Identifier
-
Mp00177:
Plane partitions
—transpose⟶
Plane partitions
St001446: Plane partitions ⟶ ℤ
Values
=>
Cc0025;cc-rep-0
Cc0025;cc-rep
[[1]]=>[[1]]=>1
[[1],[1]]=>[[1,1]]=>1
[[2]]=>[[2]]=>1
[[1,1]]=>[[1],[1]]=>2
[[1],[1],[1]]=>[[1,1,1]]=>1
[[2],[1]]=>[[2,1]]=>1
[[1,1],[1]]=>[[1,1],[1]]=>2
[[3]]=>[[3]]=>1
[[2,1]]=>[[2],[1]]=>2
[[1,1,1]]=>[[1],[1],[1]]=>3
[[1],[1],[1],[1]]=>[[1,1,1,1]]=>1
[[2],[1],[1]]=>[[2,1,1]]=>1
[[2],[2]]=>[[2,2]]=>1
[[1,1],[1],[1]]=>[[1,1,1],[1]]=>2
[[1,1],[1,1]]=>[[1,1],[1,1]]=>2
[[3],[1]]=>[[3,1]]=>1
[[2,1],[1]]=>[[2,1],[1]]=>2
[[1,1,1],[1]]=>[[1,1],[1],[1]]=>3
[[4]]=>[[4]]=>1
[[3,1]]=>[[3],[1]]=>2
[[2,2]]=>[[2],[2]]=>2
[[2,1,1]]=>[[2],[1],[1]]=>3
[[1,1,1,1]]=>[[1],[1],[1],[1]]=>4
[[1],[1],[1],[1],[1]]=>[[1,1,1,1,1]]=>1
[[2],[1],[1],[1]]=>[[2,1,1,1]]=>1
[[2],[2],[1]]=>[[2,2,1]]=>1
[[1,1],[1],[1],[1]]=>[[1,1,1,1],[1]]=>2
[[1,1],[1,1],[1]]=>[[1,1,1],[1,1]]=>2
[[3],[1],[1]]=>[[3,1,1]]=>1
[[3],[2]]=>[[3,2]]=>1
[[2,1],[1],[1]]=>[[2,1,1],[1]]=>2
[[2,1],[2]]=>[[2,2],[1]]=>2
[[2,1],[1,1]]=>[[2,1],[1,1]]=>2
[[1,1,1],[1],[1]]=>[[1,1,1],[1],[1]]=>3
[[1,1,1],[1,1]]=>[[1,1],[1,1],[1]]=>3
[[4],[1]]=>[[4,1]]=>1
[[3,1],[1]]=>[[3,1],[1]]=>2
[[2,2],[1]]=>[[2,1],[2]]=>2
[[2,1,1],[1]]=>[[2,1],[1],[1]]=>3
[[1,1,1,1],[1]]=>[[1,1],[1],[1],[1]]=>4
[[5]]=>[[5]]=>1
[[4,1]]=>[[4],[1]]=>2
[[3,2]]=>[[3],[2]]=>2
[[3,1,1]]=>[[3],[1],[1]]=>3
[[2,2,1]]=>[[2],[2],[1]]=>3
[[2,1,1,1]]=>[[2],[1],[1],[1]]=>4
[[1,1,1,1,1]]=>[[1],[1],[1],[1],[1]]=>5
[[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1]]=>1
[[2],[1],[1],[1],[1]]=>[[2,1,1,1,1]]=>1
[[2],[2],[1],[1]]=>[[2,2,1,1]]=>1
[[2],[2],[2]]=>[[2,2,2]]=>1
[[1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1],[1]]=>2
[[1,1],[1,1],[1],[1]]=>[[1,1,1,1],[1,1]]=>2
[[1,1],[1,1],[1,1]]=>[[1,1,1],[1,1,1]]=>2
[[3],[1],[1],[1]]=>[[3,1,1,1]]=>1
[[3],[2],[1]]=>[[3,2,1]]=>1
[[3],[3]]=>[[3,3]]=>1
[[2,1],[1],[1],[1]]=>[[2,1,1,1],[1]]=>2
[[2,1],[2],[1]]=>[[2,2,1],[1]]=>2
[[2,1],[1,1],[1]]=>[[2,1,1],[1,1]]=>2
[[2,1],[2,1]]=>[[2,2],[1,1]]=>2
[[1,1,1],[1],[1],[1]]=>[[1,1,1,1],[1],[1]]=>3
[[1,1,1],[1,1],[1]]=>[[1,1,1],[1,1],[1]]=>3
[[1,1,1],[1,1,1]]=>[[1,1],[1,1],[1,1]]=>3
[[4],[1],[1]]=>[[4,1,1]]=>1
[[4],[2]]=>[[4,2]]=>1
[[3,1],[1],[1]]=>[[3,1,1],[1]]=>2
[[3,1],[2]]=>[[3,2],[1]]=>2
[[3,1],[1,1]]=>[[3,1],[1,1]]=>2
[[2,2],[1],[1]]=>[[2,1,1],[2]]=>2
[[2,2],[2]]=>[[2,2],[2]]=>2
[[2,2],[1,1]]=>[[2,1],[2,1]]=>2
[[2,1,1],[1],[1]]=>[[2,1,1],[1],[1]]=>3
[[2,1,1],[2]]=>[[2,2],[1],[1]]=>3
[[2,1,1],[1,1]]=>[[2,1],[1,1],[1]]=>3
[[1,1,1,1],[1],[1]]=>[[1,1,1],[1],[1],[1]]=>4
[[1,1,1,1],[1,1]]=>[[1,1],[1,1],[1],[1]]=>4
[[5],[1]]=>[[5,1]]=>1
[[4,1],[1]]=>[[4,1],[1]]=>2
[[3,2],[1]]=>[[3,1],[2]]=>2
[[3,1,1],[1]]=>[[3,1],[1],[1]]=>3
[[2,2,1],[1]]=>[[2,1],[2],[1]]=>3
[[2,1,1,1],[1]]=>[[2,1],[1],[1],[1]]=>4
[[1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1]]=>5
[[6]]=>[[6]]=>1
[[5,1]]=>[[5],[1]]=>2
[[4,2]]=>[[4],[2]]=>2
[[4,1,1]]=>[[4],[1],[1]]=>3
[[3,3]]=>[[3],[3]]=>2
[[3,2,1]]=>[[3],[2],[1]]=>3
[[3,1,1,1]]=>[[3],[1],[1],[1]]=>4
[[2,2,2]]=>[[2],[2],[2]]=>3
[[2,2,1,1]]=>[[2],[2],[1],[1]]=>4
[[2,1,1,1,1]]=>[[2],[1],[1],[1],[1]]=>5
[[1,1,1,1,1,1]]=>[[1],[1],[1],[1],[1],[1]]=>6
[[1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1]]=>1
[[2],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1]]=>1
[[2],[2],[1],[1],[1]]=>[[2,2,1,1,1]]=>1
[[2],[2],[2],[1]]=>[[2,2,2,1]]=>1
[[1,1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1]]=>2
[[1,1],[1,1],[1],[1],[1]]=>[[1,1,1,1,1],[1,1]]=>2
[[1,1],[1,1],[1,1],[1]]=>[[1,1,1,1],[1,1,1]]=>2
[[3],[1],[1],[1],[1]]=>[[3,1,1,1,1]]=>1
[[3],[2],[1],[1]]=>[[3,2,1,1]]=>1
[[3],[2],[2]]=>[[3,2,2]]=>1
[[3],[3],[1]]=>[[3,3,1]]=>1
[[2,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[1]]=>2
[[2,1],[2],[1],[1]]=>[[2,2,1,1],[1]]=>2
[[2,1],[2],[2]]=>[[2,2,2],[1]]=>2
[[2,1],[1,1],[1],[1]]=>[[2,1,1,1],[1,1]]=>2
[[2,1],[1,1],[1,1]]=>[[2,1,1],[1,1,1]]=>2
[[2,1],[2,1],[1]]=>[[2,2,1],[1,1]]=>2
[[1,1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1],[1],[1]]=>3
[[1,1,1],[1,1],[1],[1]]=>[[1,1,1,1],[1,1],[1]]=>3
[[1,1,1],[1,1],[1,1]]=>[[1,1,1],[1,1,1],[1]]=>3
[[1,1,1],[1,1,1],[1]]=>[[1,1,1],[1,1],[1,1]]=>3
[[4],[1],[1],[1]]=>[[4,1,1,1]]=>1
[[4],[2],[1]]=>[[4,2,1]]=>1
[[4],[3]]=>[[4,3]]=>1
[[3,1],[1],[1],[1]]=>[[3,1,1,1],[1]]=>2
[[3,1],[2],[1]]=>[[3,2,1],[1]]=>2
[[3,1],[1,1],[1]]=>[[3,1,1],[1,1]]=>2
[[3,1],[3]]=>[[3,3],[1]]=>2
[[3,1],[2,1]]=>[[3,2],[1,1]]=>2
[[2,2],[1],[1],[1]]=>[[2,1,1,1],[2]]=>2
[[2,2],[2],[1]]=>[[2,2,1],[2]]=>2
[[2,2],[1,1],[1]]=>[[2,1,1],[2,1]]=>2
[[2,2],[2,1]]=>[[2,2],[2,1]]=>2
[[2,1,1],[1],[1],[1]]=>[[2,1,1,1],[1],[1]]=>3
[[2,1,1],[2],[1]]=>[[2,2,1],[1],[1]]=>3
[[2,1,1],[1,1],[1]]=>[[2,1,1],[1,1],[1]]=>3
[[2,1,1],[2,1]]=>[[2,2],[1,1],[1]]=>3
[[2,1,1],[1,1,1]]=>[[2,1],[1,1],[1,1]]=>3
[[1,1,1,1],[1],[1],[1]]=>[[1,1,1,1],[1],[1],[1]]=>4
[[1,1,1,1],[1,1],[1]]=>[[1,1,1],[1,1],[1],[1]]=>4
[[1,1,1,1],[1,1,1]]=>[[1,1],[1,1],[1,1],[1]]=>4
[[5],[1],[1]]=>[[5,1,1]]=>1
[[5],[2]]=>[[5,2]]=>1
[[4,1],[1],[1]]=>[[4,1,1],[1]]=>2
[[4,1],[2]]=>[[4,2],[1]]=>2
[[4,1],[1,1]]=>[[4,1],[1,1]]=>2
[[3,2],[1],[1]]=>[[3,1,1],[2]]=>2
[[3,2],[2]]=>[[3,2],[2]]=>2
[[3,2],[1,1]]=>[[3,1],[2,1]]=>2
[[3,1,1],[1],[1]]=>[[3,1,1],[1],[1]]=>3
[[3,1,1],[2]]=>[[3,2],[1],[1]]=>3
[[3,1,1],[1,1]]=>[[3,1],[1,1],[1]]=>3
[[2,2,1],[1],[1]]=>[[2,1,1],[2],[1]]=>3
[[2,2,1],[2]]=>[[2,2],[2],[1]]=>3
[[2,2,1],[1,1]]=>[[2,1],[2,1],[1]]=>3
[[2,1,1,1],[1],[1]]=>[[2,1,1],[1],[1],[1]]=>4
[[2,1,1,1],[2]]=>[[2,2],[1],[1],[1]]=>4
[[2,1,1,1],[1,1]]=>[[2,1],[1,1],[1],[1]]=>4
[[1,1,1,1,1],[1],[1]]=>[[1,1,1],[1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1]]=>[[1,1],[1,1],[1],[1],[1]]=>5
[[6],[1]]=>[[6,1]]=>1
[[5,1],[1]]=>[[5,1],[1]]=>2
[[4,2],[1]]=>[[4,1],[2]]=>2
[[4,1,1],[1]]=>[[4,1],[1],[1]]=>3
[[3,3],[1]]=>[[3,1],[3]]=>2
[[3,2,1],[1]]=>[[3,1],[2],[1]]=>3
[[3,1,1,1],[1]]=>[[3,1],[1],[1],[1]]=>4
[[2,2,2],[1]]=>[[2,1],[2],[2]]=>3
[[2,2,1,1],[1]]=>[[2,1],[2],[1],[1]]=>4
[[2,1,1,1,1],[1]]=>[[2,1],[1],[1],[1],[1]]=>5
[[1,1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1],[1]]=>6
[[7]]=>[[7]]=>1
[[6,1]]=>[[6],[1]]=>2
[[5,2]]=>[[5],[2]]=>2
[[5,1,1]]=>[[5],[1],[1]]=>3
[[4,3]]=>[[4],[3]]=>2
[[4,2,1]]=>[[4],[2],[1]]=>3
[[4,1,1,1]]=>[[4],[1],[1],[1]]=>4
[[3,3,1]]=>[[3],[3],[1]]=>3
[[3,2,2]]=>[[3],[2],[2]]=>3
