Identifier
Images
=>
Cc0025;cc-rep-0Cc0002;cc-rep-1
[[1]]=>[1]
[[1],[1]]=>[1,1]
[[2]]=>[2]
[[1,1]]=>[2]
[[1],[1],[1]]=>[1,1,1]
[[2],[1]]=>[2,1]
[[1,1],[1]]=>[2,1]
[[3]]=>[3]
[[2,1]]=>[3]
[[1,1,1]]=>[3]
[[1],[1],[1],[1]]=>[1,1,1,1]
[[2],[1],[1]]=>[2,1,1]
[[2],[2]]=>[2,2]
[[1,1],[1],[1]]=>[2,1,1]
[[1,1],[1,1]]=>[2,2]
[[3],[1]]=>[3,1]
[[2,1],[1]]=>[3,1]
[[1,1,1],[1]]=>[3,1]
[[4]]=>[4]
[[3,1]]=>[4]
[[2,2]]=>[4]
[[2,1,1]]=>[4]
[[1,1,1,1]]=>[4]
[[1],[1],[1],[1],[1]]=>[1,1,1,1,1]
[[2],[1],[1],[1]]=>[2,1,1,1]
[[2],[2],[1]]=>[2,2,1]
[[1,1],[1],[1],[1]]=>[2,1,1,1]
[[1,1],[1,1],[1]]=>[2,2,1]
[[3],[1],[1]]=>[3,1,1]
[[3],[2]]=>[3,2]
[[2,1],[1],[1]]=>[3,1,1]
[[2,1],[2]]=>[3,2]
[[2,1],[1,1]]=>[3,2]
[[1,1,1],[1],[1]]=>[3,1,1]
[[1,1,1],[1,1]]=>[3,2]
[[4],[1]]=>[4,1]
[[3,1],[1]]=>[4,1]
[[2,2],[1]]=>[4,1]
[[2,1,1],[1]]=>[4,1]
[[1,1,1,1],[1]]=>[4,1]
[[5]]=>[5]
[[4,1]]=>[5]
[[3,2]]=>[5]
[[3,1,1]]=>[5]
[[2,2,1]]=>[5]
[[2,1,1,1]]=>[5]
[[1,1,1,1,1]]=>[5]
[[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1]
[[2],[1],[1],[1],[1]]=>[2,1,1,1,1]
[[2],[2],[1],[1]]=>[2,2,1,1]
[[2],[2],[2]]=>[2,2,2]
[[1,1],[1],[1],[1],[1]]=>[2,1,1,1,1]
[[1,1],[1,1],[1],[1]]=>[2,2,1,1]
[[1,1],[1,1],[1,1]]=>[2,2,2]
[[3],[1],[1],[1]]=>[3,1,1,1]
[[3],[2],[1]]=>[3,2,1]
[[3],[3]]=>[3,3]
[[2,1],[1],[1],[1]]=>[3,1,1,1]
[[2,1],[2],[1]]=>[3,2,1]
[[2,1],[1,1],[1]]=>[3,2,1]
[[2,1],[2,1]]=>[3,3]
[[1,1,1],[1],[1],[1]]=>[3,1,1,1]
[[1,1,1],[1,1],[1]]=>[3,2,1]
[[1,1,1],[1,1,1]]=>[3,3]
[[4],[1],[1]]=>[4,1,1]
[[4],[2]]=>[4,2]
[[3,1],[1],[1]]=>[4,1,1]
[[3,1],[2]]=>[4,2]
[[3,1],[1,1]]=>[4,2]
[[2,2],[1],[1]]=>[4,1,1]
[[2,2],[2]]=>[4,2]
[[2,2],[1,1]]=>[4,2]
[[2,1,1],[1],[1]]=>[4,1,1]
[[2,1,1],[2]]=>[4,2]
[[2,1,1],[1,1]]=>[4,2]
[[1,1,1,1],[1],[1]]=>[4,1,1]
[[1,1,1,1],[1,1]]=>[4,2]
[[5],[1]]=>[5,1]
[[4,1],[1]]=>[5,1]
[[3,2],[1]]=>[5,1]
[[3,1,1],[1]]=>[5,1]
[[2,2,1],[1]]=>[5,1]
[[2,1,1,1],[1]]=>[5,1]
[[1,1,1,1,1],[1]]=>[5,1]
[[6]]=>[6]
[[5,1]]=>[6]
[[4,2]]=>[6]
[[4,1,1]]=>[6]
[[3,3]]=>[6]
[[3,2,1]]=>[6]
[[3,1,1,1]]=>[6]
[[2,2,2]]=>[6]
[[2,2,1,1]]=>[6]
[[2,1,1,1,1]]=>[6]
[[1,1,1,1,1,1]]=>[6]
[[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1]
[[2],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1]
[[2],[2],[1],[1],[1]]=>[2,2,1,1,1]
[[2],[2],[2],[1]]=>[2,2,2,1]
[[1,1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1]
[[1,1],[1,1],[1],[1],[1]]=>[2,2,1,1,1]
[[1,1],[1,1],[1,1],[1]]=>[2,2,2,1]
[[3],[1],[1],[1],[1]]=>[3,1,1,1,1]
[[3],[2],[1],[1]]=>[3,2,1,1]
[[3],[2],[2]]=>[3,2,2]
[[3],[3],[1]]=>[3,3,1]
[[2,1],[1],[1],[1],[1]]=>[3,1,1,1,1]
[[2,1],[2],[1],[1]]=>[3,2,1,1]
[[2,1],[2],[2]]=>[3,2,2]
[[2,1],[1,1],[1],[1]]=>[3,2,1,1]
[[2,1],[1,1],[1,1]]=>[3,2,2]
[[2,1],[2,1],[1]]=>[3,3,1]
[[1,1,1],[1],[1],[1],[1]]=>[3,1,1,1,1]
[[1,1,1],[1,1],[1],[1]]=>[3,2,1,1]
[[1,1,1],[1,1],[1,1]]=>[3,2,2]
[[1,1,1],[1,1,1],[1]]=>[3,3,1]
[[4],[1],[1],[1]]=>[4,1,1,1]
[[4],[2],[1]]=>[4,2,1]
[[4],[3]]=>[4,3]
[[3,1],[1],[1],[1]]=>[4,1,1,1]
[[3,1],[2],[1]]=>[4,2,1]
[[3,1],[1,1],[1]]=>[4,2,1]
[[3,1],[3]]=>[4,3]
[[3,1],[2,1]]=>[4,3]
[[2,2],[1],[1],[1]]=>[4,1,1,1]
[[2,2],[2],[1]]=>[4,2,1]
[[2,2],[1,1],[1]]=>[4,2,1]
[[2,2],[2,1]]=>[4,3]
[[2,1,1],[1],[1],[1]]=>[4,1,1,1]
[[2,1,1],[2],[1]]=>[4,2,1]
[[2,1,1],[1,1],[1]]=>[4,2,1]
[[2,1,1],[2,1]]=>[4,3]
[[2,1,1],[1,1,1]]=>[4,3]
[[1,1,1,1],[1],[1],[1]]=>[4,1,1,1]
[[1,1,1,1],[1,1],[1]]=>[4,2,1]
[[1,1,1,1],[1,1,1]]=>[4,3]
[[5],[1],[1]]=>[5,1,1]
[[5],[2]]=>[5,2]
[[4,1],[1],[1]]=>[5,1,1]
[[4,1],[2]]=>[5,2]
[[4,1],[1,1]]=>[5,2]
[[3,2],[1],[1]]=>[5,1,1]
[[3,2],[2]]=>[5,2]
[[3,2],[1,1]]=>[5,2]
[[3,1,1],[1],[1]]=>[5,1,1]
[[3,1,1],[2]]=>[5,2]
[[3,1,1],[1,1]]=>[5,2]
[[2,2,1],[1],[1]]=>[5,1,1]
[[2,2,1],[2]]=>[5,2]
[[2,2,1],[1,1]]=>[5,2]
[[2,1,1,1],[1],[1]]=>[5,1,1]
[[2,1,1,1],[2]]=>[5,2]
[[2,1,1,1],[1,1]]=>[5,2]
[[1,1,1,1,1],[1],[1]]=>[5,1,1]
[[1,1,1,1,1],[1,1]]=>[5,2]
[[6],[1]]=>[6,1]
[[5,1],[1]]=>[6,1]
[[4,2],[1]]=>[6,1]
[[4,1,1],[1]]=>[6,1]
[[3,3],[1]]=>[6,1]
[[3,2,1],[1]]=>[6,1]
[[3,1,1,1],[1]]=>[6,1]
[[2,2,2],[1]]=>[6,1]
[[2,2,1,1],[1]]=>[6,1]
[[2,1,1,1,1],[1]]=>[6,1]
[[1,1,1,1,1,1],[1]]=>[6,1]
[[7]]=>[7]
[[6,1]]=>[7]
[[5,2]]=>[7]
[[5,1,1]]=>[7]
[[4,3]]=>[7]
[[4,2,1]]=>[7]
[[4,1,1,1]]=>[7]
[[3,3,1]]=>[7]
[[3,2,2]]=>[7]
[[3,2,1,1]]=>[7]
[[3,1,1,1,1]]=>[7]
[[2,2,2,1]]=>[7]
