Identifier
- St000074: Gelfand-Tsetlin patterns ⟶ ℤ
Values
=>
Cc0018;cc-rep
[[1]]=>0
[[2]]=>0
[[3]]=>0
[[4]]=>0
[[5]]=>0
[[1,0],[0]]=>0
[[1,0],[1]]=>0
[[2,0],[0]]=>0
[[2,0],[1]]=>1
[[2,0],[2]]=>0
[[1,1],[1]]=>0
[[3,0],[0]]=>0
[[3,0],[1]]=>1
[[3,0],[2]]=>1
[[3,0],[3]]=>0
[[2,1],[1]]=>0
[[2,1],[2]]=>0
[[4,0],[0]]=>0
[[4,0],[1]]=>1
[[4,0],[2]]=>1
[[4,0],[3]]=>1
[[4,0],[4]]=>0
[[3,1],[1]]=>0
[[3,1],[2]]=>1
[[3,1],[3]]=>0
[[2,2],[2]]=>0
[[5,0],[0]]=>0
[[5,0],[1]]=>1
[[5,0],[2]]=>1
[[5,0],[3]]=>1
[[5,0],[4]]=>1
[[5,0],[5]]=>0
[[4,1],[1]]=>0
[[4,1],[2]]=>1
[[4,1],[3]]=>1
[[4,1],[4]]=>0
[[3,2],[2]]=>0
[[3,2],[3]]=>0
[[6,0],[0]]=>0
[[6,0],[1]]=>1
[[6,0],[2]]=>1
[[6,0],[3]]=>1
[[6,0],[4]]=>1
[[6,0],[5]]=>1
[[6,0],[6]]=>0
[[5,1],[1]]=>0
[[5,1],[2]]=>1
[[5,1],[3]]=>1
[[5,1],[4]]=>1
[[5,1],[5]]=>0
[[4,2],[2]]=>0
[[4,2],[3]]=>1
[[4,2],[4]]=>0
[[3,3],[3]]=>0
[[1,0,0],[0,0],[0]]=>0
[[1,0,0],[1,0],[0]]=>0
[[1,0,0],[1,0],[1]]=>0
[[2,0,0],[0,0],[0]]=>0
[[2,0,0],[1,0],[0]]=>1
[[2,0,0],[1,0],[1]]=>1
[[2,0,0],[2,0],[0]]=>0
[[2,0,0],[2,0],[1]]=>1
[[2,0,0],[2,0],[2]]=>0
[[1,1,0],[1,0],[0]]=>0
[[1,1,0],[1,0],[1]]=>0
[[1,1,0],[1,1],[1]]=>0
[[3,0,0],[0,0],[0]]=>0
[[3,0,0],[1,0],[0]]=>1
[[3,0,0],[1,0],[1]]=>1
[[3,0,0],[2,0],[0]]=>1
[[3,0,0],[2,0],[1]]=>2
[[3,0,0],[2,0],[2]]=>1
[[3,0,0],[3,0],[0]]=>0
[[3,0,0],[3,0],[1]]=>1
[[3,0,0],[3,0],[2]]=>1
[[3,0,0],[3,0],[3]]=>0
[[2,1,0],[1,0],[0]]=>0
[[2,1,0],[1,0],[1]]=>0
[[2,1,0],[1,1],[1]]=>0
[[2,1,0],[2,0],[0]]=>0
[[2,1,0],[2,0],[1]]=>1
[[2,1,0],[2,0],[2]]=>0
[[2,1,0],[2,1],[1]]=>0
[[2,1,0],[2,1],[2]]=>0
[[1,1,1],[1,1],[1]]=>0
[[4,0,0],[0,0],[0]]=>0
[[4,0,0],[1,0],[0]]=>1
[[4,0,0],[1,0],[1]]=>1
[[4,0,0],[2,0],[0]]=>1
[[4,0,0],[2,0],[1]]=>2
[[4,0,0],[2,0],[2]]=>1
[[4,0,0],[3,0],[0]]=>1
[[4,0,0],[3,0],[1]]=>2
[[4,0,0],[3,0],[2]]=>2
[[4,0,0],[3,0],[3]]=>1
[[4,0,0],[4,0],[0]]=>0
[[4,0,0],[4,0],[1]]=>1
[[4,0,0],[4,0],[2]]=>1
[[4,0,0],[4,0],[3]]=>1
[[4,0,0],[4,0],[4]]=>0
[[3,1,0],[1,0],[0]]=>0
[[3,1,0],[1,0],[1]]=>0
[[3,1,0],[1,1],[1]]=>0
[[3,1,0],[2,0],[0]]=>1
[[3,1,0],[2,0],[1]]=>2
[[3,1,0],[2,0],[2]]=>1
[[3,1,0],[2,1],[1]]=>1
[[3,1,0],[2,1],[2]]=>1
[[3,1,0],[3,0],[0]]=>0
[[3,1,0],[3,0],[1]]=>1
[[3,1,0],[3,0],[2]]=>1
[[3,1,0],[3,0],[3]]=>0
[[3,1,0],[3,1],[1]]=>0
[[3,1,0],[3,1],[2]]=>1
[[3,1,0],[3,1],[3]]=>0
[[2,2,0],[2,0],[0]]=>0
[[2,2,0],[2,0],[1]]=>1
[[2,2,0],[2,0],[2]]=>0
[[2,2,0],[2,1],[1]]=>1
[[2,2,0],[2,1],[2]]=>1
[[2,2,0],[2,2],[2]]=>0
[[2,1,1],[1,1],[1]]=>0
[[2,1,1],[2,1],[1]]=>0
[[2,1,1],[2,1],[2]]=>0
[[5,0,0],[0,0],[0]]=>0
[[5,0,0],[1,0],[0]]=>1
[[5,0,0],[1,0],[1]]=>1
[[5,0,0],[2,0],[0]]=>1
[[5,0,0],[2,0],[1]]=>2
[[5,0,0],[2,0],[2]]=>1
[[5,0,0],[3,0],[0]]=>1
[[5,0,0],[3,0],[1]]=>2
[[5,0,0],[3,0],[2]]=>2
[[5,0,0],[3,0],[3]]=>1
[[5,0,0],[4,0],[0]]=>1
[[5,0,0],[4,0],[1]]=>2
[[5,0,0],[4,0],[2]]=>2
[[5,0,0],[4,0],[3]]=>2
[[5,0,0],[4,0],[4]]=>1
[[5,0,0],[5,0],[1]]=>1
[[5,0,0],[5,0],[2]]=>1
[[5,0,0],[5,0],[3]]=>1
[[5,0,0],[5,0],[4]]=>1
[[5,0,0],[5,0],[5]]=>0
[[4,1,0],[1,0],[0]]=>0
[[4,1,0],[1,0],[1]]=>0
[[4,1,0],[1,1],[1]]=>0
[[4,1,0],[2,0],[0]]=>1
[[4,1,0],[2,0],[1]]=>2
[[4,1,0],[2,0],[2]]=>1
[[4,1,0],[2,1],[1]]=>1
[[4,1,0],[2,1],[2]]=>1
[[4,1,0],[3,0],[0]]=>1
[[4,1,0],[3,0],[1]]=>2
[[4,1,0],[3,0],[2]]=>2
[[4,1,0],[3,0],[3]]=>1
[[4,1,0],[3,1],[1]]=>1
[[4,1,0],[3,1],[2]]=>2
[[4,1,0],[3,1],[3]]=>1
[[4,1,0],[4,0],[0]]=>0
[[4,1,0],[4,0],[1]]=>1
[[4,1,0],[4,0],[2]]=>1
[[4,1,0],[4,0],[3]]=>1
[[4,1,0],[4,0],[4]]=>0
[[4,1,0],[4,1],[1]]=>0
[[4,1,0],[4,1],[2]]=>1
[[4,1,0],[4,1],[3]]=>1
[[4,1,0],[4,1],[4]]=>0
[[3,2,0],[2,0],[0]]=>0
[[3,2,0],[2,0],[1]]=>1
[[3,2,0],[2,0],[2]]=>0
[[3,2,0],[2,1],[1]]=>1
[[3,2,0],[2,1],[2]]=>1
[[3,2,0],[2,2],[2]]=>0
[[3,2,0],[3,0],[0]]=>0
[[3,2,0],[3,0],[1]]=>1
[[3,2,0],[3,0],[2]]=>1
[[3,2,0],[3,0],[3]]=>0
[[3,2,0],[3,1],[1]]=>1
[[3,2,0],[3,1],[2]]=>2
[[3,2,0],[3,1],[3]]=>1
[[3,2,0],[3,2],[2]]=>0
[[3,2,0],[3,2],[3]]=>0
[[3,1,1],[1,1],[1]]=>0
[[3,1,1],[2,1],[1]]=>1
[[3,1,1],[2,1],[2]]=>1
[[3,1,1],[3,1],[1]]=>0
[[3,1,1],[3,1],[2]]=>1
[[3,1,1],[3,1],[3]]=>0
[[2,2,1],[2,1],[1]]=>0
[[2,2,1],[2,1],[2]]=>0
[[2,2,1],[2,2],[2]]=>0
[[3,3,0],[3,0],[0]]=>0
[[3,3,0],[3,0],[1]]=>1
[[3,3,0],[3,0],[2]]=>1
[[3,3,0],[3,0],[3]]=>0
[[3,3,0],[3,1],[1]]=>1
[[3,3,0],[3,1],[2]]=>2
[[3,3,0],[3,1],[3]]=>1
[[3,3,0],[3,2],[2]]=>1
[[3,3,0],[3,2],[3]]=>1
[[3,3,0],[3,3],[3]]=>0
[[3,2,1],[2,1],[1]]=>0
[[3,2,1],[2,1],[2]]=>0
[[3,2,1],[2,2],[2]]=>0
[[3,2,1],[3,1],[1]]=>0
[[3,2,1],[3,1],[2]]=>1
[[3,2,1],[3,1],[3]]=>0
[[3,2,1],[3,2],[2]]=>0
[[3,2,1],[3,2],[3]]=>0
[[2,2,2],[2,2],[2]]=>0
[[3,3,1],[3,3],[3]]=>0
[[3,3,1],[3,2],[3]]=>1
[[3,3,1],[3,1],[3]]=>0
[[3,3,1],[3,2],[2]]=>1
[[3,3,1],[3,1],[2]]=>1
[[3,3,1],[3,1],[1]]=>0
[[3,2,2],[3,2],[3]]=>0
[[3,2,2],[3,2],[2]]=>0
[[3,2,2],[2,2],[2]]=>0
[[1,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,0,0,0],[1,0,0],[0,0],[0]]=>0
[[1,0,0,0],[1,0,0],[1,0],[0]]=>0
[[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[2,0,0,0],[0,0,0],[0,0],[0]]=>0
[[2,0,0,0],[1,0,0],[0,0],[0]]=>1
[[2,0,0,0],[1,0,0],[1,0],[0]]=>1
[[2,0,0,0],[1,0,0],[1,0],[1]]=>1
[[2,0,0,0],[2,0,0],[0,0],[0]]=>0
[[2,0,0,0],[2,0,0],[1,0],[0]]=>1
[[2,0,0,0],[2,0,0],[1,0],[1]]=>1
[[2,0,0,0],[2,0,0],[2,0],[0]]=>0
[[2,0,0,0],[2,0,0],[2,0],[1]]=>1
[[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[1,1,0,0],[1,0,0],[0,0],[0]]=>0
[[1,1,0,0],[1,0,0],[1,0],[0]]=>0
[[1,1,0,0],[1,0,0],[1,0],[1]]=>0
[[1,1,0,0],[1,1,0],[1,0],[0]]=>0
[[1,1,0,0],[1,1,0],[1,0],[1]]=>0
[[1,1,0,0],[1,1,0],[1,1],[1]]=>0
[[3,0,0,0],[0,0,0],[0,0],[0]]=>0
[[3,0,0,0],[1,0,0],[0,0],[0]]=>1
[[3,0,0,0],[1,0,0],[1,0],[0]]=>1
[[3,0,0,0],[1,0,0],[1,0],[1]]=>1
[[3,0,0,0],[2,0,0],[0,0],[0]]=>1
[[3,0,0,0],[2,0,0],[1,0],[0]]=>2
[[3,0,0,0],[2,0,0],[1,0],[1]]=>2
