Identifier
-
Mp00077:
Semistandard tableaux
—shape⟶
Integer partitions
St000185: Integer partitions ⟶ ℤ
Values
=>
Cc0019;cc-rep-0
Cc0002;cc-rep
[[1,2]]=>[2]=>0
[[2,2]]=>[2]=>0
[[1],[2]]=>[1,1]=>1
[[1,3]]=>[2]=>0
[[2,3]]=>[2]=>0
[[3,3]]=>[2]=>0
[[1],[3]]=>[1,1]=>1
[[2],[3]]=>[1,1]=>1
[[1,1,2]]=>[3]=>0
[[1,2,2]]=>[3]=>0
[[2,2,2]]=>[3]=>0
[[1,1],[2]]=>[2,1]=>1
[[1,2],[2]]=>[2,1]=>1
[[1,4]]=>[2]=>0
[[2,4]]=>[2]=>0
[[3,4]]=>[2]=>0
[[4,4]]=>[2]=>0
[[1],[4]]=>[1,1]=>1
[[2],[4]]=>[1,1]=>1
[[3],[4]]=>[1,1]=>1
[[1,1,3]]=>[3]=>0
[[1,2,3]]=>[3]=>0
[[1,3,3]]=>[3]=>0
[[2,2,3]]=>[3]=>0
[[2,3,3]]=>[3]=>0
[[3,3,3]]=>[3]=>0
[[1,1],[3]]=>[2,1]=>1
[[1,2],[3]]=>[2,1]=>1
[[1,3],[2]]=>[2,1]=>1
[[1,3],[3]]=>[2,1]=>1
[[2,2],[3]]=>[2,1]=>1
[[2,3],[3]]=>[2,1]=>1
[[1],[2],[3]]=>[1,1,1]=>3
[[1,1,1,2]]=>[4]=>0
[[1,1,2,2]]=>[4]=>0
[[1,2,2,2]]=>[4]=>0
[[2,2,2,2]]=>[4]=>0
[[1,1,1],[2]]=>[3,1]=>1
[[1,1,2],[2]]=>[3,1]=>1
[[1,2,2],[2]]=>[3,1]=>1
[[1,1],[2,2]]=>[2,2]=>2
[[1,5]]=>[2]=>0
[[2,5]]=>[2]=>0
[[3,5]]=>[2]=>0
[[4,5]]=>[2]=>0
[[5,5]]=>[2]=>0
[[1],[5]]=>[1,1]=>1
[[2],[5]]=>[1,1]=>1
[[3],[5]]=>[1,1]=>1
[[4],[5]]=>[1,1]=>1
[[1,1,4]]=>[3]=>0
[[1,2,4]]=>[3]=>0
[[1,3,4]]=>[3]=>0
[[1,4,4]]=>[3]=>0
[[2,2,4]]=>[3]=>0
[[2,3,4]]=>[3]=>0
[[2,4,4]]=>[3]=>0
[[3,3,4]]=>[3]=>0
[[3,4,4]]=>[3]=>0
[[4,4,4]]=>[3]=>0
[[1,1],[4]]=>[2,1]=>1
[[1,2],[4]]=>[2,1]=>1
[[1,4],[2]]=>[2,1]=>1
[[1,3],[4]]=>[2,1]=>1
[[1,4],[3]]=>[2,1]=>1
[[1,4],[4]]=>[2,1]=>1
[[2,2],[4]]=>[2,1]=>1
[[2,3],[4]]=>[2,1]=>1
[[2,4],[3]]=>[2,1]=>1
[[2,4],[4]]=>[2,1]=>1
[[3,3],[4]]=>[2,1]=>1
[[3,4],[4]]=>[2,1]=>1
[[1],[2],[4]]=>[1,1,1]=>3
[[1],[3],[4]]=>[1,1,1]=>3
[[2],[3],[4]]=>[1,1,1]=>3
[[1,1,1,3]]=>[4]=>0
[[1,1,2,3]]=>[4]=>0
[[1,1,3,3]]=>[4]=>0
[[1,2,2,3]]=>[4]=>0
[[1,2,3,3]]=>[4]=>0
[[1,3,3,3]]=>[4]=>0
[[2,2,2,3]]=>[4]=>0
[[2,2,3,3]]=>[4]=>0
[[2,3,3,3]]=>[4]=>0
[[3,3,3,3]]=>[4]=>0
[[1,1,1],[3]]=>[3,1]=>1
[[1,1,2],[3]]=>[3,1]=>1
[[1,1,3],[2]]=>[3,1]=>1
[[1,1,3],[3]]=>[3,1]=>1
[[1,2,2],[3]]=>[3,1]=>1
[[1,2,3],[2]]=>[3,1]=>1
[[1,2,3],[3]]=>[3,1]=>1
[[1,3,3],[2]]=>[3,1]=>1
[[1,3,3],[3]]=>[3,1]=>1
[[2,2,2],[3]]=>[3,1]=>1
[[2,2,3],[3]]=>[3,1]=>1
[[2,3,3],[3]]=>[3,1]=>1
[[1,1],[2,3]]=>[2,2]=>2
[[1,1],[3,3]]=>[2,2]=>2
[[1,2],[2,3]]=>[2,2]=>2
[[1,2],[3,3]]=>[2,2]=>2
[[2,2],[3,3]]=>[2,2]=>2
[[1,1],[2],[3]]=>[2,1,1]=>3
[[1,2],[2],[3]]=>[2,1,1]=>3
[[1,3],[2],[3]]=>[2,1,1]=>3
[[1,1,1,1,2]]=>[5]=>0
[[1,1,1,2,2]]=>[5]=>0
[[1,1,2,2,2]]=>[5]=>0
[[1,2,2,2,2]]=>[5]=>0
[[2,2,2,2,2]]=>[5]=>0
[[1,1,1,1],[2]]=>[4,1]=>1
[[1,1,1,2],[2]]=>[4,1]=>1
[[1,1,2,2],[2]]=>[4,1]=>1
[[1,2,2,2],[2]]=>[4,1]=>1
[[1,1,1],[2,2]]=>[3,2]=>2
[[1,1,2],[2,2]]=>[3,2]=>2
[[1,6]]=>[2]=>0
[[2,6]]=>[2]=>0
[[3,6]]=>[2]=>0
[[4,6]]=>[2]=>0
[[5,6]]=>[2]=>0
[[6,6]]=>[2]=>0
[[1],[6]]=>[1,1]=>1
[[2],[6]]=>[1,1]=>1
[[3],[6]]=>[1,1]=>1
[[4],[6]]=>[1,1]=>1
[[5],[6]]=>[1,1]=>1
[[1,1,5]]=>[3]=>0
[[1,2,5]]=>[3]=>0
[[1,3,5]]=>[3]=>0
[[1,4,5]]=>[3]=>0
[[1,5,5]]=>[3]=>0
[[2,2,5]]=>[3]=>0
[[2,3,5]]=>[3]=>0
[[2,4,5]]=>[3]=>0
[[2,5,5]]=>[3]=>0
[[3,3,5]]=>[3]=>0
[[3,4,5]]=>[3]=>0
[[3,5,5]]=>[3]=>0
[[4,4,5]]=>[3]=>0
[[4,5,5]]=>[3]=>0
[[5,5,5]]=>[3]=>0
[[1,1],[5]]=>[2,1]=>1
[[1,2],[5]]=>[2,1]=>1
[[1,5],[2]]=>[2,1]=>1
[[1,3],[5]]=>[2,1]=>1
[[1,5],[3]]=>[2,1]=>1
[[1,4],[5]]=>[2,1]=>1
[[1,5],[4]]=>[2,1]=>1
[[1,5],[5]]=>[2,1]=>1
[[2,2],[5]]=>[2,1]=>1
[[2,3],[5]]=>[2,1]=>1
[[2,5],[3]]=>[2,1]=>1
[[2,4],[5]]=>[2,1]=>1
[[2,5],[4]]=>[2,1]=>1
[[2,5],[5]]=>[2,1]=>1
[[3,3],[5]]=>[2,1]=>1
[[3,4],[5]]=>[2,1]=>1
[[3,5],[4]]=>[2,1]=>1
[[3,5],[5]]=>[2,1]=>1
[[4,4],[5]]=>[2,1]=>1
[[4,5],[5]]=>[2,1]=>1
[[1],[2],[5]]=>[1,1,1]=>3
[[1],[3],[5]]=>[1,1,1]=>3
[[1],[4],[5]]=>[1,1,1]=>3
[[2],[3],[5]]=>[1,1,1]=>3
[[2],[4],[5]]=>[1,1,1]=>3
[[3],[4],[5]]=>[1,1,1]=>3
[[1,1,1,4]]=>[4]=>0
[[1,1,2,4]]=>[4]=>0
[[1,1,3,4]]=>[4]=>0
[[1,1,4,4]]=>[4]=>0
[[1,2,2,4]]=>[4]=>0
[[1,2,3,4]]=>[4]=>0
[[1,2,4,4]]=>[4]=>0
[[1,3,3,4]]=>[4]=>0
[[1,3,4,4]]=>[4]=>0
[[1,4,4,4]]=>[4]=>0
[[2,2,2,4]]=>[4]=>0
[[2,2,3,4]]=>[4]=>0
[[2,2,4,4]]=>[4]=>0
[[2,3,3,4]]=>[4]=>0
[[2,3,4,4]]=>[4]=>0
[[2,4,4,4]]=>[4]=>0
[[3,3,3,4]]=>[4]=>0
[[3,3,4,4]]=>[4]=>0
[[3,4,4,4]]=>[4]=>0
[[4,4,4,4]]=>[4]=>0
[[1,1,1],[4]]=>[3,1]=>1
[[1,1,2],[4]]=>[3,1]=>1
[[1,1,4],[2]]=>[3,1]=>1
[[1,1,3],[4]]=>[3,1]=>1
[[1,1,4],[3]]=>[3,1]=>1
[[1,1,4],[4]]=>[3,1]=>1
[[1,2,2],[4]]=>[3,1]=>1
[[1,2,4],[2]]=>[3,1]=>1
[[1,2,3],[4]]=>[3,1]=>1
[[1,2,4],[3]]=>[3,1]=>1
[[1,3,4],[2]]=>[3,1]=>1
[[1,2,4],[4]]=>[3,1]=>1
[[1,4,4],[2]]=>[3,1]=>1
[[1,3,3],[4]]=>[3,1]=>1
[[1,3,4],[3]]=>[3,1]=>1
[[1,3,4],[4]]=>[3,1]=>1
[[1,4,4],[3]]=>[3,1]=>1
[[1,4,4],[4]]=>[3,1]=>1
[[2,2,2],[4]]=>[3,1]=>1
[[2,2,3],[4]]=>[3,1]=>1
[[2,2,4],[3]]=>[3,1]=>1
[[2,2,4],[4]]=>[3,1]=>1
[[2,3,3],[4]]=>[3,1]=>1
[[2,3,4],[3]]=>[3,1]=>1
[[2,3,4],[4]]=>[3,1]=>1
[[2,4,4],[3]]=>[3,1]=>1
[[2,4,4],[4]]=>[3,1]=>1
[[3,3,3],[4]]=>[3,1]=>1
[[3,3,4],[4]]=>[3,1]=>1
[[3,4,4],[4]]=>[3,1]=>1
[[1,1],[2,4]]=>[2,2]=>2
[[1,1],[3,4]]=>[2,2]=>2
[[1,1],[4,4]]=>[2,2]=>2
[[1,2],[2,4]]=>[2,2]=>2
[[1,2],[3,4]]=>[2,2]=>2
[[1,3],[2,4]]=>[2,2]=>2
[[1,2],[4,4]]=>[2,2]=>2
[[1,3],[3,4]]=>[2,2]=>2
[[1,3],[4,4]]=>[2,2]=>2
[[2,2],[3,4]]=>[2,2]=>2
[[2,2],[4,4]]=>[2,2]=>2
[[2,3],[3,4]]=>[2,2]=>2
[[2,3],[4,4]]=>[2,2]=>2
[[3,3],[4,4]]=>[2,2]=>2
[[1,1],[2],[4]]=>[2,1,1]=>3
[[1,1],[3],[4]]=>[2,1,1]=>3
[[1,2],[2],[4]]=>[2,1,1]=>3
[[1,2],[3],[4]]=>[2,1,1]=>3
[[1,3],[2],[4]]=>[2,1,1]=>3
[[1,4],[2],[3]]=>[2,1,1]=>3
[[1,4],[2],[4]]=>[2,1,1]=>3
[[1,3],[3],[4]]=>[2,1,1]=>3
[[1,4],[3],[4]]=>[2,1,1]=>3
[[2,2],[3],[4]]=>[2,1,1]=>3
[[2,3],[3],[4]]=>[2,1,1]=>3
[[2,4],[3],[4]]=>[2,1,1]=>3
[[1],[2],[3],[4]]=>[1,1,1,1]=>6
[[1,1,1,1,3]]=>[5]=>0
[[1,1,1,2,3]]=>[5]=>0
[[1,1,1,3,3]]=>[5]=>0
[[1,1,2,2,3]]=>[5]=>0
[[1,1,2,3,3]]=>[5]=>0
[[1,1,3,3,3]]=>[5]=>0
[[1,2,2,2,3]]=>[5]=>0
[[1,2,2,3,3]]=>[5]=>0
[[1,2,3,3,3]]=>[5]=>0
[[1,3,3,3,3]]=>[5]=>0
[[2,2,2,2,3]]=>[5]=>0
[[2,2,2,3,3]]=>[5]=>0
[[2,2,3,3,3]]=>[5]=>0
[[2,3,3,3,3]]=>[5]=>0
[[3,3,3,3,3]]=>[5]=>0
[[1,1,1,1],[3]]=>[4,1]=>1
[[1,1,1,2],[3]]=>[4,1]=>1
[[1,1,1,3],[2]]=>[4,1]=>1
[[1,1,1,3],[3]]=>[4,1]=>1
[[1,1,2,2],[3]]=>[4,1]=>1
[[1,1,2,3],[2]]=>[4,1]=>1
[[1,1,2,3],[3]]=>[4,1]=>1
[[1,1,3,3],[2]]=>[4,1]=>1
[[1,1,3,3],[3]]=>[4,1]=>1
[[1,2,2,2],[3]]=>[4,1]=>1
[[1,2,2,3],[2]]=>[4,1]=>1
[[1,2,2,3],[3]]=>[4,1]=>1
[[1,2,3,3],[2]]=>[4,1]=>1
[[1,2,3,3],[3]]=>[4,1]=>1
[[1,3,3,3],[2]]=>[4,1]=>1
[[1,3,3,3],[3]]=>[4,1]=>1
[[2,2,2,2],[3]]=>[4,1]=>1
[[2,2,2,3],[3]]=>[4,1]=>1
[[2,2,3,3],[3]]=>[4,1]=>1
[[2,3,3,3],[3]]=>[4,1]=>1
[[1,1,1],[2,3]]=>[3,2]=>2
[[1,1,1],[3,3]]=>[3,2]=>2
[[1,1,2],[2,3]]=>[3,2]=>2
[[1,1,3],[2,2]]=>[3,2]=>2
[[1,1,2],[3,3]]=>[3,2]=>2
[[1,1,3],[2,3]]=>[3,2]=>2
[[1,1,3],[3,3]]=>[3,2]=>2
[[1,2,2],[2,3]]=>[3,2]=>2
[[1,2,2],[3,3]]=>[3,2]=>2
[[1,2,3],[2,3]]=>[3,2]=>2
[[1,2,3],[3,3]]=>[3,2]=>2
[[2,2,2],[3,3]]=>[3,2]=>2
[[2,2,3],[3,3]]=>[3,2]=>2
[[1,1,1],[2],[3]]=>[3,1,1]=>3
[[1,1,2],[2],[3]]=>[3,1,1]=>3
[[1,1,3],[2],[3]]=>[3,1,1]=>3
[[1,2,2],[2],[3]]=>[3,1,1]=>3
[[1,2,3],[2],[3]]=>[3,1,1]=>3
[[1,3,3],[2],[3]]=>[3,1,1]=>3
[[1,1],[2,2],[3]]=>[2,2,1]=>4
[[1,1],[2,3],[3]]=>[2,2,1]=>4
[[1,2],[2,3],[3]]=>[2,2,1]=>4
[[1,1,1,1,1,2]]=>[6]=>0
[[1,1,1,1,2,2]]=>[6]=>0
[[1,1,1,2,2,2]]=>[6]=>0
[[1,1,2,2,2,2]]=>[6]=>0
[[1,2,2,2,2,2]]=>[6]=>0
[[2,2,2,2,2,2]]=>[6]=>0
[[1,1,1,1,1],[2]]=>[5,1]=>1
[[1,1,1,1,2],[2]]=>[5,1]=>1
[[1,1,1,2,2],[2]]=>[5,1]=>1
[[1,1,2,2,2],[2]]=>[5,1]=>1
[[1,2,2,2,2],[2]]=>[5,1]=>1
[[1,1,1,1],[2,2]]=>[4,2]=>2
[[1,1,1,2],[2,2]]=>[4,2]=>2
[[1,1,2,2],[2,2]]=>[4,2]=>2
[[1,1,1],[2,2,2]]=>[3,3]=>3
[[1,7]]=>[2]=>0
[[2,7]]=>[2]=>0
[[3,7]]=>[2]=>0
[[4,7]]=>[2]=>0
[[5,7]]=>[2]=>0
[[6,7]]=>[2]=>0
[[7,7]]=>[2]=>0
[[1],[7]]=>[1,1]=>1
[[2],[7]]=>[1,1]=>1
[[3],[7]]=>[1,1]=>1
[[4],[7]]=>[1,1]=>1
[[5],[7]]=>[1,1]=>1
[[6],[7]]=>[1,1]=>1
[[1,1,6]]=>[3]=>0
[[1,2,6]]=>[3]=>0
[[1,3,6]]=>[3]=>0
[[1,4,6]]=>[3]=>0
[[1,5,6]]=>[3]=>0
[[1,6,6]]=>[3]=>0
[[2,2,6]]=>[3]=>0
[[2,3,6]]=>[3]=>0
[[2,4,6]]=>[3]=>0
[[2,5,6]]=>[3]=>0
[[2,6,6]]=>[3]=>0
[[3,3,6]]=>[3]=>0
[[3,4,6]]=>[3]=>0
[[3,5,6]]=>[3]=>0
[[3,6,6]]=>[3]=>0
[[4,4,6]]=>[3]=>0
[[4,5,6]]=>[3]=>0
[[4,6,6]]=>[3]=>0
[[5,5,6]]=>[3]=>0
[[5,6,6]]=>[3]=>0
[[6,6,6]]=>[3]=>0
[[1,1],[6]]=>[2,1]=>1
[[1,2],[6]]=>[2,1]=>1
[[1,6],[2]]=>[2,1]=>1
[[1,3],[6]]=>[2,1]=>1
[[1,6],[3]]=>[2,1]=>1
[[1,4],[6]]=>[2,1]=>1
[[1,6],[4]]=>[2,1]=>1
[[1,5],[6]]=>[2,1]=>1
[[1,6],[5]]=>[2,1]=>1
[[1,6],[6]]=>[2,1]=>1
[[2,2],[6]]=>[2,1]=>1
[[2,3],[6]]=>[2,1]=>1
[[2,6],[3]]=>[2,1]=>1
[[2,4],[6]]=>[2,1]=>1
[[2,6],[4]]=>[2,1]=>1
[[2,5],[6]]=>[2,1]=>1
[[2,6],[5]]=>[2,1]=>1
[[2,6],[6]]=>[2,1]=>1
[[3,3],[6]]=>[2,1]=>1
[[3,4],[6]]=>[2,1]=>1
[[3,6],[4]]=>[2,1]=>1
[[3,5],[6]]=>[2,1]=>1
[[3,6],[5]]=>[2,1]=>1
[[3,6],[6]]=>[2,1]=>1
[[4,4],[6]]=>[2,1]=>1
[[4,5],[6]]=>[2,1]=>1
[[4,6],[5]]=>[2,1]=>1
[[4,6],[6]]=>[2,1]=>1
[[5,5],[6]]=>[2,1]=>1
[[5,6],[6]]=>[2,1]=>1
[[1],[2],[6]]=>[1,1,1]=>3
[[1],[3],[6]]=>[1,1,1]=>3
[[1],[4],[6]]=>[1,1,1]=>3
[[1],[5],[6]]=>[1,1,1]=>3
[[2],[3],[6]]=>[1,1,1]=>3
[[2],[4],[6]]=>[1,1,1]=>3
[[2],[5],[6]]=>[1,1,1]=>3
[[3],[4],[6]]=>[1,1,1]=>3
[[3],[5],[6]]=>[1,1,1]=>3
[[4],[5],[6]]=>[1,1,1]=>3
[[1,1,1,5]]=>[4]=>0
[[1,1,2,5]]=>[4]=>0
[[1,1,3,5]]=>[4]=>0