[[2,2,1,1,1]]=>[7]
[[2,1,1,1,1,1]]=>[7]
[[1,1,1,1,1,1,1]]=>[7]
[[1],[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1,1]
[[2],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1]
[[2],[2],[1],[1],[1],[1]]=>[2,2,1,1,1,1]
[[2],[2],[2],[1],[1]]=>[2,2,2,1,1]
[[2],[2],[2],[2]]=>[2,2,2,2]
[[1,1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1]
[[1,1],[1,1],[1],[1],[1],[1]]=>[2,2,1,1,1,1]
[[1,1],[1,1],[1,1],[1],[1]]=>[2,2,2,1,1]
[[1,1],[1,1],[1,1],[1,1]]=>[2,2,2,2]
[[3],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1]
[[3],[2],[1],[1],[1]]=>[3,2,1,1,1]
[[3],[2],[2],[1]]=>[3,2,2,1]
[[3],[3],[1],[1]]=>[3,3,1,1]
[[3],[3],[2]]=>[3,3,2]
[[2,1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1]
[[2,1],[2],[1],[1],[1]]=>[3,2,1,1,1]
[[2,1],[2],[2],[1]]=>[3,2,2,1]
[[2,1],[1,1],[1],[1],[1]]=>[3,2,1,1,1]
[[2,1],[1,1],[1,1],[1]]=>[3,2,2,1]
[[2,1],[2,1],[1],[1]]=>[3,3,1,1]
[[2,1],[2,1],[2]]=>[3,3,2]
[[2,1],[2,1],[1,1]]=>[3,3,2]
[[1,1,1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1]
[[1,1,1],[1,1],[1],[1],[1]]=>[3,2,1,1,1]
[[1,1,1],[1,1],[1,1],[1]]=>[3,2,2,1]
[[1,1,1],[1,1,1],[1],[1]]=>[3,3,1,1]
[[1,1,1],[1,1,1],[1,1]]=>[3,3,2]
[[4],[1],[1],[1],[1]]=>[4,1,1,1,1]
[[4],[2],[1],[1]]=>[4,2,1,1]
[[4],[2],[2]]=>[4,2,2]
[[4],[3],[1]]=>[4,3,1]
[[4],[4]]=>[4,4]
[[3,1],[1],[1],[1],[1]]=>[4,1,1,1,1]
[[3,1],[2],[1],[1]]=>[4,2,1,1]
[[3,1],[2],[2]]=>[4,2,2]
[[3,1],[1,1],[1],[1]]=>[4,2,1,1]
[[3,1],[1,1],[1,1]]=>[4,2,2]
[[3,1],[3],[1]]=>[4,3,1]
[[3,1],[2,1],[1]]=>[4,3,1]
[[3,1],[3,1]]=>[4,4]
[[2,2],[1],[1],[1],[1]]=>[4,1,1,1,1]
[[2,2],[2],[1],[1]]=>[4,2,1,1]
[[2,2],[2],[2]]=>[4,2,2]
[[2,2],[1,1],[1],[1]]=>[4,2,1,1]
[[2,2],[1,1],[1,1]]=>[4,2,2]
[[2,2],[2,1],[1]]=>[4,3,1]
[[2,2],[2,2]]=>[4,4]
[[2,1,1],[1],[1],[1],[1]]=>[4,1,1,1,1]
[[2,1,1],[2],[1],[1]]=>[4,2,1,1]
[[2,1,1],[2],[2]]=>[4,2,2]
[[2,1,1],[1,1],[1],[1]]=>[4,2,1,1]
[[2,1,1],[1,1],[1,1]]=>[4,2,2]
[[2,1,1],[2,1],[1]]=>[4,3,1]
[[2,1,1],[1,1,1],[1]]=>[4,3,1]
[[2,1,1],[2,1,1]]=>[4,4]
[[1,1,1,1],[1],[1],[1],[1]]=>[4,1,1,1,1]
[[1,1,1,1],[1,1],[1],[1]]=>[4,2,1,1]
[[1,1,1,1],[1,1],[1,1]]=>[4,2,2]
[[1,1,1,1],[1,1,1],[1]]=>[4,3,1]
[[1,1,1,1],[1,1,1,1]]=>[4,4]
[[5],[1],[1],[1]]=>[5,1,1,1]
[[5],[2],[1]]=>[5,2,1]
[[5],[3]]=>[5,3]
[[4,1],[1],[1],[1]]=>[5,1,1,1]
[[4,1],[2],[1]]=>[5,2,1]
[[4,1],[1,1],[1]]=>[5,2,1]
[[4,1],[3]]=>[5,3]
[[4,1],[2,1]]=>[5,3]
[[3,2],[1],[1],[1]]=>[5,1,1,1]
[[3,2],[2],[1]]=>[5,2,1]
[[3,2],[1,1],[1]]=>[5,2,1]
[[3,2],[3]]=>[5,3]
[[3,2],[2,1]]=>[5,3]
[[3,1,1],[1],[1],[1]]=>[5,1,1,1]
[[3,1,1],[2],[1]]=>[5,2,1]
[[3,1,1],[1,1],[1]]=>[5,2,1]
[[3,1,1],[3]]=>[5,3]
[[3,1,1],[2,1]]=>[5,3]
[[3,1,1],[1,1,1]]=>[5,3]
[[2,2,1],[1],[1],[1]]=>[5,1,1,1]
[[2,2,1],[2],[1]]=>[5,2,1]
[[2,2,1],[1,1],[1]]=>[5,2,1]
[[2,2,1],[2,1]]=>[5,3]
[[2,2,1],[1,1,1]]=>[5,3]
[[2,1,1,1],[1],[1],[1]]=>[5,1,1,1]
[[2,1,1,1],[2],[1]]=>[5,2,1]
[[2,1,1,1],[1,1],[1]]=>[5,2,1]
[[2,1,1,1],[2,1]]=>[5,3]
[[2,1,1,1],[1,1,1]]=>[5,3]
[[1,1,1,1,1],[1],[1],[1]]=>[5,1,1,1]
[[1,1,1,1,1],[1,1],[1]]=>[5,2,1]
[[1,1,1,1,1],[1,1,1]]=>[5,3]
[[6],[1],[1]]=>[6,1,1]
[[6],[2]]=>[6,2]
[[5,1],[1],[1]]=>[6,1,1]
[[5,1],[2]]=>[6,2]
[[5,1],[1,1]]=>[6,2]
[[4,2],[1],[1]]=>[6,1,1]
[[4,2],[2]]=>[6,2]
[[4,2],[1,1]]=>[6,2]
[[4,1,1],[1],[1]]=>[6,1,1]
[[4,1,1],[2]]=>[6,2]
[[4,1,1],[1,1]]=>[6,2]
[[3,3],[1],[1]]=>[6,1,1]
[[3,3],[2]]=>[6,2]
[[3,3],[1,1]]=>[6,2]
[[3,2,1],[1],[1]]=>[6,1,1]
[[3,2,1],[2]]=>[6,2]
[[3,2,1],[1,1]]=>[6,2]
[[3,1,1,1],[1],[1]]=>[6,1,1]
[[3,1,1,1],[2]]=>[6,2]
[[3,1,1,1],[1,1]]=>[6,2]
[[2,2,2],[1],[1]]=>[6,1,1]
[[2,2,2],[2]]=>[6,2]
[[2,2,2],[1,1]]=>[6,2]
[[2,2,1,1],[1],[1]]=>[6,1,1]
[[2,2,1,1],[2]]=>[6,2]
[[2,2,1,1],[1,1]]=>[6,2]
[[2,1,1,1,1],[1],[1]]=>[6,1,1]
[[2,1,1,1,1],[2]]=>[6,2]
[[2,1,1,1,1],[1,1]]=>[6,2]
[[1,1,1,1,1,1],[1],[1]]=>[6,1,1]
[[1,1,1,1,1,1],[1,1]]=>[6,2]
[[7],[1]]=>[7,1]
[[6,1],[1]]=>[7,1]
[[5,2],[1]]=>[7,1]
[[5,1,1],[1]]=>[7,1]
[[4,3],[1]]=>[7,1]
[[4,2,1],[1]]=>[7,1]
[[4,1,1,1],[1]]=>[7,1]
[[3,3,1],[1]]=>[7,1]
[[3,2,2],[1]]=>[7,1]
[[3,2,1,1],[1]]=>[7,1]
[[3,1,1,1,1],[1]]=>[7,1]
[[2,2,2,1],[1]]=>[7,1]
[[2,2,1,1,1],[1]]=>[7,1]
[[2,1,1,1,1,1],[1]]=>[7,1]
[[1,1,1,1,1,1,1],[1]]=>[7,1]
[[8]]=>[8]
[[7,1]]=>[8]
[[6,2]]=>[8]
[[6,1,1]]=>[8]
[[5,3]]=>[8]
[[5,2,1]]=>[8]
[[5,1,1,1]]=>[8]