[[3,0,0,0],[2,0,0],[2,0],[0]]=>1
[[3,0,0,0],[2,0,0],[2,0],[1]]=>2
[[3,0,0,0],[2,0,0],[2,0],[2]]=>1
[[3,0,0,0],[3,0,0],[0,0],[0]]=>0
[[3,0,0,0],[3,0,0],[1,0],[0]]=>1
[[3,0,0,0],[3,0,0],[1,0],[1]]=>1
[[3,0,0,0],[3,0,0],[2,0],[0]]=>1
[[3,0,0,0],[3,0,0],[2,0],[1]]=>2
[[3,0,0,0],[3,0,0],[2,0],[2]]=>1
[[3,0,0,0],[3,0,0],[3,0],[0]]=>0
[[3,0,0,0],[3,0,0],[3,0],[1]]=>1
[[3,0,0,0],[3,0,0],[3,0],[2]]=>1
[[3,0,0,0],[3,0,0],[3,0],[3]]=>0
[[2,1,0,0],[1,0,0],[0,0],[0]]=>0
[[2,1,0,0],[1,0,0],[1,0],[0]]=>0
[[2,1,0,0],[1,0,0],[1,0],[1]]=>0
[[2,1,0,0],[1,1,0],[1,0],[0]]=>0
[[2,1,0,0],[1,1,0],[1,0],[1]]=>0
[[2,1,0,0],[1,1,0],[1,1],[1]]=>0
[[2,1,0,0],[2,0,0],[0,0],[0]]=>0
[[2,1,0,0],[2,0,0],[1,0],[0]]=>1
[[2,1,0,0],[2,0,0],[1,0],[1]]=>1
[[2,1,0,0],[2,0,0],[2,0],[0]]=>0
[[2,1,0,0],[2,0,0],[2,0],[1]]=>1
[[2,1,0,0],[2,0,0],[2,0],[2]]=>0
[[2,1,0,0],[2,1,0],[1,0],[0]]=>0
[[2,1,0,0],[2,1,0],[1,0],[1]]=>0
[[2,1,0,0],[2,1,0],[1,1],[1]]=>0
[[2,1,0,0],[2,1,0],[2,0],[0]]=>0
[[2,1,0,0],[2,1,0],[2,0],[1]]=>1
[[2,1,0,0],[2,1,0],[2,0],[2]]=>0
[[2,1,0,0],[2,1,0],[2,1],[1]]=>0
[[2,1,0,0],[2,1,0],[2,1],[2]]=>0
[[1,1,1,0],[1,1,0],[1,0],[0]]=>0
[[1,1,1,0],[1,1,0],[1,0],[1]]=>0
[[1,1,1,0],[1,1,0],[1,1],[1]]=>0
[[1,1,1,0],[1,1,1],[1,1],[1]]=>0
[[4,0,0,0],[0,0,0],[0,0],[0]]=>0
[[4,0,0,0],[1,0,0],[0,0],[0]]=>1
[[4,0,0,0],[1,0,0],[1,0],[0]]=>1
[[4,0,0,0],[1,0,0],[1,0],[1]]=>1
[[4,0,0,0],[2,0,0],[0,0],[0]]=>1
[[4,0,0,0],[2,0,0],[1,0],[0]]=>2
[[4,0,0,0],[2,0,0],[1,0],[1]]=>2
[[4,0,0,0],[2,0,0],[2,0],[0]]=>1
[[4,0,0,0],[2,0,0],[2,0],[1]]=>2
[[4,0,0,0],[2,0,0],[2,0],[2]]=>1
[[4,0,0,0],[3,0,0],[0,0],[0]]=>1
[[4,0,0,0],[3,0,0],[1,0],[0]]=>2
[[4,0,0,0],[3,0,0],[1,0],[1]]=>2
[[4,0,0,0],[3,0,0],[2,0],[0]]=>2
[[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[4,0,0,0],[3,0,0],[2,0],[2]]=>2
[[4,0,0,0],[3,0,0],[3,0],[0]]=>1
[[4,0,0,0],[3,0,0],[3,0],[1]]=>2
[[4,0,0,0],[3,0,0],[3,0],[2]]=>2
[[4,0,0,0],[3,0,0],[3,0],[3]]=>1
[[4,0,0,0],[4,0,0],[1,0],[1]]=>1
[[4,0,0,0],[4,0,0],[2,0],[1]]=>2
[[4,0,0,0],[4,0,0],[2,0],[2]]=>1
[[4,0,0,0],[4,0,0],[3,0],[1]]=>2
[[4,0,0,0],[4,0,0],[3,0],[2]]=>2
[[4,0,0,0],[4,0,0],[3,0],[3]]=>1
[[4,0,0,0],[4,0,0],[4,0],[1]]=>1
[[4,0,0,0],[4,0,0],[4,0],[2]]=>1
[[4,0,0,0],[4,0,0],[4,0],[3]]=>1
[[4,0,0,0],[4,0,0],[4,0],[4]]=>0
[[3,1,0,0],[1,0,0],[0,0],[0]]=>0
[[3,1,0,0],[1,0,0],[1,0],[0]]=>0
[[3,1,0,0],[1,0,0],[1,0],[1]]=>0
[[3,1,0,0],[1,1,0],[1,0],[0]]=>0
[[3,1,0,0],[1,1,0],[1,0],[1]]=>0
[[3,1,0,0],[1,1,0],[1,1],[1]]=>0
[[3,1,0,0],[2,0,0],[0,0],[0]]=>1
[[3,1,0,0],[2,0,0],[1,0],[0]]=>2
[[3,1,0,0],[2,0,0],[1,0],[1]]=>2
[[3,1,0,0],[2,0,0],[2,0],[0]]=>1
[[3,1,0,0],[2,0,0],[2,0],[1]]=>2
[[3,1,0,0],[2,0,0],[2,0],[2]]=>1
[[3,1,0,0],[2,1,0],[1,0],[0]]=>1
[[3,1,0,0],[2,1,0],[1,0],[1]]=>1
[[3,1,0,0],[2,1,0],[1,1],[1]]=>1
[[3,1,0,0],[2,1,0],[2,0],[0]]=>1
[[3,1,0,0],[2,1,0],[2,0],[1]]=>2
[[3,1,0,0],[2,1,0],[2,0],[2]]=>1
[[3,1,0,0],[2,1,0],[2,1],[1]]=>1
[[3,1,0,0],[2,1,0],[2,1],[2]]=>1
[[3,1,0,0],[3,0,0],[0,0],[0]]=>0
[[3,1,0,0],[3,0,0],[1,0],[0]]=>1
[[3,1,0,0],[3,0,0],[1,0],[1]]=>1
[[3,1,0,0],[3,0,0],[2,0],[0]]=>1
[[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[3,1,0,0],[3,0,0],[2,0],[2]]=>1
[[3,1,0,0],[3,0,0],[3,0],[0]]=>0
[[3,1,0,0],[3,0,0],[3,0],[1]]=>1
[[3,1,0,0],[3,0,0],[3,0],[2]]=>1
[[3,1,0,0],[3,0,0],[3,0],[3]]=>0
[[3,1,0,0],[3,1,0],[1,0],[0]]=>0
[[3,1,0,0],[3,1,0],[1,0],[1]]=>0
[[3,1,0,0],[3,1,0],[1,1],[1]]=>0
[[3,1,0,0],[3,1,0],[2,0],[0]]=>1
[[3,1,0,0],[3,1,0],[2,0],[1]]=>2
[[3,1,0,0],[3,1,0],[2,0],[2]]=>1
[[3,1,0,0],[3,1,0],[2,1],[1]]=>1
[[3,1,0,0],[3,1,0],[2,1],[2]]=>1
[[3,1,0,0],[3,1,0],[3,0],[0]]=>0
[[3,1,0,0],[3,1,0],[3,0],[1]]=>1
[[3,1,0,0],[3,1,0],[3,0],[2]]=>1
[[3,1,0,0],[3,1,0],[3,0],[3]]=>0
[[3,1,0,0],[3,1,0],[3,1],[1]]=>0
[[3,1,0,0],[3,1,0],[3,1],[2]]=>1
[[3,1,0,0],[3,1,0],[3,1],[3]]=>0
[[2,2,0,0],[2,0,0],[0,0],[0]]=>0
[[2,2,0,0],[2,0,0],[1,0],[0]]=>1
[[2,2,0,0],[2,0,0],[1,0],[1]]=>1
[[2,2,0,0],[2,0,0],[2,0],[0]]=>0
[[2,2,0,0],[2,0,0],[2,0],[1]]=>1
[[2,2,0,0],[2,0,0],[2,0],[2]]=>0
[[2,2,0,0],[2,1,0],[1,0],[0]]=>1
[[2,2,0,0],[2,1,0],[1,0],[1]]=>1
[[2,2,0,0],[2,1,0],[1,1],[1]]=>1
[[2,2,0,0],[2,1,0],[2,0],[0]]=>1
[[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[2,2,0,0],[2,1,0],[2,0],[2]]=>1
[[2,2,0,0],[2,1,0],[2,1],[1]]=>1
[[2,2,0,0],[2,1,0],[2,1],[2]]=>1
[[2,2,0,0],[2,2,0],[2,0],[0]]=>0
[[2,2,0,0],[2,2,0],[2,0],[1]]=>1
[[2,2,0,0],[2,2,0],[2,0],[2]]=>0
[[2,2,0,0],[2,2,0],[2,1],[1]]=>1
[[2,2,0,0],[2,2,0],[2,1],[2]]=>1
[[2,2,0,0],[2,2,0],[2,2],[2]]=>0
[[2,1,1,0],[1,1,0],[1,0],[0]]=>0
[[2,1,1,0],[1,1,0],[1,0],[1]]=>0
[[2,1,1,0],[1,1,0],[1,1],[1]]=>0
[[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,1,1,0],[2,1,0],[1,0],[0]]=>0
[[2,1,1,0],[2,1,0],[1,0],[1]]=>0
[[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[2,1,1,0],[2,1,0],[2,0],[0]]=>0
[[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[2,1,1,0],[2,1,0],[2,0],[2]]=>0
[[2,1,1,0],[2,1,0],[2,1],[1]]=>0
[[2,1,1,0],[2,1,0],[2,1],[2]]=>0
[[2,1,1,0],[2,1,1],[1,1],[1]]=>0
[[2,1,1,0],[2,1,1],[2,1],[1]]=>0
[[2,1,1,0],[2,1,1],[2,1],[2]]=>0
[[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[3,2,0,0],[2,0,0],[0,0],[0]]=>0
[[3,2,0,0],[2,0,0],[1,0],[0]]=>1
[[3,2,0,0],[2,0,0],[1,0],[1]]=>1
[[3,2,0,0],[2,0,0],[2,0],[0]]=>0
[[3,2,0,0],[2,0,0],[2,0],[1]]=>1
[[3,2,0,0],[2,0,0],[2,0],[2]]=>0
[[3,2,0,0],[2,1,0],[1,0],[0]]=>1
[[3,2,0,0],[2,1,0],[1,0],[1]]=>1
[[3,2,0,0],[2,1,0],[1,1],[1]]=>1
[[3,2,0,0],[2,1,0],[2,0],[0]]=>1
[[3,2,0,0],[2,1,0],[2,0],[1]]=>2
[[3,2,0,0],[2,1,0],[2,0],[2]]=>1
[[3,2,0,0],[2,1,0],[2,1],[1]]=>1
[[3,2,0,0],[2,1,0],[2,1],[2]]=>1
[[3,2,0,0],[2,2,0],[2,0],[0]]=>0
[[3,2,0,0],[2,2,0],[2,0],[1]]=>1
[[3,2,0,0],[2,2,0],[2,0],[2]]=>0
[[3,2,0,0],[2,2,0],[2,1],[1]]=>1
[[3,2,0,0],[2,2,0],[2,1],[2]]=>1
