Identifier
Identifier
Values
[[1]] generating graphics... => 0
[[2]] generating graphics... => 1
[[3]] generating graphics... => 1
[[4]] generating graphics... => 1
[[1,1]] generating graphics... => 0
[[1,2]] generating graphics... => 0
[[1,3]] generating graphics... => 0
[[1,4]] generating graphics... => 0
[[2,2]] generating graphics... => 1
[[2,3]] generating graphics... => 1
[[2,4]] generating graphics... => 1
[[3,3]] generating graphics... => 1
[[3,4]] generating graphics... => 1
[[4,4]] generating graphics... => 1
[[1],[2]] generating graphics... => 0
[[1],[3]] generating graphics... => 1
[[1],[4]] generating graphics... => 1
[[2],[3]] generating graphics... => 2
[[2],[4]] generating graphics... => 2
[[3],[4]] generating graphics... => 2
[[1,1,1]] generating graphics... => 0
[[1,1,2]] generating graphics... => 0
[[1,1,3]] generating graphics... => 0
[[1,1,4]] generating graphics... => 0
[[1,2,2]] generating graphics... => 0
[[1,2,3]] generating graphics... => 0
[[1,2,4]] generating graphics... => 0
[[1,3,3]] generating graphics... => 0
[[1,3,4]] generating graphics... => 0
[[1,4,4]] generating graphics... => 0
[[2,2,2]] generating graphics... => 1
[[2,2,3]] generating graphics... => 1
[[2,2,4]] generating graphics... => 1
[[2,3,3]] generating graphics... => 1
[[2,3,4]] generating graphics... => 1
[[2,4,4]] generating graphics... => 1
[[3,3,3]] generating graphics... => 1
[[3,3,4]] generating graphics... => 1
[[3,4,4]] generating graphics... => 1
[[4,4,4]] generating graphics... => 1
[[1,1],[2]] generating graphics... => 0
[[1,1],[3]] generating graphics... => 1
[[1,1],[4]] generating graphics... => 1
[[1,2],[2]] generating graphics... => 1
[[1,2],[3]] generating graphics... => 1
[[1,3],[2]] generating graphics... => 1
[[1,2],[4]] generating graphics... => 1
[[1,4],[2]] generating graphics... => 1
[[1,3],[3]] generating graphics... => 2
[[1,3],[4]] generating graphics... => 1
[[1,4],[3]] generating graphics... => 2
[[1,4],[4]] generating graphics... => 2
[[2,2],[3]] generating graphics... => 2
[[2,2],[4]] generating graphics... => 2
[[2,3],[3]] generating graphics... => 3
[[2,3],[4]] generating graphics... => 2
[[2,4],[3]] generating graphics... => 3
[[2,4],[4]] generating graphics... => 3
[[3,3],[4]] generating graphics... => 2
[[3,4],[4]] generating graphics... => 3
[[1],[2],[3]] generating graphics... => 0
[[1],[2],[4]] generating graphics... => 1
[[1],[3],[4]] generating graphics... => 2
[[2],[3],[4]] generating graphics... => 3
[[1,1,1,1]] generating graphics... => 0
[[1,1,1,2]] generating graphics... => 0
[[1,1,1,3]] generating graphics... => 0
[[1,1,1,4]] generating graphics... => 0
[[1,1,2,2]] generating graphics... => 0
[[1,1,2,3]] generating graphics... => 0
[[1,1,2,4]] generating graphics... => 0
[[1,1,3,3]] generating graphics... => 0
[[1,1,3,4]] generating graphics... => 0
[[1,1,4,4]] generating graphics... => 0
[[1,2,2,2]] generating graphics... => 0
[[1,2,2,3]] generating graphics... => 0
[[1,2,2,4]] generating graphics... => 0
[[1,2,3,3]] generating graphics... => 0
[[1,2,3,4]] generating graphics... => 0
[[1,2,4,4]] generating graphics... => 0
[[1,3,3,3]] generating graphics... => 0
[[1,3,3,4]] generating graphics... => 0
[[1,3,4,4]] generating graphics... => 0
[[1,4,4,4]] generating graphics... => 0
[[2,2,2,2]] generating graphics... => 1
[[2,2,2,3]] generating graphics... => 1
[[2,2,2,4]] generating graphics... => 1
[[2,2,3,3]] generating graphics... => 1
[[2,2,3,4]] generating graphics... => 1
[[2,2,4,4]] generating graphics... => 1
[[2,3,3,3]] generating graphics... => 1
[[2,3,3,4]] generating graphics... => 1
[[2,3,4,4]] generating graphics... => 1
[[2,4,4,4]] generating graphics... => 1
[[3,3,3,3]] generating graphics... => 1
[[3,3,3,4]] generating graphics... => 1
[[3,3,4,4]] generating graphics... => 1
[[3,4,4,4]] generating graphics... => 1
[[4,4,4,4]] generating graphics... => 1
[[1,1,1],[2]] generating graphics... => 0
[[1,1,1],[3]] generating graphics... => 1
[[1,1,1],[4]] generating graphics... => 1
[[1,1,2],[2]] generating graphics... => 0
[[1,1,2],[3]] generating graphics... => 1
[[1,1,3],[2]] generating graphics... => 0
[[1,1,2],[4]] generating graphics... => 1
[[1,1,4],[2]] generating graphics... => 0
[[1,1,3],[3]] generating graphics... => 1
[[1,1,3],[4]] generating graphics... => 1
[[1,1,4],[3]] generating graphics... => 1
[[1,1,4],[4]] generating graphics... => 1
[[1,2,2],[2]] generating graphics... => 1
[[1,2,2],[3]] generating graphics... => 1
[[1,2,3],[2]] generating graphics... => 1
[[1,2,2],[4]] generating graphics... => 1
[[1,2,4],[2]] generating graphics... => 1
[[1,2,3],[3]] generating graphics... => 1
[[1,3,3],[2]] generating graphics... => 1
[[1,2,3],[4]] generating graphics... => 1
[[1,2,4],[3]] generating graphics... => 1
[[1,3,4],[2]] generating graphics... => 1
[[1,2,4],[4]] generating graphics... => 1
[[1,4,4],[2]] generating graphics... => 1
[[1,3,3],[3]] generating graphics... => 2
[[1,3,3],[4]] generating graphics... => 1
[[1,3,4],[3]] generating graphics... => 2
[[1,3,4],[4]] generating graphics... => 1
[[1,4,4],[3]] generating graphics... => 2
[[1,4,4],[4]] generating graphics... => 2
[[2,2,2],[3]] generating graphics... => 2
[[2,2,2],[4]] generating graphics... => 2
[[2,2,3],[3]] generating graphics... => 2
[[2,2,3],[4]] generating graphics... => 2
[[2,2,4],[3]] generating graphics... => 2
[[2,2,4],[4]] generating graphics... => 2
[[2,3,3],[3]] generating graphics... => 3
[[2,3,3],[4]] generating graphics... => 2
[[2,3,4],[3]] generating graphics... => 3
[[2,3,4],[4]] generating graphics... => 2
[[2,4,4],[3]] generating graphics... => 3
[[2,4,4],[4]] generating graphics... => 3
[[3,3,3],[4]] generating graphics... => 2
[[3,3,4],[4]] generating graphics... => 2
[[3,4,4],[4]] generating graphics... => 3
[[1,1],[2,2]] generating graphics... => 0