[[3,2,1,1]]=>[[3],[2],[1],[1]]=>4
[[3,1,1,1,1]]=>[[3],[1],[1],[1],[1]]=>5
[[2,2,2,1]]=>[[2],[2],[2],[1]]=>4
[[2,2,1,1,1]]=>[[2],[2],[1],[1],[1]]=>5
[[2,1,1,1,1,1]]=>[[2],[1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1,1]]=>[[1],[1],[1],[1],[1],[1],[1]]=>7
[[1],[1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1,1]]=>1
[[2],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1]]=>1
[[2],[2],[1],[1],[1],[1]]=>[[2,2,1,1,1,1]]=>1
[[2],[2],[2],[1],[1]]=>[[2,2,2,1,1]]=>1
[[2],[2],[2],[2]]=>[[2,2,2,2]]=>1
[[1,1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1],[1]]=>2
[[1,1],[1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1,1]]=>2
[[1,1],[1,1],[1,1],[1],[1]]=>[[1,1,1,1,1],[1,1,1]]=>2
[[1,1],[1,1],[1,1],[1,1]]=>[[1,1,1,1],[1,1,1,1]]=>2
[[3],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1]]=>1
[[3],[2],[1],[1],[1]]=>[[3,2,1,1,1]]=>1
[[3],[2],[2],[1]]=>[[3,2,2,1]]=>1
[[3],[3],[1],[1]]=>[[3,3,1,1]]=>1
[[3],[3],[2]]=>[[3,3,2]]=>1
[[2,1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1]]=>2
[[2,1],[2],[1],[1],[1]]=>[[2,2,1,1,1],[1]]=>2
[[2,1],[2],[2],[1]]=>[[2,2,2,1],[1]]=>2
[[2,1],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[1,1]]=>2
[[2,1],[1,1],[1,1],[1]]=>[[2,1,1,1],[1,1,1]]=>2
[[2,1],[2,1],[1],[1]]=>[[2,2,1,1],[1,1]]=>2
[[2,1],[2,1],[2]]=>[[2,2,2],[1,1]]=>2
[[2,1],[2,1],[1,1]]=>[[2,2,1],[1,1,1]]=>2
[[1,1,1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1],[1]]=>3
[[1,1,1],[1,1],[1],[1],[1]]=>[[1,1,1,1,1],[1,1],[1]]=>3
[[1,1,1],[1,1],[1,1],[1]]=>[[1,1,1,1],[1,1,1],[1]]=>3
[[1,1,1],[1,1,1],[1],[1]]=>[[1,1,1,1],[1,1],[1,1]]=>3
[[1,1,1],[1,1,1],[1,1]]=>[[1,1,1],[1,1,1],[1,1]]=>3
[[4],[1],[1],[1],[1]]=>[[4,1,1,1,1]]=>1
[[4],[2],[1],[1]]=>[[4,2,1,1]]=>1
[[4],[2],[2]]=>[[4,2,2]]=>1
[[4],[3],[1]]=>[[4,3,1]]=>1
[[4],[4]]=>[[4,4]]=>1
[[3,1],[1],[1],[1],[1]]=>[[3,1,1,1,1],[1]]=>2
[[3,1],[2],[1],[1]]=>[[3,2,1,1],[1]]=>2
[[3,1],[2],[2]]=>[[3,2,2],[1]]=>2
[[3,1],[1,1],[1],[1]]=>[[3,1,1,1],[1,1]]=>2
[[3,1],[1,1],[1,1]]=>[[3,1,1],[1,1,1]]=>2
[[3,1],[3],[1]]=>[[3,3,1],[1]]=>2
[[3,1],[2,1],[1]]=>[[3,2,1],[1,1]]=>2
[[3,1],[3,1]]=>[[3,3],[1,1]]=>2
[[2,2],[1],[1],[1],[1]]=>[[2,1,1,1,1],[2]]=>2
[[2,2],[2],[1],[1]]=>[[2,2,1,1],[2]]=>2
[[2,2],[2],[2]]=>[[2,2,2],[2]]=>2
[[2,2],[1,1],[1],[1]]=>[[2,1,1,1],[2,1]]=>2
[[2,2],[1,1],[1,1]]=>[[2,1,1],[2,1,1]]=>2
[[2,2],[2,1],[1]]=>[[2,2,1],[2,1]]=>2
[[2,2],[2,2]]=>[[2,2],[2,2]]=>2
[[2,1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[1],[1]]=>3
[[2,1,1],[2],[1],[1]]=>[[2,2,1,1],[1],[1]]=>3
[[2,1,1],[2],[2]]=>[[2,2,2],[1],[1]]=>3
[[2,1,1],[1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1]]=>3
[[2,1,1],[1,1],[1,1]]=>[[2,1,1],[1,1,1],[1]]=>3
[[2,1,1],[2,1],[1]]=>[[2,2,1],[1,1],[1]]=>3
[[2,1,1],[1,1,1],[1]]=>[[2,1,1],[1,1],[1,1]]=>3
[[2,1,1],[2,1,1]]=>[[2,2],[1,1],[1,1]]=>3
[[1,1,1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1],[1],[1],[1]]=>4
[[1,1,1,1],[1,1],[1],[1]]=>[[1,1,1,1],[1,1],[1],[1]]=>4
[[1,1,1,1],[1,1],[1,1]]=>[[1,1,1],[1,1,1],[1],[1]]=>4
[[1,1,1,1],[1,1,1],[1]]=>[[1,1,1],[1,1],[1,1],[1]]=>4
[[1,1,1,1],[1,1,1,1]]=>[[1,1],[1,1],[1,1],[1,1]]=>4
[[5],[1],[1],[1]]=>[[5,1,1,1]]=>1
[[5],[2],[1]]=>[[5,2,1]]=>1
[[5],[3]]=>[[5,3]]=>1
[[4,1],[1],[1],[1]]=>[[4,1,1,1],[1]]=>2
[[4,1],[2],[1]]=>[[4,2,1],[1]]=>2
[[4,1],[1,1],[1]]=>[[4,1,1],[1,1]]=>2
[[4,1],[3]]=>[[4,3],[1]]=>2
[[4,1],[2,1]]=>[[4,2],[1,1]]=>2
[[3,2],[1],[1],[1]]=>[[3,1,1,1],[2]]=>2
[[3,2],[2],[1]]=>[[3,2,1],[2]]=>2
[[3,2],[1,1],[1]]=>[[3,1,1],[2,1]]=>2
[[3,2],[3]]=>[[3,3],[2]]=>2
[[3,2],[2,1]]=>[[3,2],[2,1]]=>2
[[3,1,1],[1],[1],[1]]=>[[3,1,1,1],[1],[1]]=>3
[[3,1,1],[2],[1]]=>[[3,2,1],[1],[1]]=>3
[[3,1,1],[1,1],[1]]=>[[3,1,1],[1,1],[1]]=>3
[[3,1,1],[3]]=>[[3,3],[1],[1]]=>3
[[3,1,1],[2,1]]=>[[3,2],[1,1],[1]]=>3
[[3,1,1],[1,1,1]]=>[[3,1],[1,1],[1,1]]=>3
[[2,2,1],[1],[1],[1]]=>[[2,1,1,1],[2],[1]]=>3
[[2,2,1],[2],[1]]=>[[2,2,1],[2],[1]]=>3
[[2,2,1],[1,1],[1]]=>[[2,1,1],[2,1],[1]]=>3
[[2,2,1],[2,1]]=>[[2,2],[2,1],[1]]=>3
[[2,2,1],[1,1,1]]=>[[2,1],[2,1],[1,1]]=>3
[[2,1,1,1],[1],[1],[1]]=>[[2,1,1,1],[1],[1],[1]]=>4
[[2,1,1,1],[2],[1]]=>[[2,2,1],[1],[1],[1]]=>4
[[2,1,1,1],[1,1],[1]]=>[[2,1,1],[1,1],[1],[1]]=>4
[[2,1,1,1],[2,1]]=>[[2,2],[1,1],[1],[1]]=>4
[[2,1,1,1],[1,1,1]]=>[[2,1],[1,1],[1,1],[1]]=>4
[[1,1,1,1,1],[1],[1],[1]]=>[[1,1,1,1],[1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1],[1]]=>[[1,1,1],[1,1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1,1]]=>[[1,1],[1,1],[1,1],[1],[1]]=>5
[[6],[1],[1]]=>[[6,1,1]]=>1
[[6],[2]]=>[[6,2]]=>1
[[5,1],[1],[1]]=>[[5,1,1],[1]]=>2
[[5,1],[2]]=>[[5,2],[1]]=>2
[[5,1],[1,1]]=>[[5,1],[1,1]]=>2
[[4,2],[1],[1]]=>[[4,1,1],[2]]=>2
[[4,2],[2]]=>[[4,2],[2]]=>2
[[4,2],[1,1]]=>[[4,1],[2,1]]=>2
[[4,1,1],[1],[1]]=>[[4,1,1],[1],[1]]=>3
[[4,1,1],[2]]=>[[4,2],[1],[1]]=>3
[[4,1,1],[1,1]]=>[[4,1],[1,1],[1]]=>3
[[3,3],[1],[1]]=>[[3,1,1],[3]]=>2
[[3,3],[2]]=>[[3,2],[3]]=>2
[[3,3],[1,1]]=>[[3,1],[3,1]]=>2
[[3,2,1],[1],[1]]=>[[3,1,1],[2],[1]]=>3
[[3,2,1],[2]]=>[[3,2],[2],[1]]=>3
[[3,2,1],[1,1]]=>[[3,1],[2,1],[1]]=>3
[[3,1,1,1],[1],[1]]=>[[3,1,1],[1],[1],[1]]=>4
[[3,1,1,1],[2]]=>[[3,2],[1],[1],[1]]=>4
[[3,1,1,1],[1,1]]=>[[3,1],[1,1],[1],[1]]=>4
[[2,2,2],[1],[1]]=>[[2,1,1],[2],[2]]=>3
[[2,2,2],[2]]=>[[2,2],[2],[2]]=>3
[[2,2,2],[1,1]]=>[[2,1],[2,1],[2]]=>3
[[2,2,1,1],[1],[1]]=>[[2,1,1],[2],[1],[1]]=>4
[[2,2,1,1],[2]]=>[[2,2],[2],[1],[1]]=>4
[[2,2,1,1],[1,1]]=>[[2,1],[2,1],[1],[1]]=>4
[[2,1,1,1,1],[1],[1]]=>[[2,1,1],[1],[1],[1],[1]]=>5
[[2,1,1,1,1],[2]]=>[[2,2],[1],[1],[1],[1]]=>5
[[2,1,1,1,1],[1,1]]=>[[2,1],[1,1],[1],[1],[1]]=>5
[[1,1,1,1,1,1],[1],[1]]=>[[1,1,1],[1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1]]=>[[1,1],[1,1],[1],[1],[1],[1]]=>6
[[7],[1]]=>[[7,1]]=>1
[[6,1],[1]]=>[[6,1],[1]]=>2
[[5,2],[1]]=>[[5,1],[2]]=>2
[[5,1,1],[1]]=>[[5,1],[1],[1]]=>3
[[4,3],[1]]=>[[4,1],[3]]=>2
[[4,2,1],[1]]=>[[4,1],[2],[1]]=>3
[[4,1,1,1],[1]]=>[[4,1],[1],[1],[1]]=>4
[[3,3,1],[1]]=>[[3,1],[3],[1]]=>3
[[3,2,2],[1]]=>[[3,1],[2],[2]]=>3
[[3,2,1,1],[1]]=>[[3,1],[2],[1],[1]]=>4
[[3,1,1,1,1],[1]]=>[[3,1],[1],[1],[1],[1]]=>5
[[2,2,2,1],[1]]=>[[2,1],[2],[2],[1]]=>4
[[2,2,1,1,1],[1]]=>[[2,1],[2],[1],[1],[1]]=>5
[[2,1,1,1,1,1],[1]]=>[[2,1],[1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1],[1],[1]]=>7
[[8]]=>[[8]]=>1
[[7,1]]=>[[7],[1]]=>2
[[6,2]]=>[[6],[2]]=>2
