Identifier
- St000177: Gelfand-Tsetlin patterns ⟶ ℤ
Values
=>
Cc0018;cc-rep
[[1]]=>0
[[2,0],[0]]=>0
[[2,0],[1]]=>0
[[2,0],[2]]=>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]]=>0
[[3,0,0],[2,0],[0]]=>1
[[3,0,0],[2,0],[1]]=>1
[[3,0,0],[2,0],[2]]=>0
[[3,0,0],[3,0],[0]]=>0
[[3,0,0],[3,0],[1]]=>0
[[3,0,0],[3,0],[2]]=>0
[[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]]=>0
[[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],[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]]=>0
[[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]]=>1
[[4,0,0,0],[2,0,0],[2,0],[0]]=>1
[[4,0,0,0],[2,0,0],[2,0],[1]]=>1
[[4,0,0,0],[2,0,0],[2,0],[2]]=>0
[[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]]=>1
[[4,0,0,0],[3,0,0],[2,0],[0]]=>2
[[4,0,0,0],[3,0,0],[2,0],[1]]=>2
[[4,0,0,0],[3,0,0],[2,0],[2]]=>1
[[4,0,0,0],[3,0,0],[3,0],[0]]=>1
[[4,0,0,0],[3,0,0],[3,0],[1]]=>1
[[4,0,0,0],[3,0,0],[3,0],[2]]=>1
[[4,0,0,0],[3,0,0],[3,0],[3]]=>0
[[4,0,0,0],[4,0,0],[0,0],[0]]=>0
[[4,0,0,0],[4,0,0],[1,0],[0]]=>1
[[4,0,0,0],[4,0,0],[1,0],[1]]=>0
[[4,0,0,0],[4,0,0],[2,0],[0]]=>1
[[4,0,0,0],[4,0,0],[2,0],[1]]=>1
[[4,0,0,0],[4,0,0],[2,0],[2]]=>0
[[4,0,0,0],[4,0,0],[3,0],[0]]=>1
[[4,0,0,0],[4,0,0],[3,0],[1]]=>1
[[4,0,0,0],[4,0,0],[3,0],[2]]=>1
[[4,0,0,0],[4,0,0],[3,0],[3]]=>0
[[4,0,0,0],[4,0,0],[4,0],[0]]=>0
[[4,0,0,0],[4,0,0],[4,0],[1]]=>0
[[4,0,0,0],[4,0,0],[4,0],[2]]=>0
[[4,0,0,0],[4,0,0],[4,0],[3]]=>0
[[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]]=>1
[[3,1,0,0],[2,0,0],[2,0],[0]]=>1
[[3,1,0,0],[2,0,0],[2,0],[1]]=>1
[[3,1,0,0],[2,0,0],[2,0],[2]]=>0
[[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]]=>1
[[3,1,0,0],[2,1,0],[2,0],[2]]=>0
[[3,1,0,0],[2,1,0],[2,1],[1]]=>1
[[3,1,0,0],[2,1,0],[2,1],[2]]=>0
[[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]]=>0
[[3,1,0,0],[3,0,0],[2,0],[0]]=>1
[[3,1,0,0],[3,0,0],[2,0],[1]]=>1
[[3,1,0,0],[3,0,0],[2,0],[2]]=>0
[[3,1,0,0],[3,0,0],[3,0],[0]]=>0
[[3,1,0,0],[3,0,0],[3,0],[1]]=>0
[[3,1,0,0],[3,0,0],[3,0],[2]]=>0
[[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]]=>1
[[3,1,0,0],[3,1,0],[2,0],[2]]=>0
[[3,1,0,0],[3,1,0],[2,1],[1]]=>1
[[3,1,0,0],[3,1,0],[2,1],[2]]=>0
[[3,1,0,0],[3,1,0],[3,0],[0]]=>0
[[3,1,0,0],[3,1,0],[3,0],[1]]=>0
[[3,1,0,0],[3,1,0],[3,0],[2]]=>0
[[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]]=>0
[[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]]=>0
[[2,2,0,0],[2,0,0],[2,0],[0]]=>0
[[2,2,0,0],[2,0,0],[2,0],[1]]=>0
[[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]]=>0
[[2,2,0,0],[2,1,0],[1,1],[1]]=>0
[[2,2,0,0],[2,1,0],[2,0],[0]]=>1
[[2,2,0,0],[2,1,0],[2,0],[1]]=>1
[[2,2,0,0],[2,1,0],[2,0],[2]]=>1
[[2,2,0,0],[2,1,0],[2,1],[1]]=>0
[[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]]=>0
[[2,2,0,0],[2,2,0],[2,0],[2]]=>0
[[2,2,0,0],[2,2,0],[2,1],[1]]=>0
[[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]]=>0
[[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
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]]=>0
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]]=>1
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]=>1
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]=>0
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]]=>2
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]=>2
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]]=>1
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]=>2
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]=>1
[[5,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]]=>1
[[5,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]=>1
[[5,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]]=>2
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]]=>2
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]]=>2
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]=>2
[[5,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]=>2
[[5,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]=>2
[[5,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]]=>2
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]]=>2
[[5,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]=>2
[[5,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]]=>2
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]]=>2
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]]=>2
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]]=>3
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]=>2
[[5,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]]=>2
[[5,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]=>2
[[5,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]]=>3
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]]=>3
[[5,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]=>3
[[5,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>1
[[5,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]]=>2
[[5,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]]=>2
[[5,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]=>2
[[5,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]]=>2
[[5,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]=>2
[[5,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>2
[[5,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]]=>0
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]]=>0
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]]=>0
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]=>0
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]]=>0
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]]=>0
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]]=>1
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]]=>1
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]]=>1
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]]=>1
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]=>1
[[4,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]]=>0
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]]=>1
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]]=>1
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]]=>1
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]=>1
[[4,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]=>0
[[4,1,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]]=>0
[[4,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]]=>1
[[4,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]=>1
[[4,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]=>0
[[4,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]]=>0
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]]=>1
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]]=>2
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]]=>2
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]=>1
[[4,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]=>1
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]]=>2
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]]=>1
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>2
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>2
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>2
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]=>2
[[4,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]=>1
[[4,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]=>1
[[4,1,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]]=>2
[[4,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]]=>1
[[4,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]=>2
[[4,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]=>1
[[4,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]=>1
[[4,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>1
[[4,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]]=>0
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]]=>1
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]]=>2
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]=>1
[[4,1,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]]=>2