[[1,1,4,5]]=>[4]=>0
[[1,1,5,5]]=>[4]=>0
[[1,2,2,5]]=>[4]=>0
[[1,2,3,5]]=>[4]=>0
[[1,2,4,5]]=>[4]=>0
[[1,2,5,5]]=>[4]=>0
[[1,3,3,5]]=>[4]=>0
[[1,3,4,5]]=>[4]=>0
[[1,3,5,5]]=>[4]=>0
[[1,4,4,5]]=>[4]=>0
[[1,4,5,5]]=>[4]=>0
[[1,5,5,5]]=>[4]=>0
[[2,2,2,5]]=>[4]=>0
[[2,2,3,5]]=>[4]=>0
[[2,2,4,5]]=>[4]=>0
[[2,2,5,5]]=>[4]=>0
[[2,3,3,5]]=>[4]=>0
[[2,3,4,5]]=>[4]=>0
[[2,3,5,5]]=>[4]=>0
[[2,4,4,5]]=>[4]=>0
[[2,4,5,5]]=>[4]=>0
[[2,5,5,5]]=>[4]=>0
[[3,3,3,5]]=>[4]=>0
[[3,3,4,5]]=>[4]=>0
[[3,3,5,5]]=>[4]=>0
[[3,4,4,5]]=>[4]=>0
[[3,4,5,5]]=>[4]=>0
[[3,5,5,5]]=>[4]=>0
[[4,4,4,5]]=>[4]=>0
[[4,4,5,5]]=>[4]=>0
[[4,5,5,5]]=>[4]=>0
[[5,5,5,5]]=>[4]=>0
[[1,1,1],[5]]=>[3,1]=>1
[[1,1,2],[5]]=>[3,1]=>1
[[1,1,5],[2]]=>[3,1]=>1
[[1,1,3],[5]]=>[3,1]=>1
[[1,1,5],[3]]=>[3,1]=>1
[[1,1,4],[5]]=>[3,1]=>1
[[1,1,5],[4]]=>[3,1]=>1
[[1,1,5],[5]]=>[3,1]=>1
[[1,2,2],[5]]=>[3,1]=>1
[[1,2,5],[2]]=>[3,1]=>1
[[1,2,3],[5]]=>[3,1]=>1
[[1,2,5],[3]]=>[3,1]=>1
[[1,3,5],[2]]=>[3,1]=>1
[[1,2,4],[5]]=>[3,1]=>1
[[1,2,5],[4]]=>[3,1]=>1
[[1,4,5],[2]]=>[3,1]=>1
[[1,2,5],[5]]=>[3,1]=>1
[[1,5,5],[2]]=>[3,1]=>1
[[1,3,3],[5]]=>[3,1]=>1
[[1,3,5],[3]]=>[3,1]=>1
[[1,3,4],[5]]=>[3,1]=>1
[[1,3,5],[4]]=>[3,1]=>1
[[1,4,5],[3]]=>[3,1]=>1
[[1,3,5],[5]]=>[3,1]=>1
[[1,5,5],[3]]=>[3,1]=>1
[[1,4,4],[5]]=>[3,1]=>1
[[1,4,5],[4]]=>[3,1]=>1
[[1,4,5],[5]]=>[3,1]=>1
[[1,5,5],[4]]=>[3,1]=>1
[[1,5,5],[5]]=>[3,1]=>1
[[2,2,2],[5]]=>[3,1]=>1
[[2,2,3],[5]]=>[3,1]=>1
[[2,2,5],[3]]=>[3,1]=>1
[[2,2,4],[5]]=>[3,1]=>1
[[2,2,5],[4]]=>[3,1]=>1
[[2,2,5],[5]]=>[3,1]=>1
[[2,3,3],[5]]=>[3,1]=>1
[[2,3,5],[3]]=>[3,1]=>1
[[2,3,4],[5]]=>[3,1]=>1
[[2,3,5],[4]]=>[3,1]=>1
[[2,4,5],[3]]=>[3,1]=>1
[[2,3,5],[5]]=>[3,1]=>1
[[2,5,5],[3]]=>[3,1]=>1
[[2,4,4],[5]]=>[3,1]=>1
[[2,4,5],[4]]=>[3,1]=>1
[[2,4,5],[5]]=>[3,1]=>1
[[2,5,5],[4]]=>[3,1]=>1
[[2,5,5],[5]]=>[3,1]=>1
[[3,3,3],[5]]=>[3,1]=>1
[[3,3,4],[5]]=>[3,1]=>1
[[3,3,5],[4]]=>[3,1]=>1
[[3,3,5],[5]]=>[3,1]=>1
[[3,4,4],[5]]=>[3,1]=>1
[[3,4,5],[4]]=>[3,1]=>1
[[3,4,5],[5]]=>[3,1]=>1
[[3,5,5],[4]]=>[3,1]=>1
[[3,5,5],[5]]=>[3,1]=>1
[[4,4,4],[5]]=>[3,1]=>1
[[4,4,5],[5]]=>[3,1]=>1
[[4,5,5],[5]]=>[3,1]=>1
[[1,1],[2,5]]=>[2,2]=>2
[[1,1],[3,5]]=>[2,2]=>2
[[1,1],[4,5]]=>[2,2]=>2
[[1,1],[5,5]]=>[2,2]=>2
[[1,2],[2,5]]=>[2,2]=>2
[[1,2],[3,5]]=>[2,2]=>2
[[1,3],[2,5]]=>[2,2]=>2
[[1,2],[4,5]]=>[2,2]=>2
[[1,4],[2,5]]=>[2,2]=>2
[[1,2],[5,5]]=>[2,2]=>2
[[1,3],[3,5]]=>[2,2]=>2
[[1,3],[4,5]]=>[2,2]=>2
[[1,4],[3,5]]=>[2,2]=>2
[[1,3],[5,5]]=>[2,2]=>2
[[1,4],[4,5]]=>[2,2]=>2
[[1,4],[5,5]]=>[2,2]=>2
[[2,2],[3,5]]=>[2,2]=>2
[[2,2],[4,5]]=>[2,2]=>2
[[2,2],[5,5]]=>[2,2]=>2
[[2,3],[3,5]]=>[2,2]=>2
[[2,3],[4,5]]=>[2,2]=>2
[[2,4],[3,5]]=>[2,2]=>2
[[2,3],[5,5]]=>[2,2]=>2
[[2,4],[4,5]]=>[2,2]=>2
[[2,4],[5,5]]=>[2,2]=>2
[[3,3],[4,5]]=>[2,2]=>2
[[3,3],[5,5]]=>[2,2]=>2
[[3,4],[4,5]]=>[2,2]=>2
[[3,4],[5,5]]=>[2,2]=>2
[[4,4],[5,5]]=>[2,2]=>2
[[1,1],[2],[5]]=>[2,1,1]=>3
[[1,1],[3],[5]]=>[2,1,1]=>3
[[1,1],[4],[5]]=>[2,1,1]=>3
[[1,2],[2],[5]]=>[2,1,1]=>3
[[1,2],[3],[5]]=>[2,1,1]=>3
[[1,3],[2],[5]]=>[2,1,1]=>3
[[1,5],[2],[3]]=>[2,1,1]=>3
[[1,2],[4],[5]]=>[2,1,1]=>3
[[1,4],[2],[5]]=>[2,1,1]=>3
[[1,5],[2],[4]]=>[2,1,1]=>3
[[1,5],[2],[5]]=>[2,1,1]=>3
[[1,3],[3],[5]]=>[2,1,1]=>3
[[1,3],[4],[5]]=>[2,1,1]=>3
[[1,4],[3],[5]]=>[2,1,1]=>3
[[1,5],[3],[4]]=>[2,1,1]=>3
[[1,5],[3],[5]]=>[2,1,1]=>3
[[1,4],[4],[5]]=>[2,1,1]=>3
[[1,5],[4],[5]]=>[2,1,1]=>3
[[2,2],[3],[5]]=>[2,1,1]=>3
[[2,2],[4],[5]]=>[2,1,1]=>3
[[2,3],[3],[5]]=>[2,1,1]=>3
[[2,3],[4],[5]]=>[2,1,1]=>3
[[2,4],[3],[5]]=>[2,1,1]=>3
[[2,5],[3],[4]]=>[2,1,1]=>3
[[2,5],[3],[5]]=>[2,1,1]=>3
[[2,4],[4],[5]]=>[2,1,1]=>3
[[2,5],[4],[5]]=>[2,1,1]=>3
[[3,3],[4],[5]]=>[2,1,1]=>3
[[3,4],[4],[5]]=>[2,1,1]=>3
[[3,5],[4],[5]]=>[2,1,1]=>3
[[1],[2],[3],[5]]=>[1,1,1,1]=>6
[[1],[2],[4],[5]]=>[1,1,1,1]=>6
[[1],[3],[4],[5]]=>[1,1,1,1]=>6
[[2],[3],[4],[5]]=>[1,1,1,1]=>6
[[1,1,1,1,4]]=>[5]=>0
[[1,1,1,2,4]]=>[5]=>0
[[1,1,1,3,4]]=>[5]=>0
[[1,1,1,4,4]]=>[5]=>0
[[1,1,2,2,4]]=>[5]=>0
[[1,1,2,3,4]]=>[5]=>0
[[1,1,2,4,4]]=>[5]=>0
[[1,1,3,3,4]]=>[5]=>0
[[1,1,3,4,4]]=>[5]=>0
[[1,1,4,4,4]]=>[5]=>0
[[1,2,2,2,4]]=>[5]=>0
[[1,2,2,3,4]]=>[5]=>0
[[1,2,2,4,4]]=>[5]=>0
[[1,2,3,3,4]]=>[5]=>0
[[1,2,3,4,4]]=>[5]=>0
[[1,2,4,4,4]]=>[5]=>0
[[1,3,3,3,4]]=>[5]=>0
[[1,3,3,4,4]]=>[5]=>0
[[1,3,4,4,4]]=>[5]=>0
[[1,4,4,4,4]]=>[5]=>0
[[2,2,2,2,4]]=>[5]=>0
[[2,2,2,3,4]]=>[5]=>0
[[2,2,2,4,4]]=>[5]=>0
[[2,2,3,3,4]]=>[5]=>0
[[2,2,3,4,4]]=>[5]=>0
[[2,2,4,4,4]]=>[5]=>0
[[2,3,3,3,4]]=>[5]=>0
[[2,3,3,4,4]]=>[5]=>0
[[2,3,4,4,4]]=>[5]=>0
[[2,4,4,4,4]]=>[5]=>0
[[3,3,3,3,4]]=>[5]=>0
[[3,3,3,4,4]]=>[5]=>0
[[3,3,4,4,4]]=>[5]=>0
[[3,4,4,4,4]]=>[5]=>0
[[4,4,4,4,4]]=>[5]=>0
[[1,1,1,1],[4]]=>[4,1]=>1
[[1,1,1,2],[4]]=>[4,1]=>1
[[1,1,1,4],[2]]=>[4,1]=>1
[[1,1,1,3],[4]]=>[4,1]=>1
[[1,1,1,4],[3]]=>[4,1]=>1
[[1,1,1,4],[4]]=>[4,1]=>1
[[1,1,2,2],[4]]=>[4,1]=>1
[[1,1,2,4],[2]]=>[4,1]=>1
[[1,1,2,3],[4]]=>[4,1]=>1
[[1,1,2,4],[3]]=>[4,1]=>1
[[1,1,3,4],[2]]=>[4,1]=>1
[[1,1,2,4],[4]]=>[4,1]=>1
[[1,1,4,4],[2]]=>[4,1]=>1
[[1,1,3,3],[4]]=>[4,1]=>1
[[1,1,3,4],[3]]=>[4,1]=>1
[[1,1,3,4],[4]]=>[4,1]=>1
[[1,1,4,4],[3]]=>[4,1]=>1
[[1,1,4,4],[4]]=>[4,1]=>1
[[1,2,2,2],[4]]=>[4,1]=>1
[[1,2,2,4],[2]]=>[4,1]=>1
[[1,2,2,3],[4]]=>[4,1]=>1
[[1,2,2,4],[3]]=>[4,1]=>1
[[1,2,3,4],[2]]=>[4,1]=>1
[[1,2,2,4],[4]]=>[4,1]=>1
[[1,2,4,4],[2]]=>[4,1]=>1
[[1,2,3,3],[4]]=>[4,1]=>1
[[1,2,3,4],[3]]=>[4,1]=>1
[[1,3,3,4],[2]]=>[4,1]=>1
[[1,2,3,4],[4]]=>[4,1]=>1
[[1,2,4,4],[3]]=>[4,1]=>1
[[1,3,4,4],[2]]=>[4,1]=>1
[[1,2,4,4],[4]]=>[4,1]=>1
[[1,4,4,4],[2]]=>[4,1]=>1
[[1,3,3,3],[4]]=>[4,1]=>1
[[1,3,3,4],[3]]=>[4,1]=>1
[[1,3,3,4],[4]]=>[4,1]=>1
[[1,3,4,4],[3]]=>[4,1]=>1
[[1,3,4,4],[4]]=>[4,1]=>1
[[1,4,4,4],[3]]=>[4,1]=>1
[[1,4,4,4],[4]]=>[4,1]=>1
[[2,2,2,2],[4]]=>[4,1]=>1
[[2,2,2,3],[4]]=>[4,1]=>1
[[2,2,2,4],[3]]=>[4,1]=>1
[[2,2,2,4],[4]]=>[4,1]=>1
[[2,2,3,3],[4]]=>[4,1]=>1
[[2,2,3,4],[3]]=>[4,1]=>1
[[2,2,3,4],[4]]=>[4,1]=>1
[[2,2,4,4],[3]]=>[4,1]=>1
[[2,2,4,4],[4]]=>[4,1]=>1
[[2,3,3,3],[4]]=>[4,1]=>1
[[2,3,3,4],[3]]=>[4,1]=>1
[[2,3,3,4],[4]]=>[4,1]=>1
[[2,3,4,4],[3]]=>[4,1]=>1
[[2,3,4,4],[4]]=>[4,1]=>1
[[2,4,4,4],[3]]=>[4,1]=>1
[[2,4,4,4],[4]]=>[4,1]=>1
[[3,3,3,3],[4]]=>[4,1]=>1
[[3,3,3,4],[4]]=>[4,1]=>1
[[3,3,4,4],[4]]=>[4,1]=>1
[[3,4,4,4],[4]]=>[4,1]=>1
[[1,1,1],[2,4]]=>[3,2]=>2
[[1,1,1],[3,4]]=>[3,2]=>2
[[1,1,1],[4,4]]=>[3,2]=>2
[[1,1,2],[2,4]]=>[3,2]=>2
[[1,1,4],[2,2]]=>[3,2]=>2
[[1,1,2],[3,4]]=>[3,2]=>2
[[1,1,3],[2,4]]=>[3,2]=>2
[[1,1,4],[2,3]]=>[3,2]=>2
[[1,1,2],[4,4]]=>[3,2]=>2
[[1,1,4],[2,4]]=>[3,2]=>2
[[1,1,3],[3,4]]=>[3,2]=>2
[[1,1,4],[3,3]]=>[3,2]=>2
[[1,1,3],[4,4]]=>[3,2]=>2
[[1,1,4],[3,4]]=>[3,2]=>2
[[1,1,4],[4,4]]=>[3,2]=>2
[[1,2,2],[2,4]]=>[3,2]=>2
[[1,2,2],[3,4]]=>[3,2]=>2
[[1,2,3],[2,4]]=>[3,2]=>2
[[1,2,4],[2,3]]=>[3,2]=>2
[[1,2,2],[4,4]]=>[3,2]=>2
[[1,2,4],[2,4]]=>[3,2]=>2
[[1,2,3],[3,4]]=>[3,2]=>2
[[1,2,4],[3,3]]=>[3,2]=>2
[[1,3,3],[2,4]]=>[3,2]=>2
[[1,2,3],[4,4]]=>[3,2]=>2
[[1,2,4],[3,4]]=>[3,2]=>2
[[1,3,4],[2,4]]=>[3,2]=>2
[[1,2,4],[4,4]]=>[3,2]=>2
[[1,3,3],[3,4]]=>[3,2]=>2
[[1,3,3],[4,4]]=>[3,2]=>2
[[1,3,4],[3,4]]=>[3,2]=>2
[[1,3,4],[4,4]]=>[3,2]=>2
[[2,2,2],[3,4]]=>[3,2]=>2
[[2,2,2],[4,4]]=>[3,2]=>2
[[2,2,3],[3,4]]=>[3,2]=>2
[[2,2,4],[3,3]]=>[3,2]=>2
[[2,2,3],[4,4]]=>[3,2]=>2
[[2,2,4],[3,4]]=>[3,2]=>2
[[2,2,4],[4,4]]=>[3,2]=>2
[[2,3,3],[3,4]]=>[3,2]=>2
[[2,3,3],[4,4]]=>[3,2]=>2
[[2,3,4],[3,4]]=>[3,2]=>2
[[2,3,4],[4,4]]=>[3,2]=>2
[[3,3,3],[4,4]]=>[3,2]=>2
[[3,3,4],[4,4]]=>[3,2]=>2
[[1,1,1],[2],[4]]=>[3,1,1]=>3
[[1,1,1],[3],[4]]=>[3,1,1]=>3
[[1,1,2],[2],[4]]=>[3,1,1]=>3
[[1,1,2],[3],[4]]=>[3,1,1]=>3
[[1,1,3],[2],[4]]=>[3,1,1]=>3
[[1,1,4],[2],[3]]=>[3,1,1]=>3
[[1,1,4],[2],[4]]=>[3,1,1]=>3
[[1,1,3],[3],[4]]=>[3,1,1]=>3
[[1,1,4],[3],[4]]=>[3,1,1]=>3
[[1,2,2],[2],[4]]=>[3,1,1]=>3
[[1,2,2],[3],[4]]=>[3,1,1]=>3
[[1,2,3],[2],[4]]=>[3,1,1]=>3
[[1,2,4],[2],[3]]=>[3,1,1]=>3
[[1,2,4],[2],[4]]=>[3,1,1]=>3
[[1,2,3],[3],[4]]=>[3,1,1]=>3
[[1,3,3],[2],[4]]=>[3,1,1]=>3
[[1,3,4],[2],[3]]=>[3,1,1]=>3
[[1,2,4],[3],[4]]=>[3,1,1]=>3
[[1,3,4],[2],[4]]=>[3,1,1]=>3
[[1,4,4],[2],[3]]=>[3,1,1]=>3
[[1,4,4],[2],[4]]=>[3,1,1]=>3
[[1,3,3],[3],[4]]=>[3,1,1]=>3
[[1,3,4],[3],[4]]=>[3,1,1]=>3
[[1,4,4],[3],[4]]=>[3,1,1]=>3
[[2,2,2],[3],[4]]=>[3,1,1]=>3
[[2,2,3],[3],[4]]=>[3,1,1]=>3
[[2,2,4],[3],[4]]=>[3,1,1]=>3
[[2,3,3],[3],[4]]=>[3,1,1]=>3
[[2,3,4],[3],[4]]=>[3,1,1]=>3
[[2,4,4],[3],[4]]=>[3,1,1]=>3
[[1,1],[2,2],[4]]=>[2,2,1]=>4
[[1,1],[2,3],[4]]=>[2,2,1]=>4
[[1,1],[2,4],[3]]=>[2,2,1]=>4
[[1,1],[2,4],[4]]=>[2,2,1]=>4
[[1,1],[3,3],[4]]=>[2,2,1]=>4
[[1,1],[3,4],[4]]=>[2,2,1]=>4
[[1,2],[2,3],[4]]=>[2,2,1]=>4
[[1,2],[2,4],[3]]=>[2,2,1]=>4
[[1,2],[2,4],[4]]=>[2,2,1]=>4
[[1,2],[3,3],[4]]=>[2,2,1]=>4
[[1,3],[2,4],[3]]=>[2,2,1]=>4
[[1,2],[3,4],[4]]=>[2,2,1]=>4
[[1,3],[2,4],[4]]=>[2,2,1]=>4
[[1,3],[3,4],[4]]=>[2,2,1]=>4
[[2,2],[3,3],[4]]=>[2,2,1]=>4
[[2,2],[3,4],[4]]=>[2,2,1]=>4
[[2,3],[3,4],[4]]=>[2,2,1]=>4
[[1,1],[2],[3],[4]]=>[2,1,1,1]=>6
[[1,2],[2],[3],[4]]=>[2,1,1,1]=>6
[[1,3],[2],[3],[4]]=>[2,1,1,1]=>6
[[1,4],[2],[3],[4]]=>[2,1,1,1]=>6
[[1,1,1,1,1,3]]=>[6]=>0
[[1,1,1,1,2,3]]=>[6]=>0
[[1,1,1,1,3,3]]=>[6]=>0
[[1,1,1,2,2,3]]=>[6]=>0