[[6,1,1]]=>[[6],[1],[1]]=>3
[[5,3]]=>[[5],[3]]=>2
[[5,2,1]]=>[[5],[2],[1]]=>3
[[5,1,1,1]]=>[[5],[1],[1],[1]]=>4
[[4,4]]=>[[4],[4]]=>2
[[4,3,1]]=>[[4],[3],[1]]=>3
[[4,2,2]]=>[[4],[2],[2]]=>3
[[4,2,1,1]]=>[[4],[2],[1],[1]]=>4
[[4,1,1,1,1]]=>[[4],[1],[1],[1],[1]]=>5
[[3,3,2]]=>[[3],[3],[2]]=>3
[[3,3,1,1]]=>[[3],[3],[1],[1]]=>4
[[3,2,2,1]]=>[[3],[2],[2],[1]]=>4
[[3,2,1,1,1]]=>[[3],[2],[1],[1],[1]]=>5
[[3,1,1,1,1,1]]=>[[3],[1],[1],[1],[1],[1]]=>6
[[2,2,2,2]]=>[[2],[2],[2],[2]]=>4
[[2,2,2,1,1]]=>[[2],[2],[2],[1],[1]]=>5
[[2,2,1,1,1,1]]=>[[2],[2],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1,1]]=>[[2],[1],[1],[1],[1],[1],[1]]=>7
[[1,1,1,1,1,1,1,1]]=>[[1],[1],[1],[1],[1],[1],[1],[1]]=>8
[[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1,1,1]]=>1
[[2],[1],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1,1]]=>1
[[2],[2],[1],[1],[1],[1],[1]]=>[[2,2,1,1,1,1,1]]=>1
[[2],[2],[2],[1],[1],[1]]=>[[2,2,2,1,1,1]]=>1
[[2],[2],[2],[2],[1]]=>[[2,2,2,2,1]]=>1
[[1,1],[1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1,1],[1]]=>2
[[1,1],[1,1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1],[1,1]]=>2
[[1,1],[1,1],[1,1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1,1,1]]=>2
[[1,1],[1,1],[1,1],[1,1],[1]]=>[[1,1,1,1,1],[1,1,1,1]]=>2
[[3],[1],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1,1]]=>1
[[3],[2],[1],[1],[1],[1]]=>[[3,2,1,1,1,1]]=>1
[[3],[2],[2],[1],[1]]=>[[3,2,2,1,1]]=>1
[[3],[2],[2],[2]]=>[[3,2,2,2]]=>1
[[3],[3],[1],[1],[1]]=>[[3,3,1,1,1]]=>1
[[3],[3],[2],[1]]=>[[3,3,2,1]]=>1
[[3],[3],[3]]=>[[3,3,3]]=>1
[[2,1],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1],[1]]=>2
[[2,1],[2],[1],[1],[1],[1]]=>[[2,2,1,1,1,1],[1]]=>2
[[2,1],[2],[2],[1],[1]]=>[[2,2,2,1,1],[1]]=>2
[[2,1],[2],[2],[2]]=>[[2,2,2,2],[1]]=>2
[[2,1],[1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1,1]]=>2
[[2,1],[1,1],[1,1],[1],[1]]=>[[2,1,1,1,1],[1,1,1]]=>2
[[2,1],[1,1],[1,1],[1,1]]=>[[2,1,1,1],[1,1,1,1]]=>2
[[2,1],[2,1],[1],[1],[1]]=>[[2,2,1,1,1],[1,1]]=>2
[[2,1],[2,1],[2],[1]]=>[[2,2,2,1],[1,1]]=>2
[[2,1],[2,1],[1,1],[1]]=>[[2,2,1,1],[1,1,1]]=>2
[[2,1],[2,1],[2,1]]=>[[2,2,2],[1,1,1]]=>2
[[1,1,1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1],[1],[1]]=>3
[[1,1,1],[1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1,1],[1]]=>3
[[1,1,1],[1,1],[1,1],[1],[1]]=>[[1,1,1,1,1],[1,1,1],[1]]=>3
[[1,1,1],[1,1],[1,1],[1,1]]=>[[1,1,1,1],[1,1,1,1],[1]]=>3
[[1,1,1],[1,1,1],[1],[1],[1]]=>[[1,1,1,1,1],[1,1],[1,1]]=>3
[[1,1,1],[1,1,1],[1,1],[1]]=>[[1,1,1,1],[1,1,1],[1,1]]=>3
[[1,1,1],[1,1,1],[1,1,1]]=>[[1,1,1],[1,1,1],[1,1,1]]=>3
[[4],[1],[1],[1],[1],[1]]=>[[4,1,1,1,1,1]]=>1
[[4],[2],[1],[1],[1]]=>[[4,2,1,1,1]]=>1
[[4],[2],[2],[1]]=>[[4,2,2,1]]=>1
[[4],[3],[1],[1]]=>[[4,3,1,1]]=>1
[[4],[3],[2]]=>[[4,3,2]]=>1
[[4],[4],[1]]=>[[4,4,1]]=>1
[[3,1],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1],[1]]=>2
[[3,1],[2],[1],[1],[1]]=>[[3,2,1,1,1],[1]]=>2
[[3,1],[2],[2],[1]]=>[[3,2,2,1],[1]]=>2
[[3,1],[1,1],[1],[1],[1]]=>[[3,1,1,1,1],[1,1]]=>2
[[3,1],[1,1],[1,1],[1]]=>[[3,1,1,1],[1,1,1]]=>2
[[3,1],[3],[1],[1]]=>[[3,3,1,1],[1]]=>2
[[3,1],[3],[2]]=>[[3,3,2],[1]]=>2
[[3,1],[2,1],[1],[1]]=>[[3,2,1,1],[1,1]]=>2
[[3,1],[2,1],[2]]=>[[3,2,2],[1,1]]=>2
[[3,1],[2,1],[1,1]]=>[[3,2,1],[1,1,1]]=>2
[[3,1],[3,1],[1]]=>[[3,3,1],[1,1]]=>2
[[2,2],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[2]]=>2
[[2,2],[2],[1],[1],[1]]=>[[2,2,1,1,1],[2]]=>2
[[2,2],[2],[2],[1]]=>[[2,2,2,1],[2]]=>2
[[2,2],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[2,1]]=>2
[[2,2],[1,1],[1,1],[1]]=>[[2,1,1,1],[2,1,1]]=>2
[[2,2],[2,1],[1],[1]]=>[[2,2,1,1],[2,1]]=>2
[[2,2],[2,1],[2]]=>[[2,2,2],[2,1]]=>2
[[2,2],[2,1],[1,1]]=>[[2,2,1],[2,1,1]]=>2
[[2,2],[2,2],[1]]=>[[2,2,1],[2,2]]=>2
[[2,1,1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1],[1]]=>3
[[2,1,1],[2],[1],[1],[1]]=>[[2,2,1,1,1],[1],[1]]=>3
[[2,1,1],[2],[2],[1]]=>[[2,2,2,1],[1],[1]]=>3
[[2,1,1],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[1,1],[1]]=>3
[[2,1,1],[1,1],[1,1],[1]]=>[[2,1,1,1],[1,1,1],[1]]=>3
[[2,1,1],[2,1],[1],[1]]=>[[2,2,1,1],[1,1],[1]]=>3
[[2,1,1],[2,1],[2]]=>[[2,2,2],[1,1],[1]]=>3
[[2,1,1],[2,1],[1,1]]=>[[2,2,1],[1,1,1],[1]]=>3
[[2,1,1],[1,1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1,1]]=>3
[[2,1,1],[1,1,1],[1,1]]=>[[2,1,1],[1,1,1],[1,1]]=>3
[[2,1,1],[2,1,1],[1]]=>[[2,2,1],[1,1],[1,1]]=>3
[[1,1,1,1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1],[1],[1]]=>4
[[1,1,1,1],[1,1],[1],[1],[1]]=>[[1,1,1,1,1],[1,1],[1],[1]]=>4
[[1,1,1,1],[1,1],[1,1],[1]]=>[[1,1,1,1],[1,1,1],[1],[1]]=>4
[[1,1,1,1],[1,1,1],[1],[1]]=>[[1,1,1,1],[1,1],[1,1],[1]]=>4
[[1,1,1,1],[1,1,1],[1,1]]=>[[1,1,1],[1,1,1],[1,1],[1]]=>4
[[1,1,1,1],[1,1,1,1],[1]]=>[[1,1,1],[1,1],[1,1],[1,1]]=>4
[[5],[1],[1],[1],[1]]=>[[5,1,1,1,1]]=>1
[[5],[2],[1],[1]]=>[[5,2,1,1]]=>1
[[5],[2],[2]]=>[[5,2,2]]=>1
[[5],[3],[1]]=>[[5,3,1]]=>1
[[5],[4]]=>[[5,4]]=>1
[[4,1],[1],[1],[1],[1]]=>[[4,1,1,1,1],[1]]=>2
[[4,1],[2],[1],[1]]=>[[4,2,1,1],[1]]=>2
[[4,1],[2],[2]]=>[[4,2,2],[1]]=>2
[[4,1],[1,1],[1],[1]]=>[[4,1,1,1],[1,1]]=>2
[[4,1],[1,1],[1,1]]=>[[4,1,1],[1,1,1]]=>2
[[4,1],[3],[1]]=>[[4,3,1],[1]]=>2
[[4,1],[2,1],[1]]=>[[4,2,1],[1,1]]=>2
[[4,1],[4]]=>[[4,4],[1]]=>2
[[4,1],[3,1]]=>[[4,3],[1,1]]=>2
[[3,2],[1],[1],[1],[1]]=>[[3,1,1,1,1],[2]]=>2
[[3,2],[2],[1],[1]]=>[[3,2,1,1],[2]]=>2
[[3,2],[2],[2]]=>[[3,2,2],[2]]=>2
[[3,2],[1,1],[1],[1]]=>[[3,1,1,1],[2,1]]=>2
[[3,2],[1,1],[1,1]]=>[[3,1,1],[2,1,1]]=>2
[[3,2],[3],[1]]=>[[3,3,1],[2]]=>2
[[3,2],[2,1],[1]]=>[[3,2,1],[2,1]]=>2
[[3,2],[3,1]]=>[[3,3],[2,1]]=>2
[[3,2],[2,2]]=>[[3,2],[2,2]]=>2
[[3,1,1],[1],[1],[1],[1]]=>[[3,1,1,1,1],[1],[1]]=>3
[[3,1,1],[2],[1],[1]]=>[[3,2,1,1],[1],[1]]=>3
[[3,1,1],[2],[2]]=>[[3,2,2],[1],[1]]=>3
[[3,1,1],[1,1],[1],[1]]=>[[3,1,1,1],[1,1],[1]]=>3
[[3,1,1],[1,1],[1,1]]=>[[3,1,1],[1,1,1],[1]]=>3
[[3,1,1],[3],[1]]=>[[3,3,1],[1],[1]]=>3
[[3,1,1],[2,1],[1]]=>[[3,2,1],[1,1],[1]]=>3
[[3,1,1],[1,1,1],[1]]=>[[3,1,1],[1,1],[1,1]]=>3
[[3,1,1],[3,1]]=>[[3,3],[1,1],[1]]=>3
[[3,1,1],[2,1,1]]=>[[3,2],[1,1],[1,1]]=>3
[[2,2,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[2],[1]]=>3
[[2,2,1],[2],[1],[1]]=>[[2,2,1,1],[2],[1]]=>3
[[2,2,1],[2],[2]]=>[[2,2,2],[2],[1]]=>3
[[2,2,1],[1,1],[1],[1]]=>[[2,1,1,1],[2,1],[1]]=>3
[[2,2,1],[1,1],[1,1]]=>[[2,1,1],[2,1,1],[1]]=>3
