Identifier
- St000186: Gelfand-Tsetlin patterns ⟶ ℤ
Values
=>
Cc0018;cc-rep
[[1]]=>1
[[2]]=>2
[[3]]=>3
[[4]]=>4
[[1,0],[0]]=>1
[[1,0],[1]]=>1
[[2,0],[0]]=>2
[[2,0],[1]]=>2
[[2,0],[2]]=>2
[[1,1],[1]]=>2
[[3,0],[0]]=>3
[[3,0],[1]]=>3
[[3,0],[2]]=>3
[[3,0],[3]]=>3
[[2,1],[1]]=>3
[[2,1],[2]]=>3
[[4,0],[0]]=>4
[[4,0],[1]]=>4
[[4,0],[2]]=>4
[[4,0],[3]]=>4
[[4,0],[4]]=>4
[[3,1],[1]]=>4
[[3,1],[2]]=>4
[[3,1],[3]]=>4
[[2,2],[2]]=>4
[[4,1],[1]]=>5
[[4,1],[2]]=>5
[[4,1],[3]]=>5
[[4,1],[4]]=>5
[[3,2],[2]]=>5
[[3,2],[3]]=>5
[[4,2],[2]]=>6
[[4,2],[3]]=>6
[[4,2],[4]]=>6
[[3,3],[3]]=>6
[[4,3],[3]]=>7
[[4,3],[4]]=>7
[[4,4],[4]]=>8
[[1,0,0],[0,0],[0]]=>1
[[1,0,0],[1,0],[0]]=>1
[[1,0,0],[1,0],[1]]=>1
[[2,0,0],[0,0],[0]]=>2
[[2,0,0],[1,0],[0]]=>2
[[2,0,0],[1,0],[1]]=>2
[[2,0,0],[2,0],[0]]=>2
[[2,0,0],[2,0],[1]]=>2
[[2,0,0],[2,0],[2]]=>2
[[1,1,0],[1,0],[0]]=>2
[[1,1,0],[1,0],[1]]=>2
[[1,1,0],[1,1],[1]]=>2
[[3,0,0],[0,0],[0]]=>3
[[3,0,0],[1,0],[0]]=>3
[[3,0,0],[1,0],[1]]=>3
[[3,0,0],[2,0],[0]]=>3
[[3,0,0],[2,0],[1]]=>3
[[3,0,0],[2,0],[2]]=>3
[[3,0,0],[3,0],[0]]=>3
[[3,0,0],[3,0],[1]]=>3
[[3,0,0],[3,0],[2]]=>3
[[3,0,0],[3,0],[3]]=>3
[[2,1,0],[1,0],[0]]=>3
[[2,1,0],[1,0],[1]]=>3
[[2,1,0],[1,1],[1]]=>3
[[2,1,0],[2,0],[0]]=>3
[[2,1,0],[2,0],[1]]=>3
[[2,1,0],[2,0],[2]]=>3
[[2,1,0],[2,1],[1]]=>3
[[2,1,0],[2,1],[2]]=>3
[[1,1,1],[1,1],[1]]=>3
[[4,0,0],[0,0],[0]]=>4
[[4,0,0],[1,0],[0]]=>4
[[4,0,0],[1,0],[1]]=>4
[[4,0,0],[2,0],[0]]=>4
[[4,0,0],[2,0],[1]]=>4
[[4,0,0],[2,0],[2]]=>4
[[4,0,0],[3,0],[0]]=>4
[[4,0,0],[3,0],[1]]=>4
[[4,0,0],[3,0],[2]]=>4
[[4,0,0],[3,0],[3]]=>4
[[4,0,0],[4,0],[0]]=>4
[[4,0,0],[4,0],[1]]=>4
[[4,0,0],[4,0],[2]]=>4
[[4,0,0],[4,0],[3]]=>4
[[4,0,0],[4,0],[4]]=>4
[[3,1,0],[1,0],[0]]=>4
[[3,1,0],[1,0],[1]]=>4
[[3,1,0],[1,1],[1]]=>4
[[3,1,0],[2,0],[0]]=>4
[[3,1,0],[2,0],[1]]=>4
[[3,1,0],[2,0],[2]]=>4
[[3,1,0],[2,1],[1]]=>4
[[3,1,0],[2,1],[2]]=>4
[[3,1,0],[3,0],[0]]=>4
[[3,1,0],[3,0],[1]]=>4
[[3,1,0],[3,0],[2]]=>4
[[3,1,0],[3,0],[3]]=>4
[[3,1,0],[3,1],[1]]=>4
[[3,1,0],[3,1],[2]]=>4
[[3,1,0],[3,1],[3]]=>4
[[2,2,0],[2,0],[0]]=>4
[[2,2,0],[2,0],[1]]=>4
[[2,2,0],[2,0],[2]]=>4
[[2,2,0],[2,1],[1]]=>4
[[2,2,0],[2,1],[2]]=>4
[[2,2,0],[2,2],[2]]=>4
[[2,1,1],[1,1],[1]]=>4
[[2,1,1],[2,1],[1]]=>4
[[2,1,1],[2,1],[2]]=>4
[[4,1,0],[1,0],[0]]=>5
[[4,1,0],[1,0],[1]]=>5
[[4,1,0],[1,1],[1]]=>5
[[4,1,0],[2,0],[0]]=>5
[[4,1,0],[2,0],[1]]=>5
[[4,1,0],[2,0],[2]]=>5
[[4,1,0],[2,1],[1]]=>5
[[4,1,0],[2,1],[2]]=>5
[[4,1,0],[3,0],[0]]=>5
[[4,1,0],[3,0],[1]]=>5
[[4,1,0],[3,0],[2]]=>5
[[4,1,0],[3,0],[3]]=>5
[[4,1,0],[3,1],[1]]=>5
[[4,1,0],[3,1],[2]]=>5
[[4,1,0],[3,1],[3]]=>5
[[4,1,0],[4,0],[0]]=>5
[[4,1,0],[4,0],[1]]=>5
[[4,1,0],[4,0],[2]]=>5
[[4,1,0],[4,0],[3]]=>5
[[4,1,0],[4,0],[4]]=>5
[[4,1,0],[4,1],[1]]=>5
[[4,1,0],[4,1],[2]]=>5
[[4,1,0],[4,1],[3]]=>5
[[4,1,0],[4,1],[4]]=>5
[[3,2,0],[2,0],[0]]=>5
[[3,2,0],[2,0],[1]]=>5
[[3,2,0],[2,0],[2]]=>5
[[3,2,0],[2,1],[1]]=>5
[[3,2,0],[2,1],[2]]=>5
[[3,2,0],[2,2],[2]]=>5
[[3,2,0],[3,0],[0]]=>5
[[3,2,0],[3,0],[1]]=>5
[[3,2,0],[3,0],[2]]=>5
[[3,2,0],[3,0],[3]]=>5
[[3,2,0],[3,1],[1]]=>5
[[3,2,0],[3,1],[2]]=>5
[[3,2,0],[3,1],[3]]=>5
[[3,2,0],[3,2],[2]]=>5
[[3,2,0],[3,2],[3]]=>5
[[3,1,1],[1,1],[1]]=>5
[[3,1,1],[2,1],[1]]=>5
[[3,1,1],[2,1],[2]]=>5
[[3,1,1],[3,1],[1]]=>5
[[3,1,1],[3,1],[2]]=>5
[[3,1,1],[3,1],[3]]=>5
[[2,2,1],[2,1],[1]]=>5
[[2,2,1],[2,1],[2]]=>5
[[2,2,1],[2,2],[2]]=>5
[[4,2,0],[2,0],[0]]=>6
[[4,2,0],[2,0],[1]]=>6
[[4,2,0],[2,0],[2]]=>6
[[4,2,0],[2,1],[1]]=>6
[[4,2,0],[2,1],[2]]=>6
[[4,2,0],[2,2],[2]]=>6
[[4,2,0],[3,0],[0]]=>6
[[4,2,0],[3,0],[1]]=>6
[[4,2,0],[3,0],[2]]=>6
[[4,2,0],[3,0],[3]]=>6
[[4,2,0],[3,1],[1]]=>6
[[4,2,0],[3,1],[2]]=>6
[[4,2,0],[3,1],[3]]=>6
[[4,2,0],[3,2],[2]]=>6
[[4,2,0],[3,2],[3]]=>6
[[4,2,0],[4,0],[0]]=>6
[[4,2,0],[4,0],[1]]=>6
[[4,2,0],[4,0],[2]]=>6
[[4,2,0],[4,0],[3]]=>6
[[4,2,0],[4,0],[4]]=>6
[[4,2,0],[4,1],[1]]=>6
[[4,2,0],[4,1],[2]]=>6
[[4,2,0],[4,1],[3]]=>6
[[4,2,0],[4,1],[4]]=>6
[[4,2,0],[4,2],[2]]=>6
[[4,2,0],[4,2],[3]]=>6
[[4,2,0],[4,2],[4]]=>6
[[4,1,1],[1,1],[1]]=>6
[[4,1,1],[2,1],[1]]=>6
[[4,1,1],[2,1],[2]]=>6
[[4,1,1],[3,1],[1]]=>6
[[4,1,1],[3,1],[2]]=>6
[[4,1,1],[3,1],[3]]=>6
[[4,1,1],[4,1],[1]]=>6
[[4,1,1],[4,1],[2]]=>6
[[4,1,1],[4,1],[3]]=>6
[[4,1,1],[4,1],[4]]=>6
[[3,3,0],[3,0],[0]]=>6
[[3,3,0],[3,0],[1]]=>6
[[3,3,0],[3,0],[2]]=>6
[[3,3,0],[3,0],[3]]=>6
[[3,3,0],[3,1],[1]]=>6
[[3,3,0],[3,1],[2]]=>6
[[3,3,0],[3,1],[3]]=>6
[[3,3,0],[3,2],[2]]=>6
[[3,3,0],[3,2],[3]]=>6
[[3,3,0],[3,3],[3]]=>6
[[3,2,1],[2,1],[1]]=>6
[[3,2,1],[2,1],[2]]=>6
[[3,2,1],[2,2],[2]]=>6
[[3,2,1],[3,1],[1]]=>6
[[3,2,1],[3,1],[2]]=>6
[[3,2,1],[3,1],[3]]=>6