[[4,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]]=>1
[[4,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]=>2
[[4,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]=>1
[[4,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]=>0
[[4,1,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]]=>0
[[4,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]=>0
[[4,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]]=>1
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]]=>1
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]=>1
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]]=>2
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]]=>2
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]]=>2
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]]=>2
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]=>2
[[4,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]=>1
[[4,1,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]]=>2
[[4,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]=>2
[[4,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]=>1
[[4,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>1
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]]=>1
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]]=>2
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]=>1
[[4,1,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]]=>3
[[4,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]]=>1
[[4,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]=>3
[[4,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]=>1
[[4,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]=>0
[[4,1,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]]=>1
[[4,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]=>1
[[4,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]=>0
[[4,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>0
[[4,1,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]]=>0
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]]=>2
[[4,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]=>2
[[4,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]=>2
[[4,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>2
[[4,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]=>0
[[4,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>0
[[4,1,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]]=>0
[[4,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]]=>1
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]]=>1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]]=>1
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]=>0
[[3,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]]=>1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]]=>1
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]=>0
[[3,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]=>1
[[3,2,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]]=>0
[[3,2,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]=>0
[[3,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]=>1
[[3,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]]=>1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]]=>0
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]=>0
[[3,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>2
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>0
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]=>1
[[3,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]=>1
[[3,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]]=>0
[[3,2,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]=>1
[[3,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]=>1
[[3,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]=>0
[[3,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]]=>1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]]=>1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]=>1
[[3,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]=>1
[[3,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]=>0
[[3,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]]=>1
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]]=>2
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]]=>1
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]=>1
[[3,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]=>1
[[3,2,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]]=>0
[[3,2,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]=>1
[[3,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]=>1
[[3,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>0
[[3,2,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]]=>2
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]]=>3
[[3,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]=>2
[[3,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]=>2
[[3,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]=>1
[[3,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]]=>1
[[3,2,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]=>0
[[3,2,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]]=>2
[[3,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]]=>0
[[3,2,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]=>1
[[3,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]=>1
[[3,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>0
[[3,2,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]]=>1
[[3,2,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]=>1
[[3,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]=>1
[[3,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>1
[[3,2,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]=>0
[[3,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[3,1],[3]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[3,0],[3]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[3,0],[3]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[3,1],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[3,0],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[2,1],[2]]=>0
[[3,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[3,0],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,1],[2]]=>0
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]]=>0
[[3,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[2,0],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[2]]=>0
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]]=>0
[[3,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[2,0,0],[2,0],[2]]=>0
[[3,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[3,1],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[3,0],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[2,1],[1]]=>1
[[3,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[3,0],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,1],[1]]=>1
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[2,0],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[1,1],[1]]=>0
[[3,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>1
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>1
[[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
[[3,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[2,0,0],[2,0],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[1,1,0],[1,1],[1]]=>0
[[3,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]=>1
[[3,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]=>1
[[3,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]]=>0
[[3,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[1,0],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[1,0],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,0],[1]]=>1
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[2,0,0],[1,0],[1]]=>1
[[3,1,1,0,0],[3,1,0,0],[1,1,0],[1,0],[1]]=>0
[[3,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]=>1
[[3,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]=>1
[[3,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]]=>0