[[2,2,1],[2,1],[1]]=>[[2,2,1],[2,1],[1]]=>3
[[2,2,1],[1,1,1],[1]]=>[[2,1,1],[2,1],[1,1]]=>3
[[2,2,1],[2,2]]=>[[2,2],[2,2],[1]]=>3
[[2,2,1],[2,1,1]]=>[[2,2],[2,1],[1,1]]=>3
[[2,1,1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[1],[1],[1]]=>4
[[2,1,1,1],[2],[1],[1]]=>[[2,2,1,1],[1],[1],[1]]=>4
[[2,1,1,1],[2],[2]]=>[[2,2,2],[1],[1],[1]]=>4
[[2,1,1,1],[1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1],[1]]=>4
[[2,1,1,1],[1,1],[1,1]]=>[[2,1,1],[1,1,1],[1],[1]]=>4
[[2,1,1,1],[2,1],[1]]=>[[2,2,1],[1,1],[1],[1]]=>4
[[2,1,1,1],[1,1,1],[1]]=>[[2,1,1],[1,1],[1,1],[1]]=>4
[[2,1,1,1],[2,1,1]]=>[[2,2],[1,1],[1,1],[1]]=>4
[[2,1,1,1],[1,1,1,1]]=>[[2,1],[1,1],[1,1],[1,1]]=>4
[[1,1,1,1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1],[1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1],[1],[1]]=>[[1,1,1,1],[1,1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1],[1,1]]=>[[1,1,1],[1,1,1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1,1],[1]]=>[[1,1,1],[1,1],[1,1],[1],[1]]=>5
[[1,1,1,1,1],[1,1,1,1]]=>[[1,1],[1,1],[1,1],[1,1],[1]]=>5
[[6],[1],[1],[1]]=>[[6,1,1,1]]=>1
[[6],[2],[1]]=>[[6,2,1]]=>1
[[6],[3]]=>[[6,3]]=>1
[[5,1],[1],[1],[1]]=>[[5,1,1,1],[1]]=>2
[[5,1],[2],[1]]=>[[5,2,1],[1]]=>2
[[5,1],[1,1],[1]]=>[[5,1,1],[1,1]]=>2
[[5,1],[3]]=>[[5,3],[1]]=>2
[[5,1],[2,1]]=>[[5,2],[1,1]]=>2
[[4,2],[1],[1],[1]]=>[[4,1,1,1],[2]]=>2
[[4,2],[2],[1]]=>[[4,2,1],[2]]=>2
[[4,2],[1,1],[1]]=>[[4,1,1],[2,1]]=>2
[[4,2],[3]]=>[[4,3],[2]]=>2
[[4,2],[2,1]]=>[[4,2],[2,1]]=>2
[[4,1,1],[1],[1],[1]]=>[[4,1,1,1],[1],[1]]=>3
[[4,1,1],[2],[1]]=>[[4,2,1],[1],[1]]=>3
[[4,1,1],[1,1],[1]]=>[[4,1,1],[1,1],[1]]=>3
[[4,1,1],[3]]=>[[4,3],[1],[1]]=>3
[[4,1,1],[2,1]]=>[[4,2],[1,1],[1]]=>3
[[4,1,1],[1,1,1]]=>[[4,1],[1,1],[1,1]]=>3
[[3,3],[1],[1],[1]]=>[[3,1,1,1],[3]]=>2
[[3,3],[2],[1]]=>[[3,2,1],[3]]=>2
[[3,3],[1,1],[1]]=>[[3,1,1],[3,1]]=>2
[[3,3],[3]]=>[[3,3],[3]]=>2
[[3,3],[2,1]]=>[[3,2],[3,1]]=>2
[[3,2,1],[1],[1],[1]]=>[[3,1,1,1],[2],[1]]=>3
[[3,2,1],[2],[1]]=>[[3,2,1],[2],[1]]=>3
[[3,2,1],[1,1],[1]]=>[[3,1,1],[2,1],[1]]=>3
[[3,2,1],[3]]=>[[3,3],[2],[1]]=>3
[[3,2,1],[2,1]]=>[[3,2],[2,1],[1]]=>3
[[3,2,1],[1,1,1]]=>[[3,1],[2,1],[1,1]]=>3
[[3,1,1,1],[1],[1],[1]]=>[[3,1,1,1],[1],[1],[1]]=>4
[[3,1,1,1],[2],[1]]=>[[3,2,1],[1],[1],[1]]=>4
[[3,1,1,1],[1,1],[1]]=>[[3,1,1],[1,1],[1],[1]]=>4
[[3,1,1,1],[3]]=>[[3,3],[1],[1],[1]]=>4
[[3,1,1,1],[2,1]]=>[[3,2],[1,1],[1],[1]]=>4
[[3,1,1,1],[1,1,1]]=>[[3,1],[1,1],[1,1],[1]]=>4
[[2,2,2],[1],[1],[1]]=>[[2,1,1,1],[2],[2]]=>3
[[2,2,2],[2],[1]]=>[[2,2,1],[2],[2]]=>3
[[2,2,2],[1,1],[1]]=>[[2,1,1],[2,1],[2]]=>3
[[2,2,2],[2,1]]=>[[2,2],[2,1],[2]]=>3
[[2,2,2],[1,1,1]]=>[[2,1],[2,1],[2,1]]=>3
[[2,2,1,1],[1],[1],[1]]=>[[2,1,1,1],[2],[1],[1]]=>4
[[2,2,1,1],[2],[1]]=>[[2,2,1],[2],[1],[1]]=>4
[[2,2,1,1],[1,1],[1]]=>[[2,1,1],[2,1],[1],[1]]=>4
[[2,2,1,1],[2,1]]=>[[2,2],[2,1],[1],[1]]=>4
[[2,2,1,1],[1,1,1]]=>[[2,1],[2,1],[1,1],[1]]=>4
[[2,1,1,1,1],[1],[1],[1]]=>[[2,1,1,1],[1],[1],[1],[1]]=>5
[[2,1,1,1,1],[2],[1]]=>[[2,2,1],[1],[1],[1],[1]]=>5
[[2,1,1,1,1],[1,1],[1]]=>[[2,1,1],[1,1],[1],[1],[1]]=>5
[[2,1,1,1,1],[2,1]]=>[[2,2],[1,1],[1],[1],[1]]=>5
[[2,1,1,1,1],[1,1,1]]=>[[2,1],[1,1],[1,1],[1],[1]]=>5
[[1,1,1,1,1,1],[1],[1],[1]]=>[[1,1,1,1],[1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1],[1]]=>[[1,1,1],[1,1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1,1]]=>[[1,1],[1,1],[1,1],[1],[1],[1]]=>6
[[7],[1],[1]]=>[[7,1,1]]=>1
[[7],[2]]=>[[7,2]]=>1
[[6,1],[1],[1]]=>[[6,1,1],[1]]=>2
[[6,1],[2]]=>[[6,2],[1]]=>2
[[6,1],[1,1]]=>[[6,1],[1,1]]=>2
[[5,2],[1],[1]]=>[[5,1,1],[2]]=>2
[[5,2],[2]]=>[[5,2],[2]]=>2
[[5,2],[1,1]]=>[[5,1],[2,1]]=>2
[[5,1,1],[1],[1]]=>[[5,1,1],[1],[1]]=>3
[[5,1,1],[2]]=>[[5,2],[1],[1]]=>3
[[5,1,1],[1,1]]=>[[5,1],[1,1],[1]]=>3
[[4,3],[1],[1]]=>[[4,1,1],[3]]=>2
[[4,3],[2]]=>[[4,2],[3]]=>2
[[4,3],[1,1]]=>[[4,1],[3,1]]=>2
[[4,2,1],[1],[1]]=>[[4,1,1],[2],[1]]=>3
[[4,2,1],[2]]=>[[4,2],[2],[1]]=>3
[[4,2,1],[1,1]]=>[[4,1],[2,1],[1]]=>3
[[4,1,1,1],[1],[1]]=>[[4,1,1],[1],[1],[1]]=>4
[[4,1,1,1],[2]]=>[[4,2],[1],[1],[1]]=>4
[[4,1,1,1],[1,1]]=>[[4,1],[1,1],[1],[1]]=>4
[[3,3,1],[1],[1]]=>[[3,1,1],[3],[1]]=>3
[[3,3,1],[2]]=>[[3,2],[3],[1]]=>3
[[3,3,1],[1,1]]=>[[3,1],[3,1],[1]]=>3
[[3,2,2],[1],[1]]=>[[3,1,1],[2],[2]]=>3
[[3,2,2],[2]]=>[[3,2],[2],[2]]=>3
[[3,2,2],[1,1]]=>[[3,1],[2,1],[2]]=>3
[[3,2,1,1],[1],[1]]=>[[3,1,1],[2],[1],[1]]=>4
[[3,2,1,1],[2]]=>[[3,2],[2],[1],[1]]=>4
[[3,2,1,1],[1,1]]=>[[3,1],[2,1],[1],[1]]=>4
[[3,1,1,1,1],[1],[1]]=>[[3,1,1],[1],[1],[1],[1]]=>5
[[3,1,1,1,1],[2]]=>[[3,2],[1],[1],[1],[1]]=>5
[[3,1,1,1,1],[1,1]]=>[[3,1],[1,1],[1],[1],[1]]=>5
[[2,2,2,1],[1],[1]]=>[[2,1,1],[2],[2],[1]]=>4
[[2,2,2,1],[2]]=>[[2,2],[2],[2],[1]]=>4
[[2,2,2,1],[1,1]]=>[[2,1],[2,1],[2],[1]]=>4
[[2,2,1,1,1],[1],[1]]=>[[2,1,1],[2],[1],[1],[1]]=>5
[[2,2,1,1,1],[2]]=>[[2,2],[2],[1],[1],[1]]=>5
[[2,2,1,1,1],[1,1]]=>[[2,1],[2,1],[1],[1],[1]]=>5
[[2,1,1,1,1,1],[1],[1]]=>[[2,1,1],[1],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1],[2]]=>[[2,2],[1],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1],[1,1]]=>[[2,1],[1,1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1,1],[1],[1]]=>[[1,1,1],[1],[1],[1],[1],[1],[1]]=>7
[[1,1,1,1,1,1,1],[1,1]]=>[[1,1],[1,1],[1],[1],[1],[1],[1]]=>7
[[8],[1]]=>[[8,1]]=>1
[[7,1],[1]]=>[[7,1],[1]]=>2
[[6,2],[1]]=>[[6,1],[2]]=>2
[[6,1,1],[1]]=>[[6,1],[1],[1]]=>3
[[5,3],[1]]=>[[5,1],[3]]=>2
[[5,2,1],[1]]=>[[5,1],[2],[1]]=>3
[[5,1,1,1],[1]]=>[[5,1],[1],[1],[1]]=>4
[[4,4],[1]]=>[[4,1],[4]]=>2
[[4,3,1],[1]]=>[[4,1],[3],[1]]=>3
[[4,2,2],[1]]=>[[4,1],[2],[2]]=>3
[[4,2,1,1],[1]]=>[[4,1],[2],[1],[1]]=>4
[[4,1,1,1,1],[1]]=>[[4,1],[1],[1],[1],[1]]=>5
[[3,3,2],[1]]=>[[3,1],[3],[2]]=>3
[[3,3,1,1],[1]]=>[[3,1],[3],[1],[1]]=>4
[[3,2,2,1],[1]]=>[[3,1],[2],[2],[1]]=>4
[[3,2,1,1,1],[1]]=>[[3,1],[2],[1],[1],[1]]=>5
[[3,1,1,1,1,1],[1]]=>[[3,1],[1],[1],[1],[1],[1]]=>6
[[2,2,2,2],[1]]=>[[2,1],[2],[2],[2]]=>4
[[2,2,2,1,1],[1]]=>[[2,1],[2],[2],[1],[1]]=>5
[[2,2,1,1,1,1],[1]]=>[[2,1],[2],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1,1],[1]]=>[[2,1],[1],[1],[1],[1],[1],[1]]=>7
[[1,1,1,1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1],[1],[1],[1]]=>8
[[9]]=>[[9]]=>1
[[8,1]]=>[[8],[1]]=>2
[[7,2]]=>[[7],[2]]=>2
[[7,1,1]]=>[[7],[1],[1]]=>3
[[6,3]]=>[[6],[3]]=>2
[[6,2,1]]=>[[6],[2],[1]]=>3