[[4,4]]=>[8]
[[4,3,1]]=>[8]
[[4,2,2]]=>[8]
[[4,2,1,1]]=>[8]
[[4,1,1,1,1]]=>[8]
[[3,3,2]]=>[8]
[[3,3,1,1]]=>[8]
[[3,2,2,1]]=>[8]
[[3,2,1,1,1]]=>[8]
[[3,1,1,1,1,1]]=>[8]
[[2,2,2,2]]=>[8]
[[2,2,2,1,1]]=>[8]
[[2,2,1,1,1,1]]=>[8]
[[2,1,1,1,1,1,1]]=>[8]
[[1,1,1,1,1,1,1,1]]=>[8]
[[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1,1,1]
[[2],[1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1,1]
[[2],[2],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1]
[[2],[2],[2],[1],[1],[1]]=>[2,2,2,1,1,1]
[[2],[2],[2],[2],[1]]=>[2,2,2,2,1]
[[1,1],[1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1,1]
[[1,1],[1,1],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1]
[[1,1],[1,1],[1,1],[1],[1],[1]]=>[2,2,2,1,1,1]
[[1,1],[1,1],[1,1],[1,1],[1]]=>[2,2,2,2,1]
[[3],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1]
[[3],[2],[1],[1],[1],[1]]=>[3,2,1,1,1,1]
[[3],[2],[2],[1],[1]]=>[3,2,2,1,1]
[[3],[2],[2],[2]]=>[3,2,2,2]
[[3],[3],[1],[1],[1]]=>[3,3,1,1,1]
[[3],[3],[2],[1]]=>[3,3,2,1]
[[3],[3],[3]]=>[3,3,3]
[[2,1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1]
[[2,1],[2],[1],[1],[1],[1]]=>[3,2,1,1,1,1]
[[2,1],[2],[2],[1],[1]]=>[3,2,2,1,1]
[[2,1],[2],[2],[2]]=>[3,2,2,2]
[[2,1],[1,1],[1],[1],[1],[1]]=>[3,2,1,1,1,1]
[[2,1],[1,1],[1,1],[1],[1]]=>[3,2,2,1,1]
[[2,1],[1,1],[1,1],[1,1]]=>[3,2,2,2]
[[2,1],[2,1],[1],[1],[1]]=>[3,3,1,1,1]
[[2,1],[2,1],[2],[1]]=>[3,3,2,1]
[[2,1],[2,1],[1,1],[1]]=>[3,3,2,1]
[[2,1],[2,1],[2,1]]=>[3,3,3]
[[1,1,1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1]
[[1,1,1],[1,1],[1],[1],[1],[1]]=>[3,2,1,1,1,1]
[[1,1,1],[1,1],[1,1],[1],[1]]=>[3,2,2,1,1]
[[1,1,1],[1,1],[1,1],[1,1]]=>[3,2,2,2]
[[1,1,1],[1,1,1],[1],[1],[1]]=>[3,3,1,1,1]
[[1,1,1],[1,1,1],[1,1],[1]]=>[3,3,2,1]
[[1,1,1],[1,1,1],[1,1,1]]=>[3,3,3]
[[4],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]
[[4],[2],[1],[1],[1]]=>[4,2,1,1,1]
[[4],[2],[2],[1]]=>[4,2,2,1]
[[4],[3],[1],[1]]=>[4,3,1,1]
[[4],[3],[2]]=>[4,3,2]
[[4],[4],[1]]=>[4,4,1]
[[3,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]
[[3,1],[2],[1],[1],[1]]=>[4,2,1,1,1]
[[3,1],[2],[2],[1]]=>[4,2,2,1]
[[3,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1]
[[3,1],[1,1],[1,1],[1]]=>[4,2,2,1]
[[3,1],[3],[1],[1]]=>[4,3,1,1]
[[3,1],[3],[2]]=>[4,3,2]
[[3,1],[2,1],[1],[1]]=>[4,3,1,1]
[[3,1],[2,1],[2]]=>[4,3,2]
[[3,1],[2,1],[1,1]]=>[4,3,2]
[[3,1],[3,1],[1]]=>[4,4,1]
[[2,2],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]
[[2,2],[2],[1],[1],[1]]=>[4,2,1,1,1]
[[2,2],[2],[2],[1]]=>[4,2,2,1]
[[2,2],[1,1],[1],[1],[1]]=>[4,2,1,1,1]
[[2,2],[1,1],[1,1],[1]]=>[4,2,2,1]
[[2,2],[2,1],[1],[1]]=>[4,3,1,1]
[[2,2],[2,1],[2]]=>[4,3,2]
[[2,2],[2,1],[1,1]]=>[4,3,2]
[[2,2],[2,2],[1]]=>[4,4,1]
[[2,1,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]
[[2,1,1],[2],[1],[1],[1]]=>[4,2,1,1,1]
[[2,1,1],[2],[2],[1]]=>[4,2,2,1]
[[2,1,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1]
[[2,1,1],[1,1],[1,1],[1]]=>[4,2,2,1]
[[2,1,1],[2,1],[1],[1]]=>[4,3,1,1]
[[2,1,1],[2,1],[2]]=>[4,3,2]
[[2,1,1],[2,1],[1,1]]=>[4,3,2]
[[2,1,1],[1,1,1],[1],[1]]=>[4,3,1,1]
[[2,1,1],[1,1,1],[1,1]]=>[4,3,2]
[[2,1,1],[2,1,1],[1]]=>[4,4,1]
[[1,1,1,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]
[[1,1,1,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1]
[[1,1,1,1],[1,1],[1,1],[1]]=>[4,2,2,1]
[[1,1,1,1],[1,1,1],[1],[1]]=>[4,3,1,1]
[[1,1,1,1],[1,1,1],[1,1]]=>[4,3,2]
[[1,1,1,1],[1,1,1,1],[1]]=>[4,4,1]
[[5],[1],[1],[1],[1]]=>[5,1,1,1,1]
[[5],[2],[1],[1]]=>[5,2,1,1]
[[5],[2],[2]]=>[5,2,2]
[[5],[3],[1]]=>[5,3,1]
[[5],[4]]=>[5,4]
[[4,1],[1],[1],[1],[1]]=>[5,1,1,1,1]
[[4,1],[2],[1],[1]]=>[5,2,1,1]
[[4,1],[2],[2]]=>[5,2,2]
[[4,1],[1,1],[1],[1]]=>[5,2,1,1]
[[4,1],[1,1],[1,1]]=>[5,2,2]
[[4,1],[3],[1]]=>[5,3,1]
[[4,1],[2,1],[1]]=>[5,3,1]
[[4,1],[4]]=>[5,4]
[[4,1],[3,1]]=>[5,4]
[[3,2],[1],[1],[1],[1]]=>[5,1,1,1,1]
[[3,2],[2],[1],[1]]=>[5,2,1,1]
[[3,2],[2],[2]]=>[5,2,2]
[[3,2],[1,1],[1],[1]]=>[5,2,1,1]
[[3,2],[1,1],[1,1]]=>[5,2,2]
[[3,2],[3],[1]]=>[5,3,1]
[[3,2],[2,1],[1]]=>[5,3,1]
[[3,2],[3,1]]=>[5,4]
[[3,2],[2,2]]=>[5,4]
[[3,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1]
[[3,1,1],[2],[1],[1]]=>[5,2,1,1]
[[3,1,1],[2],[2]]=>[5,2,2]
[[3,1,1],[1,1],[1],[1]]=>[5,2,1,1]
[[3,1,1],[1,1],[1,1]]=>[5,2,2]
