Identifier
Images
=>
Cc0028;cc-rep-0Cc0002;cc-rep-1
[[1],[]]=>[1]
[[2],[]]=>[2]
[[1,1],[]]=>[1,1]
[[2,1],[1]]=>[2]
[[3],[]]=>[3]
[[2,1],[]]=>[2,1]
[[3,1],[1]]=>[3]
[[2,2],[1]]=>[2,1]
[[3,2],[2]]=>[3]
[[1,1,1],[]]=>[1,1,1]
[[2,2,1],[1,1]]=>[2,1]
[[2,1,1],[1]]=>[2,1]
[[3,2,1],[2,1]]=>[3]
[[4],[]]=>[4]
[[3,1],[]]=>[3,1]
[[4,1],[1]]=>[4]
[[2,2],[]]=>[2,2]
[[3,2],[1]]=>[3,1]
[[4,2],[2]]=>[4]
[[2,1,1],[]]=>[2,1,1]
[[3,2,1],[1,1]]=>[3,1]
[[3,1,1],[1]]=>[3,1]
[[4,2,1],[2,1]]=>[4]
[[3,3],[2]]=>[3,1]
[[4,3],[3]]=>[4]
[[2,2,1],[1]]=>[2,2]
[[3,3,1],[2,1]]=>[3,1]
[[3,2,1],[2]]=>[3,1]
[[4,3,1],[3,1]]=>[4]
[[2,2,2],[1,1]]=>[2,1,1]
[[3,3,2],[2,2]]=>[3,1]
[[3,2,2],[2,1]]=>[3,1]
[[4,3,2],[3,2]]=>[4]
[[1,1,1,1],[]]=>[1,1,1,1]
[[2,2,2,1],[1,1,1]]=>[2,1,1]
[[2,2,1,1],[1,1]]=>[2,2]
[[3,3,2,1],[2,2,1]]=>[3,1]
[[2,1,1,1],[1]]=>[2,1,1]
[[3,2,2,1],[2,1,1]]=>[3,1]
[[3,2,1,1],[2,1]]=>[3,1]
[[4,3,2,1],[3,2,1]]=>[4]
[[5],[]]=>[5]
[[4,1],[]]=>[4,1]
[[5,1],[1]]=>[5]
[[3,2],[]]=>[3,2]
[[4,2],[1]]=>[4,1]
[[5,2],[2]]=>[5]
[[3,1,1],[]]=>[3,1,1]
[[4,2,1],[1,1]]=>[4,1]
[[4,1,1],[1]]=>[4,1]
[[5,2,1],[2,1]]=>[5]
[[3,3],[1]]=>[3,2]
[[4,3],[2]]=>[4,1]
[[5,3],[3]]=>[5]
[[2,2,1],[]]=>[2,2,1]
[[3,3,1],[1,1]]=>[3,2]
[[3,2,1],[1]]=>[3,2]
[[4,3,1],[2,1]]=>[4,1]
[[4,2,1],[2]]=>[4,1]
[[5,3,1],[3,1]]=>[5]
[[3,2,2],[1,1]]=>[3,1,1]
[[4,3,2],[2,2]]=>[4,1]
[[4,2,2],[2,1]]=>[4,1]
[[5,3,2],[3,2]]=>[5]
[[2,1,1,1],[]]=>[2,1,1,1]
[[3,2,2,1],[1,1,1]]=>[3,1,1]
[[3,2,1,1],[1,1]]=>[3,2]
[[4,3,2,1],[2,2,1]]=>[4,1]
[[3,1,1,1],[1]]=>[3,1,1]
[[4,2,2,1],[2,1,1]]=>[4,1]
[[4,2,1,1],[2,1]]=>[4,1]
[[5,3,2,1],[3,2,1]]=>[5]
[[4,4],[3]]=>[4,1]
[[5,4],[4]]=>[5]
[[3,3,1],[2]]=>[3,2]
[[4,4,1],[3,1]]=>[4,1]
[[4,3,1],[3]]=>[4,1]
[[5,4,1],[4,1]]=>[5]
[[2,2,2],[1]]=>[2,2,1]
[[3,3,2],[2,1]]=>[3,2]
[[4,4,2],[3,2]]=>[4,1]
[[3,2,2],[2]]=>[3,2]
[[4,3,2],[3,1]]=>[4,1]
[[5,4,2],[4,2]]=>[5]
[[2,2,1,1],[1]]=>[2,2,1]
[[3,3,2,1],[2,1,1]]=>[3,2]
[[3,3,1,1],[2,1]]=>[3,2]
[[4,4,2,1],[3,2,1]]=>[4,1]
[[3,2,1,1],[2]]=>[3,1,1]
[[4,3,2,1],[3,1,1]]=>[4,1]
[[4,3,1,1],[3,1]]=>[4,1]
[[5,4,2,1],[4,2,1]]=>[5]
[[3,3,3],[2,2]]=>[3,1,1]
[[4,4,3],[3,3]]=>[4,1]
[[4,3,3],[3,2]]=>[4,1]
[[5,4,3],[4,3]]=>[5]
[[2,2,2,1],[1,1]]=>[2,2,1]
[[3,3,3,1],[2,2,1]]=>[3,1,1]
[[3,3,2,1],[2,2]]=>[3,2]
[[4,4,3,1],[3,3,1]]=>[4,1]
[[3,2,2,1],[2,1]]=>[3,2]
[[4,3,3,1],[3,2,1]]=>[4,1]
[[4,3,2,1],[3,2]]=>[4,1]
[[5,4,3,1],[4,3,1]]=>[5]
[[2,2,2,2],[1,1,1]]=>[2,1,1,1]
[[3,3,3,2],[2,2,2]]=>[3,1,1]
[[3,3,2,2],[2,2,1]]=>[3,2]
[[4,4,3,2],[3,3,2]]=>[4,1]
[[3,2,2,2],[2,1,1]]=>[3,1,1]
[[4,3,3,2],[3,2,2]]=>[4,1]
[[4,3,2,2],[3,2,1]]=>[4,1]
[[5,4,3,2],[4,3,2]]=>[5]
[[1,1,1,1,1],[]]=>[1,1,1,1,1]
[[2,2,2,2,1],[1,1,1,1]]=>[2,1,1,1]
[[2,2,2,1,1],[1,1,1]]=>[2,2,1]
[[3,3,3,2,1],[2,2,2,1]]=>[3,1,1]
[[2,2,1,1,1],[1,1]]=>[2,2,1]
[[3,3,2,2,1],[2,2,1,1]]=>[3,2]
[[3,3,2,1,1],[2,2,1]]=>[3,2]
[[4,4,3,2,1],[3,3,2,1]]=>[4,1]
[[2,1,1,1,1],[1]]=>[2,1,1,1]
[[3,2,2,2,1],[2,1,1,1]]=>[3,1,1]
[[3,2,2,1,1],[2,1,1]]=>[3,2]
[[4,3,3,2,1],[3,2,2,1]]=>[4,1]
[[3,2,1,1,1],[2,1]]=>[3,1,1]
[[4,3,2,2,1],[3,2,1,1]]=>[4,1]
[[4,3,2,1,1],[3,2,1]]=>[4,1]
[[5,4,3,2,1],[4,3,2,1]]=>[5]
[[6],[]]=>[6]
[[5,1],[]]=>[5,1]
[[6,1],[1]]=>[6]
[[4,2],[]]=>[4,2]
[[5,2],[1]]=>[5,1]
[[6,2],[2]]=>[6]
[[4,1,1],[]]=>[4,1,1]
[[5,2,1],[1,1]]=>[5,1]
[[5,1,1],[1]]=>[5,1]
[[6,2,1],[2,1]]=>[6]
[[3,3],[]]=>[3,3]
[[4,3],[1]]=>[4,2]
[[5,3],[2]]=>[5,1]
[[6,3],[3]]=>[6]