[[1,1],[2,3]] generating graphics... => 0
[[1,1],[2,4]] generating graphics... => 0
[[1,1],[3,3]] generating graphics... => 1
[[1,1],[3,4]] generating graphics... => 1
[[1,1],[4,4]] generating graphics... => 1
[[1,2],[2,3]] generating graphics... => 1
[[1,2],[2,4]] generating graphics... => 1
[[1,2],[3,3]] generating graphics... => 1
[[1,2],[3,4]] generating graphics... => 2
[[1,3],[2,4]] generating graphics... => 1
[[1,2],[4,4]] generating graphics... => 1
[[1,3],[3,4]] generating graphics... => 2
[[1,3],[4,4]] generating graphics... => 1
[[2,2],[3,3]] generating graphics... => 2
[[2,2],[3,4]] generating graphics... => 2
[[2,2],[4,4]] generating graphics... => 2
[[2,3],[3,4]] generating graphics... => 3
[[2,3],[4,4]] generating graphics... => 2
[[3,3],[4,4]] generating graphics... => 2
[[1,1],[2],[3]] generating graphics... => 0
[[1,1],[2],[4]] generating graphics... => 1
[[1,1],[3],[4]] generating graphics... => 2
[[1,2],[2],[3]] generating graphics... => 1
[[1,2],[2],[4]] generating graphics... => 2
[[1,3],[2],[3]] generating graphics... => 1
[[1,2],[3],[4]] generating graphics... => 2
[[1,3],[2],[4]] generating graphics... => 2
[[1,4],[2],[3]] generating graphics... => 1
[[1,4],[2],[4]] generating graphics... => 2
[[1,3],[3],[4]] generating graphics... => 3
[[1,4],[3],[4]] generating graphics... => 3
[[2,2],[3],[4]] generating graphics... => 3
[[2,3],[3],[4]] generating graphics... => 4
[[2,4],[3],[4]] generating graphics... => 4
[[1],[2],[3],[4]] generating graphics... => 0
[[1,1,1,1,1]] generating graphics... => 0
[[1,1,1,1,2]] generating graphics... => 0
[[1,1,1,1,3]] generating graphics... => 0
[[1,1,1,1,4]] generating graphics... => 0
[[1,1,1,2,2]] generating graphics... => 0
[[1,1,1,2,3]] generating graphics... => 0
[[1,1,1,2,4]] generating graphics... => 0
[[1,1,1,3,3]] generating graphics... => 0
[[1,1,1,3,4]] generating graphics... => 0
[[1,1,1,4,4]] generating graphics... => 0
[[1,1,2,2,2]] generating graphics... => 0
[[1,1,2,2,3]] generating graphics... => 0
[[1,1,2,2,4]] generating graphics... => 0
[[1,1,2,3,3]] generating graphics... => 0
[[1,1,2,3,4]] generating graphics... => 0
[[1,1,2,4,4]] generating graphics... => 0
[[1,1,3,3,3]] generating graphics... => 0
[[1,1,3,3,4]] generating graphics... => 0
[[1,1,3,4,4]] generating graphics... => 0
[[1,1,4,4,4]] generating graphics... => 0
[[1,2,2,2,2]] generating graphics... => 0
[[1,2,2,2,3]] generating graphics... => 0
[[1,2,2,2,4]] generating graphics... => 0
[[1,2,2,3,3]] generating graphics... => 0
[[1,2,2,3,4]] generating graphics... => 0
[[1,2,2,4,4]] generating graphics... => 0
[[1,2,3,3,3]] generating graphics... => 0
[[1,2,3,3,4]] generating graphics... => 0
[[1,2,3,4,4]] generating graphics... => 0
[[1,2,4,4,4]] generating graphics... => 0
[[1,3,3,3,3]] generating graphics... => 0
[[1,3,3,3,4]] generating graphics... => 0
[[1,3,3,4,4]] generating graphics... => 0
[[1,3,4,4,4]] generating graphics... => 0
[[1,4,4,4,4]] generating graphics... => 0
[[2,2,2,2,2]] generating graphics... => 1
[[2,2,2,2,3]] generating graphics... => 1
[[2,2,2,2,4]] generating graphics... => 1
[[2,2,2,3,3]] generating graphics... => 1
[[2,2,2,3,4]] generating graphics... => 1
[[2,2,2,4,4]] generating graphics... => 1
[[2,2,3,3,3]] generating graphics... => 1
[[2,2,3,3,4]] generating graphics... => 1
[[2,2,3,4,4]] generating graphics... => 1
[[2,2,4,4,4]] generating graphics... => 1
[[2,3,3,3,3]] generating graphics... => 1
[[2,3,3,3,4]] generating graphics... => 1
[[2,3,3,4,4]] generating graphics... => 1
[[2,3,4,4,4]] generating graphics... => 1
[[2,4,4,4,4]] generating graphics... => 1
[[3,3,3,3,3]] generating graphics... => 1
[[3,3,3,3,4]] generating graphics... => 1
[[3,3,3,4,4]] generating graphics... => 1
[[3,3,4,4,4]] generating graphics... => 1
[[3,4,4,4,4]] generating graphics... => 1
[[4,4,4,4,4]] generating graphics... => 1
[[1,1,1,1],[2]] generating graphics... => 0
[[1,1,1,1],[3]] generating graphics... => 1
[[1,1,1,1],[4]] generating graphics... => 1
[[1,1,1,2],[2]] generating graphics... => 0
[[1,1,1,2],[3]] generating graphics... => 1
[[1,1,1,3],[2]] generating graphics... => 0
[[1,1,1,2],[4]] generating graphics... => 1
[[1,1,1,4],[2]] generating graphics... => 0
[[1,1,1,3],[3]] generating graphics... => 1
[[1,1,1,3],[4]] generating graphics... => 1
[[1,1,1,4],[3]] generating graphics... => 1
[[1,1,1,4],[4]] generating graphics... => 1
[[1,1,2,2],[2]] generating graphics... => 0
[[1,1,2,2],[3]] generating graphics... => 1
[[1,1,2,3],[2]] generating graphics... => 0
[[1,1,2,2],[4]] generating graphics... => 1
[[1,1,2,4],[2]] generating graphics... => 0
[[1,1,2,3],[3]] generating graphics... => 1
[[1,1,3,3],[2]] generating graphics... => 0
[[1,1,2,3],[4]] generating graphics... => 1
[[1,1,2,4],[3]] generating graphics... => 1
[[1,1,3,4],[2]] generating graphics... => 0
[[1,1,2,4],[4]] generating graphics... => 1
[[1,1,4,4],[2]] generating graphics... => 0
[[1,1,3,3],[3]] generating graphics... => 1
[[1,1,3,3],[4]] generating graphics... => 1
[[1,1,3,4],[3]] generating graphics... => 1
[[1,1,3,4],[4]] generating graphics... => 1
[[1,1,4,4],[3]] generating graphics... => 1
[[1,1,4,4],[4]] generating graphics... => 1
[[1,2,2,2],[2]] generating graphics... => 1
[[1,2,2,2],[3]] generating graphics... => 1
[[1,2,2,3],[2]] generating graphics... => 1
[[1,2,2,2],[4]] generating graphics... => 1
[[1,2,2,4],[2]] generating graphics... => 1
[[1,2,2,3],[3]] generating graphics... => 1
[[1,2,3,3],[2]] generating graphics... => 1
[[1,2,2,3],[4]] generating graphics... => 1
[[1,2,2,4],[3]] generating graphics... => 1
[[1,2,3,4],[2]] generating graphics... => 1
[[1,2,2,4],[4]] generating graphics... => 1
[[1,2,4,4],[2]] generating graphics... => 1
[[1,2,3,3],[3]] generating graphics... => 1
[[1,3,3,3],[2]] generating graphics... => 1
[[1,2,3,3],[4]] generating graphics... => 1