[[3,2,1],[3,2],[2]]=>6
[[3,2,1],[3,2],[3]]=>6
[[2,2,2],[2,2],[2]]=>6
[[4,3,0],[4,2],[4]]=>7
[[4,3,0],[4,1],[4]]=>7
[[4,3,0],[4,0],[4]]=>7
[[4,3,0],[4,2],[3]]=>7
[[4,3,0],[3,3],[3]]=>7
[[4,3,0],[4,1],[3]]=>7
[[4,3,0],[3,2],[3]]=>7
[[4,3,0],[4,0],[3]]=>7
[[4,3,0],[3,1],[3]]=>7
[[4,3,0],[3,0],[3]]=>7
[[4,3,0],[4,2],[2]]=>7
[[4,3,0],[4,1],[2]]=>7
[[4,3,0],[3,2],[2]]=>7
[[4,3,0],[4,0],[2]]=>7
[[4,3,0],[3,1],[2]]=>7
[[4,3,0],[3,0],[2]]=>7
[[4,3,0],[4,1],[1]]=>7
[[4,3,0],[4,0],[1]]=>7
[[4,3,0],[3,1],[1]]=>7
[[4,3,0],[3,0],[1]]=>7
[[4,3,0],[4,0],[0]]=>7
[[4,3,0],[3,0],[0]]=>7
[[4,2,1],[4,2],[4]]=>7
[[4,2,1],[4,1],[4]]=>7
[[4,2,1],[4,2],[3]]=>7
[[4,2,1],[4,1],[3]]=>7
[[4,2,1],[3,2],[3]]=>7
[[4,2,1],[3,1],[3]]=>7
[[4,2,1],[4,2],[2]]=>7
[[4,2,1],[4,1],[2]]=>7
[[4,2,1],[3,2],[2]]=>7
[[4,2,1],[3,1],[2]]=>7
[[4,2,1],[2,2],[2]]=>7
[[4,2,1],[2,1],[2]]=>7
[[4,2,1],[4,1],[1]]=>7
[[4,2,1],[3,1],[1]]=>7
[[4,2,1],[2,1],[1]]=>7
[[3,3,1],[3,3],[3]]=>7
[[3,3,1],[3,2],[3]]=>7
[[3,3,1],[3,1],[3]]=>7
[[3,3,1],[3,2],[2]]=>7
[[3,3,1],[3,1],[2]]=>7
[[3,3,1],[3,1],[1]]=>7
[[3,2,2],[3,2],[3]]=>7
[[3,2,2],[3,2],[2]]=>7
[[3,2,2],[2,2],[2]]=>7
[[1,0,0,0],[0,0,0],[0,0],[0]]=>1
[[1,0,0,0],[1,0,0],[0,0],[0]]=>1
[[1,0,0,0],[1,0,0],[1,0],[0]]=>1
[[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[2,0,0,0],[0,0,0],[0,0],[0]]=>2
[[2,0,0,0],[1,0,0],[0,0],[0]]=>2
[[2,0,0,0],[1,0,0],[1,0],[0]]=>2
[[2,0,0,0],[1,0,0],[1,0],[1]]=>2
[[2,0,0,0],[2,0,0],[0,0],[0]]=>2
[[2,0,0,0],[2,0,0],[1,0],[0]]=>2
[[2,0,0,0],[2,0,0],[1,0],[1]]=>2
[[2,0,0,0],[2,0,0],[2,0],[0]]=>2
[[2,0,0,0],[2,0,0],[2,0],[1]]=>2
[[2,0,0,0],[2,0,0],[2,0],[2]]=>2
[[1,1,0,0],[1,0,0],[0,0],[0]]=>2
[[1,1,0,0],[1,0,0],[1,0],[0]]=>2
[[1,1,0,0],[1,0,0],[1,0],[1]]=>2
[[1,1,0,0],[1,1,0],[1,0],[0]]=>2
[[1,1,0,0],[1,1,0],[1,0],[1]]=>2
[[1,1,0,0],[1,1,0],[1,1],[1]]=>2
[[3,0,0,0],[0,0,0],[0,0],[0]]=>3
[[3,0,0,0],[1,0,0],[0,0],[0]]=>3
[[3,0,0,0],[1,0,0],[1,0],[0]]=>3
[[3,0,0,0],[1,0,0],[1,0],[1]]=>3
[[3,0,0,0],[2,0,0],[0,0],[0]]=>3
[[3,0,0,0],[2,0,0],[1,0],[0]]=>3
[[3,0,0,0],[2,0,0],[1,0],[1]]=>3
[[3,0,0,0],[2,0,0],[2,0],[0]]=>3
[[3,0,0,0],[2,0,0],[2,0],[1]]=>3
[[3,0,0,0],[2,0,0],[2,0],[2]]=>3
[[3,0,0,0],[3,0,0],[0,0],[0]]=>3
[[3,0,0,0],[3,0,0],[1,0],[0]]=>3
[[3,0,0,0],[3,0,0],[1,0],[1]]=>3
[[3,0,0,0],[3,0,0],[2,0],[0]]=>3
[[3,0,0,0],[3,0,0],[2,0],[1]]=>3
[[3,0,0,0],[3,0,0],[2,0],[2]]=>3
[[3,0,0,0],[3,0,0],[3,0],[0]]=>3
[[3,0,0,0],[3,0,0],[3,0],[1]]=>3
[[3,0,0,0],[3,0,0],[3,0],[2]]=>3
[[3,0,0,0],[3,0,0],[3,0],[3]]=>3
[[2,1,0,0],[1,0,0],[0,0],[0]]=>3
[[2,1,0,0],[1,0,0],[1,0],[0]]=>3
[[2,1,0,0],[1,0,0],[1,0],[1]]=>3
[[2,1,0,0],[1,1,0],[1,0],[0]]=>3
[[2,1,0,0],[1,1,0],[1,0],[1]]=>3
[[2,1,0,0],[1,1,0],[1,1],[1]]=>3
[[2,1,0,0],[2,0,0],[0,0],[0]]=>3
[[2,1,0,0],[2,0,0],[1,0],[0]]=>3
[[2,1,0,0],[2,0,0],[1,0],[1]]=>3
[[2,1,0,0],[2,0,0],[2,0],[0]]=>3
[[2,1,0,0],[2,0,0],[2,0],[1]]=>3
[[2,1,0,0],[2,0,0],[2,0],[2]]=>3
[[2,1,0,0],[2,1,0],[1,0],[0]]=>3
[[2,1,0,0],[2,1,0],[1,0],[1]]=>3
[[2,1,0,0],[2,1,0],[1,1],[1]]=>3
[[2,1,0,0],[2,1,0],[2,0],[0]]=>3
[[2,1,0,0],[2,1,0],[2,0],[1]]=>3
[[2,1,0,0],[2,1,0],[2,0],[2]]=>3
[[2,1,0,0],[2,1,0],[2,1],[1]]=>3
[[2,1,0,0],[2,1,0],[2,1],[2]]=>3
[[1,1,1,0],[1,1,0],[1,0],[0]]=>3
[[1,1,1,0],[1,1,0],[1,0],[1]]=>3
[[1,1,1,0],[1,1,0],[1,1],[1]]=>3
[[1,1,1,0],[1,1,1],[1,1],[1]]=>3
[[4,0,0,0],[0,0,0],[0,0],[0]]=>4
[[4,0,0,0],[1,0,0],[0,0],[0]]=>4
[[4,0,0,0],[1,0,0],[1,0],[0]]=>4
[[4,0,0,0],[1,0,0],[1,0],[1]]=>4
[[4,0,0,0],[2,0,0],[0,0],[0]]=>4
[[4,0,0,0],[2,0,0],[1,0],[0]]=>4
[[4,0,0,0],[2,0,0],[1,0],[1]]=>4
[[4,0,0,0],[2,0,0],[2,0],[0]]=>4
[[4,0,0,0],[2,0,0],[2,0],[1]]=>4
[[4,0,0,0],[2,0,0],[2,0],[2]]=>4
[[4,0,0,0],[3,0,0],[0,0],[0]]=>4
[[4,0,0,0],[3,0,0],[1,0],[0]]=>4
[[4,0,0,0],[3,0,0],[1,0],[1]]=>4
[[4,0,0,0],[3,0,0],[2,0],[0]]=>4
[[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,0,0,0],[3,0,0],[2,0],[2]]=>4
[[4,0,0,0],[3,0,0],[3,0],[0]]=>4
[[4,0,0,0],[3,0,0],[3,0],[1]]=>4
[[4,0,0,0],[3,0,0],[3,0],[2]]=>4
[[4,0,0,0],[3,0,0],[3,0],[3]]=>4
[[4,0,0,0],[4,0,0],[0,0],[0]]=>4
[[4,0,0,0],[4,0,0],[1,0],[0]]=>4
[[4,0,0,0],[4,0,0],[1,0],[1]]=>4
[[4,0,0,0],[4,0,0],[2,0],[0]]=>4
[[4,0,0,0],[4,0,0],[2,0],[1]]=>4
[[4,0,0,0],[4,0,0],[2,0],[2]]=>4
[[4,0,0,0],[4,0,0],[3,0],[0]]=>4
[[4,0,0,0],[4,0,0],[3,0],[1]]=>4
[[4,0,0,0],[4,0,0],[3,0],[2]]=>4
[[4,0,0,0],[4,0,0],[3,0],[3]]=>4
[[4,0,0,0],[4,0,0],[4,0],[0]]=>4
[[4,0,0,0],[4,0,0],[4,0],[1]]=>4
[[4,0,0,0],[4,0,0],[4,0],[2]]=>4
[[4,0,0,0],[4,0,0],[4,0],[3]]=>4
[[4,0,0,0],[4,0,0],[4,0],[4]]=>4
[[3,1,0,0],[1,0,0],[0,0],[0]]=>4
[[3,1,0,0],[1,0,0],[1,0],[0]]=>4
[[3,1,0,0],[1,0,0],[1,0],[1]]=>4
