... => 5
[3,1,1] generating graphics... => 5
[2,2,1] generating graphics... => 5
[2,1,1,1] generating graphics... => 1
[1,1,1,1,1] generating graphics... => 5
[6] generating graphics... => 6
[5,1] generating graphics... => 1
[4,2] generating graphics... => 6
[4,1,1] generating graphics... => 3
[3,3] generating graphics... => 3
[3,2,1] generating graphics... => 2
[3,1,1,1] generating graphics... => 3
[2,2,2] generating graphics... => 6
[2,2,1,1] generating graphics... => 3
[2,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1] generating graphics... => 3
[7] generating graphics... => 7
[6,1] generating graphics... => 1
[5,2] generating graphics... => 7
[5,1,1] generating graphics... => 7
[4,3] generating graphics... => 7
[4,2,1] generating graphics... => 7
[4,1,1,1] generating graphics... => 1
[3,3,1] generating graphics... => 7
[3,2,2] generating graphics... => 7
[3,2,1,1] generating graphics... => 7
[3,1,1,1,1] generating graphics... => 7
[2,2,2,1] generating graphics... => 7
[2,2,1,1,1] generating graphics... => 7
[2,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1] generating graphics... => 7
[8] generating graphics... => 8
[7,1] generating graphics... => 1
[6,2] generating graphics... => 8
[6,1,1] generating graphics... => 1
[5,3] generating graphics... => 1
[5,2,1] generating graphics... => 8
[5,1,1,1] generating graphics... => 2
[4,4] generating graphics... => 8
[4,3,1] generating graphics... => 1
[4,2,2] generating graphics... => 8
[4,2,1,1] generating graphics... => 1
[4,1,1,1,1] generating graphics... => 2
[3,3,2] generating graphics... => 1
[3,3,1,1] generating graphics... => 8
[3,2,2,1] generating graphics... => 1
[3,2,1,1,1] generating graphics... => 8
[3,1,1,1,1,1] generating graphics... => 1
[2,2,2,2] generating graphics... => 8
[2,2,2,1,1] generating graphics... => 1
[2,2,1,1,1,1] generating graphics... => 8
[2,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1] generating graphics... => 4
[9] generating graphics... => 9
[8,1] generating graphics... => 1
[7,2] generating graphics... => 9
[7,1,1] generating graphics... => 9
[6,3] generating graphics... => 9
[6,2,1] generating graphics... => 1
[6,1,1,1] generating graphics... => 3
[5,4] generating graphics... => 1
[5,3,1] generating graphics... => 9
[5,2,2] generating graphics... => 9
[5,2,1,1] generating graphics... => 9
[5,1,1,1,1] generating graphics... => 1
[4,4,1] generating graphics... => 9
[4,3,2] generating graphics... => 1
[4,3,1,1] generating graphics... => 9
[4,2,2,1] generating graphics... => 9
[4,2,1,1,1] generating graphics... => 9
[4,1,1,1,1,1] generating graphics... => 3
[3,3,3] generating graphics... => 9
[3,3,2,1] generating graphics... => 1
[3,3,1,1,1] generating graphics... => 9
[3,2,2,2] generating graphics... => 9
[3,2,2,1,1] generating graphics... => 9
[3,2,1,1,1,1] generating graphics... => 1
[3,1,1,1,1,1,1] generating graphics... => 9
[2,2,2,2,1] generating graphics... => 1
[2,2,2,1,1,1] generating graphics... => 9
[2,2,1,1,1,1,1] generating graphics... => 9
[2,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1] generating graphics... => 9
[10] generating graphics... => 10
[9,1] generating graphics... => 1
[8,2] generating graphics... => 10
[8,1,1] generating graphics... => 5
[7,3] generating graphics... => 5
[7,2,1] generating graphics... => 10
[7,1,1,1] generating graphics... => 2
[6,4] generating graphics... => 10
[6,3,1] generating graphics... => 5
[6,2,2] generating graphics... => 10
[6,2,1,1] generating graphics... => 5
[6,1,1,1,1] generating graphics... => 10
[5,5] generating graphics... => 5
[5,4,1] generating graphics... => 2
[5,3,2] generating graphics... => 5
[5,3,1,1] generating graphics... => 10
[5,2,2,1] generating graphics... => 5
[5,2,1,1,1] generating graphics... => 2
[5,1,1,1,1,1] generating graphics... => 5
[4,4,2] generating graphics... => 10
[4,4,1,1] generating graphics... => 5
[4,3,3] generating graphics... => 5
[4,3,2,1] generating graphics... => 2
[4,3,1,1,1] generating graphics... => 10
[4,2,2,2] generating graphics... => 10
[4,2,2,1,1] generating graphics... => 5
[4,2,1,1,1,1] generating graphics... => 10
[4,1,1,1,1,1,1] generating graphics... => 1
[3,3,3,1] generating graphics... => 10
[3,3,2,2] generating graphics... => 5
[3,3,2,1,1] generating graphics... => 10
[3,3,1,1,1,1] generating graphics... => 5
[3,2,2,2,1] generating graphics... => 2
[3,2,2,1,1,1] generating graphics... => 10
[3,2,1,1,1,1,1] generating graphics... => 10
[3,1,1,1,1,1,1,1] generating graphics... => 5
[2,2,2,2,2] generating graphics... => 10
[2,2,2,2,1,1] generating graphics... => 5
[2,2,2,1,1,1,1] generating graphics... => 10
[2,2,1,1,1,1,1,1] generating graphics... => 5
[2,1,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 5
[11] generating graphics... => 11
[10,1] generating graphics... => 1
[9,2] generating graphics... => 11
[9,1,1] generating graphics... => 11
[8,3] generating graphics... => 11
[8,2,1] generating graphics... => 11
[8,1,1,1] generating graphics... => 1
[7,4] generating graphics... => 11
[7,3,1] generating graphics... => 11
[7,2,2] generating graphics... => 11
[7,2,1,1] generating graphics... => 11
[7,1,1,1,1] generating graphics... => 11
[6,5] generating graphics... => 11
[6,4,1] generating graphics... => 11
[6,3,2] generating graphics... => 11
[6,3,1,1] generating graphics... => 11
[6,2,2,1] generating graphics... => 11
[6,2,1,1,1] generating graphics... => 11
[6,1,1,1,1,1] generating graphics... => 1
[5,5,1] generating graphics... => 11
[5,4,2] generating graphics... => 11
[5,4,1,1] generating graphics... => 11
[5,3,3] generating graphics... => 11
[5,3,2,1] generating graphics... => 11
[5,3,1,1,1] generating graphics... => 11
[5,2,2,2] generating graphics... => 11
[5,2,2,1,1] generating graphics... => 11
[5,2,1,1,1,1] generating graphics... => 11
[5,1,1,1,1,1,1] generating graphics... => 11
[4,4,3] generating graphics... => 11
[4,4,2,1] generating graphics... => 11
[4,4,1,1,1] generating graphics... => 11
[4,3,3,1] generating graphics... => 11
[4,3,2,2] generating graphics... => 11
[4,3,2,1,1] generating graphics... => 11
[4,3,1,1,1,1] generating graphics... => 11
[4,2,2,2,1] generating graphics... => 11
[4,2,2,1,1,1] generating graphics... => 11
[4,2,1,1,1,1,1] generating graphics... => 11
[4,1,1,1,1,1,1,1] generating graphics... => 1
[3,3,3,2] generating graphics... => 11
[3,3,3,1,1] generating graphics... => 11
[3,3,2,2,1] generating graphics... => 11
[3,3,2,1,1,1] generating graphics... => 11
[3,3,1,1,1,1,1] generating graphics... => 11