[[1,2,3,4],[3]] generating graphics... => 1
[[1,3,3,4],[2]] generating graphics... => 1
[[1,2,3,4],[4]] generating graphics... => 1
[[1,2,4,4],[3]] generating graphics... => 1
[[1,3,4,4],[2]] generating graphics... => 1
[[1,2,4,4],[4]] generating graphics... => 1
[[1,4,4,4],[2]] generating graphics... => 1
[[1,3,3,3],[3]] generating graphics... => 2
[[1,3,3,3],[4]] generating graphics... => 1
[[1,3,3,4],[3]] generating graphics... => 2
[[1,3,3,4],[4]] generating graphics... => 1
[[1,3,4,4],[3]] generating graphics... => 2
[[1,3,4,4],[4]] generating graphics... => 1
[[1,4,4,4],[3]] generating graphics... => 2
[[1,4,4,4],[4]] generating graphics... => 2
[[2,2,2,2],[3]] generating graphics... => 2
[[2,2,2,2],[4]] generating graphics... => 2
[[2,2,2,3],[3]] generating graphics... => 2
[[2,2,2,3],[4]] generating graphics... => 2
[[2,2,2,4],[3]] generating graphics... => 2
[[2,2,2,4],[4]] generating graphics... => 2
[[2,2,3,3],[3]] generating graphics... => 2
[[2,2,3,3],[4]] generating graphics... => 2
[[2,2,3,4],[3]] generating graphics... => 2
[[2,2,3,4],[4]] generating graphics... => 2
[[2,2,4,4],[3]] generating graphics... => 2
[[2,2,4,4],[4]] generating graphics... => 2
[[2,3,3,3],[3]] generating graphics... => 3
[[2,3,3,3],[4]] generating graphics... => 2
[[2,3,3,4],[3]] generating graphics... => 3
[[2,3,3,4],[4]] generating graphics... => 2
[[2,3,4,4],[3]] generating graphics... => 3
[[2,3,4,4],[4]] generating graphics... => 2
[[2,4,4,4],[3]] generating graphics... => 3
[[2,4,4,4],[4]] generating graphics... => 3
[[3,3,3,3],[4]] generating graphics... => 2
[[3,3,3,4],[4]] generating graphics... => 2
[[3,3,4,4],[4]] generating graphics... => 2
[[3,4,4,4],[4]] generating graphics... => 3
[[1,1,1],[2,2]] generating graphics... => 0
[[1,1,1],[2,3]] generating graphics... => 0
[[1,1,1],[2,4]] generating graphics... => 0
[[1,1,1],[3,3]] generating graphics... => 1
[[1,1,1],[3,4]] generating graphics... => 1
[[1,1,1],[4,4]] generating graphics... => 1
[[1,1,2],[2,2]] generating graphics... => 1
[[1,1,2],[2,3]] generating graphics... => 0
[[1,1,3],[2,2]] generating graphics... => 1
[[1,1,2],[2,4]] generating graphics... => 0
[[1,1,4],[2,2]] generating graphics... => 1
[[1,1,2],[3,3]] generating graphics... => 1
[[1,1,3],[2,3]] generating graphics... => 1
[[1,1,2],[3,4]] generating graphics... => 1
[[1,1,3],[2,4]] generating graphics... => 0
[[1,1,4],[2,3]] generating graphics... => 1
[[1,1,2],[4,4]] generating graphics... => 1
[[1,1,4],[2,4]] generating graphics... => 1
[[1,1,3],[3,3]] generating graphics... => 2
[[1,1,3],[3,4]] generating graphics... => 1
[[1,1,4],[3,3]] generating graphics... => 2
[[1,1,3],[4,4]] generating graphics... => 1
[[1,1,4],[3,4]] generating graphics... => 2
[[1,1,4],[4,4]] generating graphics... => 2
[[1,2,2],[2,3]] generating graphics... => 1
[[1,2,2],[2,4]] generating graphics... => 1
[[1,2,2],[3,3]] generating graphics... => 1
[[1,2,3],[2,3]] generating graphics... => 2
[[1,2,2],[3,4]] generating graphics... => 2
[[1,2,3],[2,4]] generating graphics... => 1
[[1,2,4],[2,3]] generating graphics... => 2
[[1,2,2],[4,4]] generating graphics... => 1
[[1,2,4],[2,4]] generating graphics... => 2
[[1,2,3],[3,3]] generating graphics... => 2
[[1,2,3],[3,4]] generating graphics... => 2
[[1,2,4],[3,3]] generating graphics... => 2
[[1,3,3],[2,4]] generating graphics... => 1
[[1,2,3],[4,4]] generating graphics... => 1
[[1,2,4],[3,4]] generating graphics... => 3
[[1,3,4],[2,4]] generating graphics... => 2
[[1,2,4],[4,4]] generating graphics... => 2
[[1,3,3],[3,4]] generating graphics... => 2
[[1,3,3],[4,4]] generating graphics... => 1
[[1,3,4],[3,4]] generating graphics... => 3
[[1,3,4],[4,4]] generating graphics... => 2
[[2,2,2],[3,3]] generating graphics... => 2
[[2,2,2],[3,4]] generating graphics... => 2
[[2,2,2],[4,4]] generating graphics... => 2
[[2,2,3],[3,3]] generating graphics... => 3
[[2,2,3],[3,4]] generating graphics... => 2
[[2,2,4],[3,3]] generating graphics... => 3
[[2,2,3],[4,4]] generating graphics... => 2
[[2,2,4],[3,4]] generating graphics... => 3
[[2,2,4],[4,4]] generating graphics... => 3
[[2,3,3],[3,4]] generating graphics... => 3
[[2,3,3],[4,4]] generating graphics... => 2
[[2,3,4],[3,4]] generating graphics... => 4
[[2,3,4],[4,4]] generating graphics... => 3
[[3,3,3],[4,4]] generating graphics... => 2
[[3,3,4],[4,4]] generating graphics... => 3
[[1,1,1],[2],[3]] generating graphics... => 0
[[1,1,1],[2],[4]] generating graphics... => 1
[[1,1,1],[3],[4]] generating graphics... => 2
[[1,1,2],[2],[3]] generating graphics... => 0
[[1,1,2],[2],[4]] generating graphics... => 1
[[1,1,3],[2],[3]] generating graphics... => 0
[[1,1,2],[3],[4]] generating graphics... => 2
[[1,1,3],[2],[4]] generating graphics... => 1
[[1,1,4],[2],[3]] generating graphics... => 0
[[1,1,4],[2],[4]] generating graphics... => 1
[[1,1,3],[3],[4]] generating graphics... => 2
[[1,1,4],[3],[4]] generating graphics... => 2
[[1,2,2],[2],[3]] generating graphics... => 1
[[1,2,2],[2],[4]] generating graphics... => 2
[[1,2,3],[2],[3]] generating graphics... => 1
[[1,2,2],[3],[4]] generating graphics... => 2
[[1,2,3],[2],[4]] generating graphics... => 2
[[1,2,4],[2],[3]] generating graphics... => 1
[[1,2,4],[2],[4]] generating graphics... => 2
[[1,3,3],[2],[3]] generating graphics... => 1
[[1,2,3],[3],[4]] generating graphics... => 2
[[1,3,3],[2],[4]] generating graphics... => 2
[[1,3,4],[2],[3]] generating graphics... => 1
[[1,2,4],[3],[4]] generating graphics... => 2
[[1,3,4],[2],[4]] generating graphics... => 2
[[1,4,4],[2],[3]] generating graphics... => 1
[[1,4,4],[2],[4]] generating graphics... => 2
[[1,3,3],[3],[4]] generating graphics... => 3
[[1,3,4],[3],[4]] generating graphics... => 3
[[1,4,4],[3],[4]] generating graphics... => 3
[[2,2,2],[3],[4]] generating graphics... => 3