[[3,2,0,0],[2,2,0],[2,2],[2]]=>0
[[3,2,0,0],[3,0,0],[0,0],[0]]=>0
[[3,2,0,0],[3,0,0],[1,0],[0]]=>1
[[3,2,0,0],[3,0,0],[1,0],[1]]=>1
[[3,2,0,0],[3,0,0],[2,0],[0]]=>1
[[3,2,0,0],[3,0,0],[2,0],[1]]=>2
[[3,2,0,0],[3,0,0],[2,0],[2]]=>1
[[3,2,0,0],[3,0,0],[3,0],[0]]=>0
[[3,2,0,0],[3,0,0],[3,0],[1]]=>1
[[3,2,0,0],[3,0,0],[3,0],[2]]=>1
[[3,2,0,0],[3,0,0],[3,0],[3]]=>0
[[3,2,0,0],[3,1,0],[1,0],[0]]=>1
[[3,2,0,0],[3,1,0],[1,0],[1]]=>1
[[3,2,0,0],[3,1,0],[1,1],[1]]=>1
[[3,2,0,0],[3,1,0],[2,0],[0]]=>2
[[3,2,0,0],[3,1,0],[2,0],[1]]=>3
[[3,2,0,0],[3,1,0],[2,0],[2]]=>2
[[3,2,0,0],[3,1,0],[2,1],[1]]=>2
[[3,2,0,0],[3,1,0],[2,1],[2]]=>2
[[3,2,0,0],[3,1,0],[3,0],[0]]=>1
[[3,2,0,0],[3,1,0],[3,0],[1]]=>2
[[3,2,0,0],[3,1,0],[3,0],[2]]=>2
[[3,2,0,0],[3,1,0],[3,0],[3]]=>1
[[3,2,0,0],[3,1,0],[3,1],[1]]=>1
[[3,2,0,0],[3,1,0],[3,1],[2]]=>2
[[3,2,0,0],[3,1,0],[3,1],[3]]=>1
[[3,2,0,0],[3,2,0],[2,0],[0]]=>0
[[3,2,0,0],[3,2,0],[2,0],[1]]=>1
[[3,2,0,0],[3,2,0],[2,0],[2]]=>0
[[3,2,0,0],[3,2,0],[2,1],[1]]=>1
[[3,2,0,0],[3,2,0],[2,1],[2]]=>1
[[3,2,0,0],[3,2,0],[2,2],[2]]=>0
[[3,2,0,0],[3,2,0],[3,0],[0]]=>0
[[3,2,0,0],[3,2,0],[3,0],[1]]=>1
[[3,2,0,0],[3,2,0],[3,0],[2]]=>1
[[3,2,0,0],[3,2,0],[3,0],[3]]=>0
[[3,2,0,0],[3,2,0],[3,1],[1]]=>1
[[3,2,0,0],[3,2,0],[3,1],[2]]=>2
[[3,2,0,0],[3,2,0],[3,1],[3]]=>1
[[3,2,0,0],[3,2,0],[3,2],[2]]=>0
[[3,2,0,0],[3,2,0],[3,2],[3]]=>0
[[3,1,1,0],[1,1,0],[1,0],[0]]=>0
[[3,1,1,0],[1,1,0],[1,0],[1]]=>0
[[3,1,1,0],[1,1,0],[1,1],[1]]=>0
[[3,1,1,0],[1,1,1],[1,1],[1]]=>0
[[3,1,1,0],[2,1,0],[1,0],[0]]=>1
[[3,1,1,0],[2,1,0],[1,0],[1]]=>1
[[3,1,1,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,0],[2,1,0],[2,0],[0]]=>1
[[3,1,1,0],[2,1,0],[2,0],[1]]=>2
[[3,1,1,0],[2,1,0],[2,0],[2]]=>1
[[3,1,1,0],[2,1,0],[2,1],[1]]=>1
[[3,1,1,0],[2,1,0],[2,1],[2]]=>1
[[3,1,1,0],[2,1,1],[1,1],[1]]=>1
[[3,1,1,0],[2,1,1],[2,1],[1]]=>1
[[3,1,1,0],[2,1,1],[2,1],[2]]=>1
[[3,1,1,0],[3,1,0],[1,0],[0]]=>0
[[3,1,1,0],[3,1,0],[1,0],[1]]=>0
[[3,1,1,0],[3,1,0],[1,1],[1]]=>0
[[3,1,1,0],[3,1,0],[2,0],[0]]=>1
[[3,1,1,0],[3,1,0],[2,0],[1]]=>2
[[3,1,1,0],[3,1,0],[2,0],[2]]=>1
[[3,1,1,0],[3,1,0],[2,1],[1]]=>1
[[3,1,1,0],[3,1,0],[2,1],[2]]=>1
[[3,1,1,0],[3,1,0],[3,0],[0]]=>0
[[3,1,1,0],[3,1,0],[3,0],[1]]=>1
[[3,1,1,0],[3,1,0],[3,0],[2]]=>1
[[3,1,1,0],[3,1,0],[3,0],[3]]=>0
[[3,1,1,0],[3,1,0],[3,1],[1]]=>0
[[3,1,1,0],[3,1,0],[3,1],[2]]=>1
[[3,1,1,0],[3,1,0],[3,1],[3]]=>0
[[3,1,1,0],[3,1,1],[1,1],[1]]=>0
[[3,1,1,0],[3,1,1],[2,1],[1]]=>1
[[3,1,1,0],[3,1,1],[2,1],[2]]=>1
[[3,1,1,0],[3,1,1],[3,1],[1]]=>0
[[3,1,1,0],[3,1,1],[3,1],[2]]=>1
[[3,1,1,0],[3,1,1],[3,1],[3]]=>0
[[2,2,1,0],[2,1,0],[1,0],[0]]=>0
[[2,2,1,0],[2,1,0],[1,0],[1]]=>0
[[2,2,1,0],[2,1,0],[1,1],[1]]=>0
[[2,2,1,0],[2,1,0],[2,0],[0]]=>0
[[2,2,1,0],[2,1,0],[2,0],[1]]=>1
[[2,2,1,0],[2,1,0],[2,0],[2]]=>0
[[2,2,1,0],[2,1,0],[2,1],[1]]=>0
[[2,2,1,0],[2,1,0],[2,1],[2]]=>0
[[2,2,1,0],[2,1,1],[1,1],[1]]=>0
[[2,2,1,0],[2,1,1],[2,1],[1]]=>0
[[2,2,1,0],[2,1,1],[2,1],[2]]=>0
[[2,2,1,0],[2,2,0],[2,0],[0]]=>0
[[2,2,1,0],[2,2,0],[2,0],[1]]=>1
[[2,2,1,0],[2,2,0],[2,0],[2]]=>0
[[2,2,1,0],[2,2,0],[2,1],[1]]=>1
[[2,2,1,0],[2,2,0],[2,1],[2]]=>1
[[2,2,1,0],[2,2,0],[2,2],[2]]=>0
[[2,2,1,0],[2,2,1],[2,1],[1]]=>0
[[2,2,1,0],[2,2,1],[2,1],[2]]=>0
[[2,2,1,0],[2,2,1],[2,2],[2]]=>0
[[2,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1],[2,1,1],[1,1],[1]]=>0
[[2,1,1,1],[2,1,1],[2,1],[1]]=>0
[[2,1,1,1],[2,1,1],[2,1],[2]]=>0
[[3,3,0,0],[3,2,0],[3,2],[3]]=>1
[[3,3,0,0],[3,2,0],[3,1],[3]]=>2
[[3,3,0,0],[3,1,0],[3,1],[3]]=>1
[[3,3,0,0],[3,2,0],[3,0],[3]]=>1
[[3,3,0,0],[3,1,0],[3,0],[3]]=>1
[[3,3,0,0],[3,0,0],[3,0],[3]]=>0
[[3,3,0,0],[3,2,0],[3,2],[2]]=>1
[[3,3,0,0],[3,2,0],[3,1],[2]]=>3
[[3,3,0,0],[3,2,0],[2,2],[2]]=>1
[[3,3,0,0],[3,1,0],[3,1],[2]]=>2
[[3,3,0,0],[3,2,0],[3,0],[2]]=>2
[[3,3,0,0],[3,2,0],[2,1],[2]]=>2
[[3,3,0,0],[3,1,0],[3,0],[2]]=>2
[[3,3,0,0],[3,1,0],[2,1],[2]]=>2
[[3,3,0,0],[3,0,0],[3,0],[2]]=>1
[[3,3,0,0],[3,2,0],[2,0],[2]]=>1
[[3,3,0,0],[3,1,0],[2,0],[2]]=>2
[[3,3,0,0],[3,0,0],[2,0],[2]]=>1
[[3,3,0,0],[3,2,0],[3,1],[1]]=>2
[[3,3,0,0],[3,1,0],[3,1],[1]]=>1
[[3,3,0,0],[3,2,0],[3,0],[1]]=>2
[[3,3,0,0],[3,2,0],[2,1],[1]]=>2
[[3,3,0,0],[3,1,0],[3,0],[1]]=>2
[[3,3,0,0],[3,1,0],[2,1],[1]]=>2
[[3,3,0,0],[3,0,0],[3,0],[1]]=>1
[[3,3,0,0],[3,2,0],[2,0],[1]]=>2
[[3,3,0,0],[3,1,0],[2,0],[1]]=>3
[[3,3,0,0],[3,1,0],[1,1],[1]]=>1
[[3,3,0,0],[3,0,0],[2,0],[1]]=>2
[[3,3,0,0],[3,1,0],[1,0],[1]]=>1
[[3,3,0,0],[3,0,0],[1,0],[1]]=>1
[[3,3,0,0],[3,2,0],[3,0],[0]]=>1
[[3,3,0,0],[3,1,0],[3,0],[0]]=>1
[[3,3,0,0],[3,0,0],[3,0],[0]]=>0
[[3,3,0,0],[3,2,0],[2,0],[0]]=>1
[[3,3,0,0],[3,1,0],[2,0],[0]]=>2
[[3,3,0,0],[3,0,0],[2,0],[0]]=>1
[[3,3,0,0],[3,1,0],[1,0],[0]]=>1
[[3,3,0,0],[3,0,0],[1,0],[0]]=>1
[[3,3,0,0],[3,0,0],[0,0],[0]]=>0
[[3,2,1,0],[3,2,0],[3,2],[3]]=>0
[[3,2,1,0],[3,2,0],[3,1],[3]]=>1
[[3,2,1,0],[3,1,1],[3,1],[3]]=>0
[[3,2,1,0],[3,1,0],[3,1],[3]]=>0
[[3,2,1,0],[3,2,0],[3,0],[3]]=>0
[[3,2,1,0],[3,1,0],[3,0],[3]]=>0
[[3,2,1,0],[3,2,0],[3,2],[2]]=>0
[[3,2,1,0],[3,2,0],[3,1],[2]]=>2
[[3,2,1,0],[3,1,1],[3,1],[2]]=>1
[[3,2,1,0],[3,2,0],[2,2],[2]]=>0
[[3,2,1,0],[2,2,1],[2,2],[2]]=>0
[[3,2,1,0],[3,1,0],[3,1],[2]]=>1
[[3,2,1,0],[2,2,0],[2,2],[2]]=>0
[[3,2,1,0],[3,2,0],[3,0],[2]]=>1
[[3,2,1,0],[3,2,0],[2,1],[2]]=>1
[[3,2,1,0],[3,1,1],[2,1],[2]]=>1
[[3,2,1,0],[2,2,1],[2,1],[2]]=>0
[[3,2,1,0],[3,1,0],[3,0],[2]]=>1
[[3,2,1,0],[3,1,0],[2,1],[2]]=>1
[[3,2,1,0],[2,2,0],[2,1],[2]]=>1
[[3,2,1,0],[2,1,1],[2,1],[2]]=>0
[[3,2,1,0],[2,1,0],[2,1],[2]]=>0
[[3,2,1,0],[3,2,0],[2,0],[2]]=>0
[[3,2,1,0],[3,1,0],[2,0],[2]]=>1
[[3,2,1,0],[2,2,0],[2,0],[2]]=>0
[[3,2,1,0],[2,1,0],[2,0],[2]]=>0
[[3,2,1,0],[3,2,0],[3,1],[1]]=>1
[[3,2,1,0],[3,1,1],[3,1],[1]]=>0
[[3,2,1,0],[3,1,0],[3,1],[1]]=>0
