Identifier
- St001921: Plane partitions ⟶ ℤ
Values
=>
Cc0025;cc-rep
[[1]]=>3
[[1],[1]]=>4
[[2]]=>3
[[1,1]]=>3
[[1],[1],[1]]=>5
[[2],[1]]=>5
[[1,1],[1]]=>4
[[3]]=>3
[[2,1]]=>4
[[1,1,1]]=>3
[[1],[1],[1],[1]]=>6
[[2],[1],[1]]=>6
[[2],[2]]=>4
[[1,1],[1],[1]]=>5
[[1,1],[1,1]]=>4
[[3],[1]]=>5
[[2,1],[1]]=>6
[[1,1,1],[1]]=>4
[[4]]=>3
[[3,1]]=>4
[[2,2]]=>3
[[2,1,1]]=>4
[[1,1,1,1]]=>3
[[1],[1],[1],[1],[1]]=>7
[[2],[1],[1],[1]]=>7
[[2],[2],[1]]=>6
[[1,1],[1],[1],[1]]=>6
[[1,1],[1,1],[1]]=>5
[[3],[1],[1]]=>6
[[3],[2]]=>5
[[2,1],[1],[1]]=>7
[[2,1],[2]]=>5
[[2,1],[1,1]]=>6
[[1,1,1],[1],[1]]=>5
[[1,1,1],[1,1]]=>4
[[4],[1]]=>5
[[3,1],[1]]=>6
[[2,2],[1]]=>5
[[2,1,1],[1]]=>6
[[1,1,1,1],[1]]=>4
[[5]]=>3
[[4,1]]=>4
[[3,2]]=>4
[[3,1,1]]=>4
[[2,2,1]]=>4
[[2,1,1,1]]=>4
[[1,1,1,1,1]]=>3
[[1],[1],[1],[1],[1],[1]]=>8
[[2],[1],[1],[1],[1]]=>8
[[2],[2],[1],[1]]=>7
[[2],[2],[2]]=>5
[[1,1],[1],[1],[1],[1]]=>7
[[1,1],[1,1],[1],[1]]=>6
[[1,1],[1,1],[1,1]]=>5
[[3],[1],[1],[1]]=>7
[[3],[2],[1]]=>7
[[3],[3]]=>4
[[2,1],[1],[1],[1]]=>8
[[2,1],[2],[1]]=>7
[[2,1],[1,1],[1]]=>7
[[2,1],[2,1]]=>5
[[1,1,1],[1],[1],[1]]=>6
[[1,1,1],[1,1],[1]]=>5
[[1,1,1],[1,1,1]]=>4
[[4],[1],[1]]=>6
[[4],[2]]=>5
[[3,1],[1],[1]]=>7
[[3,1],[2]]=>6
[[3,1],[1,1]]=>6
[[2,2],[1],[1]]=>6
[[2,2],[2]]=>4
[[2,2],[1,1]]=>5
[[2,1,1],[1],[1]]=>7
[[2,1,1],[2]]=>5
[[2,1,1],[1,1]]=>6
[[1,1,1,1],[1],[1]]=>5
[[1,1,1,1],[1,1]]=>4
[[5],[1]]=>5
[[4,1],[1]]=>6
[[3,2],[1]]=>6
[[3,1,1],[1]]=>6
[[2,2,1],[1]]=>6
[[2,1,1,1],[1]]=>6
[[1,1,1,1,1],[1]]=>4
[[6]]=>3
[[5,1]]=>4
[[4,2]]=>4
[[4,1,1]]=>4
[[3,3]]=>3
[[3,2,1]]=>5
[[3,1,1,1]]=>4
[[2,2,2]]=>3
[[2,2,1,1]]=>4
[[2,1,1,1,1]]=>4
[[1,1,1,1,1,1]]=>3
[[1],[1],[1],[1],[1],[1],[1]]=>9
[[2],[1],[1],[1],[1],[1]]=>9
[[2],[2],[1],[1],[1]]=>8
[[2],[2],[2],[1]]=>7
[[1,1],[1],[1],[1],[1],[1]]=>8
[[1,1],[1,1],[1],[1],[1]]=>7
[[1,1],[1,1],[1,1],[1]]=>6
[[3],[1],[1],[1],[1]]=>8
[[3],[2],[1],[1]]=>8
[[3],[2],[2]]=>6
[[3],[3],[1]]=>6
[[2,1],[1],[1],[1],[1]]=>9
[[2,1],[2],[1],[1]]=>8
[[2,1],[2],[2]]=>6
[[2,1],[1,1],[1],[1]]=>8
[[2,1],[1,1],[1,1]]=>7
[[2,1],[2,1],[1]]=>7
[[1,1,1],[1],[1],[1],[1]]=>7
[[1,1,1],[1,1],[1],[1]]=>6
[[1,1,1],[1,1],[1,1]]=>5
[[1,1,1],[1,1,1],[1]]=>5
[[4],[1],[1],[1]]=>7
[[4],[2],[1]]=>7
[[4],[3]]=>5
[[3,1],[1],[1],[1]]=>8
[[3,1],[2],[1]]=>8
[[3,1],[1,1],[1]]=>7
[[3,1],[3]]=>5
[[3,1],[2,1]]=>6
[[2,2],[1],[1],[1]]=>7
[[2,2],[2],[1]]=>6
[[2,2],[1,1],[1]]=>6
[[2,2],[2,1]]=>5
[[2,1,1],[1],[1],[1]]=>8
[[2,1,1],[2],[1]]=>7
[[2,1,1],[1,1],[1]]=>7
[[2,1,1],[2,1]]=>5
[[2,1,1],[1,1,1]]=>6
[[1,1,1,1],[1],[1],[1]]=>6
[[1,1,1,1],[1,1],[1]]=>5
[[1,1,1,1],[1,1,1]]=>4
[[5],[1],[1]]=>6
[[5],[2]]=>5
[[4,1],[1],[1]]=>7
[[4,1],[2]]=>6
[[4,1],[1,1]]=>6
[[3,2],[1],[1]]=>7
[[3,2],[2]]=>6
[[3,2],[1,1]]=>6
[[3,1,1],[1],[1]]=>7
[[3,1,1],[2]]=>6
[[3,1,1],[1,1]]=>6
[[2,2,1],[1],[1]]=>7
[[2,2,1],[2]]=>5
[[2,2,1],[1,1]]=>6
[[2,1,1,1],[1],[1]]=>7
[[2,1,1,1],[2]]=>5
[[2,1,1,1],[1,1]]=>6
[[1,1,1,1,1],[1],[1]]=>5
[[1,1,1,1,1],[1,1]]=>4
[[6],[1]]=>5
[[5,1],[1]]=>6
[[4,2],[1]]=>6
[[4,1,1],[1]]=>6
[[3,3],[1]]=>5
[[3,2,1],[1]]=>7
[[3,1,1,1],[1]]=>6
[[2,2,2],[1]]=>5
[[2,2,1,1],[1]]=>6
[[2,1,1,1,1],[1]]=>6
[[1,1,1,1,1,1],[1]]=>4
[[7]]=>3
[[6,1]]=>4
[[5,2]]=>4
[[5,1,1]]=>4
[[4,3]]=>4
[[4,2,1]]=>5
[[4,1,1,1]]=>4
[[3,3,1]]=>4
[[3,2,2]]=>4