[[3,2,1],[]]=>[3,2,1]
[[4,3,1],[1,1]]=>[4,2]
[[4,2,1],[1]]=>[4,2]
[[5,3,1],[2,1]]=>[5,1]
[[5,2,1],[2]]=>[5,1]
[[6,3,1],[3,1]]=>[6]
[[4,2,2],[1,1]]=>[4,1,1]
[[5,3,2],[2,2]]=>[5,1]
[[5,2,2],[2,1]]=>[5,1]
[[6,3,2],[3,2]]=>[6]
[[3,1,1,1],[]]=>[3,1,1,1]
[[4,2,2,1],[1,1,1]]=>[4,1,1]
[[4,2,1,1],[1,1]]=>[4,2]
[[5,3,2,1],[2,2,1]]=>[5,1]
[[4,1,1,1],[1]]=>[4,1,1]
[[5,2,2,1],[2,1,1]]=>[5,1]
[[5,2,1,1],[2,1]]=>[5,1]
[[6,3,2,1],[3,2,1]]=>[6]
[[4,4],[2]]=>[4,2]
[[5,4],[3]]=>[5,1]
[[6,4],[4]]=>[6]
[[3,3,1],[1]]=>[3,3]
[[4,4,1],[2,1]]=>[4,2]
[[4,3,1],[2]]=>[4,2]
[[5,4,1],[3,1]]=>[5,1]
[[5,3,1],[3]]=>[5,1]
[[6,4,1],[4,1]]=>[6]
[[2,2,2],[]]=>[2,2,2]
[[3,3,2],[1,1]]=>[3,2,1]
[[4,4,2],[2,2]]=>[4,2]
[[3,2,2],[1]]=>[3,2,1]
[[4,3,2],[2,1]]=>[4,2]
[[5,4,2],[3,2]]=>[5,1]
[[4,2,2],[2]]=>[4,2]
[[5,3,2],[3,1]]=>[5,1]
[[6,4,2],[4,2]]=>[6]
[[2,2,1,1],[]]=>[2,2,1,1]
[[3,3,2,1],[1,1,1]]=>[3,2,1]
[[3,3,1,1],[1,1]]=>[3,3]
[[4,4,2,1],[2,2,1]]=>[4,2]
[[3,2,1,1],[1]]=>[3,2,1]
[[4,3,2,1],[2,1,1]]=>[4,2]
[[4,3,1,1],[2,1]]=>[4,2]
[[5,4,2,1],[3,2,1]]=>[5,1]
[[4,2,1,1],[2]]=>[4,1,1]
[[5,3,2,1],[3,1,1]]=>[5,1]
[[5,3,1,1],[3,1]]=>[5,1]
[[6,4,2,1],[4,2,1]]=>[6]
[[4,3,3],[2,2]]=>[4,1,1]
[[5,4,3],[3,3]]=>[5,1]
[[5,3,3],[3,2]]=>[5,1]
[[6,4,3],[4,3]]=>[6]
[[3,2,2,1],[1,1]]=>[3,2,1]
[[4,3,3,1],[2,2,1]]=>[4,1,1]
[[4,3,2,1],[2,2]]=>[4,2]
[[5,4,3,1],[3,3,1]]=>[5,1]
[[4,2,2,1],[2,1]]=>[4,2]
[[5,3,3,1],[3,2,1]]=>[5,1]
[[5,3,2,1],[3,2]]=>[5,1]
[[6,4,3,1],[4,3,1]]=>[6]
[[3,2,2,2],[1,1,1]]=>[3,1,1,1]
[[4,3,3,2],[2,2,2]]=>[4,1,1]
[[4,3,2,2],[2,2,1]]=>[4,2]
[[5,4,3,2],[3,3,2]]=>[5,1]
[[4,2,2,2],[2,1,1]]=>[4,1,1]
[[5,3,3,2],[3,2,2]]=>[5,1]
[[5,3,2,2],[3,2,1]]=>[5,1]
[[6,4,3,2],[4,3,2]]=>[6]
[[2,1,1,1,1],[]]=>[2,1,1,1,1]
[[3,2,2,2,1],[1,1,1,1]]=>[3,1,1,1]
[[3,2,2,1,1],[1,1,1]]=>[3,2,1]
[[4,3,3,2,1],[2,2,2,1]]=>[4,1,1]
[[3,2,1,1,1],[1,1]]=>[3,2,1]
[[4,3,2,2,1],[2,2,1,1]]=>[4,2]
[[4,3,2,1,1],[2,2,1]]=>[4,2]
[[5,4,3,2,1],[3,3,2,1]]=>[5,1]
[[3,1,1,1,1],[1]]=>[3,1,1,1]
[[4,2,2,2,1],[2,1,1,1]]=>[4,1,1]
[[4,2,2,1,1],[2,1,1]]=>[4,2]
[[5,3,3,2,1],[3,2,2,1]]=>[5,1]
[[4,2,1,1,1],[2,1]]=>[4,1,1]
[[5,3,2,2,1],[3,2,1,1]]=>[5,1]
[[5,3,2,1,1],[3,2,1]]=>[5,1]
[[6,4,3,2,1],[4,3,2,1]]=>[6]
[[5,5],[4]]=>[5,1]
[[6,5],[5]]=>[6]
[[4,4,1],[3]]=>[4,2]
[[5,5,1],[4,1]]=>[5,1]
[[5,4,1],[4]]=>[5,1]
[[6,5,1],[5,1]]=>[6]
[[3,3,2],[2]]=>[3,3]
[[4,4,2],[3,1]]=>[4,2]
[[5,5,2],[4,2]]=>[5,1]
[[4,3,2],[3]]=>[4,2]
[[5,4,2],[4,1]]=>[5,1]
[[6,5,2],[5,2]]=>[6]
[[3,3,1,1],[2]]=>[3,2,1]
[[4,4,2,1],[3,1,1]]=>[4,2]
[[4,4,1,1],[3,1]]=>[4,2]
[[5,5,2,1],[4,2,1]]=>[5,1]
[[4,3,1,1],[3]]=>[4,1,1]
[[5,4,2,1],[4,1,1]]=>[5,1]
[[5,4,1,1],[4,1]]=>[5,1]
[[6,5,2,1],[5,2,1]]=>[6]
[[3,3,3],[2,1]]=>[3,2,1]
[[4,4,3],[3,2]]=>[4,2]
[[5,5,3],[4,3]]=>[5,1]
[[4,3,3],[3,1]]=>[4,2]
[[5,4,3],[4,2]]=>[5,1]
[[6,5,3],[5,3]]=>[6]
[[2,2,2,1],[1]]=>[2,2,2]
[[3,3,3,1],[2,1,1]]=>[3,2,1]
[[3,3,2,1],[2,1]]=>[3,3]
[[4,4,3,1],[3,2,1]]=>[4,2]
[[4,4,2,1],[3,2]]=>[4,2]
[[5,5,3,1],[4,3,1]]=>[5,1]
[[3,2,2,1],[2]]=>[3,2,1]
[[4,3,3,1],[3,1,1]]=>[4,2]
[[4,3,2,1],[3,1]]=>[4,2]
[[5,4,3,1],[4,2,1]]=>[5,1]
[[5,4,2,1],[4,2]]=>[5,1]
[[6,5,3,1],[5,3,1]]=>[6]
[[3,3,2,2],[2,1,1]]=>[3,2,1]
[[4,4,3,2],[3,2,2]]=>[4,2]
[[4,4,2,2],[3,2,1]]=>[4,2]
[[5,5,3,2],[4,3,2]]=>[5,1]
[[4,3,2,2],[3,1,1]]=>[4,1,1]
[[5,4,3,2],[4,2,2]]=>[5,1]
[[5,4,2,2],[4,2,1]]=>[5,1]
[[6,5,3,2],[5,3,2]]=>[6]
[[2,2,1,1,1],[1]]=>[2,2,1,1]