[[1,1,1,2,3,3]]=>[6]=>0
[[1,1,1,3,3,3]]=>[6]=>0
[[1,1,2,2,2,3]]=>[6]=>0
[[1,1,2,2,3,3]]=>[6]=>0
[[1,1,2,3,3,3]]=>[6]=>0
[[1,1,3,3,3,3]]=>[6]=>0
[[1,2,2,2,2,3]]=>[6]=>0
[[1,2,2,2,3,3]]=>[6]=>0
[[1,2,2,3,3,3]]=>[6]=>0
[[1,2,3,3,3,3]]=>[6]=>0
[[1,3,3,3,3,3]]=>[6]=>0
[[2,2,2,2,2,3]]=>[6]=>0
[[2,2,2,2,3,3]]=>[6]=>0
[[2,2,2,3,3,3]]=>[6]=>0
[[2,2,3,3,3,3]]=>[6]=>0
[[2,3,3,3,3,3]]=>[6]=>0
[[3,3,3,3,3,3]]=>[6]=>0
[[1,1,1,1,1],[3]]=>[5,1]=>1
[[1,1,1,1,2],[3]]=>[5,1]=>1
[[1,1,1,1,3],[2]]=>[5,1]=>1
[[1,1,1,1,3],[3]]=>[5,1]=>1
[[1,1,1,2,2],[3]]=>[5,1]=>1
[[1,1,1,2,3],[2]]=>[5,1]=>1
[[1,1,1,2,3],[3]]=>[5,1]=>1
[[1,1,1,3,3],[2]]=>[5,1]=>1
[[1,1,1,3,3],[3]]=>[5,1]=>1
[[1,1,2,2,2],[3]]=>[5,1]=>1
[[1,1,2,2,3],[2]]=>[5,1]=>1
[[1,1,2,2,3],[3]]=>[5,1]=>1
[[1,1,2,3,3],[2]]=>[5,1]=>1
[[1,1,2,3,3],[3]]=>[5,1]=>1
[[1,1,3,3,3],[2]]=>[5,1]=>1
[[1,1,3,3,3],[3]]=>[5,1]=>1
[[1,2,2,2,2],[3]]=>[5,1]=>1
[[1,2,2,2,3],[2]]=>[5,1]=>1
[[1,2,2,2,3],[3]]=>[5,1]=>1
[[1,2,2,3,3],[2]]=>[5,1]=>1
[[1,2,2,3,3],[3]]=>[5,1]=>1
[[1,2,3,3,3],[2]]=>[5,1]=>1
[[1,2,3,3,3],[3]]=>[5,1]=>1
[[1,3,3,3,3],[2]]=>[5,1]=>1
[[1,3,3,3,3],[3]]=>[5,1]=>1
[[2,2,2,2,2],[3]]=>[5,1]=>1
[[2,2,2,2,3],[3]]=>[5,1]=>1
[[2,2,2,3,3],[3]]=>[5,1]=>1
[[2,2,3,3,3],[3]]=>[5,1]=>1
[[2,3,3,3,3],[3]]=>[5,1]=>1
[[1,1,1,1],[2,3]]=>[4,2]=>2
[[1,1,1,1],[3,3]]=>[4,2]=>2
[[1,1,1,2],[2,3]]=>[4,2]=>2
[[1,1,1,3],[2,2]]=>[4,2]=>2
[[1,1,1,2],[3,3]]=>[4,2]=>2
[[1,1,1,3],[2,3]]=>[4,2]=>2
[[1,1,1,3],[3,3]]=>[4,2]=>2
[[1,1,2,2],[2,3]]=>[4,2]=>2
[[1,1,2,3],[2,2]]=>[4,2]=>2
[[1,1,2,2],[3,3]]=>[4,2]=>2
[[1,1,2,3],[2,3]]=>[4,2]=>2
[[1,1,3,3],[2,2]]=>[4,2]=>2
[[1,1,2,3],[3,3]]=>[4,2]=>2
[[1,1,3,3],[2,3]]=>[4,2]=>2
[[1,1,3,3],[3,3]]=>[4,2]=>2
[[1,2,2,2],[2,3]]=>[4,2]=>2
[[1,2,2,2],[3,3]]=>[4,2]=>2
[[1,2,2,3],[2,3]]=>[4,2]=>2
[[1,2,2,3],[3,3]]=>[4,2]=>2
[[1,2,3,3],[2,3]]=>[4,2]=>2
[[1,2,3,3],[3,3]]=>[4,2]=>2
[[2,2,2,2],[3,3]]=>[4,2]=>2
[[2,2,2,3],[3,3]]=>[4,2]=>2
[[2,2,3,3],[3,3]]=>[4,2]=>2
[[1,1,1,1],[2],[3]]=>[4,1,1]=>3
[[1,1,1,2],[2],[3]]=>[4,1,1]=>3
[[1,1,1,3],[2],[3]]=>[4,1,1]=>3
[[1,1,2,2],[2],[3]]=>[4,1,1]=>3
[[1,1,2,3],[2],[3]]=>[4,1,1]=>3
[[1,1,3,3],[2],[3]]=>[4,1,1]=>3
[[1,2,2,2],[2],[3]]=>[4,1,1]=>3
[[1,2,2,3],[2],[3]]=>[4,1,1]=>3
[[1,2,3,3],[2],[3]]=>[4,1,1]=>3
[[1,3,3,3],[2],[3]]=>[4,1,1]=>3
[[1,1,1],[2,2,3]]=>[3,3]=>3
[[1,1,1],[2,3,3]]=>[3,3]=>3
[[1,1,1],[3,3,3]]=>[3,3]=>3
[[1,1,2],[2,2,3]]=>[3,3]=>3
[[1,1,2],[2,3,3]]=>[3,3]=>3
[[1,1,2],[3,3,3]]=>[3,3]=>3
[[1,2,2],[2,3,3]]=>[3,3]=>3
[[1,2,2],[3,3,3]]=>[3,3]=>3
[[2,2,2],[3,3,3]]=>[3,3]=>3
[[1,1,1],[2,2],[3]]=>[3,2,1]=>4
[[1,1,1],[2,3],[3]]=>[3,2,1]=>4
[[1,1,2],[2,2],[3]]=>[3,2,1]=>4
[[1,1,2],[2,3],[3]]=>[3,2,1]=>4
[[1,1,3],[2,2],[3]]=>[3,2,1]=>4
[[1,1,3],[2,3],[3]]=>[3,2,1]=>4
[[1,2,2],[2,3],[3]]=>[3,2,1]=>4
[[1,2,3],[2,3],[3]]=>[3,2,1]=>4
[[1,1],[2,2],[3,3]]=>[2,2,2]=>6
[[1,1,1,1,1,1,2]]=>[7]=>0
[[1,1,1,1,1,2,2]]=>[7]=>0
[[1,1,1,1,2,2,2]]=>[7]=>0
[[1,1,1,2,2,2,2]]=>[7]=>0
[[1,1,2,2,2,2,2]]=>[7]=>0
[[1,2,2,2,2,2,2]]=>[7]=>0
[[2,2,2,2,2,2,2]]=>[7]=>0
[[1,1,1,1,1,1],[2]]=>[6,1]=>1
[[1,1,1,1,1,2],[2]]=>[6,1]=>1
[[1,1,1,1,2,2],[2]]=>[6,1]=>1
[[1,1,1,2,2,2],[2]]=>[6,1]=>1
[[1,1,2,2,2,2],[2]]=>[6,1]=>1
[[1,2,2,2,2,2],[2]]=>[6,1]=>1
[[1,1,1,1,1],[2,2]]=>[5,2]=>2
[[1,1,1,1,2],[2,2]]=>[5,2]=>2
[[1,1,1,2,2],[2,2]]=>[5,2]=>2
[[1,1,2,2,2],[2,2]]=>[5,2]=>2
[[1,1,1,1],[2,2,2]]=>[4,3]=>3
[[1,1,1,2],[2,2,2]]=>[4,3]=>3
[[1,8]]=>[2]=>0
[[2,8]]=>[2]=>0
[[3,8]]=>[2]=>0
[[4,8]]=>[2]=>0
[[5,8]]=>[2]=>0
[[6,8]]=>[2]=>0
[[7,8]]=>[2]=>0
[[8,8]]=>[2]=>0
[[1],[8]]=>[1,1]=>1
[[2],[8]]=>[1,1]=>1
[[3],[8]]=>[1,1]=>1
[[4],[8]]=>[1,1]=>1
[[5],[8]]=>[1,1]=>1
[[6],[8]]=>[1,1]=>1
[[7],[8]]=>[1,1]=>1
[[1,1,7]]=>[3]=>0
[[1,2,7]]=>[3]=>0
[[1,3,7]]=>[3]=>0
[[1,4,7]]=>[3]=>0
[[1,5,7]]=>[3]=>0
[[1,6,7]]=>[3]=>0
[[1,7,7]]=>[3]=>0
[[2,2,7]]=>[3]=>0
[[2,3,7]]=>[3]=>0
[[2,4,7]]=>[3]=>0
[[2,5,7]]=>[3]=>0
[[2,6,7]]=>[3]=>0
[[2,7,7]]=>[3]=>0
[[3,3,7]]=>[3]=>0
[[3,4,7]]=>[3]=>0
[[3,5,7]]=>[3]=>0
[[3,6,7]]=>[3]=>0
[[3,7,7]]=>[3]=>0
[[4,4,7]]=>[3]=>0
[[4,5,7]]=>[3]=>0
[[4,6,7]]=>[3]=>0
[[4,7,7]]=>[3]=>0
[[5,5,7]]=>[3]=>0
[[5,6,7]]=>[3]=>0
[[5,7,7]]=>[3]=>0
[[6,6,7]]=>[3]=>0
[[6,7,7]]=>[3]=>0
[[7,7,7]]=>[3]=>0
[[1,1],[7]]=>[2,1]=>1
[[1,2],[7]]=>[2,1]=>1
[[1,7],[2]]=>[2,1]=>1
[[1,3],[7]]=>[2,1]=>1
[[1,7],[3]]=>[2,1]=>1
[[1,4],[7]]=>[2,1]=>1
[[1,7],[4]]=>[2,1]=>1
[[1,5],[7]]=>[2,1]=>1
[[1,7],[5]]=>[2,1]=>1
[[1,6],[7]]=>[2,1]=>1
[[1,7],[6]]=>[2,1]=>1
[[1,7],[7]]=>[2,1]=>1
[[2,2],[7]]=>[2,1]=>1
[[2,3],[7]]=>[2,1]=>1
[[2,7],[3]]=>[2,1]=>1
[[2,4],[7]]=>[2,1]=>1
[[2,7],[4]]=>[2,1]=>1
[[2,5],[7]]=>[2,1]=>1
[[2,7],[5]]=>[2,1]=>1
[[2,6],[7]]=>[2,1]=>1
[[2,7],[6]]=>[2,1]=>1
[[2,7],[7]]=>[2,1]=>1
[[3,3],[7]]=>[2,1]=>1
[[3,4],[7]]=>[2,1]=>1
[[3,7],[4]]=>[2,1]=>1
[[3,5],[7]]=>[2,1]=>1
[[3,7],[5]]=>[2,1]=>1
[[3,6],[7]]=>[2,1]=>1
[[3,7],[6]]=>[2,1]=>1
[[3,7],[7]]=>[2,1]=>1
[[4,4],[7]]=>[2,1]=>1
[[4,5],[7]]=>[2,1]=>1
[[4,7],[5]]=>[2,1]=>1
[[4,6],[7]]=>[2,1]=>1
[[4,7],[6]]=>[2,1]=>1
[[4,7],[7]]=>[2,1]=>1
[[5,5],[7]]=>[2,1]=>1
[[5,6],[7]]=>[2,1]=>1
[[5,7],[6]]=>[2,1]=>1
[[5,7],[7]]=>[2,1]=>1
[[6,6],[7]]=>[2,1]=>1
[[6,7],[7]]=>[2,1]=>1
[[1],[2],[7]]=>[1,1,1]=>3
[[1],[3],[7]]=>[1,1,1]=>3
[[1],[4],[7]]=>[1,1,1]=>3
[[1],[5],[7]]=>[1,1,1]=>3
[[1],[6],[7]]=>[1,1,1]=>3
[[2],[3],[7]]=>[1,1,1]=>3
[[2],[4],[7]]=>[1,1,1]=>3
[[2],[5],[7]]=>[1,1,1]=>3
[[2],[6],[7]]=>[1,1,1]=>3
[[3],[4],[7]]=>[1,1,1]=>3
[[3],[5],[7]]=>[1,1,1]=>3
[[3],[6],[7]]=>[1,1,1]=>3
[[4],[5],[7]]=>[1,1,1]=>3
[[4],[6],[7]]=>[1,1,1]=>3
[[5],[6],[7]]=>[1,1,1]=>3
[[1,1,1,6]]=>[4]=>0
[[1,1,2,6]]=>[4]=>0
[[1,1,3,6]]=>[4]=>0
[[1,1,4,6]]=>[4]=>0
[[1,1,5,6]]=>[4]=>0
[[1,1,6,6]]=>[4]=>0
[[1,2,2,6]]=>[4]=>0
[[1,2,3,6]]=>[4]=>0
[[1,2,4,6]]=>[4]=>0
[[1,2,5,6]]=>[4]=>0
[[1,2,6,6]]=>[4]=>0
[[1,3,3,6]]=>[4]=>0
[[1,3,4,6]]=>[4]=>0
[[1,3,5,6]]=>[4]=>0
[[1,3,6,6]]=>[4]=>0
[[1,4,4,6]]=>[4]=>0
[[1,4,5,6]]=>[4]=>0
[[1,4,6,6]]=>[4]=>0
[[1,5,5,6]]=>[4]=>0
[[1,5,6,6]]=>[4]=>0
[[1,6,6,6]]=>[4]=>0
[[2,2,2,6]]=>[4]=>0
[[2,2,3,6]]=>[4]=>0
[[2,2,4,6]]=>[4]=>0
[[2,2,5,6]]=>[4]=>0
[[2,2,6,6]]=>[4]=>0
[[2,3,3,6]]=>[4]=>0
[[2,3,4,6]]=>[4]=>0
[[2,3,5,6]]=>[4]=>0
[[2,3,6,6]]=>[4]=>0
[[2,4,4,6]]=>[4]=>0
[[2,4,5,6]]=>[4]=>0
[[2,4,6,6]]=>[4]=>0
[[2,5,5,6]]=>[4]=>0
[[2,5,6,6]]=>[4]=>0
[[2,6,6,6]]=>[4]=>0
[[3,3,3,6]]=>[4]=>0
[[3,3,4,6]]=>[4]=>0
[[3,3,5,6]]=>[4]=>0
[[3,3,6,6]]=>[4]=>0
[[3,4,4,6]]=>[4]=>0
[[3,4,5,6]]=>[4]=>0
[[3,4,6,6]]=>[4]=>0
[[3,5,5,6]]=>[4]=>0
[[3,5,6,6]]=>[4]=>0
[[3,6,6,6]]=>[4]=>0
[[4,4,4,6]]=>[4]=>0
[[4,4,5,6]]=>[4]=>0
[[4,4,6,6]]=>[4]=>0
[[4,5,5,6]]=>[4]=>0
[[4,5,6,6]]=>[4]=>0
[[4,6,6,6]]=>[4]=>0
[[5,5,5,6]]=>[4]=>0
[[5,5,6,6]]=>[4]=>0
[[5,6,6,6]]=>[4]=>0
[[6,6,6,6]]=>[4]=>0
[[1,1,1],[6]]=>[3,1]=>1
[[1,1,2],[6]]=>[3,1]=>1
[[1,1,6],[2]]=>[3,1]=>1
[[1,1,3],[6]]=>[3,1]=>1
[[1,1,6],[3]]=>[3,1]=>1
[[1,1,4],[6]]=>[3,1]=>1
[[1,1,6],[4]]=>[3,1]=>1
[[1,1,5],[6]]=>[3,1]=>1
[[1,1,6],[5]]=>[3,1]=>1
[[1,1,6],[6]]=>[3,1]=>1
[[1,2,2],[6]]=>[3,1]=>1
[[1,2,6],[2]]=>[3,1]=>1
[[1,2,3],[6]]=>[3,1]=>1
[[1,2,6],[3]]=>[3,1]=>1
[[1,3,6],[2]]=>[3,1]=>1
[[1,2,4],[6]]=>[3,1]=>1
[[1,2,6],[4]]=>[3,1]=>1
[[1,4,6],[2]]=>[3,1]=>1
[[1,2,5],[6]]=>[3,1]=>1
[[1,2,6],[5]]=>[3,1]=>1
[[1,5,6],[2]]=>[3,1]=>1
[[1,2,6],[6]]=>[3,1]=>1
[[1,6,6],[2]]=>[3,1]=>1
[[1,3,3],[6]]=>[3,1]=>1
[[1,3,6],[3]]=>[3,1]=>1
[[1,3,4],[6]]=>[3,1]=>1
[[1,3,6],[4]]=>[3,1]=>1
[[1,4,6],[3]]=>[3,1]=>1
[[1,3,5],[6]]=>[3,1]=>1
[[1,3,6],[5]]=>[3,1]=>1
[[1,5,6],[3]]=>[3,1]=>1
[[1,3,6],[6]]=>[3,1]=>1
[[1,6,6],[3]]=>[3,1]=>1
[[1,4,4],[6]]=>[3,1]=>1
[[1,4,6],[4]]=>[3,1]=>1
[[1,4,5],[6]]=>[3,1]=>1
[[1,4,6],[5]]=>[3,1]=>1
[[1,5,6],[4]]=>[3,1]=>1
[[1,4,6],[6]]=>[3,1]=>1
[[1,6,6],[4]]=>[3,1]=>1
[[1,5,5],[6]]=>[3,1]=>1
[[1,5,6],[5]]=>[3,1]=>1
[[1,5,6],[6]]=>[3,1]=>1
[[1,6,6],[5]]=>[3,1]=>1
[[1,6,6],[6]]=>[3,1]=>1
[[2,2,2],[6]]=>[3,1]=>1
[[2,2,3],[6]]=>[3,1]=>1
[[2,2,6],[3]]=>[3,1]=>1
[[2,2,4],[6]]=>[3,1]=>1
[[2,2,6],[4]]=>[3,1]=>1
[[2,2,5],[6]]=>[3,1]=>1
[[2,2,6],[5]]=>[3,1]=>1
[[2,2,6],[6]]=>[3,1]=>1
[[2,3,3],[6]]=>[3,1]=>1
[[2,3,6],[3]]=>[3,1]=>1
[[2,3,4],[6]]=>[3,1]=>1
[[2,3,6],[4]]=>[3,1]=>1
[[2,4,6],[3]]=>[3,1]=>1
[[2,3,5],[6]]=>[3,1]=>1
[[2,3,6],[5]]=>[3,1]=>1
[[2,5,6],[3]]=>[3,1]=>1
[[2,3,6],[6]]=>[3,1]=>1
[[2,6,6],[3]]=>[3,1]=>1
[[2,4,4],[6]]=>[3,1]=>1
[[2,4,6],[4]]=>[3,1]=>1
[[2,4,5],[6]]=>[3,1]=>1
[[2,4,6],[5]]=>[3,1]=>1
[[2,5,6],[4]]=>[3,1]=>1
[[2,4,6],[6]]=>[3,1]=>1
[[2,6,6],[4]]=>[3,1]=>1
[[2,5,5],[6]]=>[3,1]=>1
[[2,5,6],[5]]=>[3,1]=>1
[[2,5,6],[6]]=>[3,1]=>1
[[2,6,6],[5]]=>[3,1]=>1
[[2,6,6],[6]]=>[3,1]=>1
[[3,3,3],[6]]=>[3,1]=>1
[[3,3,4],[6]]=>[3,1]=>1
[[3,3,6],[4]]=>[3,1]=>1
[[3,3,5],[6]]=>[3,1]=>1
[[3,3,6],[5]]=>[3,1]=>1
[[3,3,6],[6]]=>[3,1]=>1
[[3,4,4],[6]]=>[3,1]=>1
[[3,4,6],[4]]=>[3,1]=>1
[[3,4,5],[6]]=>[3,1]=>1
[[3,4,6],[5]]=>[3,1]=>1
[[3,5,6],[4]]=>[3,1]=>1
[[3,4,6],[6]]=>[3,1]=>1
[[3,6,6],[4]]=>[3,1]=>1
[[3,5,5],[6]]=>[3,1]=>1
[[3,5,6],[5]]=>[3,1]=>1
[[3,5,6],[6]]=>[3,1]=>1
[[3,6,6],[5]]=>[3,1]=>1
[[3,6,6],[6]]=>[3,1]=>1
[[4,4,4],[6]]=>[3,1]=>1
[[4,4,5],[6]]=>[3,1]=>1
[[4,4,6],[5]]=>[3,1]=>1
[[4,4,6],[6]]=>[3,1]=>1
[[4,5,5],[6]]=>[3,1]=>1
[[4,5,6],[5]]=>[3,1]=>1