[[3,2,1,1]]=>5
[[3,1,1,1,1]]=>4
[[2,2,2,1]]=>4
[[2,2,1,1,1]]=>4
[[2,1,1,1,1,1]]=>4
[[1,1,1,1,1,1,1]]=>3
[[1],[1],[1],[1],[1],[1],[1],[1]]=>10
[[2],[1],[1],[1],[1],[1],[1]]=>10
[[2],[2],[1],[1],[1],[1]]=>9
[[2],[2],[2],[1],[1]]=>8
[[2],[2],[2],[2]]=>6
[[1,1],[1],[1],[1],[1],[1],[1]]=>9
[[1,1],[1,1],[1],[1],[1],[1]]=>8
[[1,1],[1,1],[1,1],[1],[1]]=>7
[[1,1],[1,1],[1,1],[1,1]]=>6
[[3],[1],[1],[1],[1],[1]]=>9
[[3],[2],[1],[1],[1]]=>9
[[3],[2],[2],[1]]=>8
[[3],[3],[1],[1]]=>7
[[3],[3],[2]]=>6
[[2,1],[1],[1],[1],[1],[1]]=>10
[[2,1],[2],[1],[1],[1]]=>9
[[2,1],[2],[2],[1]]=>8
[[2,1],[1,1],[1],[1],[1]]=>9
[[2,1],[1,1],[1,1],[1]]=>8
[[2,1],[2,1],[1],[1]]=>8
[[2,1],[2,1],[2]]=>6
[[2,1],[2,1],[1,1]]=>7
[[1,1,1],[1],[1],[1],[1],[1]]=>8
[[1,1,1],[1,1],[1],[1],[1]]=>7
[[1,1,1],[1,1],[1,1],[1]]=>6
[[1,1,1],[1,1,1],[1],[1]]=>6
[[1,1,1],[1,1,1],[1,1]]=>5
[[4],[1],[1],[1],[1]]=>8
[[4],[2],[1],[1]]=>8
[[4],[2],[2]]=>6
[[4],[3],[1]]=>7
[[4],[4]]=>4
[[3,1],[1],[1],[1],[1]]=>9
[[3,1],[2],[1],[1]]=>9
[[3,1],[2],[2]]=>7
[[3,1],[1,1],[1],[1]]=>8
[[3,1],[1,1],[1,1]]=>7
[[3,1],[3],[1]]=>7
[[3,1],[2,1],[1]]=>8
[[3,1],[3,1]]=>5
[[2,2],[1],[1],[1],[1]]=>8
[[2,2],[2],[1],[1]]=>7
[[2,2],[2],[2]]=>5
[[2,2],[1,1],[1],[1]]=>7
[[2,2],[1,1],[1,1]]=>6
[[2,2],[2,1],[1]]=>7
[[2,2],[2,2]]=>4
[[2,1,1],[1],[1],[1],[1]]=>9
[[2,1,1],[2],[1],[1]]=>8
[[2,1,1],[2],[2]]=>6
[[2,1,1],[1,1],[1],[1]]=>8
[[2,1,1],[1,1],[1,1]]=>7
[[2,1,1],[2,1],[1]]=>7
[[2,1,1],[1,1,1],[1]]=>7
[[2,1,1],[2,1,1]]=>5
[[1,1,1,1],[1],[1],[1],[1]]=>7
[[1,1,1,1],[1,1],[1],[1]]=>6
[[1,1,1,1],[1,1],[1,1]]=>5
[[1,1,1,1],[1,1,1],[1]]=>5
[[1,1,1,1],[1,1,1,1]]=>4
[[5],[1],[1],[1]]=>7
[[5],[2],[1]]=>7
[[5],[3]]=>5
[[4,1],[1],[1],[1]]=>8
[[4,1],[2],[1]]=>8
[[4,1],[1,1],[1]]=>7
[[4,1],[3]]=>6
[[4,1],[2,1]]=>6
[[3,2],[1],[1],[1]]=>8
[[3,2],[2],[1]]=>8
[[3,2],[1,1],[1]]=>7
[[3,2],[3]]=>5
[[3,2],[2,1]]=>7
[[3,1,1],[1],[1],[1]]=>8
[[3,1,1],[2],[1]]=>8
[[3,1,1],[1,1],[1]]=>7
[[3,1,1],[3]]=>5
[[3,1,1],[2,1]]=>6
[[3,1,1],[1,1,1]]=>6
[[2,2,1],[1],[1],[1]]=>8
[[2,2,1],[2],[1]]=>7
[[2,2,1],[1,1],[1]]=>7
[[2,2,1],[2,1]]=>6
[[2,2,1],[1,1,1]]=>6
[[2,1,1,1],[1],[1],[1]]=>8
[[2,1,1,1],[2],[1]]=>7
[[2,1,1,1],[1,1],[1]]=>7
[[2,1,1,1],[2,1]]=>5
[[2,1,1,1],[1,1,1]]=>6
[[1,1,1,1,1],[1],[1],[1]]=>6
[[1,1,1,1,1],[1,1],[1]]=>5
[[1,1,1,1,1],[1,1,1]]=>4
[[6],[1],[1]]=>6
[[6],[2]]=>5
[[5,1],[1],[1]]=>7
[[5,1],[2]]=>6
[[5,1],[1,1]]=>6
[[4,2],[1],[1]]=>7
[[4,2],[2]]=>6
[[4,2],[1,1]]=>6
[[4,1,1],[1],[1]]=>7
[[4,1,1],[2]]=>6
[[4,1,1],[1,1]]=>6
[[3,3],[1],[1]]=>6
[[3,3],[2]]=>5
[[3,3],[1,1]]=>5
[[3,2,1],[1],[1]]=>8
[[3,2,1],[2]]=>7
[[3,2,1],[1,1]]=>7
[[3,1,1,1],[1],[1]]=>7
[[3,1,1,1],[2]]=>6
[[3,1,1,1],[1,1]]=>6
[[2,2,2],[1],[1]]=>6
[[2,2,2],[2]]=>4
[[2,2,2],[1,1]]=>5
[[2,2,1,1],[1],[1]]=>7
[[2,2,1,1],[2]]=>5
[[2,2,1,1],[1,1]]=>6
[[2,1,1,1,1],[1],[1]]=>7
[[2,1,1,1,1],[2]]=>5
[[2,1,1,1,1],[1,1]]=>6
[[1,1,1,1,1,1],[1],[1]]=>5
[[1,1,1,1,1,1],[1,1]]=>4
[[7],[1]]=>5
[[6,1],[1]]=>6
[[5,2],[1]]=>6
[[5,1,1],[1]]=>6
[[4,3],[1]]=>6
[[4,2,1],[1]]=>7
[[4,1,1,1],[1]]=>6
[[3,3,1],[1]]=>6
[[3,2,2],[1]]=>6
[[3,2,1,1],[1]]=>7
[[3,1,1,1,1],[1]]=>6
[[2,2,2,1],[1]]=>6
[[2,2,1,1,1],[1]]=>6
[[2,1,1,1,1,1],[1]]=>6
[[1,1,1,1,1,1,1],[1]]=>4
[[8]]=>3
[[7,1]]=>4
[[6,2]]=>4
[[6,1,1]]=>4
[[5,3]]=>4
[[5,2,1]]=>5