[[2,2,3],[3],[4]] generating graphics... => 3
[[2,2,4],[3],[4]] generating graphics... => 3
[[2,3,3],[3],[4]] generating graphics... => 4
[[2,3,4],[3],[4]] generating graphics... => 4
[[2,4,4],[3],[4]] generating graphics... => 4
[[1,1],[2,2],[3]] generating graphics... => 0
[[1,1],[2,2],[4]] generating graphics... => 1
[[1,1],[2,3],[3]] generating graphics... => 1
[[1,1],[2,3],[4]] generating graphics... => 1
[[1,1],[2,4],[3]] generating graphics... => 1
[[1,1],[2,4],[4]] generating graphics... => 2
[[1,1],[3,3],[4]] generating graphics... => 2
[[1,1],[3,4],[4]] generating graphics... => 3
[[1,2],[2,3],[3]] generating graphics... => 2
[[1,2],[2,3],[4]] generating graphics... => 2
[[1,2],[2,4],[3]] generating graphics... => 2
[[1,2],[2,4],[4]] generating graphics... => 3
[[1,2],[3,3],[4]] generating graphics... => 2
[[1,3],[2,4],[3]] generating graphics... => 2
[[1,2],[3,4],[4]] generating graphics... => 4
[[1,3],[2,4],[4]] generating graphics... => 3
[[1,3],[3,4],[4]] generating graphics... => 4
[[2,2],[3,3],[4]] generating graphics... => 3
[[2,2],[3,4],[4]] generating graphics... => 4
[[2,3],[3,4],[4]] generating graphics... => 5
[[1,1],[2],[3],[4]] generating graphics... => 0
[[1,2],[2],[3],[4]] generating graphics... => 1
[[1,3],[2],[3],[4]] generating graphics... => 1
[[1,4],[2],[3],[4]] generating graphics... => 1
[[1,1,1,1,1,1]] generating graphics... => 0
[[1,1,1,1,1,2]] generating graphics... => 0
[[1,1,1,1,1,3]] generating graphics... => 0
[[1,1,1,1,1,4]] generating graphics... => 0
[[1,1,1,1,2,2]] generating graphics... => 0
[[1,1,1,1,2,3]] generating graphics... => 0
[[1,1,1,1,2,4]] generating graphics... => 0
[[1,1,1,1,3,3]] generating graphics... => 0
[[1,1,1,1,3,4]] generating graphics... => 0
[[1,1,1,1,4,4]] generating graphics... => 0
[[1,1,1,2,2,2]] generating graphics... => 0
[[1,1,1,2,2,3]] generating graphics... => 0
[[1,1,1,2,2,4]] generating graphics... => 0
[[1,1,1,2,3,3]] generating graphics... => 0
[[1,1,1,2,3,4]] generating graphics... => 0
[[1,1,1,2,4,4]] generating graphics... => 0
[[1,1,1,3,3,3]] generating graphics... => 0
[[1,1,1,3,3,4]] generating graphics... => 0
[[1,1,1,3,4,4]] generating graphics... => 0
[[1,1,1,4,4,4]] generating graphics... => 0
[[1,1,2,2,2,2]] generating graphics... => 0
[[1,1,2,2,2,3]] generating graphics... => 0
[[1,1,2,2,2,4]] generating graphics... => 0
[[1,1,2,2,3,3]] generating graphics... => 0
[[1,1,2,2,3,4]] generating graphics... => 0
[[1,1,2,2,4,4]] generating graphics... => 0
[[1,1,2,3,3,3]] generating graphics... => 0
[[1,1,2,3,3,4]] generating graphics... => 0
[[1,1,2,3,4,4]] generating graphics... => 0
[[1,1,2,4,4,4]] generating graphics... => 0
[[1,1,3,3,3,3]] generating graphics... => 0
[[1,1,3,3,3,4]] generating graphics... => 0
[[1,1,3,3,4,4]] generating graphics... => 0
[[1,1,3,4,4,4]] generating graphics... => 0
[[1,1,4,4,4,4]] generating graphics... => 0
[[1,2,2,2,2,2]] generating graphics... => 0
[[1,2,2,2,2,3]] generating graphics... => 0
[[1,2,2,2,2,4]] generating graphics... => 0
[[1,2,2,2,3,3]] generating graphics... => 0
[[1,2,2,2,3,4]] generating graphics... => 0
[[1,2,2,2,4,4]] generating graphics... => 0
[[1,2,2,3,3,3]] generating graphics... => 0
[[1,2,2,3,3,4]] generating graphics... => 0
[[1,2,2,3,4,4]] generating graphics... => 0
[[1,2,2,4,4,4]] generating graphics... => 0
[[1,2,3,3,3,3]] generating graphics... => 0
[[1,2,3,3,3,4]] generating graphics... => 0
[[1,2,3,3,4,4]] generating graphics... => 0
[[1,2,3,4,4,4]] generating graphics... => 0
[[1,2,4,4,4,4]] generating graphics... => 0
[[1,3,3,3,3,3]] generating graphics... => 0
[[1,3,3,3,3,4]] generating graphics... => 0
[[1,3,3,3,4,4]] generating graphics... => 0
[[1,3,3,4,4,4]] generating graphics... => 0
[[1,3,4,4,4,4]] generating graphics... => 0
[[1,4,4,4,4,4]] generating graphics... => 0
[[2,2,2,2,2,2]] generating graphics... => 1
[[2,2,2,2,2,3]] generating graphics... => 1
[[2,2,2,2,2,4]] generating graphics... => 1
[[2,2,2,2,3,3]] generating graphics... => 1
[[2,2,2,2,3,4]] generating graphics... => 1
[[2,2,2,2,4,4]] generating graphics... => 1
[[2,2,2,3,3,3]] generating graphics... => 1
[[2,2,2,3,3,4]] generating graphics... => 1
[[2,2,2,3,4,4]] generating graphics... => 1
[[2,2,2,4,4,4]] generating graphics... => 1
[[2,2,3,3,3,3]] generating graphics... => 1
[[2,2,3,3,3,4]] generating graphics... => 1
[[2,2,3,3,4,4]] generating graphics... => 1
[[2,2,3,4,4,4]] generating graphics... => 1
[[2,2,4,4,4,4]] generating graphics... => 1
[[2,3,3,3,3,3]] generating graphics... => 1
[[2,3,3,3,3,4]] generating graphics... => 1
[[2,3,3,3,4,4]] generating graphics... => 1
[[2,3,3,4,4,4]] generating graphics... => 1
[[2,3,4,4,4,4]] generating graphics... => 1
[[2,4,4,4,4,4]] generating graphics... => 1
[[3,3,3,3,3,3]] generating graphics... => 1
[[3,3,3,3,3,4]] generating graphics... => 1
[[3,3,3,3,4,4]] generating graphics... => 1
[[3,3,3,4,4,4]] generating graphics... => 1
[[3,3,4,4,4,4]] generating graphics... => 1
[[3,4,4,4,4,4]] generating graphics... => 1
[[4,4,4,4,4,4]] generating graphics... => 1
[[1,1,1,1,1],[2]] generating graphics... => 0
[[1,1,1,1,1],[3]] generating graphics... => 1
[[1,1,1,1,1],[4]] generating graphics... => 1
[[1,1,1,1,2],[2]] generating graphics... => 0
[[1,1,1,1,2],[3]] generating graphics... => 1
[[1,1,1,1,3],[2]] generating graphics... => 0
[[1,1,1,1,2],[4]] generating graphics... => 1
[[1,1,1,1,4],[2]] generating graphics... => 0
[[1,1,1,1,3],[3]] generating graphics... => 1
[[1,1,1,1,3],[4]] generating graphics... => 1
[[1,1,1,1,4],[3]] generating graphics... => 1
[[1,1,1,1,4],[4]] generating graphics... => 1
[[1,1,1,2,2],[2]] generating graphics... => 0
[[1,1,1,2,2],[3]] generating graphics... => 1
[[1,1,1,2,3],[2]] generating graphics... => 0
[[1,1,1,2,2],[4]] generating graphics... => 1
[[1,1,1,2,4],[2]] generating graphics... => 0