[[6,1,1,1]]=>[[6],[1],[1],[1]]=>4
[[5,4]]=>[[5],[4]]=>2
[[5,3,1]]=>[[5],[3],[1]]=>3
[[5,2,2]]=>[[5],[2],[2]]=>3
[[5,2,1,1]]=>[[5],[2],[1],[1]]=>4
[[5,1,1,1,1]]=>[[5],[1],[1],[1],[1]]=>5
[[4,4,1]]=>[[4],[4],[1]]=>3
[[4,3,2]]=>[[4],[3],[2]]=>3
[[4,3,1,1]]=>[[4],[3],[1],[1]]=>4
[[4,2,2,1]]=>[[4],[2],[2],[1]]=>4
[[4,2,1,1,1]]=>[[4],[2],[1],[1],[1]]=>5
[[4,1,1,1,1,1]]=>[[4],[1],[1],[1],[1],[1]]=>6
[[3,3,3]]=>[[3],[3],[3]]=>3
[[3,3,2,1]]=>[[3],[3],[2],[1]]=>4
[[3,3,1,1,1]]=>[[3],[3],[1],[1],[1]]=>5
[[3,2,2,2]]=>[[3],[2],[2],[2]]=>4
[[3,2,2,1,1]]=>[[3],[2],[2],[1],[1]]=>5
[[3,2,1,1,1,1]]=>[[3],[2],[1],[1],[1],[1]]=>6
[[3,1,1,1,1,1,1]]=>[[3],[1],[1],[1],[1],[1],[1]]=>7
[[2,2,2,2,1]]=>[[2],[2],[2],[2],[1]]=>5
[[2,2,2,1,1,1]]=>[[2],[2],[2],[1],[1],[1]]=>6
[[2,2,1,1,1,1,1]]=>[[2],[2],[1],[1],[1],[1],[1]]=>7
[[2,1,1,1,1,1,1,1]]=>[[2],[1],[1],[1],[1],[1],[1],[1]]=>8
[[1,1,1,1,1,1,1,1,1]]=>[[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>9
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1,1,1,1]]=>1
[[2],[1],[1],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1,1,1]]=>1
[[2],[2],[1],[1],[1],[1],[1],[1]]=>[[2,2,1,1,1,1,1,1]]=>1
[[2],[2],[2],[1],[1],[1],[1]]=>[[2,2,2,1,1,1,1]]=>1
[[2],[2],[2],[2],[1],[1]]=>[[2,2,2,2,1,1]]=>1
[[2],[2],[2],[2],[2]]=>[[2,2,2,2,2]]=>1
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1,1,1],[1]]=>2
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1,1],[1,1]]=>2
[[1,1],[1,1],[1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1],[1,1,1]]=>2
[[1,1],[1,1],[1,1],[1,1],[1],[1]]=>[[1,1,1,1,1,1],[1,1,1,1]]=>2
[[1,1],[1,1],[1,1],[1,1],[1,1]]=>[[1,1,1,1,1],[1,1,1,1,1]]=>2
[[3],[1],[1],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1,1,1]]=>1
[[3],[2],[1],[1],[1],[1],[1]]=>[[3,2,1,1,1,1,1]]=>1
[[3],[2],[2],[1],[1],[1]]=>[[3,2,2,1,1,1]]=>1
[[3],[2],[2],[2],[1]]=>[[3,2,2,2,1]]=>1
[[3],[3],[1],[1],[1],[1]]=>[[3,3,1,1,1,1]]=>1
[[3],[3],[2],[1],[1]]=>[[3,3,2,1,1]]=>1
[[3],[3],[2],[2]]=>[[3,3,2,2]]=>1
[[3],[3],[3],[1]]=>[[3,3,3,1]]=>1
[[2,1],[1],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1,1],[1]]=>2
[[2,1],[2],[1],[1],[1],[1],[1]]=>[[2,2,1,1,1,1,1],[1]]=>2
[[2,1],[2],[2],[1],[1],[1]]=>[[2,2,2,1,1,1],[1]]=>2
[[2,1],[2],[2],[2],[1]]=>[[2,2,2,2,1],[1]]=>2
[[2,1],[1,1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1],[1,1]]=>2
[[2,1],[1,1],[1,1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1,1,1]]=>2
[[2,1],[1,1],[1,1],[1,1],[1]]=>[[2,1,1,1,1],[1,1,1,1]]=>2
[[2,1],[2,1],[1],[1],[1],[1]]=>[[2,2,1,1,1,1],[1,1]]=>2
[[2,1],[2,1],[2],[1],[1]]=>[[2,2,2,1,1],[1,1]]=>2
[[2,1],[2,1],[2],[2]]=>[[2,2,2,2],[1,1]]=>2
[[2,1],[2,1],[1,1],[1],[1]]=>[[2,2,1,1,1],[1,1,1]]=>2
[[2,1],[2,1],[1,1],[1,1]]=>[[2,2,1,1],[1,1,1,1]]=>2
[[2,1],[2,1],[2,1],[1]]=>[[2,2,2,1],[1,1,1]]=>2
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1,1],[1],[1]]=>3
[[1,1,1],[1,1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1],[1,1],[1]]=>3
[[1,1,1],[1,1],[1,1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1,1,1],[1]]=>3
[[1,1,1],[1,1],[1,1],[1,1],[1]]=>[[1,1,1,1,1],[1,1,1,1],[1]]=>3
[[1,1,1],[1,1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1,1],[1,1]]=>3
[[1,1,1],[1,1,1],[1,1],[1],[1]]=>[[1,1,1,1,1],[1,1,1],[1,1]]=>3
[[1,1,1],[1,1,1],[1,1],[1,1]]=>[[1,1,1,1],[1,1,1,1],[1,1]]=>3
[[1,1,1],[1,1,1],[1,1,1],[1]]=>[[1,1,1,1],[1,1,1],[1,1,1]]=>3
[[4],[1],[1],[1],[1],[1],[1]]=>[[4,1,1,1,1,1,1]]=>1
[[4],[2],[1],[1],[1],[1]]=>[[4,2,1,1,1,1]]=>1
[[4],[2],[2],[1],[1]]=>[[4,2,2,1,1]]=>1
[[4],[2],[2],[2]]=>[[4,2,2,2]]=>1
[[4],[3],[1],[1],[1]]=>[[4,3,1,1,1]]=>1
[[4],[3],[2],[1]]=>[[4,3,2,1]]=>1
[[4],[3],[3]]=>[[4,3,3]]=>1
[[4],[4],[1],[1]]=>[[4,4,1,1]]=>1
[[4],[4],[2]]=>[[4,4,2]]=>1
[[3,1],[1],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1,1],[1]]=>2
[[3,1],[2],[1],[1],[1],[1]]=>[[3,2,1,1,1,1],[1]]=>2
[[3,1],[2],[2],[1],[1]]=>[[3,2,2,1,1],[1]]=>2
[[3,1],[2],[2],[2]]=>[[3,2,2,2],[1]]=>2
[[3,1],[1,1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1],[1,1]]=>2
[[3,1],[1,1],[1,1],[1],[1]]=>[[3,1,1,1,1],[1,1,1]]=>2
[[3,1],[1,1],[1,1],[1,1]]=>[[3,1,1,1],[1,1,1,1]]=>2
[[3,1],[3],[1],[1],[1]]=>[[3,3,1,1,1],[1]]=>2
[[3,1],[3],[2],[1]]=>[[3,3,2,1],[1]]=>2
[[3,1],[3],[3]]=>[[3,3,3],[1]]=>2
[[3,1],[2,1],[1],[1],[1]]=>[[3,2,1,1,1],[1,1]]=>2
[[3,1],[2,1],[2],[1]]=>[[3,2,2,1],[1,1]]=>2
[[3,1],[2,1],[1,1],[1]]=>[[3,2,1,1],[1,1,1]]=>2
[[3,1],[2,1],[2,1]]=>[[3,2,2],[1,1,1]]=>2
[[3,1],[3,1],[1],[1]]=>[[3,3,1,1],[1,1]]=>2
[[3,1],[3,1],[2]]=>[[3,3,2],[1,1]]=>2
[[3,1],[3,1],[1,1]]=>[[3,3,1],[1,1,1]]=>2
[[2,2],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1],[2]]=>2
[[2,2],[2],[1],[1],[1],[1]]=>[[2,2,1,1,1,1],[2]]=>2
[[2,2],[2],[2],[1],[1]]=>[[2,2,2,1,1],[2]]=>2
[[2,2],[2],[2],[2]]=>[[2,2,2,2],[2]]=>2
[[2,2],[1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[2,1]]=>2
[[2,2],[1,1],[1,1],[1],[1]]=>[[2,1,1,1,1],[2,1,1]]=>2
[[2,2],[1,1],[1,1],[1,1]]=>[[2,1,1,1],[2,1,1,1]]=>2
[[2,2],[2,1],[1],[1],[1]]=>[[2,2,1,1,1],[2,1]]=>2
[[2,2],[2,1],[2],[1]]=>[[2,2,2,1],[2,1]]=>2
[[2,2],[2,1],[1,1],[1]]=>[[2,2,1,1],[2,1,1]]=>2
[[2,2],[2,1],[2,1]]=>[[2,2,2],[2,1,1]]=>2
[[2,2],[2,2],[1],[1]]=>[[2,2,1,1],[2,2]]=>2
[[2,2],[2,2],[2]]=>[[2,2,2],[2,2]]=>2
[[2,2],[2,2],[1,1]]=>[[2,2,1],[2,2,1]]=>2
[[2,1,1],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1],[1],[1]]=>3
[[2,1,1],[2],[1],[1],[1],[1]]=>[[2,2,1,1,1,1],[1],[1]]=>3
[[2,1,1],[2],[2],[1],[1]]=>[[2,2,2,1,1],[1],[1]]=>3
[[2,1,1],[2],[2],[2]]=>[[2,2,2,2],[1],[1]]=>3
[[2,1,1],[1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1,1],[1]]=>3
[[2,1,1],[1,1],[1,1],[1],[1]]=>[[2,1,1,1,1],[1,1,1],[1]]=>3
[[2,1,1],[1,1],[1,1],[1,1]]=>[[2,1,1,1],[1,1,1,1],[1]]=>3
[[2,1,1],[2,1],[1],[1],[1]]=>[[2,2,1,1,1],[1,1],[1]]=>3
[[2,1,1],[2,1],[2],[1]]=>[[2,2,2,1],[1,1],[1]]=>3
[[2,1,1],[2,1],[1,1],[1]]=>[[2,2,1,1],[1,1,1],[1]]=>3
[[2,1,1],[2,1],[2,1]]=>[[2,2,2],[1,1,1],[1]]=>3
[[2,1,1],[1,1,1],[1],[1],[1]]=>[[2,1,1,1,1],[1,1],[1,1]]=>3
[[2,1,1],[1,1,1],[1,1],[1]]=>[[2,1,1,1],[1,1,1],[1,1]]=>3
[[2,1,1],[1,1,1],[1,1,1]]=>[[2,1,1],[1,1,1],[1,1,1]]=>3
[[2,1,1],[2,1,1],[1],[1]]=>[[2,2,1,1],[1,1],[1,1]]=>3
[[2,1,1],[2,1,1],[2]]=>[[2,2,2],[1,1],[1,1]]=>3
[[2,1,1],[2,1,1],[1,1]]=>[[2,2,1],[1,1,1],[1,1]]=>3
[[1,1,1,1],[1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1,1],[1],[1],[1]]=>4