[[5,1,1,1]]=>4
[[4,4]]=>3
[[4,3,1]]=>5
[[4,2,2]]=>4
[[4,2,1,1]]=>5
[[4,1,1,1,1]]=>4
[[3,3,2]]=>4
[[3,3,1,1]]=>4
[[3,2,2,1]]=>5
[[3,2,1,1,1]]=>5
[[3,1,1,1,1,1]]=>4
[[2,2,2,2]]=>3
[[2,2,2,1,1]]=>4
[[2,2,1,1,1,1]]=>4
[[2,1,1,1,1,1,1]]=>4
[[1,1,1,1,1,1,1,1]]=>3
[[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>11
[[2],[1],[1],[1],[1],[1],[1],[1]]=>11
[[2],[2],[1],[1],[1],[1],[1]]=>10
[[2],[2],[2],[1],[1],[1]]=>9
[[2],[2],[2],[2],[1]]=>8
[[1,1],[1],[1],[1],[1],[1],[1],[1]]=>10
[[1,1],[1,1],[1],[1],[1],[1],[1]]=>9
[[1,1],[1,1],[1,1],[1],[1],[1]]=>8
[[1,1],[1,1],[1,1],[1,1],[1]]=>7
[[3],[1],[1],[1],[1],[1],[1]]=>10
[[3],[2],[1],[1],[1],[1]]=>10
[[3],[2],[2],[1],[1]]=>9
[[3],[2],[2],[2]]=>7
[[3],[3],[1],[1],[1]]=>8
[[3],[3],[2],[1]]=>8
[[3],[3],[3]]=>5
[[2,1],[1],[1],[1],[1],[1],[1]]=>11
[[2,1],[2],[1],[1],[1],[1]]=>10
[[2,1],[2],[2],[1],[1]]=>9
[[2,1],[2],[2],[2]]=>7
[[2,1],[1,1],[1],[1],[1],[1]]=>10
[[2,1],[1,1],[1,1],[1],[1]]=>9
[[2,1],[1,1],[1,1],[1,1]]=>8
[[2,1],[2,1],[1],[1],[1]]=>9
[[2,1],[2,1],[2],[1]]=>8
[[2,1],[2,1],[1,1],[1]]=>8
[[2,1],[2,1],[2,1]]=>6
[[1,1,1],[1],[1],[1],[1],[1],[1]]=>9
[[1,1,1],[1,1],[1],[1],[1],[1]]=>8
[[1,1,1],[1,1],[1,1],[1],[1]]=>7
[[1,1,1],[1,1],[1,1],[1,1]]=>6
[[1,1,1],[1,1,1],[1],[1],[1]]=>7
[[1,1,1],[1,1,1],[1,1],[1]]=>6
[[1,1,1],[1,1,1],[1,1,1]]=>5
[[4],[1],[1],[1],[1],[1]]=>9
[[4],[2],[1],[1],[1]]=>9
[[4],[2],[2],[1]]=>8
[[4],[3],[1],[1]]=>8
[[4],[3],[2]]=>7
[[4],[4],[1]]=>6
[[3,1],[1],[1],[1],[1],[1]]=>10
[[3,1],[2],[1],[1],[1]]=>10
[[3,1],[2],[2],[1]]=>9
[[3,1],[1,1],[1],[1],[1]]=>9
[[3,1],[1,1],[1,1],[1]]=>8
[[3,1],[3],[1],[1]]=>8
[[3,1],[3],[2]]=>7
[[3,1],[2,1],[1],[1]]=>9
[[3,1],[2,1],[2]]=>7
[[3,1],[2,1],[1,1]]=>8
[[3,1],[3,1],[1]]=>7
[[2,2],[1],[1],[1],[1],[1]]=>9
[[2,2],[2],[1],[1],[1]]=>8
[[2,2],[2],[2],[1]]=>7
[[2,2],[1,1],[1],[1],[1]]=>8
[[2,2],[1,1],[1,1],[1]]=>7
[[2,2],[2,1],[1],[1]]=>8
[[2,2],[2,1],[2]]=>6
[[2,2],[2,1],[1,1]]=>7
[[2,2],[2,2],[1]]=>6
[[2,1,1],[1],[1],[1],[1],[1]]=>10
[[2,1,1],[2],[1],[1],[1]]=>9
[[2,1,1],[2],[2],[1]]=>8
[[2,1,1],[1,1],[1],[1],[1]]=>9
[[2,1,1],[1,1],[1,1],[1]]=>8
[[2,1,1],[2,1],[1],[1]]=>8
[[2,1,1],[2,1],[2]]=>6
[[2,1,1],[2,1],[1,1]]=>7
[[2,1,1],[1,1,1],[1],[1]]=>8
[[2,1,1],[1,1,1],[1,1]]=>7
[[2,1,1],[2,1,1],[1]]=>7
[[1,1,1,1],[1],[1],[1],[1],[1]]=>8
[[1,1,1,1],[1,1],[1],[1],[1]]=>7
[[1,1,1,1],[1,1],[1,1],[1]]=>6
[[1,1,1,1],[1,1,1],[1],[1]]=>6
[[1,1,1,1],[1,1,1],[1,1]]=>5
[[1,1,1,1],[1,1,1,1],[1]]=>5
[[5],[1],[1],[1],[1]]=>8
[[5],[2],[1],[1]]=>8
[[5],[2],[2]]=>6
[[5],[3],[1]]=>7
[[5],[4]]=>5
[[4,1],[1],[1],[1],[1]]=>9
[[4,1],[2],[1],[1]]=>9
[[4,1],[2],[2]]=>7
[[4,1],[1,1],[1],[1]]=>8
[[4,1],[1,1],[1,1]]=>7
[[4,1],[3],[1]]=>8
[[4,1],[2,1],[1]]=>8
[[4,1],[4]]=>5
[[4,1],[3,1]]=>6
[[3,2],[1],[1],[1],[1]]=>9
[[3,2],[2],[1],[1]]=>9
[[3,2],[2],[2]]=>7
[[3,2],[1,1],[1],[1]]=>8
[[3,2],[1,1],[1,1]]=>7
[[3,2],[3],[1]]=>7
[[3,2],[2,1],[1]]=>9
[[3,2],[3,1]]=>6
[[3,2],[2,2]]=>6
[[3,1,1],[1],[1],[1],[1]]=>9
[[3,1,1],[2],[1],[1]]=>9
[[3,1,1],[2],[2]]=>7
[[3,1,1],[1,1],[1],[1]]=>8
[[3,1,1],[1,1],[1,1]]=>7
[[3,1,1],[3],[1]]=>7
[[3,1,1],[2,1],[1]]=>8
[[3,1,1],[1,1,1],[1]]=>7
[[3,1,1],[3,1]]=>5
[[3,1,1],[2,1,1]]=>6
[[2,2,1],[1],[1],[1],[1]]=>9
[[2,2,1],[2],[1],[1]]=>8
[[2,2,1],[2],[2]]=>6
[[2,2,1],[1,1],[1],[1]]=>8