[[3,3,2,2,1],[2,1,1,1]]=>[3,2,1]
[[3,3,2,1,1],[2,1,1]]=>[3,3]
[[4,4,3,2,1],[3,2,2,1]]=>[4,2]
[[3,3,1,1,1],[2,1]]=>[3,2,1]
[[4,4,2,2,1],[3,2,1,1]]=>[4,2]
[[4,4,2,1,1],[3,2,1]]=>[4,2]
[[5,5,3,2,1],[4,3,2,1]]=>[5,1]
[[3,2,1,1,1],[2]]=>[3,1,1,1]
[[4,3,2,2,1],[3,1,1,1]]=>[4,1,1]
[[4,3,2,1,1],[3,1,1]]=>[4,2]
[[5,4,3,2,1],[4,2,2,1]]=>[5,1]
[[4,3,1,1,1],[3,1]]=>[4,1,1]
[[5,4,2,2,1],[4,2,1,1]]=>[5,1]
[[5,4,2,1,1],[4,2,1]]=>[5,1]
[[6,5,3,2,1],[5,3,2,1]]=>[6]
[[4,4,4],[3,3]]=>[4,1,1]
[[5,5,4],[4,4]]=>[5,1]
[[5,4,4],[4,3]]=>[5,1]
[[6,5,4],[5,4]]=>[6]
[[3,3,3,1],[2,2]]=>[3,2,1]
[[4,4,4,1],[3,3,1]]=>[4,1,1]
[[4,4,3,1],[3,3]]=>[4,2]
[[5,5,4,1],[4,4,1]]=>[5,1]
[[4,3,3,1],[3,2]]=>[4,2]
[[5,4,4,1],[4,3,1]]=>[5,1]
[[5,4,3,1],[4,3]]=>[5,1]
[[6,5,4,1],[5,4,1]]=>[6]
[[2,2,2,2],[1,1]]=>[2,2,1,1]
[[3,3,3,2],[2,2,1]]=>[3,2,1]
[[4,4,4,2],[3,3,2]]=>[4,1,1]
[[3,3,2,2],[2,2]]=>[3,3]
[[4,4,3,2],[3,3,1]]=>[4,2]
[[5,5,4,2],[4,4,2]]=>[5,1]
[[3,2,2,2],[2,1]]=>[3,2,1]
[[4,3,3,2],[3,2,1]]=>[4,2]
[[5,4,4,2],[4,3,2]]=>[5,1]
[[4,3,2,2],[3,2]]=>[4,2]
[[5,4,3,2],[4,3,1]]=>[5,1]
[[6,5,4,2],[5,4,2]]=>[6]
[[2,2,2,1,1],[1,1]]=>[2,2,2]
[[3,3,3,2,1],[2,2,1,1]]=>[3,2,1]
[[3,3,3,1,1],[2,2,1]]=>[3,2,1]
[[4,4,4,2,1],[3,3,2,1]]=>[4,1,1]
[[3,3,2,1,1],[2,2]]=>[3,2,1]
[[4,4,3,2,1],[3,3,1,1]]=>[4,2]
[[4,4,3,1,1],[3,3,1]]=>[4,2]
[[5,5,4,2,1],[4,4,2,1]]=>[5,1]
[[3,2,2,1,1],[2,1]]=>[3,2,1]
[[4,3,3,2,1],[3,2,1,1]]=>[4,2]
[[4,3,3,1,1],[3,2,1]]=>[4,2]
[[5,4,4,2,1],[4,3,2,1]]=>[5,1]
[[4,3,2,1,1],[3,2]]=>[4,1,1]
[[5,4,3,2,1],[4,3,1,1]]=>[5,1]
[[5,4,3,1,1],[4,3,1]]=>[5,1]
[[6,5,4,2,1],[5,4,2,1]]=>[6]
[[3,3,3,3],[2,2,2]]=>[3,1,1,1]
[[4,4,4,3],[3,3,3]]=>[4,1,1]
[[4,4,3,3],[3,3,2]]=>[4,2]
[[5,5,4,3],[4,4,3]]=>[5,1]
[[4,3,3,3],[3,2,2]]=>[4,1,1]
[[5,4,4,3],[4,3,3]]=>[5,1]
[[5,4,3,3],[4,3,2]]=>[5,1]
[[6,5,4,3],[5,4,3]]=>[6]
[[2,2,2,2,1],[1,1,1]]=>[2,2,1,1]
[[3,3,3,3,1],[2,2,2,1]]=>[3,1,1,1]
[[3,3,3,2,1],[2,2,2]]=>[3,2,1]
[[4,4,4,3,1],[3,3,3,1]]=>[4,1,1]
[[3,3,2,2,1],[2,2,1]]=>[3,3]
[[4,4,3,3,1],[3,3,2,1]]=>[4,2]
[[4,4,3,2,1],[3,3,2]]=>[4,2]
[[5,5,4,3,1],[4,4,3,1]]=>[5,1]
[[3,2,2,2,1],[2,1,1]]=>[3,2,1]
[[4,3,3,3,1],[3,2,2,1]]=>[4,1,1]
[[4,3,3,2,1],[3,2,2]]=>[4,2]
[[5,4,4,3,1],[4,3,3,1]]=>[5,1]
[[4,3,2,2,1],[3,2,1]]=>[4,2]
[[5,4,3,3,1],[4,3,2,1]]=>[5,1]
[[5,4,3,2,1],[4,3,2]]=>[5,1]
[[6,5,4,3,1],[5,4,3,1]]=>[6]
[[2,2,2,2,2],[1,1,1,1]]=>[2,1,1,1,1]
[[3,3,3,3,2],[2,2,2,2]]=>[3,1,1,1]
[[3,3,3,2,2],[2,2,2,1]]=>[3,2,1]
[[4,4,4,3,2],[3,3,3,2]]=>[4,1,1]
[[3,3,2,2,2],[2,2,1,1]]=>[3,2,1]
[[4,4,3,3,2],[3,3,2,2]]=>[4,2]
[[4,4,3,2,2],[3,3,2,1]]=>[4,2]
[[5,5,4,3,2],[4,4,3,2]]=>[5,1]
[[3,2,2,2,2],[2,1,1,1]]=>[3,1,1,1]
[[4,3,3,3,2],[3,2,2,2]]=>[4,1,1]
[[4,3,3,2,2],[3,2,2,1]]=>[4,2]
[[5,4,4,3,2],[4,3,3,2]]=>[5,1]
[[4,3,2,2,2],[3,2,1,1]]=>[4,1,1]
[[5,4,3,3,2],[4,3,2,2]]=>[5,1]
[[5,4,3,2,2],[4,3,2,1]]=>[5,1]
[[6,5,4,3,2],[5,4,3,2]]=>[6]
[[1,1,1,1,1,1],[]]=>[1,1,1,1,1,1]
[[2,2,2,2,2,1],[1,1,1,1,1]]=>[2,1,1,1,1]
[[2,2,2,2,1,1],[1,1,1,1]]=>[2,2,1,1]
[[3,3,3,3,2,1],[2,2,2,2,1]]=>[3,1,1,1]
[[2,2,2,1,1,1],[1,1,1]]=>[2,2,2]
[[3,3,3,2,2,1],[2,2,2,1,1]]=>[3,2,1]
[[3,3,3,2,1,1],[2,2,2,1]]=>[3,2,1]
[[4,4,4,3,2,1],[3,3,3,2,1]]=>[4,1,1]
[[2,2,1,1,1,1],[1,1]]=>[2,2,1,1]
[[3,3,2,2,2,1],[2,2,1,1,1]]=>[3,2,1]
[[3,3,2,2,1,1],[2,2,1,1]]=>[3,3]
[[4,4,3,3,2,1],[3,3,2,2,1]]=>[4,2]
[[3,3,2,1,1,1],[2,2,1]]=>[3,2,1]
[[4,4,3,2,2,1],[3,3,2,1,1]]=>[4,2]
[[4,4,3,2,1,1],[3,3,2,1]]=>[4,2]