[[3,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[1,0,0],[1,0],[1]]=>0
[[3,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]=>1
[[3,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[3,0],[0]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[3,0],[0]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[2,0],[0]]=>1
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[0]]=>1
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[0]]=>1
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]=>1
[[3,1,1,0,0],[3,1,0,0],[2,0,0],[2,0],[0]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]=>1
[[3,1,1,0,0],[3,1,0,0],[3,1,0],[1,0],[0]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[1,0],[0]]=>1
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,0],[0]]=>1
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]=>1
[[3,1,1,0,0],[3,1,0,0],[2,0,0],[1,0],[0]]=>2
[[3,1,1,0,0],[3,1,0,0],[1,1,0],[1,0],[0]]=>0
[[3,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]=>2
[[3,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]=>1
[[3,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]]=>0
[[3,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]]=>0
[[3,1,1,0,0],[3,1,0,0],[1,0,0],[1,0],[0]]=>0
[[3,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]=>1
[[3,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]]=>0
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[0,0],[0]]=>0
[[3,1,1,0,0],[3,1,0,0],[2,0,0],[0,0],[0]]=>1
[[3,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]=>1
[[3,1,1,0,0],[3,1,0,0],[1,0,0],[0,0],[0]]=>0
[[3,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]=>1
[[3,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,2,0],[2,2],[2]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,2,0],[2,1],[2]]=>1
[[2,2,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,1],[2]]=>1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,2,0],[2,0],[2]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[2]]=>1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,0,0],[2,0],[2]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,2,0],[2,1],[1]]=>0
[[2,2,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,1],[1]]=>0
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,2,0],[2,0],[1]]=>0
[[2,2,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>0
[[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
[[2,2,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,0,0],[2,0],[1]]=>0
[[2,2,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]]=>0
[[2,2,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,0,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,2,0],[2,0],[0]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[0]]=>1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,0,0],[2,0],[0]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,0],[0]]=>1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,0,0],[1,0],[0]]=>1
[[2,2,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]]=>1
[[2,2,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]]=>0
[[2,2,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]]=>0
[[2,2,1,0,0],[2,2,0,0],[2,0,0],[0,0],[0]]=>0
[[2,2,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]]=>0
[[2,2,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,1],[2,1],[2]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,1],[2]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[2]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,1],[2,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,1],[1,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>0
[[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
[[2,1,1,1,0],[1,1,1,0],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[1,1,0],[1,1],[1]]=>0
[[2,1,1,1,0],[1,1,1,0],[1,1,0],[1,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,0],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[1,1,0],[1,0],[1]]=>0
[[2,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[1]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[0]]=>0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,0],[0]]=>0
[[2,1,1,1,0],[2,1,1,0],[1,1,0],[1,0],[0]]=>0
[[2,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]]=>0
[[1,1,1,1,1],[1,1,1,1],[1,1,1],[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]]=>4
[[5,0,0,0,0],[5,0,0,0],[0,0,0],[0,0],[0]]=>0
[[5,0,0,0,0],[5,0,0,0],[1,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[1,0,0],[1,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[1,0,0],[1,0],[1]]=>0
[[5,0,0,0,0],[5,0,0,0],[2,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[2,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[5,0,0,0],[2,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[2,0,0],[2,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[2,0,0],[2,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[2,0,0],[2,0],[2]]=>0
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[2,0],[0]]=>2
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[2,0],[1]]=>2
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[2,0],[2]]=>1
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[3,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[3,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[3,0],[2]]=>1
[[5,0,0,0,0],[5,0,0,0],[3,0,0],[3,0],[3]]=>0
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[0,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[1,0],[0]]=>2
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[1,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[2,0],[0]]=>2
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[2,0],[1]]=>2
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[2,0],[2]]=>1
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[3,0],[0]]=>2
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[3,0],[1]]=>2
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[3,0],[2]]=>2
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[3,0],[3]]=>1
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[2]]=>1
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[3]]=>1
[[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[4]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[0,0],[0]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[1,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[1,0],[1]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[2,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[2,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[2,0],[2]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[3,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[3,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[3,0],[2]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[3,0],[3]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[0]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[1]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[2]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[3]]=>1
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[4]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[0]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[1]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[2]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[3]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[4]]=>0
[[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[5]]=>0
[[4,1,0,0,0],[4,1,0,0],[1,0,0],[0,0],[0]]=>0
[[4,1,0,0,0],[4,1,0,0],[1,0,0],[1,0],[0]]=>0
[[4,1,0,0,0],[4,1,0,0],[1,0,0],[1,0],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[1,1,0],[1,0],[0]]=>0