[[2,2,1],[1,1],[1,1]]=>7
[[2,2,1],[2,1],[1]]=>8
[[2,2,1],[1,1,1],[1]]=>7
[[2,2,1],[2,2]]=>5
[[2,2,1],[2,1,1]]=>6
[[2,1,1,1],[1],[1],[1],[1]]=>9
[[2,1,1,1],[2],[1],[1]]=>8
[[2,1,1,1],[2],[2]]=>6
[[2,1,1,1],[1,1],[1],[1]]=>8
[[2,1,1,1],[1,1],[1,1]]=>7
[[2,1,1,1],[2,1],[1]]=>7
[[2,1,1,1],[1,1,1],[1]]=>7
[[2,1,1,1],[2,1,1]]=>5
[[2,1,1,1],[1,1,1,1]]=>6
[[1,1,1,1,1],[1],[1],[1],[1]]=>7
[[1,1,1,1,1],[1,1],[1],[1]]=>6
[[1,1,1,1,1],[1,1],[1,1]]=>5
[[1,1,1,1,1],[1,1,1],[1]]=>5
[[1,1,1,1,1],[1,1,1,1]]=>4
[[6],[1],[1],[1]]=>7
[[6],[2],[1]]=>7
[[6],[3]]=>5
[[5,1],[1],[1],[1]]=>8
[[5,1],[2],[1]]=>8
[[5,1],[1,1],[1]]=>7
[[5,1],[3]]=>6
[[5,1],[2,1]]=>6
[[4,2],[1],[1],[1]]=>8
[[4,2],[2],[1]]=>8
[[4,2],[1,1],[1]]=>7
[[4,2],[3]]=>6
[[4,2],[2,1]]=>7
[[4,1,1],[1],[1],[1]]=>8
[[4,1,1],[2],[1]]=>8
[[4,1,1],[1,1],[1]]=>7
[[4,1,1],[3]]=>6
[[4,1,1],[2,1]]=>6
[[4,1,1],[1,1,1]]=>6
[[3,3],[1],[1],[1]]=>7
[[3,3],[2],[1]]=>7
[[3,3],[1,1],[1]]=>6
[[3,3],[3]]=>4
[[3,3],[2,1]]=>6
[[3,2,1],[1],[1],[1]]=>9
[[3,2,1],[2],[1]]=>9
[[3,2,1],[1,1],[1]]=>8
[[3,2,1],[3]]=>6
[[3,2,1],[2,1]]=>8
[[3,2,1],[1,1,1]]=>7
[[3,1,1,1],[1],[1],[1]]=>8
[[3,1,1,1],[2],[1]]=>8
[[3,1,1,1],[1,1],[1]]=>7
[[3,1,1,1],[3]]=>5
[[3,1,1,1],[2,1]]=>6
[[3,1,1,1],[1,1,1]]=>6
[[2,2,2],[1],[1],[1]]=>7
[[2,2,2],[2],[1]]=>6
[[2,2,2],[1,1],[1]]=>6
[[2,2,2],[2,1]]=>5
[[2,2,2],[1,1,1]]=>5
[[2,2,1,1],[1],[1],[1]]=>8
[[2,2,1,1],[2],[1]]=>7
[[2,2,1,1],[1,1],[1]]=>7
[[2,2,1,1],[2,1]]=>6
[[2,2,1,1],[1,1,1]]=>6
[[2,1,1,1,1],[1],[1],[1]]=>8
[[2,1,1,1,1],[2],[1]]=>7
[[2,1,1,1,1],[1,1],[1]]=>7
[[2,1,1,1,1],[2,1]]=>5
[[2,1,1,1,1],[1,1,1]]=>6
[[1,1,1,1,1,1],[1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1],[1]]=>5
[[1,1,1,1,1,1],[1,1,1]]=>4
[[7],[1],[1]]=>6
[[7],[2]]=>5
[[6,1],[1],[1]]=>7
[[6,1],[2]]=>6
[[6,1],[1,1]]=>6
[[5,2],[1],[1]]=>7
[[5,2],[2]]=>6
[[5,2],[1,1]]=>6
[[5,1,1],[1],[1]]=>7
[[5,1,1],[2]]=>6
[[5,1,1],[1,1]]=>6
[[4,3],[1],[1]]=>7
[[4,3],[2]]=>6
[[4,3],[1,1]]=>6
[[4,2,1],[1],[1]]=>8
[[4,2,1],[2]]=>7
[[4,2,1],[1,1]]=>7
[[4,1,1,1],[1],[1]]=>7
[[4,1,1,1],[2]]=>6
[[4,1,1,1],[1,1]]=>6
[[3,3,1],[1],[1]]=>7
[[3,3,1],[2]]=>6
[[3,3,1],[1,1]]=>6
[[3,2,2],[1],[1]]=>7
[[3,2,2],[2]]=>6
[[3,2,2],[1,1]]=>6
[[3,2,1,1],[1],[1]]=>8
[[3,2,1,1],[2]]=>7
[[3,2,1,1],[1,1]]=>7
[[3,1,1,1,1],[1],[1]]=>7
[[3,1,1,1,1],[2]]=>6
[[3,1,1,1,1],[1,1]]=>6
[[2,2,2,1],[1],[1]]=>7
[[2,2,2,1],[2]]=>5
[[2,2,2,1],[1,1]]=>6
[[2,2,1,1,1],[1],[1]]=>7
[[2,2,1,1,1],[2]]=>5
[[2,2,1,1,1],[1,1]]=>6
[[2,1,1,1,1,1],[1],[1]]=>7
[[2,1,1,1,1,1],[2]]=>5
[[2,1,1,1,1,1],[1,1]]=>6
[[1,1,1,1,1,1,1],[1],[1]]=>5
[[1,1,1,1,1,1,1],[1,1]]=>4
[[8],[1]]=>5
[[7,1],[1]]=>6
[[6,2],[1]]=>6
[[6,1,1],[1]]=>6
[[5,3],[1]]=>6
[[5,2,1],[1]]=>7
[[5,1,1,1],[1]]=>6
[[4,4],[1]]=>5
[[4,3,1],[1]]=>7
[[4,2,2],[1]]=>6
[[4,2,1,1],[1]]=>7
[[4,1,1,1,1],[1]]=>6
[[3,3,2],[1]]=>6
[[3,3,1,1],[1]]=>6
[[3,2,2,1],[1]]=>7
[[3,2,1,1,1],[1]]=>7
[[3,1,1,1,1,1],[1]]=>6
[[2,2,2,2],[1]]=>5
[[2,2,2,1,1],[1]]=>6
[[2,2,1,1,1,1],[1]]=>6
[[2,1,1,1,1,1,1],[1]]=>6
[[1,1,1,1,1,1,1,1],[1]]=>4
[[9]]=>3
[[8,1]]=>4
[[7,2]]=>4
[[7,1,1]]=>4
[[6,3]]=>4
[[6,2,1]]=>5
[[6,1,1,1]]=>4
[[5,4]]=>4
[[5,3,1]]=>5
[[5,2,2]]=>4
[[5,2,1,1]]=>5
[[5,1,1,1,1]]=>4
[[4,4,1]]=>4
[[4,3,2]]=>5
[[4,3,1,1]]=>5
[[4,2,2,1]]=>5
[[4,2,1,1,1]]=>5
[[4,1,1,1,1,1]]=>4