[[3,1,1],[3],[1]]=>[5,3,1]
[[3,1,1],[2,1],[1]]=>[5,3,1]
[[3,1,1],[1,1,1],[1]]=>[5,3,1]
[[3,1,1],[3,1]]=>[5,4]
[[3,1,1],[2,1,1]]=>[5,4]
[[2,2,1],[1],[1],[1],[1]]=>[5,1,1,1,1]
[[2,2,1],[2],[1],[1]]=>[5,2,1,1]
[[2,2,1],[2],[2]]=>[5,2,2]
[[2,2,1],[1,1],[1],[1]]=>[5,2,1,1]
[[2,2,1],[1,1],[1,1]]=>[5,2,2]
[[2,2,1],[2,1],[1]]=>[5,3,1]
[[2,2,1],[1,1,1],[1]]=>[5,3,1]
[[2,2,1],[2,2]]=>[5,4]
[[2,2,1],[2,1,1]]=>[5,4]
[[2,1,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1]
[[2,1,1,1],[2],[1],[1]]=>[5,2,1,1]
[[2,1,1,1],[2],[2]]=>[5,2,2]
[[2,1,1,1],[1,1],[1],[1]]=>[5,2,1,1]
[[2,1,1,1],[1,1],[1,1]]=>[5,2,2]
[[2,1,1,1],[2,1],[1]]=>[5,3,1]
[[2,1,1,1],[1,1,1],[1]]=>[5,3,1]
[[2,1,1,1],[2,1,1]]=>[5,4]
[[2,1,1,1],[1,1,1,1]]=>[5,4]
[[1,1,1,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1]
[[1,1,1,1,1],[1,1],[1],[1]]=>[5,2,1,1]
[[1,1,1,1,1],[1,1],[1,1]]=>[5,2,2]
[[1,1,1,1,1],[1,1,1],[1]]=>[5,3,1]
[[1,1,1,1,1],[1,1,1,1]]=>[5,4]
[[6],[1],[1],[1]]=>[6,1,1,1]
[[6],[2],[1]]=>[6,2,1]
[[6],[3]]=>[6,3]
[[5,1],[1],[1],[1]]=>[6,1,1,1]
[[5,1],[2],[1]]=>[6,2,1]
[[5,1],[1,1],[1]]=>[6,2,1]
[[5,1],[3]]=>[6,3]
[[5,1],[2,1]]=>[6,3]
[[4,2],[1],[1],[1]]=>[6,1,1,1]
[[4,2],[2],[1]]=>[6,2,1]
[[4,2],[1,1],[1]]=>[6,2,1]
[[4,2],[3]]=>[6,3]
[[4,2],[2,1]]=>[6,3]
[[4,1,1],[1],[1],[1]]=>[6,1,1,1]
[[4,1,1],[2],[1]]=>[6,2,1]
[[4,1,1],[1,1],[1]]=>[6,2,1]
[[4,1,1],[3]]=>[6,3]
[[4,1,1],[2,1]]=>[6,3]
[[4,1,1],[1,1,1]]=>[6,3]
[[3,3],[1],[1],[1]]=>[6,1,1,1]
[[3,3],[2],[1]]=>[6,2,1]
[[3,3],[1,1],[1]]=>[6,2,1]
[[3,3],[3]]=>[6,3]
[[3,3],[2,1]]=>[6,3]
[[3,2,1],[1],[1],[1]]=>[6,1,1,1]
[[3,2,1],[2],[1]]=>[6,2,1]
[[3,2,1],[1,1],[1]]=>[6,2,1]
[[3,2,1],[3]]=>[6,3]
[[3,2,1],[2,1]]=>[6,3]
[[3,2,1],[1,1,1]]=>[6,3]
[[3,1,1,1],[1],[1],[1]]=>[6,1,1,1]
[[3,1,1,1],[2],[1]]=>[6,2,1]
[[3,1,1,1],[1,1],[1]]=>[6,2,1]
[[3,1,1,1],[3]]=>[6,3]
[[3,1,1,1],[2,1]]=>[6,3]
[[3,1,1,1],[1,1,1]]=>[6,3]
[[2,2,2],[1],[1],[1]]=>[6,1,1,1]
[[2,2,2],[2],[1]]=>[6,2,1]
[[2,2,2],[1,1],[1]]=>[6,2,1]
[[2,2,2],[2,1]]=>[6,3]
[[2,2,2],[1,1,1]]=>[6,3]
[[2,2,1,1],[1],[1],[1]]=>[6,1,1,1]
[[2,2,1,1],[2],[1]]=>[6,2,1]
[[2,2,1,1],[1,1],[1]]=>[6,2,1]
[[2,2,1,1],[2,1]]=>[6,3]
[[2,2,1,1],[1,1,1]]=>[6,3]
[[2,1,1,1,1],[1],[1],[1]]=>[6,1,1,1]
[[2,1,1,1,1],[2],[1]]=>[6,2,1]
[[2,1,1,1,1],[1,1],[1]]=>[6,2,1]
[[2,1,1,1,1],[2,1]]=>[6,3]
[[2,1,1,1,1],[1,1,1]]=>[6,3]
[[1,1,1,1,1,1],[1],[1],[1]]=>[6,1,1,1]
[[1,1,1,1,1,1],[1,1],[1]]=>[6,2,1]
[[1,1,1,1,1,1],[1,1,1]]=>[6,3]
[[7],[1],[1]]=>[7,1,1]
[[7],[2]]=>[7,2]
[[6,1],[1],[1]]=>[7,1,1]
[[6,1],[2]]=>[7,2]
[[6,1],[1,1]]=>[7,2]
[[5,2],[1],[1]]=>[7,1,1]
[[5,2],[2]]=>[7,2]
[[5,2],[1,1]]=>[7,2]
[[5,1,1],[1],[1]]=>[7,1,1]
[[5,1,1],[2]]=>[7,2]
[[5,1,1],[1,1]]=>[7,2]
[[4,3],[1],[1]]=>[7,1,1]
[[4,3],[2]]=>[7,2]
[[4,3],[1,1]]=>[7,2]
[[4,2,1],[1],[1]]=>[7,1,1]
[[4,2,1],[2]]=>[7,2]
[[4,2,1],[1,1]]=>[7,2]
[[4,1,1,1],[1],[1]]=>[7,1,1]
[[4,1,1,1],[2]]=>[7,2]
[[4,1,1,1],[1,1]]=>[7,2]
[[3,3,1],[1],[1]]=>[7,1,1]
[[3,3,1],[2]]=>[7,2]
[[3,3,1],[1,1]]=>[7,2]
[[3,2,2],[1],[1]]=>[7,1,1]
[[3,2,2],[2]]=>[7,2]
[[3,2,2],[1,1]]=>[7,2]
[[3,2,1,1],[1],[1]]=>[7,1,1]
[[3,2,1,1],[2]]=>[7,2]
[[3,2,1,1],[1,1]]=>[7,2]
[[3,1,1,1,1],[1],[1]]=>[7,1,1]
[[3,1,1,1,1],[2]]=>[7,2]
[[3,1,1,1,1],[1,1]]=>[7,2]
[[2,2,2,1],[1],[1]]=>[7,1,1]
[[2,2,2,1],[2]]=>[7,2]
[[2,2,2,1],[1,1]]=>[7,2]
[[2,2,1,1,1],[1],[1]]=>[7,1,1]
[[2,2,1,1,1],[2]]=>[7,2]
[[2,2,1,1,1],[1,1]]=>[7,2]
[[2,1,1,1,1,1],[1],[1]]=>[7,1,1]
[[2,1,1,1,1,1],[2]]=>[7,2]
[[2,1,1,1,1,1],[1,1]]=>[7,2]
[[1,1,1,1,1,1,1],[1],[1]]=>[7,1,1]
[[1,1,1,1,1,1,1],[1,1]]=>[7,2]
[[8],[1]]=>[8,1]
[[7,1],[1]]=>[8,1]
[[6,2],[1]]=>[8,1]
[[6,1,1],[1]]=>[8,1]
[[5,3],[1]]=>[8,1]
[[5,2,1],[1]]=>[8,1]
[[5,1,1,1],[1]]=>[8,1]
[[4,4],[1]]=>[8,1]
[[4,3,1],[1]]=>[8,1]
[[4,2,2],[1]]=>[8,1]
[[4,2,1,1],[1]]=>[8,1]
[[4,1,1,1,1],[1]]=>[8,1]
[[3,3,2],[1]]=>[8,1]
[[3,3,1,1],[1]]=>[8,1]
[[3,2,2,1],[1]]=>[8,1]
[[3,2,1,1,1],[1]]=>[8,1]
[[3,1,1,1,1,1],[1]]=>[8,1]
[[2,2,2,2],[1]]=>[8,1]
[[2,2,2,1,1],[1]]=>[8,1]
[[2,2,1,1,1,1],[1]]=>[8,1]
[[2,1,1,1,1,1,1],[1]]=>[8,1]
[[1,1,1,1,1,1,1,1],[1]]=>[8,1]
[[9]]=>[9]
[[8,1]]=>[9]
[[7,2]]=>[9]
[[7,1,1]]=>[9]
[[6,3]]=>[9]
[[6,2,1]]=>[9]
[[6,1,1,1]]=>[9]
[[5,4]]=>[9]
[[5,3,1]]=>[9]
[[5,2,2]]=>[9]
[[5,2,1,1]]=>[9]
[[5,1,1,1,1]]=>[9]
[[4,4,1]]=>[9]
[[4,3,2]]=>[9]
[[4,3,1,1]]=>[9]