[[4,1,0,0,0],[4,1,0,0],[1,1,0],[1,0],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[1,1,0],[1,1],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[2,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[4,1,0,0],[2,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,0,0],[2,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,0,0],[2,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,0,0],[2,0],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[2,1,0],[1,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,1,0],[1,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,1,0],[1,1],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,1,0],[2,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,1,0],[2,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,1,0],[2,0],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[2,1,0],[2,1],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[2,1,0],[2,1],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[0,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[1,0],[0]]=>2
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[1,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[2,0],[0]]=>2
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[2,0],[1]]=>2
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[2,0],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[3,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[3,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[3,0],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,0,0],[3,0],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[1,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[1,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[1,1],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[2,0],[0]]=>2
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[2,0],[1]]=>2
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[2,0],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[2,1],[1]]=>2
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[2,1],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[3,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[3,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[3,0],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[3,0],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[3,1],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[3,1],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[3,1,0],[3,1],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[0,0],[0]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[1,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[1,0],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[2,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[2,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[2,0],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[3,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[3,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[3,0],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[3,0],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[4,0],[0]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[4,0],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[4,0],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[4,0],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,0,0],[4,0],[4]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[1,0],[0]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[1,0],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[1,1],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[2,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[2,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[2,0],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[2,1],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[2,1],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[3,0],[0]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[3,0],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[3,0],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[3,0],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[3,1],[1]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[3,1],[2]]=>1
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[3,1],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,0],[0]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,0],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,0],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,0],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,0],[4]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,1],[1]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,1],[2]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,1],[3]]=>0
[[4,1,0,0,0],[4,1,0,0],[4,1,0],[4,1],[4]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,0,0],[0,0],[0]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,2,0,0],[2,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,0,0],[2,0],[0]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,0,0],[2,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,0,0],[2,0],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,1,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,2,0,0],[2,1,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,1,0],[1,1],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,1,0],[2,0],[0]]=>1
[[3,2,0,0,0],[3,2,0,0],[2,1,0],[2,0],[1]]=>1
[[3,2,0,0,0],[3,2,0,0],[2,1,0],[2,0],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[2,1,0],[2,1],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,1,0],[2,1],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[2,2,0],[2,0],[0]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,2,0],[2,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,2,0],[2,0],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,2,0],[2,1],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[2,2,0],[2,1],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[2,2,0],[2,2],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[0,0],[0]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[2,0],[0]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[2,0],[1]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[2,0],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[3,0],[0]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[3,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[3,0],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,0,0],[3,0],[3]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[1,0],[0]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[1,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[1,1],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[2,0],[0]]=>2
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[2,0],[1]]=>2
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[2,0],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[2,1],[1]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[2,1],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[3,0],[0]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[3,0],[1]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[3,0],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[3,0],[3]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[3,1],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[3,1],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,1,0],[3,1],[3]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[2,0],[0]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[2,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[2,0],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[2,1],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[2,1],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[2,2],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,0],[0]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,0],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,0],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,0],[3]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,1],[1]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,1],[2]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,1],[3]]=>1
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,2],[2]]=>0
[[3,2,0,0,0],[3,2,0,0],[3,2,0],[3,2],[3]]=>0
[[3,1,1,0,0],[3,1,1,0],[1,1,0],[1,0],[0]]=>0