[[5,5,4,3,2,1],[4,4,3,2,1]]=>[5,1]
[[2,1,1,1,1,1],[1]]=>[2,1,1,1,1]
[[3,2,2,2,2,1],[2,1,1,1,1]]=>[3,1,1,1]
[[3,2,2,2,1,1],[2,1,1,1]]=>[3,2,1]
[[4,3,3,3,2,1],[3,2,2,2,1]]=>[4,1,1]
[[3,2,2,1,1,1],[2,1,1]]=>[3,2,1]
[[4,3,3,2,2,1],[3,2,2,1,1]]=>[4,2]
[[4,3,3,2,1,1],[3,2,2,1]]=>[4,2]
[[5,4,4,3,2,1],[4,3,3,2,1]]=>[5,1]
[[3,2,1,1,1,1],[2,1]]=>[3,1,1,1]
[[4,3,2,2,2,1],[3,2,1,1,1]]=>[4,1,1]
[[4,3,2,2,1,1],[3,2,1,1]]=>[4,2]
[[5,4,3,3,2,1],[4,3,2,2,1]]=>[5,1]
[[4,3,2,1,1,1],[3,2,1]]=>[4,1,1]
[[5,4,3,2,2,1],[4,3,2,1,1]]=>[5,1]
[[5,4,3,2,1,1],[4,3,2,1]]=>[5,1]
[[6,5,4,3,2,1],[5,4,3,2,1]]=>[6]
[[7],[]]=>[7]
[[6,1],[]]=>[6,1]
[[7,1],[1]]=>[7]
[[5,2],[]]=>[5,2]
[[6,2],[1]]=>[6,1]
[[7,2],[2]]=>[7]
[[5,1,1],[]]=>[5,1,1]
[[6,2,1],[1,1]]=>[6,1]
[[6,1,1],[1]]=>[6,1]
[[7,2,1],[2,1]]=>[7]
[[4,3],[]]=>[4,3]
[[5,3],[1]]=>[5,2]
[[6,3],[2]]=>[6,1]
[[7,3],[3]]=>[7]
[[4,2,1],[]]=>[4,2,1]
[[5,3,1],[1,1]]=>[5,2]
[[5,2,1],[1]]=>[5,2]
[[6,3,1],[2,1]]=>[6,1]
[[6,2,1],[2]]=>[6,1]
[[7,3,1],[3,1]]=>[7]
[[5,2,2],[1,1]]=>[5,1,1]
[[6,3,2],[2,2]]=>[6,1]
[[6,2,2],[2,1]]=>[6,1]
[[7,3,2],[3,2]]=>[7]
[[4,1,1,1],[]]=>[4,1,1,1]
[[5,2,2,1],[1,1,1]]=>[5,1,1]
[[5,2,1,1],[1,1]]=>[5,2]
[[6,3,2,1],[2,2,1]]=>[6,1]
[[5,1,1,1],[1]]=>[5,1,1]
[[6,2,2,1],[2,1,1]]=>[6,1]
[[6,2,1,1],[2,1]]=>[6,1]
[[7,3,2,1],[3,2,1]]=>[7]
[[4,4],[1]]=>[4,3]
[[5,4],[2]]=>[5,2]
[[6,4],[3]]=>[6,1]
[[7,4],[4]]=>[7]
[[3,3,1],[]]=>[3,3,1]
[[4,4,1],[1,1]]=>[4,3]
[[4,3,1],[1]]=>[4,3]
[[5,4,1],[2,1]]=>[5,2]
[[5,3,1],[2]]=>[5,2]
[[6,4,1],[3,1]]=>[6,1]
[[6,3,1],[3]]=>[6,1]
[[7,4,1],[4,1]]=>[7]
[[3,2,2],[]]=>[3,2,2]
[[4,3,2],[1,1]]=>[4,2,1]
[[5,4,2],[2,2]]=>[5,2]
[[4,2,2],[1]]=>[4,2,1]
[[5,3,2],[2,1]]=>[5,2]
[[6,4,2],[3,2]]=>[6,1]
[[5,2,2],[2]]=>[5,2]
[[6,3,2],[3,1]]=>[6,1]
[[7,4,2],[4,2]]=>[7]
[[3,2,1,1],[]]=>[3,2,1,1]
[[4,3,2,1],[1,1,1]]=>[4,2,1]
[[4,3,1,1],[1,1]]=>[4,3]
[[5,4,2,1],[2,2,1]]=>[5,2]
[[4,2,1,1],[1]]=>[4,2,1]
[[5,3,2,1],[2,1,1]]=>[5,2]
[[5,3,1,1],[2,1]]=>[5,2]
[[6,4,2,1],[3,2,1]]=>[6,1]
[[5,2,1,1],[2]]=>[5,1,1]
[[6,3,2,1],[3,1,1]]=>[6,1]
[[6,3,1,1],[3,1]]=>[6,1]
[[7,4,2,1],[4,2,1]]=>[7]
[[5,3,3],[2,2]]=>[5,1,1]
[[6,4,3],[3,3]]=>[6,1]
[[6,3,3],[3,2]]=>[6,1]
[[7,4,3],[4,3]]=>[7]
[[4,2,2,1],[1,1]]=>[4,2,1]
[[5,3,3,1],[2,2,1]]=>[5,1,1]
[[5,3,2,1],[2,2]]=>[5,2]
[[6,4,3,1],[3,3,1]]=>[6,1]
[[5,2,2,1],[2,1]]=>[5,2]
[[6,3,3,1],[3,2,1]]=>[6,1]
[[6,3,2,1],[3,2]]=>[6,1]
[[7,4,3,1],[4,3,1]]=>[7]
[[4,2,2,2],[1,1,1]]=>[4,1,1,1]
[[5,3,3,2],[2,2,2]]=>[5,1,1]
[[5,3,2,2],[2,2,1]]=>[5,2]
[[6,4,3,2],[3,3,2]]=>[6,1]
[[5,2,2,2],[2,1,1]]=>[5,1,1]
[[6,3,3,2],[3,2,2]]=>[6,1]
[[6,3,2,2],[3,2,1]]=>[6,1]
[[7,4,3,2],[4,3,2]]=>[7]
[[3,1,1,1,1],[]]=>[3,1,1,1,1]
[[4,2,2,2,1],[1,1,1,1]]=>[4,1,1,1]
[[4,2,2,1,1],[1,1,1]]=>[4,2,1]
[[5,3,3,2,1],[2,2,2,1]]=>[5,1,1]
[[4,2,1,1,1],[1,1]]=>[4,2,1]
[[5,3,2,2,1],[2,2,1,1]]=>[5,2]
[[5,3,2,1,1],[2,2,1]]=>[5,2]
[[6,4,3,2,1],[3,3,2,1]]=>[6,1]
[[4,1,1,1,1],[1]]=>[4,1,1,1]
[[5,2,2,2,1],[2,1,1,1]]=>[5,1,1]
[[5,2,2,1,1],[2,1,1]]=>[5,2]
[[6,3,3,2,1],[3,2,2,1]]=>[6,1]
[[5,2,1,1,1],[2,1]]=>[5,1,1]
[[6,3,2,2,1],[3,2,1,1]]=>[6,1]
[[6,3,2,1,1],[3,2,1]]=>[6,1]
[[7,4,3,2,1],[4,3,2,1]]=>[7]
[[5,5],[3]]=>[5,2]
[[6,5],[4]]=>[6,1]
[[7,5],[5]]=>[7]
[[4,4,1],[2]]=>[4,3]
[[5,5,1],[3,1]]=>[5,2]
[[5,4,1],[3]]=>[5,2]
[[6,5,1],[4,1]]=>[6,1]
[[6,4,1],[4]]=>[6,1]
[[7,5,1],[5,1]]=>[7]
[[3,3,2],[1]]=>[3,3,1]
[[4,4,2],[2,1]]=>[4,3]
[[5,5,2],[3,2]]=>[5,2]