[3,2,2,2,2] generating graphics... => 11
[3,2,2,2,1,1] generating graphics... => 11
[3,2,2,1,1,1,1] generating graphics... => 11
[3,2,1,1,1,1,1,1] generating graphics... => 11
[3,1,1,1,1,1,1,1,1] generating graphics... => 11
[2,2,2,2,2,1] generating graphics... => 11
[2,2,2,2,1,1,1] generating graphics... => 11
[2,2,2,1,1,1,1,1] generating graphics... => 11
[2,2,1,1,1,1,1,1,1] generating graphics... => 11
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 11
[12] generating graphics... => 12
[11,1] generating graphics... => 1
[10,2] generating graphics... => 12
[10,1,1] generating graphics... => 3
[9,3] generating graphics... => 3
[9,2,1] generating graphics... => 4
[9,1,1,1] generating graphics... => 3
[8,4] generating graphics... => 4
[8,3,1] generating graphics... => 3
[8,2,2] generating graphics... => 12
[8,2,1,1] generating graphics... => 3
[8,1,1,1,1] generating graphics... => 2
[7,5] generating graphics... => 3
[7,4,1] generating graphics... => 12
[7,3,2] generating graphics... => 1
[7,3,1,1] generating graphics... => 12
[7,2,2,1] generating graphics... => 3
[7,2,1,1,1] generating graphics... => 12
[7,1,1,1,1,1] generating graphics... => 3
[6,6] generating graphics... => 12
[6,5,1] generating graphics... => 1
[6,4,2] generating graphics... => 6
[6,4,1,1] generating graphics... => 3
[6,3,3] generating graphics... => 3
[6,3,2,1] generating graphics... => 4
[6,3,1,1,1] generating graphics... => 4
[6,2,2,2] generating graphics... => 12
[6,2,2,1,1] generating graphics... => 3
[6,2,1,1,1,1] generating graphics... => 4
[6,1,1,1,1,1,1] generating graphics... => 3
[5,5,2] generating graphics... => 3
[5,5,1,1] generating graphics... => 6
[5,4,3] generating graphics... => 4
[5,4,2,1] generating graphics... => 3
[5,4,1,1,1] generating graphics... => 4
[5,3,3,1] generating graphics... => 12
[5,3,2,2] generating graphics... => 3
[5,3,2,1,1] generating graphics... => 12
[5,3,1,1,1,1] generating graphics... => 3
[5,2,2,2,1] generating graphics... => 4
[5,2,2,1,1,1] generating graphics... => 4
[5,2,1,1,1,1,1] generating graphics... => 12
[5,1,1,1,1,1,1,1] generating graphics... => 4
[4,4,4] generating graphics... => 12
[4,4,3,1] generating graphics... => 3
[4,4,2,2] generating graphics... => 4
[4,4,2,1,1] generating graphics... => 3
[4,4,1,1,1,1] generating graphics... => 6
[4,3,3,2] generating graphics... => 3
[4,3,3,1,1] generating graphics... => 12
[4,3,2,2,1] generating graphics... => 3
[4,3,2,1,1,1] generating graphics... => 4
[4,3,1,1,1,1,1] generating graphics... => 3
[4,2,2,2,2] generating graphics... => 12
[4,2,2,2,1,1] generating graphics... => 3
[4,2,2,1,1,1,1] generating graphics... => 12
[4,2,1,1,1,1,1,1] generating graphics... => 3
[4,1,1,1,1,1,1,1,1] generating graphics... => 4
[3,3,3,3] generating graphics... => 6
[3,3,3,2,1] generating graphics... => 4
[3,3,3,1,1,1] generating graphics... => 3
[3,3,2,2,2] generating graphics... => 3
[3,3,2,2,1,1] generating graphics... => 12
[3,3,2,1,1,1,1] generating graphics... => 1
[3,3,1,1,1,1,1,1] generating graphics... => 12
[3,2,2,2,2,1] generating graphics... => 1
[3,2,2,2,1,1,1] generating graphics... => 12
[3,2,2,1,1,1,1,1] generating graphics... => 3
[3,2,1,1,1,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[2,2,2,2,2,2] generating graphics... => 12
[2,2,2,2,2,1,1] generating graphics... => 3
[2,2,2,2,1,1,1,1] generating graphics... => 2
[2,2,2,1,1,1,1,1,1] generating graphics... => 3
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 12
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 6
[13] generating graphics... => 13
[12,1] generating graphics... => 1
[11,2] generating graphics... => 13
[11,1,1] generating graphics... => 13
[10,3] generating graphics... => 13
[10,2,1] generating graphics... => 13
[10,1,1,1] generating graphics... => 1
[9,4] generating graphics... => 13
[9,3,1] generating graphics... => 13
[9,2,2] generating graphics... => 13
[9,2,1,1] generating graphics... => 13
[9,1,1,1,1] generating graphics... => 13
[8,5] generating graphics... => 13
[8,4,1] generating graphics... => 13
[8,3,2] generating graphics... => 13
[8,3,1,1] generating graphics... => 13
[8,2,2,1] generating graphics... => 13
[8,2,1,1,1] generating graphics... => 13
[8,1,1,1,1,1] generating graphics... => 1
[7,6] generating graphics... => 13
[7,5,1] generating graphics... => 13
[7,4,2] generating graphics... => 13
[7,4,1,1] generating graphics... => 13
[7,3,3] generating graphics... => 13
[7,3,2,1] generating graphics... => 13
[7,3,1,1,1] generating graphics... => 13
[7,2,2,2] generating graphics... => 13
[7,2,2,1,1] generating graphics... => 13
[7,2,1,1,1,1] generating graphics... => 13
[7,1,1,1,1,1,1] generating graphics... => 13
[6,6,1] generating graphics... => 13
[6,5,2] generating graphics... => 13
[6,5,1,1] generating graphics... => 13
[6,4,3] generating graphics... => 13
[6,4,2,1] generating graphics... => 13
[6,4,1,1,1] generating graphics... => 13
[6,3,3,1] generating graphics... => 13
[6,3,2,2] generating graphics... => 13
[6,3,2,1,1] generating graphics... => 13
[6,3,1,1,1,1] generating graphics... => 13
[6,2,2,2,1] generating graphics... => 13
[6,2,2,1,1,1] generating graphics... => 13
[6,2,1,1,1,1,1] generating graphics... => 13
[6,1,1,1,1,1,1,1] generating graphics... => 1
[5,5,3] generating graphics... => 13
[5,5,2,1] generating graphics... => 13
[5,5,1,1,1] generating graphics... => 13
[5,4,4] generating graphics... => 13
[5,4,3,1] generating graphics... => 13
[5,4,2,2] generating graphics... => 13
[5,4,2,1,1] generating graphics... => 13
[5,4,1,1,1,1] generating graphics... => 13
[5,3,3,2] generating graphics... => 13
[5,3,3,1,1] generating graphics... => 13
[5,3,2,2,1] generating graphics... => 13
[5,3,2,1,1,1] generating graphics... => 13
[5,3,1,1,1,1,1] generating graphics... => 13
[5,2,2,2,2] generating graphics... => 13
[5,2,2,2,1,1] generating graphics... => 13
[5,2,2,1,1,1,1] generating graphics... => 13
[5,2,1,1,1,1,1,1] generating graphics... => 13
[5,1,1,1,1,1,1,1,1] generating graphics... => 13
[4,4,4,1] generating graphics... => 13
[4,4,3,2] generating graphics... => 13
[4,4,3,1,1] generating graphics... => 13
[4,4,2,2,1] generating graphics... => 13
[4,4,2,1,1,1] generating graphics... => 13
[4,4,1,1,1,1,1] generating graphics... => 13
[4,3,3,3] generating graphics... => 13
[4,3,3,2,1] generating graphics... => 13
[4,3,3,1,1,1] generating graphics... => 13
[4,3,2,2,2] generating graphics... => 13
[4,3,2,2,1,1] generating graphics... => 13
[4,3,2,1,1,1,1] generating graphics... => 13