[[3,3,3]]=>3
[[3,3,2,1]]=>5
[[3,3,1,1,1]]=>4
[[3,2,2,2]]=>4
[[3,2,2,1,1]]=>5
[[3,2,1,1,1,1]]=>5
[[3,1,1,1,1,1,1]]=>4
[[2,2,2,2,1]]=>4
[[2,2,2,1,1,1]]=>4
[[2,2,1,1,1,1,1]]=>4
[[2,1,1,1,1,1,1,1]]=>4
[[1,1,1,1,1,1,1,1,1]]=>3
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>12
[[2],[1],[1],[1],[1],[1],[1],[1],[1]]=>12
[[2],[2],[1],[1],[1],[1],[1],[1]]=>11
[[2],[2],[2],[1],[1],[1],[1]]=>10
[[2],[2],[2],[2],[1],[1]]=>9
[[2],[2],[2],[2],[2]]=>7
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]]=>11
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]]=>10
[[1,1],[1,1],[1,1],[1],[1],[1],[1]]=>9
[[1,1],[1,1],[1,1],[1,1],[1],[1]]=>8
[[1,1],[1,1],[1,1],[1,1],[1,1]]=>7
[[3],[1],[1],[1],[1],[1],[1],[1]]=>11
[[3],[2],[1],[1],[1],[1],[1]]=>11
[[3],[2],[2],[1],[1],[1]]=>10
[[3],[2],[2],[2],[1]]=>9
[[3],[3],[1],[1],[1],[1]]=>9
[[3],[3],[2],[1],[1]]=>9
[[3],[3],[2],[2]]=>7
[[3],[3],[3],[1]]=>7
[[2,1],[1],[1],[1],[1],[1],[1],[1]]=>12
[[2,1],[2],[1],[1],[1],[1],[1]]=>11
[[2,1],[2],[2],[1],[1],[1]]=>10
[[2,1],[2],[2],[2],[1]]=>9
[[2,1],[1,1],[1],[1],[1],[1],[1]]=>11
[[2,1],[1,1],[1,1],[1],[1],[1]]=>10
[[2,1],[1,1],[1,1],[1,1],[1]]=>9
[[2,1],[2,1],[1],[1],[1],[1]]=>10
[[2,1],[2,1],[2],[1],[1]]=>9
[[2,1],[2,1],[2],[2]]=>7
[[2,1],[2,1],[1,1],[1],[1]]=>9
[[2,1],[2,1],[1,1],[1,1]]=>8
[[2,1],[2,1],[2,1],[1]]=>8
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]]=>10
[[1,1,1],[1,1],[1],[1],[1],[1],[1]]=>9
[[1,1,1],[1,1],[1,1],[1],[1],[1]]=>8
[[1,1,1],[1,1],[1,1],[1,1],[1]]=>7
[[1,1,1],[1,1,1],[1],[1],[1],[1]]=>8
[[1,1,1],[1,1,1],[1,1],[1],[1]]=>7
[[1,1,1],[1,1,1],[1,1],[1,1]]=>6
[[1,1,1],[1,1,1],[1,1,1],[1]]=>6
[[4],[1],[1],[1],[1],[1],[1]]=>10
[[4],[2],[1],[1],[1],[1]]=>10
[[4],[2],[2],[1],[1]]=>9
[[4],[2],[2],[2]]=>7
[[4],[3],[1],[1],[1]]=>9
[[4],[3],[2],[1]]=>9
[[4],[3],[3]]=>6
[[4],[4],[1],[1]]=>7
[[4],[4],[2]]=>6
[[3,1],[1],[1],[1],[1],[1],[1]]=>11
[[3,1],[2],[1],[1],[1],[1]]=>11
[[3,1],[2],[2],[1],[1]]=>10
[[3,1],[2],[2],[2]]=>8
[[3,1],[1,1],[1],[1],[1],[1]]=>10
[[3,1],[1,1],[1,1],[1],[1]]=>9
[[3,1],[1,1],[1,1],[1,1]]=>8
[[3,1],[3],[1],[1],[1]]=>9
[[3,1],[3],[2],[1]]=>9
[[3,1],[3],[3]]=>6
[[3,1],[2,1],[1],[1],[1]]=>10
[[3,1],[2,1],[2],[1]]=>9
[[3,1],[2,1],[1,1],[1]]=>9
[[3,1],[2,1],[2,1]]=>7
[[3,1],[3,1],[1],[1]]=>8
[[3,1],[3,1],[2]]=>7
[[3,1],[3,1],[1,1]]=>7
[[2,2],[1],[1],[1],[1],[1],[1]]=>10
[[2,2],[2],[1],[1],[1],[1]]=>9
[[2,2],[2],[2],[1],[1]]=>8
[[2,2],[2],[2],[2]]=>6
[[2,2],[1,1],[1],[1],[1],[1]]=>9
[[2,2],[1,1],[1,1],[1],[1]]=>8
[[2,2],[1,1],[1,1],[1,1]]=>7
[[2,2],[2,1],[1],[1],[1]]=>9
[[2,2],[2,1],[2],[1]]=>8
[[2,2],[2,1],[1,1],[1]]=>8
[[2,2],[2,1],[2,1]]=>6
[[2,2],[2,2],[1],[1]]=>7
[[2,2],[2,2],[2]]=>5
[[2,2],[2,2],[1,1]]=>6
[[2,1,1],[1],[1],[1],[1],[1],[1]]=>11
[[2,1,1],[2],[1],[1],[1],[1]]=>10
[[2,1,1],[2],[2],[1],[1]]=>9
[[2,1,1],[2],[2],[2]]=>7
[[2,1,1],[1,1],[1],[1],[1],[1]]=>10
[[2,1,1],[1,1],[1,1],[1],[1]]=>9
[[2,1,1],[1,1],[1,1],[1,1]]=>8
[[2,1,1],[2,1],[1],[1],[1]]=>9
[[2,1,1],[2,1],[2],[1]]=>8
[[2,1,1],[2,1],[1,1],[1]]=>8
[[2,1,1],[2,1],[2,1]]=>6
[[2,1,1],[1,1,1],[1],[1],[1]]=>9
[[2,1,1],[1,1,1],[1,1],[1]]=>8
[[2,1,1],[1,1,1],[1,1,1]]=>7
[[2,1,1],[2,1,1],[1],[1]]=>8
[[2,1,1],[2,1,1],[2]]=>6
[[2,1,1],[2,1,1],[1,1]]=>7
[[1,1,1,1],[1],[1],[1],[1],[1],[1]]=>9