[[4,5,6],[6]]=>[3,1]=>1
[[4,6,6],[5]]=>[3,1]=>1
[[4,6,6],[6]]=>[3,1]=>1
[[5,5,5],[6]]=>[3,1]=>1
[[5,5,6],[6]]=>[3,1]=>1
[[5,6,6],[6]]=>[3,1]=>1
[[1,1],[2,6]]=>[2,2]=>2
[[1,1],[3,6]]=>[2,2]=>2
[[1,1],[4,6]]=>[2,2]=>2
[[1,1],[5,6]]=>[2,2]=>2
[[1,1],[6,6]]=>[2,2]=>2
[[1,2],[2,6]]=>[2,2]=>2
[[1,2],[3,6]]=>[2,2]=>2
[[1,3],[2,6]]=>[2,2]=>2
[[1,2],[4,6]]=>[2,2]=>2
[[1,4],[2,6]]=>[2,2]=>2
[[1,2],[5,6]]=>[2,2]=>2
[[1,5],[2,6]]=>[2,2]=>2
[[1,2],[6,6]]=>[2,2]=>2
[[1,3],[3,6]]=>[2,2]=>2
[[1,3],[4,6]]=>[2,2]=>2
[[1,4],[3,6]]=>[2,2]=>2
[[1,3],[5,6]]=>[2,2]=>2
[[1,5],[3,6]]=>[2,2]=>2
[[1,3],[6,6]]=>[2,2]=>2
[[1,4],[4,6]]=>[2,2]=>2
[[1,4],[5,6]]=>[2,2]=>2
[[1,5],[4,6]]=>[2,2]=>2
[[1,4],[6,6]]=>[2,2]=>2
[[1,5],[5,6]]=>[2,2]=>2
[[1,5],[6,6]]=>[2,2]=>2
[[2,2],[3,6]]=>[2,2]=>2
[[2,2],[4,6]]=>[2,2]=>2
[[2,2],[5,6]]=>[2,2]=>2
[[2,2],[6,6]]=>[2,2]=>2
[[2,3],[3,6]]=>[2,2]=>2
[[2,3],[4,6]]=>[2,2]=>2
[[2,4],[3,6]]=>[2,2]=>2
[[2,3],[5,6]]=>[2,2]=>2
[[2,5],[3,6]]=>[2,2]=>2
[[2,3],[6,6]]=>[2,2]=>2
[[2,4],[4,6]]=>[2,2]=>2
[[2,4],[5,6]]=>[2,2]=>2
[[2,5],[4,6]]=>[2,2]=>2
[[2,4],[6,6]]=>[2,2]=>2
[[2,5],[5,6]]=>[2,2]=>2
[[2,5],[6,6]]=>[2,2]=>2
[[3,3],[4,6]]=>[2,2]=>2
[[3,3],[5,6]]=>[2,2]=>2
[[3,3],[6,6]]=>[2,2]=>2
[[3,4],[4,6]]=>[2,2]=>2
[[3,4],[5,6]]=>[2,2]=>2
[[3,5],[4,6]]=>[2,2]=>2
[[3,4],[6,6]]=>[2,2]=>2
[[3,5],[5,6]]=>[2,2]=>2
[[3,5],[6,6]]=>[2,2]=>2
[[4,4],[5,6]]=>[2,2]=>2
[[4,4],[6,6]]=>[2,2]=>2
[[4,5],[5,6]]=>[2,2]=>2
[[4,5],[6,6]]=>[2,2]=>2
[[5,5],[6,6]]=>[2,2]=>2
[[1,1],[2],[6]]=>[2,1,1]=>3
[[1,1],[3],[6]]=>[2,1,1]=>3
[[1,1],[4],[6]]=>[2,1,1]=>3
[[1,1],[5],[6]]=>[2,1,1]=>3
[[1,2],[2],[6]]=>[2,1,1]=>3
[[1,2],[3],[6]]=>[2,1,1]=>3
[[1,3],[2],[6]]=>[2,1,1]=>3
[[1,6],[2],[3]]=>[2,1,1]=>3
[[1,2],[4],[6]]=>[2,1,1]=>3
[[1,4],[2],[6]]=>[2,1,1]=>3
[[1,6],[2],[4]]=>[2,1,1]=>3
[[1,2],[5],[6]]=>[2,1,1]=>3
[[1,5],[2],[6]]=>[2,1,1]=>3
[[1,6],[2],[5]]=>[2,1,1]=>3
[[1,6],[2],[6]]=>[2,1,1]=>3
[[1,3],[3],[6]]=>[2,1,1]=>3
[[1,3],[4],[6]]=>[2,1,1]=>3
[[1,4],[3],[6]]=>[2,1,1]=>3
[[1,6],[3],[4]]=>[2,1,1]=>3
[[1,3],[5],[6]]=>[2,1,1]=>3
[[1,5],[3],[6]]=>[2,1,1]=>3
[[1,6],[3],[5]]=>[2,1,1]=>3
[[1,6],[3],[6]]=>[2,1,1]=>3
[[1,4],[4],[6]]=>[2,1,1]=>3
[[1,4],[5],[6]]=>[2,1,1]=>3
[[1,5],[4],[6]]=>[2,1,1]=>3
[[1,6],[4],[5]]=>[2,1,1]=>3
[[1,6],[4],[6]]=>[2,1,1]=>3
[[1,5],[5],[6]]=>[2,1,1]=>3
[[1,6],[5],[6]]=>[2,1,1]=>3
[[2,2],[3],[6]]=>[2,1,1]=>3
[[2,2],[4],[6]]=>[2,1,1]=>3
[[2,2],[5],[6]]=>[2,1,1]=>3
[[2,3],[3],[6]]=>[2,1,1]=>3
[[2,3],[4],[6]]=>[2,1,1]=>3
[[2,4],[3],[6]]=>[2,1,1]=>3
[[2,6],[3],[4]]=>[2,1,1]=>3
[[2,3],[5],[6]]=>[2,1,1]=>3
[[2,5],[3],[6]]=>[2,1,1]=>3
[[2,6],[3],[5]]=>[2,1,1]=>3
[[2,6],[3],[6]]=>[2,1,1]=>3
[[2,4],[4],[6]]=>[2,1,1]=>3
[[2,4],[5],[6]]=>[2,1,1]=>3
[[2,5],[4],[6]]=>[2,1,1]=>3
[[2,6],[4],[5]]=>[2,1,1]=>3
[[2,6],[4],[6]]=>[2,1,1]=>3
[[2,5],[5],[6]]=>[2,1,1]=>3
[[2,6],[5],[6]]=>[2,1,1]=>3
[[3,3],[4],[6]]=>[2,1,1]=>3
[[3,3],[5],[6]]=>[2,1,1]=>3
[[3,4],[4],[6]]=>[2,1,1]=>3
[[3,4],[5],[6]]=>[2,1,1]=>3
[[3,5],[4],[6]]=>[2,1,1]=>3
[[3,6],[4],[5]]=>[2,1,1]=>3
[[3,6],[4],[6]]=>[2,1,1]=>3
[[3,5],[5],[6]]=>[2,1,1]=>3
[[3,6],[5],[6]]=>[2,1,1]=>3
[[4,4],[5],[6]]=>[2,1,1]=>3
[[4,5],[5],[6]]=>[2,1,1]=>3
[[4,6],[5],[6]]=>[2,1,1]=>3
[[1],[2],[3],[6]]=>[1,1,1,1]=>6
[[1],[2],[4],[6]]=>[1,1,1,1]=>6
[[1],[2],[5],[6]]=>[1,1,1,1]=>6
[[1],[3],[4],[6]]=>[1,1,1,1]=>6
[[1],[3],[5],[6]]=>[1,1,1,1]=>6
[[1],[4],[5],[6]]=>[1,1,1,1]=>6
[[2],[3],[4],[6]]=>[1,1,1,1]=>6
[[2],[3],[5],[6]]=>[1,1,1,1]=>6
[[2],[4],[5],[6]]=>[1,1,1,1]=>6
[[3],[4],[5],[6]]=>[1,1,1,1]=>6
[[1,1,1,1,5]]=>[5]=>0
[[1,1,1,2,5]]=>[5]=>0
[[1,1,1,3,5]]=>[5]=>0
[[1,1,1,4,5]]=>[5]=>0
[[1,1,1,5,5]]=>[5]=>0
[[1,1,2,2,5]]=>[5]=>0
[[1,1,2,3,5]]=>[5]=>0
[[1,1,2,4,5]]=>[5]=>0
[[1,1,2,5,5]]=>[5]=>0
[[1,1,3,3,5]]=>[5]=>0
[[1,1,3,4,5]]=>[5]=>0
[[1,1,3,5,5]]=>[5]=>0
[[1,1,4,4,5]]=>[5]=>0
[[1,1,4,5,5]]=>[5]=>0
[[1,1,5,5,5]]=>[5]=>0
[[1,2,2,2,5]]=>[5]=>0
[[1,2,2,3,5]]=>[5]=>0
[[1,2,2,4,5]]=>[5]=>0
[[1,2,2,5,5]]=>[5]=>0
[[1,2,3,3,5]]=>[5]=>0
[[1,2,3,4,5]]=>[5]=>0
[[1,2,3,5,5]]=>[5]=>0
[[1,2,4,4,5]]=>[5]=>0
[[1,2,4,5,5]]=>[5]=>0
[[1,2,5,5,5]]=>[5]=>0
[[1,3,3,3,5]]=>[5]=>0
[[1,3,3,4,5]]=>[5]=>0
[[1,3,3,5,5]]=>[5]=>0
[[1,3,4,4,5]]=>[5]=>0
[[1,3,4,5,5]]=>[5]=>0
[[1,3,5,5,5]]=>[5]=>0
[[1,4,4,4,5]]=>[5]=>0
[[1,4,4,5,5]]=>[5]=>0
[[1,4,5,5,5]]=>[5]=>0
[[1,5,5,5,5]]=>[5]=>0
[[2,2,2,2,5]]=>[5]=>0
[[2,2,2,3,5]]=>[5]=>0
[[2,2,2,4,5]]=>[5]=>0
[[2,2,2,5,5]]=>[5]=>0
[[2,2,3,3,5]]=>[5]=>0
[[2,2,3,4,5]]=>[5]=>0
[[2,2,3,5,5]]=>[5]=>0
[[2,2,4,4,5]]=>[5]=>0
[[2,2,4,5,5]]=>[5]=>0
[[2,2,5,5,5]]=>[5]=>0
[[2,3,3,3,5]]=>[5]=>0
[[2,3,3,4,5]]=>[5]=>0
[[2,3,3,5,5]]=>[5]=>0
[[2,3,4,4,5]]=>[5]=>0
[[2,3,4,5,5]]=>[5]=>0
[[2,3,5,5,5]]=>[5]=>0
[[2,4,4,4,5]]=>[5]=>0
[[2,4,4,5,5]]=>[5]=>0
[[2,4,5,5,5]]=>[5]=>0
[[2,5,5,5,5]]=>[5]=>0
[[3,3,3,3,5]]=>[5]=>0
[[3,3,3,4,5]]=>[5]=>0
[[3,3,3,5,5]]=>[5]=>0
[[3,3,4,4,5]]=>[5]=>0
[[3,3,4,5,5]]=>[5]=>0
[[3,3,5,5,5]]=>[5]=>0
[[3,4,4,4,5]]=>[5]=>0
[[3,4,4,5,5]]=>[5]=>0
[[3,4,5,5,5]]=>[5]=>0
[[3,5,5,5,5]]=>[5]=>0
[[4,4,4,4,5]]=>[5]=>0
[[4,4,4,5,5]]=>[5]=>0
[[4,4,5,5,5]]=>[5]=>0
[[4,5,5,5,5]]=>[5]=>0
[[5,5,5,5,5]]=>[5]=>0
[[1,1,1,1],[5]]=>[4,1]=>1
[[1,1,1,2],[5]]=>[4,1]=>1
[[1,1,1,5],[2]]=>[4,1]=>1
[[1,1,1,3],[5]]=>[4,1]=>1
[[1,1,1,5],[3]]=>[4,1]=>1
[[1,1,1,4],[5]]=>[4,1]=>1
[[1,1,1,5],[4]]=>[4,1]=>1
[[1,1,1,5],[5]]=>[4,1]=>1
[[1,1,2,2],[5]]=>[4,1]=>1
[[1,1,2,5],[2]]=>[4,1]=>1
[[1,1,2,3],[5]]=>[4,1]=>1
[[1,1,2,5],[3]]=>[4,1]=>1
[[1,1,3,5],[2]]=>[4,1]=>1
[[1,1,2,4],[5]]=>[4,1]=>1
[[1,1,2,5],[4]]=>[4,1]=>1
[[1,1,4,5],[2]]=>[4,1]=>1
[[1,1,2,5],[5]]=>[4,1]=>1
[[1,1,5,5],[2]]=>[4,1]=>1
[[1,1,3,3],[5]]=>[4,1]=>1
[[1,1,3,5],[3]]=>[4,1]=>1
[[1,1,3,4],[5]]=>[4,1]=>1
[[1,1,3,5],[4]]=>[4,1]=>1
[[1,1,4,5],[3]]=>[4,1]=>1
[[1,1,3,5],[5]]=>[4,1]=>1
[[1,1,5,5],[3]]=>[4,1]=>1
[[1,1,4,4],[5]]=>[4,1]=>1
[[1,1,4,5],[4]]=>[4,1]=>1
[[1,1,4,5],[5]]=>[4,1]=>1
[[1,1,5,5],[4]]=>[4,1]=>1
[[1,1,5,5],[5]]=>[4,1]=>1
[[1,2,2,2],[5]]=>[4,1]=>1
[[1,2,2,5],[2]]=>[4,1]=>1
[[1,2,2,3],[5]]=>[4,1]=>1
[[1,2,2,5],[3]]=>[4,1]=>1
[[1,2,3,5],[2]]=>[4,1]=>1
[[1,2,2,4],[5]]=>[4,1]=>1
[[1,2,2,5],[4]]=>[4,1]=>1
[[1,2,4,5],[2]]=>[4,1]=>1
[[1,2,2,5],[5]]=>[4,1]=>1
[[1,2,5,5],[2]]=>[4,1]=>1
[[1,2,3,3],[5]]=>[4,1]=>1
[[1,2,3,5],[3]]=>[4,1]=>1
[[1,3,3,5],[2]]=>[4,1]=>1
[[1,2,3,4],[5]]=>[4,1]=>1
[[1,2,3,5],[4]]=>[4,1]=>1
[[1,2,4,5],[3]]=>[4,1]=>1
[[1,3,4,5],[2]]=>[4,1]=>1
[[1,2,3,5],[5]]=>[4,1]=>1
[[1,2,5,5],[3]]=>[4,1]=>1
[[1,3,5,5],[2]]=>[4,1]=>1
[[1,2,4,4],[5]]=>[4,1]=>1
[[1,2,4,5],[4]]=>[4,1]=>1
[[1,4,4,5],[2]]=>[4,1]=>1
[[1,2,4,5],[5]]=>[4,1]=>1
[[1,2,5,5],[4]]=>[4,1]=>1
[[1,4,5,5],[2]]=>[4,1]=>1
[[1,2,5,5],[5]]=>[4,1]=>1
[[1,5,5,5],[2]]=>[4,1]=>1
[[1,3,3,3],[5]]=>[4,1]=>1
[[1,3,3,5],[3]]=>[4,1]=>1
[[1,3,3,4],[5]]=>[4,1]=>1
[[1,3,3,5],[4]]=>[4,1]=>1
[[1,3,4,5],[3]]=>[4,1]=>1
[[1,3,3,5],[5]]=>[4,1]=>1
[[1,3,5,5],[3]]=>[4,1]=>1
[[1,3,4,4],[5]]=>[4,1]=>1
[[1,3,4,5],[4]]=>[4,1]=>1
[[1,4,4,5],[3]]=>[4,1]=>1
[[1,3,4,5],[5]]=>[4,1]=>1
[[1,3,5,5],[4]]=>[4,1]=>1
[[1,4,5,5],[3]]=>[4,1]=>1
[[1,3,5,5],[5]]=>[4,1]=>1
[[1,5,5,5],[3]]=>[4,1]=>1
[[1,4,4,4],[5]]=>[4,1]=>1
[[1,4,4,5],[4]]=>[4,1]=>1
[[1,4,4,5],[5]]=>[4,1]=>1
[[1,4,5,5],[4]]=>[4,1]=>1
[[1,4,5,5],[5]]=>[4,1]=>1
[[1,5,5,5],[4]]=>[4,1]=>1
[[1,5,5,5],[5]]=>[4,1]=>1
[[2,2,2,2],[5]]=>[4,1]=>1
[[2,2,2,3],[5]]=>[4,1]=>1
[[2,2,2,5],[3]]=>[4,1]=>1
[[2,2,2,4],[5]]=>[4,1]=>1
[[2,2,2,5],[4]]=>[4,1]=>1
[[2,2,2,5],[5]]=>[4,1]=>1
[[2,2,3,3],[5]]=>[4,1]=>1
[[2,2,3,5],[3]]=>[4,1]=>1
[[2,2,3,4],[5]]=>[4,1]=>1
[[2,2,3,5],[4]]=>[4,1]=>1
[[2,2,4,5],[3]]=>[4,1]=>1
[[2,2,3,5],[5]]=>[4,1]=>1
[[2,2,5,5],[3]]=>[4,1]=>1
[[2,2,4,4],[5]]=>[4,1]=>1
[[2,2,4,5],[4]]=>[4,1]=>1
[[2,2,4,5],[5]]=>[4,1]=>1
[[2,2,5,5],[4]]=>[4,1]=>1
[[2,2,5,5],[5]]=>[4,1]=>1
[[2,3,3,3],[5]]=>[4,1]=>1
[[2,3,3,5],[3]]=>[4,1]=>1
[[2,3,3,4],[5]]=>[4,1]=>1
[[2,3,3,5],[4]]=>[4,1]=>1
[[2,3,4,5],[3]]=>[4,1]=>1
[[2,3,3,5],[5]]=>[4,1]=>1
[[2,3,5,5],[3]]=>[4,1]=>1
[[2,3,4,4],[5]]=>[4,1]=>1
[[2,3,4,5],[4]]=>[4,1]=>1
[[2,4,4,5],[3]]=>[4,1]=>1
[[2,3,4,5],[5]]=>[4,1]=>1
[[2,3,5,5],[4]]=>[4,1]=>1
[[2,4,5,5],[3]]=>[4,1]=>1
[[2,3,5,5],[5]]=>[4,1]=>1
[[2,5,5,5],[3]]=>[4,1]=>1
[[2,4,4,4],[5]]=>[4,1]=>1
[[2,4,4,5],[4]]=>[4,1]=>1
[[2,4,4,5],[5]]=>[4,1]=>1
[[2,4,5,5],[4]]=>[4,1]=>1
[[2,4,5,5],[5]]=>[4,1]=>1
[[2,5,5,5],[4]]=>[4,1]=>1
[[2,5,5,5],[5]]=>[4,1]=>1
[[3,3,3,3],[5]]=>[4,1]=>1
[[3,3,3,4],[5]]=>[4,1]=>1
[[3,3,3,5],[4]]=>[4,1]=>1
[[3,3,3,5],[5]]=>[4,1]=>1
[[3,3,4,4],[5]]=>[4,1]=>1
[[3,3,4,5],[4]]=>[4,1]=>1
[[3,3,4,5],[5]]=>[4,1]=>1
[[3,3,5,5],[4]]=>[4,1]=>1
[[3,3,5,5],[5]]=>[4,1]=>1
[[3,4,4,4],[5]]=>[4,1]=>1
[[3,4,4,5],[4]]=>[4,1]=>1
[[3,4,4,5],[5]]=>[4,1]=>1
[[3,4,5,5],[4]]=>[4,1]=>1
[[3,4,5,5],[5]]=>[4,1]=>1
[[3,5,5,5],[4]]=>[4,1]=>1
[[3,5,5,5],[5]]=>[4,1]=>1
[[4,4,4,4],[5]]=>[4,1]=>1
[[4,4,4,5],[5]]=>[4,1]=>1
[[4,4,5,5],[5]]=>[4,1]=>1
[[4,5,5,5],[5]]=>[4,1]=>1
[[1,1,1],[2,5]]=>[3,2]=>2
[[1,1,1],[3,5]]=>[3,2]=>2
[[1,1,1],[4,5]]=>[3,2]=>2
[[1,1,1],[5,5]]=>[3,2]=>2
[[1,1,2],[2,5]]=>[3,2]=>2
[[1,1,5],[2,2]]=>[3,2]=>2
[[1,1,2],[3,5]]=>[3,2]=>2
[[1,1,3],[2,5]]=>[3,2]=>2
[[1,1,5],[2,3]]=>[3,2]=>2
[[1,1,2],[4,5]]=>[3,2]=>2