[[3,2,1,0],[3,2,0],[3,0],[1]]=>1
[[3,2,1,0],[3,2,0],[2,1],[1]]=>1
[[3,2,1,0],[3,1,1],[2,1],[1]]=>1
[[3,2,1,0],[2,2,1],[2,1],[1]]=>0
[[3,2,1,0],[3,1,0],[3,0],[1]]=>1
[[3,2,1,0],[3,1,0],[2,1],[1]]=>1
[[3,2,1,0],[2,2,0],[2,1],[1]]=>1
[[3,2,1,0],[2,1,1],[2,1],[1]]=>0
[[3,2,1,0],[2,1,0],[2,1],[1]]=>0
[[3,2,1,0],[3,2,0],[2,0],[1]]=>1
[[3,2,1,0],[3,1,1],[1,1],[1]]=>0
[[3,2,1,0],[3,1,0],[2,0],[1]]=>2
[[3,2,1,0],[2,2,0],[2,0],[1]]=>1
[[3,2,1,0],[3,1,0],[1,1],[1]]=>0
[[3,2,1,0],[2,1,1],[1,1],[1]]=>0
[[3,2,1,0],[2,1,0],[2,0],[1]]=>1
[[3,2,1,0],[2,1,0],[1,1],[1]]=>0
[[3,2,1,0],[3,1,0],[1,0],[1]]=>0
[[3,2,1,0],[2,1,0],[1,0],[1]]=>0
[[3,2,1,0],[3,2,0],[3,0],[0]]=>0
[[3,2,1,0],[3,1,0],[3,0],[0]]=>0
[[3,2,1,0],[3,2,0],[2,0],[0]]=>0
[[3,2,1,0],[3,1,0],[2,0],[0]]=>1
[[3,2,1,0],[2,2,0],[2,0],[0]]=>0
[[3,2,1,0],[2,1,0],[2,0],[0]]=>0
[[3,2,1,0],[3,1,0],[1,0],[0]]=>0
[[3,2,1,0],[2,1,0],[1,0],[0]]=>0
[[3,1,1,1],[3,1,1],[3,1],[3]]=>0
[[3,1,1,1],[3,1,1],[3,1],[2]]=>1
[[3,1,1,1],[3,1,1],[2,1],[2]]=>1
[[3,1,1,1],[2,1,1],[2,1],[2]]=>1
[[3,1,1,1],[3,1,1],[3,1],[1]]=>0
[[3,1,1,1],[3,1,1],[2,1],[1]]=>1
[[3,1,1,1],[2,1,1],[2,1],[1]]=>1
[[3,1,1,1],[3,1,1],[1,1],[1]]=>0
[[3,1,1,1],[2,1,1],[1,1],[1]]=>1
[[3,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,2,2,0],[2,2,1],[2,2],[2]]=>1
[[2,2,2,0],[2,2,0],[2,2],[2]]=>0
[[2,2,2,0],[2,2,1],[2,1],[2]]=>1
[[2,2,2,0],[2,2,0],[2,1],[2]]=>1
[[2,2,2,0],[2,2,0],[2,0],[2]]=>0
[[2,2,2,0],[2,2,1],[2,1],[1]]=>1
[[2,2,2,0],[2,2,0],[2,1],[1]]=>1
[[2,2,2,0],[2,2,0],[2,0],[1]]=>1
[[2,2,2,0],[2,2,0],[2,0],[0]]=>0
[[2,2,1,1],[2,2,1],[2,2],[2]]=>0
[[2,2,1,1],[2,2,1],[2,1],[2]]=>0
[[2,2,1,1],[2,1,1],[2,1],[2]]=>0
[[2,2,1,1],[2,2,1],[2,1],[1]]=>0
[[2,2,1,1],[2,1,1],[2,1],[1]]=>0
[[2,2,1,1],[2,1,1],[1,1],[1]]=>0
[[4,3,2,1],[4,3,2],[4,3],[4]]=>0
[[4,3,2,1],[4,3,2],[4,3],[3]]=>0
[[4,3,2,1],[4,3,2],[4,2],[4]]=>0
[[4,3,2,1],[4,3,2],[4,2],[3]]=>1
[[4,3,2,1],[4,3,2],[3,2],[3]]=>0
[[4,3,2,1],[4,3,2],[4,2],[2]]=>0
[[4,3,2,1],[4,3,2],[3,2],[2]]=>0
[[4,3,2,1],[4,3,1],[4,3],[4]]=>0
[[4,3,2,1],[4,3,1],[4,3],[3]]=>0
[[4,3,2,1],[4,3,1],[4,2],[4]]=>1
[[4,3,2,1],[4,3,1],[4,2],[3]]=>2
[[4,3,2,1],[4,3,1],[3,2],[3]]=>1
[[4,3,2,1],[4,3,1],[4,2],[2]]=>1
[[4,3,2,1],[4,3,1],[3,2],[2]]=>1
[[4,3,2,1],[4,2,1],[4,2],[4]]=>0
[[4,3,2,1],[4,2,1],[4,2],[3]]=>1
[[4,3,2,1],[4,2,1],[3,2],[3]]=>1
[[4,3,2,1],[3,2,1],[3,2],[3]]=>0
[[4,3,2,1],[4,2,1],[4,2],[2]]=>0
[[4,3,2,1],[4,2,1],[3,2],[2]]=>1
[[4,3,2,1],[3,2,1],[3,2],[2]]=>0
[[4,3,2,1],[4,3,1],[4,1],[4]]=>0
[[4,3,2,1],[4,3,1],[4,1],[3]]=>1
[[4,3,2,1],[4,3,1],[3,1],[3]]=>0
[[4,3,2,1],[4,3,1],[4,1],[2]]=>1
[[4,3,2,1],[4,3,1],[3,1],[2]]=>1
[[4,3,2,1],[4,2,1],[4,1],[4]]=>0
[[4,3,2,1],[4,2,1],[4,1],[3]]=>1
[[4,3,2,1],[4,2,1],[3,1],[3]]=>1
[[4,3,2,1],[3,2,1],[3,1],[3]]=>0
[[4,3,2,1],[4,2,1],[4,1],[2]]=>1
[[4,3,2,1],[4,2,1],[3,1],[2]]=>2
[[4,3,2,1],[3,2,1],[3,1],[2]]=>1
[[4,3,2,1],[4,2,1],[2,1],[2]]=>0
[[4,3,2,1],[3,2,1],[2,1],[2]]=>0
[[4,3,2,1],[4,3,1],[4,1],[1]]=>0
[[4,3,2,1],[4,3,1],[3,1],[1]]=>0
[[4,3,2,1],[4,2,1],[4,1],[1]]=>0
[[4,3,2,1],[4,2,1],[3,1],[1]]=>1
[[4,3,2,1],[3,2,1],[3,1],[1]]=>0
[[4,3,2,1],[4,2,1],[2,1],[1]]=>0
[[4,3,2,1],[3,2,1],[2,1],[1]]=>0
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>1
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>1
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>1
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>0
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>1
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>1
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>1
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]=>0
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]=>0
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]=>0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]=>0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]=>0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]=>0
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>1
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>1
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>1
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>1
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>2
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>2
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>1
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>1
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]=>1
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]=>2
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]=>2
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]=>1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]=>1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]=>2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]=>1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]=>1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]=>1
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]=>0
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]=>0
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]=>0
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]=>0
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]=>0
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]=>0
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]=>0
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>0
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>1
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>1
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>1
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>1
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>1
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>1