[[4,2,2,1]]=>[9]
[[4,2,1,1,1]]=>[9]
[[4,1,1,1,1,1]]=>[9]
[[3,3,3]]=>[9]
[[3,3,2,1]]=>[9]
[[3,3,1,1,1]]=>[9]
[[3,2,2,2]]=>[9]
[[3,2,2,1,1]]=>[9]
[[3,2,1,1,1,1]]=>[9]
[[3,1,1,1,1,1,1]]=>[9]
[[2,2,2,2,1]]=>[9]
[[2,2,2,1,1,1]]=>[9]
[[2,2,1,1,1,1,1]]=>[9]
[[2,1,1,1,1,1,1,1]]=>[9]
[[1,1,1,1,1,1,1,1,1]]=>[9]
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1,1,1,1]
[[2],[1],[1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1,1,1]
[[2],[2],[1],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1,1]
[[2],[2],[2],[1],[1],[1],[1]]=>[2,2,2,1,1,1,1]
[[2],[2],[2],[2],[1],[1]]=>[2,2,2,2,1,1]
[[2],[2],[2],[2],[2]]=>[2,2,2,2,2]
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1,1,1]
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1,1]
[[1,1],[1,1],[1,1],[1],[1],[1],[1]]=>[2,2,2,1,1,1,1]
[[1,1],[1,1],[1,1],[1,1],[1],[1]]=>[2,2,2,2,1,1]
[[1,1],[1,1],[1,1],[1,1],[1,1]]=>[2,2,2,2,2]
[[3],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1]
[[3],[2],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1]
[[3],[2],[2],[1],[1],[1]]=>[3,2,2,1,1,1]
[[3],[2],[2],[2],[1]]=>[3,2,2,2,1]
[[3],[3],[1],[1],[1],[1]]=>[3,3,1,1,1,1]
[[3],[3],[2],[1],[1]]=>[3,3,2,1,1]
[[3],[3],[2],[2]]=>[3,3,2,2]
[[3],[3],[3],[1]]=>[3,3,3,1]
[[2,1],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1]
[[2,1],[2],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1]
[[2,1],[2],[2],[1],[1],[1]]=>[3,2,2,1,1,1]
[[2,1],[2],[2],[2],[1]]=>[3,2,2,2,1]
[[2,1],[1,1],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1]
[[2,1],[1,1],[1,1],[1],[1],[1]]=>[3,2,2,1,1,1]
[[2,1],[1,1],[1,1],[1,1],[1]]=>[3,2,2,2,1]
[[2,1],[2,1],[1],[1],[1],[1]]=>[3,3,1,1,1,1]
[[2,1],[2,1],[2],[1],[1]]=>[3,3,2,1,1]
[[2,1],[2,1],[2],[2]]=>[3,3,2,2]
[[2,1],[2,1],[1,1],[1],[1]]=>[3,3,2,1,1]
[[2,1],[2,1],[1,1],[1,1]]=>[3,3,2,2]
[[2,1],[2,1],[2,1],[1]]=>[3,3,3,1]
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1]
[[1,1,1],[1,1],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1]
[[1,1,1],[1,1],[1,1],[1],[1],[1]]=>[3,2,2,1,1,1]
[[1,1,1],[1,1],[1,1],[1,1],[1]]=>[3,2,2,2,1]
[[1,1,1],[1,1,1],[1],[1],[1],[1]]=>[3,3,1,1,1,1]
[[1,1,1],[1,1,1],[1,1],[1],[1]]=>[3,3,2,1,1]
[[1,1,1],[1,1,1],[1,1],[1,1]]=>[3,3,2,2]
[[1,1,1],[1,1,1],[1,1,1],[1]]=>[3,3,3,1]
[[4],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]
[[4],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1]
[[4],[2],[2],[1],[1]]=>[4,2,2,1,1]
[[4],[2],[2],[2]]=>[4,2,2,2]
[[4],[3],[1],[1],[1]]=>[4,3,1,1,1]
[[4],[3],[2],[1]]=>[4,3,2,1]
[[4],[3],[3]]=>[4,3,3]
[[4],[4],[1],[1]]=>[4,4,1,1]
[[4],[4],[2]]=>[4,4,2]
[[3,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]
[[3,1],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1]
[[3,1],[2],[2],[1],[1]]=>[4,2,2,1,1]
[[3,1],[2],[2],[2]]=>[4,2,2,2]
[[3,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1]
[[3,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1]
[[3,1],[1,1],[1,1],[1,1]]=>[4,2,2,2]
[[3,1],[3],[1],[1],[1]]=>[4,3,1,1,1]
[[3,1],[3],[2],[1]]=>[4,3,2,1]
[[3,1],[3],[3]]=>[4,3,3]
[[3,1],[2,1],[1],[1],[1]]=>[4,3,1,1,1]
[[3,1],[2,1],[2],[1]]=>[4,3,2,1]
[[3,1],[2,1],[1,1],[1]]=>[4,3,2,1]
[[3,1],[2,1],[2,1]]=>[4,3,3]
[[3,1],[3,1],[1],[1]]=>[4,4,1,1]
[[3,1],[3,1],[2]]=>[4,4,2]
[[3,1],[3,1],[1,1]]=>[4,4,2]
[[2,2],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]
[[2,2],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1]
[[2,2],[2],[2],[1],[1]]=>[4,2,2,1,1]
[[2,2],[2],[2],[2]]=>[4,2,2,2]
[[2,2],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1]
[[2,2],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1]
[[2,2],[1,1],[1,1],[1,1]]=>[4,2,2,2]
[[2,2],[2,1],[1],[1],[1]]=>[4,3,1,1,1]
[[2,2],[2,1],[2],[1]]=>[4,3,2,1]
[[2,2],[2,1],[1,1],[1]]=>[4,3,2,1]
[[2,2],[2,1],[2,1]]=>[4,3,3]
[[2,2],[2,2],[1],[1]]=>[4,4,1,1]
[[2,2],[2,2],[2]]=>[4,4,2]
[[2,2],[2,2],[1,1]]=>[4,4,2]
[[2,1,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]
[[2,1,1],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1]
[[2,1,1],[2],[2],[1],[1]]=>[4,2,2,1,1]
[[2,1,1],[2],[2],[2]]=>[4,2,2,2]
[[2,1,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1]
[[2,1,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1]
[[2,1,1],[1,1],[1,1],[1,1]]=>[4,2,2,2]
[[2,1,1],[2,1],[1],[1],[1]]=>[4,3,1,1,1]