[[1,1,4],[2,5]]=>[3,2]=>2
[[1,1,5],[2,4]]=>[3,2]=>2
[[1,1,2],[5,5]]=>[3,2]=>2
[[1,1,5],[2,5]]=>[3,2]=>2
[[1,1,3],[3,5]]=>[3,2]=>2
[[1,1,5],[3,3]]=>[3,2]=>2
[[1,1,3],[4,5]]=>[3,2]=>2
[[1,1,4],[3,5]]=>[3,2]=>2
[[1,1,5],[3,4]]=>[3,2]=>2
[[1,1,3],[5,5]]=>[3,2]=>2
[[1,1,5],[3,5]]=>[3,2]=>2
[[1,1,4],[4,5]]=>[3,2]=>2
[[1,1,5],[4,4]]=>[3,2]=>2
[[1,1,4],[5,5]]=>[3,2]=>2
[[1,1,5],[4,5]]=>[3,2]=>2
[[1,1,5],[5,5]]=>[3,2]=>2
[[1,2,2],[2,5]]=>[3,2]=>2
[[1,2,2],[3,5]]=>[3,2]=>2
[[1,2,3],[2,5]]=>[3,2]=>2
[[1,2,5],[2,3]]=>[3,2]=>2
[[1,2,2],[4,5]]=>[3,2]=>2
[[1,2,4],[2,5]]=>[3,2]=>2
[[1,2,5],[2,4]]=>[3,2]=>2
[[1,2,2],[5,5]]=>[3,2]=>2
[[1,2,5],[2,5]]=>[3,2]=>2
[[1,2,3],[3,5]]=>[3,2]=>2
[[1,2,5],[3,3]]=>[3,2]=>2
[[1,3,3],[2,5]]=>[3,2]=>2
[[1,2,3],[4,5]]=>[3,2]=>2
[[1,2,4],[3,5]]=>[3,2]=>2
[[1,2,5],[3,4]]=>[3,2]=>2
[[1,3,4],[2,5]]=>[3,2]=>2
[[1,3,5],[2,4]]=>[3,2]=>2
[[1,2,3],[5,5]]=>[3,2]=>2
[[1,2,5],[3,5]]=>[3,2]=>2
[[1,3,5],[2,5]]=>[3,2]=>2
[[1,2,4],[4,5]]=>[3,2]=>2
[[1,2,5],[4,4]]=>[3,2]=>2
[[1,4,4],[2,5]]=>[3,2]=>2
[[1,2,4],[5,5]]=>[3,2]=>2
[[1,2,5],[4,5]]=>[3,2]=>2
[[1,4,5],[2,5]]=>[3,2]=>2
[[1,2,5],[5,5]]=>[3,2]=>2
[[1,3,3],[3,5]]=>[3,2]=>2
[[1,3,3],[4,5]]=>[3,2]=>2
[[1,3,4],[3,5]]=>[3,2]=>2
[[1,3,5],[3,4]]=>[3,2]=>2
[[1,3,3],[5,5]]=>[3,2]=>2
[[1,3,5],[3,5]]=>[3,2]=>2
[[1,3,4],[4,5]]=>[3,2]=>2
[[1,3,5],[4,4]]=>[3,2]=>2
[[1,4,4],[3,5]]=>[3,2]=>2
[[1,3,4],[5,5]]=>[3,2]=>2
[[1,3,5],[4,5]]=>[3,2]=>2
[[1,4,5],[3,5]]=>[3,2]=>2
[[1,3,5],[5,5]]=>[3,2]=>2
[[1,4,4],[4,5]]=>[3,2]=>2
[[1,4,4],[5,5]]=>[3,2]=>2
[[1,4,5],[4,5]]=>[3,2]=>2
[[1,4,5],[5,5]]=>[3,2]=>2
[[2,2,2],[3,5]]=>[3,2]=>2
[[2,2,2],[4,5]]=>[3,2]=>2
[[2,2,2],[5,5]]=>[3,2]=>2
[[2,2,3],[3,5]]=>[3,2]=>2
[[2,2,5],[3,3]]=>[3,2]=>2
[[2,2,3],[4,5]]=>[3,2]=>2
[[2,2,4],[3,5]]=>[3,2]=>2
[[2,2,5],[3,4]]=>[3,2]=>2
[[2,2,3],[5,5]]=>[3,2]=>2
[[2,2,5],[3,5]]=>[3,2]=>2
[[2,2,4],[4,5]]=>[3,2]=>2
[[2,2,5],[4,4]]=>[3,2]=>2
[[2,2,4],[5,5]]=>[3,2]=>2
[[2,2,5],[4,5]]=>[3,2]=>2
[[2,2,5],[5,5]]=>[3,2]=>2
[[2,3,3],[3,5]]=>[3,2]=>2
[[2,3,3],[4,5]]=>[3,2]=>2
[[2,3,4],[3,5]]=>[3,2]=>2
[[2,3,5],[3,4]]=>[3,2]=>2
[[2,3,3],[5,5]]=>[3,2]=>2
[[2,3,5],[3,5]]=>[3,2]=>2
[[2,3,4],[4,5]]=>[3,2]=>2
[[2,3,5],[4,4]]=>[3,2]=>2
[[2,4,4],[3,5]]=>[3,2]=>2
[[2,3,4],[5,5]]=>[3,2]=>2
[[2,3,5],[4,5]]=>[3,2]=>2
[[2,4,5],[3,5]]=>[3,2]=>2
[[2,3,5],[5,5]]=>[3,2]=>2
[[2,4,4],[4,5]]=>[3,2]=>2
[[2,4,4],[5,5]]=>[3,2]=>2
[[2,4,5],[4,5]]=>[3,2]=>2
[[2,4,5],[5,5]]=>[3,2]=>2
[[3,3,3],[4,5]]=>[3,2]=>2
[[3,3,3],[5,5]]=>[3,2]=>2
[[3,3,4],[4,5]]=>[3,2]=>2
[[3,3,5],[4,4]]=>[3,2]=>2
[[3,3,4],[5,5]]=>[3,2]=>2
[[3,3,5],[4,5]]=>[3,2]=>2
[[3,3,5],[5,5]]=>[3,2]=>2
[[3,4,4],[4,5]]=>[3,2]=>2
[[3,4,4],[5,5]]=>[3,2]=>2
[[3,4,5],[4,5]]=>[3,2]=>2
[[3,4,5],[5,5]]=>[3,2]=>2
[[4,4,4],[5,5]]=>[3,2]=>2
[[4,4,5],[5,5]]=>[3,2]=>2
[[1,1,1],[2],[5]]=>[3,1,1]=>3
[[1,1,1],[3],[5]]=>[3,1,1]=>3
[[1,1,1],[4],[5]]=>[3,1,1]=>3
[[1,1,2],[2],[5]]=>[3,1,1]=>3
[[1,1,2],[3],[5]]=>[3,1,1]=>3
[[1,1,3],[2],[5]]=>[3,1,1]=>3
[[1,1,5],[2],[3]]=>[3,1,1]=>3
[[1,1,2],[4],[5]]=>[3,1,1]=>3
[[1,1,4],[2],[5]]=>[3,1,1]=>3
[[1,1,5],[2],[4]]=>[3,1,1]=>3
[[1,1,5],[2],[5]]=>[3,1,1]=>3
[[1,1,3],[3],[5]]=>[3,1,1]=>3
[[1,1,3],[4],[5]]=>[3,1,1]=>3
[[1,1,4],[3],[5]]=>[3,1,1]=>3
[[1,1,5],[3],[4]]=>[3,1,1]=>3
[[1,1,5],[3],[5]]=>[3,1,1]=>3
[[1,1,4],[4],[5]]=>[3,1,1]=>3
[[1,1,5],[4],[5]]=>[3,1,1]=>3
[[1,2,2],[2],[5]]=>[3,1,1]=>3
[[1,2,2],[3],[5]]=>[3,1,1]=>3
[[1,2,3],[2],[5]]=>[3,1,1]=>3
[[1,2,5],[2],[3]]=>[3,1,1]=>3
[[1,2,2],[4],[5]]=>[3,1,1]=>3
[[1,2,4],[2],[5]]=>[3,1,1]=>3
[[1,2,5],[2],[4]]=>[3,1,1]=>3
[[1,2,5],[2],[5]]=>[3,1,1]=>3
[[1,2,3],[3],[5]]=>[3,1,1]=>3
[[1,3,3],[2],[5]]=>[3,1,1]=>3
[[1,3,5],[2],[3]]=>[3,1,1]=>3
[[1,2,3],[4],[5]]=>[3,1,1]=>3
[[1,2,4],[3],[5]]=>[3,1,1]=>3
[[1,2,5],[3],[4]]=>[3,1,1]=>3
[[1,3,4],[2],[5]]=>[3,1,1]=>3
[[1,3,5],[2],[4]]=>[3,1,1]=>3
[[1,4,5],[2],[3]]=>[3,1,1]=>3
[[1,2,5],[3],[5]]=>[3,1,1]=>3
[[1,3,5],[2],[5]]=>[3,1,1]=>3
[[1,5,5],[2],[3]]=>[3,1,1]=>3
[[1,2,4],[4],[5]]=>[3,1,1]=>3
[[1,4,4],[2],[5]]=>[3,1,1]=>3
[[1,4,5],[2],[4]]=>[3,1,1]=>3
[[1,2,5],[4],[5]]=>[3,1,1]=>3
[[1,4,5],[2],[5]]=>[3,1,1]=>3
[[1,5,5],[2],[4]]=>[3,1,1]=>3
[[1,5,5],[2],[5]]=>[3,1,1]=>3
[[1,3,3],[3],[5]]=>[3,1,1]=>3
[[1,3,3],[4],[5]]=>[3,1,1]=>3
[[1,3,4],[3],[5]]=>[3,1,1]=>3
[[1,3,5],[3],[4]]=>[3,1,1]=>3
[[1,3,5],[3],[5]]=>[3,1,1]=>3
[[1,3,4],[4],[5]]=>[3,1,1]=>3
[[1,4,4],[3],[5]]=>[3,1,1]=>3
[[1,4,5],[3],[4]]=>[3,1,1]=>3
[[1,3,5],[4],[5]]=>[3,1,1]=>3
[[1,4,5],[3],[5]]=>[3,1,1]=>3
[[1,5,5],[3],[4]]=>[3,1,1]=>3
[[1,5,5],[3],[5]]=>[3,1,1]=>3
[[1,4,4],[4],[5]]=>[3,1,1]=>3
[[1,4,5],[4],[5]]=>[3,1,1]=>3
[[1,5,5],[4],[5]]=>[3,1,1]=>3
[[2,2,2],[3],[5]]=>[3,1,1]=>3
[[2,2,2],[4],[5]]=>[3,1,1]=>3
[[2,2,3],[3],[5]]=>[3,1,1]=>3
[[2,2,3],[4],[5]]=>[3,1,1]=>3
[[2,2,4],[3],[5]]=>[3,1,1]=>3
[[2,2,5],[3],[4]]=>[3,1,1]=>3
[[2,2,5],[3],[5]]=>[3,1,1]=>3
[[2,2,4],[4],[5]]=>[3,1,1]=>3
[[2,2,5],[4],[5]]=>[3,1,1]=>3
[[2,3,3],[3],[5]]=>[3,1,1]=>3
[[2,3,3],[4],[5]]=>[3,1,1]=>3
[[2,3,4],[3],[5]]=>[3,1,1]=>3
[[2,3,5],[3],[4]]=>[3,1,1]=>3
[[2,3,5],[3],[5]]=>[3,1,1]=>3
[[2,3,4],[4],[5]]=>[3,1,1]=>3
[[2,4,4],[3],[5]]=>[3,1,1]=>3
[[2,4,5],[3],[4]]=>[3,1,1]=>3
[[2,3,5],[4],[5]]=>[3,1,1]=>3
[[2,4,5],[3],[5]]=>[3,1,1]=>3
[[2,5,5],[3],[4]]=>[3,1,1]=>3
[[2,5,5],[3],[5]]=>[3,1,1]=>3
[[2,4,4],[4],[5]]=>[3,1,1]=>3
[[2,4,5],[4],[5]]=>[3,1,1]=>3
[[2,5,5],[4],[5]]=>[3,1,1]=>3
[[3,3,3],[4],[5]]=>[3,1,1]=>3
[[3,3,4],[4],[5]]=>[3,1,1]=>3
[[3,3,5],[4],[5]]=>[3,1,1]=>3
[[3,4,4],[4],[5]]=>[3,1,1]=>3
[[3,4,5],[4],[5]]=>[3,1,1]=>3
[[3,5,5],[4],[5]]=>[3,1,1]=>3
[[1,1],[2,2],[5]]=>[2,2,1]=>4
[[1,1],[2,3],[5]]=>[2,2,1]=>4
[[1,1],[2,5],[3]]=>[2,2,1]=>4
[[1,1],[2,4],[5]]=>[2,2,1]=>4
[[1,1],[2,5],[4]]=>[2,2,1]=>4
[[1,1],[2,5],[5]]=>[2,2,1]=>4
[[1,1],[3,3],[5]]=>[2,2,1]=>4
[[1,1],[3,4],[5]]=>[2,2,1]=>4
[[1,1],[3,5],[4]]=>[2,2,1]=>4
[[1,1],[3,5],[5]]=>[2,2,1]=>4
[[1,1],[4,4],[5]]=>[2,2,1]=>4
[[1,1],[4,5],[5]]=>[2,2,1]=>4
[[1,2],[2,3],[5]]=>[2,2,1]=>4
[[1,2],[2,5],[3]]=>[2,2,1]=>4
[[1,2],[2,4],[5]]=>[2,2,1]=>4
[[1,2],[2,5],[4]]=>[2,2,1]=>4
[[1,2],[2,5],[5]]=>[2,2,1]=>4
[[1,2],[3,3],[5]]=>[2,2,1]=>4
[[1,3],[2,5],[3]]=>[2,2,1]=>4
[[1,2],[3,4],[5]]=>[2,2,1]=>4
[[1,2],[3,5],[4]]=>[2,2,1]=>4
[[1,3],[2,4],[5]]=>[2,2,1]=>4
[[1,3],[2,5],[4]]=>[2,2,1]=>4
[[1,4],[2,5],[3]]=>[2,2,1]=>4
[[1,2],[3,5],[5]]=>[2,2,1]=>4
[[1,3],[2,5],[5]]=>[2,2,1]=>4
[[1,2],[4,4],[5]]=>[2,2,1]=>4
[[1,4],[2,5],[4]]=>[2,2,1]=>4
[[1,2],[4,5],[5]]=>[2,2,1]=>4
[[1,4],[2,5],[5]]=>[2,2,1]=>4
[[1,3],[3,4],[5]]=>[2,2,1]=>4
[[1,3],[3,5],[4]]=>[2,2,1]=>4
[[1,3],[3,5],[5]]=>[2,2,1]=>4
[[1,3],[4,4],[5]]=>[2,2,1]=>4
[[1,4],[3,5],[4]]=>[2,2,1]=>4
[[1,3],[4,5],[5]]=>[2,2,1]=>4
[[1,4],[3,5],[5]]=>[2,2,1]=>4
[[1,4],[4,5],[5]]=>[2,2,1]=>4
[[2,2],[3,3],[5]]=>[2,2,1]=>4
[[2,2],[3,4],[5]]=>[2,2,1]=>4
[[2,2],[3,5],[4]]=>[2,2,1]=>4
[[2,2],[3,5],[5]]=>[2,2,1]=>4
[[2,2],[4,4],[5]]=>[2,2,1]=>4
[[2,2],[4,5],[5]]=>[2,2,1]=>4
[[2,3],[3,4],[5]]=>[2,2,1]=>4
[[2,3],[3,5],[4]]=>[2,2,1]=>4
[[2,3],[3,5],[5]]=>[2,2,1]=>4
[[2,3],[4,4],[5]]=>[2,2,1]=>4
[[2,4],[3,5],[4]]=>[2,2,1]=>4
[[2,3],[4,5],[5]]=>[2,2,1]=>4
[[2,4],[3,5],[5]]=>[2,2,1]=>4
[[2,4],[4,5],[5]]=>[2,2,1]=>4
[[3,3],[4,4],[5]]=>[2,2,1]=>4
[[3,3],[4,5],[5]]=>[2,2,1]=>4
[[3,4],[4,5],[5]]=>[2,2,1]=>4
[[1,1],[2],[3],[5]]=>[2,1,1,1]=>6
[[1,1],[2],[4],[5]]=>[2,1,1,1]=>6
[[1,1],[3],[4],[5]]=>[2,1,1,1]=>6
[[1,2],[2],[3],[5]]=>[2,1,1,1]=>6
[[1,2],[2],[4],[5]]=>[2,1,1,1]=>6
[[1,3],[2],[3],[5]]=>[2,1,1,1]=>6
[[1,2],[3],[4],[5]]=>[2,1,1,1]=>6
[[1,3],[2],[4],[5]]=>[2,1,1,1]=>6
[[1,4],[2],[3],[5]]=>[2,1,1,1]=>6
[[1,5],[2],[3],[4]]=>[2,1,1,1]=>6
[[1,5],[2],[3],[5]]=>[2,1,1,1]=>6
[[1,4],[2],[4],[5]]=>[2,1,1,1]=>6
[[1,5],[2],[4],[5]]=>[2,1,1,1]=>6
[[1,3],[3],[4],[5]]=>[2,1,1,1]=>6
[[1,4],[3],[4],[5]]=>[2,1,1,1]=>6
[[1,5],[3],[4],[5]]=>[2,1,1,1]=>6
[[2,2],[3],[4],[5]]=>[2,1,1,1]=>6
[[2,3],[3],[4],[5]]=>[2,1,1,1]=>6
[[2,4],[3],[4],[5]]=>[2,1,1,1]=>6
[[2,5],[3],[4],[5]]=>[2,1,1,1]=>6
[[1],[2],[3],[4],[5]]=>[1,1,1,1,1]=>10
[[1,1,1,1,1,4]]=>[6]=>0
[[1,1,1,1,2,4]]=>[6]=>0
[[1,1,1,1,3,4]]=>[6]=>0
[[1,1,1,1,4,4]]=>[6]=>0
[[1,1,1,2,2,4]]=>[6]=>0
[[1,1,1,2,3,4]]=>[6]=>0
[[1,1,1,2,4,4]]=>[6]=>0
[[1,1,1,3,3,4]]=>[6]=>0
[[1,1,1,3,4,4]]=>[6]=>0
[[1,1,1,4,4,4]]=>[6]=>0
[[1,1,2,2,2,4]]=>[6]=>0
[[1,1,2,2,3,4]]=>[6]=>0
[[1,1,2,2,4,4]]=>[6]=>0
[[1,1,2,3,3,4]]=>[6]=>0
[[1,1,2,3,4,4]]=>[6]=>0
[[1,1,2,4,4,4]]=>[6]=>0
[[1,1,3,3,3,4]]=>[6]=>0
[[1,1,3,3,4,4]]=>[6]=>0
[[1,1,3,4,4,4]]=>[6]=>0
[[1,1,4,4,4,4]]=>[6]=>0
[[1,2,2,2,2,4]]=>[6]=>0
[[1,2,2,2,3,4]]=>[6]=>0
[[1,2,2,2,4,4]]=>[6]=>0
[[1,2,2,3,3,4]]=>[6]=>0
[[1,2,2,3,4,4]]=>[6]=>0
[[1,2,2,4,4,4]]=>[6]=>0
[[1,2,3,3,3,4]]=>[6]=>0
[[1,2,3,3,4,4]]=>[6]=>0
[[1,2,3,4,4,4]]=>[6]=>0
[[1,2,4,4,4,4]]=>[6]=>0
[[1,3,3,3,3,4]]=>[6]=>0
[[1,3,3,3,4,4]]=>[6]=>0
[[1,3,3,4,4,4]]=>[6]=>0
[[1,3,4,4,4,4]]=>[6]=>0
[[1,4,4,4,4,4]]=>[6]=>0
[[2,2,2,2,2,4]]=>[6]=>0
[[2,2,2,2,3,4]]=>[6]=>0
[[2,2,2,2,4,4]]=>[6]=>0
[[2,2,2,3,3,4]]=>[6]=>0
[[2,2,2,3,4,4]]=>[6]=>0
[[2,2,2,4,4,4]]=>[6]=>0
[[2,2,3,3,3,4]]=>[6]=>0
[[2,2,3,3,4,4]]=>[6]=>0
[[2,2,3,4,4,4]]=>[6]=>0
[[2,2,4,4,4,4]]=>[6]=>0
[[2,3,3,3,3,4]]=>[6]=>0
[[2,3,3,3,4,4]]=>[6]=>0