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]=>0
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]=>0
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]=>0
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]=>1
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]=>1
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]=>0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]=>0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]=>0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]=>1
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]=>0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]=>0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]=>0
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]=>0
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]=>0
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]=>0
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]=>0
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]=>0
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]=>0
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]=>0
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]]=>0
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]=>0
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>3
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>2
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>3
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>2
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>2
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>1
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>1
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>1
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>1
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>1
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>1
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]=>0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]=>0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]=>0
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>3
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>4
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>2
[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>3
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>4
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>3
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>4
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>2
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>2
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>3
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>2
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>3
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>2
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>3
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>2
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>3
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>4
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>1
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>1
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>2
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>1
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>2
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>1
[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>2
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>3
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>1
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>1
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>2
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>1
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>2
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>2
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>2
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>2
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>4
[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>3
[[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>1
[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>2
[[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>2
[[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>1
[[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>5
[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>5
[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>4
[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>5
[[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>2
[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>3
[[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>3
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>4
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>5
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>5
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>4
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>5
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>5
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>6
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>6
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>5
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>6
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>6
[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>2
[[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>1
[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>2
[[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>5
[[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>2
[[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>1
[[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>6
[[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>5
[[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>5
[[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[2,2,2,1,1,1,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>6
[[7,2,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>6
[[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>5
[[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>6
[[6,2,1,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>3
[[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>4
[[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[5,3,1,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>3
[[5,2,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>5
[[5,2,1,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>2
[[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>3
[[4,4,1,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>4
[[4,3,2,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[4,3,1,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>2
[[4,2,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>1
[[4,2,1,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>1
[[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>2
[[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[3,3,1,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>2
[[3,2,2,2,0,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[3,2,2,1,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[3,2,1,1,1,1,0,0,0],[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>1
[[2,2,2,2,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[2,2,2,1,1,1,0,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,2,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,1,1,1,1,0],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>4
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>5
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>5
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>5
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>5
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>6
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>9
[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[7,1,1,1,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[6,3,1,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[6,2,1,1,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[5,3,1,1,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[4,4,1,1,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[4,3,2,1,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>6
[[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>5
[[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>4
[[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[3,3,3,1,0,0,0,0,0,0],[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>6
[[3,3,2,2,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>6
[[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>5
[[3,3,1,1,1,1,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>5
[[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>4
[[3,2,1,1,1,1,1,0,0,0],[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[3,1,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>5
[[2,2,2,2,1,1,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[2,2,2,1,1,1,1,0,0,0],[2,2,2,1,1,1,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>2
[[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[9,1,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[8,2,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>7
[[8,1,1,0,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>6
[[7,3,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>7
[[7,2,1,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>4
[[7,1,1,1,0,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>5
[[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>7
[[6,3,1,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>4
[[6,2,2,0,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>6
[[6,2,1,1,0,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>3
[[6,1,1,1,1,0,0,0,0,0],[5,1,1,1,1,0,0,0,0],[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>4
[[5,4,1,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>4
[[5,3,2,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[5,3,1,1,0,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>3
[[5,2,2,1,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>2
[[5,2,1,1,1,0,0,0,0,0],[4,2,1,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>2
[[5,1,1,1,1,1,0,0,0,0],[4,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>3
[[4,4,2,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>5
[[4,4,1,1,0,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>4
[[4,3,3,0,0,0,0,0,0,0],[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>6
[[4,3,2,1,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[4,3,1,1,1,0,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>2
[[4,2,2,2,0,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>5
[[4,2,2,1,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>1
[[4,2,1,1,1,1,0,0,0,0],[3,2,1,1,1,1,0,0,0],[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>1
[[4,1,1,1,1,1,1,0,0,0],[3,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>2
[[3,3,3,1,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>3
[[3,3,2,2,0,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>4
[[3,3,2,1,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[3,3,1,1,1,1,0,0,0,0],[3,2,1,1,1,1,0,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>2
[[3,2,2,2,1,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>0