[[1,1,1,2,3],[3]] generating graphics... => 1
[[1,1,1,3,3],[2]] generating graphics... => 0
[[1,1,1,2,3],[4]] generating graphics... => 1
[[1,1,1,2,4],[3]] generating graphics... => 1
[[1,1,1,3,4],[2]] generating graphics... => 0
[[1,1,1,2,4],[4]] generating graphics... => 1
[[1,1,1,4,4],[2]] generating graphics... => 0
[[1,1,1,3,3],[3]] generating graphics... => 1
[[1,1,1,3,3],[4]] generating graphics... => 1
[[1,1,1,3,4],[3]] generating graphics... => 1
[[1,1,1,3,4],[4]] generating graphics... => 1
[[1,1,1,4,4],[3]] generating graphics... => 1
[[1,1,1,4,4],[4]] generating graphics... => 1
[[1,1,2,2,2],[2]] generating graphics... => 0
[[1,1,2,2,2],[3]] generating graphics... => 1
[[1,1,2,2,3],[2]] generating graphics... => 0
[[1,1,2,2,2],[4]] generating graphics... => 1
[[1,1,2,2,4],[2]] generating graphics... => 0
[[1,1,2,2,3],[3]] generating graphics... => 1
[[1,1,2,3,3],[2]] generating graphics... => 0
[[1,1,2,2,3],[4]] generating graphics... => 1
[[1,1,2,2,4],[3]] generating graphics... => 1
[[1,1,2,3,4],[2]] generating graphics... => 0
[[1,1,2,2,4],[4]] generating graphics... => 1
[[1,1,2,4,4],[2]] generating graphics... => 0
[[1,1,2,3,3],[3]] generating graphics... => 1
[[1,1,3,3,3],[2]] generating graphics... => 0
[[1,1,2,3,3],[4]] generating graphics... => 1
[[1,1,2,3,4],[3]] generating graphics... => 1
[[1,1,3,3,4],[2]] generating graphics... => 0
[[1,1,2,3,4],[4]] generating graphics... => 1
[[1,1,2,4,4],[3]] generating graphics... => 1
[[1,1,3,4,4],[2]] generating graphics... => 0
[[1,1,2,4,4],[4]] generating graphics... => 1
[[1,1,4,4,4],[2]] generating graphics... => 0
[[1,1,3,3,3],[3]] generating graphics... => 1
[[1,1,3,3,3],[4]] generating graphics... => 1
[[1,1,3,3,4],[3]] generating graphics... => 1
[[1,1,3,3,4],[4]] generating graphics... => 1
[[1,1,3,4,4],[3]] generating graphics... => 1
[[1,1,3,4,4],[4]] generating graphics... => 1
[[1,1,4,4,4],[3]] generating graphics... => 1
[[1,1,4,4,4],[4]] generating graphics... => 1
[[1,2,2,2,2],[2]] generating graphics... => 1
[[1,2,2,2,2],[3]] generating graphics... => 1
[[1,2,2,2,3],[2]] generating graphics... => 1
[[1,2,2,2,2],[4]] generating graphics... => 1
[[1,2,2,2,4],[2]] generating graphics... => 1
[[1,2,2,2,3],[3]] generating graphics... => 1
[[1,2,2,3,3],[2]] generating graphics... => 1
[[1,2,2,2,3],[4]] generating graphics... => 1
[[1,2,2,2,4],[3]] generating graphics... => 1
[[1,2,2,3,4],[2]] generating graphics... => 1
[[1,2,2,2,4],[4]] generating graphics... => 1
[[1,2,2,4,4],[2]] generating graphics... => 1
[[1,2,2,3,3],[3]] generating graphics... => 1
[[1,2,3,3,3],[2]] generating graphics... => 1
[[1,2,2,3,3],[4]] generating graphics... => 1
[[1,2,2,3,4],[3]] generating graphics... => 1
[[1,2,3,3,4],[2]] generating graphics... => 1
[[1,2,2,3,4],[4]] generating graphics... => 1
[[1,2,2,4,4],[3]] generating graphics... => 1
[[1,2,3,4,4],[2]] generating graphics... => 1
[[1,2,2,4,4],[4]] generating graphics... => 1
[[1,2,4,4,4],[2]] generating graphics... => 1
[[1,2,3,3,3],[3]] generating graphics... => 1
[[1,3,3,3,3],[2]] generating graphics... => 1
[[1,2,3,3,3],[4]] generating graphics... => 1
[[1,2,3,3,4],[3]] generating graphics... => 1
[[1,3,3,3,4],[2]] generating graphics... => 1
[[1,2,3,3,4],[4]] generating graphics... => 1
[[1,2,3,4,4],[3]] generating graphics... => 1
[[1,3,3,4,4],[2]] generating graphics... => 1
[[1,2,3,4,4],[4]] generating graphics... => 1
[[1,2,4,4,4],[3]] generating graphics... => 1
[[1,3,4,4,4],[2]] generating graphics... => 1
[[1,2,4,4,4],[4]] generating graphics... => 1
[[1,4,4,4,4],[2]] generating graphics... => 1
[[1,3,3,3,3],[3]] generating graphics... => 2
[[1,3,3,3,3],[4]] generating graphics... => 1
[[1,3,3,3,4],[3]] generating graphics... => 2
[[1,3,3,3,4],[4]] generating graphics... => 1
[[1,3,3,4,4],[3]] generating graphics... => 2
[[1,3,3,4,4],[4]] generating graphics... => 1
[[1,3,4,4,4],[3]] generating graphics... => 2
[[1,3,4,4,4],[4]] generating graphics... => 1
[[1,4,4,4,4],[3]] generating graphics... => 2
[[1,4,4,4,4],[4]] generating graphics... => 2
[[2,2,2,2,2],[3]] generating graphics... => 2
[[2,2,2,2,2],[4]] generating graphics... => 2
[[2,2,2,2,3],[3]] generating graphics... => 2
[[2,2,2,2,3],[4]] generating graphics... => 2
[[2,2,2,2,4],[3]] generating graphics... => 2
[[2,2,2,2,4],[4]] generating graphics... => 2
[[2,2,2,3,3],[3]] generating graphics... => 2
[[2,2,2,3,3],[4]] generating graphics... => 2
[[2,2,2,3,4],[3]] generating graphics... => 2
[[2,2,2,3,4],[4]] generating graphics... => 2
[[2,2,2,4,4],[3]] generating graphics... => 2
[[2,2,2,4,4],[4]] generating graphics... => 2
[[2,2,3,3,3],[3]] generating graphics... => 2
[[2,2,3,3,3],[4]] generating graphics... => 2
[[2,2,3,3,4],[3]] generating graphics... => 2
[[2,2,3,3,4],[4]] generating graphics... => 2
[[2,2,3,4,4],[3]] generating graphics... => 2
[[2,2,3,4,4],[4]] generating graphics... => 2
[[2,2,4,4,4],[3]] generating graphics... => 2
[[2,2,4,4,4],[4]] generating graphics... => 2
[[2,3,3,3,3],[3]] generating graphics... => 3
[[2,3,3,3,3],[4]] generating graphics... => 2
[[2,3,3,3,4],[3]] generating graphics... => 3
[[2,3,3,3,4],[4]] generating graphics... => 2
[[2,3,3,4,4],[3]] generating graphics... => 3
[[2,3,3,4,4],[4]] generating graphics... => 2
[[2,3,4,4,4],[3]] generating graphics... => 3
[[2,3,4,4,4],[4]] generating graphics... => 2
[[2,4,4,4,4],[3]] generating graphics... => 3
[[2,4,4,4,4],[4]] generating graphics... => 3
[[3,3,3,3,3],[4]] generating graphics... => 2
[[3,3,3,3,4],[4]] generating graphics... => 2
[[3,3,3,4,4],[4]] generating graphics... => 2
[[3,3,4,4,4],[4]] generating graphics... => 2
[[3,4,4,4,4],[4]] generating graphics... => 3
[[1,1,1,1],[2,2]] generating graphics... => 0
[[1,1,1,1],[2,3]] generating graphics... => 0
[[1,1,1,1],[2,4]] generating graphics... => 0
[[1,1,1,1],[3,3]] generating graphics... => 1