[[3,1,0,0],[1,1,0],[1,0],[0]]=>4
[[3,1,0,0],[1,1,0],[1,0],[1]]=>4
[[3,1,0,0],[1,1,0],[1,1],[1]]=>4
[[3,1,0,0],[2,0,0],[0,0],[0]]=>4
[[3,1,0,0],[2,0,0],[1,0],[0]]=>4
[[3,1,0,0],[2,0,0],[1,0],[1]]=>4
[[3,1,0,0],[2,0,0],[2,0],[0]]=>4
[[3,1,0,0],[2,0,0],[2,0],[1]]=>4
[[3,1,0,0],[2,0,0],[2,0],[2]]=>4
[[3,1,0,0],[2,1,0],[1,0],[0]]=>4
[[3,1,0,0],[2,1,0],[1,0],[1]]=>4
[[3,1,0,0],[2,1,0],[1,1],[1]]=>4
[[3,1,0,0],[2,1,0],[2,0],[0]]=>4
[[3,1,0,0],[2,1,0],[2,0],[1]]=>4
[[3,1,0,0],[2,1,0],[2,0],[2]]=>4
[[3,1,0,0],[2,1,0],[2,1],[1]]=>4
[[3,1,0,0],[2,1,0],[2,1],[2]]=>4
[[3,1,0,0],[3,0,0],[0,0],[0]]=>4
[[3,1,0,0],[3,0,0],[1,0],[0]]=>4
[[3,1,0,0],[3,0,0],[1,0],[1]]=>4
[[3,1,0,0],[3,0,0],[2,0],[0]]=>4
[[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,1,0,0],[3,0,0],[2,0],[2]]=>4
[[3,1,0,0],[3,0,0],[3,0],[0]]=>4
[[3,1,0,0],[3,0,0],[3,0],[1]]=>4
[[3,1,0,0],[3,0,0],[3,0],[2]]=>4
[[3,1,0,0],[3,0,0],[3,0],[3]]=>4
[[3,1,0,0],[3,1,0],[1,0],[0]]=>4
[[3,1,0,0],[3,1,0],[1,0],[1]]=>4
[[3,1,0,0],[3,1,0],[1,1],[1]]=>4
[[3,1,0,0],[3,1,0],[2,0],[0]]=>4
[[3,1,0,0],[3,1,0],[2,0],[1]]=>4
[[3,1,0,0],[3,1,0],[2,0],[2]]=>4
[[3,1,0,0],[3,1,0],[2,1],[1]]=>4
[[3,1,0,0],[3,1,0],[2,1],[2]]=>4
[[3,1,0,0],[3,1,0],[3,0],[0]]=>4
[[3,1,0,0],[3,1,0],[3,0],[1]]=>4
[[3,1,0,0],[3,1,0],[3,0],[2]]=>4
[[3,1,0,0],[3,1,0],[3,0],[3]]=>4
[[3,1,0,0],[3,1,0],[3,1],[1]]=>4
[[3,1,0,0],[3,1,0],[3,1],[2]]=>4
[[3,1,0,0],[3,1,0],[3,1],[3]]=>4
[[2,2,0,0],[2,0,0],[0,0],[0]]=>4
[[2,2,0,0],[2,0,0],[1,0],[0]]=>4
[[2,2,0,0],[2,0,0],[1,0],[1]]=>4
[[2,2,0,0],[2,0,0],[2,0],[0]]=>4
[[2,2,0,0],[2,0,0],[2,0],[1]]=>4
[[2,2,0,0],[2,0,0],[2,0],[2]]=>4
[[2,2,0,0],[2,1,0],[1,0],[0]]=>4
[[2,2,0,0],[2,1,0],[1,0],[1]]=>4
[[2,2,0,0],[2,1,0],[1,1],[1]]=>4
[[2,2,0,0],[2,1,0],[2,0],[0]]=>4
[[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[2,2,0,0],[2,1,0],[2,0],[2]]=>4
[[2,2,0,0],[2,1,0],[2,1],[1]]=>4
[[2,2,0,0],[2,1,0],[2,1],[2]]=>4
[[2,2,0,0],[2,2,0],[2,0],[0]]=>4
[[2,2,0,0],[2,2,0],[2,0],[1]]=>4
[[2,2,0,0],[2,2,0],[2,0],[2]]=>4
[[2,2,0,0],[2,2,0],[2,1],[1]]=>4
[[2,2,0,0],[2,2,0],[2,1],[2]]=>4
[[2,2,0,0],[2,2,0],[2,2],[2]]=>4
[[2,1,1,0],[1,1,0],[1,0],[0]]=>4
[[2,1,1,0],[1,1,0],[1,0],[1]]=>4
[[2,1,1,0],[1,1,0],[1,1],[1]]=>4
[[2,1,1,0],[1,1,1],[1,1],[1]]=>4
[[2,1,1,0],[2,1,0],[1,0],[0]]=>4
[[2,1,1,0],[2,1,0],[1,0],[1]]=>4
[[2,1,1,0],[2,1,0],[1,1],[1]]=>4
[[2,1,1,0],[2,1,0],[2,0],[0]]=>4
[[2,1,1,0],[2,1,0],[2,0],[1]]=>4
[[2,1,1,0],[2,1,0],[2,0],[2]]=>4
[[2,1,1,0],[2,1,0],[2,1],[1]]=>4
[[2,1,1,0],[2,1,0],[2,1],[2]]=>4
[[2,1,1,0],[2,1,1],[1,1],[1]]=>4
[[2,1,1,0],[2,1,1],[2,1],[1]]=>4
[[2,1,1,0],[2,1,1],[2,1],[2]]=>4
[[1,1,1,1],[1,1,1],[1,1],[1]]=>4
[[4,1,0,0],[1,0,0],[0,0],[0]]=>5
[[4,1,0,0],[1,0,0],[1,0],[0]]=>5
[[4,1,0,0],[1,0,0],[1,0],[1]]=>5
[[4,1,0,0],[1,1,0],[1,0],[0]]=>5
[[4,1,0,0],[1,1,0],[1,0],[1]]=>5
[[4,1,0,0],[1,1,0],[1,1],[1]]=>5
[[4,1,0,0],[2,0,0],[0,0],[0]]=>5
[[4,1,0,0],[2,0,0],[1,0],[0]]=>5
[[4,1,0,0],[2,0,0],[1,0],[1]]=>5
[[4,1,0,0],[2,0,0],[2,0],[0]]=>5
[[4,1,0,0],[2,0,0],[2,0],[1]]=>5
[[4,1,0,0],[2,0,0],[2,0],[2]]=>5
[[4,1,0,0],[2,1,0],[1,0],[0]]=>5
[[4,1,0,0],[2,1,0],[1,0],[1]]=>5
[[4,1,0,0],[2,1,0],[1,1],[1]]=>5
[[4,1,0,0],[2,1,0],[2,0],[0]]=>5
[[4,1,0,0],[2,1,0],[2,0],[1]]=>5
[[4,1,0,0],[2,1,0],[2,0],[2]]=>5
[[4,1,0,0],[2,1,0],[2,1],[1]]=>5
[[4,1,0,0],[2,1,0],[2,1],[2]]=>5
[[4,1,0,0],[3,0,0],[0,0],[0]]=>5
[[4,1,0,0],[3,0,0],[1,0],[0]]=>5
[[4,1,0,0],[3,0,0],[1,0],[1]]=>5
[[4,1,0,0],[3,0,0],[2,0],[0]]=>5
[[4,1,0,0],[3,0,0],[2,0],[1]]=>5
[[4,1,0,0],[3,0,0],[2,0],[2]]=>5
[[4,1,0,0],[3,0,0],[3,0],[0]]=>5
[[4,1,0,0],[3,0,0],[3,0],[1]]=>5
[[4,1,0,0],[3,0,0],[3,0],[2]]=>5
[[4,1,0,0],[3,0,0],[3,0],[3]]=>5
[[4,1,0,0],[3,1,0],[1,0],[0]]=>5
[[4,1,0,0],[3,1,0],[1,0],[1]]=>5
[[4,1,0,0],[3,1,0],[1,1],[1]]=>5
[[4,1,0,0],[3,1,0],[2,0],[0]]=>5
[[4,1,0,0],[3,1,0],[2,0],[1]]=>5
[[4,1,0,0],[3,1,0],[2,0],[2]]=>5
[[4,1,0,0],[3,1,0],[2,1],[1]]=>5
[[4,1,0,0],[3,1,0],[2,1],[2]]=>5
[[4,1,0,0],[3,1,0],[3,0],[0]]=>5
[[4,1,0,0],[3,1,0],[3,0],[1]]=>5
[[4,1,0,0],[3,1,0],[3,0],[2]]=>5
[[4,1,0,0],[3,1,0],[3,0],[3]]=>5
[[4,1,0,0],[3,1,0],[3,1],[1]]=>5
[[4,1,0,0],[3,1,0],[3,1],[2]]=>5
[[4,1,0,0],[3,1,0],[3,1],[3]]=>5
[[4,1,0,0],[4,0,0],[0,0],[0]]=>5
[[4,1,0,0],[4,0,0],[1,0],[0]]=>5
[[4,1,0,0],[4,0,0],[1,0],[1]]=>5
[[4,1,0,0],[4,0,0],[2,0],[0]]=>5
[[4,1,0,0],[4,0,0],[2,0],[1]]=>5
[[4,1,0,0],[4,0,0],[2,0],[2]]=>5
[[4,1,0,0],[4,0,0],[3,0],[0]]=>5
[[4,1,0,0],[4,0,0],[3,0],[1]]=>5
[[4,1,0,0],[4,0,0],[3,0],[2]]=>5
[[4,1,0,0],[4,0,0],[3,0],[3]]=>5
[[4,1,0,0],[4,0,0],[4,0],[0]]=>5
[[4,1,0,0],[4,0,0],[4,0],[1]]=>5
[[4,1,0,0],[4,0,0],[4,0],[2]]=>5
[[4,1,0,0],[4,0,0],[4,0],[3]]=>5