[[1,1,1,1],[1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1,1],[1],[1]]=>4
[[1,1,1,1],[1,1],[1,1],[1],[1]]=>[[1,1,1,1,1],[1,1,1],[1],[1]]=>4
[[1,1,1,1],[1,1],[1,1],[1,1]]=>[[1,1,1,1],[1,1,1,1],[1],[1]]=>4
[[1,1,1,1],[1,1,1],[1],[1],[1]]=>[[1,1,1,1,1],[1,1],[1,1],[1]]=>4
[[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,1,1,1],[1,1,1],[1,1],[1]]=>4
[[1,1,1,1],[1,1,1],[1,1,1]]=>[[1,1,1],[1,1,1],[1,1,1],[1]]=>4
[[1,1,1,1],[1,1,1,1],[1],[1]]=>[[1,1,1,1],[1,1],[1,1],[1,1]]=>4
[[1,1,1,1],[1,1,1,1],[1,1]]=>[[1,1,1],[1,1,1],[1,1],[1,1]]=>4
[[5],[1],[1],[1],[1],[1]]=>[[5,1,1,1,1,1]]=>1
[[5],[2],[1],[1],[1]]=>[[5,2,1,1,1]]=>1
[[5],[2],[2],[1]]=>[[5,2,2,1]]=>1
[[5],[3],[1],[1]]=>[[5,3,1,1]]=>1
[[5],[3],[2]]=>[[5,3,2]]=>1
[[5],[4],[1]]=>[[5,4,1]]=>1
[[5],[5]]=>[[5,5]]=>1
[[4,1],[1],[1],[1],[1],[1]]=>[[4,1,1,1,1,1],[1]]=>2
[[4,1],[2],[1],[1],[1]]=>[[4,2,1,1,1],[1]]=>2
[[4,1],[2],[2],[1]]=>[[4,2,2,1],[1]]=>2
[[4,1],[1,1],[1],[1],[1]]=>[[4,1,1,1,1],[1,1]]=>2
[[4,1],[1,1],[1,1],[1]]=>[[4,1,1,1],[1,1,1]]=>2
[[4,1],[3],[1],[1]]=>[[4,3,1,1],[1]]=>2
[[4,1],[3],[2]]=>[[4,3,2],[1]]=>2
[[4,1],[2,1],[1],[1]]=>[[4,2,1,1],[1,1]]=>2
[[4,1],[2,1],[2]]=>[[4,2,2],[1,1]]=>2
[[4,1],[2,1],[1,1]]=>[[4,2,1],[1,1,1]]=>2
[[4,1],[4],[1]]=>[[4,4,1],[1]]=>2
[[4,1],[3,1],[1]]=>[[4,3,1],[1,1]]=>2
[[4,1],[4,1]]=>[[4,4],[1,1]]=>2
[[3,2],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1],[2]]=>2
[[3,2],[2],[1],[1],[1]]=>[[3,2,1,1,1],[2]]=>2
[[3,2],[2],[2],[1]]=>[[3,2,2,1],[2]]=>2
[[3,2],[1,1],[1],[1],[1]]=>[[3,1,1,1,1],[2,1]]=>2
[[3,2],[1,1],[1,1],[1]]=>[[3,1,1,1],[2,1,1]]=>2
[[3,2],[3],[1],[1]]=>[[3,3,1,1],[2]]=>2
[[3,2],[3],[2]]=>[[3,3,2],[2]]=>2
[[3,2],[2,1],[1],[1]]=>[[3,2,1,1],[2,1]]=>2
[[3,2],[2,1],[2]]=>[[3,2,2],[2,1]]=>2
[[3,2],[2,1],[1,1]]=>[[3,2,1],[2,1,1]]=>2
[[3,2],[3,1],[1]]=>[[3,3,1],[2,1]]=>2
[[3,2],[2,2],[1]]=>[[3,2,1],[2,2]]=>2
[[3,2],[3,2]]=>[[3,3],[2,2]]=>2
[[3,1,1],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1],[1],[1]]=>3
[[3,1,1],[2],[1],[1],[1]]=>[[3,2,1,1,1],[1],[1]]=>3
[[3,1,1],[2],[2],[1]]=>[[3,2,2,1],[1],[1]]=>3
[[3,1,1],[1,1],[1],[1],[1]]=>[[3,1,1,1,1],[1,1],[1]]=>3
[[3,1,1],[1,1],[1,1],[1]]=>[[3,1,1,1],[1,1,1],[1]]=>3
[[3,1,1],[3],[1],[1]]=>[[3,3,1,1],[1],[1]]=>3
[[3,1,1],[3],[2]]=>[[3,3,2],[1],[1]]=>3
[[3,1,1],[2,1],[1],[1]]=>[[3,2,1,1],[1,1],[1]]=>3
[[3,1,1],[2,1],[2]]=>[[3,2,2],[1,1],[1]]=>3
[[3,1,1],[2,1],[1,1]]=>[[3,2,1],[1,1,1],[1]]=>3
[[3,1,1],[1,1,1],[1],[1]]=>[[3,1,1,1],[1,1],[1,1]]=>3
[[3,1,1],[1,1,1],[1,1]]=>[[3,1,1],[1,1,1],[1,1]]=>3
[[3,1,1],[3,1],[1]]=>[[3,3,1],[1,1],[1]]=>3
[[3,1,1],[2,1,1],[1]]=>[[3,2,1],[1,1],[1,1]]=>3
[[3,1,1],[3,1,1]]=>[[3,3],[1,1],[1,1]]=>3
[[2,2,1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[2],[1]]=>3
[[2,2,1],[2],[1],[1],[1]]=>[[2,2,1,1,1],[2],[1]]=>3
[[2,2,1],[2],[2],[1]]=>[[2,2,2,1],[2],[1]]=>3
[[2,2,1],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[2,1],[1]]=>3
[[2,2,1],[1,1],[1,1],[1]]=>[[2,1,1,1],[2,1,1],[1]]=>3
[[2,2,1],[2,1],[1],[1]]=>[[2,2,1,1],[2,1],[1]]=>3
[[2,2,1],[2,1],[2]]=>[[2,2,2],[2,1],[1]]=>3
[[2,2,1],[2,1],[1,1]]=>[[2,2,1],[2,1,1],[1]]=>3
[[2,2,1],[1,1,1],[1],[1]]=>[[2,1,1,1],[2,1],[1,1]]=>3
[[2,2,1],[1,1,1],[1,1]]=>[[2,1,1],[2,1,1],[1,1]]=>3
[[2,2,1],[2,2],[1]]=>[[2,2,1],[2,2],[1]]=>3
[[2,2,1],[2,1,1],[1]]=>[[2,2,1],[2,1],[1,1]]=>3
[[2,2,1],[2,2,1]]=>[[2,2],[2,2],[1,1]]=>3
[[2,1,1,1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1],[1],[1]]=>4
[[2,1,1,1],[2],[1],[1],[1]]=>[[2,2,1,1,1],[1],[1],[1]]=>4
[[2,1,1,1],[2],[2],[1]]=>[[2,2,2,1],[1],[1],[1]]=>4
[[2,1,1,1],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[1,1],[1],[1]]=>4
[[2,1,1,1],[1,1],[1,1],[1]]=>[[2,1,1,1],[1,1,1],[1],[1]]=>4
[[2,1,1,1],[2,1],[1],[1]]=>[[2,2,1,1],[1,1],[1],[1]]=>4
[[2,1,1,1],[2,1],[2]]=>[[2,2,2],[1,1],[1],[1]]=>4
[[2,1,1,1],[2,1],[1,1]]=>[[2,2,1],[1,1,1],[1],[1]]=>4
[[2,1,1,1],[1,1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1,1],[1]]=>4
[[2,1,1,1],[1,1,1],[1,1]]=>[[2,1,1],[1,1,1],[1,1],[1]]=>4
[[2,1,1,1],[2,1,1],[1]]=>[[2,2,1],[1,1],[1,1],[1]]=>4
[[2,1,1,1],[1,1,1,1],[1]]=>[[2,1,1],[1,1],[1,1],[1,1]]=>4
[[2,1,1,1],[2,1,1,1]]=>[[2,2],[1,1],[1,1],[1,1]]=>4
[[1,1,1,1,1],[1],[1],[1],[1],[1]]=>[[1,1,1,1,1,1],[1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1],[1],[1],[1]]=>[[1,1,1,1,1],[1,1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1],[1,1],[1]]=>[[1,1,1,1],[1,1,1],[1],[1],[1]]=>5
[[1,1,1,1,1],[1,1,1],[1],[1]]=>[[1,1,1,1],[1,1],[1,1],[1],[1]]=>5
[[1,1,1,1,1],[1,1,1],[1,1]]=>[[1,1,1],[1,1,1],[1,1],[1],[1]]=>5
[[1,1,1,1,1],[1,1,1,1],[1]]=>[[1,1,1],[1,1],[1,1],[1,1],[1]]=>5
[[1,1,1,1,1],[1,1,1,1,1]]=>[[1,1],[1,1],[1,1],[1,1],[1,1]]=>5
[[6],[1],[1],[1],[1]]=>[[6,1,1,1,1]]=>1
[[6],[2],[1],[1]]=>[[6,2,1,1]]=>1
[[6],[2],[2]]=>[[6,2,2]]=>1
[[6],[3],[1]]=>[[6,3,1]]=>1
[[6],[4]]=>[[6,4]]=>1
[[5,1],[1],[1],[1],[1]]=>[[5,1,1,1,1],[1]]=>2
[[5,1],[2],[1],[1]]=>[[5,2,1,1],[1]]=>2
[[5,1],[2],[2]]=>[[5,2,2],[1]]=>2
[[5,1],[1,1],[1],[1]]=>[[5,1,1,1],[1,1]]=>2
[[5,1],[1,1],[1,1]]=>[[5,1,1],[1,1,1]]=>2
[[5,1],[3],[1]]=>[[5,3,1],[1]]=>2
[[5,1],[2,1],[1]]=>[[5,2,1],[1,1]]=>2
[[5,1],[4]]=>[[5,4],[1]]=>2
[[5,1],[3,1]]=>[[5,3],[1,1]]=>2
[[4,2],[1],[1],[1],[1]]=>[[4,1,1,1,1],[2]]=>2
[[4,2],[2],[1],[1]]=>[[4,2,1,1],[2]]=>2
[[4,2],[2],[2]]=>[[4,2,2],[2]]=>2
[[4,2],[1,1],[1],[1]]=>[[4,1,1,1],[2,1]]=>2
[[4,2],[1,1],[1,1]]=>[[4,1,1],[2,1,1]]=>2
[[4,2],[3],[1]]=>[[4,3,1],[2]]=>2
[[4,2],[2,1],[1]]=>[[4,2,1],[2,1]]=>2
[[4,2],[4]]=>[[4,4],[2]]=>2
[[4,2],[3,1]]=>[[4,3],[2,1]]=>2
[[4,2],[2,2]]=>[[4,2],[2,2]]=>2
[[4,1,1],[1],[1],[1],[1]]=>[[4,1,1,1,1],[1],[1]]=>3
[[4,1,1],[2],[1],[1]]=>[[4,2,1,1],[1],[1]]=>3
[[4,1,1],[2],[2]]=>[[4,2,2],[1],[1]]=>3
[[4,1,1],[1,1],[1],[1]]=>[[4,1,1,1],[1,1],[1]]=>3
[[4,1,1],[1,1],[1,1]]=>[[4,1,1],[1,1,1],[1]]=>3
[[4,1,1],[3],[1]]=>[[4,3,1],[1],[1]]=>3
[[4,1,1],[2,1],[1]]=>[[4,2,1],[1,1],[1]]=>3
[[4,1,1],[1,1,1],[1]]=>[[4,1,1],[1,1],[1,1]]=>3
[[4,1,1],[4]]=>[[4,4],[1],[1]]=>3
[[4,1,1],[3,1]]=>[[4,3],[1,1],[1]]=>3
[[4,1,1],[2,1,1]]=>[[4,2],[1,1],[1,1]]=>3
[[3,3],[1],[1],[1],[1]]=>[[3,1,1,1,1],[3]]=>2
[[3,3],[2],[1],[1]]=>[[3,2,1,1],[3]]=>2
[[3,3],[2],[2]]=>[[3,2,2],[3]]=>2
[[3,3],[1,1],[1],[1]]=>[[3,1,1,1],[3,1]]=>2
[[3,3],[1,1],[1,1]]=>[[3,1,1],[3,1,1]]=>2
[[3,3],[3],[1]]=>[[3,3,1],[3]]=>2
[[3,3],[2,1],[1]]=>[[3,2,1],[3,1]]=>2