[4,3,1,1,1,1,1,1] generating graphics... => 13
[4,2,2,2,2,1] generating graphics... => 13
[4,2,2,2,1,1,1] generating graphics... => 13
[4,2,2,1,1,1,1,1] generating graphics... => 13
[4,2,1,1,1,1,1,1,1] generating graphics... => 13
[4,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[3,3,3,3,1] generating graphics... => 13
[3,3,3,2,2] generating graphics... => 13
[3,3,3,2,1,1] generating graphics... => 13
[3,3,3,1,1,1,1] generating graphics... => 13
[3,3,2,2,2,1] generating graphics... => 13
[3,3,2,2,1,1,1] generating graphics... => 13
[3,3,2,1,1,1,1,1] generating graphics... => 13
[3,3,1,1,1,1,1,1,1] generating graphics... => 13
[3,2,2,2,2,2] generating graphics... => 13
[3,2,2,2,2,1,1] generating graphics... => 13
[3,2,2,2,1,1,1,1] generating graphics... => 13
[3,2,2,1,1,1,1,1,1] generating graphics... => 13
[3,2,1,1,1,1,1,1,1,1] generating graphics... => 13
[3,1,1,1,1,1,1,1,1,1,1] generating graphics... => 13
[2,2,2,2,2,2,1] generating graphics... => 13
[2,2,2,2,2,1,1,1] generating graphics... => 13
[2,2,2,2,1,1,1,1,1] generating graphics... => 13
[2,2,2,1,1,1,1,1,1,1] generating graphics... => 13
[2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 13
[2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 13
[14] generating graphics... => 14
[13,1] generating graphics... => 1
[12,2] generating graphics... => 14
[12,1,1] generating graphics... => 7
[11,3] generating graphics... => 7
[11,2,1] generating graphics... => 14
[11,1,1,1] generating graphics... => 2
[10,4] generating graphics... => 14
[10,3,1] generating graphics... => 7
[10,2,2] generating graphics... => 14
[10,2,1,1] generating graphics... => 7
[10,1,1,1,1] generating graphics... => 14
[9,5] generating graphics... => 7
[9,4,1] generating graphics... => 14
[9,3,2] generating graphics... => 7
[9,3,1,1] generating graphics... => 14
[9,2,2,1] generating graphics... => 7
[9,2,1,1,1] generating graphics... => 14
[9,1,1,1,1,1] generating graphics... => 1
[8,6] generating graphics... => 14
[8,5,1] generating graphics... => 7
[8,4,2] generating graphics... => 14
[8,4,1,1] generating graphics... => 7
[8,3,3] generating graphics... => 7
[8,3,2,1] generating graphics... => 14
[8,3,1,1,1] generating graphics... => 14
[8,2,2,2] generating graphics... => 14
[8,2,2,1,1] generating graphics... => 7
[8,2,1,1,1,1] generating graphics... => 14
[8,1,1,1,1,1,1] generating graphics... => 7
[7,7] generating graphics... => 7
[7,6,1] generating graphics... => 2
[7,5,2] generating graphics... => 7
[7,5,1,1] generating graphics... => 14
[7,4,3] generating graphics... => 14
[7,4,2,1] generating graphics... => 7
[7,4,1,1,1] generating graphics... => 2
[7,3,3,1] generating graphics... => 14
[7,3,2,2] generating graphics... => 7
[7,3,2,1,1] generating graphics... => 14
[7,3,1,1,1,1] generating graphics... => 7
[7,2,2,2,1] generating graphics... => 14
[7,2,2,1,1,1] generating graphics... => 14
[7,2,1,1,1,1,1] generating graphics... => 2
[7,1,1,1,1,1,1,1] generating graphics... => 7
[6,6,2] generating graphics... => 14
[6,6,1,1] generating graphics... => 7
[6,5,3] generating graphics... => 7
[6,5,2,1] generating graphics... => 2
[6,5,1,1,1] generating graphics... => 14
[6,4,4] generating graphics... => 14
[6,4,3,1] generating graphics... => 7
[6,4,2,2] generating graphics... => 14
[6,4,2,1,1] generating graphics... => 7
[6,4,1,1,1,1] generating graphics... => 14
[6,3,3,2] generating graphics... => 7
[6,3,3,1,1] generating graphics... => 14
[6,3,2,2,1] generating graphics... => 7
[6,3,2,1,1,1] generating graphics... => 2
[6,3,1,1,1,1,1] generating graphics... => 7
[6,2,2,2,2] generating graphics... => 14
[6,2,2,2,1,1] generating graphics... => 7
[6,2,2,1,1,1,1] generating graphics... => 14
[6,2,1,1,1,1,1,1] generating graphics... => 7
[6,1,1,1,1,1,1,1,1] generating graphics... => 2
[5,5,4] generating graphics... => 7
[5,5,3,1] generating graphics... => 14
[5,5,2,2] generating graphics... => 7
[5,5,2,1,1] generating graphics... => 14
[5,5,1,1,1,1] generating graphics... => 7
[5,4,4,1] generating graphics... => 7
[5,4,3,2] generating graphics... => 14
[5,4,3,1,1] generating graphics... => 14
[5,4,2,2,1] generating graphics... => 2
[5,4,2,1,1,1] generating graphics... => 14
[5,4,1,1,1,1,1] generating graphics... => 14
[5,3,3,3] generating graphics... => 14
[5,3,3,2,1] generating graphics... => 14
[5,3,3,1,1,1] generating graphics... => 7
[5,3,2,2,2] generating graphics... => 7
[5,3,2,2,1,1] generating graphics... => 14
[5,3,2,1,1,1,1] generating graphics... => 7
[5,3,1,1,1,1,1,1] generating graphics... => 14
[5,2,2,2,2,1] generating graphics... => 7
[5,2,2,2,1,1,1] generating graphics... => 2
[5,2,2,1,1,1,1,1] generating graphics... => 7
[5,2,1,1,1,1,1,1,1] generating graphics... => 14
[5,1,1,1,1,1,1,1,1,1] generating graphics... => 7
[4,4,4,2] generating graphics... => 14
[4,4,4,1,1] generating graphics... => 7
[4,4,3,3] generating graphics... => 7
[4,4,3,2,1] generating graphics... => 14
[4,4,3,1,1,1] generating graphics... => 14
[4,4,2,2,2] generating graphics... => 14
[4,4,2,2,1,1] generating graphics... => 7
[4,4,2,1,1,1,1] generating graphics... => 14
[4,4,1,1,1,1,1,1] generating graphics... => 7
[4,3,3,3,1] generating graphics... => 14
[4,3,3,2,2] generating graphics... => 7
[4,3,3,2,1,1] generating graphics... => 14
[4,3,3,1,1,1,1] generating graphics... => 7
[4,3,2,2,2,1] generating graphics... => 2
[4,3,2,2,1,1,1] generating graphics... => 14
[4,3,2,1,1,1,1,1] generating graphics... => 14
[4,3,1,1,1,1,1,1,1] generating graphics... => 14
[4,2,2,2,2,2] generating graphics... => 14
[4,2,2,2,2,1,1] generating graphics... => 7
[4,2,2,2,1,1,1,1] generating graphics... => 14
[4,2,2,1,1,1,1,1,1] generating graphics... => 7
[4,2,1,1,1,1,1,1,1,1] generating graphics... => 14
[4,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[3,3,3,3,2] generating graphics... => 14
[3,3,3,3,1,1] generating graphics... => 7
[3,3,3,2,2,1] generating graphics... => 14
[3,3,3,2,1,1,1] generating graphics... => 14
[3,3,3,1,1,1,1,1] generating graphics... => 14
[3,3,2,2,2,2] generating graphics... => 7
[3,3,2,2,2,1,1] generating graphics... => 14
[3,3,2,2,1,1,1,1] generating graphics... => 7
[3,3,2,1,1,1,1,1,1] generating graphics... => 14
[3,3,1,1,1,1,1,1,1,1] generating graphics... => 7
[3,2,2,2,2,2,1] generating graphics... => 2
[3,2,2,2,2,1,1,1] generating graphics... => 14
[3,2,2,2,1,1,1,1,1] generating graphics... => 14
[3,2,2,1,1,1,1,1,1,1] generating graphics... => 14
[3,2,1,1,1,1,1,1,1,1,1] generating graphics... => 14
[3,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 7