[[2,3,3,4,4,4]]=>[6]=>0
[[2,3,4,4,4,4]]=>[6]=>0
[[2,4,4,4,4,4]]=>[6]=>0
[[3,3,3,3,3,4]]=>[6]=>0
[[3,3,3,3,4,4]]=>[6]=>0
[[3,3,3,4,4,4]]=>[6]=>0
[[3,3,4,4,4,4]]=>[6]=>0
[[3,4,4,4,4,4]]=>[6]=>0
[[4,4,4,4,4,4]]=>[6]=>0
[[1,1,1,1,1],[4]]=>[5,1]=>1
[[1,1,1,1,2],[4]]=>[5,1]=>1
[[1,1,1,1,4],[2]]=>[5,1]=>1
[[1,1,1,1,3],[4]]=>[5,1]=>1
[[1,1,1,1,4],[3]]=>[5,1]=>1
[[1,1,1,1,4],[4]]=>[5,1]=>1
[[1,1,1,2,2],[4]]=>[5,1]=>1
[[1,1,1,2,4],[2]]=>[5,1]=>1
[[1,1,1,2,3],[4]]=>[5,1]=>1
[[1,1,1,2,4],[3]]=>[5,1]=>1
[[1,1,1,3,4],[2]]=>[5,1]=>1
[[1,1,1,2,4],[4]]=>[5,1]=>1
[[1,1,1,4,4],[2]]=>[5,1]=>1
[[1,1,1,3,3],[4]]=>[5,1]=>1
[[1,1,1,3,4],[3]]=>[5,1]=>1
[[1,1,1,3,4],[4]]=>[5,1]=>1
[[1,1,1,4,4],[3]]=>[5,1]=>1
[[1,1,1,4,4],[4]]=>[5,1]=>1
[[1,1,2,2,2],[4]]=>[5,1]=>1
[[1,1,2,2,4],[2]]=>[5,1]=>1
[[1,1,2,2,3],[4]]=>[5,1]=>1
[[1,1,2,2,4],[3]]=>[5,1]=>1
[[1,1,2,3,4],[2]]=>[5,1]=>1
[[1,1,2,2,4],[4]]=>[5,1]=>1
[[1,1,2,4,4],[2]]=>[5,1]=>1
[[1,1,2,3,3],[4]]=>[5,1]=>1
[[1,1,2,3,4],[3]]=>[5,1]=>1
[[1,1,3,3,4],[2]]=>[5,1]=>1
[[1,1,2,3,4],[4]]=>[5,1]=>1
[[1,1,2,4,4],[3]]=>[5,1]=>1
[[1,1,3,4,4],[2]]=>[5,1]=>1
[[1,1,2,4,4],[4]]=>[5,1]=>1
[[1,1,4,4,4],[2]]=>[5,1]=>1
[[1,1,3,3,3],[4]]=>[5,1]=>1
[[1,1,3,3,4],[3]]=>[5,1]=>1
[[1,1,3,3,4],[4]]=>[5,1]=>1
[[1,1,3,4,4],[3]]=>[5,1]=>1
[[1,1,3,4,4],[4]]=>[5,1]=>1
[[1,1,4,4,4],[3]]=>[5,1]=>1
[[1,1,4,4,4],[4]]=>[5,1]=>1
[[1,2,2,2,2],[4]]=>[5,1]=>1
[[1,2,2,2,4],[2]]=>[5,1]=>1
[[1,2,2,2,3],[4]]=>[5,1]=>1
[[1,2,2,2,4],[3]]=>[5,1]=>1
[[1,2,2,3,4],[2]]=>[5,1]=>1
[[1,2,2,2,4],[4]]=>[5,1]=>1
[[1,2,2,4,4],[2]]=>[5,1]=>1
[[1,2,2,3,3],[4]]=>[5,1]=>1
[[1,2,2,3,4],[3]]=>[5,1]=>1
[[1,2,3,3,4],[2]]=>[5,1]=>1
[[1,2,2,3,4],[4]]=>[5,1]=>1
[[1,2,2,4,4],[3]]=>[5,1]=>1
[[1,2,3,4,4],[2]]=>[5,1]=>1
[[1,2,2,4,4],[4]]=>[5,1]=>1
[[1,2,4,4,4],[2]]=>[5,1]=>1
[[1,2,3,3,3],[4]]=>[5,1]=>1
[[1,2,3,3,4],[3]]=>[5,1]=>1
[[1,3,3,3,4],[2]]=>[5,1]=>1
[[1,2,3,3,4],[4]]=>[5,1]=>1
[[1,2,3,4,4],[3]]=>[5,1]=>1
[[1,3,3,4,4],[2]]=>[5,1]=>1
[[1,2,3,4,4],[4]]=>[5,1]=>1
[[1,2,4,4,4],[3]]=>[5,1]=>1
[[1,3,4,4,4],[2]]=>[5,1]=>1
[[1,2,4,4,4],[4]]=>[5,1]=>1
[[1,4,4,4,4],[2]]=>[5,1]=>1
[[1,3,3,3,3],[4]]=>[5,1]=>1
[[1,3,3,3,4],[3]]=>[5,1]=>1
[[1,3,3,3,4],[4]]=>[5,1]=>1
[[1,3,3,4,4],[3]]=>[5,1]=>1
[[1,3,3,4,4],[4]]=>[5,1]=>1
[[1,3,4,4,4],[3]]=>[5,1]=>1
[[1,3,4,4,4],[4]]=>[5,1]=>1
[[1,4,4,4,4],[3]]=>[5,1]=>1
[[1,4,4,4,4],[4]]=>[5,1]=>1
[[2,2,2,2,2],[4]]=>[5,1]=>1
[[2,2,2,2,3],[4]]=>[5,1]=>1
[[2,2,2,2,4],[3]]=>[5,1]=>1
[[2,2,2,2,4],[4]]=>[5,1]=>1
[[2,2,2,3,3],[4]]=>[5,1]=>1
[[2,2,2,3,4],[3]]=>[5,1]=>1
[[2,2,2,3,4],[4]]=>[5,1]=>1
[[2,2,2,4,4],[3]]=>[5,1]=>1
[[2,2,2,4,4],[4]]=>[5,1]=>1
[[2,2,3,3,3],[4]]=>[5,1]=>1
[[2,2,3,3,4],[3]]=>[5,1]=>1
[[2,2,3,3,4],[4]]=>[5,1]=>1
[[2,2,3,4,4],[3]]=>[5,1]=>1
[[2,2,3,4,4],[4]]=>[5,1]=>1
[[2,2,4,4,4],[3]]=>[5,1]=>1
[[2,2,4,4,4],[4]]=>[5,1]=>1
[[2,3,3,3,3],[4]]=>[5,1]=>1
[[2,3,3,3,4],[3]]=>[5,1]=>1
[[2,3,3,3,4],[4]]=>[5,1]=>1
[[2,3,3,4,4],[3]]=>[5,1]=>1
[[2,3,3,4,4],[4]]=>[5,1]=>1
[[2,3,4,4,4],[3]]=>[5,1]=>1
[[2,3,4,4,4],[4]]=>[5,1]=>1
[[2,4,4,4,4],[3]]=>[5,1]=>1
[[2,4,4,4,4],[4]]=>[5,1]=>1
[[3,3,3,3,3],[4]]=>[5,1]=>1
[[3,3,3,3,4],[4]]=>[5,1]=>1
[[3,3,3,4,4],[4]]=>[5,1]=>1
[[3,3,4,4,4],[4]]=>[5,1]=>1
[[3,4,4,4,4],[4]]=>[5,1]=>1
[[1,1,1,1],[2,4]]=>[4,2]=>2
[[1,1,1,1],[3,4]]=>[4,2]=>2
[[1,1,1,1],[4,4]]=>[4,2]=>2
[[1,1,1,2],[2,4]]=>[4,2]=>2
[[1,1,1,4],[2,2]]=>[4,2]=>2
[[1,1,1,2],[3,4]]=>[4,2]=>2
[[1,1,1,3],[2,4]]=>[4,2]=>2
[[1,1,1,4],[2,3]]=>[4,2]=>2
[[1,1,1,2],[4,4]]=>[4,2]=>2
[[1,1,1,4],[2,4]]=>[4,2]=>2
[[1,1,1,3],[3,4]]=>[4,2]=>2
[[1,1,1,4],[3,3]]=>[4,2]=>2
[[1,1,1,3],[4,4]]=>[4,2]=>2
[[1,1,1,4],[3,4]]=>[4,2]=>2
[[1,1,1,4],[4,4]]=>[4,2]=>2
[[1,1,2,2],[2,4]]=>[4,2]=>2
[[1,1,2,4],[2,2]]=>[4,2]=>2
[[1,1,2,2],[3,4]]=>[4,2]=>2
[[1,1,2,3],[2,4]]=>[4,2]=>2
[[1,1,2,4],[2,3]]=>[4,2]=>2
[[1,1,3,4],[2,2]]=>[4,2]=>2
[[1,1,2,2],[4,4]]=>[4,2]=>2
[[1,1,2,4],[2,4]]=>[4,2]=>2
[[1,1,4,4],[2,2]]=>[4,2]=>2
[[1,1,2,3],[3,4]]=>[4,2]=>2
[[1,1,2,4],[3,3]]=>[4,2]=>2
[[1,1,3,3],[2,4]]=>[4,2]=>2
[[1,1,3,4],[2,3]]=>[4,2]=>2
[[1,1,2,3],[4,4]]=>[4,2]=>2
[[1,1,2,4],[3,4]]=>[4,2]=>2
[[1,1,3,4],[2,4]]=>[4,2]=>2
[[1,1,4,4],[2,3]]=>[4,2]=>2
[[1,1,2,4],[4,4]]=>[4,2]=>2
[[1,1,4,4],[2,4]]=>[4,2]=>2
[[1,1,3,3],[3,4]]=>[4,2]=>2
[[1,1,3,4],[3,3]]=>[4,2]=>2
[[1,1,3,3],[4,4]]=>[4,2]=>2
[[1,1,3,4],[3,4]]=>[4,2]=>2
[[1,1,4,4],[3,3]]=>[4,2]=>2
[[1,1,3,4],[4,4]]=>[4,2]=>2
[[1,1,4,4],[3,4]]=>[4,2]=>2
[[1,1,4,4],[4,4]]=>[4,2]=>2
[[1,2,2,2],[2,4]]=>[4,2]=>2
[[1,2,2,2],[3,4]]=>[4,2]=>2
[[1,2,2,3],[2,4]]=>[4,2]=>2
[[1,2,2,4],[2,3]]=>[4,2]=>2
[[1,2,2,2],[4,4]]=>[4,2]=>2
[[1,2,2,4],[2,4]]=>[4,2]=>2
[[1,2,2,3],[3,4]]=>[4,2]=>2
[[1,2,2,4],[3,3]]=>[4,2]=>2
[[1,2,3,3],[2,4]]=>[4,2]=>2
[[1,2,3,4],[2,3]]=>[4,2]=>2
[[1,2,2,3],[4,4]]=>[4,2]=>2
[[1,2,2,4],[3,4]]=>[4,2]=>2
[[1,2,3,4],[2,4]]=>[4,2]=>2
[[1,2,4,4],[2,3]]=>[4,2]=>2
[[1,2,2,4],[4,4]]=>[4,2]=>2
[[1,2,4,4],[2,4]]=>[4,2]=>2
[[1,2,3,3],[3,4]]=>[4,2]=>2
[[1,2,3,4],[3,3]]=>[4,2]=>2
[[1,3,3,3],[2,4]]=>[4,2]=>2
[[1,2,3,3],[4,4]]=>[4,2]=>2
[[1,2,3,4],[3,4]]=>[4,2]=>2
[[1,2,4,4],[3,3]]=>[4,2]=>2
[[1,3,3,4],[2,4]]=>[4,2]=>2
[[1,2,3,4],[4,4]]=>[4,2]=>2
[[1,2,4,4],[3,4]]=>[4,2]=>2
[[1,3,4,4],[2,4]]=>[4,2]=>2
[[1,2,4,4],[4,4]]=>[4,2]=>2
[[1,3,3,3],[3,4]]=>[4,2]=>2
[[1,3,3,3],[4,4]]=>[4,2]=>2
[[1,3,3,4],[3,4]]=>[4,2]=>2
[[1,3,3,4],[4,4]]=>[4,2]=>2
[[1,3,4,4],[3,4]]=>[4,2]=>2
[[1,3,4,4],[4,4]]=>[4,2]=>2
[[2,2,2,2],[3,4]]=>[4,2]=>2
[[2,2,2,2],[4,4]]=>[4,2]=>2
[[2,2,2,3],[3,4]]=>[4,2]=>2
[[2,2,2,4],[3,3]]=>[4,2]=>2
[[2,2,2,3],[4,4]]=>[4,2]=>2
[[2,2,2,4],[3,4]]=>[4,2]=>2
[[2,2,2,4],[4,4]]=>[4,2]=>2
[[2,2,3,3],[3,4]]=>[4,2]=>2
[[2,2,3,4],[3,3]]=>[4,2]=>2
[[2,2,3,3],[4,4]]=>[4,2]=>2
[[2,2,3,4],[3,4]]=>[4,2]=>2
[[2,2,4,4],[3,3]]=>[4,2]=>2
[[2,2,3,4],[4,4]]=>[4,2]=>2
[[2,2,4,4],[3,4]]=>[4,2]=>2
[[2,2,4,4],[4,4]]=>[4,2]=>2
[[2,3,3,3],[3,4]]=>[4,2]=>2
[[2,3,3,3],[4,4]]=>[4,2]=>2
[[2,3,3,4],[3,4]]=>[4,2]=>2
[[2,3,3,4],[4,4]]=>[4,2]=>2
[[2,3,4,4],[3,4]]=>[4,2]=>2
[[2,3,4,4],[4,4]]=>[4,2]=>2
[[3,3,3,3],[4,4]]=>[4,2]=>2
[[3,3,3,4],[4,4]]=>[4,2]=>2
[[3,3,4,4],[4,4]]=>[4,2]=>2
[[1,1,1,1],[2],[4]]=>[4,1,1]=>3
[[1,1,1,1],[3],[4]]=>[4,1,1]=>3
[[1,1,1,2],[2],[4]]=>[4,1,1]=>3
[[1,1,1,2],[3],[4]]=>[4,1,1]=>3
[[1,1,1,3],[2],[4]]=>[4,1,1]=>3
[[1,1,1,4],[2],[3]]=>[4,1,1]=>3
[[1,1,1,4],[2],[4]]=>[4,1,1]=>3
[[1,1,1,3],[3],[4]]=>[4,1,1]=>3
[[1,1,1,4],[3],[4]]=>[4,1,1]=>3
[[1,1,2,2],[2],[4]]=>[4,1,1]=>3
[[1,1,2,2],[3],[4]]=>[4,1,1]=>3
[[1,1,2,3],[2],[4]]=>[4,1,1]=>3
[[1,1,2,4],[2],[3]]=>[4,1,1]=>3
[[1,1,2,4],[2],[4]]=>[4,1,1]=>3
[[1,1,2,3],[3],[4]]=>[4,1,1]=>3
[[1,1,3,3],[2],[4]]=>[4,1,1]=>3
[[1,1,3,4],[2],[3]]=>[4,1,1]=>3
[[1,1,2,4],[3],[4]]=>[4,1,1]=>3
[[1,1,3,4],[2],[4]]=>[4,1,1]=>3
[[1,1,4,4],[2],[3]]=>[4,1,1]=>3
[[1,1,4,4],[2],[4]]=>[4,1,1]=>3
[[1,1,3,3],[3],[4]]=>[4,1,1]=>3
[[1,1,3,4],[3],[4]]=>[4,1,1]=>3
[[1,1,4,4],[3],[4]]=>[4,1,1]=>3
[[1,2,2,2],[2],[4]]=>[4,1,1]=>3
[[1,2,2,2],[3],[4]]=>[4,1,1]=>3
[[1,2,2,3],[2],[4]]=>[4,1,1]=>3
[[1,2,2,4],[2],[3]]=>[4,1,1]=>3
[[1,2,2,4],[2],[4]]=>[4,1,1]=>3
[[1,2,2,3],[3],[4]]=>[4,1,1]=>3
[[1,2,3,3],[2],[4]]=>[4,1,1]=>3
[[1,2,3,4],[2],[3]]=>[4,1,1]=>3
[[1,2,2,4],[3],[4]]=>[4,1,1]=>3
[[1,2,3,4],[2],[4]]=>[4,1,1]=>3
[[1,2,4,4],[2],[3]]=>[4,1,1]=>3
[[1,2,4,4],[2],[4]]=>[4,1,1]=>3
[[1,2,3,3],[3],[4]]=>[4,1,1]=>3
[[1,3,3,3],[2],[4]]=>[4,1,1]=>3
[[1,3,3,4],[2],[3]]=>[4,1,1]=>3
[[1,2,3,4],[3],[4]]=>[4,1,1]=>3
[[1,3,3,4],[2],[4]]=>[4,1,1]=>3
[[1,3,4,4],[2],[3]]=>[4,1,1]=>3
[[1,2,4,4],[3],[4]]=>[4,1,1]=>3
[[1,3,4,4],[2],[4]]=>[4,1,1]=>3
[[1,4,4,4],[2],[3]]=>[4,1,1]=>3
[[1,4,4,4],[2],[4]]=>[4,1,1]=>3
[[1,3,3,3],[3],[4]]=>[4,1,1]=>3
[[1,3,3,4],[3],[4]]=>[4,1,1]=>3
[[1,3,4,4],[3],[4]]=>[4,1,1]=>3
[[1,4,4,4],[3],[4]]=>[4,1,1]=>3
[[2,2,2,2],[3],[4]]=>[4,1,1]=>3
[[2,2,2,3],[3],[4]]=>[4,1,1]=>3
[[2,2,2,4],[3],[4]]=>[4,1,1]=>3
[[2,2,3,3],[3],[4]]=>[4,1,1]=>3
[[2,2,3,4],[3],[4]]=>[4,1,1]=>3
[[2,2,4,4],[3],[4]]=>[4,1,1]=>3
[[2,3,3,3],[3],[4]]=>[4,1,1]=>3
[[2,3,3,4],[3],[4]]=>[4,1,1]=>3
[[2,3,4,4],[3],[4]]=>[4,1,1]=>3
[[2,4,4,4],[3],[4]]=>[4,1,1]=>3
[[1,1,1],[2,2,4]]=>[3,3]=>3
[[1,1,1],[2,3,4]]=>[3,3]=>3
[[1,1,1],[2,4,4]]=>[3,3]=>3
[[1,1,1],[3,3,4]]=>[3,3]=>3
[[1,1,1],[3,4,4]]=>[3,3]=>3
[[1,1,1],[4,4,4]]=>[3,3]=>3
[[1,1,2],[2,2,4]]=>[3,3]=>3
[[1,1,2],[2,3,4]]=>[3,3]=>3
[[1,1,3],[2,2,4]]=>[3,3]=>3
[[1,1,2],[2,4,4]]=>[3,3]=>3
[[1,1,2],[3,3,4]]=>[3,3]=>3
[[1,1,3],[2,3,4]]=>[3,3]=>3
[[1,1,2],[3,4,4]]=>[3,3]=>3
[[1,1,3],[2,4,4]]=>[3,3]=>3
[[1,1,2],[4,4,4]]=>[3,3]=>3
[[1,1,3],[3,3,4]]=>[3,3]=>3
[[1,1,3],[3,4,4]]=>[3,3]=>3
[[1,1,3],[4,4,4]]=>[3,3]=>3
[[1,2,2],[2,3,4]]=>[3,3]=>3
[[1,2,2],[2,4,4]]=>[3,3]=>3
[[1,2,2],[3,3,4]]=>[3,3]=>3
[[1,2,3],[2,3,4]]=>[3,3]=>3
[[1,2,2],[3,4,4]]=>[3,3]=>3
[[1,2,3],[2,4,4]]=>[3,3]=>3
[[1,2,2],[4,4,4]]=>[3,3]=>3
[[1,2,3],[3,3,4]]=>[3,3]=>3
[[1,2,3],[3,4,4]]=>[3,3]=>3
[[1,3,3],[2,4,4]]=>[3,3]=>3
[[1,2,3],[4,4,4]]=>[3,3]=>3
[[1,3,3],[3,4,4]]=>[3,3]=>3
[[1,3,3],[4,4,4]]=>[3,3]=>3
[[2,2,2],[3,3,4]]=>[3,3]=>3
[[2,2,2],[3,4,4]]=>[3,3]=>3
[[2,2,2],[4,4,4]]=>[3,3]=>3
[[2,2,3],[3,3,4]]=>[3,3]=>3
[[2,2,3],[3,4,4]]=>[3,3]=>3
[[2,2,3],[4,4,4]]=>[3,3]=>3
[[2,3,3],[3,4,4]]=>[3,3]=>3