[[3,3],[3,1]]=>[[3,3],[3,1]]=>2
[[3,3],[2,2]]=>[[3,2],[3,2]]=>2
[[3,2,1],[1],[1],[1],[1]]=>[[3,1,1,1,1],[2],[1]]=>3
[[3,2,1],[2],[1],[1]]=>[[3,2,1,1],[2],[1]]=>3
[[3,2,1],[2],[2]]=>[[3,2,2],[2],[1]]=>3
[[3,2,1],[1,1],[1],[1]]=>[[3,1,1,1],[2,1],[1]]=>3
[[3,2,1],[1,1],[1,1]]=>[[3,1,1],[2,1,1],[1]]=>3
[[3,2,1],[3],[1]]=>[[3,3,1],[2],[1]]=>3
[[3,2,1],[2,1],[1]]=>[[3,2,1],[2,1],[1]]=>3
[[3,2,1],[1,1,1],[1]]=>[[3,1,1],[2,1],[1,1]]=>3
[[3,2,1],[3,1]]=>[[3,3],[2,1],[1]]=>3
[[3,2,1],[2,2]]=>[[3,2],[2,2],[1]]=>3
[[3,2,1],[2,1,1]]=>[[3,2],[2,1],[1,1]]=>3
[[3,1,1,1],[1],[1],[1],[1]]=>[[3,1,1,1,1],[1],[1],[1]]=>4
[[3,1,1,1],[2],[1],[1]]=>[[3,2,1,1],[1],[1],[1]]=>4
[[3,1,1,1],[2],[2]]=>[[3,2,2],[1],[1],[1]]=>4
[[3,1,1,1],[1,1],[1],[1]]=>[[3,1,1,1],[1,1],[1],[1]]=>4
[[3,1,1,1],[1,1],[1,1]]=>[[3,1,1],[1,1,1],[1],[1]]=>4
[[3,1,1,1],[3],[1]]=>[[3,3,1],[1],[1],[1]]=>4
[[3,1,1,1],[2,1],[1]]=>[[3,2,1],[1,1],[1],[1]]=>4
[[3,1,1,1],[1,1,1],[1]]=>[[3,1,1],[1,1],[1,1],[1]]=>4
[[3,1,1,1],[3,1]]=>[[3,3],[1,1],[1],[1]]=>4
[[3,1,1,1],[2,1,1]]=>[[3,2],[1,1],[1,1],[1]]=>4
[[3,1,1,1],[1,1,1,1]]=>[[3,1],[1,1],[1,1],[1,1]]=>4
[[2,2,2],[1],[1],[1],[1]]=>[[2,1,1,1,1],[2],[2]]=>3
[[2,2,2],[2],[1],[1]]=>[[2,2,1,1],[2],[2]]=>3
[[2,2,2],[2],[2]]=>[[2,2,2],[2],[2]]=>3
[[2,2,2],[1,1],[1],[1]]=>[[2,1,1,1],[2,1],[2]]=>3
[[2,2,2],[1,1],[1,1]]=>[[2,1,1],[2,1,1],[2]]=>3
[[2,2,2],[2,1],[1]]=>[[2,2,1],[2,1],[2]]=>3
[[2,2,2],[1,1,1],[1]]=>[[2,1,1],[2,1],[2,1]]=>3
[[2,2,2],[2,2]]=>[[2,2],[2,2],[2]]=>3
[[2,2,2],[2,1,1]]=>[[2,2],[2,1],[2,1]]=>3
[[2,2,1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[2],[1],[1]]=>4
[[2,2,1,1],[2],[1],[1]]=>[[2,2,1,1],[2],[1],[1]]=>4
[[2,2,1,1],[2],[2]]=>[[2,2,2],[2],[1],[1]]=>4
[[2,2,1,1],[1,1],[1],[1]]=>[[2,1,1,1],[2,1],[1],[1]]=>4
[[2,2,1,1],[1,1],[1,1]]=>[[2,1,1],[2,1,1],[1],[1]]=>4
[[2,2,1,1],[2,1],[1]]=>[[2,2,1],[2,1],[1],[1]]=>4
[[2,2,1,1],[1,1,1],[1]]=>[[2,1,1],[2,1],[1,1],[1]]=>4
[[2,2,1,1],[2,2]]=>[[2,2],[2,2],[1],[1]]=>4
[[2,2,1,1],[2,1,1]]=>[[2,2],[2,1],[1,1],[1]]=>4
[[2,2,1,1],[1,1,1,1]]=>[[2,1],[2,1],[1,1],[1,1]]=>4
[[2,1,1,1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[1],[1],[1],[1]]=>5
[[2,1,1,1,1],[2],[1],[1]]=>[[2,2,1,1],[1],[1],[1],[1]]=>5
[[2,1,1,1,1],[2],[2]]=>[[2,2,2],[1],[1],[1],[1]]=>5
[[2,1,1,1,1],[1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1],[1],[1]]=>5
[[2,1,1,1,1],[1,1],[1,1]]=>[[2,1,1],[1,1,1],[1],[1],[1]]=>5
[[2,1,1,1,1],[2,1],[1]]=>[[2,2,1],[1,1],[1],[1],[1]]=>5
[[2,1,1,1,1],[1,1,1],[1]]=>[[2,1,1],[1,1],[1,1],[1],[1]]=>5
[[2,1,1,1,1],[2,1,1]]=>[[2,2],[1,1],[1,1],[1],[1]]=>5
[[2,1,1,1,1],[1,1,1,1]]=>[[2,1],[1,1],[1,1],[1,1],[1]]=>5
[[1,1,1,1,1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1],[1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1],[1],[1]]=>[[1,1,1,1],[1,1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1],[1,1]]=>[[1,1,1],[1,1,1],[1],[1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1,1],[1]]=>[[1,1,1],[1,1],[1,1],[1],[1],[1]]=>6
[[1,1,1,1,1,1],[1,1,1,1]]=>[[1,1],[1,1],[1,1],[1,1],[1],[1]]=>6
[[7],[1],[1],[1]]=>[[7,1,1,1]]=>1
[[7],[2],[1]]=>[[7,2,1]]=>1
[[7],[3]]=>[[7,3]]=>1
[[6,1],[1],[1],[1]]=>[[6,1,1,1],[1]]=>2
[[6,1],[2],[1]]=>[[6,2,1],[1]]=>2
[[6,1],[1,1],[1]]=>[[6,1,1],[1,1]]=>2
[[6,1],[3]]=>[[6,3],[1]]=>2
[[6,1],[2,1]]=>[[6,2],[1,1]]=>2
[[5,2],[1],[1],[1]]=>[[5,1,1,1],[2]]=>2
[[5,2],[2],[1]]=>[[5,2,1],[2]]=>2
[[5,2],[1,1],[1]]=>[[5,1,1],[2,1]]=>2
[[5,2],[3]]=>[[5,3],[2]]=>2
[[5,2],[2,1]]=>[[5,2],[2,1]]=>2
[[5,1,1],[1],[1],[1]]=>[[5,1,1,1],[1],[1]]=>3
[[5,1,1],[2],[1]]=>[[5,2,1],[1],[1]]=>3
[[5,1,1],[1,1],[1]]=>[[5,1,1],[1,1],[1]]=>3
[[5,1,1],[3]]=>[[5,3],[1],[1]]=>3
[[5,1,1],[2,1]]=>[[5,2],[1,1],[1]]=>3
[[5,1,1],[1,1,1]]=>[[5,1],[1,1],[1,1]]=>3
[[4,3],[1],[1],[1]]=>[[4,1,1,1],[3]]=>2
[[4,3],[2],[1]]=>[[4,2,1],[3]]=>2
[[4,3],[1,1],[1]]=>[[4,1,1],[3,1]]=>2
[[4,3],[3]]=>[[4,3],[3]]=>2
[[4,3],[2,1]]=>[[4,2],[3,1]]=>2
[[4,2,1],[1],[1],[1]]=>[[4,1,1,1],[2],[1]]=>3
[[4,2,1],[2],[1]]=>[[4,2,1],[2],[1]]=>3
[[4,2,1],[1,1],[1]]=>[[4,1,1],[2,1],[1]]=>3
[[4,2,1],[3]]=>[[4,3],[2],[1]]=>3
[[4,2,1],[2,1]]=>[[4,2],[2,1],[1]]=>3
[[4,2,1],[1,1,1]]=>[[4,1],[2,1],[1,1]]=>3
[[4,1,1,1],[1],[1],[1]]=>[[4,1,1,1],[1],[1],[1]]=>4
[[4,1,1,1],[2],[1]]=>[[4,2,1],[1],[1],[1]]=>4
[[4,1,1,1],[1,1],[1]]=>[[4,1,1],[1,1],[1],[1]]=>4
[[4,1,1,1],[3]]=>[[4,3],[1],[1],[1]]=>4
[[4,1,1,1],[2,1]]=>[[4,2],[1,1],[1],[1]]=>4
[[4,1,1,1],[1,1,1]]=>[[4,1],[1,1],[1,1],[1]]=>4
[[3,3,1],[1],[1],[1]]=>[[3,1,1,1],[3],[1]]=>3
[[3,3,1],[2],[1]]=>[[3,2,1],[3],[1]]=>3
[[3,3,1],[1,1],[1]]=>[[3,1,1],[3,1],[1]]=>3
[[3,3,1],[3]]=>[[3,3],[3],[1]]=>3
[[3,3,1],[2,1]]=>[[3,2],[3,1],[1]]=>3
[[3,3,1],[1,1,1]]=>[[3,1],[3,1],[1,1]]=>3
[[3,2,2],[1],[1],[1]]=>[[3,1,1,1],[2],[2]]=>3
[[3,2,2],[2],[1]]=>[[3,2,1],[2],[2]]=>3
[[3,2,2],[1,1],[1]]=>[[3,1,1],[2,1],[2]]=>3
[[3,2,2],[3]]=>[[3,3],[2],[2]]=>3
[[3,2,2],[2,1]]=>[[3,2],[2,1],[2]]=>3
[[3,2,2],[1,1,1]]=>[[3,1],[2,1],[2,1]]=>3
[[3,2,1,1],[1],[1],[1]]=>[[3,1,1,1],[2],[1],[1]]=>4
[[3,2,1,1],[2],[1]]=>[[3,2,1],[2],[1],[1]]=>4
[[3,2,1,1],[1,1],[1]]=>[[3,1,1],[2,1],[1],[1]]=>4
[[3,2,1,1],[3]]=>[[3,3],[2],[1],[1]]=>4
[[3,2,1,1],[2,1]]=>[[3,2],[2,1],[1],[1]]=>4
[[3,2,1,1],[1,1,1]]=>[[3,1],[2,1],[1,1],[1]]=>4
[[3,1,1,1,1],[1],[1],[1]]=>[[3,1,1,1],[1],[1],[1],[1]]=>5
[[3,1,1,1,1],[2],[1]]=>[[3,2,1],[1],[1],[1],[1]]=>5
[[3,1,1,1,1],[1,1],[1]]=>[[3,1,1],[1,1],[1],[1],[1]]=>5
[[3,1,1,1,1],[3]]=>[[3,3],[1],[1],[1],[1]]=>5
[[3,1,1,1,1],[2,1]]=>[[3,2],[1,1],[1],[1],[1]]=>5
[[3,1,1,1,1],[1,1,1]]=>[[3,1],[1,1],[1,1],[1],[1]]=>5
[[2,2,2,1],[1],[1],[1]]=>[[2,1,1,1],[2],[2],[1]]=>4
[[2,2,2,1],[2],[1]]=>[[2,2,1],[2],[2],[1]]=>4
[[2,2,2,1],[1,1],[1]]=>[[2,1,1],[2,1],[2],[1]]=>4
[[2,2,2,1],[2,1]]=>[[2,2],[2,1],[2],[1]]=>4
[[2,2,2,1],[1,1,1]]=>[[2,1],[2,1],[2,1],[1]]=>4
[[2,2,1,1,1],[1],[1],[1]]=>[[2,1,1,1],[2],[1],[1],[1]]=>5
[[2,2,1,1,1],[2],[1]]=>[[2,2,1],[2],[1],[1],[1]]=>5
[[2,2,1,1,1],[1,1],[1]]=>[[2,1,1],[2,1],[1],[1],[1]]=>5
[[2,2,1,1,1],[2,1]]=>[[2,2],[2,1],[1],[1],[1]]=>5
[[2,2,1,1,1],[1,1,1]]=>[[2,1],[2,1],[1,1],[1],[1]]=>5
[[2,1,1,1,1,1],[1],[1],[1]]=>[[2,1,1,1],[1],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1],[2],[1]]=>[[2,2,1],[1],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1],[1,1],[1]]=>[[2,1,1],[1,1],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1],[2,1]]=>[[2,2],[1,1],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1],[1,1,1]]=>[[2,1],[1,1],[1,1],[1],[1],[1]]=>6