[[4,3,2],[2]]=>[4,3]
[[5,4,2],[3,1]]=>[5,2]
[[6,5,2],[4,2]]=>[6,1]
[[5,3,2],[3]]=>[5,2]
[[6,4,2],[4,1]]=>[6,1]
[[7,5,2],[5,2]]=>[7]
[[3,3,1,1],[1]]=>[3,3,1]
[[4,4,2,1],[2,1,1]]=>[4,3]
[[4,4,1,1],[2,1]]=>[4,3]
[[5,5,2,1],[3,2,1]]=>[5,2]
[[4,3,1,1],[2]]=>[4,2,1]
[[5,4,2,1],[3,1,1]]=>[5,2]
[[5,4,1,1],[3,1]]=>[5,2]
[[6,5,2,1],[4,2,1]]=>[6,1]
[[5,3,1,1],[3]]=>[5,1,1]
[[6,4,2,1],[4,1,1]]=>[6,1]
[[6,4,1,1],[4,1]]=>[6,1]
[[7,5,2,1],[5,2,1]]=>[7]
[[3,3,3],[1,1]]=>[3,2,2]
[[4,4,3],[2,2]]=>[4,2,1]
[[5,5,3],[3,3]]=>[5,2]
[[4,3,3],[2,1]]=>[4,2,1]
[[5,4,3],[3,2]]=>[5,2]
[[6,5,3],[4,3]]=>[6,1]
[[5,3,3],[3,1]]=>[5,2]
[[6,4,3],[4,2]]=>[6,1]
[[7,5,3],[5,3]]=>[7]
[[2,2,2,1],[]]=>[2,2,2,1]
[[3,3,3,1],[1,1,1]]=>[3,2,2]
[[3,3,2,1],[1,1]]=>[3,3,1]
[[4,4,3,1],[2,2,1]]=>[4,2,1]
[[4,4,2,1],[2,2]]=>[4,3]
[[5,5,3,1],[3,3,1]]=>[5,2]
[[3,2,2,1],[1]]=>[3,2,2]
[[4,3,3,1],[2,1,1]]=>[4,2,1]
[[4,3,2,1],[2,1]]=>[4,3]
[[5,4,3,1],[3,2,1]]=>[5,2]
[[5,4,2,1],[3,2]]=>[5,2]
[[6,5,3,1],[4,3,1]]=>[6,1]
[[4,2,2,1],[2]]=>[4,2,1]
[[5,3,3,1],[3,1,1]]=>[5,2]
[[5,3,2,1],[3,1]]=>[5,2]
[[6,4,3,1],[4,2,1]]=>[6,1]
[[6,4,2,1],[4,2]]=>[6,1]
[[7,5,3,1],[5,3,1]]=>[7]
[[3,3,2,2],[1,1,1]]=>[3,2,1,1]
[[4,4,3,2],[2,2,2]]=>[4,2,1]
[[4,4,2,2],[2,2,1]]=>[4,3]
[[5,5,3,2],[3,3,2]]=>[5,2]
[[4,3,2,2],[2,1,1]]=>[4,2,1]
[[5,4,3,2],[3,2,2]]=>[5,2]
[[5,4,2,2],[3,2,1]]=>[5,2]
[[6,5,3,2],[4,3,2]]=>[6,1]
[[5,3,2,2],[3,1,1]]=>[5,1,1]
[[6,4,3,2],[4,2,2]]=>[6,1]
[[6,4,2,2],[4,2,1]]=>[6,1]
[[7,5,3,2],[5,3,2]]=>[7]
[[2,2,1,1,1],[]]=>[2,2,1,1,1]
[[3,3,2,2,1],[1,1,1,1]]=>[3,2,1,1]
[[3,3,2,1,1],[1,1,1]]=>[3,3,1]
[[4,4,3,2,1],[2,2,2,1]]=>[4,2,1]
[[3,3,1,1,1],[1,1]]=>[3,3,1]
[[4,4,2,2,1],[2,2,1,1]]=>[4,3]
[[4,4,2,1,1],[2,2,1]]=>[4,3]
[[5,5,3,2,1],[3,3,2,1]]=>[5,2]
[[3,2,1,1,1],[1]]=>[3,2,1,1]
[[4,3,2,2,1],[2,1,1,1]]=>[4,2,1]
[[4,3,2,1,1],[2,1,1]]=>[4,3]
[[5,4,3,2,1],[3,2,2,1]]=>[5,2]
[[4,3,1,1,1],[2,1]]=>[4,2,1]
[[5,4,2,2,1],[3,2,1,1]]=>[5,2]
[[5,4,2,1,1],[3,2,1]]=>[5,2]
[[6,5,3,2,1],[4,3,2,1]]=>[6,1]
[[4,2,1,1,1],[2]]=>[4,1,1,1]
[[5,3,2,2,1],[3,1,1,1]]=>[5,1,1]
[[5,3,2,1,1],[3,1,1]]=>[5,2]
[[6,4,3,2,1],[4,2,2,1]]=>[6,1]
[[5,3,1,1,1],[3,1]]=>[5,1,1]
[[6,4,2,2,1],[4,2,1,1]]=>[6,1]
[[6,4,2,1,1],[4,2,1]]=>[6,1]
[[7,5,3,2,1],[5,3,2,1]]=>[7]
[[5,4,4],[3,3]]=>[5,1,1]
[[6,5,4],[4,4]]=>[6,1]
[[6,4,4],[4,3]]=>[6,1]
[[7,5,4],[5,4]]=>[7]
[[4,3,3,1],[2,2]]=>[4,2,1]
[[5,4,4,1],[3,3,1]]=>[5,1,1]
[[5,4,3,1],[3,3]]=>[5,2]
[[6,5,4,1],[4,4,1]]=>[6,1]
[[5,3,3,1],[3,2]]=>[5,2]
[[6,4,4,1],[4,3,1]]=>[6,1]
[[6,4,3,1],[4,3]]=>[6,1]
[[7,5,4,1],[5,4,1]]=>[7]
[[3,2,2,2],[1,1]]=>[3,2,1,1]
[[4,3,3,2],[2,2,1]]=>[4,2,1]
[[5,4,4,2],[3,3,2]]=>[5,1,1]
[[4,3,2,2],[2,2]]=>[4,3]
[[5,4,3,2],[3,3,1]]=>[5,2]
[[6,5,4,2],[4,4,2]]=>[6,1]
[[4,2,2,2],[2,1]]=>[4,2,1]
[[5,3,3,2],[3,2,1]]=>[5,2]
[[6,4,4,2],[4,3,2]]=>[6,1]
[[5,3,2,2],[3,2]]=>[5,2]
[[6,4,3,2],[4,3,1]]=>[6,1]
[[7,5,4,2],[5,4,2]]=>[7]
[[3,2,2,1,1],[1,1]]=>[3,2,2]
[[4,3,3,2,1],[2,2,1,1]]=>[4,2,1]
[[4,3,3,1,1],[2,2,1]]=>[4,2,1]
[[5,4,4,2,1],[3,3,2,1]]=>[5,1,1]
[[4,3,2,1,1],[2,2]]=>[4,2,1]
[[5,4,3,2,1],[3,3,1,1]]=>[5,2]
[[5,4,3,1,1],[3,3,1]]=>[5,2]
[[6,5,4,2,1],[4,4,2,1]]=>[6,1]
[[4,2,2,1,1],[2,1]]=>[4,2,1]
[[5,3,3,2,1],[3,2,1,1]]=>[5,2]
[[5,3,3,1,1],[3,2,1]]=>[5,2]
[[6,4,4,2,1],[4,3,2,1]]=>[6,1]
[[5,3,2,1,1],[3,2]]=>[5,1,1]
[[6,4,3,2,1],[4,3,1,1]]=>[6,1]
[[6,4,3,1,1],[4,3,1]]=>[6,1]
[[7,5,4,2,1],[5,4,2,1]]=>[7]