[2,2,2,2,2,2,2] generating graphics... => 14
[2,2,2,2,2,2,1,1] generating graphics... => 7
[2,2,2,2,2,1,1,1,1] generating graphics... => 14
[2,2,2,2,1,1,1,1,1,1] generating graphics... => 7
[2,2,2,1,1,1,1,1,1,1,1] generating graphics... => 14
[2,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 7
[2,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 7
[15] generating graphics... => 15
[14,1] generating graphics... => 1
[13,2] generating graphics... => 15
[13,1,1] generating graphics... => 15
[12,3] generating graphics... => 15
[12,2,1] generating graphics... => 5
[12,1,1,1] generating graphics... => 3
[11,4] generating graphics... => 5
[11,3,1] generating graphics... => 15
[11,2,2] generating graphics... => 15
[11,2,1,1] generating graphics... => 15
[11,1,1,1,1] generating graphics... => 5
[10,5] generating graphics... => 15
[10,4,1] generating graphics... => 3
[10,3,2] generating graphics... => 5
[10,3,1,1] generating graphics... => 15
[10,2,2,1] generating graphics... => 15
[10,2,1,1,1] generating graphics... => 3
[10,1,1,1,1,1] generating graphics... => 5
[9,6] generating graphics... => 3
[9,5,1] generating graphics... => 5
[9,4,2] generating graphics... => 15
[9,4,1,1] generating graphics... => 15
[9,3,3] generating graphics... => 15
[9,3,2,1] generating graphics... => 1
[9,3,1,1,1] generating graphics... => 15
[9,2,2,2] generating graphics... => 15
[9,2,2,1,1] generating graphics... => 15
[9,2,1,1,1,1] generating graphics... => 5
[9,1,1,1,1,1,1] generating graphics... => 3
[8,7] generating graphics... => 5
[8,6,1] generating graphics... => 15
[8,5,2] generating graphics... => 3
[8,5,1,1] generating graphics... => 15
[8,4,3] generating graphics... => 5
[8,4,2,1] generating graphics... => 15
[8,4,1,1,1] generating graphics... => 5
[8,3,3,1] generating graphics... => 15
[8,3,2,2] generating graphics... => 15
[8,3,2,1,1] generating graphics... => 15
[8,3,1,1,1,1] generating graphics... => 15
[8,2,2,2,1] generating graphics... => 1
[8,2,2,1,1,1] generating graphics... => 15
[8,2,1,1,1,1,1] generating graphics... => 15
[8,1,1,1,1,1,1,1] generating graphics... => 5
[7,7,1] generating graphics... => 15
[7,6,2] generating graphics... => 5
[7,6,1,1] generating graphics... => 3
[7,5,3] generating graphics... => 15
[7,5,2,1] generating graphics... => 15
[7,5,1,1,1] generating graphics... => 15
[7,4,4] generating graphics... => 15
[7,4,3,1] generating graphics... => 15
[7,4,2,2] generating graphics... => 1
[7,4,2,1,1] generating graphics... => 15
[7,4,1,1,1,1] generating graphics... => 15
[7,3,3,2] generating graphics... => 15
[7,3,3,1,1] generating graphics... => 15
[7,3,2,2,1] generating graphics... => 15
[7,3,2,1,1,1] generating graphics... => 5
[7,3,1,1,1,1,1] generating graphics... => 15
[7,2,2,2,2] generating graphics... => 15
[7,2,2,2,1,1] generating graphics... => 15
[7,2,2,1,1,1,1] generating graphics... => 15
[7,2,1,1,1,1,1,1] generating graphics... => 15
[7,1,1,1,1,1,1,1,1] generating graphics... => 3
[6,6,3] generating graphics... => 15
[6,6,2,1] generating graphics... => 5
[6,6,1,1,1] generating graphics... => 15
[6,5,4] generating graphics... => 5
[6,5,3,1] generating graphics... => 15
[6,5,2,2] generating graphics... => 15
[6,5,2,1,1] generating graphics... => 3
[6,5,1,1,1,1] generating graphics... => 5
[6,4,4,1] generating graphics... => 15
[6,4,3,2] generating graphics... => 5
[6,4,3,1,1] generating graphics... => 15
[6,4,2,2,1] generating graphics... => 15
[6,4,2,1,1,1] generating graphics... => 15
[6,4,1,1,1,1,1] generating graphics... => 15
[6,3,3,3] generating graphics... => 15
[6,3,3,2,1] generating graphics... => 5
[6,3,3,1,1,1] generating graphics... => 15
[6,3,2,2,2] generating graphics... => 3
[6,3,2,2,1,1] generating graphics... => 15
[6,3,2,1,1,1,1] generating graphics... => 5
[6,3,1,1,1,1,1,1] generating graphics... => 15
[6,2,2,2,2,1] generating graphics... => 5
[6,2,2,2,1,1,1] generating graphics... => 15
[6,2,2,1,1,1,1,1] generating graphics... => 15
[6,2,1,1,1,1,1,1,1] generating graphics... => 5
[6,1,1,1,1,1,1,1,1,1] generating graphics... => 5
[5,5,5] generating graphics... => 15
[5,5,4,1] generating graphics... => 3
[5,5,3,2] generating graphics... => 15
[5,5,3,1,1] generating graphics... => 15
[5,5,2,2,1] generating graphics... => 5
[5,5,2,1,1,1] generating graphics... => 3
[5,5,1,1,1,1,1] generating graphics... => 15
[5,4,4,2] generating graphics... => 15
[5,4,4,1,1] generating graphics... => 5
[5,4,3,3] generating graphics... => 5
[5,4,3,2,1] generating graphics... => 3
[5,4,3,1,1,1] generating graphics... => 5
[5,4,2,2,2] generating graphics... => 5
[5,4,2,2,1,1] generating graphics... => 15
[5,4,2,1,1,1,1] generating graphics... => 15
[5,4,1,1,1,1,1,1] generating graphics... => 1
[5,3,3,3,1] generating graphics... => 5
[5,3,3,2,2] generating graphics... => 15
[5,3,3,2,1,1] generating graphics... => 15
[5,3,3,1,1,1,1] generating graphics... => 15
[5,3,2,2,2,1] generating graphics... => 3
[5,3,2,2,1,1,1] generating graphics... => 15
[5,3,2,1,1,1,1,1] generating graphics... => 15
[5,3,1,1,1,1,1,1,1] generating graphics... => 15
[5,2,2,2,2,2] generating graphics... => 15
[5,2,2,2,2,1,1] generating graphics... => 15
[5,2,2,2,1,1,1,1] generating graphics... => 5
[5,2,2,1,1,1,1,1,1] generating graphics... => 15
[5,2,1,1,1,1,1,1,1,1] generating graphics... => 3
[5,1,1,1,1,1,1,1,1,1,1] generating graphics... => 5
[4,4,4,3] generating graphics... => 3
[4,4,4,2,1] generating graphics... => 5
[4,4,4,1,1,1] generating graphics... => 15
[4,4,3,3,1] generating graphics... => 15
[4,4,3,2,2] generating graphics... => 15
[4,4,3,2,1,1] generating graphics... => 5
[4,4,3,1,1,1,1] generating graphics... => 15
[4,4,2,2,2,1] generating graphics... => 15
[4,4,2,2,1,1,1] generating graphics... => 1
[4,4,2,1,1,1,1,1] generating graphics... => 15
[4,4,1,1,1,1,1,1,1] generating graphics... => 15
[4,3,3,3,2] generating graphics... => 3
[4,3,3,3,1,1] generating graphics... => 15
[4,3,3,2,2,1] generating graphics... => 15
[4,3,3,2,1,1,1] generating graphics... => 15
[4,3,3,1,1,1,1,1] generating graphics... => 15
[4,3,2,2,2,2] generating graphics... => 5
[4,3,2,2,2,1,1] generating graphics... => 15
[4,3,2,2,1,1,1,1] generating graphics... => 15
[4,3,2,1,1,1,1,1,1] generating graphics... => 1
[4,3,1,1,1,1,1,1,1,1] generating graphics... => 15
[4,2,2,2,2,2,1] generating graphics... => 3
[4,2,2,2,2,1,1,1] generating graphics... => 15
[4,2,2,2,1,1,1,1,1] generating graphics... => 15
[4,2,2,1,1,1,1,1,1,1] generating graphics... => 15