[[4,1,0,0],[4,0,0],[4,0],[4]]=>5
[[4,1,0,0],[4,1,0],[1,0],[0]]=>5
[[4,1,0,0],[4,1,0],[1,0],[1]]=>5
[[4,1,0,0],[4,1,0],[1,1],[1]]=>5
[[4,1,0,0],[4,1,0],[2,0],[0]]=>5
[[4,1,0,0],[4,1,0],[2,0],[1]]=>5
[[4,1,0,0],[4,1,0],[2,0],[2]]=>5
[[4,1,0,0],[4,1,0],[2,1],[1]]=>5
[[4,1,0,0],[4,1,0],[2,1],[2]]=>5
[[4,1,0,0],[4,1,0],[3,0],[0]]=>5
[[4,1,0,0],[4,1,0],[3,0],[1]]=>5
[[4,1,0,0],[4,1,0],[3,0],[2]]=>5
[[4,1,0,0],[4,1,0],[3,0],[3]]=>5
[[4,1,0,0],[4,1,0],[3,1],[1]]=>5
[[4,1,0,0],[4,1,0],[3,1],[2]]=>5
[[4,1,0,0],[4,1,0],[3,1],[3]]=>5
[[4,1,0,0],[4,1,0],[4,0],[0]]=>5
[[4,1,0,0],[4,1,0],[4,0],[1]]=>5
[[4,1,0,0],[4,1,0],[4,0],[2]]=>5
[[4,1,0,0],[4,1,0],[4,0],[3]]=>5
[[4,1,0,0],[4,1,0],[4,0],[4]]=>5
[[4,1,0,0],[4,1,0],[4,1],[1]]=>5
[[4,1,0,0],[4,1,0],[4,1],[2]]=>5
[[4,1,0,0],[4,1,0],[4,1],[3]]=>5
[[4,1,0,0],[4,1,0],[4,1],[4]]=>5
[[3,2,0,0],[2,0,0],[0,0],[0]]=>5
[[3,2,0,0],[2,0,0],[1,0],[0]]=>5
[[3,2,0,0],[2,0,0],[1,0],[1]]=>5
[[3,2,0,0],[2,0,0],[2,0],[0]]=>5
[[3,2,0,0],[2,0,0],[2,0],[1]]=>5
[[3,2,0,0],[2,0,0],[2,0],[2]]=>5
[[3,2,0,0],[2,1,0],[1,0],[0]]=>5
[[3,2,0,0],[2,1,0],[1,0],[1]]=>5
[[3,2,0,0],[2,1,0],[1,1],[1]]=>5
[[3,2,0,0],[2,1,0],[2,0],[0]]=>5
[[3,2,0,0],[2,1,0],[2,0],[1]]=>5
[[3,2,0,0],[2,1,0],[2,0],[2]]=>5
[[3,2,0,0],[2,1,0],[2,1],[1]]=>5
[[3,2,0,0],[2,1,0],[2,1],[2]]=>5
[[3,2,0,0],[2,2,0],[2,0],[0]]=>5
[[3,2,0,0],[2,2,0],[2,0],[1]]=>5
[[3,2,0,0],[2,2,0],[2,0],[2]]=>5
[[3,2,0,0],[2,2,0],[2,1],[1]]=>5
[[3,2,0,0],[2,2,0],[2,1],[2]]=>5
[[3,2,0,0],[2,2,0],[2,2],[2]]=>5
[[3,2,0,0],[3,0,0],[0,0],[0]]=>5
[[3,2,0,0],[3,0,0],[1,0],[0]]=>5
[[3,2,0,0],[3,0,0],[1,0],[1]]=>5
[[3,2,0,0],[3,0,0],[2,0],[0]]=>5
[[3,2,0,0],[3,0,0],[2,0],[1]]=>5
[[3,2,0,0],[3,0,0],[2,0],[2]]=>5
[[3,2,0,0],[3,0,0],[3,0],[0]]=>5
[[3,2,0,0],[3,0,0],[3,0],[1]]=>5
[[3,2,0,0],[3,0,0],[3,0],[2]]=>5
[[3,2,0,0],[3,0,0],[3,0],[3]]=>5
[[3,2,0,0],[3,1,0],[1,0],[0]]=>5
[[3,2,0,0],[3,1,0],[1,0],[1]]=>5
[[3,2,0,0],[3,1,0],[1,1],[1]]=>5
[[3,2,0,0],[3,1,0],[2,0],[0]]=>5
[[3,2,0,0],[3,1,0],[2,0],[1]]=>5
[[3,2,0,0],[3,1,0],[2,0],[2]]=>5
[[3,2,0,0],[3,1,0],[2,1],[1]]=>5
[[3,2,0,0],[3,1,0],[2,1],[2]]=>5
[[3,2,0,0],[3,1,0],[3,0],[0]]=>5
[[3,2,0,0],[3,1,0],[3,0],[1]]=>5
[[3,2,0,0],[3,1,0],[3,0],[2]]=>5
[[3,2,0,0],[3,1,0],[3,0],[3]]=>5
[[3,2,0,0],[3,1,0],[3,1],[1]]=>5
[[3,2,0,0],[3,1,0],[3,1],[2]]=>5
[[3,2,0,0],[3,1,0],[3,1],[3]]=>5
[[3,2,0,0],[3,2,0],[2,0],[0]]=>5
[[3,2,0,0],[3,2,0],[2,0],[1]]=>5
[[3,2,0,0],[3,2,0],[2,0],[2]]=>5
[[3,2,0,0],[3,2,0],[2,1],[1]]=>5
[[3,2,0,0],[3,2,0],[2,1],[2]]=>5
[[3,2,0,0],[3,2,0],[2,2],[2]]=>5
[[3,2,0,0],[3,2,0],[3,0],[0]]=>5
[[3,2,0,0],[3,2,0],[3,0],[1]]=>5
[[3,2,0,0],[3,2,0],[3,0],[2]]=>5
[[3,2,0,0],[3,2,0],[3,0],[3]]=>5
[[3,2,0,0],[3,2,0],[3,1],[1]]=>5
[[3,2,0,0],[3,2,0],[3,1],[2]]=>5
[[3,2,0,0],[3,2,0],[3,1],[3]]=>5
[[3,2,0,0],[3,2,0],[3,2],[2]]=>5
[[3,2,0,0],[3,2,0],[3,2],[3]]=>5
[[3,1,1,0],[1,1,0],[1,0],[0]]=>5
[[3,1,1,0],[1,1,0],[1,0],[1]]=>5
[[3,1,1,0],[1,1,0],[1,1],[1]]=>5
[[3,1,1,0],[1,1,1],[1,1],[1]]=>5
[[3,1,1,0],[2,1,0],[1,0],[0]]=>5
[[3,1,1,0],[2,1,0],[1,0],[1]]=>5
[[3,1,1,0],[2,1,0],[1,1],[1]]=>5
[[3,1,1,0],[2,1,0],[2,0],[0]]=>5
[[3,1,1,0],[2,1,0],[2,0],[1]]=>5
[[3,1,1,0],[2,1,0],[2,0],[2]]=>5
[[3,1,1,0],[2,1,0],[2,1],[1]]=>5
[[3,1,1,0],[2,1,0],[2,1],[2]]=>5
[[3,1,1,0],[2,1,1],[1,1],[1]]=>5
[[3,1,1,0],[2,1,1],[2,1],[1]]=>5
[[3,1,1,0],[2,1,1],[2,1],[2]]=>5
[[3,1,1,0],[3,1,0],[1,0],[0]]=>5
[[3,1,1,0],[3,1,0],[1,0],[1]]=>5
[[3,1,1,0],[3,1,0],[1,1],[1]]=>5
[[3,1,1,0],[3,1,0],[2,0],[0]]=>5
[[3,1,1,0],[3,1,0],[2,0],[1]]=>5
[[3,1,1,0],[3,1,0],[2,0],[2]]=>5
[[3,1,1,0],[3,1,0],[2,1],[1]]=>5
[[3,1,1,0],[3,1,0],[2,1],[2]]=>5
[[3,1,1,0],[3,1,0],[3,0],[0]]=>5
[[3,1,1,0],[3,1,0],[3,0],[1]]=>5
[[3,1,1,0],[3,1,0],[3,0],[2]]=>5
[[3,1,1,0],[3,1,0],[3,0],[3]]=>5
[[3,1,1,0],[3,1,0],[3,1],[1]]=>5
[[3,1,1,0],[3,1,0],[3,1],[2]]=>5
[[3,1,1,0],[3,1,0],[3,1],[3]]=>5
[[3,1,1,0],[3,1,1],[1,1],[1]]=>5
[[3,1,1,0],[3,1,1],[2,1],[1]]=>5
[[3,1,1,0],[3,1,1],[2,1],[2]]=>5
[[3,1,1,0],[3,1,1],[3,1],[1]]=>5
[[3,1,1,0],[3,1,1],[3,1],[2]]=>5
[[3,1,1,0],[3,1,1],[3,1],[3]]=>5
[[2,2,1,0],[2,1,0],[1,0],[0]]=>5
[[2,2,1,0],[2,1,0],[1,0],[1]]=>5
[[2,2,1,0],[2,1,0],[1,1],[1]]=>5
[[2,2,1,0],[2,1,0],[2,0],[0]]=>5
[[2,2,1,0],[2,1,0],[2,0],[1]]=>5
[[2,2,1,0],[2,1,0],[2,0],[2]]=>5
[[2,2,1,0],[2,1,0],[2,1],[1]]=>5
[[2,2,1,0],[2,1,0],[2,1],[2]]=>5
[[2,2,1,0],[2,1,1],[1,1],[1]]=>5
[[2,2,1,0],[2,1,1],[2,1],[1]]=>5
[[2,2,1,0],[2,1,1],[2,1],[2]]=>5
[[2,2,1,0],[2,2,0],[2,0],[0]]=>5
[[2,2,1,0],[2,2,0],[2,0],[1]]=>5
[[2,2,1,0],[2,2,0],[2,0],[2]]=>5
[[2,2,1,0],[2,2,0],[2,1],[1]]=>5
[[2,2,1,0],[2,2,0],[2,1],[2]]=>5
[[2,2,1,0],[2,2,0],[2,2],[2]]=>5