[[4,3,3,3],[2,2,2]]=>[4,1,1,1]
[[5,4,4,3],[3,3,3]]=>[5,1,1]
[[5,4,3,3],[3,3,2]]=>[5,2]
[[6,5,4,3],[4,4,3]]=>[6,1]
[[5,3,3,3],[3,2,2]]=>[5,1,1]
[[6,4,4,3],[4,3,3]]=>[6,1]
[[6,4,3,3],[4,3,2]]=>[6,1]
[[7,5,4,3],[5,4,3]]=>[7]
[[3,2,2,2,1],[1,1,1]]=>[3,2,1,1]
[[4,3,3,3,1],[2,2,2,1]]=>[4,1,1,1]
[[4,3,3,2,1],[2,2,2]]=>[4,2,1]
[[5,4,4,3,1],[3,3,3,1]]=>[5,1,1]
[[4,3,2,2,1],[2,2,1]]=>[4,3]
[[5,4,3,3,1],[3,3,2,1]]=>[5,2]
[[5,4,3,2,1],[3,3,2]]=>[5,2]
[[6,5,4,3,1],[4,4,3,1]]=>[6,1]
[[4,2,2,2,1],[2,1,1]]=>[4,2,1]
[[5,3,3,3,1],[3,2,2,1]]=>[5,1,1]
[[5,3,3,2,1],[3,2,2]]=>[5,2]
[[6,4,4,3,1],[4,3,3,1]]=>[6,1]
[[5,3,2,2,1],[3,2,1]]=>[5,2]
[[6,4,3,3,1],[4,3,2,1]]=>[6,1]
[[6,4,3,2,1],[4,3,2]]=>[6,1]
[[7,5,4,3,1],[5,4,3,1]]=>[7]
[[3,2,2,2,2],[1,1,1,1]]=>[3,1,1,1,1]
[[4,3,3,3,2],[2,2,2,2]]=>[4,1,1,1]
[[4,3,3,2,2],[2,2,2,1]]=>[4,2,1]
[[5,4,4,3,2],[3,3,3,2]]=>[5,1,1]
[[4,3,2,2,2],[2,2,1,1]]=>[4,2,1]
[[5,4,3,3,2],[3,3,2,2]]=>[5,2]
[[5,4,3,2,2],[3,3,2,1]]=>[5,2]
[[6,5,4,3,2],[4,4,3,2]]=>[6,1]
[[4,2,2,2,2],[2,1,1,1]]=>[4,1,1,1]
[[5,3,3,3,2],[3,2,2,2]]=>[5,1,1]
[[5,3,3,2,2],[3,2,2,1]]=>[5,2]
[[6,4,4,3,2],[4,3,3,2]]=>[6,1]
[[5,3,2,2,2],[3,2,1,1]]=>[5,1,1]
[[6,4,3,3,2],[4,3,2,2]]=>[6,1]
[[6,4,3,2,2],[4,3,2,1]]=>[6,1]
[[7,5,4,3,2],[5,4,3,2]]=>[7]
[[2,1,1,1,1,1],[]]=>[2,1,1,1,1,1]
[[3,2,2,2,2,1],[1,1,1,1,1]]=>[3,1,1,1,1]
[[3,2,2,2,1,1],[1,1,1,1]]=>[3,2,1,1]
[[4,3,3,3,2,1],[2,2,2,2,1]]=>[4,1,1,1]
[[3,2,2,1,1,1],[1,1,1]]=>[3,2,2]
[[4,3,3,2,2,1],[2,2,2,1,1]]=>[4,2,1]
[[4,3,3,2,1,1],[2,2,2,1]]=>[4,2,1]
[[5,4,4,3,2,1],[3,3,3,2,1]]=>[5,1,1]
[[3,2,1,1,1,1],[1,1]]=>[3,2,1,1]
[[4,3,2,2,2,1],[2,2,1,1,1]]=>[4,2,1]
[[4,3,2,2,1,1],[2,2,1,1]]=>[4,3]
[[5,4,3,3,2,1],[3,3,2,2,1]]=>[5,2]
[[4,3,2,1,1,1],[2,2,1]]=>[4,2,1]
[[5,4,3,2,2,1],[3,3,2,1,1]]=>[5,2]
[[5,4,3,2,1,1],[3,3,2,1]]=>[5,2]
[[6,5,4,3,2,1],[4,4,3,2,1]]=>[6,1]
[[3,1,1,1,1,1],[1]]=>[3,1,1,1,1]
[[4,2,2,2,2,1],[2,1,1,1,1]]=>[4,1,1,1]
[[4,2,2,2,1,1],[2,1,1,1]]=>[4,2,1]
[[5,3,3,3,2,1],[3,2,2,2,1]]=>[5,1,1]
[[4,2,2,1,1,1],[2,1,1]]=>[4,2,1]
[[5,3,3,2,2,1],[3,2,2,1,1]]=>[5,2]
[[5,3,3,2,1,1],[3,2,2,1]]=>[5,2]
[[6,4,4,3,2,1],[4,3,3,2,1]]=>[6,1]
[[4,2,1,1,1,1],[2,1]]=>[4,1,1,1]
[[5,3,2,2,2,1],[3,2,1,1,1]]=>[5,1,1]
[[5,3,2,2,1,1],[3,2,1,1]]=>[5,2]
[[6,4,3,3,2,1],[4,3,2,2,1]]=>[6,1]
[[5,3,2,1,1,1],[3,2,1]]=>[5,1,1]
[[6,4,3,2,2,1],[4,3,2,1,1]]=>[6,1]
[[6,4,3,2,1,1],[4,3,2,1]]=>[6,1]
[[7,5,4,3,2,1],[5,4,3,2,1]]=>[7]
[[6,6],[5]]=>[6,1]
[[7,6],[6]]=>[7]
[[5,5,1],[4]]=>[5,2]
[[6,6,1],[5,1]]=>[6,1]
[[6,5,1],[5]]=>[6,1]
[[7,6,1],[6,1]]=>[7]
[[4,4,2],[3]]=>[4,3]
[[5,5,2],[4,1]]=>[5,2]
[[6,6,2],[5,2]]=>[6,1]
[[5,4,2],[4]]=>[5,2]
[[6,5,2],[5,1]]=>[6,1]
[[7,6,2],[6,2]]=>[7]
[[4,4,1,1],[3]]=>[4,2,1]
[[5,5,2,1],[4,1,1]]=>[5,2]
[[5,5,1,1],[4,1]]=>[5,2]
[[6,6,2,1],[5,2,1]]=>[6,1]
[[5,4,1,1],[4]]=>[5,1,1]
[[6,5,2,1],[5,1,1]]=>[6,1]
[[6,5,1,1],[5,1]]=>[6,1]
[[7,6,2,1],[6,2,1]]=>[7]
[[3,3,3],[2]]=>[3,3,1]
[[4,4,3],[3,1]]=>[4,3]
[[5,5,3],[4,2]]=>[5,2]
[[6,6,3],[5,3]]=>[6,1]
[[4,3,3],[3]]=>[4,3]
[[5,4,3],[4,1]]=>[5,2]
[[6,5,3],[5,2]]=>[6,1]
[[7,6,3],[6,3]]=>[7]
[[3,3,2,1],[2]]=>[3,3,1]
[[4,4,3,1],[3,1,1]]=>[4,3]
[[4,4,2,1],[3,1]]=>[4,3]
[[5,5,3,1],[4,2,1]]=>[5,2]
[[5,5,2,1],[4,2]]=>[5,2]
[[6,6,3,1],[5,3,1]]=>[6,1]
[[4,3,2,1],[3]]=>[4,2,1]
[[5,4,3,1],[4,1,1]]=>[5,2]
[[5,4,2,1],[4,1]]=>[5,2]
[[6,5,3,1],[5,2,1]]=>[6,1]
[[6,5,2,1],[5,2]]=>[6,1]
[[7,6,3,1],[6,3,1]]=>[7]