[[1,1,1,1],[1,1],[1],[1],[1],[1]]=>8
[[1,1,1,1],[1,1],[1,1],[1],[1]]=>7
[[1,1,1,1],[1,1],[1,1],[1,1]]=>6
[[1,1,1,1],[1,1,1],[1],[1],[1]]=>7
[[1,1,1,1],[1,1,1],[1,1],[1]]=>6
[[1,1,1,1],[1,1,1],[1,1,1]]=>5
[[1,1,1,1],[1,1,1,1],[1],[1]]=>6
[[1,1,1,1],[1,1,1,1],[1,1]]=>5
[[5],[1],[1],[1],[1],[1]]=>9
[[5],[2],[1],[1],[1]]=>9
[[5],[2],[2],[1]]=>8
[[5],[3],[1],[1]]=>8
[[5],[3],[2]]=>7
[[5],[4],[1]]=>7
[[5],[5]]=>4
[[4,1],[1],[1],[1],[1],[1]]=>10
[[4,1],[2],[1],[1],[1]]=>10
[[4,1],[2],[2],[1]]=>9
[[4,1],[1,1],[1],[1],[1]]=>9
[[4,1],[1,1],[1,1],[1]]=>8
[[4,1],[3],[1],[1]]=>9
[[4,1],[3],[2]]=>8
[[4,1],[2,1],[1],[1]]=>9
[[4,1],[2,1],[2]]=>7
[[4,1],[2,1],[1,1]]=>8
[[4,1],[4],[1]]=>7
[[4,1],[3,1],[1]]=>8
[[4,1],[4,1]]=>5
[[3,2],[1],[1],[1],[1],[1]]=>10
[[3,2],[2],[1],[1],[1]]=>10
[[3,2],[2],[2],[1]]=>9
[[3,2],[1,1],[1],[1],[1]]=>9
[[3,2],[1,1],[1,1],[1]]=>8
[[3,2],[3],[1],[1]]=>8
[[3,2],[3],[2]]=>7
[[3,2],[2,1],[1],[1]]=>10
[[3,2],[2,1],[2]]=>8
[[3,2],[2,1],[1,1]]=>9
[[3,2],[3,1],[1]]=>8
[[3,2],[2,2],[1]]=>8
[[3,2],[3,2]]=>5
[[3,1,1],[1],[1],[1],[1],[1]]=>10
[[3,1,1],[2],[1],[1],[1]]=>10
[[3,1,1],[2],[2],[1]]=>9
[[3,1,1],[1,1],[1],[1],[1]]=>9
[[3,1,1],[1,1],[1,1],[1]]=>8
[[3,1,1],[3],[1],[1]]=>8
[[3,1,1],[3],[2]]=>7
[[3,1,1],[2,1],[1],[1]]=>9
[[3,1,1],[2,1],[2]]=>7
[[3,1,1],[2,1],[1,1]]=>8
[[3,1,1],[1,1,1],[1],[1]]=>8
[[3,1,1],[1,1,1],[1,1]]=>7
[[3,1,1],[3,1],[1]]=>7
[[3,1,1],[2,1,1],[1]]=>8
[[3,1,1],[3,1,1]]=>5
[[2,2,1],[1],[1],[1],[1],[1]]=>10
[[2,2,1],[2],[1],[1],[1]]=>9
[[2,2,1],[2],[2],[1]]=>8
[[2,2,1],[1,1],[1],[1],[1]]=>9
[[2,2,1],[1,1],[1,1],[1]]=>8
[[2,2,1],[2,1],[1],[1]]=>9
[[2,2,1],[2,1],[2]]=>7
[[2,2,1],[2,1],[1,1]]=>8
[[2,2,1],[1,1,1],[1],[1]]=>8
[[2,2,1],[1,1,1],[1,1]]=>7
[[2,2,1],[2,2],[1]]=>7
[[2,2,1],[2,1,1],[1]]=>8
[[2,2,1],[2,2,1]]=>5
[[2,1,1,1],[1],[1],[1],[1],[1]]=>10
[[2,1,1,1],[2],[1],[1],[1]]=>9
[[2,1,1,1],[2],[2],[1]]=>8
[[2,1,1,1],[1,1],[1],[1],[1]]=>9
[[2,1,1,1],[1,1],[1,1],[1]]=>8
[[2,1,1,1],[2,1],[1],[1]]=>8
[[2,1,1,1],[2,1],[2]]=>6
[[2,1,1,1],[2,1],[1,1]]=>7
[[2,1,1,1],[1,1,1],[1],[1]]=>8
[[2,1,1,1],[1,1,1],[1,1]]=>7
[[2,1,1,1],[2,1,1],[1]]=>7
[[2,1,1,1],[1,1,1,1],[1]]=>7
[[2,1,1,1],[2,1,1,1]]=>5
[[1,1,1,1,1],[1],[1],[1],[1],[1]]=>8
[[1,1,1,1,1],[1,1],[1],[1],[1]]=>7
[[1,1,1,1,1],[1,1],[1,1],[1]]=>6
[[1,1,1,1,1],[1,1,1],[1],[1]]=>6
[[1,1,1,1,1],[1,1,1],[1,1]]=>5
[[1,1,1,1,1],[1,1,1,1],[1]]=>5
[[1,1,1,1,1],[1,1,1,1,1]]=>4
[[6],[1],[1],[1],[1]]=>8
[[6],[2],[1],[1]]=>8
[[6],[2],[2]]=>6
[[6],[3],[1]]=>7
[[6],[4]]=>5
[[5,1],[1],[1],[1],[1]]=>9
[[5,1],[2],[1],[1]]=>9
[[5,1],[2],[2]]=>7
[[5,1],[1,1],[1],[1]]=>8
[[5,1],[1,1],[1,1]]=>7
[[5,1],[3],[1]]=>8
[[5,1],[2,1],[1]]=>8
[[5,1],[4]]=>6
[[5,1],[3,1]]=>6
[[4,2],[1],[1],[1],[1]]=>9
[[4,2],[2],[1],[1]]=>9
[[4,2],[2],[2]]=>7
[[4,2],[1,1],[1],[1]]=>8
[[4,2],[1,1],[1,1]]=>7
[[4,2],[3],[1]]=>8
[[4,2],[2,1],[1]]=>9
[[4,2],[4]]=>5
[[4,2],[3,1]]=>7
[[4,2],[2,2]]=>6
[[4,1,1],[1],[1],[1],[1]]=>9
[[4,1,1],[2],[1],[1]]=>9
[[4,1,1],[2],[2]]=>7
[[4,1,1],[1,1],[1],[1]]=>8
[[4,1,1],[1,1],[1,1]]=>7
[[4,1,1],[3],[1]]=>8
[[4,1,1],[2,1],[1]]=>8
[[4,1,1],[1,1,1],[1]]=>7
[[4,1,1],[4]]=>5
[[4,1,1],[3,1]]=>6
[[4,1,1],[2,1,1]]=>6
[[3,3],[1],[1],[1],[1]]=>8
[[3,3],[2],[1],[1]]=>8
[[3,3],[2],[2]]=>6
[[3,3],[1,1],[1],[1]]=>7