[[1,1,1,1],[3,4]] generating graphics... => 1
[[1,1,1,1],[4,4]] generating graphics... => 1
[[1,1,1,2],[2,2]] generating graphics... => 0
[[1,1,1,2],[2,3]] generating graphics... => 0
[[1,1,1,3],[2,2]] generating graphics... => 0
[[1,1,1,2],[2,4]] generating graphics... => 0
[[1,1,1,4],[2,2]] generating graphics... => 0
[[1,1,1,2],[3,3]] generating graphics... => 1
[[1,1,1,3],[2,3]] generating graphics... => 0
[[1,1,1,2],[3,4]] generating graphics... => 1
[[1,1,1,3],[2,4]] generating graphics... => 0
[[1,1,1,4],[2,3]] generating graphics... => 0
[[1,1,1,2],[4,4]] generating graphics... => 1
[[1,1,1,4],[2,4]] generating graphics... => 0
[[1,1,1,3],[3,3]] generating graphics... => 1
[[1,1,1,3],[3,4]] generating graphics... => 1
[[1,1,1,4],[3,3]] generating graphics... => 1
[[1,1,1,3],[4,4]] generating graphics... => 1
[[1,1,1,4],[3,4]] generating graphics... => 1
[[1,1,1,4],[4,4]] generating graphics... => 1
[[1,1,2,2],[2,2]] generating graphics... => 1
[[1,1,2,2],[2,3]] generating graphics... => 0
[[1,1,2,3],[2,2]] generating graphics... => 1
[[1,1,2,2],[2,4]] generating graphics... => 0
[[1,1,2,4],[2,2]] generating graphics... => 1
[[1,1,2,2],[3,3]] generating graphics... => 1
[[1,1,2,3],[2,3]] generating graphics... => 0
[[1,1,3,3],[2,2]] generating graphics... => 1
[[1,1,2,2],[3,4]] generating graphics... => 1
[[1,1,2,3],[2,4]] generating graphics... => 0
[[1,1,2,4],[2,3]] generating graphics... => 0
[[1,1,3,4],[2,2]] generating graphics... => 1
[[1,1,2,2],[4,4]] generating graphics... => 1
[[1,1,2,4],[2,4]] generating graphics... => 0
[[1,1,4,4],[2,2]] generating graphics... => 1
[[1,1,2,3],[3,3]] generating graphics... => 1
[[1,1,3,3],[2,3]] generating graphics... => 1
[[1,1,2,3],[3,4]] generating graphics... => 1
[[1,1,2,4],[3,3]] generating graphics... => 1
[[1,1,3,3],[2,4]] generating graphics... => 0
[[1,1,3,4],[2,3]] generating graphics... => 1
[[1,1,2,3],[4,4]] generating graphics... => 1
[[1,1,2,4],[3,4]] generating graphics... => 1
[[1,1,3,4],[2,4]] generating graphics... => 0
[[1,1,4,4],[2,3]] generating graphics... => 1
[[1,1,2,4],[4,4]] generating graphics... => 1
[[1,1,4,4],[2,4]] generating graphics... => 1
[[1,1,3,3],[3,3]] generating graphics... => 2
[[1,1,3,3],[3,4]] generating graphics... => 1
[[1,1,3,4],[3,3]] generating graphics... => 2
[[1,1,3,3],[4,4]] generating graphics... => 1
[[1,1,3,4],[3,4]] generating graphics... => 1
[[1,1,4,4],[3,3]] generating graphics... => 2
[[1,1,3,4],[4,4]] generating graphics... => 1
[[1,1,4,4],[3,4]] generating graphics... => 2
[[1,1,4,4],[4,4]] generating graphics... => 2
[[1,2,2,2],[2,3]] generating graphics... => 1
[[1,2,2,2],[2,4]] generating graphics... => 1
[[1,2,2,2],[3,3]] generating graphics... => 1
[[1,2,2,3],[2,3]] generating graphics... => 1
[[1,2,2,2],[3,4]] generating graphics... => 2
[[1,2,2,3],[2,4]] generating graphics... => 1
[[1,2,2,4],[2,3]] generating graphics... => 1
[[1,2,2,2],[4,4]] generating graphics... => 1
[[1,2,2,4],[2,4]] generating graphics... => 1
[[1,2,2,3],[3,3]] generating graphics... => 1
[[1,2,3,3],[2,3]] generating graphics... => 2
[[1,2,2,3],[3,4]] generating graphics... => 2
[[1,2,2,4],[3,3]] generating graphics... => 1
[[1,2,3,3],[2,4]] generating graphics... => 1
[[1,2,3,4],[2,3]] generating graphics... => 2
[[1,2,2,3],[4,4]] generating graphics... => 1
[[1,2,2,4],[3,4]] generating graphics... => 2
[[1,2,3,4],[2,4]] generating graphics... => 1
[[1,2,4,4],[2,3]] generating graphics... => 2
[[1,2,2,4],[4,4]] generating graphics... => 1
[[1,2,4,4],[2,4]] generating graphics... => 2
[[1,2,3,3],[3,3]] generating graphics... => 2
[[1,2,3,3],[3,4]] generating graphics... => 2
[[1,2,3,4],[3,3]] generating graphics... => 2
[[1,3,3,3],[2,4]] generating graphics... => 1
[[1,2,3,3],[4,4]] generating graphics... => 1
[[1,2,3,4],[3,4]] generating graphics... => 2
[[1,2,4,4],[3,3]] generating graphics... => 2
[[1,3,3,4],[2,4]] generating graphics... => 1
[[1,2,3,4],[4,4]] generating graphics... => 1
[[1,2,4,4],[3,4]] generating graphics... => 3
[[1,3,4,4],[2,4]] generating graphics... => 2
[[1,2,4,4],[4,4]] generating graphics... => 2
[[1,3,3,3],[3,4]] generating graphics... => 2
[[1,3,3,3],[4,4]] generating graphics... => 1
[[1,3,3,4],[3,4]] generating graphics... => 2
[[1,3,3,4],[4,4]] generating graphics... => 1
[[1,3,4,4],[3,4]] generating graphics... => 3
[[1,3,4,4],[4,4]] generating graphics... => 2
[[2,2,2,2],[3,3]] generating graphics... => 2
[[2,2,2,2],[3,4]] generating graphics... => 2
[[2,2,2,2],[4,4]] generating graphics... => 2
[[2,2,2,3],[3,3]] generating graphics... => 2
[[2,2,2,3],[3,4]] generating graphics... => 2
[[2,2,2,4],[3,3]] generating graphics... => 2
[[2,2,2,3],[4,4]] generating graphics... => 2
[[2,2,2,4],[3,4]] generating graphics... => 2
[[2,2,2,4],[4,4]] generating graphics... => 2
[[2,2,3,3],[3,3]] generating graphics... => 3
[[2,2,3,3],[3,4]] generating graphics... => 2
[[2,2,3,4],[3,3]] generating graphics... => 3
[[2,2,3,3],[4,4]] generating graphics... => 2
[[2,2,3,4],[3,4]] generating graphics... => 2
[[2,2,4,4],[3,3]] generating graphics... => 3
[[2,2,3,4],[4,4]] generating graphics... => 2
[[2,2,4,4],[3,4]] generating graphics... => 3
[[2,2,4,4],[4,4]] generating graphics... => 3
[[2,3,3,3],[3,4]] generating graphics... => 3
[[2,3,3,3],[4,4]] generating graphics... => 2
[[2,3,3,4],[3,4]] generating graphics... => 3
[[2,3,3,4],[4,4]] generating graphics... => 2
[[2,3,4,4],[3,4]] generating graphics... => 4
[[2,3,4,4],[4,4]] generating graphics... => 3
[[3,3,3,3],[4,4]] generating graphics... => 2
[[3,3,3,4],[4,4]] generating graphics... => 2
[[3,3,4,4],[4,4]] generating graphics... => 3
[[1,1,1,1],[2],[3]] generating graphics... => 0
[[1,1,1,1],[2],[4]] generating graphics... => 1
[[1,1,1,1],[3],[4]] generating graphics... => 2
[[1,1,1,2],[2],[3]] generating graphics... => 0