[[2,3,3],[4,4,4]]=>[3,3]=>3
[[3,3,3],[4,4,4]]=>[3,3]=>3
[[1,1,1],[2,2],[4]]=>[3,2,1]=>4
[[1,1,1],[2,3],[4]]=>[3,2,1]=>4
[[1,1,1],[2,4],[3]]=>[3,2,1]=>4
[[1,1,1],[2,4],[4]]=>[3,2,1]=>4
[[1,1,1],[3,3],[4]]=>[3,2,1]=>4
[[1,1,1],[3,4],[4]]=>[3,2,1]=>4
[[1,1,2],[2,2],[4]]=>[3,2,1]=>4
[[1,1,2],[2,3],[4]]=>[3,2,1]=>4
[[1,1,2],[2,4],[3]]=>[3,2,1]=>4
[[1,1,3],[2,2],[4]]=>[3,2,1]=>4
[[1,1,4],[2,2],[3]]=>[3,2,1]=>4
[[1,1,2],[2,4],[4]]=>[3,2,1]=>4
[[1,1,4],[2,2],[4]]=>[3,2,1]=>4
[[1,1,2],[3,3],[4]]=>[3,2,1]=>4
[[1,1,3],[2,3],[4]]=>[3,2,1]=>4
[[1,1,3],[2,4],[3]]=>[3,2,1]=>4
[[1,1,4],[2,3],[3]]=>[3,2,1]=>4
[[1,1,2],[3,4],[4]]=>[3,2,1]=>4
[[1,1,3],[2,4],[4]]=>[3,2,1]=>4
[[1,1,4],[2,3],[4]]=>[3,2,1]=>4
[[1,1,4],[2,4],[3]]=>[3,2,1]=>4
[[1,1,4],[2,4],[4]]=>[3,2,1]=>4
[[1,1,3],[3,3],[4]]=>[3,2,1]=>4
[[1,1,3],[3,4],[4]]=>[3,2,1]=>4
[[1,1,4],[3,3],[4]]=>[3,2,1]=>4
[[1,1,4],[3,4],[4]]=>[3,2,1]=>4
[[1,2,2],[2,3],[4]]=>[3,2,1]=>4
[[1,2,2],[2,4],[3]]=>[3,2,1]=>4
[[1,2,2],[2,4],[4]]=>[3,2,1]=>4
[[1,2,2],[3,3],[4]]=>[3,2,1]=>4
[[1,2,3],[2,3],[4]]=>[3,2,1]=>4
[[1,2,3],[2,4],[3]]=>[3,2,1]=>4
[[1,2,4],[2,3],[3]]=>[3,2,1]=>4
[[1,2,2],[3,4],[4]]=>[3,2,1]=>4
[[1,2,3],[2,4],[4]]=>[3,2,1]=>4
[[1,2,4],[2,3],[4]]=>[3,2,1]=>4
[[1,2,4],[2,4],[3]]=>[3,2,1]=>4
[[1,2,4],[2,4],[4]]=>[3,2,1]=>4
[[1,2,3],[3,3],[4]]=>[3,2,1]=>4
[[1,3,3],[2,4],[3]]=>[3,2,1]=>4
[[1,2,3],[3,4],[4]]=>[3,2,1]=>4
[[1,2,4],[3,3],[4]]=>[3,2,1]=>4
[[1,3,3],[2,4],[4]]=>[3,2,1]=>4
[[1,3,4],[2,4],[3]]=>[3,2,1]=>4
[[1,2,4],[3,4],[4]]=>[3,2,1]=>4
[[1,3,4],[2,4],[4]]=>[3,2,1]=>4
[[1,3,3],[3,4],[4]]=>[3,2,1]=>4
[[1,3,4],[3,4],[4]]=>[3,2,1]=>4
[[2,2,2],[3,3],[4]]=>[3,2,1]=>4
[[2,2,2],[3,4],[4]]=>[3,2,1]=>4
[[2,2,3],[3,3],[4]]=>[3,2,1]=>4
[[2,2,3],[3,4],[4]]=>[3,2,1]=>4
[[2,2,4],[3,3],[4]]=>[3,2,1]=>4
[[2,2,4],[3,4],[4]]=>[3,2,1]=>4
[[2,3,3],[3,4],[4]]=>[3,2,1]=>4
[[2,3,4],[3,4],[4]]=>[3,2,1]=>4
[[1,1,1],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,1,2],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,1,3],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,1,4],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,2,2],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,2,3],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,2,4],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,3,3],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,3,4],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,4,4],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,1],[2,2],[3,4]]=>[2,2,2]=>6
[[1,1],[2,2],[4,4]]=>[2,2,2]=>6
[[1,1],[2,3],[3,4]]=>[2,2,2]=>6
[[1,1],[2,3],[4,4]]=>[2,2,2]=>6
[[1,1],[3,3],[4,4]]=>[2,2,2]=>6
[[1,2],[2,3],[3,4]]=>[2,2,2]=>6
[[1,2],[2,3],[4,4]]=>[2,2,2]=>6
[[1,2],[3,3],[4,4]]=>[2,2,2]=>6
[[2,2],[3,3],[4,4]]=>[2,2,2]=>6
[[1,1],[2,2],[3],[4]]=>[2,2,1,1]=>7
[[1,1],[2,3],[3],[4]]=>[2,2,1,1]=>7
[[1,1],[2,4],[3],[4]]=>[2,2,1,1]=>7
[[1,2],[2,3],[3],[4]]=>[2,2,1,1]=>7
[[1,2],[2,4],[3],[4]]=>[2,2,1,1]=>7
[[1,3],[2,4],[3],[4]]=>[2,2,1,1]=>7
[[1,1,1,1,1,1,3]]=>[7]=>0
[[1,1,1,1,1,2,3]]=>[7]=>0
[[1,1,1,1,1,3,3]]=>[7]=>0
[[1,1,1,1,2,2,3]]=>[7]=>0
[[1,1,1,1,2,3,3]]=>[7]=>0
[[1,1,1,1,3,3,3]]=>[7]=>0
[[1,1,1,2,2,2,3]]=>[7]=>0
[[1,1,1,2,2,3,3]]=>[7]=>0
[[1,1,1,2,3,3,3]]=>[7]=>0
[[1,1,1,3,3,3,3]]=>[7]=>0
[[1,1,2,2,2,2,3]]=>[7]=>0
[[1,1,2,2,2,3,3]]=>[7]=>0
[[1,1,2,2,3,3,3]]=>[7]=>0
[[1,1,2,3,3,3,3]]=>[7]=>0
[[1,1,3,3,3,3,3]]=>[7]=>0
[[1,2,2,2,2,2,3]]=>[7]=>0
[[1,2,2,2,2,3,3]]=>[7]=>0
[[1,2,2,2,3,3,3]]=>[7]=>0
[[1,2,2,3,3,3,3]]=>[7]=>0
[[1,2,3,3,3,3,3]]=>[7]=>0
[[1,3,3,3,3,3,3]]=>[7]=>0
[[2,2,2,2,2,2,3]]=>[7]=>0
[[2,2,2,2,2,3,3]]=>[7]=>0
[[2,2,2,2,3,3,3]]=>[7]=>0
[[2,2,2,3,3,3,3]]=>[7]=>0
[[2,2,3,3,3,3,3]]=>[7]=>0
[[2,3,3,3,3,3,3]]=>[7]=>0
[[3,3,3,3,3,3,3]]=>[7]=>0
[[1,1,1,1,1,1],[3]]=>[6,1]=>1
[[1,1,1,1,1,2],[3]]=>[6,1]=>1
[[1,1,1,1,1,3],[2]]=>[6,1]=>1
[[1,1,1,1,1,3],[3]]=>[6,1]=>1
[[1,1,1,1,2,2],[3]]=>[6,1]=>1
[[1,1,1,1,2,3],[2]]=>[6,1]=>1
[[1,1,1,1,2,3],[3]]=>[6,1]=>1
[[1,1,1,1,3,3],[2]]=>[6,1]=>1
[[1,1,1,1,3,3],[3]]=>[6,1]=>1
[[1,1,1,2,2,2],[3]]=>[6,1]=>1
[[1,1,1,2,2,3],[2]]=>[6,1]=>1
[[1,1,1,2,2,3],[3]]=>[6,1]=>1
[[1,1,1,2,3,3],[2]]=>[6,1]=>1
[[1,1,1,2,3,3],[3]]=>[6,1]=>1
[[1,1,1,3,3,3],[2]]=>[6,1]=>1
[[1,1,1,3,3,3],[3]]=>[6,1]=>1
[[1,1,2,2,2,2],[3]]=>[6,1]=>1
[[1,1,2,2,2,3],[2]]=>[6,1]=>1
[[1,1,2,2,2,3],[3]]=>[6,1]=>1
[[1,1,2,2,3,3],[2]]=>[6,1]=>1
[[1,1,2,2,3,3],[3]]=>[6,1]=>1
[[1,1,2,3,3,3],[2]]=>[6,1]=>1
[[1,1,2,3,3,3],[3]]=>[6,1]=>1
[[1,1,3,3,3,3],[2]]=>[6,1]=>1
[[1,1,3,3,3,3],[3]]=>[6,1]=>1
[[1,2,2,2,2,2],[3]]=>[6,1]=>1
[[1,2,2,2,2,3],[2]]=>[6,1]=>1
[[1,2,2,2,2,3],[3]]=>[6,1]=>1
[[1,2,2,2,3,3],[2]]=>[6,1]=>1
[[1,2,2,2,3,3],[3]]=>[6,1]=>1
[[1,2,2,3,3,3],[2]]=>[6,1]=>1
[[1,2,2,3,3,3],[3]]=>[6,1]=>1
[[1,2,3,3,3,3],[2]]=>[6,1]=>1
[[1,2,3,3,3,3],[3]]=>[6,1]=>1
[[1,3,3,3,3,3],[2]]=>[6,1]=>1
[[1,3,3,3,3,3],[3]]=>[6,1]=>1
[[2,2,2,2,2,2],[3]]=>[6,1]=>1
[[2,2,2,2,2,3],[3]]=>[6,1]=>1
[[2,2,2,2,3,3],[3]]=>[6,1]=>1
[[2,2,2,3,3,3],[3]]=>[6,1]=>1
[[2,2,3,3,3,3],[3]]=>[6,1]=>1
[[2,3,3,3,3,3],[3]]=>[6,1]=>1
[[1,1,1,1,1],[2,3]]=>[5,2]=>2
[[1,1,1,1,1],[3,3]]=>[5,2]=>2
[[1,1,1,1,2],[2,3]]=>[5,2]=>2
[[1,1,1,1,3],[2,2]]=>[5,2]=>2
[[1,1,1,1,2],[3,3]]=>[5,2]=>2
[[1,1,1,1,3],[2,3]]=>[5,2]=>2
[[1,1,1,1,3],[3,3]]=>[5,2]=>2
[[1,1,1,2,2],[2,3]]=>[5,2]=>2
[[1,1,1,2,3],[2,2]]=>[5,2]=>2
[[1,1,1,2,2],[3,3]]=>[5,2]=>2
[[1,1,1,2,3],[2,3]]=>[5,2]=>2
[[1,1,1,3,3],[2,2]]=>[5,2]=>2
[[1,1,1,2,3],[3,3]]=>[5,2]=>2
[[1,1,1,3,3],[2,3]]=>[5,2]=>2
[[1,1,1,3,3],[3,3]]=>[5,2]=>2
[[1,1,2,2,2],[2,3]]=>[5,2]=>2
[[1,1,2,2,3],[2,2]]=>[5,2]=>2
[[1,1,2,2,2],[3,3]]=>[5,2]=>2
[[1,1,2,2,3],[2,3]]=>[5,2]=>2
[[1,1,2,3,3],[2,2]]=>[5,2]=>2
[[1,1,2,2,3],[3,3]]=>[5,2]=>2
[[1,1,2,3,3],[2,3]]=>[5,2]=>2
[[1,1,3,3,3],[2,2]]=>[5,2]=>2
[[1,1,2,3,3],[3,3]]=>[5,2]=>2
[[1,1,3,3,3],[2,3]]=>[5,2]=>2
[[1,1,3,3,3],[3,3]]=>[5,2]=>2
[[1,2,2,2,2],[2,3]]=>[5,2]=>2
[[1,2,2,2,2],[3,3]]=>[5,2]=>2
[[1,2,2,2,3],[2,3]]=>[5,2]=>2
[[1,2,2,2,3],[3,3]]=>[5,2]=>2
[[1,2,2,3,3],[2,3]]=>[5,2]=>2
[[1,2,2,3,3],[3,3]]=>[5,2]=>2
[[1,2,3,3,3],[2,3]]=>[5,2]=>2
[[1,2,3,3,3],[3,3]]=>[5,2]=>2
[[2,2,2,2,2],[3,3]]=>[5,2]=>2
[[2,2,2,2,3],[3,3]]=>[5,2]=>2
[[2,2,2,3,3],[3,3]]=>[5,2]=>2
[[2,2,3,3,3],[3,3]]=>[5,2]=>2
[[1,1,1,1,1],[2],[3]]=>[5,1,1]=>3
[[1,1,1,1,2],[2],[3]]=>[5,1,1]=>3
[[1,1,1,1,3],[2],[3]]=>[5,1,1]=>3
[[1,1,1,2,2],[2],[3]]=>[5,1,1]=>3
[[1,1,1,2,3],[2],[3]]=>[5,1,1]=>3
[[1,1,1,3,3],[2],[3]]=>[5,1,1]=>3
[[1,1,2,2,2],[2],[3]]=>[5,1,1]=>3
[[1,1,2,2,3],[2],[3]]=>[5,1,1]=>3
[[1,1,2,3,3],[2],[3]]=>[5,1,1]=>3
[[1,1,3,3,3],[2],[3]]=>[5,1,1]=>3
[[1,2,2,2,2],[2],[3]]=>[5,1,1]=>3
[[1,2,2,2,3],[2],[3]]=>[5,1,1]=>3
[[1,2,2,3,3],[2],[3]]=>[5,1,1]=>3
[[1,2,3,3,3],[2],[3]]=>[5,1,1]=>3
[[1,3,3,3,3],[2],[3]]=>[5,1,1]=>3
[[1,1,1,1],[2,2,3]]=>[4,3]=>3
[[1,1,1,1],[2,3,3]]=>[4,3]=>3
[[1,1,1,1],[3,3,3]]=>[4,3]=>3
[[1,1,1,2],[2,2,3]]=>[4,3]=>3
[[1,1,1,3],[2,2,2]]=>[4,3]=>3
[[1,1,1,2],[2,3,3]]=>[4,3]=>3
[[1,1,1,3],[2,2,3]]=>[4,3]=>3
[[1,1,1,2],[3,3,3]]=>[4,3]=>3
[[1,1,1,3],[2,3,3]]=>[4,3]=>3
[[1,1,1,3],[3,3,3]]=>[4,3]=>3
[[1,1,2,2],[2,2,3]]=>[4,3]=>3
[[1,1,2,2],[2,3,3]]=>[4,3]=>3
[[1,1,2,3],[2,2,3]]=>[4,3]=>3
[[1,1,2,2],[3,3,3]]=>[4,3]=>3
[[1,1,2,3],[2,3,3]]=>[4,3]=>3
[[1,1,2,3],[3,3,3]]=>[4,3]=>3
[[1,2,2,2],[2,3,3]]=>[4,3]=>3
[[1,2,2,2],[3,3,3]]=>[4,3]=>3
[[1,2,2,3],[2,3,3]]=>[4,3]=>3
[[1,2,2,3],[3,3,3]]=>[4,3]=>3
[[2,2,2,2],[3,3,3]]=>[4,3]=>3
[[2,2,2,3],[3,3,3]]=>[4,3]=>3
[[1,1,1,1],[2,2],[3]]=>[4,2,1]=>4
[[1,1,1,1],[2,3],[3]]=>[4,2,1]=>4
[[1,1,1,2],[2,2],[3]]=>[4,2,1]=>4
[[1,1,1,2],[2,3],[3]]=>[4,2,1]=>4
[[1,1,1,3],[2,2],[3]]=>[4,2,1]=>4
[[1,1,1,3],[2,3],[3]]=>[4,2,1]=>4
[[1,1,2,2],[2,2],[3]]=>[4,2,1]=>4
[[1,1,2,2],[2,3],[3]]=>[4,2,1]=>4
[[1,1,2,3],[2,2],[3]]=>[4,2,1]=>4
[[1,1,2,3],[2,3],[3]]=>[4,2,1]=>4
[[1,1,3,3],[2,2],[3]]=>[4,2,1]=>4
[[1,1,3,3],[2,3],[3]]=>[4,2,1]=>4
[[1,2,2,2],[2,3],[3]]=>[4,2,1]=>4
[[1,2,2,3],[2,3],[3]]=>[4,2,1]=>4
[[1,2,3,3],[2,3],[3]]=>[4,2,1]=>4
[[1,1,1],[2,2,2],[3]]=>[3,3,1]=>5
[[1,1,1],[2,2,3],[3]]=>[3,3,1]=>5
[[1,1,1],[2,3,3],[3]]=>[3,3,1]=>5
[[1,1,2],[2,2,3],[3]]=>[3,3,1]=>5
[[1,1,2],[2,3,3],[3]]=>[3,3,1]=>5
[[1,2,2],[2,3,3],[3]]=>[3,3,1]=>5
[[1,1,1],[2,2],[3,3]]=>[3,2,2]=>6
[[1,1,2],[2,2],[3,3]]=>[3,2,2]=>6
[[1,1,3],[2,2],[3,3]]=>[3,2,2]=>6
[[1,1,1,1,1,1,1,2]]=>[8]=>0
[[1,1,1,1,1,1,2,2]]=>[8]=>0
[[1,1,1,1,1,2,2,2]]=>[8]=>0
[[1,1,1,1,2,2,2,2]]=>[8]=>0
[[1,1,1,2,2,2,2,2]]=>[8]=>0
[[1,1,2,2,2,2,2,2]]=>[8]=>0
[[1,2,2,2,2,2,2,2]]=>[8]=>0
[[2,2,2,2,2,2,2,2]]=>[8]=>0
[[1,1,1,1,1,1,1],[2]]=>[7,1]=>1
[[1,1,1,1,1,1,2],[2]]=>[7,1]=>1
[[1,1,1,1,1,2,2],[2]]=>[7,1]=>1
[[1,1,1,1,2,2,2],[2]]=>[7,1]=>1
[[1,1,1,2,2,2,2],[2]]=>[7,1]=>1
[[1,1,2,2,2,2,2],[2]]=>[7,1]=>1
[[1,2,2,2,2,2,2],[2]]=>[7,1]=>1
[[1,1,1,1,1,1],[2,2]]=>[6,2]=>2
[[1,1,1,1,1,2],[2,2]]=>[6,2]=>2
[[1,1,1,1,2,2],[2,2]]=>[6,2]=>2
[[1,1,1,2,2,2],[2,2]]=>[6,2]=>2
[[1,1,2,2,2,2],[2,2]]=>[6,2]=>2
[[1,1,1,1,1],[2,2,2]]=>[5,3]=>3
[[1,1,1,1,2],[2,2,2]]=>[5,3]=>3
[[1,1,1,2,2],[2,2,2]]=>[5,3]=>3
[[1,1,1,1],[2,2,2,2]]=>[4,4]=>4
[[1]]=>[1]=>0
[[1,1,1,1],[2,2,2],[3,3],[4]]=>[4,3,2,1]=>10
[[1,1,1,2],[2,2,2],[3,3],[4]]=>[4,3,2,1]=>10