[[3,3],[1,1],[1,1]]=>6
[[3,3],[3],[1]]=>6
[[3,3],[2,1],[1]]=>8
[[3,3],[3,1]]=>5
[[3,3],[2,2]]=>5
[[3,2,1],[1],[1],[1],[1]]=>10
[[3,2,1],[2],[1],[1]]=>10
[[3,2,1],[2],[2]]=>8
[[3,2,1],[1,1],[1],[1]]=>9
[[3,2,1],[1,1],[1,1]]=>8
[[3,2,1],[3],[1]]=>8
[[3,2,1],[2,1],[1]]=>10
[[3,2,1],[1,1,1],[1]]=>8
[[3,2,1],[3,1]]=>7
[[3,2,1],[2,2]]=>7
[[3,2,1],[2,1,1]]=>8
[[3,1,1,1],[1],[1],[1],[1]]=>9
[[3,1,1,1],[2],[1],[1]]=>9
[[3,1,1,1],[2],[2]]=>7
[[3,1,1,1],[1,1],[1],[1]]=>8
[[3,1,1,1],[1,1],[1,1]]=>7
[[3,1,1,1],[3],[1]]=>7
[[3,1,1,1],[2,1],[1]]=>8
[[3,1,1,1],[1,1,1],[1]]=>7
[[3,1,1,1],[3,1]]=>5
[[3,1,1,1],[2,1,1]]=>6
[[3,1,1,1],[1,1,1,1]]=>6
[[2,2,2],[1],[1],[1],[1]]=>8
[[2,2,2],[2],[1],[1]]=>7
[[2,2,2],[2],[2]]=>5
[[2,2,2],[1,1],[1],[1]]=>7
[[2,2,2],[1,1],[1,1]]=>6
[[2,2,2],[2,1],[1]]=>7
[[2,2,2],[1,1,1],[1]]=>6
[[2,2,2],[2,2]]=>4
[[2,2,2],[2,1,1]]=>5
[[2,2,1,1],[1],[1],[1],[1]]=>9
[[2,2,1,1],[2],[1],[1]]=>8
[[2,2,1,1],[2],[2]]=>6
[[2,2,1,1],[1,1],[1],[1]]=>8
[[2,2,1,1],[1,1],[1,1]]=>7
[[2,2,1,1],[2,1],[1]]=>8
[[2,2,1,1],[1,1,1],[1]]=>7
[[2,2,1,1],[2,2]]=>5
[[2,2,1,1],[2,1,1]]=>6
[[2,2,1,1],[1,1,1,1]]=>6
[[2,1,1,1,1],[1],[1],[1],[1]]=>9
[[2,1,1,1,1],[2],[1],[1]]=>8
[[2,1,1,1,1],[2],[2]]=>6
[[2,1,1,1,1],[1,1],[1],[1]]=>8
[[2,1,1,1,1],[1,1],[1,1]]=>7
[[2,1,1,1,1],[2,1],[1]]=>7
[[2,1,1,1,1],[1,1,1],[1]]=>7
[[2,1,1,1,1],[2,1,1]]=>5
[[2,1,1,1,1],[1,1,1,1]]=>6
[[1,1,1,1,1,1],[1],[1],[1],[1]]=>7
[[1,1,1,1,1,1],[1,1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1],[1,1]]=>5
[[1,1,1,1,1,1],[1,1,1],[1]]=>5
[[1,1,1,1,1,1],[1,1,1,1]]=>4
[[7],[1],[1],[1]]=>7
[[7],[2],[1]]=>7
[[7],[3]]=>5
[[6,1],[1],[1],[1]]=>8
[[6,1],[2],[1]]=>8
[[6,1],[1,1],[1]]=>7
[[6,1],[3]]=>6
[[6,1],[2,1]]=>6
[[5,2],[1],[1],[1]]=>8
[[5,2],[2],[1]]=>8
[[5,2],[1,1],[1]]=>7
[[5,2],[3]]=>6
[[5,2],[2,1]]=>7
[[5,1,1],[1],[1],[1]]=>8
[[5,1,1],[2],[1]]=>8
[[5,1,1],[1,1],[1]]=>7
[[5,1,1],[3]]=>6
[[5,1,1],[2,1]]=>6
[[5,1,1],[1,1,1]]=>6
[[4,3],[1],[1],[1]]=>8
[[4,3],[2],[1]]=>8
[[4,3],[1,1],[1]]=>7
[[4,3],[3]]=>6
[[4,3],[2,1]]=>7
[[4,2,1],[1],[1],[1]]=>9
[[4,2,1],[2],[1]]=>9
[[4,2,1],[1,1],[1]]=>8
[[4,2,1],[3]]=>7
[[4,2,1],[2,1]]=>8
[[4,2,1],[1,1,1]]=>7
[[4,1,1,1],[1],[1],[1]]=>8
[[4,1,1,1],[2],[1]]=>8
[[4,1,1,1],[1,1],[1]]=>7
[[4,1,1,1],[3]]=>6
[[4,1,1,1],[2,1]]=>6
[[4,1,1,1],[1,1,1]]=>6
[[3,3,1],[1],[1],[1]]=>8
[[3,3,1],[2],[1]]=>8
[[3,3,1],[1,1],[1]]=>7
[[3,3,1],[3]]=>5
[[3,3,1],[2,1]]=>7
[[3,3,1],[1,1,1]]=>6
[[3,2,2],[1],[1],[1]]=>8
[[3,2,2],[2],[1]]=>8
[[3,2,2],[1,1],[1]]=>7
[[3,2,2],[3]]=>5
[[3,2,2],[2,1]]=>7
[[3,2,2],[1,1,1]]=>6
[[3,2,1,1],[1],[1],[1]]=>9
[[3,2,1,1],[2],[1]]=>9
[[3,2,1,1],[1,1],[1]]=>8
[[3,2,1,1],[3]]=>6
[[3,2,1,1],[2,1]]=>8
[[3,2,1,1],[1,1,1]]=>7
[[3,1,1,1,1],[1],[1],[1]]=>8
[[3,1,1,1,1],[2],[1]]=>8
[[3,1,1,1,1],[1,1],[1]]=>7
[[3,1,1,1,1],[3]]=>5
[[3,1,1,1,1],[2,1]]=>6
[[3,1,1,1,1],[1,1,1]]=>6
[[2,2,2,1],[1],[1],[1]]=>8
[[2,2,2,1],[2],[1]]=>7
[[2,2,2,1],[1,1],[1]]=>7
[[2,2,2,1],[2,1]]=>6
[[2,2,2,1],[1,1,1]]=>6
[[2,2,1,1,1],[1],[1],[1]]=>8
[[2,2,1,1,1],[2],[1]]=>7
[[2,2,1,1,1],[1,1],[1]]=>7
[[2,2,1,1,1],[2,1]]=>6
[[2,2,1,1,1],[1,1,1]]=>6
[[2,1,1,1,1,1],[1],[1],[1]]=>8
[[2,1,1,1,1,1],[2],[1]]=>7
[[2,1,1,1,1,1],[1,1],[1]]=>7
[[2,1,1,1,1,1],[2,1]]=>5
[[2,1,1,1,1,1],[1,1,1]]=>6
[[1,1,1,1,1,1,1],[1],[1],[1]]=>6