[[2,2,1,0],[2,2,1],[2,1],[1]]=>5
[[2,2,1,0],[2,2,1],[2,1],[2]]=>5
[[2,2,1,0],[2,2,1],[2,2],[2]]=>5
[[2,1,1,1],[1,1,1],[1,1],[1]]=>5
[[2,1,1,1],[2,1,1],[1,1],[1]]=>5
[[2,1,1,1],[2,1,1],[2,1],[1]]=>5
[[2,1,1,1],[2,1,1],[2,1],[2]]=>5
[[4,1,1,0],[4,1,0],[4,1],[4]]=>6
[[4,1,1,0],[4,1,0],[4,0],[4]]=>6
[[4,1,1,0],[4,1,0],[4,1],[3]]=>6
[[4,1,1,0],[4,1,0],[4,0],[3]]=>6
[[4,1,1,0],[4,1,0],[3,1],[3]]=>6
[[4,1,1,0],[3,1,1],[3,1],[3]]=>6
[[4,1,1,0],[3,1,0],[3,1],[3]]=>6
[[4,1,1,0],[4,1,0],[3,0],[3]]=>6
[[4,1,1,0],[3,1,0],[3,0],[3]]=>6
[[4,1,1,0],[4,1,0],[4,1],[2]]=>6
[[4,1,1,0],[4,1,0],[4,0],[2]]=>6
[[4,1,1,0],[4,1,0],[3,1],[2]]=>6
[[4,1,1,0],[3,1,1],[3,1],[2]]=>6
[[4,1,1,0],[3,1,0],[3,1],[2]]=>6
[[4,1,1,0],[4,1,0],[3,0],[2]]=>6
[[4,1,1,0],[4,1,0],[2,1],[2]]=>6
[[4,1,1,0],[3,1,1],[2,1],[2]]=>6
[[4,1,1,0],[3,1,0],[3,0],[2]]=>6
[[4,1,1,0],[3,1,0],[2,1],[2]]=>6
[[4,1,1,0],[2,1,1],[2,1],[2]]=>6
[[4,1,1,0],[2,1,0],[2,1],[2]]=>6
[[4,1,1,0],[4,1,0],[2,0],[2]]=>6
[[4,1,1,0],[3,1,0],[2,0],[2]]=>6
[[4,1,1,0],[2,1,0],[2,0],[2]]=>6
[[4,1,1,0],[4,1,0],[4,1],[1]]=>6
[[4,1,1,0],[4,1,0],[4,0],[1]]=>6
[[4,1,1,0],[4,1,0],[3,1],[1]]=>6
[[4,1,1,0],[3,1,1],[3,1],[1]]=>6
[[4,1,1,0],[3,1,0],[3,1],[1]]=>6
[[4,1,1,0],[4,1,0],[3,0],[1]]=>6
[[4,1,1,0],[4,1,0],[2,1],[1]]=>6
[[4,1,1,0],[3,1,1],[2,1],[1]]=>6
[[4,1,1,0],[3,1,0],[3,0],[1]]=>6
[[4,1,1,0],[3,1,0],[2,1],[1]]=>6
[[4,1,1,0],[2,1,1],[2,1],[1]]=>6
[[4,1,1,0],[2,1,0],[2,1],[1]]=>6
[[4,1,1,0],[4,1,0],[2,0],[1]]=>6
[[4,1,1,0],[4,1,0],[1,1],[1]]=>6
[[4,1,1,0],[3,1,1],[1,1],[1]]=>6
[[4,1,1,0],[3,1,0],[2,0],[1]]=>6
[[4,1,1,0],[3,1,0],[1,1],[1]]=>6
[[4,1,1,0],[2,1,1],[1,1],[1]]=>6
[[4,1,1,0],[2,1,0],[2,0],[1]]=>6
[[4,1,1,0],[2,1,0],[1,1],[1]]=>6
[[4,1,1,0],[1,1,1],[1,1],[1]]=>6
[[4,1,1,0],[1,1,0],[1,1],[1]]=>6
[[4,1,1,0],[4,1,0],[1,0],[1]]=>6
[[4,1,1,0],[3,1,0],[1,0],[1]]=>6
[[4,1,1,0],[2,1,0],[1,0],[1]]=>6
[[4,1,1,0],[1,1,0],[1,0],[1]]=>6
[[4,1,1,0],[4,1,0],[4,0],[0]]=>6
[[4,1,1,0],[4,1,0],[3,0],[0]]=>6
[[4,1,1,0],[3,1,0],[3,0],[0]]=>6
[[4,1,1,0],[4,1,0],[2,0],[0]]=>6
[[4,1,1,0],[3,1,0],[2,0],[0]]=>6
[[4,1,1,0],[2,1,0],[2,0],[0]]=>6
[[4,1,1,0],[4,1,0],[1,0],[0]]=>6
[[4,1,1,0],[3,1,0],[1,0],[0]]=>6
[[4,1,1,0],[2,1,0],[1,0],[0]]=>6
[[4,1,1,0],[1,1,0],[1,0],[0]]=>6
[[3,3,0,0],[3,2,0],[3,2],[3]]=>6
[[3,3,0,0],[3,2,0],[3,1],[3]]=>6
[[3,3,0,0],[3,1,0],[3,1],[3]]=>6
[[3,3,0,0],[3,2,0],[3,0],[3]]=>6
[[3,3,0,0],[3,1,0],[3,0],[3]]=>6
[[3,3,0,0],[3,0,0],[3,0],[3]]=>6
[[3,3,0,0],[3,2,0],[3,2],[2]]=>6
[[3,3,0,0],[3,2,0],[3,1],[2]]=>6
[[3,3,0,0],[3,2,0],[2,2],[2]]=>6
[[3,3,0,0],[3,1,0],[3,1],[2]]=>6
[[3,3,0,0],[3,2,0],[3,0],[2]]=>6
[[3,3,0,0],[3,2,0],[2,1],[2]]=>6
[[3,3,0,0],[3,1,0],[3,0],[2]]=>6
[[3,3,0,0],[3,1,0],[2,1],[2]]=>6
[[3,3,0,0],[3,0,0],[3,0],[2]]=>6
[[3,3,0,0],[3,2,0],[2,0],[2]]=>6
[[3,3,0,0],[3,1,0],[2,0],[2]]=>6
[[3,3,0,0],[3,0,0],[2,0],[2]]=>6
[[3,3,0,0],[3,2,0],[3,1],[1]]=>6
[[3,3,0,0],[3,1,0],[3,1],[1]]=>6
[[3,3,0,0],[3,2,0],[3,0],[1]]=>6
[[3,3,0,0],[3,2,0],[2,1],[1]]=>6
[[3,3,0,0],[3,1,0],[3,0],[1]]=>6
[[3,3,0,0],[3,1,0],[2,1],[1]]=>6
[[3,3,0,0],[3,0,0],[3,0],[1]]=>6
[[3,3,0,0],[3,2,0],[2,0],[1]]=>6
[[3,3,0,0],[3,1,0],[2,0],[1]]=>6
[[3,3,0,0],[3,1,0],[1,1],[1]]=>6
[[3,3,0,0],[3,0,0],[2,0],[1]]=>6
[[3,3,0,0],[3,1,0],[1,0],[1]]=>6
[[3,3,0,0],[3,0,0],[1,0],[1]]=>6
[[3,3,0,0],[3,2,0],[3,0],[0]]=>6
[[3,3,0,0],[3,1,0],[3,0],[0]]=>6
[[3,3,0,0],[3,0,0],[3,0],[0]]=>6
[[3,3,0,0],[3,2,0],[2,0],[0]]=>6
[[3,3,0,0],[3,1,0],[2,0],[0]]=>6
[[3,3,0,0],[3,0,0],[2,0],[0]]=>6
[[3,3,0,0],[3,1,0],[1,0],[0]]=>6
[[3,3,0,0],[3,0,0],[1,0],[0]]=>6
[[3,3,0,0],[3,0,0],[0,0],[0]]=>6
[[3,2,1,0],[3,2,0],[3,2],[3]]=>6
[[3,2,1,0],[3,2,0],[3,1],[3]]=>6
[[3,2,1,0],[3,1,1],[3,1],[3]]=>6
[[3,2,1,0],[3,1,0],[3,1],[3]]=>6
[[3,2,1,0],[3,2,0],[3,0],[3]]=>6
[[3,2,1,0],[3,1,0],[3,0],[3]]=>6
[[3,2,1,0],[3,2,0],[3,2],[2]]=>6
[[3,2,1,0],[3,2,0],[3,1],[2]]=>6
[[3,2,1,0],[3,1,1],[3,1],[2]]=>6
[[3,2,1,0],[3,2,0],[2,2],[2]]=>6
[[3,2,1,0],[2,2,1],[2,2],[2]]=>6
[[3,2,1,0],[3,1,0],[3,1],[2]]=>6
[[3,2,1,0],[2,2,0],[2,2],[2]]=>6
[[3,2,1,0],[3,2,0],[3,0],[2]]=>6
[[3,2,1,0],[3,2,0],[2,1],[2]]=>6
[[3,2,1,0],[3,1,1],[2,1],[2]]=>6
[[3,2,1,0],[2,2,1],[2,1],[2]]=>6
[[3,2,1,0],[3,1,0],[3,0],[2]]=>6
[[3,2,1,0],[3,1,0],[2,1],[2]]=>6
[[3,2,1,0],[2,2,0],[2,1],[2]]=>6
[[3,2,1,0],[2,1,1],[2,1],[2]]=>6
[[3,2,1,0],[2,1,0],[2,1],[2]]=>6
[[3,2,1,0],[3,2,0],[2,0],[2]]=>6
[[3,2,1,0],[3,1,0],[2,0],[2]]=>6
[[3,2,1,0],[2,2,0],[2,0],[2]]=>6
[[3,2,1,0],[2,1,0],[2,0],[2]]=>6
[[3,2,1,0],[3,2,0],[3,1],[1]]=>6
[[3,2,1,0],[3,1,1],[3,1],[1]]=>6
[[3,2,1,0],[3,1,0],[3,1],[1]]=>6
[[3,2,1,0],[3,2,0],[3,0],[1]]=>6
[[3,2,1,0],[3,2,0],[2,1],[1]]=>6