[[2,1,1],[2,1],[2],[1]]=>[4,3,2,1]
[[2,1,1],[2,1],[1,1],[1]]=>[4,3,2,1]
[[2,1,1],[2,1],[2,1]]=>[4,3,3]
[[2,1,1],[1,1,1],[1],[1],[1]]=>[4,3,1,1,1]
[[2,1,1],[1,1,1],[1,1],[1]]=>[4,3,2,1]
[[2,1,1],[1,1,1],[1,1,1]]=>[4,3,3]
[[2,1,1],[2,1,1],[1],[1]]=>[4,4,1,1]
[[2,1,1],[2,1,1],[2]]=>[4,4,2]
[[2,1,1],[2,1,1],[1,1]]=>[4,4,2]
[[1,1,1,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]
[[1,1,1,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1]
[[1,1,1,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1]
[[1,1,1,1],[1,1],[1,1],[1,1]]=>[4,2,2,2]
[[1,1,1,1],[1,1,1],[1],[1],[1]]=>[4,3,1,1,1]
[[1,1,1,1],[1,1,1],[1,1],[1]]=>[4,3,2,1]
[[1,1,1,1],[1,1,1],[1,1,1]]=>[4,3,3]
[[1,1,1,1],[1,1,1,1],[1],[1]]=>[4,4,1,1]
[[1,1,1,1],[1,1,1,1],[1,1]]=>[4,4,2]
[[5],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]
[[5],[2],[1],[1],[1]]=>[5,2,1,1,1]
[[5],[2],[2],[1]]=>[5,2,2,1]
[[5],[3],[1],[1]]=>[5,3,1,1]
[[5],[3],[2]]=>[5,3,2]
[[5],[4],[1]]=>[5,4,1]
[[5],[5]]=>[5,5]
[[4,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]
[[4,1],[2],[1],[1],[1]]=>[5,2,1,1,1]
[[4,1],[2],[2],[1]]=>[5,2,2,1]
[[4,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]
[[4,1],[1,1],[1,1],[1]]=>[5,2,2,1]
[[4,1],[3],[1],[1]]=>[5,3,1,1]
[[4,1],[3],[2]]=>[5,3,2]
[[4,1],[2,1],[1],[1]]=>[5,3,1,1]
[[4,1],[2,1],[2]]=>[5,3,2]
[[4,1],[2,1],[1,1]]=>[5,3,2]
[[4,1],[4],[1]]=>[5,4,1]
[[4,1],[3,1],[1]]=>[5,4,1]
[[4,1],[4,1]]=>[5,5]
[[3,2],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]
[[3,2],[2],[1],[1],[1]]=>[5,2,1,1,1]
[[3,2],[2],[2],[1]]=>[5,2,2,1]
[[3,2],[1,1],[1],[1],[1]]=>[5,2,1,1,1]
[[3,2],[1,1],[1,1],[1]]=>[5,2,2,1]
[[3,2],[3],[1],[1]]=>[5,3,1,1]
[[3,2],[3],[2]]=>[5,3,2]
[[3,2],[2,1],[1],[1]]=>[5,3,1,1]
[[3,2],[2,1],[2]]=>[5,3,2]
[[3,2],[2,1],[1,1]]=>[5,3,2]
[[3,2],[3,1],[1]]=>[5,4,1]
[[3,2],[2,2],[1]]=>[5,4,1]
[[3,2],[3,2]]=>[5,5]
[[3,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]
[[3,1,1],[2],[1],[1],[1]]=>[5,2,1,1,1]
[[3,1,1],[2],[2],[1]]=>[5,2,2,1]
[[3,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]
[[3,1,1],[1,1],[1,1],[1]]=>[5,2,2,1]
[[3,1,1],[3],[1],[1]]=>[5,3,1,1]
[[3,1,1],[3],[2]]=>[5,3,2]
[[3,1,1],[2,1],[1],[1]]=>[5,3,1,1]
[[3,1,1],[2,1],[2]]=>[5,3,2]
[[3,1,1],[2,1],[1,1]]=>[5,3,2]
[[3,1,1],[1,1,1],[1],[1]]=>[5,3,1,1]
[[3,1,1],[1,1,1],[1,1]]=>[5,3,2]
[[3,1,1],[3,1],[1]]=>[5,4,1]
[[3,1,1],[2,1,1],[1]]=>[5,4,1]
[[3,1,1],[3,1,1]]=>[5,5]
[[2,2,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]
[[2,2,1],[2],[1],[1],[1]]=>[5,2,1,1,1]
[[2,2,1],[2],[2],[1]]=>[5,2,2,1]
[[2,2,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]
[[2,2,1],[1,1],[1,1],[1]]=>[5,2,2,1]
[[2,2,1],[2,1],[1],[1]]=>[5,3,1,1]
[[2,2,1],[2,1],[2]]=>[5,3,2]
[[2,2,1],[2,1],[1,1]]=>[5,3,2]
[[2,2,1],[1,1,1],[1],[1]]=>[5,3,1,1]
[[2,2,1],[1,1,1],[1,1]]=>[5,3,2]
[[2,2,1],[2,2],[1]]=>[5,4,1]
[[2,2,1],[2,1,1],[1]]=>[5,4,1]
[[2,2,1],[2,2,1]]=>[5,5]
[[2,1,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]
[[2,1,1,1],[2],[1],[1],[1]]=>[5,2,1,1,1]
[[2,1,1,1],[2],[2],[1]]=>[5,2,2,1]
[[2,1,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]
[[2,1,1,1],[1,1],[1,1],[1]]=>[5,2,2,1]
[[2,1,1,1],[2,1],[1],[1]]=>[5,3,1,1]
[[2,1,1,1],[2,1],[2]]=>[5,3,2]
[[2,1,1,1],[2,1],[1,1]]=>[5,3,2]
[[2,1,1,1],[1,1,1],[1],[1]]=>[5,3,1,1]
[[2,1,1,1],[1,1,1],[1,1]]=>[5,3,2]
[[2,1,1,1],[2,1,1],[1]]=>[5,4,1]
[[2,1,1,1],[1,1,1,1],[1]]=>[5,4,1]
[[2,1,1,1],[2,1,1,1]]=>[5,5]
[[1,1,1,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]
[[1,1,1,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]
[[1,1,1,1,1],[1,1],[1,1],[1]]=>[5,2,2,1]
[[1,1,1,1,1],[1,1,1],[1],[1]]=>[5,3,1,1]
[[1,1,1,1,1],[1,1,1],[1,1]]=>[5,3,2]
[[1,1,1,1,1],[1,1,1,1],[1]]=>[5,4,1]
[[1,1,1,1,1],[1,1,1,1,1]]=>[5,5]
[[6],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[6],[2],[1],[1]]=>[6,2,1,1]
[[6],[2],[2]]=>[6,2,2]
[[6],[3],[1]]=>[6,3,1]
[[6],[4]]=>[6,4]
[[5,1],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[5,1],[2],[1],[1]]=>[6,2,1,1]
[[5,1],[2],[2]]=>[6,2,2]
[[5,1],[1,1],[1],[1]]=>[6,2,1,1]
[[5,1],[1,1],[1,1]]=>[6,2,2]
[[5,1],[3],[1]]=>[6,3,1]
[[5,1],[2,1],[1]]=>[6,3,1]
[[5,1],[4]]=>[6,4]
[[5,1],[3,1]]=>[6,4]
[[4,2],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[4,2],[2],[1],[1]]=>[6,2,1,1]