[[3,2,2,1,1,1,0,0,0,0],[2,2,2,1,1,1,0,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[3,2,1,1,1,1,1,0,0,0],[2,2,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[3,1,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,1,0],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>1
[[2,2,2,2,1,1,0,0,0,0],[2,2,2,1,1,1,0,0,0],[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,2,2,1,1,1,1,0,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,2,1,1,1,1,1,1,0,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,1,1,1,1,1,0],[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>0
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>5
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>6
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>6
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>6
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>6
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>6
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>7
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>8
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>9
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>10
[]=>0
[[0]]=>0
[[0,0],[0]]=>0
[[0,0,0],[0,0],[0]]=>0
[[3,3,2],[3,2],[2]]=>0
[[3,3,2],[3,2],[3]]=>0
[[3,3,2],[3,3],[3]]=>0
[[3,3,3],[3,3],[3]]=>0
[[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[2,2,2,0],[2,2,2],[2,2],[2]]=>0
[[2,2,2,1],[2,2,1],[2,1],[1]]=>0
[[2,2,2,1],[2,2,1],[2,1],[2]]=>0
[[2,2,2,1],[2,2,1],[2,2],[2]]=>0
[[2,2,2,1],[2,2,2],[2,2],[2]]=>0
[[2,2,2,2],[2,2,2],[2,2],[2]]=>0
[[3,2,1,0],[3,2,1],[2,1],[1]]=>0
[[3,2,1,0],[3,2,1],[2,1],[2]]=>0
[[3,2,1,0],[3,2,1],[2,2],[2]]=>0
[[3,2,1,0],[3,2,1],[3,1],[1]]=>0
[[3,2,1,0],[3,2,1],[3,1],[2]]=>1
[[3,2,1,0],[3,2,1],[3,1],[3]]=>0
[[3,2,1,0],[3,2,1],[3,2],[2]]=>0
[[3,2,1,0],[3,2,1],[3,2],[3]]=>0
[[3,2,1,1],[2,1,1],[1,1],[1]]=>0
[[3,2,1,1],[2,1,1],[2,1],[1]]=>0
[[3,2,1,1],[2,1,1],[2,1],[2]]=>0
[[3,2,1,1],[2,2,1],[2,1],[1]]=>0
[[3,2,1,1],[2,2,1],[2,1],[2]]=>0
[[3,2,1,1],[2,2,1],[2,2],[2]]=>0
[[3,2,1,1],[3,1,1],[1,1],[1]]=>0
[[3,2,1,1],[3,1,1],[2,1],[1]]=>1
[[3,2,1,1],[3,1,1],[2,1],[2]]=>1
[[3,2,1,1],[3,1,1],[3,1],[1]]=>0
[[3,2,1,1],[3,1,1],[3,1],[2]]=>1
[[3,2,1,1],[3,1,1],[3,1],[3]]=>0
[[3,2,1,1],[3,2,1],[2,1],[1]]=>0
[[3,2,1,1],[3,2,1],[2,1],[2]]=>0
[[3,2,1,1],[3,2,1],[2,2],[2]]=>0
[[3,2,1,1],[3,2,1],[3,1],[1]]=>0
[[3,2,1,1],[3,2,1],[3,1],[2]]=>1
[[3,2,1,1],[3,2,1],[3,1],[3]]=>0
[[3,2,1,1],[3,2,1],[3,2],[2]]=>0
[[3,2,1,1],[3,2,1],[3,2],[3]]=>0
[[3,2,2,0],[2,2,0],[2,0],[0]]=>0
[[3,2,2,0],[2,2,0],[2,0],[1]]=>1
[[3,2,2,0],[2,2,0],[2,0],[2]]=>0
[[3,2,2,0],[2,2,0],[2,1],[1]]=>1
[[3,2,2,0],[2,2,0],[2,1],[2]]=>1
[[3,2,2,0],[2,2,0],[2,2],[2]]=>0
[[3,2,2,0],[2,2,1],[2,1],[1]]=>1
[[3,2,2,0],[2,2,1],[2,1],[2]]=>1
[[3,2,2,0],[2,2,1],[2,2],[2]]=>1
[[3,2,2,0],[2,2,2],[2,2],[2]]=>0
[[3,2,2,0],[3,2,0],[2,0],[0]]=>0
[[3,2,2,0],[3,2,0],[2,0],[1]]=>1
[[3,2,2,0],[3,2,0],[2,0],[2]]=>0
[[3,2,2,0],[3,2,0],[2,1],[1]]=>1
[[3,2,2,0],[3,2,0],[2,1],[2]]=>1
[[3,2,2,0],[3,2,0],[2,2],[2]]=>0
[[3,2,2,0],[3,2,0],[3,0],[0]]=>0
[[3,2,2,0],[3,2,0],[3,0],[1]]=>1
[[3,2,2,0],[3,2,0],[3,0],[2]]=>1
[[3,2,2,0],[3,2,0],[3,0],[3]]=>0
[[3,2,2,0],[3,2,0],[3,1],[1]]=>1
[[3,2,2,0],[3,2,0],[3,1],[2]]=>2
[[3,2,2,0],[3,2,0],[3,1],[3]]=>1
[[3,2,2,0],[3,2,0],[3,2],[2]]=>0
[[3,2,2,0],[3,2,0],[3,2],[3]]=>0
[[3,2,2,0],[3,2,1],[2,1],[1]]=>1
[[3,2,2,0],[3,2,1],[2,1],[2]]=>1
[[3,2,2,0],[3,2,1],[2,2],[2]]=>1
[[3,2,2,0],[3,2,1],[3,1],[1]]=>1
[[3,2,2,0],[3,2,1],[3,1],[2]]=>2
[[3,2,2,0],[3,2,1],[3,1],[3]]=>1
[[3,2,2,0],[3,2,1],[3,2],[2]]=>1
[[3,2,2,0],[3,2,1],[3,2],[3]]=>1
[[3,2,2,0],[3,2,2],[2,2],[2]]=>0
[[3,2,2,0],[3,2,2],[3,2],[2]]=>0
[[3,2,2,0],[3,2,2],[3,2],[3]]=>0
[[3,2,2,1],[2,2,1],[2,1],[1]]=>0
[[3,2,2,1],[2,2,1],[2,1],[2]]=>0
[[3,2,2,1],[2,2,1],[2,2],[2]]=>0
[[3,2,2,1],[2,2,2],[2,2],[2]]=>0
[[3,2,2,1],[3,2,1],[2,1],[1]]=>0
[[3,2,2,1],[3,2,1],[2,1],[2]]=>0
[[3,2,2,1],[3,2,1],[2,2],[2]]=>0
[[3,2,2,1],[3,2,1],[3,1],[1]]=>0
[[3,2,2,1],[3,2,1],[3,1],[2]]=>1
[[3,2,2,1],[3,2,1],[3,1],[3]]=>0
[[3,2,2,1],[3,2,1],[3,2],[2]]=>0
[[3,2,2,1],[3,2,1],[3,2],[3]]=>0
[[3,2,2,1],[3,2,2],[2,2],[2]]=>0
[[3,2,2,1],[3,2,2],[3,2],[2]]=>0
[[3,2,2,1],[3,2,2],[3,2],[3]]=>0
[[3,2,2,2],[2,2,2],[2,2],[2]]=>0
[[3,2,2,2],[3,2,2],[2,2],[2]]=>0
[[3,2,2,2],[3,2,2],[3,2],[2]]=>0
[[3,2,2,2],[3,2,2],[3,2],[3]]=>0
[[3,3,0,0],[3,3,0],[3,0],[0]]=>0
[[3,3,0,0],[3,3,0],[3,0],[1]]=>1
[[3,3,0,0],[3,3,0],[3,0],[2]]=>1
[[3,3,0,0],[3,3,0],[3,0],[3]]=>0
[[3,3,0,0],[3,3,0],[3,1],[1]]=>1
[[3,3,0,0],[3,3,0],[3,1],[2]]=>2
[[3,3,0,0],[3,3,0],[3,1],[3]]=>1
[[3,3,0,0],[3,3,0],[3,2],[2]]=>1
[[3,3,0,0],[3,3,0],[3,2],[3]]=>1
[[3,3,0,0],[3,3,0],[3,3],[3]]=>0
[[3,3,1,0],[3,1,0],[1,0],[0]]=>0
[[3,3,1,0],[3,1,0],[1,0],[1]]=>0
[[3,3,1,0],[3,1,0],[1,1],[1]]=>0
[[3,3,1,0],[3,1,0],[2,0],[0]]=>1
[[3,3,1,0],[3,1,0],[2,0],[1]]=>2
[[3,3,1,0],[3,1,0],[2,0],[2]]=>1
[[3,3,1,0],[3,1,0],[2,1],[1]]=>1
[[3,3,1,0],[3,1,0],[2,1],[2]]=>1
[[3,3,1,0],[3,1,0],[3,0],[0]]=>0
[[3,3,1,0],[3,1,0],[3,0],[1]]=>1
[[3,3,1,0],[3,1,0],[3,0],[2]]=>1
[[3,3,1,0],[3,1,0],[3,0],[3]]=>0
[[3,3,1,0],[3,1,0],[3,1],[1]]=>0
[[3,3,1,0],[3,1,0],[3,1],[2]]=>1
[[3,3,1,0],[3,1,0],[3,1],[3]]=>0
[[3,3,1,0],[3,1,1],[1,1],[1]]=>0
[[3,3,1,0],[3,1,1],[2,1],[1]]=>1
[[3,3,1,0],[3,1,1],[2,1],[2]]=>1
[[3,3,1,0],[3,1,1],[3,1],[1]]=>0
[[3,3,1,0],[3,1,1],[3,1],[2]]=>1
[[3,3,1,0],[3,1,1],[3,1],[3]]=>0
[[3,3,1,0],[3,2,0],[2,0],[0]]=>1
[[3,3,1,0],[3,2,0],[2,0],[1]]=>2
[[3,3,1,0],[3,2,0],[2,0],[2]]=>1
[[3,3,1,0],[3,2,0],[2,1],[1]]=>2
[[3,3,1,0],[3,2,0],[2,1],[2]]=>2
[[3,3,1,0],[3,2,0],[2,2],[2]]=>1
[[3,3,1,0],[3,2,0],[3,0],[0]]=>1
[[3,3,1,0],[3,2,0],[3,0],[1]]=>2
[[3,3,1,0],[3,2,0],[3,0],[2]]=>2
[[3,3,1,0],[3,2,0],[3,0],[3]]=>1
[[3,3,1,0],[3,2,0],[3,1],[1]]=>2
[[3,3,1,0],[3,2,0],[3,1],[2]]=>3