[[3,2,1,0],[3,1,1],[2,1],[1]]=>6
[[3,2,1,0],[2,2,1],[2,1],[1]]=>6
[[3,2,1,0],[3,1,0],[3,0],[1]]=>6
[[3,2,1,0],[3,1,0],[2,1],[1]]=>6
[[3,2,1,0],[2,2,0],[2,1],[1]]=>6
[[3,2,1,0],[2,1,1],[2,1],[1]]=>6
[[3,2,1,0],[2,1,0],[2,1],[1]]=>6
[[3,2,1,0],[3,2,0],[2,0],[1]]=>6
[[3,2,1,0],[3,1,1],[1,1],[1]]=>6
[[3,2,1,0],[3,1,0],[2,0],[1]]=>6
[[3,2,1,0],[2,2,0],[2,0],[1]]=>6
[[3,2,1,0],[3,1,0],[1,1],[1]]=>6
[[3,2,1,0],[2,1,1],[1,1],[1]]=>6
[[3,2,1,0],[2,1,0],[2,0],[1]]=>6
[[3,2,1,0],[2,1,0],[1,1],[1]]=>6
[[3,2,1,0],[3,1,0],[1,0],[1]]=>6
[[3,2,1,0],[2,1,0],[1,0],[1]]=>6
[[3,2,1,0],[3,2,0],[3,0],[0]]=>6
[[3,2,1,0],[3,1,0],[3,0],[0]]=>6
[[3,2,1,0],[3,2,0],[2,0],[0]]=>6
[[3,2,1,0],[3,1,0],[2,0],[0]]=>6
[[3,2,1,0],[2,2,0],[2,0],[0]]=>6
[[3,2,1,0],[2,1,0],[2,0],[0]]=>6
[[3,2,1,0],[3,1,0],[1,0],[0]]=>6
[[3,2,1,0],[2,1,0],[1,0],[0]]=>6
[[3,1,1,1],[3,1,1],[3,1],[3]]=>6
[[3,1,1,1],[3,1,1],[3,1],[2]]=>6
[[3,1,1,1],[3,1,1],[2,1],[2]]=>6
[[3,1,1,1],[2,1,1],[2,1],[2]]=>6
[[3,1,1,1],[3,1,1],[3,1],[1]]=>6
[[3,1,1,1],[3,1,1],[2,1],[1]]=>6
[[3,1,1,1],[2,1,1],[2,1],[1]]=>6
[[3,1,1,1],[3,1,1],[1,1],[1]]=>6
[[3,1,1,1],[2,1,1],[1,1],[1]]=>6
[[3,1,1,1],[1,1,1],[1,1],[1]]=>6
[[2,2,2,0],[2,2,1],[2,2],[2]]=>6
[[2,2,2,0],[2,2,0],[2,2],[2]]=>6
[[2,2,2,0],[2,2,1],[2,1],[2]]=>6
[[2,2,2,0],[2,2,0],[2,1],[2]]=>6
[[2,2,2,0],[2,2,0],[2,0],[2]]=>6
[[2,2,2,0],[2,2,1],[2,1],[1]]=>6
[[2,2,2,0],[2,2,0],[2,1],[1]]=>6
[[2,2,2,0],[2,2,0],[2,0],[1]]=>6
[[2,2,2,0],[2,2,0],[2,0],[0]]=>6
[[2,2,1,1],[2,2,1],[2,2],[2]]=>6
[[2,2,1,1],[2,2,1],[2,1],[2]]=>6
[[2,2,1,1],[2,1,1],[2,1],[2]]=>6
[[2,2,1,1],[2,2,1],[2,1],[1]]=>6
[[2,2,1,1],[2,1,1],[2,1],[1]]=>6
[[2,2,1,1],[2,1,1],[1,1],[1]]=>6
[[0]]=>0
[[0,0],[0]]=>0
[[0,0,0],[0,0],[0]]=>0
[[3,3,2],[3,2],[2]]=>8
[[3,3,2],[3,2],[3]]=>8
[[3,3,2],[3,3],[3]]=>8
[[3,3,3],[3,3],[3]]=>9
[[4,2,2],[2,2],[2]]=>8
[[4,2,2],[3,2],[2]]=>8
[[4,2,2],[3,2],[3]]=>8
[[4,2,2],[4,2],[2]]=>8
[[4,2,2],[4,2],[3]]=>8
[[4,2,2],[4,2],[4]]=>8
[[4,3,0],[4,3],[3]]=>7
[[4,3,0],[4,3],[4]]=>7
[[4,3,1],[3,1],[1]]=>8
[[4,3,1],[3,1],[2]]=>8
[[4,3,1],[3,1],[3]]=>8
[[4,3,1],[3,2],[2]]=>8
[[4,3,1],[3,2],[3]]=>8
[[4,3,1],[3,3],[3]]=>8
[[4,3,1],[4,1],[1]]=>8
[[4,3,1],[4,1],[2]]=>8
[[4,3,1],[4,1],[3]]=>8
[[4,3,1],[4,1],[4]]=>8
[[4,3,1],[4,2],[2]]=>8
[[4,3,1],[4,2],[3]]=>8
[[4,3,1],[4,2],[4]]=>8
[[4,3,1],[4,3],[3]]=>8
[[4,3,1],[4,3],[4]]=>8
[[4,3,2],[3,2],[2]]=>9
[[4,3,2],[3,2],[3]]=>9
[[4,3,2],[3,3],[3]]=>9
[[4,3,2],[4,2],[2]]=>9
[[4,3,2],[4,2],[3]]=>9
[[4,3,2],[4,2],[4]]=>9
[[4,3,2],[4,3],[3]]=>9
[[4,3,2],[4,3],[4]]=>9
[[4,3,3],[3,3],[3]]=>10
[[4,3,3],[4,3],[3]]=>10
[[4,3,3],[4,3],[4]]=>10
[[4,4,0],[4,0],[0]]=>8
[[4,4,0],[4,0],[1]]=>8
[[4,4,0],[4,0],[2]]=>8
[[4,4,0],[4,0],[3]]=>8
[[4,4,0],[4,0],[4]]=>8
[[4,4,0],[4,1],[1]]=>8
[[4,4,0],[4,1],[2]]=>8
[[4,4,0],[4,1],[3]]=>8
[[4,4,0],[4,1],[4]]=>8
[[4,4,0],[4,2],[2]]=>8
[[4,4,0],[4,2],[3]]=>8
[[4,4,0],[4,2],[4]]=>8
[[4,4,0],[4,3],[3]]=>8
[[4,4,0],[4,3],[4]]=>8
[[4,4,0],[4,4],[4]]=>8
[[4,4,1],[4,1],[1]]=>9
[[4,4,1],[4,1],[2]]=>9
[[4,4,1],[4,1],[3]]=>9
[[4,4,1],[4,1],[4]]=>9
[[4,4,1],[4,2],[2]]=>9
[[4,4,1],[4,2],[3]]=>9
[[4,4,1],[4,2],[4]]=>9
[[4,4,1],[4,3],[3]]=>9
[[4,4,1],[4,3],[4]]=>9
[[4,4,1],[4,4],[4]]=>9
[[4,4,2],[4,2],[2]]=>10
[[4,4,2],[4,2],[3]]=>10
[[4,4,2],[4,2],[4]]=>10
[[4,4,2],[4,3],[3]]=>10
[[4,4,2],[4,3],[4]]=>10
[[4,4,2],[4,4],[4]]=>10
[[4,4,3],[4,3],[3]]=>11
[[4,4,3],[4,3],[4]]=>11
[[4,4,3],[4,4],[4]]=>11
[[4,4,4],[4,4],[4]]=>12
[[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[2,2,2,0],[2,2,2],[2,2],[2]]=>6
[[2,2,2,1],[2,2,1],[2,1],[1]]=>7
[[2,2,2,1],[2,2,1],[2,1],[2]]=>7
[[2,2,2,1],[2,2,1],[2,2],[2]]=>7
[[2,2,2,1],[2,2,2],[2,2],[2]]=>7
[[2,2,2,2],[2,2,2],[2,2],[2]]=>8
[[3,2,1,0],[3,2,1],[2,1],[1]]=>6
[[3,2,1,0],[3,2,1],[2,1],[2]]=>6
[[3,2,1,0],[3,2,1],[2,2],[2]]=>6
[[3,2,1,0],[3,2,1],[3,1],[1]]=>6
[[3,2,1,0],[3,2,1],[3,1],[2]]=>6
[[3,2,1,0],[3,2,1],[3,1],[3]]=>6
[[3,2,1,0],[3,2,1],[3,2],[2]]=>6
[[3,2,1,0],[3,2,1],[3,2],[3]]=>6
[[3,2,1,1],[2,1,1],[1,1],[1]]=>7
[[3,2,1,1],[2,1,1],[2,1],[1]]=>7
[[3,2,1,1],[2,1,1],[2,1],[2]]=>7
[[3,2,1,1],[2,2,1],[2,1],[1]]=>7
[[3,2,1,1],[2,2,1],[2,1],[2]]=>7
[[3,2,1,1],[2,2,1],[2,2],[2]]=>7
[[3,2,1,1],[3,1,1],[1,1],[1]]=>7
[[3,2,1,1],[3,1,1],[2,1],[1]]=>7
[[3,2,1,1],[3,1,1],[2,1],[2]]=>7
[[3,2,1,1],[3,1,1],[3,1],[1]]=>7
[[3,2,1,1],[3,1,1],[3,1],[2]]=>7
[[3,2,1,1],[3,1,1],[3,1],[3]]=>7
[[3,2,1,1],[3,2,1],[2,1],[1]]=>7
[[3,2,1,1],[3,2,1],[2,1],[2]]=>7
[[3,2,1,1],[3,2,1],[2,2],[2]]=>7
[[3,2,1,1],[3,2,1],[3,1],[1]]=>7
[[3,2,1,1],[3,2,1],[3,1],[2]]=>7
[[3,2,1,1],[3,2,1],[3,1],[3]]=>7
[[3,2,1,1],[3,2,1],[3,2],[2]]=>7