[[4,4,2,2],[3,1,1]]=>[4,2,1]
[[5,5,3,2],[4,2,2]]=>[5,2]
[[5,5,2,2],[4,2,1]]=>[5,2]
[[6,6,3,2],[5,3,2]]=>[6,1]
[[5,4,2,2],[4,1,1]]=>[5,1,1]
[[6,5,3,2],[5,2,2]]=>[6,1]
[[6,5,2,2],[5,2,1]]=>[6,1]
[[7,6,3,2],[6,3,2]]=>[7]
[[3,3,1,1,1],[2]]=>[3,2,1,1]
[[4,4,2,2,1],[3,1,1,1]]=>[4,2,1]
[[4,4,2,1,1],[3,1,1]]=>[4,3]
[[5,5,3,2,1],[4,2,2,1]]=>[5,2]
[[4,4,1,1,1],[3,1]]=>[4,2,1]
[[5,5,2,2,1],[4,2,1,1]]=>[5,2]
[[5,5,2,1,1],[4,2,1]]=>[5,2]
[[6,6,3,2,1],[5,3,2,1]]=>[6,1]
[[4,3,1,1,1],[3]]=>[4,1,1,1]
[[5,4,2,2,1],[4,1,1,1]]=>[5,1,1]
[[5,4,2,1,1],[4,1,1]]=>[5,2]
[[6,5,3,2,1],[5,2,2,1]]=>[6,1]
[[5,4,1,1,1],[4,1]]=>[5,1,1]
[[6,5,2,2,1],[5,2,1,1]]=>[6,1]
[[6,5,2,1,1],[5,2,1]]=>[6,1]
[[7,6,3,2,1],[6,3,2,1]]=>[7]
[[4,4,4],[3,2]]=>[4,2,1]
[[5,5,4],[4,3]]=>[5,2]
[[6,6,4],[5,4]]=>[6,1]
[[5,4,4],[4,2]]=>[5,2]
[[6,5,4],[5,3]]=>[6,1]
[[7,6,4],[6,4]]=>[7]
[[3,3,3,1],[2,1]]=>[3,3,1]
[[4,4,4,1],[3,2,1]]=>[4,2,1]
[[4,4,3,1],[3,2]]=>[4,3]
[[5,5,4,1],[4,3,1]]=>[5,2]
[[5,5,3,1],[4,3]]=>[5,2]
[[6,6,4,1],[5,4,1]]=>[6,1]
[[4,3,3,1],[3,1]]=>[4,3]
[[5,4,4,1],[4,2,1]]=>[5,2]
[[5,4,3,1],[4,2]]=>[5,2]
[[6,5,4,1],[5,3,1]]=>[6,1]
[[6,5,3,1],[5,3]]=>[6,1]
[[7,6,4,1],[6,4,1]]=>[7]
[[2,2,2,2],[1]]=>[2,2,2,1]
[[3,3,3,2],[2,1,1]]=>[3,2,2]
[[4,4,4,2],[3,2,2]]=>[4,2,1]
[[3,3,2,2],[2,1]]=>[3,3,1]
[[4,4,3,2],[3,2,1]]=>[4,3]
[[5,5,4,2],[4,3,2]]=>[5,2]
[[4,4,2,2],[3,2]]=>[4,3]
[[5,5,3,2],[4,3,1]]=>[5,2]
[[6,6,4,2],[5,4,2]]=>[6,1]
[[3,2,2,2],[2]]=>[3,2,2]
[[4,3,3,2],[3,1,1]]=>[4,2,1]
[[5,4,4,2],[4,2,2]]=>[5,2]
[[4,3,2,2],[3,1]]=>[4,2,1]
[[5,4,3,2],[4,2,1]]=>[5,2]
[[6,5,4,2],[5,3,2]]=>[6,1]
[[5,4,2,2],[4,2]]=>[5,2]
[[6,5,3,2],[5,3,1]]=>[6,1]
[[7,6,4,2],[6,4,2]]=>[7]
[[2,2,2,1,1],[1]]=>[2,2,2,1]
[[3,3,3,2,1],[2,1,1,1]]=>[3,2,2]
[[3,3,3,1,1],[2,1,1]]=>[3,3,1]
[[4,4,4,2,1],[3,2,2,1]]=>[4,2,1]
[[3,3,2,1,1],[2,1]]=>[3,3,1]
[[4,4,3,2,1],[3,2,1,1]]=>[4,3]
[[4,4,3,1,1],[3,2,1]]=>[4,3]
[[5,5,4,2,1],[4,3,2,1]]=>[5,2]
[[4,4,2,1,1],[3,2]]=>[4,2,1]
[[5,5,3,2,1],[4,3,1,1]]=>[5,2]
[[5,5,3,1,1],[4,3,1]]=>[5,2]
[[6,6,4,2,1],[5,4,2,1]]=>[6,1]
[[3,2,2,1,1],[2]]=>[3,2,1,1]
[[4,3,3,2,1],[3,1,1,1]]=>[4,2,1]
[[4,3,3,1,1],[3,1,1]]=>[4,3]
[[5,4,4,2,1],[4,2,2,1]]=>[5,2]
[[4,3,2,1,1],[3,1]]=>[4,2,1]
[[5,4,3,2,1],[4,2,1,1]]=>[5,2]
[[5,4,3,1,1],[4,2,1]]=>[5,2]
[[6,5,4,2,1],[5,3,2,1]]=>[6,1]
[[5,4,2,1,1],[4,2]]=>[5,1,1]
[[6,5,3,2,1],[5,3,1,1]]=>[6,1]
[[6,5,3,1,1],[5,3,1]]=>[6,1]
[[7,6,4,2,1],[6,4,2,1]]=>[7]
[[4,4,3,3],[3,2,2]]=>[4,2,1]
[[5,5,4,3],[4,3,3]]=>[5,2]
[[5,5,3,3],[4,3,2]]=>[5,2]
[[6,6,4,3],[5,4,3]]=>[6,1]
[[5,4,3,3],[4,2,2]]=>[5,1,1]
[[6,5,4,3],[5,3,3]]=>[6,1]
[[6,5,3,3],[5,3,2]]=>[6,1]
[[7,6,4,3],[6,4,3]]=>[7]
[[3,3,2,2,1],[2,1,1]]=>[3,3,1]
[[4,4,3,3,1],[3,2,2,1]]=>[4,2,1]
[[4,4,3,2,1],[3,2,2]]=>[4,3]
[[5,5,4,3,1],[4,3,3,1]]=>[5,2]
[[4,4,2,2,1],[3,2,1]]=>[4,3]
[[5,5,3,3,1],[4,3,2,1]]=>[5,2]
[[5,5,3,2,1],[4,3,2]]=>[5,2]
[[6,6,4,3,1],[5,4,3,1]]=>[6,1]
[[4,3,2,2,1],[3,1,1]]=>[4,2,1]
[[5,4,3,3,1],[4,2,2,1]]=>[5,1,1]
[[5,4,3,2,1],[4,2,2]]=>[5,2]
[[6,5,4,3,1],[5,3,3,1]]=>[6,1]
[[5,4,2,2,1],[4,2,1]]=>[5,2]
[[6,5,3,3,1],[5,3,2,1]]=>[6,1]
[[6,5,3,2,1],[5,3,2]]=>[6,1]
[[7,6,4,3,1],[6,4,3,1]]=>[7]
[[3,3,2,2,2],[2,1,1,1]]=>[3,2,1,1]
[[4,4,3,3,2],[3,2,2,2]]=>[4,2,1]
[[4,4,3,2,2],[3,2,2,1]]=>[4,3]
[[5,5,4,3,2],[4,3,3,2]]=>[5,2]
[[4,4,2,2,2],[3,2,1,1]]=>[4,2,1]
[[5,5,3,3,2],[4,3,2,2]]=>[5,2]
[[5,5,3,2,2],[4,3,2,1]]=>[5,2]
[[6,6,4,3,2],[5,4,3,2]]=>[6,1]