[[3,3,1,0],[3,2,0],[3,1],[3]]=>2
[[3,3,1,0],[3,2,0],[3,2],[2]]=>1
[[3,3,1,0],[3,2,0],[3,2],[3]]=>1
[[3,3,1,0],[3,2,1],[2,1],[1]]=>1
[[3,3,1,0],[3,2,1],[2,1],[2]]=>1
[[3,3,1,0],[3,2,1],[2,2],[2]]=>1
[[3,3,1,0],[3,2,1],[3,1],[1]]=>1
[[3,3,1,0],[3,2,1],[3,1],[2]]=>2
[[3,3,1,0],[3,2,1],[3,1],[3]]=>1
[[3,3,1,0],[3,2,1],[3,2],[2]]=>1
[[3,3,1,0],[3,2,1],[3,2],[3]]=>1
[[3,3,1,0],[3,3,0],[3,0],[0]]=>0
[[3,3,1,0],[3,3,0],[3,0],[1]]=>1
[[3,3,1,0],[3,3,0],[3,0],[2]]=>1
[[3,3,1,0],[3,3,0],[3,0],[3]]=>0
[[3,3,1,0],[3,3,0],[3,1],[1]]=>1
[[3,3,1,0],[3,3,0],[3,1],[2]]=>2
[[3,3,1,0],[3,3,0],[3,1],[3]]=>1
[[3,3,1,0],[3,3,0],[3,2],[2]]=>1
[[3,3,1,0],[3,3,0],[3,2],[3]]=>1
[[3,3,1,0],[3,3,0],[3,3],[3]]=>0
[[3,3,1,0],[3,3,1],[3,1],[1]]=>0
[[3,3,1,0],[3,3,1],[3,1],[2]]=>1
[[3,3,1,0],[3,3,1],[3,1],[3]]=>0
[[3,3,1,0],[3,3,1],[3,2],[2]]=>1
[[3,3,1,0],[3,3,1],[3,2],[3]]=>1
[[3,3,1,0],[3,3,1],[3,3],[3]]=>0
[[3,3,1,1],[3,1,1],[1,1],[1]]=>0
[[3,3,1,1],[3,1,1],[2,1],[1]]=>1
[[3,3,1,1],[3,1,1],[2,1],[2]]=>1
[[3,3,1,1],[3,1,1],[3,1],[1]]=>0
[[3,3,1,1],[3,1,1],[3,1],[2]]=>1
[[3,3,1,1],[3,1,1],[3,1],[3]]=>0
[[3,3,1,1],[3,2,1],[2,1],[1]]=>1
[[3,3,1,1],[3,2,1],[2,1],[2]]=>1
[[3,3,1,1],[3,2,1],[2,2],[2]]=>1
[[3,3,1,1],[3,2,1],[3,1],[1]]=>1
[[3,3,1,1],[3,2,1],[3,1],[2]]=>2
[[3,3,1,1],[3,2,1],[3,1],[3]]=>1
[[3,3,1,1],[3,2,1],[3,2],[2]]=>1
[[3,3,1,1],[3,2,1],[3,2],[3]]=>1
[[3,3,1,1],[3,3,1],[3,1],[1]]=>0
[[3,3,1,1],[3,3,1],[3,1],[2]]=>1
[[3,3,1,1],[3,3,1],[3,1],[3]]=>0
[[3,3,1,1],[3,3,1],[3,2],[2]]=>1
[[3,3,1,1],[3,3,1],[3,2],[3]]=>1
[[3,3,1,1],[3,3,1],[3,3],[3]]=>0
[[3,3,2,0],[3,2,0],[2,0],[0]]=>0
[[3,3,2,0],[3,2,0],[2,0],[1]]=>1
[[3,3,2,0],[3,2,0],[2,0],[2]]=>0
[[3,3,2,0],[3,2,0],[2,1],[1]]=>1
[[3,3,2,0],[3,2,0],[2,1],[2]]=>1
[[3,3,2,0],[3,2,0],[2,2],[2]]=>0
[[3,3,2,0],[3,2,0],[3,0],[0]]=>0
[[3,3,2,0],[3,2,0],[3,0],[1]]=>1
[[3,3,2,0],[3,2,0],[3,0],[2]]=>1
[[3,3,2,0],[3,2,0],[3,0],[3]]=>0
[[3,3,2,0],[3,2,0],[3,1],[1]]=>1
[[3,3,2,0],[3,2,0],[3,1],[2]]=>2
[[3,3,2,0],[3,2,0],[3,1],[3]]=>1
[[3,3,2,0],[3,2,0],[3,2],[2]]=>0
[[3,3,2,0],[3,2,0],[3,2],[3]]=>0
[[3,3,2,0],[3,2,1],[2,1],[1]]=>1
[[3,3,2,0],[3,2,1],[2,1],[2]]=>1
[[3,3,2,0],[3,2,1],[2,2],[2]]=>1
[[3,3,2,0],[3,2,1],[3,1],[1]]=>1
[[3,3,2,0],[3,2,1],[3,1],[2]]=>2
[[3,3,2,0],[3,2,1],[3,1],[3]]=>1
[[3,3,2,0],[3,2,1],[3,2],[2]]=>1
[[3,3,2,0],[3,2,1],[3,2],[3]]=>1
[[3,3,2,0],[3,2,2],[2,2],[2]]=>0
[[3,3,2,0],[3,2,2],[3,2],[2]]=>0
[[3,3,2,0],[3,2,2],[3,2],[3]]=>0
[[3,3,2,0],[3,3,0],[3,0],[0]]=>0
[[3,3,2,0],[3,3,0],[3,0],[1]]=>1
[[3,3,2,0],[3,3,0],[3,0],[2]]=>1
[[3,3,2,0],[3,3,0],[3,0],[3]]=>0
[[3,3,2,0],[3,3,0],[3,1],[1]]=>1
[[3,3,2,0],[3,3,0],[3,1],[2]]=>2
[[3,3,2,0],[3,3,0],[3,1],[3]]=>1
[[3,3,2,0],[3,3,0],[3,2],[2]]=>1
[[3,3,2,0],[3,3,0],[3,2],[3]]=>1
[[3,3,2,0],[3,3,0],[3,3],[3]]=>0
[[3,3,2,0],[3,3,1],[3,1],[1]]=>1
[[3,3,2,0],[3,3,1],[3,1],[2]]=>2
[[3,3,2,0],[3,3,1],[3,1],[3]]=>1
[[3,3,2,0],[3,3,1],[3,2],[2]]=>2
[[3,3,2,0],[3,3,1],[3,2],[3]]=>2
[[3,3,2,0],[3,3,1],[3,3],[3]]=>1
[[3,3,2,0],[3,3,2],[3,2],[2]]=>0
[[3,3,2,0],[3,3,2],[3,2],[3]]=>0
[[3,3,2,0],[3,3,2],[3,3],[3]]=>0
[[3,3,2,1],[3,2,1],[2,1],[1]]=>0
[[3,3,2,1],[3,2,1],[2,1],[2]]=>0
[[3,3,2,1],[3,2,1],[2,2],[2]]=>0
[[3,3,2,1],[3,2,1],[3,1],[1]]=>0
[[3,3,2,1],[3,2,1],[3,1],[2]]=>1
[[3,3,2,1],[3,2,1],[3,1],[3]]=>0
[[3,3,2,1],[3,2,1],[3,2],[2]]=>0
[[3,3,2,1],[3,2,1],[3,2],[3]]=>0
[[3,3,2,1],[3,2,2],[2,2],[2]]=>0
[[3,3,2,1],[3,2,2],[3,2],[2]]=>0
[[3,3,2,1],[3,2,2],[3,2],[3]]=>0
[[3,3,2,1],[3,3,1],[3,1],[1]]=>0
[[3,3,2,1],[3,3,1],[3,1],[2]]=>1
[[3,3,2,1],[3,3,1],[3,1],[3]]=>0
[[3,3,2,1],[3,3,1],[3,2],[2]]=>1
[[3,3,2,1],[3,3,1],[3,2],[3]]=>1
[[3,3,2,1],[3,3,1],[3,3],[3]]=>0
[[3,3,2,1],[3,3,2],[3,2],[2]]=>0
[[3,3,2,1],[3,3,2],[3,2],[3]]=>0
[[3,3,2,1],[3,3,2],[3,3],[3]]=>0
[[3,3,2,2],[3,2,2],[2,2],[2]]=>0
[[3,3,2,2],[3,2,2],[3,2],[2]]=>0
[[3,3,2,2],[3,2,2],[3,2],[3]]=>0
[[3,3,2,2],[3,3,2],[3,2],[2]]=>0
[[3,3,2,2],[3,3,2],[3,2],[3]]=>0
[[3,3,2,2],[3,3,2],[3,3],[3]]=>0
[[3,3,3,0],[3,3,0],[3,0],[0]]=>0
[[3,3,3,0],[3,3,0],[3,0],[1]]=>1
[[3,3,3,0],[3,3,0],[3,0],[2]]=>1
[[3,3,3,0],[3,3,0],[3,0],[3]]=>0
[[3,3,3,0],[3,3,0],[3,1],[1]]=>1
[[3,3,3,0],[3,3,0],[3,1],[2]]=>2
[[3,3,3,0],[3,3,0],[3,1],[3]]=>1
[[3,3,3,0],[3,3,0],[3,2],[2]]=>1
[[3,3,3,0],[3,3,0],[3,2],[3]]=>1
[[3,3,3,0],[3,3,0],[3,3],[3]]=>0
[[3,3,3,0],[3,3,1],[3,1],[1]]=>1
[[3,3,3,0],[3,3,1],[3,1],[2]]=>2
[[3,3,3,0],[3,3,1],[3,1],[3]]=>1
[[3,3,3,0],[3,3,1],[3,2],[2]]=>2
[[3,3,3,0],[3,3,1],[3,2],[3]]=>2
[[3,3,3,0],[3,3,1],[3,3],[3]]=>1
[[3,3,3,0],[3,3,2],[3,2],[2]]=>1
[[3,3,3,0],[3,3,2],[3,2],[3]]=>1
[[3,3,3,0],[3,3,2],[3,3],[3]]=>1
[[3,3,3,0],[3,3,3],[3,3],[3]]=>0
[[3,3,3,1],[3,3,1],[3,1],[1]]=>0
[[3,3,3,1],[3,3,1],[3,1],[2]]=>1
[[3,3,3,1],[3,3,1],[3,1],[3]]=>0
[[3,3,3,1],[3,3,1],[3,2],[2]]=>1
[[3,3,3,1],[3,3,1],[3,2],[3]]=>1
[[3,3,3,1],[3,3,1],[3,3],[3]]=>0
[[3,3,3,1],[3,3,2],[3,2],[2]]=>1
[[3,3,3,1],[3,3,2],[3,2],[3]]=>1
[[3,3,3,1],[3,3,2],[3,3],[3]]=>1
[[3,3,3,1],[3,3,3],[3,3],[3]]=>0
[[3,3,3,2],[3,3,2],[3,2],[2]]=>0
[[3,3,3,2],[3,3,2],[3,2],[3]]=>0
[[3,3,3,2],[3,3,2],[3,3],[3]]=>0
[[3,3,3,2],[3,3,3],[3,3],[3]]=>0
[[3,3,3,3],[3,3,3],[3,3],[3]]=>0
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Description
The number of special entries.
An entry $a_{i,j}$ of a Gelfand-Tsetlin pattern is special if $a_{i-1,j-i} > a_{i,j} > a_{i-1,j}$. That is, it is neither boxed nor circled.
An entry $a_{i,j}$ of a Gelfand-Tsetlin pattern is special if $a_{i-1,j-i} > a_{i,j} > a_{i-1,j}$. That is, it is neither boxed nor circled.
Code
def statistic(g): return g.number_of_special_entries()
Created
Jun 11, 2013 at 14:48 by Travis Scrimshaw
Updated
Jun 01, 2019 at 09:02 by Martin Rubey
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