[4,2,1,1,1,1,1,1,1,1,1] generating graphics... => 15
[4,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[3,3,3,3,3] generating graphics... => 15
[3,3,3,3,2,1] generating graphics... => 5
[3,3,3,3,1,1,1] generating graphics... => 15
[3,3,3,2,2,2] generating graphics... => 15
[3,3,3,2,2,1,1] generating graphics... => 15
[3,3,3,2,1,1,1,1] generating graphics... => 5
[3,3,3,1,1,1,1,1,1] generating graphics... => 15
[3,3,2,2,2,2,1] generating graphics... => 5
[3,3,2,2,2,1,1,1] generating graphics... => 3
[3,3,2,2,1,1,1,1,1] generating graphics... => 15
[3,3,2,1,1,1,1,1,1,1] generating graphics... => 5
[3,3,1,1,1,1,1,1,1,1,1] generating graphics... => 15
[3,2,2,2,2,2,2] generating graphics... => 15
[3,2,2,2,2,2,1,1] generating graphics... => 15
[3,2,2,2,2,1,1,1,1] generating graphics... => 5
[3,2,2,2,1,1,1,1,1,1] generating graphics... => 3
[3,2,2,1,1,1,1,1,1,1,1] generating graphics... => 15
[3,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 15
[2,2,2,2,2,2,2,1] generating graphics... => 5
[2,2,2,2,2,2,1,1,1] generating graphics... => 3
[2,2,2,2,2,1,1,1,1,1] generating graphics... => 15
[2,2,2,2,1,1,1,1,1,1,1] generating graphics... => 5
[2,2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 15
[2,2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 15
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 15
[16] generating graphics... => 16
[15,1] generating graphics... => 1
[14,2] generating graphics... => 16
[14,1,1] generating graphics... => 1
[13,3] generating graphics... => 1
[13,2,1] generating graphics... => 16
[13,1,1,1] generating graphics... => 2
[12,4] generating graphics... => 16
[12,3,1] generating graphics... => 1
[12,2,2] generating graphics... => 16
[12,2,1,1] generating graphics... => 1
[12,1,1,1,1] generating graphics... => 2
[11,5] generating graphics... => 1
[11,4,1] generating graphics... => 16
[11,3,2] generating graphics... => 1
[11,3,1,1] generating graphics... => 16
[11,2,2,1] generating graphics... => 1
[11,2,1,1,1] generating graphics... => 16
[11,1,1,1,1,1] generating graphics... => 1
[10,6] generating graphics... => 16
[10,5,1] generating graphics... => 1
[10,4,2] generating graphics... => 2
[10,4,1,1] generating graphics... => 1
[10,3,3] generating graphics... => 1
[10,3,2,1] generating graphics... => 16
[10,3,1,1,1] generating graphics... => 16
[10,2,2,2] generating graphics... => 16
[10,2,2,1,1] generating graphics... => 1
[10,2,1,1,1,1] generating graphics... => 16
[10,1,1,1,1,1,1] generating graphics... => 1
[9,7] generating graphics... => 1
[9,6,1] generating graphics... => 16
[9,5,2] generating graphics... => 1
[9,5,1,1] generating graphics... => 2
[9,4,3] generating graphics... => 16
[9,4,2,1] generating graphics... => 1
[9,4,1,1,1] generating graphics... => 16
[9,3,3,1] generating graphics... => 16
[9,3,2,2] generating graphics... => 1
[9,3,2,1,1] generating graphics... => 16
[9,3,1,1,1,1] generating graphics... => 1
[9,2,2,2,1] generating graphics... => 16
[9,2,2,1,1,1] generating graphics... => 16
[9,2,1,1,1,1,1] generating graphics... => 16
[9,1,1,1,1,1,1,1] generating graphics... => 4
[8,8] generating graphics... => 16
[8,7,1] generating graphics... => 1
[8,6,2] generating graphics... => 16
[8,6,1,1] generating graphics... => 1
[8,5,3] generating graphics... => 1
[8,5,2,1] generating graphics... => 16
[8,5,1,1,1] generating graphics... => 2
[8,4,4] generating graphics... => 16
[8,4,3,1] generating graphics... => 1
[8,4,2,2] generating graphics... => 16
[8,4,2,1,1] generating graphics... => 1
[8,4,1,1,1,1] generating graphics... => 2
[8,3,3,2] generating graphics... => 1
[8,3,3,1,1] generating graphics... => 16
[8,3,2,2,1] generating graphics... => 1
[8,3,2,1,1,1] generating graphics... => 16
[8,3,1,1,1,1,1] generating graphics... => 1
[8,2,2,2,2] generating graphics... => 16
[8,2,2,2,1,1] generating graphics... => 1
[8,2,2,1,1,1,1] generating graphics... => 16
[8,2,1,1,1,1,1,1] generating graphics... => 1
[8,1,1,1,1,1,1,1,1] generating graphics... => 4
[7,7,2] generating graphics... => 1
[7,7,1,1] generating graphics... => 16
[7,6,3] generating graphics... => 16
[7,6,2,1] generating graphics... => 1
[7,6,1,1,1] generating graphics... => 16
[7,5,4] generating graphics... => 1
[7,5,3,1] generating graphics... => 16
[7,5,2,2] generating graphics... => 1
[7,5,2,1,1] generating graphics... => 2
[7,5,1,1,1,1] generating graphics... => 1
[7,4,4,1] generating graphics... => 1
[7,4,3,2] generating graphics... => 16
[7,4,3,1,1] generating graphics... => 16
[7,4,2,2,1] generating graphics... => 16
[7,4,2,1,1,1] generating graphics... => 2
[7,4,1,1,1,1,1] generating graphics... => 16
[7,3,3,3] generating graphics... => 2
[7,3,3,2,1] generating graphics... => 16
[7,3,3,1,1,1] generating graphics... => 1
[7,3,2,2,2] generating graphics... => 1
[7,3,2,2,1,1] generating graphics... => 16
[7,3,2,1,1,1,1] generating graphics... => 1
[7,3,1,1,1,1,1,1] generating graphics... => 16
[7,2,2,2,2,1] generating graphics... => 1
[7,2,2,2,1,1,1] generating graphics... => 16
[7,2,2,1,1,1,1,1] generating graphics... => 1
[7,2,1,1,1,1,1,1,1] generating graphics... => 16
[7,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[6,6,4] generating graphics... => 16
[6,6,3,1] generating graphics... => 1
[6,6,2,2] generating graphics... => 16
[6,6,2,1,1] generating graphics... => 1
[6,6,1,1,1,1] generating graphics... => 16
[6,5,5] generating graphics... => 1
[6,5,4,1] generating graphics... => 16
[6,5,3,2] generating graphics... => 1
[6,5,3,1,1] generating graphics... => 16
[6,5,2,2,1] generating graphics... => 1
[6,5,2,1,1,1] generating graphics... => 16
[6,5,1,1,1,1,1] generating graphics... => 1
[6,4,4,2] generating graphics... => 16
[6,4,4,1,1] generating graphics... => 1
[6,4,3,3] generating graphics... => 1
[6,4,3,2,1] generating graphics... => 16
[6,4,3,1,1,1] generating graphics... => 16
[6,4,2,2,2] generating graphics... => 16
[6,4,2,2,1,1] generating graphics... => 1
[6,4,2,1,1,1,1] generating graphics... => 16
[6,4,1,1,1,1,1,1] generating graphics... => 1
[6,3,3,3,1] generating graphics... => 16
[6,3,3,2,2] generating graphics... => 1
[6,3,3,2,1,1] generating graphics... => 16
[6,3,3,1,1,1,1] generating graphics... => 1
[6,3,2,2,2,1] generating graphics... => 16
[6,3,2,2,1,1,1] generating graphics... => 2
[6,3,2,1,1,1,1,1] generating graphics... => 16
[6,3,1,1,1,1,1,1,1] generating graphics... => 16
[6,2,2,2,2,2] generating graphics... => 16
[6,2,2,2,2,1,1] generating graphics... => 1
[6,2,2,2,1,1,1,1] generating graphics... => 2
[6,2,2,1,1,1,1,1,1] generating graphics... => 1