[[1,1,1,2],[2],[4]] generating graphics... => 1
[[1,1,1,3],[2],[3]] generating graphics... => 0
[[1,1,1,2],[3],[4]] generating graphics... => 2
[[1,1,1,3],[2],[4]] generating graphics... => 1
[[1,1,1,4],[2],[3]] generating graphics... => 0
[[1,1,1,4],[2],[4]] generating graphics... => 1
[[1,1,1,3],[3],[4]] generating graphics... => 2
[[1,1,1,4],[3],[4]] generating graphics... => 2
[[1,1,2,2],[2],[3]] generating graphics... => 0
[[1,1,2,2],[2],[4]] generating graphics... => 1
[[1,1,2,3],[2],[3]] generating graphics... => 0
[[1,1,2,2],[3],[4]] generating graphics... => 2
[[1,1,2,3],[2],[4]] generating graphics... => 1
[[1,1,2,4],[2],[3]] generating graphics... => 0
[[1,1,2,4],[2],[4]] generating graphics... => 1
[[1,1,3,3],[2],[3]] generating graphics... => 0
[[1,1,2,3],[3],[4]] generating graphics... => 2
[[1,1,3,3],[2],[4]] generating graphics... => 1
[[1,1,3,4],[2],[3]] generating graphics... => 0
[[1,1,2,4],[3],[4]] generating graphics... => 2
[[1,1,3,4],[2],[4]] generating graphics... => 1
[[1,1,4,4],[2],[3]] generating graphics... => 0
[[1,1,4,4],[2],[4]] generating graphics... => 1
[[1,1,3,3],[3],[4]] generating graphics... => 2
[[1,1,3,4],[3],[4]] generating graphics... => 2
[[1,1,4,4],[3],[4]] generating graphics... => 2
[[1,2,2,2],[2],[3]] generating graphics... => 1
[[1,2,2,2],[2],[4]] generating graphics... => 2
[[1,2,2,3],[2],[3]] generating graphics... => 1
[[1,2,2,2],[3],[4]] generating graphics... => 2
[[1,2,2,3],[2],[4]] generating graphics... => 2
[[1,2,2,4],[2],[3]] generating graphics... => 1
[[1,2,2,4],[2],[4]] generating graphics... => 2
[[1,2,3,3],[2],[3]] generating graphics... => 1
[[1,2,2,3],[3],[4]] generating graphics... => 2
[[1,2,3,3],[2],[4]] generating graphics... => 2
[[1,2,3,4],[2],[3]] generating graphics... => 1
[[1,2,2,4],[3],[4]] generating graphics... => 2
[[1,2,3,4],[2],[4]] generating graphics... => 2
[[1,2,4,4],[2],[3]] generating graphics... => 1
[[1,2,4,4],[2],[4]] generating graphics... => 2
[[1,3,3,3],[2],[3]] generating graphics... => 1
[[1,2,3,3],[3],[4]] generating graphics... => 2
[[1,3,3,3],[2],[4]] generating graphics... => 2
[[1,3,3,4],[2],[3]] generating graphics... => 1
[[1,2,3,4],[3],[4]] generating graphics... => 2
[[1,3,3,4],[2],[4]] generating graphics... => 2
[[1,3,4,4],[2],[3]] generating graphics... => 1
[[1,2,4,4],[3],[4]] generating graphics... => 2
[[1,3,4,4],[2],[4]] generating graphics... => 2
[[1,4,4,4],[2],[3]] generating graphics... => 1
[[1,4,4,4],[2],[4]] generating graphics... => 2
[[1,3,3,3],[3],[4]] generating graphics... => 3
[[1,3,3,4],[3],[4]] generating graphics... => 3
[[1,3,4,4],[3],[4]] generating graphics... => 3
[[1,4,4,4],[3],[4]] generating graphics... => 3
[[2,2,2,2],[3],[4]] generating graphics... => 3
[[2,2,2,3],[3],[4]] generating graphics... => 3
[[2,2,2,4],[3],[4]] generating graphics... => 3
[[2,2,3,3],[3],[4]] generating graphics... => 3
[[2,2,3,4],[3],[4]] generating graphics... => 3
[[2,2,4,4],[3],[4]] generating graphics... => 3
[[2,3,3,3],[3],[4]] generating graphics... => 4
[[2,3,3,4],[3],[4]] generating graphics... => 4
[[2,3,4,4],[3],[4]] generating graphics... => 4
[[2,4,4,4],[3],[4]] generating graphics... => 4
[[1,1,1],[2,2,2]] generating graphics... => 0
[[1,1,1],[2,2,3]] generating graphics... => 0
[[1,1,1],[2,2,4]] generating graphics... => 0
[[1,1,1],[2,3,3]] generating graphics... => 0
[[1,1,1],[2,3,4]] generating graphics... => 0
[[1,1,1],[2,4,4]] generating graphics... => 0
[[1,1,1],[3,3,3]] generating graphics... => 1
[[1,1,1],[3,3,4]] generating graphics... => 1
[[1,1,1],[3,4,4]] generating graphics... => 1
[[1,1,1],[4,4,4]] generating graphics... => 1
[[1,1,2],[2,2,3]] generating graphics... => 1
[[1,1,2],[2,2,4]] generating graphics... => 1
[[1,1,2],[2,3,3]] generating graphics... => 0
[[1,1,2],[2,3,4]] generating graphics... => 1
[[1,1,3],[2,2,4]] generating graphics... => 1
[[1,1,2],[2,4,4]] generating graphics... => 0
[[1,1,2],[3,3,3]] generating graphics... => 1
[[1,1,2],[3,3,4]] generating graphics... => 2
[[1,1,3],[2,3,4]] generating graphics... => 1
[[1,1,2],[3,4,4]] generating graphics... => 1
[[1,1,3],[2,4,4]] generating graphics... => 0
[[1,1,2],[4,4,4]] generating graphics... => 1
[[1,1,3],[3,3,4]] generating graphics... => 2
[[1,1,3],[3,4,4]] generating graphics... => 1
[[1,1,3],[4,4,4]] generating graphics... => 1
[[1,2,2],[2,3,3]] generating graphics... => 1
[[1,2,2],[2,3,4]] generating graphics... => 1
[[1,2,2],[2,4,4]] generating graphics... => 1
[[1,2,2],[3,3,3]] generating graphics... => 1
[[1,2,2],[3,3,4]] generating graphics... => 1
[[1,2,3],[2,3,4]] generating graphics... => 2
[[1,2,2],[3,4,4]] generating graphics... => 2
[[1,2,3],[2,4,4]] generating graphics... => 1
[[1,2,2],[4,4,4]] generating graphics... => 1
[[1,2,3],[3,3,4]] generating graphics... => 2
[[1,2,3],[3,4,4]] generating graphics... => 2
[[1,3,3],[2,4,4]] generating graphics... => 1
[[1,2,3],[4,4,4]] generating graphics... => 1
[[1,3,3],[3,4,4]] generating graphics... => 2
[[1,3,3],[4,4,4]] generating graphics... => 1
[[2,2,2],[3,3,3]] generating graphics... => 2
[[2,2,2],[3,3,4]] generating graphics... => 2
[[2,2,2],[3,4,4]] generating graphics... => 2
[[2,2,2],[4,4,4]] generating graphics... => 2
[[2,2,3],[3,3,4]] generating graphics... => 3
[[2,2,3],[3,4,4]] generating graphics... => 2
[[2,2,3],[4,4,4]] generating graphics... => 2
[[2,3,3],[3,4,4]] generating graphics... => 3
[[2,3,3],[4,4,4]] generating graphics... => 2
[[3,3,3],[4,4,4]] generating graphics... => 2
[[1,1,1],[2,2],[3]] generating graphics... => 0
[[1,1,1],[2,2],[4]] generating graphics... => 1
[[1,1,1],[2,3],[3]] generating graphics... => 1
[[1,1,1],[2,3],[4]] generating graphics... => 1
[[1,1,1],[2,4],[3]] generating graphics... => 1
[[1,1,1],[2,4],[4]] generating graphics... => 2
[[1,1,1],[3,3],[4]] generating graphics... => 2