[[1,1,1,1,1,1,1],[1,1],[1]]=>5
[[1,1,1,1,1,1,1],[1,1,1]]=>4
[[8],[1],[1]]=>6
[[8],[2]]=>5
[[7,1],[1],[1]]=>7
[[7,1],[2]]=>6
[[7,1],[1,1]]=>6
[[6,2],[1],[1]]=>7
[[6,2],[2]]=>6
[[6,2],[1,1]]=>6
[[6,1,1],[1],[1]]=>7
[[6,1,1],[2]]=>6
[[6,1,1],[1,1]]=>6
[[5,3],[1],[1]]=>7
[[5,3],[2]]=>6
[[5,3],[1,1]]=>6
[[5,2,1],[1],[1]]=>8
[[5,2,1],[2]]=>7
[[5,2,1],[1,1]]=>7
[[5,1,1,1],[1],[1]]=>7
[[5,1,1,1],[2]]=>6
[[5,1,1,1],[1,1]]=>6
[[4,4],[1],[1]]=>6
[[4,4],[2]]=>5
[[4,4],[1,1]]=>5
[[4,3,1],[1],[1]]=>8
[[4,3,1],[2]]=>7
[[4,3,1],[1,1]]=>7
[[4,2,2],[1],[1]]=>7
[[4,2,2],[2]]=>6
[[4,2,2],[1,1]]=>6
[[4,2,1,1],[1],[1]]=>8
[[4,2,1,1],[2]]=>7
[[4,2,1,1],[1,1]]=>7
[[4,1,1,1,1],[1],[1]]=>7
[[4,1,1,1,1],[2]]=>6
[[4,1,1,1,1],[1,1]]=>6
[[3,3,2],[1],[1]]=>7
[[3,3,2],[2]]=>6
[[3,3,2],[1,1]]=>6
[[3,3,1,1],[1],[1]]=>7
[[3,3,1,1],[2]]=>6
[[3,3,1,1],[1,1]]=>6
[[3,2,2,1],[1],[1]]=>8
[[3,2,2,1],[2]]=>7
[[3,2,2,1],[1,1]]=>7
[[3,2,1,1,1],[1],[1]]=>8
[[3,2,1,1,1],[2]]=>7
[[3,2,1,1,1],[1,1]]=>7
[[3,1,1,1,1,1],[1],[1]]=>7
[[3,1,1,1,1,1],[2]]=>6
[[3,1,1,1,1,1],[1,1]]=>6
[[2,2,2,2],[1],[1]]=>6
[[2,2,2,2],[2]]=>4
[[2,2,2,2],[1,1]]=>5
[[2,2,2,1,1],[1],[1]]=>7
[[2,2,2,1,1],[2]]=>5
[[2,2,2,1,1],[1,1]]=>6
[[2,2,1,1,1,1],[1],[1]]=>7
[[2,2,1,1,1,1],[2]]=>5
[[2,2,1,1,1,1],[1,1]]=>6
[[2,1,1,1,1,1,1],[1],[1]]=>7
[[2,1,1,1,1,1,1],[2]]=>5
[[2,1,1,1,1,1,1],[1,1]]=>6
[[1,1,1,1,1,1,1,1],[1],[1]]=>5
[[1,1,1,1,1,1,1,1],[1,1]]=>4
[[9],[1]]=>5
[[8,1],[1]]=>6
[[7,2],[1]]=>6
[[7,1,1],[1]]=>6
[[6,3],[1]]=>6
[[6,2,1],[1]]=>7
[[6,1,1,1],[1]]=>6
[[5,4],[1]]=>6
[[5,3,1],[1]]=>7
[[5,2,2],[1]]=>6
[[5,2,1,1],[1]]=>7
[[5,1,1,1,1],[1]]=>6
[[4,4,1],[1]]=>6
[[4,3,2],[1]]=>7
[[4,3,1,1],[1]]=>7
[[4,2,2,1],[1]]=>7
[[4,2,1,1,1],[1]]=>7
[[4,1,1,1,1,1],[1]]=>6
[[3,3,3],[1]]=>5
[[3,3,2,1],[1]]=>7
[[3,3,1,1,1],[1]]=>6
[[3,2,2,2],[1]]=>6
[[3,2,2,1,1],[1]]=>7
[[3,2,1,1,1,1],[1]]=>7
[[3,1,1,1,1,1,1],[1]]=>6
[[2,2,2,2,1],[1]]=>6
[[2,2,2,1,1,1],[1]]=>6
[[2,2,1,1,1,1,1],[1]]=>6
[[2,1,1,1,1,1,1,1],[1]]=>6
[[1,1,1,1,1,1,1,1,1],[1]]=>4
[[10]]=>3
[[9,1]]=>4
[[8,2]]=>4
[[8,1,1]]=>4
[[7,3]]=>4
[[7,2,1]]=>5
[[7,1,1,1]]=>4
[[6,4]]=>4
[[6,3,1]]=>5
[[6,2,2]]=>4
[[6,2,1,1]]=>5
[[6,1,1,1,1]]=>4
[[5,5]]=>3
[[5,4,1]]=>5
[[5,3,2]]=>5
[[5,3,1,1]]=>5
[[5,2,2,1]]=>5
[[5,2,1,1,1]]=>5
[[5,1,1,1,1,1]]=>4
[[4,4,2]]=>4
[[4,4,1,1]]=>4
[[4,3,3]]=>4
[[4,3,2,1]]=>6
[[4,3,1,1,1]]=>5
[[4,2,2,2]]=>4
[[4,2,2,1,1]]=>5
[[4,2,1,1,1,1]]=>5
[[4,1,1,1,1,1,1]]=>4
[[3,3,3,1]]=>4
[[3,3,2,2]]=>4
[[3,3,2,1,1]]=>5
[[3,3,1,1,1,1]]=>4
[[3,2,2,2,1]]=>5
[[3,2,2,1,1,1]]=>5
[[3,2,1,1,1,1,1]]=>5
[[3,1,1,1,1,1,1,1]]=>4
[[2,2,2,2,2]]=>3
[[2,2,2,2,1,1]]=>4
[[2,2,2,1,1,1,1]]=>4
[[2,2,1,1,1,1,1,1]]=>4
[[2,1,1,1,1,1,1,1,1]]=>4
[[1,1,1,1,1,1,1,1,1,1]]=>3
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Description
The number of boxes that can be added such that the result is a plane partition.
Code
def statistic(p): c = 0 for i, row in enumerate(list(p) + [(0,)]): for j, entry in enumerate(row + (0,)): h = None if not j else row[j-1] v = None if not i or len(p[i-1]) == j else p[i-1][j] if (h is None or entry < h) and (v is None or entry < v): c += 1 return c
Created
Aug 28, 2023 at 09:50 by Martin Rubey
Updated
Aug 28, 2023 at 09:50 by Martin Rubey
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