[[4,2],[2],[2]]=>[6,2,2]
[[4,2],[1,1],[1],[1]]=>[6,2,1,1]
[[4,2],[1,1],[1,1]]=>[6,2,2]
[[4,2],[3],[1]]=>[6,3,1]
[[4,2],[2,1],[1]]=>[6,3,1]
[[4,2],[4]]=>[6,4]
[[4,2],[3,1]]=>[6,4]
[[4,2],[2,2]]=>[6,4]
[[4,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[4,1,1],[2],[1],[1]]=>[6,2,1,1]
[[4,1,1],[2],[2]]=>[6,2,2]
[[4,1,1],[1,1],[1],[1]]=>[6,2,1,1]
[[4,1,1],[1,1],[1,1]]=>[6,2,2]
[[4,1,1],[3],[1]]=>[6,3,1]
[[4,1,1],[2,1],[1]]=>[6,3,1]
[[4,1,1],[1,1,1],[1]]=>[6,3,1]
[[4,1,1],[4]]=>[6,4]
[[4,1,1],[3,1]]=>[6,4]
[[4,1,1],[2,1,1]]=>[6,4]
[[3,3],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[3,3],[2],[1],[1]]=>[6,2,1,1]
[[3,3],[2],[2]]=>[6,2,2]
[[3,3],[1,1],[1],[1]]=>[6,2,1,1]
[[3,3],[1,1],[1,1]]=>[6,2,2]
[[3,3],[3],[1]]=>[6,3,1]
[[3,3],[2,1],[1]]=>[6,3,1]
[[3,3],[3,1]]=>[6,4]
[[3,3],[2,2]]=>[6,4]
[[3,2,1],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[3,2,1],[2],[1],[1]]=>[6,2,1,1]
[[3,2,1],[2],[2]]=>[6,2,2]
[[3,2,1],[1,1],[1],[1]]=>[6,2,1,1]
[[3,2,1],[1,1],[1,1]]=>[6,2,2]
[[3,2,1],[3],[1]]=>[6,3,1]
[[3,2,1],[2,1],[1]]=>[6,3,1]
[[3,2,1],[1,1,1],[1]]=>[6,3,1]
[[3,2,1],[3,1]]=>[6,4]
[[3,2,1],[2,2]]=>[6,4]
[[3,2,1],[2,1,1]]=>[6,4]
[[3,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[3,1,1,1],[2],[1],[1]]=>[6,2,1,1]
[[3,1,1,1],[2],[2]]=>[6,2,2]
[[3,1,1,1],[1,1],[1],[1]]=>[6,2,1,1]
[[3,1,1,1],[1,1],[1,1]]=>[6,2,2]
[[3,1,1,1],[3],[1]]=>[6,3,1]
[[3,1,1,1],[2,1],[1]]=>[6,3,1]
[[3,1,1,1],[1,1,1],[1]]=>[6,3,1]
[[3,1,1,1],[3,1]]=>[6,4]
[[3,1,1,1],[2,1,1]]=>[6,4]
[[3,1,1,1],[1,1,1,1]]=>[6,4]
[[2,2,2],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[2,2,2],[2],[1],[1]]=>[6,2,1,1]
[[2,2,2],[2],[2]]=>[6,2,2]
[[2,2,2],[1,1],[1],[1]]=>[6,2,1,1]
[[2,2,2],[1,1],[1,1]]=>[6,2,2]
[[2,2,2],[2,1],[1]]=>[6,3,1]
[[2,2,2],[1,1,1],[1]]=>[6,3,1]
[[2,2,2],[2,2]]=>[6,4]
[[2,2,2],[2,1,1]]=>[6,4]
[[2,2,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[2,2,1,1],[2],[1],[1]]=>[6,2,1,1]
[[2,2,1,1],[2],[2]]=>[6,2,2]
[[2,2,1,1],[1,1],[1],[1]]=>[6,2,1,1]
[[2,2,1,1],[1,1],[1,1]]=>[6,2,2]
[[2,2,1,1],[2,1],[1]]=>[6,3,1]
[[2,2,1,1],[1,1,1],[1]]=>[6,3,1]
[[2,2,1,1],[2,2]]=>[6,4]
[[2,2,1,1],[2,1,1]]=>[6,4]
[[2,2,1,1],[1,1,1,1]]=>[6,4]
[[2,1,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[2,1,1,1,1],[2],[1],[1]]=>[6,2,1,1]
[[2,1,1,1,1],[2],[2]]=>[6,2,2]
[[2,1,1,1,1],[1,1],[1],[1]]=>[6,2,1,1]
[[2,1,1,1,1],[1,1],[1,1]]=>[6,2,2]
[[2,1,1,1,1],[2,1],[1]]=>[6,3,1]
[[2,1,1,1,1],[1,1,1],[1]]=>[6,3,1]
[[2,1,1,1,1],[2,1,1]]=>[6,4]
[[2,1,1,1,1],[1,1,1,1]]=>[6,4]
[[1,1,1,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]
[[1,1,1,1,1,1],[1,1],[1],[1]]=>[6,2,1,1]
[[1,1,1,1,1,1],[1,1],[1,1]]=>[6,2,2]
[[1,1,1,1,1,1],[1,1,1],[1]]=>[6,3,1]
[[1,1,1,1,1,1],[1,1,1,1]]=>[6,4]
[[7],[1],[1],[1]]=>[7,1,1,1]
[[7],[2],[1]]=>[7,2,1]
[[7],[3]]=>[7,3]
[[6,1],[1],[1],[1]]=>[7,1,1,1]
[[6,1],[2],[1]]=>[7,2,1]
[[6,1],[1,1],[1]]=>[7,2,1]
[[6,1],[3]]=>[7,3]
[[6,1],[2,1]]=>[7,3]
[[5,2],[1],[1],[1]]=>[7,1,1,1]
[[5,2],[2],[1]]=>[7,2,1]
[[5,2],[1,1],[1]]=>[7,2,1]
[[5,2],[3]]=>[7,3]
[[5,2],[2,1]]=>[7,3]
[[5,1,1],[1],[1],[1]]=>[7,1,1,1]
[[5,1,1],[2],[1]]=>[7,2,1]
[[5,1,1],[1,1],[1]]=>[7,2,1]
[[5,1,1],[3]]=>[7,3]
[[5,1,1],[2,1]]=>[7,3]
[[5,1,1],[1,1,1]]=>[7,3]
[[4,3],[1],[1],[1]]=>[7,1,1,1]
[[4,3],[2],[1]]=>[7,2,1]
[[4,3],[1,1],[1]]=>[7,2,1]
[[4,3],[3]]=>[7,3]
[[4,3],[2,1]]=>[7,3]
[[4,2,1],[1],[1],[1]]=>[7,1,1,1]
[[4,2,1],[2],[1]]=>[7,2,1]
[[4,2,1],[1,1],[1]]=>[7,2,1]
[[4,2,1],[3]]=>[7,3]
[[4,2,1],[2,1]]=>[7,3]
[[4,2,1],[1,1,1]]=>[7,3]
[[4,1,1,1],[1],[1],[1]]=>[7,1,1,1]
[[4,1,1,1],[2],[1]]=>[7,2,1]
[[4,1,1,1],[1,1],[1]]=>[7,2,1]
[[4,1,1,1],[3]]=>[7,3]
[[4,1,1,1],[2,1]]=>[7,3]
[[4,1,1,1],[1,1,1]]=>[7,3]
[[3,3,1],[1],[1],[1]]=>[7,1,1,1]
[[3,3,1],[2],[1]]=>[7,2,1]
[[3,3,1],[1,1],[1]]=>[7,2,1]
[[3,3,1],[3]]=>[7,3]
[[3,3,1],[2,1]]=>[7,3]
[[3,3,1],[1,1,1]]=>[7,3]
[[3,2,2],[1],[1],[1]]=>[7,1,1,1]
[[3,2,2],[2],[1]]=>[7,2,1]
[[3,2,2],[1,1],[1]]=>[7,2,1]
[[3,2,2],[3]]=>[7,3]
[[3,2,2],[2,1]]=>[7,3]
[[3,2,2],[1,1,1]]=>[7,3]
[[3,2,1,1],[1],[1],[1]]=>[7,1,1,1]
[[3,2,1,1],[2],[1]]=>[7,2,1]
[[3,2,1,1],[1,1],[1]]=>[7,2,1]
[[3,2,1,1],[3]]=>[7,3]
[[3,2,1,1],[2,1]]=>[7,3]
[[3,2,1,1],[1,1,1]]=>[7,3]
[[3,1,1,1,1],[1],[1],[1]]=>[7,1,1,1]
[[3,1,1,1,1],[2],[1]]=>[7,2,1]