[6,2,1,1,1,1,1,1,1,1] generating graphics... => 16
[6,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[5,5,5,1] generating graphics... => 2
[5,5,4,2] generating graphics... => 1
[5,5,4,1,1] generating graphics... => 16
[5,5,3,3] generating graphics... => 16
[5,5,3,2,1] generating graphics... => 16
[5,5,3,1,1,1] generating graphics... => 1
[5,5,2,2,2] generating graphics... => 1
[5,5,2,2,1,1] generating graphics... => 16
[5,5,2,1,1,1,1] generating graphics... => 1
[5,5,1,1,1,1,1,1] generating graphics... => 16
[5,4,4,3] generating graphics... => 1
[5,4,4,2,1] generating graphics... => 16
[5,4,4,1,1,1] generating graphics... => 16
[5,4,3,3,1] generating graphics... => 16
[5,4,3,2,2] generating graphics... => 16
[5,4,3,2,1,1] generating graphics... => 16
[5,4,3,1,1,1,1] generating graphics... => 16
[5,4,2,2,2,1] generating graphics... => 1
[5,4,2,2,1,1,1] generating graphics... => 16
[5,4,2,1,1,1,1,1] generating graphics... => 1
[5,4,1,1,1,1,1,1,1] generating graphics... => 16
[5,3,3,3,2] generating graphics... => 16
[5,3,3,3,1,1] generating graphics... => 1
[5,3,3,2,2,1] generating graphics... => 16
[5,3,3,2,1,1,1] generating graphics... => 16
[5,3,3,1,1,1,1,1] generating graphics... => 16
[5,3,2,2,2,2] generating graphics... => 1
[5,3,2,2,2,1,1] generating graphics... => 2
[5,3,2,2,1,1,1,1] generating graphics... => 1
[5,3,2,1,1,1,1,1,1] generating graphics... => 16
[5,3,1,1,1,1,1,1,1,1] generating graphics... => 1
[5,2,2,2,2,2,1] generating graphics... => 16
[5,2,2,2,2,1,1,1] generating graphics... => 2
[5,2,2,2,1,1,1,1,1] generating graphics... => 16
[5,2,2,1,1,1,1,1,1,1] generating graphics... => 16
[5,2,1,1,1,1,1,1,1,1,1] generating graphics... => 16
[5,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[4,4,4,4] generating graphics... => 16
[4,4,4,3,1] generating graphics... => 1
[4,4,4,2,2] generating graphics... => 16
[4,4,4,2,1,1] generating graphics... => 1
[4,4,4,1,1,1,1] generating graphics... => 2
[4,4,3,3,2] generating graphics... => 1
[4,4,3,3,1,1] generating graphics... => 16
[4,4,3,2,2,1] generating graphics... => 1
[4,4,3,2,1,1,1] generating graphics... => 16
[4,4,3,1,1,1,1,1] generating graphics... => 1
[4,4,2,2,2,2] generating graphics... => 16
[4,4,2,2,2,1,1] generating graphics... => 1
[4,4,2,2,1,1,1,1] generating graphics... => 16
[4,4,2,1,1,1,1,1,1] generating graphics... => 1
[4,4,1,1,1,1,1,1,1,1] generating graphics... => 16
[4,3,3,3,3] generating graphics... => 2
[4,3,3,3,2,1] generating graphics... => 16
[4,3,3,3,1,1,1] generating graphics... => 1
[4,3,3,2,2,2] generating graphics... => 1
[4,3,3,2,2,1,1] generating graphics... => 16
[4,3,3,2,1,1,1,1] generating graphics... => 1
[4,3,3,1,1,1,1,1,1] generating graphics... => 16
[4,3,2,2,2,2,1] generating graphics... => 1
[4,3,2,2,2,1,1,1] generating graphics... => 16
[4,3,2,2,1,1,1,1,1] generating graphics... => 1
[4,3,2,1,1,1,1,1,1,1] generating graphics... => 16
[4,3,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[4,2,2,2,2,2,2] generating graphics... => 16
[4,2,2,2,2,2,1,1] generating graphics... => 1
[4,2,2,2,2,1,1,1,1] generating graphics... => 2
[4,2,2,2,1,1,1,1,1,1] generating graphics... => 1
[4,2,2,1,1,1,1,1,1,1,1] generating graphics... => 16
[4,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[4,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[3,3,3,3,3,1] generating graphics... => 1
[3,3,3,3,2,2] generating graphics... => 16
[3,3,3,3,2,1,1] generating graphics... => 1
[3,3,3,3,1,1,1,1] generating graphics... => 16
[3,3,3,2,2,2,1] generating graphics... => 16
[3,3,3,2,2,1,1,1] generating graphics... => 1
[3,3,3,2,1,1,1,1,1] generating graphics... => 16
[3,3,3,1,1,1,1,1,1,1] generating graphics... => 1
[3,3,2,2,2,2,2] generating graphics... => 1
[3,3,2,2,2,2,1,1] generating graphics... => 16
[3,3,2,2,2,1,1,1,1] generating graphics... => 1
[3,3,2,2,1,1,1,1,1,1] generating graphics... => 2
[3,3,2,1,1,1,1,1,1,1,1] generating graphics... => 1
[3,3,1,1,1,1,1,1,1,1,1,1] generating graphics... => 16
[3,2,2,2,2,2,2,1] generating graphics... => 1
[3,2,2,2,2,2,1,1,1] generating graphics... => 16
[3,2,2,2,2,1,1,1,1,1] generating graphics... => 1
[3,2,2,2,1,1,1,1,1,1,1] generating graphics... => 16
[3,2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[3,2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 16
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[2,2,2,2,2,2,2,2] generating graphics... => 16
[2,2,2,2,2,2,2,1,1] generating graphics... => 1
[2,2,2,2,2,2,1,1,1,1] generating graphics... => 16
[2,2,2,2,2,1,1,1,1,1,1] generating graphics... => 1
[2,2,2,2,1,1,1,1,1,1,1,1] generating graphics... => 16
[2,2,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 16
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 8
[17] generating graphics... => 17
[16,1] generating graphics... => 1
[15,2] generating graphics... => 17
[15,1,1] generating graphics... => 17
[14,3] generating graphics... => 17
[14,2,1] generating graphics... => 17
[14,1,1,1] generating graphics... => 1
[13,4] generating graphics... => 17
[13,3,1] generating graphics... => 17
[13,2,2] generating graphics... => 17
[13,2,1,1] generating graphics... => 17
[13,1,1,1,1] generating graphics... => 17
[12,5] generating graphics... => 17
[12,4,1] generating graphics... => 17
[12,3,2] generating graphics... => 17
[12,3,1,1] generating graphics... => 17
[12,2,2,1] generating graphics... => 17
[12,2,1,1,1] generating graphics... => 17
[12,1,1,1,1,1] generating graphics... => 1
[11,6] generating graphics... => 17
[11,5,1] generating graphics... => 17
[11,4,2] generating graphics... => 17
[11,4,1,1] generating graphics... => 17
[11,3,3] generating graphics... => 17
[11,3,2,1] generating graphics... => 17
[11,3,1,1,1] generating graphics... => 17
[11,2,2,2] generating graphics... => 17
[11,2,2,1,1] generating graphics... => 17
[11,2,1,1,1,1] generating graphics... => 17
[11,1,1,1,1,1,1] generating graphics... => 17
[10,7] generating graphics... => 17
[10,6,1] generating graphics... => 17
[10,5,2] generating graphics... => 17
[10,5,1,1] generating graphics... => 17
[10,4,3] generating graphics... => 17
[10,4,2,1] generating graphics... => 17
[10,4,1,1,1] generating graphics... => 17
[10,3,3,1] generating graphics... => 17
[10,3,2,2] generating graphics... => 17
[10,3,2,1,1] generating graphics... => 17
[10,3,1,1,1,1] generating graphics... => 17
[10,2,2,2,1] generating graphics... => 17
[10,2,2,1,1,1] generating graphics... => 17
[10,2,1,1,1,1,1] generating graphics... => 17
[10,1,1,1,1,1,1,1] generating graphics... => 1