[[1,1,1],[3,4],[4]] generating graphics... => 3
[[1,1,2],[2,2],[3]] generating graphics... => 1
[[1,1,2],[2,2],[4]] generating graphics... => 2
[[1,1,2],[2,3],[3]] generating graphics... => 1
[[1,1,3],[2,2],[3]] generating graphics... => 1
[[1,1,2],[2,3],[4]] generating graphics... => 1
[[1,1,2],[2,4],[3]] generating graphics... => 1
[[1,1,3],[2,2],[4]] generating graphics... => 2
[[1,1,4],[2,2],[3]] generating graphics... => 1
[[1,1,2],[2,4],[4]] generating graphics... => 2
[[1,1,4],[2,2],[4]] generating graphics... => 2
[[1,1,3],[2,3],[3]] generating graphics... => 2
[[1,1,2],[3,3],[4]] generating graphics... => 2
[[1,1,3],[2,3],[4]] generating graphics... => 2
[[1,1,3],[2,4],[3]] generating graphics... => 1
[[1,1,4],[2,3],[3]] generating graphics... => 2
[[1,1,2],[3,4],[4]] generating graphics... => 3
[[1,1,3],[2,4],[4]] generating graphics... => 2
[[1,1,4],[2,3],[4]] generating graphics... => 2
[[1,1,4],[2,4],[3]] generating graphics... => 2
[[1,1,4],[2,4],[4]] generating graphics... => 3
[[1,1,3],[3,3],[4]] generating graphics... => 3
[[1,1,3],[3,4],[4]] generating graphics... => 3
[[1,1,4],[3,3],[4]] generating graphics... => 3
[[1,1,4],[3,4],[4]] generating graphics... => 4
[[1,2,2],[2,3],[3]] generating graphics... => 2
[[1,2,2],[2,3],[4]] generating graphics... => 2
[[1,2,2],[2,4],[3]] generating graphics... => 2
[[1,2,2],[2,4],[4]] generating graphics... => 3
[[1,2,3],[2,3],[3]] generating graphics... => 3
[[1,2,2],[3,3],[4]] generating graphics... => 2
[[1,2,3],[2,3],[4]] generating graphics... => 3
[[1,2,3],[2,4],[3]] generating graphics... => 2
[[1,2,4],[2,3],[3]] generating graphics... => 3
[[1,2,2],[3,4],[4]] generating graphics... => 4
[[1,2,3],[2,4],[4]] generating graphics... => 3
[[1,2,4],[2,3],[4]] generating graphics... => 3
[[1,2,4],[2,4],[3]] generating graphics... => 3
[[1,2,4],[2,4],[4]] generating graphics... => 4
[[1,2,3],[3,3],[4]] generating graphics... => 3
[[1,3,3],[2,4],[3]] generating graphics... => 2
[[1,2,3],[3,4],[4]] generating graphics... => 4
[[1,2,4],[3,3],[4]] generating graphics... => 3
[[1,3,3],[2,4],[4]] generating graphics... => 3
[[1,3,4],[2,4],[3]] generating graphics... => 3
[[1,2,4],[3,4],[4]] generating graphics... => 5
[[1,3,4],[2,4],[4]] generating graphics... => 4
[[1,3,3],[3,4],[4]] generating graphics... => 4
[[1,3,4],[3,4],[4]] generating graphics... => 5
[[2,2,2],[3,3],[4]] generating graphics... => 3
[[2,2,2],[3,4],[4]] generating graphics... => 4
[[2,2,3],[3,3],[4]] generating graphics... => 4
[[2,2,3],[3,4],[4]] generating graphics... => 4
[[2,2,4],[3,3],[4]] generating graphics... => 4
[[2,2,4],[3,4],[4]] generating graphics... => 5
[[2,3,3],[3,4],[4]] generating graphics... => 5
[[2,3,4],[3,4],[4]] generating graphics... => 6
[[1,1,1],[2],[3],[4]] generating graphics... => 0
[[1,1,2],[2],[3],[4]] generating graphics... => 0
[[1,1,3],[2],[3],[4]] generating graphics... => 0
[[1,1,4],[2],[3],[4]] generating graphics... => 0
[[1,2,2],[2],[3],[4]] generating graphics... => 1
[[1,2,3],[2],[3],[4]] generating graphics... => 1
[[1,2,4],[2],[3],[4]] generating graphics... => 1
[[1,3,3],[2],[3],[4]] generating graphics... => 1
[[1,3,4],[2],[3],[4]] generating graphics... => 1
[[1,4,4],[2],[3],[4]] generating graphics... => 1
[[1,1],[2,2],[3,3]] generating graphics... => 0
[[1,1],[2,2],[3,4]] generating graphics... => 0
[[1,1],[2,2],[4,4]] generating graphics... => 1
[[1,1],[2,3],[3,4]] generating graphics... => 1
[[1,1],[2,3],[4,4]] generating graphics... => 1
[[1,1],[3,3],[4,4]] generating graphics... => 2
[[1,2],[2,3],[3,4]] generating graphics... => 2
[[1,2],[2,3],[4,4]] generating graphics... => 2
[[1,2],[3,3],[4,4]] generating graphics... => 2
[[2,2],[3,3],[4,4]] generating graphics... => 3
[[1,1],[2,2],[3],[4]] generating graphics... => 0
[[1,1],[2,3],[3],[4]] generating graphics... => 1
[[1,1],[2,4],[3],[4]] generating graphics... => 1
[[1,2],[2,3],[3],[4]] generating graphics... => 2
[[1,2],[2,4],[3],[4]] generating graphics... => 2
[[1,3],[2,4],[3],[4]] generating graphics... => 2
Description
The flush statistic of a semistandard tableau.
Let $T$ be a tableaux with $r$ rows such that each row is longer than the row beneath it by at least one box. Let $1 \leq i < k \leq r+1$ and suppose $l$ is the smallest integer greater than $k$ such that there exists an $l$-segment in the $(i+1)$-st row of $T$. A $k$-segment in the $i$-th row of $T$ is called flush if the leftmost box in the $k$-segment and the leftmost box of the $l$-segment are in the same column of $T$. If, however, no such $l$ exists, then this $k$-segment is said to be flush if the number of boxes in the $k$-segment is equal to difference of the number of boxes between the $i$-th row and $(i+1)$-st row. The flush statistic is given by the number of $k$-segments in $T$.
References
[1] Salisbury, B. The flush statistic on semistandard Young tableaux arXiv:1401.1185
Code
def statistic(T):
    f = 0
    segments = {}
    for r in range(len(T)):
        for c in range(len(T[r])):
            for j in range(c+1):
                if T[r][j] != r+1:
                    if (r,T[r][j]) not in segments.keys():
                        segments[(r,T[r][j])] = j
    L = segments.items()
    for s in segments.iteritems():
        if s[0][0] != len(T)-1 and s[1] == len(T[s[0][0]+1]) and T[s[0][0]+1][-1] <= s[0][1]:
            f += 1
        if s[0][0] == len(T)-1 and s[1] == 0:
            f += 1
        else:
            for t in L:
                if s[0][0]+1 == t[0][0] and s[1] == t[1]:
                    if s[1] >= 1 and T[s[0][0]+1][s[1]] != T[s[0][0]+1][s[1]-1]:
                        f += 1
                    if s[1] < 1 and T[s[0][0]+1][s[1]] != s[0][0]+2:
                        f += 1
    return f
Created
Jan 15, 2014 at 19:13 by Ben Salisbury
Updated
Oct 19, 2015 at 16:34 by Christian Stump