[[3,1,1,0,0],[3,1,1,0],[1,1,0],[1,0],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[1,1,0],[1,1],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[1,1,1],[1,1],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[2,1,0],[1,0],[0]]=>1
[[3,1,1,0,0],[3,1,1,0],[2,1,0],[1,0],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[2,1,0],[1,1],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[2,1,0],[2,0],[0]]=>1
[[3,1,1,0,0],[3,1,1,0],[2,1,0],[2,0],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[2,1,0],[2,0],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[2,1,0],[2,1],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[2,1,0],[2,1],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[2,1,1],[1,1],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[2,1,1],[2,1],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[2,1,1],[2,1],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[1,0],[0]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[1,0],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[1,1],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[2,0],[0]]=>1
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[2,0],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[2,0],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[2,1],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[2,1],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[3,0],[0]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[3,0],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[3,0],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[3,0],[3]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[3,1],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[3,1],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,0],[3,1],[3]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,1],[1,1],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,1],[2,1],[1]]=>1
[[3,1,1,0,0],[3,1,1,0],[3,1,1],[2,1],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,1],[3,1],[1]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,1],[3,1],[2]]=>0
[[3,1,1,0,0],[3,1,1,0],[3,1,1],[3,1],[3]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,0],[1,0],[0]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,0],[1,0],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,0],[1,1],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,0],[2,0],[0]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,0],[2,0],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,0],[2,0],[2]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,0],[2,1],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,0],[2,1],[2]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,1],[1,1],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,1],[2,1],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,1,1],[2,1],[2]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,2,0],[2,0],[0]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,2,0],[2,0],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,2,0],[2,0],[2]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,2,0],[2,1],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,2,0],[2,1],[2]]=>1
[[2,2,1,0,0],[2,2,1,0],[2,2,0],[2,2],[2]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,2,1],[2,1],[1]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,2,1],[2,1],[2]]=>0
[[2,2,1,0,0],[2,2,1,0],[2,2,1],[2,2],[2]]=>0
[[2,1,1,1,0],[2,1,1,1],[1,1,1],[1,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,1],[2,1,1],[1,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,1],[2,1,1],[2,1],[1]]=>0
[[2,1,1,1,0],[2,1,1,1],[2,1,1],[2,1],[2]]=>0
[[6,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[6,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>1
[[6,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[6,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>1
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>1
[[6,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[6,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]=>1
[[6,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]=>0
[[6,0,0,0,0,0],[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]=>4
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]]=>2
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]]=>1
[[6,0,0,0,0,0],[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]]=>0
[[6,0,0,0,0,0],[5,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]=>4
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]]=>4
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]]=>4
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]]=>4
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[2,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[2,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[2,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[2,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[2,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[2,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[3,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[3,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[3,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[3,0,0],[3,0],[3]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[3,0],[0]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[3,0],[1]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[3,0],[2]]=>3
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[3,0],[3]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[3]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[4,0,0],[4,0],[4]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[3,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[3,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[3,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[3,0],[3]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[0]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[1]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[2]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[3]]=>2
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[4,0],[4]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[0]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[1]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[2]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[3]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[4]]=>1
[[6,0,0,0,0,0],[5,0,0,0,0],[5,0,0,0],[5,0,0],[5,0],[5]]=>0
[[6,0,0,0,0,0],[6,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]=>0
[[6,0,0,0,0,0],[6,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]=>0
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]=>0
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]=>0
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]]=>3
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]]=>3
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>3
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]=>2
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]]=>1
[[6,0,0,0,0,0],[6,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]]=>2
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of free tiles in the pattern.
The tiling of a pattern is the finest partition of the entries in the pattern, such that adjacent (NW,NE,SW,SE) entries that are equal belong to the same part. These parts are called tiles, and each entry in a pattern belong to exactly one tile.
A tile is free if it does not intersect any of the first and the last row.
The tiling of a pattern is the finest partition of the entries in the pattern, such that adjacent (NW,NE,SW,SE) entries that are equal belong to the same part. These parts are called tiles, and each entry in a pattern belong to exactly one tile.
A tile is free if it does not intersect any of the first and the last row.
References
[1] De Loera, Jesús A., McAllister, T. B. Vertices of Gelfand-Tsetlin polytopes MathSciNet:2096742
Created
Mar 21, 2014 at 22:51 by Per Alexandersson
Updated
May 29, 2015 at 17:08 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!