[9,8] generating graphics... => 17
[9,7,1] generating graphics... => 17
[9,6,2] generating graphics... => 17
[9,6,1,1] generating graphics... => 17
[9,5,3] generating graphics... => 17
[9,5,2,1] generating graphics... => 17
[9,5,1,1,1] generating graphics... => 17
[9,4,4] generating graphics... => 17
[9,4,3,1] generating graphics... => 17
[9,4,2,2] generating graphics... => 17
[9,4,2,1,1] generating graphics... => 17
[9,4,1,1,1,1] generating graphics... => 17
[9,3,3,2] generating graphics... => 17
[9,3,3,1,1] generating graphics... => 17
[9,3,2,2,1] generating graphics... => 17
[9,3,2,1,1,1] generating graphics... => 17
[9,3,1,1,1,1,1] generating graphics... => 17
[9,2,2,2,2] generating graphics... => 17
[9,2,2,2,1,1] generating graphics... => 17
[9,2,2,1,1,1,1] generating graphics... => 17
[9,2,1,1,1,1,1,1] generating graphics... => 17
[9,1,1,1,1,1,1,1,1] generating graphics... => 17
[8,8,1] generating graphics... => 17
[8,7,2] generating graphics... => 17
[8,7,1,1] generating graphics... => 17
[8,6,3] generating graphics... => 17
[8,6,2,1] generating graphics... => 17
[8,6,1,1,1] generating graphics... => 17
[8,5,4] generating graphics... => 17
[8,5,3,1] generating graphics... => 17
[8,5,2,2] generating graphics... => 17
[8,5,2,1,1] generating graphics... => 17
[8,5,1,1,1,1] generating graphics... => 17
[8,4,4,1] generating graphics... => 17
[8,4,3,2] generating graphics... => 17
[8,4,3,1,1] generating graphics... => 17
[8,4,2,2,1] generating graphics... => 17
[8,4,2,1,1,1] generating graphics... => 17
[8,4,1,1,1,1,1] generating graphics... => 17
[8,3,3,3] generating graphics... => 17
[8,3,3,2,1] generating graphics... => 17
[8,3,3,1,1,1] generating graphics... => 17
[8,3,2,2,2] generating graphics... => 17
[8,3,2,2,1,1] generating graphics... => 17
[8,3,2,1,1,1,1] generating graphics... => 17
[8,3,1,1,1,1,1,1] generating graphics... => 17
[8,2,2,2,2,1] generating graphics... => 17
[8,2,2,2,1,1,1] generating graphics... => 17
[8,2,2,1,1,1,1,1] generating graphics... => 17
[8,2,1,1,1,1,1,1,1] generating graphics... => 17
[8,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[7,7,3] generating graphics... => 17
[7,7,2,1] generating graphics... => 17
[7,7,1,1,1] generating graphics... => 17
[7,6,4] generating graphics... => 17
[7,6,3,1] generating graphics... => 17
[7,6,2,2] generating graphics... => 17
[7,6,2,1,1] generating graphics... => 17
[7,6,1,1,1,1] generating graphics... => 17
[7,5,5] generating graphics... => 17
[7,5,4,1] generating graphics... => 17
[7,5,3,2] generating graphics... => 17
[7,5,3,1,1] generating graphics... => 17
[7,5,2,2,1] generating graphics... => 17
[7,5,2,1,1,1] generating graphics... => 17
[7,5,1,1,1,1,1] generating graphics... => 17
[7,4,4,2] generating graphics... => 17
[7,4,4,1,1] generating graphics... => 17
[7,4,3,3] generating graphics... => 17
[7,4,3,2,1] generating graphics... => 17
[7,4,3,1,1,1] generating graphics... => 17
[7,4,2,2,2] generating graphics... => 17
[7,4,2,2,1,1] generating graphics... => 17
[7,4,2,1,1,1,1] generating graphics... => 17
[7,4,1,1,1,1,1,1] generating graphics... => 17
[7,3,3,3,1] generating graphics... => 17
[7,3,3,2,2] generating graphics... => 17
[7,3,3,2,1,1] generating graphics... => 17
[7,3,3,1,1,1,1] generating graphics... => 17
[7,3,2,2,2,1] generating graphics... => 17
[7,3,2,2,1,1,1] generating graphics... => 17
[7,3,2,1,1,1,1,1] generating graphics... => 17
[7,3,1,1,1,1,1,1,1] generating graphics... => 17
[7,2,2,2,2,2] generating graphics... => 17
[7,2,2,2,2,1,1] generating graphics... => 17
[7,2,2,2,1,1,1,1] generating graphics... => 17
[7,2,2,1,1,1,1,1,1] generating graphics... => 17
[7,2,1,1,1,1,1,1,1,1] generating graphics... => 17
[7,1,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[6,6,5] generating graphics... => 17
[6,6,4,1] generating graphics... => 17
[6,6,3,2] generating graphics... => 17
[6,6,3,1,1] generating graphics... => 17
[6,6,2,2,1] generating graphics... => 17
[6,6,2,1,1,1] generating graphics... => 17
[6,6,1,1,1,1,1] generating graphics... => 17
[6,5,5,1] generating graphics... => 17
[6,5,4,2] generating graphics... => 17
[6,5,4,1,1] generating graphics... => 17
[6,5,3,3] generating graphics... => 17
[6,5,3,2,1] generating graphics... => 17
[6,5,3,1,1,1] generating graphics... => 17
[6,5,2,2,2] generating graphics... => 17
[6,5,2,2,1,1] generating graphics... => 17
[6,5,2,1,1,1,1] generating graphics... => 17
[6,5,1,1,1,1,1,1] generating graphics... => 17
[6,4,4,3] generating graphics... => 17
[6,4,4,2,1] generating graphics... => 17
[6,4,4,1,1,1] generating graphics... => 17
[6,4,3,3,1] generating graphics... => 17
[6,4,3,2,2] generating graphics... => 17
[6,4,3,2,1,1] generating graphics... => 17
[6,4,3,1,1,1,1] generating graphics... => 17
[6,4,2,2,2,1] generating graphics... => 17
[6,4,2,2,1,1,1] generating graphics... => 17
[6,4,2,1,1,1,1,1] generating graphics... => 17
[6,4,1,1,1,1,1,1,1] generating graphics... => 17
[6,3,3,3,2] generating graphics... => 17
[6,3,3,3,1,1] generating graphics... => 17
[6,3,3,2,2,1] generating graphics... => 17
[6,3,3,2,1,1,1] generating graphics... => 17
[6,3,3,1,1,1,1,1] generating graphics... => 17
[6,3,2,2,2,2] generating graphics... => 17
[6,3,2,2,2,1,1] generating graphics... => 17
[6,3,2,2,1,1,1,1] generating graphics... => 17
[6,3,2,1,1,1,1,1,1] generating graphics... => 17
[6,3,1,1,1,1,1,1,1,1] generating graphics... => 17
[6,2,2,2,2,2,1] generating graphics... => 17
[6,2,2,2,2,1,1,1] generating graphics... => 17
[6,2,2,2,1,1,1,1,1] generating graphics... => 17
[6,2,2,1,1,1,1,1,1,1] generating graphics... => 17
[6,2,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[6,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[5,5,5,2] generating graphics... => 17
[5,5,5,1,1] generating graphics... => 17
[5,5,4,3] generating graphics... => 17
[5,5,4,2,1] generating graphics... => 17
[5,5,4,1,1,1] generating graphics... => 17
[5,5,3,3,1] generating graphics... => 17
[5,5,3,2,2] generating graphics... => 17
[5,5,3,2,1,1] generating graphics... => 17
[5,5,3,1,1,1,1] generating graphics... => 17
[5,5,2,2,2,1] generating graphics... => 17
[5,5,2,2,1,1,1] generating graphics... => 17
[5,5,2,1,1,1,1,1] generating graphics... => 17
[5,5,1,1,1,1,1,1,1] generating graphics... => 17
[5,4,4,4] generating graphics... => 17
[5,4,4,3,1] generating graphics... => 17
[5,4,4,2,2] generating graphics... => 17
[5,4,4,2,1,1] generating graphics... => 17
[5,4,4,1,1,1,1] generating graphics... => 17
[5,4,3,3,2] generating graphics... => 17