[[3,2,1,1],[3,2,1],[3,2],[3]]=>7
[[3,2,2,0],[2,2,0],[2,0],[0]]=>7
[[3,2,2,0],[2,2,0],[2,0],[1]]=>7
[[3,2,2,0],[2,2,0],[2,0],[2]]=>7
[[3,2,2,0],[2,2,0],[2,1],[1]]=>7
[[3,2,2,0],[2,2,0],[2,1],[2]]=>7
[[3,2,2,0],[2,2,0],[2,2],[2]]=>7
[[3,2,2,0],[2,2,1],[2,1],[1]]=>7
[[3,2,2,0],[2,2,1],[2,1],[2]]=>7
[[3,2,2,0],[2,2,1],[2,2],[2]]=>7
[[3,2,2,0],[2,2,2],[2,2],[2]]=>7
[[3,2,2,0],[3,2,0],[2,0],[0]]=>7
[[3,2,2,0],[3,2,0],[2,0],[1]]=>7
[[3,2,2,0],[3,2,0],[2,0],[2]]=>7
[[3,2,2,0],[3,2,0],[2,1],[1]]=>7
[[3,2,2,0],[3,2,0],[2,1],[2]]=>7
[[3,2,2,0],[3,2,0],[2,2],[2]]=>7
[[3,2,2,0],[3,2,0],[3,0],[0]]=>7
[[3,2,2,0],[3,2,0],[3,0],[1]]=>7
[[3,2,2,0],[3,2,0],[3,0],[2]]=>7
[[3,2,2,0],[3,2,0],[3,0],[3]]=>7
[[3,2,2,0],[3,2,0],[3,1],[1]]=>7
[[3,2,2,0],[3,2,0],[3,1],[2]]=>7
[[3,2,2,0],[3,2,0],[3,1],[3]]=>7
[[3,2,2,0],[3,2,0],[3,2],[2]]=>7
[[3,2,2,0],[3,2,0],[3,2],[3]]=>7
[[3,2,2,0],[3,2,1],[2,1],[1]]=>7
[[3,2,2,0],[3,2,1],[2,1],[2]]=>7
[[3,2,2,0],[3,2,1],[2,2],[2]]=>7
[[3,2,2,0],[3,2,1],[3,1],[1]]=>7
[[3,2,2,0],[3,2,1],[3,1],[2]]=>7
[[3,2,2,0],[3,2,1],[3,1],[3]]=>7
[[3,2,2,0],[3,2,1],[3,2],[2]]=>7
[[3,2,2,0],[3,2,1],[3,2],[3]]=>7
[[3,2,2,0],[3,2,2],[2,2],[2]]=>7
[[3,2,2,0],[3,2,2],[3,2],[2]]=>7
[[3,2,2,0],[3,2,2],[3,2],[3]]=>7
[[3,2,2,1],[2,2,1],[2,1],[1]]=>8
[[3,2,2,1],[2,2,1],[2,1],[2]]=>8
[[3,2,2,1],[2,2,1],[2,2],[2]]=>8
[[3,2,2,1],[2,2,2],[2,2],[2]]=>8
[[3,2,2,1],[3,2,1],[2,1],[1]]=>8
[[3,2,2,1],[3,2,1],[2,1],[2]]=>8
[[3,2,2,1],[3,2,1],[2,2],[2]]=>8
[[3,2,2,1],[3,2,1],[3,1],[1]]=>8
[[3,2,2,1],[3,2,1],[3,1],[2]]=>8
[[3,2,2,1],[3,2,1],[3,1],[3]]=>8
[[3,2,2,1],[3,2,1],[3,2],[2]]=>8
[[3,2,2,1],[3,2,1],[3,2],[3]]=>8
[[3,2,2,1],[3,2,2],[2,2],[2]]=>8
[[3,2,2,1],[3,2,2],[3,2],[2]]=>8
[[3,2,2,1],[3,2,2],[3,2],[3]]=>8
[[3,2,2,2],[2,2,2],[2,2],[2]]=>9
[[3,2,2,2],[3,2,2],[2,2],[2]]=>9
[[3,2,2,2],[3,2,2],[3,2],[2]]=>9
[[3,2,2,2],[3,2,2],[3,2],[3]]=>9
[[3,3,0,0],[3,3,0],[3,0],[0]]=>6
[[3,3,0,0],[3,3,0],[3,0],[1]]=>6
[[3,3,0,0],[3,3,0],[3,0],[2]]=>6
[[3,3,0,0],[3,3,0],[3,0],[3]]=>6
[[3,3,0,0],[3,3,0],[3,1],[1]]=>6
[[3,3,0,0],[3,3,0],[3,1],[2]]=>6
[[3,3,0,0],[3,3,0],[3,1],[3]]=>6
[[3,3,0,0],[3,3,0],[3,2],[2]]=>6
[[3,3,0,0],[3,3,0],[3,2],[3]]=>6
[[3,3,0,0],[3,3,0],[3,3],[3]]=>6
[[3,3,1,0],[3,1,0],[1,0],[0]]=>7
[[3,3,1,0],[3,1,0],[1,0],[1]]=>7
[[3,3,1,0],[3,1,0],[1,1],[1]]=>7
[[3,3,1,0],[3,1,0],[2,0],[0]]=>7
[[3,3,1,0],[3,1,0],[2,0],[1]]=>7
[[3,3,1,0],[3,1,0],[2,0],[2]]=>7
[[3,3,1,0],[3,1,0],[2,1],[1]]=>7
[[3,3,1,0],[3,1,0],[2,1],[2]]=>7
[[3,3,1,0],[3,1,0],[3,0],[0]]=>7
[[3,3,1,0],[3,1,0],[3,0],[1]]=>7
[[3,3,1,0],[3,1,0],[3,0],[2]]=>7
[[3,3,1,0],[3,1,0],[3,0],[3]]=>7
[[3,3,1,0],[3,1,0],[3,1],[1]]=>7
[[3,3,1,0],[3,1,0],[3,1],[2]]=>7
[[3,3,1,0],[3,1,0],[3,1],[3]]=>7
[[3,3,1,0],[3,1,1],[1,1],[1]]=>7
[[3,3,1,0],[3,1,1],[2,1],[1]]=>7
[[3,3,1,0],[3,1,1],[2,1],[2]]=>7
[[3,3,1,0],[3,1,1],[3,1],[1]]=>7
[[3,3,1,0],[3,1,1],[3,1],[2]]=>7
[[3,3,1,0],[3,1,1],[3,1],[3]]=>7
[[3,3,1,0],[3,2,0],[2,0],[0]]=>7
[[3,3,1,0],[3,2,0],[2,0],[1]]=>7
[[3,3,1,0],[3,2,0],[2,0],[2]]=>7
[[3,3,1,0],[3,2,0],[2,1],[1]]=>7
[[3,3,1,0],[3,2,0],[2,1],[2]]=>7
[[3,3,1,0],[3,2,0],[2,2],[2]]=>7
[[3,3,1,0],[3,2,0],[3,0],[0]]=>7
[[3,3,1,0],[3,2,0],[3,0],[1]]=>7
[[3,3,1,0],[3,2,0],[3,0],[2]]=>7
[[3,3,1,0],[3,2,0],[3,0],[3]]=>7
[[3,3,1,0],[3,2,0],[3,1],[1]]=>7
[[3,3,1,0],[3,2,0],[3,1],[2]]=>7
[[3,3,1,0],[3,2,0],[3,1],[3]]=>7
[[3,3,1,0],[3,2,0],[3,2],[2]]=>7
[[3,3,1,0],[3,2,0],[3,2],[3]]=>7
[[3,3,1,0],[3,2,1],[2,1],[1]]=>7
[[3,3,1,0],[3,2,1],[2,1],[2]]=>7
[[3,3,1,0],[3,2,1],[2,2],[2]]=>7
[[3,3,1,0],[3,2,1],[3,1],[1]]=>7
[[3,3,1,0],[3,2,1],[3,1],[2]]=>7
[[3,3,1,0],[3,2,1],[3,1],[3]]=>7
[[3,3,1,0],[3,2,1],[3,2],[2]]=>7
[[3,3,1,0],[3,2,1],[3,2],[3]]=>7
[[3,3,1,0],[3,3,0],[3,0],[0]]=>7
[[3,3,1,0],[3,3,0],[3,0],[1]]=>7
[[3,3,1,0],[3,3,0],[3,0],[2]]=>7
[[3,3,1,0],[3,3,0],[3,0],[3]]=>7
[[3,3,1,0],[3,3,0],[3,1],[1]]=>7
[[3,3,1,0],[3,3,0],[3,1],[2]]=>7
[[3,3,1,0],[3,3,0],[3,1],[3]]=>7
[[3,3,1,0],[3,3,0],[3,2],[2]]=>7
[[3,3,1,0],[3,3,0],[3,2],[3]]=>7
[[3,3,1,0],[3,3,0],[3,3],[3]]=>7
[[3,3,1,0],[3,3,1],[3,1],[1]]=>7
[[3,3,1,0],[3,3,1],[3,1],[2]]=>7
[[3,3,1,0],[3,3,1],[3,1],[3]]=>7
[[3,3,1,0],[3,3,1],[3,2],[2]]=>7
[[3,3,1,0],[3,3,1],[3,2],[3]]=>7
[[3,3,1,0],[3,3,1],[3,3],[3]]=>7
[[3,3,1,1],[3,1,1],[1,1],[1]]=>8
[[3,3,1,1],[3,1,1],[2,1],[1]]=>8
[[3,3,1,1],[3,1,1],[2,1],[2]]=>8
[[3,3,1,1],[3,1,1],[3,1],[1]]=>8
[[3,3,1,1],[3,1,1],[3,1],[2]]=>8
[[3,3,1,1],[3,1,1],[3,1],[3]]=>8
[[3,3,1,1],[3,2,1],[2,1],[1]]=>8
[[3,3,1,1],[3,2,1],[2,1],[2]]=>8
[[3,3,1,1],[3,2,1],[2,2],[2]]=>8
[[3,3,1,1],[3,2,1],[3,1],[1]]=>8
[[3,3,1,1],[3,2,1],[3,1],[2]]=>8
[[3,3,1,1],[3,2,1],[3,1],[3]]=>8