[[1,1,1,1],[2,2,3],[3,3],[4]]=>[4,3,2,1]=>10
[[1,1,1,2],[2,2,3],[3,3],[4]]=>[4,3,2,1]=>10
[[1,1,1,3],[2,2,3],[3,3],[4]]=>[4,3,2,1]=>10
[[1,1,2,2],[2,2,3],[3,3],[4]]=>[4,3,2,1]=>10
[[1,1,2,3],[2,2,3],[3,3],[4]]=>[4,3,2,1]=>10
[[1,1,1,1],[2,2,2],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,2],[2,2,2],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,1],[2,2,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,2],[2,2,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,3],[2,2,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,2],[2,2,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,3],[2,2,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,1],[2,2,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,2],[2,2,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,3],[2,2,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,4],[2,2,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,2],[2,2,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,3],[2,2,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,4],[2,2,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,1],[2,3,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,2],[2,3,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,3],[2,3,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,2],[2,3,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,3],[2,3,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,1],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,2],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,3],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,1,4],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,2],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,3],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,2,4],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,3,3],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,1,3,4],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,2,2,2],[2,3,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,2,2,3],[2,3,3],[3,4],[4]]=>[4,3,2,1]=>10
[[1,2,2,2],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,2,2,3],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,2,2,4],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,2,3,3],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[1,2,3,4],[2,3,4],[3,4],[4]]=>[4,3,2,1]=>10
[[2]]=>[1]=>0
[[1,1]]=>[2]=>0
[[3]]=>[1]=>0
[[1,1,1]]=>[3]=>0
[[4]]=>[1]=>0
[[1,1,1,1]]=>[4]=>0
[[5]]=>[1]=>0
[[1,1,1,1,1]]=>[5]=>0
[[6]]=>[1]=>0
[[1,2,3,4,5,6]]=>[6]=>0
[[1,2,3,4,5],[6]]=>[5,1]=>1
[[1,2,3,4,6],[5]]=>[5,1]=>1
[[1,2,3,4],[5],[6]]=>[4,1,1]=>3
[[1,2,3,5,6],[4]]=>[5,1]=>1
[[1,2,3,5],[4,6]]=>[4,2]=>2
[[1,2,3,5],[4],[6]]=>[4,1,1]=>3
[[1,2,3,4],[5,6]]=>[4,2]=>2
[[1,2,3,6],[4],[5]]=>[4,1,1]=>3
[[1,2,3],[4],[5],[6]]=>[3,1,1,1]=>6
[[1,2,4,5,6],[3]]=>[5,1]=>1
[[1,2,4,5],[3,6]]=>[4,2]=>2
[[1,2,4,6],[3,5]]=>[4,2]=>2
[[1,2,4],[3,5],[6]]=>[3,2,1]=>4
[[1,2,4,5],[3],[6]]=>[4,1,1]=>3
[[1,2,4,6],[3],[5]]=>[4,1,1]=>3
[[1,2,4],[3],[5],[6]]=>[3,1,1,1]=>6
[[1,2,3,6],[4,5]]=>[4,2]=>2
[[1,2,3],[4,5],[6]]=>[3,2,1]=>4
[[1,2,5,6],[3],[4]]=>[4,1,1]=>3
[[1,2,5],[3,6],[4]]=>[3,2,1]=>4
[[1,2,5],[3],[4],[6]]=>[3,1,1,1]=>6
[[1,2,3],[4,6],[5]]=>[3,2,1]=>4
[[1,2,4],[3,6],[5]]=>[3,2,1]=>4
[[1,2,6],[3],[4],[5]]=>[3,1,1,1]=>6
[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]=>10
[[1,3,4,5,6],[2]]=>[5,1]=>1
[[1,3,4,5],[2,6]]=>[4,2]=>2
[[1,3,4,6],[2,5]]=>[4,2]=>2
[[1,3,4],[2,5],[6]]=>[3,2,1]=>4
[[1,3,5,6],[2,4]]=>[4,2]=>2
[[1,3,5],[2,4,6]]=>[3,3]=>3
[[1,3,5],[2,4],[6]]=>[3,2,1]=>4
[[1,3,4],[2,5,6]]=>[3,3]=>3
[[1,3,6],[2,4],[5]]=>[3,2,1]=>4
[[1,3],[2,4],[5],[6]]=>[2,2,1,1]=>7
[[1,3,4,5],[2],[6]]=>[4,1,1]=>3
[[1,3,4,6],[2],[5]]=>[4,1,1]=>3
[[1,3,4],[2],[5],[6]]=>[3,1,1,1]=>6
[[1,3,5,6],[2],[4]]=>[4,1,1]=>3
[[1,3,5],[2,6],[4]]=>[3,2,1]=>4
[[1,3,5],[2],[4],[6]]=>[3,1,1,1]=>6
[[1,3,4],[2,6],[5]]=>[3,2,1]=>4
[[1,3,6],[2],[4],[5]]=>[3,1,1,1]=>6
[[1,3],[2],[4],[5],[6]]=>[2,1,1,1,1]=>10
[[1,2,5,6],[3,4]]=>[4,2]=>2
[[1,2,5],[3,4,6]]=>[3,3]=>3
[[1,2,5],[3,4],[6]]=>[3,2,1]=>4
[[1,2,4],[3,5,6]]=>[3,3]=>3
[[1,2,6],[3,4],[5]]=>[3,2,1]=>4
[[1,2],[3,4],[5],[6]]=>[2,2,1,1]=>7
[[1,4,5,6],[2],[3]]=>[4,1,1]=>3
[[1,4,5],[2,6],[3]]=>[3,2,1]=>4
[[1,4,6],[2,5],[3]]=>[3,2,1]=>4
[[1,4],[2,5],[3,6]]=>[2,2,2]=>6
[[1,4],[2,5],[3],[6]]=>[2,2,1,1]=>7
[[1,4,5],[2],[3],[6]]=>[3,1,1,1]=>6
[[1,4,6],[2],[3],[5]]=>[3,1,1,1]=>6
[[1,4],[2],[3],[5],[6]]=>[2,1,1,1,1]=>10
[[1,2,3],[4,5,6]]=>[3,3]=>3
[[1,2,6],[3,5],[4]]=>[3,2,1]=>4
[[1,2],[3,5],[4],[6]]=>[2,2,1,1]=>7
[[1,3,6],[2,5],[4]]=>[3,2,1]=>4
[[1,3],[2,5],[4,6]]=>[2,2,2]=>6
[[1,3],[2,5],[4],[6]]=>[2,2,1,1]=>7
[[1,2],[3,5],[4,6]]=>[2,2,2]=>6
[[1,5,6],[2],[3],[4]]=>[3,1,1,1]=>6
[[1,5],[2,6],[3],[4]]=>[2,2,1,1]=>7
[[1,5],[2],[3],[4],[6]]=>[2,1,1,1,1]=>10
[[1,2],[3,6],[4],[5]]=>[2,2,1,1]=>7
[[1,3],[2,4],[5,6]]=>[2,2,2]=>6
[[1,3],[2,6],[4],[5]]=>[2,2,1,1]=>7
[[1,2],[3,4],[5,6]]=>[2,2,2]=>6
[[1,4],[2,6],[3],[5]]=>[2,2,1,1]=>7
[[1,6],[2],[3],[4],[5]]=>[2,1,1,1,1]=>10
[[1],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,1]=>15
[[1,1,1,1,2,2,2],[3,3],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,2,2],[3,3],[4]]=>[7,2,1]=>4
[[1,1,1,1,2,2,3],[3,3],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,2,3],[3,3],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,3,3],[3,3],[4]]=>[7,2,1]=>4
[[1,1,2,2,2,2,3],[3,3],[4]]=>[7,2,1]=>4
[[1,1,2,2,2,3,3],[3,3],[4]]=>[7,2,1]=>4
[[1,1,1,1,2,2,2],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,2,2],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,1,2,2,3],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,2,3],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,3],[3,3,4],[4]]=>[6,3,1]=>5
[[1,1,2,2,2,2,3],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,2,2,3],[3,3,4],[4]]=>[6,3,1]=>5
[[1,1,1,1,2,2,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,2,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,4,4],[3,3],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,4,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,2,2,2,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,2,2,4,4],[3,3],[4]]=>[7,2,1]=>4
[[1,1,2,2,2,4,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,1,2,3,3],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,3,3],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,3,3,3],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,2,2,3,3],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,2,3,3,3],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,1,2,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,2,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,3,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,1,2,3,4,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,2,2,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,2,3,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,2,3,4,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,3,3,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,1,2,3,3,4,4],[3,4],[4]]=>[7,2,1]=>4
[[1,2,2,2,2,3,3],[3,4],[4]]=>[7,2,1]=>4
[[1,2,2,2,3,3,3],[3,4],[4]]=>[7,2,1]=>4
[[1,2,2,2,2,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,2,2,2,3,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,2,2,2,3,4,4],[3,4],[4]]=>[7,2,1]=>4
[[1,2,2,3,3,3,4],[3,4],[4]]=>[7,2,1]=>4
[[1,2,2,3,3,4,4],[3,4],[4]]=>[7,2,1]=>4
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Description
The weighted size of a partition.
Let $\lambda = (\lambda_0\geq\lambda_1 \geq \dots\geq\lambda_m)$ be an integer partition. Then the weighted size of $\lambda$ is
$$\sum_{i=0}^m i \cdot \lambda_i.$$
This is also the sum of the leg lengths of the cells in $\lambda$, or
$$ \sum_i \binom{\lambda^{\prime}_i}{2} $$
where $\lambda^{\prime}$ is the conjugate partition of $\lambda$.
This is the minimal number of inversions a permutation with the given shape can have, see [1, cor.2.2].
This is also the smallest possible sum of the entries of a semistandard tableau (allowing 0 as a part) of shape $\lambda=(\lambda_0,\lambda_1,\ldots,\lambda_m)$, obtained uniquely by placing $i-1$ in all the cells of the $i$th row of $\lambda$, see [2, eq.7.103].
Let $\lambda = (\lambda_0\geq\lambda_1 \geq \dots\geq\lambda_m)$ be an integer partition. Then the weighted size of $\lambda$ is
$$\sum_{i=0}^m i \cdot \lambda_i.$$
This is also the sum of the leg lengths of the cells in $\lambda$, or
$$ \sum_i \binom{\lambda^{\prime}_i}{2} $$
where $\lambda^{\prime}$ is the conjugate partition of $\lambda$.
This is the minimal number of inversions a permutation with the given shape can have, see [1, cor.2.2].
This is also the smallest possible sum of the entries of a semistandard tableau (allowing 0 as a part) of shape $\lambda=(\lambda_0,\lambda_1,\ldots,\lambda_m)$, obtained uniquely by placing $i-1$ in all the cells of the $i$th row of $\lambda$, see [2, eq.7.103].
Map
shape
Description
Return the shape of a tableau.
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