[5,4,3,3,1,1] generating graphics... => 17
[5,4,3,2,2,1] generating graphics... => 17
[5,4,3,2,1,1,1] generating graphics... => 17
[5,4,3,1,1,1,1,1] generating graphics... => 17
[5,4,2,2,2,2] generating graphics... => 17
[5,4,2,2,2,1,1] generating graphics... => 17
[5,4,2,2,1,1,1,1] generating graphics... => 17
[5,4,2,1,1,1,1,1,1] generating graphics... => 17
[5,4,1,1,1,1,1,1,1,1] generating graphics... => 17
[5,3,3,3,3] generating graphics... => 17
[5,3,3,3,2,1] generating graphics... => 17
[5,3,3,3,1,1,1] generating graphics... => 17
[5,3,3,2,2,2] generating graphics... => 17
[5,3,3,2,2,1,1] generating graphics... => 17
[5,3,3,2,1,1,1,1] generating graphics... => 17
[5,3,3,1,1,1,1,1,1] generating graphics... => 17
[5,3,2,2,2,2,1] generating graphics... => 17
[5,3,2,2,2,1,1,1] generating graphics... => 17
[5,3,2,2,1,1,1,1,1] generating graphics... => 17
[5,3,2,1,1,1,1,1,1,1] generating graphics... => 17
[5,3,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[5,2,2,2,2,2,2] generating graphics... => 17
[5,2,2,2,2,2,1,1] generating graphics... => 17
[5,2,2,2,2,1,1,1,1] generating graphics... => 17
[5,2,2,2,1,1,1,1,1,1] generating graphics... => 17
[5,2,2,1,1,1,1,1,1,1,1] generating graphics... => 17
[5,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[5,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[4,4,4,4,1] generating graphics... => 17
[4,4,4,3,2] generating graphics... => 17
[4,4,4,3,1,1] generating graphics... => 17
[4,4,4,2,2,1] generating graphics... => 17
[4,4,4,2,1,1,1] generating graphics... => 17
[4,4,4,1,1,1,1,1] generating graphics... => 17
[4,4,3,3,3] generating graphics... => 17
[4,4,3,3,2,1] generating graphics... => 17
[4,4,3,3,1,1,1] generating graphics... => 17
[4,4,3,2,2,2] generating graphics... => 17
[4,4,3,2,2,1,1] generating graphics... => 17
[4,4,3,2,1,1,1,1] generating graphics... => 17
[4,4,3,1,1,1,1,1,1] generating graphics... => 17
[4,4,2,2,2,2,1] generating graphics... => 17
[4,4,2,2,2,1,1,1] generating graphics... => 17
[4,4,2,2,1,1,1,1,1] generating graphics... => 17
[4,4,2,1,1,1,1,1,1,1] generating graphics... => 17
[4,4,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[4,3,3,3,3,1] generating graphics... => 17
[4,3,3,3,2,2] generating graphics... => 17
[4,3,3,3,2,1,1] generating graphics... => 17
[4,3,3,3,1,1,1,1] generating graphics... => 17
[4,3,3,2,2,2,1] generating graphics... => 17
[4,3,3,2,2,1,1,1] generating graphics... => 17
[4,3,3,2,1,1,1,1,1] generating graphics... => 17
[4,3,3,1,1,1,1,1,1,1] generating graphics... => 17
[4,3,2,2,2,2,2] generating graphics... => 17
[4,3,2,2,2,2,1,1] generating graphics... => 17
[4,3,2,2,2,1,1,1,1] generating graphics... => 17
[4,3,2,2,1,1,1,1,1,1] generating graphics... => 17
[4,3,2,1,1,1,1,1,1,1,1] generating graphics... => 17
[4,3,1,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[4,2,2,2,2,2,2,1] generating graphics... => 17
[4,2,2,2,2,2,1,1,1] generating graphics... => 17
[4,2,2,2,2,1,1,1,1,1] generating graphics... => 17
[4,2,2,2,1,1,1,1,1,1,1] generating graphics... => 17
[4,2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[4,2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[3,3,3,3,3,2] generating graphics... => 17
[3,3,3,3,3,1,1] generating graphics... => 17
[3,3,3,3,2,2,1] generating graphics... => 17
[3,3,3,3,2,1,1,1] generating graphics... => 17
[3,3,3,3,1,1,1,1,1] generating graphics... => 17
[3,3,3,2,2,2,2] generating graphics... => 17
[3,3,3,2,2,2,1,1] generating graphics... => 17
[3,3,3,2,2,1,1,1,1] generating graphics... => 17
[3,3,3,2,1,1,1,1,1,1] generating graphics... => 17
[3,3,3,1,1,1,1,1,1,1,1] generating graphics... => 17
[3,3,2,2,2,2,2,1] generating graphics... => 17
[3,3,2,2,2,2,1,1,1] generating graphics... => 17
[3,3,2,2,2,1,1,1,1,1] generating graphics... => 17
[3,3,2,2,1,1,1,1,1,1,1] generating graphics... => 17
[3,3,2,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[3,3,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 17
[3,2,2,2,2,2,2,2] generating graphics... => 17
[3,2,2,2,2,2,2,1,1] generating graphics... => 17
[3,2,2,2,2,2,1,1,1,1] generating graphics... => 17
[3,2,2,2,2,1,1,1,1,1,1] generating graphics... => 17
[3,2,2,2,1,1,1,1,1,1,1,1] generating graphics... => 17
[3,2,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 17
click to show generating function       
Description
The cyclic permutation representation number of an integer partition.
This is the size of the largest cyclic group $C$ such that the fake degree is the character of a permutation representation of $C$.
References
[1] Alexandersson, P., Amini, N. The cone of cyclic sieving phenomena MathSciNet:3922156
Code
def fdeg(p):
    R. = QQ[]
    f = prod([ 1-q*q^j for j in range(p.size()) ])
    b = sum([ j*k for j, k in enumerate(p) ])
    return (q^b)*(f/p.hook_polynomial(q,q))

def fake_degree(a):
    R. = QQ[]
    if a == 0:
        return R(0)
    else:
        z = SymmetricFunctions(QQ).schur()(a)
        return R(sum([z.coefficient(p)*fdeg(p) for p in z.support()]))

def standard_CSP(p, r):
    P = parent(p)
    q = P.gen()
    PP. = PolynomialRing(QQ)
    R. = PP.quo(q^r-1)
    return R(p).lift()

def orbit_lengths(p, r):
    p = standard_CSP(p, r)
    p = {k: p[k] for k in range(r)}
    divs = sorted(divisors(r))
    O = dict()
    for d in divs:
        count = p[r-d]
        if count:
            O[r//d] = count
        if count:
            for k in range(0, r, d):
                p[k] -= count
    assert all(c == 0 for c in p.values()), "%s" % p
    return O

def has_cyclic_permutation_representation(p, r):
    if p == 0:
        return True
    try:
        lo = orbit_lengths(p, r)
    except AssertionError:
        return False
    return all(v in ZZ and ZZ(v) >= 0 for v in lo.values())

def statistic(la):
    s = SymmetricFunctions(QQ).schur()
    f = fake_degree(s(la))
    for r in reversed(divisors(la.size())):
        if has_cyclic_permutation_representation(f, r):
            return r

# alternative implementation using Theorem 2.7
def has_cyclic_permutation_representation_slow(p, r):
    for k in divisors(r):
        if sum(moebius(k//j) * p.subs(q=QQbar.zeta(r)^j) for j in divisors(k)) < 0:
            return False
    return True

def statistic_slow(la):
    s = SymmetricFunctions(QQ).schur()
    f = fake_degree(s(la))
    for r in reversed(divisors(la.size())):
        if has_cyclic_permutation_representation_slow(f, r):
            return r

Created
Mar 25, 2020 at 10:08 by Martin Rubey
Updated
Mar 25, 2020 at 10:08 by Martin Rubey