[[1,1,1,1,1,1,1],[1],[1],[1]]=>[[1,1,1,1],[1],[1],[1],[1],[1],[1]]=>7
[[1,1,1,1,1,1,1],[1,1],[1]]=>[[1,1,1],[1,1],[1],[1],[1],[1],[1]]=>7
[[1,1,1,1,1,1,1],[1,1,1]]=>[[1,1],[1,1],[1,1],[1],[1],[1],[1]]=>7
[[8],[1],[1]]=>[[8,1,1]]=>1
[[8],[2]]=>[[8,2]]=>1
[[7,1],[1],[1]]=>[[7,1,1],[1]]=>2
[[7,1],[2]]=>[[7,2],[1]]=>2
[[7,1],[1,1]]=>[[7,1],[1,1]]=>2
[[6,2],[1],[1]]=>[[6,1,1],[2]]=>2
[[6,2],[2]]=>[[6,2],[2]]=>2
[[6,2],[1,1]]=>[[6,1],[2,1]]=>2
[[6,1,1],[1],[1]]=>[[6,1,1],[1],[1]]=>3
[[6,1,1],[2]]=>[[6,2],[1],[1]]=>3
[[6,1,1],[1,1]]=>[[6,1],[1,1],[1]]=>3
[[5,3],[1],[1]]=>[[5,1,1],[3]]=>2
[[5,3],[2]]=>[[5,2],[3]]=>2
[[5,3],[1,1]]=>[[5,1],[3,1]]=>2
[[5,2,1],[1],[1]]=>[[5,1,1],[2],[1]]=>3
[[5,2,1],[2]]=>[[5,2],[2],[1]]=>3
[[5,2,1],[1,1]]=>[[5,1],[2,1],[1]]=>3
[[5,1,1,1],[1],[1]]=>[[5,1,1],[1],[1],[1]]=>4
[[5,1,1,1],[2]]=>[[5,2],[1],[1],[1]]=>4
[[5,1,1,1],[1,1]]=>[[5,1],[1,1],[1],[1]]=>4
[[4,4],[1],[1]]=>[[4,1,1],[4]]=>2
[[4,4],[2]]=>[[4,2],[4]]=>2
[[4,4],[1,1]]=>[[4,1],[4,1]]=>2
[[4,3,1],[1],[1]]=>[[4,1,1],[3],[1]]=>3
[[4,3,1],[2]]=>[[4,2],[3],[1]]=>3
[[4,3,1],[1,1]]=>[[4,1],[3,1],[1]]=>3
[[4,2,2],[1],[1]]=>[[4,1,1],[2],[2]]=>3
[[4,2,2],[2]]=>[[4,2],[2],[2]]=>3
[[4,2,2],[1,1]]=>[[4,1],[2,1],[2]]=>3
[[4,2,1,1],[1],[1]]=>[[4,1,1],[2],[1],[1]]=>4
[[4,2,1,1],[2]]=>[[4,2],[2],[1],[1]]=>4
[[4,2,1,1],[1,1]]=>[[4,1],[2,1],[1],[1]]=>4
[[4,1,1,1,1],[1],[1]]=>[[4,1,1],[1],[1],[1],[1]]=>5
[[4,1,1,1,1],[2]]=>[[4,2],[1],[1],[1],[1]]=>5
[[4,1,1,1,1],[1,1]]=>[[4,1],[1,1],[1],[1],[1]]=>5
[[3,3,2],[1],[1]]=>[[3,1,1],[3],[2]]=>3
[[3,3,2],[2]]=>[[3,2],[3],[2]]=>3
[[3,3,2],[1,1]]=>[[3,1],[3,1],[2]]=>3
[[3,3,1,1],[1],[1]]=>[[3,1,1],[3],[1],[1]]=>4
[[3,3,1,1],[2]]=>[[3,2],[3],[1],[1]]=>4
[[3,3,1,1],[1,1]]=>[[3,1],[3,1],[1],[1]]=>4
[[3,2,2,1],[1],[1]]=>[[3,1,1],[2],[2],[1]]=>4
[[3,2,2,1],[2]]=>[[3,2],[2],[2],[1]]=>4
[[3,2,2,1],[1,1]]=>[[3,1],[2,1],[2],[1]]=>4
[[3,2,1,1,1],[1],[1]]=>[[3,1,1],[2],[1],[1],[1]]=>5
[[3,2,1,1,1],[2]]=>[[3,2],[2],[1],[1],[1]]=>5
[[3,2,1,1,1],[1,1]]=>[[3,1],[2,1],[1],[1],[1]]=>5
[[3,1,1,1,1,1],[1],[1]]=>[[3,1,1],[1],[1],[1],[1],[1]]=>6
[[3,1,1,1,1,1],[2]]=>[[3,2],[1],[1],[1],[1],[1]]=>6
[[3,1,1,1,1,1],[1,1]]=>[[3,1],[1,1],[1],[1],[1],[1]]=>6
[[2,2,2,2],[1],[1]]=>[[2,1,1],[2],[2],[2]]=>4
[[2,2,2,2],[2]]=>[[2,2],[2],[2],[2]]=>4
[[2,2,2,2],[1,1]]=>[[2,1],[2,1],[2],[2]]=>4
[[2,2,2,1,1],[1],[1]]=>[[2,1,1],[2],[2],[1],[1]]=>5
[[2,2,2,1,1],[2]]=>[[2,2],[2],[2],[1],[1]]=>5
[[2,2,2,1,1],[1,1]]=>[[2,1],[2,1],[2],[1],[1]]=>5
[[2,2,1,1,1,1],[1],[1]]=>[[2,1,1],[2],[1],[1],[1],[1]]=>6
[[2,2,1,1,1,1],[2]]=>[[2,2],[2],[1],[1],[1],[1]]=>6
[[2,2,1,1,1,1],[1,1]]=>[[2,1],[2,1],[1],[1],[1],[1]]=>6
[[2,1,1,1,1,1,1],[1],[1]]=>[[2,1,1],[1],[1],[1],[1],[1],[1]]=>7
[[2,1,1,1,1,1,1],[2]]=>[[2,2],[1],[1],[1],[1],[1],[1]]=>7
[[2,1,1,1,1,1,1],[1,1]]=>[[2,1],[1,1],[1],[1],[1],[1],[1]]=>7
[[1,1,1,1,1,1,1,1],[1],[1]]=>[[1,1,1],[1],[1],[1],[1],[1],[1],[1]]=>8
[[1,1,1,1,1,1,1,1],[1,1]]=>[[1,1],[1,1],[1],[1],[1],[1],[1],[1]]=>8
[[9],[1]]=>[[9,1]]=>1
[[8,1],[1]]=>[[8,1],[1]]=>2
[[7,2],[1]]=>[[7,1],[2]]=>2
[[7,1,1],[1]]=>[[7,1],[1],[1]]=>3
[[6,3],[1]]=>[[6,1],[3]]=>2
[[6,2,1],[1]]=>[[6,1],[2],[1]]=>3
[[6,1,1,1],[1]]=>[[6,1],[1],[1],[1]]=>4
[[5,4],[1]]=>[[5,1],[4]]=>2
[[5,3,1],[1]]=>[[5,1],[3],[1]]=>3
[[5,2,2],[1]]=>[[5,1],[2],[2]]=>3
[[5,2,1,1],[1]]=>[[5,1],[2],[1],[1]]=>4
[[5,1,1,1,1],[1]]=>[[5,1],[1],[1],[1],[1]]=>5
[[4,4,1],[1]]=>[[4,1],[4],[1]]=>3
[[4,3,2],[1]]=>[[4,1],[3],[2]]=>3
[[4,3,1,1],[1]]=>[[4,1],[3],[1],[1]]=>4
[[4,2,2,1],[1]]=>[[4,1],[2],[2],[1]]=>4
[[4,2,1,1,1],[1]]=>[[4,1],[2],[1],[1],[1]]=>5
[[4,1,1,1,1,1],[1]]=>[[4,1],[1],[1],[1],[1],[1]]=>6
[[3,3,3],[1]]=>[[3,1],[3],[3]]=>3
[[3,3,2,1],[1]]=>[[3,1],[3],[2],[1]]=>4
[[3,3,1,1,1],[1]]=>[[3,1],[3],[1],[1],[1]]=>5
[[3,2,2,2],[1]]=>[[3,1],[2],[2],[2]]=>4
[[3,2,2,1,1],[1]]=>[[3,1],[2],[2],[1],[1]]=>5
[[3,2,1,1,1,1],[1]]=>[[3,1],[2],[1],[1],[1],[1]]=>6
[[3,1,1,1,1,1,1],[1]]=>[[3,1],[1],[1],[1],[1],[1],[1]]=>7
[[2,2,2,2,1],[1]]=>[[2,1],[2],[2],[2],[1]]=>5
[[2,2,2,1,1,1],[1]]=>[[2,1],[2],[2],[1],[1],[1]]=>6
[[2,2,1,1,1,1,1],[1]]=>[[2,1],[2],[1],[1],[1],[1],[1]]=>7
[[2,1,1,1,1,1,1,1],[1]]=>[[2,1],[1],[1],[1],[1],[1],[1],[1]]=>8
[[1,1,1,1,1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]]=>9
[[10]]=>[[10]]=>1
[[9,1]]=>[[9],[1]]=>2
[[8,2]]=>[[8],[2]]=>2
[[8,1,1]]=>[[8],[1],[1]]=>3
[[7,3]]=>[[7],[3]]=>2
[[7,2,1]]=>[[7],[2],[1]]=>3
[[7,1,1,1]]=>[[7],[1],[1],[1]]=>4
[[6,4]]=>[[6],[4]]=>2
[[6,3,1]]=>[[6],[3],[1]]=>3
[[6,2,2]]=>[[6],[2],[2]]=>3
[[6,2,1,1]]=>[[6],[2],[1],[1]]=>4
[[6,1,1,1,1]]=>[[6],[1],[1],[1],[1]]=>5
[[5,5]]=>[[5],[5]]=>2
[[5,4,1]]=>[[5],[4],[1]]=>3
[[5,3,2]]=>[[5],[3],[2]]=>3
[[5,3,1,1]]=>[[5],[3],[1],[1]]=>4
[[5,2,2,1]]=>[[5],[2],[2],[1]]=>4
[[5,2,1,1,1]]=>[[5],[2],[1],[1],[1]]=>5
[[5,1,1,1,1,1]]=>[[5],[1],[1],[1],[1],[1]]=>6
[[4,4,2]]=>[[4],[4],[2]]=>3
[[4,4,1,1]]=>[[4],[4],[1],[1]]=>4
[[4,3,3]]=>[[4],[3],[3]]=>3
[[4,3,2,1]]=>[[4],[3],[2],[1]]=>4
[[4,3,1,1,1]]=>[[4],[3],[1],[1],[1]]=>5
[[4,2,2,2]]=>[[4],[2],[2],[2]]=>4
[[4,2,2,1,1]]=>[[4],[2],[2],[1],[1]]=>5
[[4,2,1,1,1,1]]=>[[4],[2],[1],[1],[1],[1]]=>6
[[4,1,1,1,1,1,1]]=>[[4],[1],[1],[1],[1],[1],[1]]=>7
[[3,3,3,1]]=>[[3],[3],[3],[1]]=>4
[[3,3,2,2]]=>[[3],[3],[2],[2]]=>4
[[3,3,2,1,1]]=>[[3],[3],[2],[1],[1]]=>5
[[3,3,1,1,1,1]]=>[[3],[3],[1],[1],[1],[1]]=>6
[[3,2,2,2,1]]=>[[3],[2],[2],[2],[1]]=>5
[[3,2,2,1,1,1]]=>[[3],[2],[2],[1],[1],[1]]=>6
[[3,2,1,1,1,1,1]]=>[[3],[2],[1],[1],[1],[1],[1]]=>7
[[3,1,1,1,1,1,1,1]]=>[[3],[1],[1],[1],[1],[1],[1],[1]]=>8
[[2,2,2,2,2]]=>[[2],[2],[2],[2],[2]]=>5
[[2,2,2,2,1,1]]=>[[2],[2],[2],[2],[1],[1]]=>6
[[2,2,2,1,1,1,1]]=>[[2],[2],[2],[1],[1],[1],[1]]=>7
[[2,2,1,1,1,1,1,1]]=>[[2],[2],[1],[1],[1],[1],[1],[1]]=>8
[[2,1,1,1,1,1,1,1,1]]=>[[2],[1],[1],[1],[1],[1],[1],[1],[1]]=>9
[[1,1,1,1,1,1,1,1,1,1]]=>[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>10
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Description
Number of rows in the plane partition.
Map
transpose
Description
The transpose of a plane partition.
This is the mirror symmetry along the vertical axis.
This is the mirror symmetry along the vertical axis.
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