[[3,1,1,1,1],[1,1],[1]]=>[7,2,1]
[[3,1,1,1,1],[3]]=>[7,3]
[[3,1,1,1,1],[2,1]]=>[7,3]
[[3,1,1,1,1],[1,1,1]]=>[7,3]
[[2,2,2,1],[1],[1],[1]]=>[7,1,1,1]
[[2,2,2,1],[2],[1]]=>[7,2,1]
[[2,2,2,1],[1,1],[1]]=>[7,2,1]
[[2,2,2,1],[2,1]]=>[7,3]
[[2,2,2,1],[1,1,1]]=>[7,3]
[[2,2,1,1,1],[1],[1],[1]]=>[7,1,1,1]
[[2,2,1,1,1],[2],[1]]=>[7,2,1]
[[2,2,1,1,1],[1,1],[1]]=>[7,2,1]
[[2,2,1,1,1],[2,1]]=>[7,3]
[[2,2,1,1,1],[1,1,1]]=>[7,3]
[[2,1,1,1,1,1],[1],[1],[1]]=>[7,1,1,1]
[[2,1,1,1,1,1],[2],[1]]=>[7,2,1]
[[2,1,1,1,1,1],[1,1],[1]]=>[7,2,1]
[[2,1,1,1,1,1],[2,1]]=>[7,3]
[[2,1,1,1,1,1],[1,1,1]]=>[7,3]
[[1,1,1,1,1,1,1],[1],[1],[1]]=>[7,1,1,1]
[[1,1,1,1,1,1,1],[1,1],[1]]=>[7,2,1]
[[1,1,1,1,1,1,1],[1,1,1]]=>[7,3]
[[8],[1],[1]]=>[8,1,1]
[[8],[2]]=>[8,2]
[[7,1],[1],[1]]=>[8,1,1]
[[7,1],[2]]=>[8,2]
[[7,1],[1,1]]=>[8,2]
[[6,2],[1],[1]]=>[8,1,1]
[[6,2],[2]]=>[8,2]
[[6,2],[1,1]]=>[8,2]
[[6,1,1],[1],[1]]=>[8,1,1]
[[6,1,1],[2]]=>[8,2]
[[6,1,1],[1,1]]=>[8,2]
[[5,3],[1],[1]]=>[8,1,1]
[[5,3],[2]]=>[8,2]
[[5,3],[1,1]]=>[8,2]
[[5,2,1],[1],[1]]=>[8,1,1]
[[5,2,1],[2]]=>[8,2]
[[5,2,1],[1,1]]=>[8,2]
[[5,1,1,1],[1],[1]]=>[8,1,1]
[[5,1,1,1],[2]]=>[8,2]
[[5,1,1,1],[1,1]]=>[8,2]
[[4,4],[1],[1]]=>[8,1,1]
[[4,4],[2]]=>[8,2]
[[4,4],[1,1]]=>[8,2]
[[4,3,1],[1],[1]]=>[8,1,1]
[[4,3,1],[2]]=>[8,2]
[[4,3,1],[1,1]]=>[8,2]
[[4,2,2],[1],[1]]=>[8,1,1]
[[4,2,2],[2]]=>[8,2]
[[4,2,2],[1,1]]=>[8,2]
[[4,2,1,1],[1],[1]]=>[8,1,1]
[[4,2,1,1],[2]]=>[8,2]
[[4,2,1,1],[1,1]]=>[8,2]
[[4,1,1,1,1],[1],[1]]=>[8,1,1]
[[4,1,1,1,1],[2]]=>[8,2]
[[4,1,1,1,1],[1,1]]=>[8,2]
[[3,3,2],[1],[1]]=>[8,1,1]
[[3,3,2],[2]]=>[8,2]
[[3,3,2],[1,1]]=>[8,2]
[[3,3,1,1],[1],[1]]=>[8,1,1]
[[3,3,1,1],[2]]=>[8,2]
[[3,3,1,1],[1,1]]=>[8,2]
[[3,2,2,1],[1],[1]]=>[8,1,1]
[[3,2,2,1],[2]]=>[8,2]
[[3,2,2,1],[1,1]]=>[8,2]
[[3,2,1,1,1],[1],[1]]=>[8,1,1]
[[3,2,1,1,1],[2]]=>[8,2]
[[3,2,1,1,1],[1,1]]=>[8,2]
[[3,1,1,1,1,1],[1],[1]]=>[8,1,1]
[[3,1,1,1,1,1],[2]]=>[8,2]
[[3,1,1,1,1,1],[1,1]]=>[8,2]
[[2,2,2,2],[1],[1]]=>[8,1,1]
[[2,2,2,2],[2]]=>[8,2]
[[2,2,2,2],[1,1]]=>[8,2]
[[2,2,2,1,1],[1],[1]]=>[8,1,1]
[[2,2,2,1,1],[2]]=>[8,2]
[[2,2,2,1,1],[1,1]]=>[8,2]
[[2,2,1,1,1,1],[1],[1]]=>[8,1,1]
[[2,2,1,1,1,1],[2]]=>[8,2]
[[2,2,1,1,1,1],[1,1]]=>[8,2]
[[2,1,1,1,1,1,1],[1],[1]]=>[8,1,1]
[[2,1,1,1,1,1,1],[2]]=>[8,2]
[[2,1,1,1,1,1,1],[1,1]]=>[8,2]
[[1,1,1,1,1,1,1,1],[1],[1]]=>[8,1,1]
[[1,1,1,1,1,1,1,1],[1,1]]=>[8,2]
[[9],[1]]=>[9,1]
[[8,1],[1]]=>[9,1]
[[7,2],[1]]=>[9,1]
[[7,1,1],[1]]=>[9,1]
[[6,3],[1]]=>[9,1]
[[6,2,1],[1]]=>[9,1]
[[6,1,1,1],[1]]=>[9,1]
[[5,4],[1]]=>[9,1]
[[5,3,1],[1]]=>[9,1]
[[5,2,2],[1]]=>[9,1]
[[5,2,1,1],[1]]=>[9,1]
[[5,1,1,1,1],[1]]=>[9,1]
[[4,4,1],[1]]=>[9,1]
[[4,3,2],[1]]=>[9,1]
[[4,3,1,1],[1]]=>[9,1]
[[4,2,2,1],[1]]=>[9,1]
[[4,2,1,1,1],[1]]=>[9,1]
[[4,1,1,1,1,1],[1]]=>[9,1]
[[3,3,3],[1]]=>[9,1]
[[3,3,2,1],[1]]=>[9,1]
[[3,3,1,1,1],[1]]=>[9,1]
[[3,2,2,2],[1]]=>[9,1]
[[3,2,2,1,1],[1]]=>[9,1]
[[3,2,1,1,1,1],[1]]=>[9,1]
[[3,1,1,1,1,1,1],[1]]=>[9,1]
[[2,2,2,2,1],[1]]=>[9,1]
[[2,2,2,1,1,1],[1]]=>[9,1]
[[2,2,1,1,1,1,1],[1]]=>[9,1]
[[2,1,1,1,1,1,1,1],[1]]=>[9,1]
[[1,1,1,1,1,1,1,1,1],[1]]=>[9,1]
[[10]]=>[10]
[[9,1]]=>[10]
[[8,2]]=>[10]
[[8,1,1]]=>[10]
[[7,3]]=>[10]
[[7,2,1]]=>[10]
[[7,1,1,1]]=>[10]
[[6,4]]=>[10]
[[6,3,1]]=>[10]
[[6,2,2]]=>[10]
[[6,2,1,1]]=>[10]
[[6,1,1,1,1]]=>[10]
[[5,5]]=>[10]
[[5,4,1]]=>[10]
[[5,3,2]]=>[10]
[[5,3,1,1]]=>[10]
[[5,2,2,1]]=>[10]
[[5,2,1,1,1]]=>[10]
[[5,1,1,1,1,1]]=>[10]
[[4,4,2]]=>[10]
[[4,4,1,1]]=>[10]
[[4,3,3]]=>[10]
[[4,3,2,1]]=>[10]
[[4,3,1,1,1]]=>[10]
[[4,2,2,2]]=>[10]
[[4,2,2,1,1]]=>[10]
[[4,2,1,1,1,1]]=>[10]
[[4,1,1,1,1,1,1]]=>[10]
[[3,3,3,1]]=>[10]
[[3,3,2,2]]=>[10]
[[3,3,2,1,1]]=>[10]
[[3,3,1,1,1,1]]=>[10]
[[3,2,2,2,1]]=>[10]
[[3,2,2,1,1,1]]=>[10]
[[3,2,1,1,1,1,1]]=>[10]
[[3,1,1,1,1,1,1,1]]=>[10]
[[2,2,2,2,2]]=>[10]
[[2,2,2,2,1,1]]=>[10]
[[2,2,2,1,1,1,1]]=>[10]
[[2,2,1,1,1,1,1,1]]=>[10]
[[2,1,1,1,1,1,1,1,1]]=>[10]
[[1,1,1,1,1,1,1,1,1,1]]=>[10]
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Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
Properties
graded
Sage code
def mapping(p): return Partition(sum(row) for row in p)
Weight
40
Created
Aug 28, 2023 at 10:00 by Martin Rubey
Updated
Aug 28, 2023 at 10:00 by Martin Rubey
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