[[3,3,1,1],[3,2,1],[3,2],[2]]=>8
[[3,3,1,1],[3,2,1],[3,2],[3]]=>8
[[3,3,1,1],[3,3,1],[3,1],[1]]=>8
[[3,3,1,1],[3,3,1],[3,1],[2]]=>8
[[3,3,1,1],[3,3,1],[3,1],[3]]=>8
[[3,3,1,1],[3,3,1],[3,2],[2]]=>8
[[3,3,1,1],[3,3,1],[3,2],[3]]=>8
[[3,3,1,1],[3,3,1],[3,3],[3]]=>8
[[3,3,2,0],[3,2,0],[2,0],[0]]=>8
[[3,3,2,0],[3,2,0],[2,0],[1]]=>8
[[3,3,2,0],[3,2,0],[2,0],[2]]=>8
[[3,3,2,0],[3,2,0],[2,1],[1]]=>8
[[3,3,2,0],[3,2,0],[2,1],[2]]=>8
[[3,3,2,0],[3,2,0],[2,2],[2]]=>8
[[3,3,2,0],[3,2,0],[3,0],[0]]=>8
[[3,3,2,0],[3,2,0],[3,0],[1]]=>8
[[3,3,2,0],[3,2,0],[3,0],[2]]=>8
[[3,3,2,0],[3,2,0],[3,0],[3]]=>8
[[3,3,2,0],[3,2,0],[3,1],[1]]=>8
[[3,3,2,0],[3,2,0],[3,1],[2]]=>8
[[3,3,2,0],[3,2,0],[3,1],[3]]=>8
[[3,3,2,0],[3,2,0],[3,2],[2]]=>8
[[3,3,2,0],[3,2,0],[3,2],[3]]=>8
[[3,3,2,0],[3,2,1],[2,1],[1]]=>8
[[3,3,2,0],[3,2,1],[2,1],[2]]=>8
[[3,3,2,0],[3,2,1],[2,2],[2]]=>8
[[3,3,2,0],[3,2,1],[3,1],[1]]=>8
[[3,3,2,0],[3,2,1],[3,1],[2]]=>8
[[3,3,2,0],[3,2,1],[3,1],[3]]=>8
[[3,3,2,0],[3,2,1],[3,2],[2]]=>8
[[3,3,2,0],[3,2,1],[3,2],[3]]=>8
[[3,3,2,0],[3,2,2],[2,2],[2]]=>8
[[3,3,2,0],[3,2,2],[3,2],[2]]=>8
[[3,3,2,0],[3,2,2],[3,2],[3]]=>8
[[3,3,2,0],[3,3,0],[3,0],[0]]=>8
[[3,3,2,0],[3,3,0],[3,0],[1]]=>8
[[3,3,2,0],[3,3,0],[3,0],[2]]=>8
[[3,3,2,0],[3,3,0],[3,0],[3]]=>8
[[3,3,2,0],[3,3,0],[3,1],[1]]=>8
[[3,3,2,0],[3,3,0],[3,1],[2]]=>8
[[3,3,2,0],[3,3,0],[3,1],[3]]=>8
[[3,3,2,0],[3,3,0],[3,2],[2]]=>8
[[3,3,2,0],[3,3,0],[3,2],[3]]=>8
[[3,3,2,0],[3,3,0],[3,3],[3]]=>8
[[3,3,2,0],[3,3,1],[3,1],[1]]=>8
[[3,3,2,0],[3,3,1],[3,1],[2]]=>8
[[3,3,2,0],[3,3,1],[3,1],[3]]=>8
[[3,3,2,0],[3,3,1],[3,2],[2]]=>8
[[3,3,2,0],[3,3,1],[3,2],[3]]=>8
[[3,3,2,0],[3,3,1],[3,3],[3]]=>8
[[3,3,2,0],[3,3,2],[3,2],[2]]=>8
[[3,3,2,0],[3,3,2],[3,2],[3]]=>8
[[3,3,2,0],[3,3,2],[3,3],[3]]=>8
[[3,3,2,1],[3,2,1],[2,1],[1]]=>9
[[3,3,2,1],[3,2,1],[2,1],[2]]=>9
[[3,3,2,1],[3,2,1],[2,2],[2]]=>9
[[3,3,2,1],[3,2,1],[3,1],[1]]=>9
[[3,3,2,1],[3,2,1],[3,1],[2]]=>9
[[3,3,2,1],[3,2,1],[3,1],[3]]=>9
[[3,3,2,1],[3,2,1],[3,2],[2]]=>9
[[3,3,2,1],[3,2,1],[3,2],[3]]=>9
[[3,3,2,1],[3,2,2],[2,2],[2]]=>9
[[3,3,2,1],[3,2,2],[3,2],[2]]=>9
[[3,3,2,1],[3,2,2],[3,2],[3]]=>9
[[3,3,2,1],[3,3,1],[3,1],[1]]=>9
[[3,3,2,1],[3,3,1],[3,1],[2]]=>9
[[3,3,2,1],[3,3,1],[3,1],[3]]=>9
[[3,3,2,1],[3,3,1],[3,2],[2]]=>9
[[3,3,2,1],[3,3,1],[3,2],[3]]=>9
[[3,3,2,1],[3,3,1],[3,3],[3]]=>9
[[3,3,2,1],[3,3,2],[3,2],[2]]=>9
[[3,3,2,1],[3,3,2],[3,2],[3]]=>9
[[3,3,2,1],[3,3,2],[3,3],[3]]=>9
[[3,3,2,2],[3,2,2],[2,2],[2]]=>10
[[3,3,2,2],[3,2,2],[3,2],[2]]=>10
[[3,3,2,2],[3,2,2],[3,2],[3]]=>10
[[3,3,2,2],[3,3,2],[3,2],[2]]=>10
[[3,3,2,2],[3,3,2],[3,2],[3]]=>10
[[3,3,2,2],[3,3,2],[3,3],[3]]=>10
[[3,3,3,0],[3,3,0],[3,0],[0]]=>9
[[3,3,3,0],[3,3,0],[3,0],[1]]=>9
[[3,3,3,0],[3,3,0],[3,0],[2]]=>9
[[3,3,3,0],[3,3,0],[3,0],[3]]=>9
[[3,3,3,0],[3,3,0],[3,1],[1]]=>9
[[3,3,3,0],[3,3,0],[3,1],[2]]=>9
[[3,3,3,0],[3,3,0],[3,1],[3]]=>9
[[3,3,3,0],[3,3,0],[3,2],[2]]=>9
[[3,3,3,0],[3,3,0],[3,2],[3]]=>9
[[3,3,3,0],[3,3,0],[3,3],[3]]=>9
[[3,3,3,0],[3,3,1],[3,1],[1]]=>9
[[3,3,3,0],[3,3,1],[3,1],[2]]=>9
[[3,3,3,0],[3,3,1],[3,1],[3]]=>9
[[3,3,3,0],[3,3,1],[3,2],[2]]=>9
[[3,3,3,0],[3,3,1],[3,2],[3]]=>9
[[3,3,3,0],[3,3,1],[3,3],[3]]=>9
[[3,3,3,0],[3,3,2],[3,2],[2]]=>9
[[3,3,3,0],[3,3,2],[3,2],[3]]=>9
[[3,3,3,0],[3,3,2],[3,3],[3]]=>9
[[3,3,3,0],[3,3,3],[3,3],[3]]=>9
[[3,3,3,1],[3,3,1],[3,1],[1]]=>10
[[3,3,3,1],[3,3,1],[3,1],[2]]=>10
[[3,3,3,1],[3,3,1],[3,1],[3]]=>10
[[3,3,3,1],[3,3,1],[3,2],[2]]=>10
[[3,3,3,1],[3,3,1],[3,2],[3]]=>10
[[3,3,3,1],[3,3,1],[3,3],[3]]=>10
[[3,3,3,1],[3,3,2],[3,2],[2]]=>10
[[3,3,3,1],[3,3,2],[3,2],[3]]=>10
[[3,3,3,1],[3,3,2],[3,3],[3]]=>10
[[3,3,3,1],[3,3,3],[3,3],[3]]=>10
[[3,3,3,2],[3,3,2],[3,2],[2]]=>11
[[3,3,3,2],[3,3,2],[3,2],[3]]=>11
[[3,3,3,2],[3,3,2],[3,3],[3]]=>11
[[3,3,3,2],[3,3,3],[3,3],[3]]=>11
[[3,3,3,3],[3,3,3],[3,3],[3]]=>12
[[4,1,1,0],[4,1,1],[1,1],[1]]=>6
[[4,1,1,0],[4,1,1],[2,1],[1]]=>6
[[4,1,1,0],[4,1,1],[2,1],[2]]=>6
[[4,1,1,0],[4,1,1],[3,1],[1]]=>6
[[4,1,1,0],[4,1,1],[3,1],[2]]=>6
[[4,1,1,0],[4,1,1],[3,1],[3]]=>6
[[4,1,1,0],[4,1,1],[4,1],[1]]=>6
[[4,1,1,0],[4,1,1],[4,1],[2]]=>6
[[4,1,1,0],[4,1,1],[4,1],[3]]=>6
[[4,1,1,0],[4,1,1],[4,1],[4]]=>6
[[4,1,1,1],[1,1,1],[1,1],[1]]=>7
[[4,1,1,1],[2,1,1],[1,1],[1]]=>7
[[4,1,1,1],[2,1,1],[2,1],[1]]=>7
[[4,1,1,1],[2,1,1],[2,1],[2]]=>7
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Description
The sum of the first row in a Gelfand-Tsetlin pattern.
Code
def statistic(GT): return sum(GT[0])
Created
May 07, 2014 at 21:43 by Shahana Norton
Updated
May 20, 2016 at 22:11 by Martin Rubey
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