[[4,3,2,2,2],[3,1,1,1]]=>[4,1,1,1]
[[5,4,3,3,2],[4,2,2,2]]=>[5,1,1]
[[5,4,3,2,2],[4,2,2,1]]=>[5,2]
[[6,5,4,3,2],[5,3,3,2]]=>[6,1]
[[5,4,2,2,2],[4,2,1,1]]=>[5,1,1]
[[6,5,3,3,2],[5,3,2,2]]=>[6,1]
[[6,5,3,2,2],[5,3,2,1]]=>[6,1]
[[7,6,4,3,2],[6,4,3,2]]=>[7]
[[2,2,1,1,1,1],[1]]=>[2,2,1,1,1]
[[3,3,2,2,2,1],[2,1,1,1,1]]=>[3,2,1,1]
[[3,3,2,2,1,1],[2,1,1,1]]=>[3,3,1]
[[4,4,3,3,2,1],[3,2,2,2,1]]=>[4,2,1]
[[3,3,2,1,1,1],[2,1,1]]=>[3,3,1]
[[4,4,3,2,2,1],[3,2,2,1,1]]=>[4,3]
[[4,4,3,2,1,1],[3,2,2,1]]=>[4,3]
[[5,5,4,3,2,1],[4,3,3,2,1]]=>[5,2]
[[3,3,1,1,1,1],[2,1]]=>[3,2,1,1]
[[4,4,2,2,2,1],[3,2,1,1,1]]=>[4,2,1]
[[4,4,2,2,1,1],[3,2,1,1]]=>[4,3]
[[5,5,3,3,2,1],[4,3,2,2,1]]=>[5,2]
[[4,4,2,1,1,1],[3,2,1]]=>[4,2,1]
[[5,5,3,2,2,1],[4,3,2,1,1]]=>[5,2]
[[5,5,3,2,1,1],[4,3,2,1]]=>[5,2]
[[6,6,4,3,2,1],[5,4,3,2,1]]=>[6,1]
[[3,2,1,1,1,1],[2]]=>[3,1,1,1,1]
[[4,3,2,2,2,1],[3,1,1,1,1]]=>[4,1,1,1]
[[4,3,2,2,1,1],[3,1,1,1]]=>[4,2,1]
[[5,4,3,3,2,1],[4,2,2,2,1]]=>[5,1,1]
[[4,3,2,1,1,1],[3,1,1]]=>[4,2,1]
[[5,4,3,2,2,1],[4,2,2,1,1]]=>[5,2]
[[5,4,3,2,1,1],[4,2,2,1]]=>[5,2]
[[6,5,4,3,2,1],[5,3,3,2,1]]=>[6,1]
[[4,3,1,1,1,1],[3,1]]=>[4,1,1,1]
[[5,4,2,2,2,1],[4,2,1,1,1]]=>[5,1,1]
[[5,4,2,2,1,1],[4,2,1,1]]=>[5,2]
[[6,5,3,3,2,1],[5,3,2,2,1]]=>[6,1]
[[5,4,2,1,1,1],[4,2,1]]=>[5,1,1]
[[6,5,3,2,2,1],[5,3,2,1,1]]=>[6,1]
[[6,5,3,2,1,1],[5,3,2,1]]=>[6,1]
[[7,6,4,3,2,1],[6,4,3,2,1]]=>[7]
[[5,5,5],[4,4]]=>[5,1,1]
[[6,6,5],[5,5]]=>[6,1]
[[6,5,5],[5,4]]=>[6,1]
[[7,6,5],[6,5]]=>[7]
[[4,4,4,1],[3,3]]=>[4,2,1]
[[5,5,5,1],[4,4,1]]=>[5,1,1]
[[5,5,4,1],[4,4]]=>[5,2]
[[6,6,5,1],[5,5,1]]=>[6,1]
[[5,4,4,1],[4,3]]=>[5,2]
[[6,5,5,1],[5,4,1]]=>[6,1]
[[6,5,4,1],[5,4]]=>[6,1]
[[7,6,5,1],[6,5,1]]=>[7]
[[3,3,3,2],[2,2]]=>[3,3,1]
[[4,4,4,2],[3,3,1]]=>[4,2,1]
[[5,5,5,2],[4,4,2]]=>[5,1,1]
[[4,4,3,2],[3,3]]=>[4,3]
[[5,5,4,2],[4,4,1]]=>[5,2]
[[6,6,5,2],[5,5,2]]=>[6,1]
[[4,3,3,2],[3,2]]=>[4,3]
[[5,4,4,2],[4,3,1]]=>[5,2]
[[6,5,5,2],[5,4,2]]=>[6,1]
[[5,4,3,2],[4,3]]=>[5,2]
[[6,5,4,2],[5,4,1]]=>[6,1]
[[7,6,5,2],[6,5,2]]=>[7]
[[3,3,3,1,1],[2,2]]=>[3,2,2]
[[4,4,4,2,1],[3,3,1,1]]=>[4,2,1]
[[4,4,4,1,1],[3,3,1]]=>[4,2,1]
[[5,5,5,2,1],[4,4,2,1]]=>[5,1,1]
[[4,4,3,1,1],[3,3]]=>[4,2,1]
[[5,5,4,2,1],[4,4,1,1]]=>[5,2]
[[5,5,4,1,1],[4,4,1]]=>[5,2]
[[6,6,5,2,1],[5,5,2,1]]=>[6,1]
[[4,3,3,1,1],[3,2]]=>[4,2,1]
[[5,4,4,2,1],[4,3,1,1]]=>[5,2]
[[5,4,4,1,1],[4,3,1]]=>[5,2]
[[6,5,5,2,1],[5,4,2,1]]=>[6,1]
[[5,4,3,1,1],[4,3]]=>[5,1,1]
[[6,5,4,2,1],[5,4,1,1]]=>[6,1]
[[6,5,4,1,1],[5,4,1]]=>[6,1]
[[7,6,5,2,1],[6,5,2,1]]=>[7]
[[3,3,3,3],[2,2,1]]=>[3,2,1,1]
[[4,4,4,3],[3,3,2]]=>[4,2,1]
[[5,5,5,3],[4,4,3]]=>[5,1,1]
[[4,4,3,3],[3,3,1]]=>[4,3]
[[5,5,4,3],[4,4,2]]=>[5,2]
[[6,6,5,3],[5,5,3]]=>[6,1]
[[4,3,3,3],[3,2,1]]=>[4,2,1]
[[5,4,4,3],[4,3,2]]=>[5,2]
[[6,5,5,3],[5,4,3]]=>[6,1]
[[5,4,3,3],[4,3,1]]=>[5,2]
[[6,5,4,3],[5,4,2]]=>[6,1]
[[7,6,5,3],[6,5,3]]=>[7]
[[2,2,2,2,1],[1,1]]=>[2,2,2,1]
[[3,3,3,3,1],[2,2,1,1]]=>[3,2,1,1]
[[3,3,3,2,1],[2,2,1]]=>[3,3,1]
[[4,4,4,3,1],[3,3,2,1]]=>[4,2,1]
[[4,4,4,2,1],[3,3,2]]=>[4,2,1]
[[5,5,5,3,1],[4,4,3,1]]=>[5,1,1]
[[3,3,2,2,1],[2,2]]=>[3,3,1]
[[4,4,3,3,1],[3,3,1,1]]=>[4,3]
[[4,4,3,2,1],[3,3,1]]=>[4,3]
[[5,5,4,3,1],[4,4,2,1]]=>[5,2]
[[5,5,4,2,1],[4,4,2]]=>[5,2]
[[6,6,5,3,1],[5,5,3,1]]=>[6,1]
[[3,2,2,2,1],[2,1]]=>[3,2,2]
[[4,3,3,3,1],[3,2,1,1]]=>[4,2,1]
[[4,3,3,2,1],[3,2,1]]=>[4,3]
[[5,4,4,3,1],[4,3,2,1]]=>[5,2]
[[5,4,4,2,1],[4,3,2]]=>[5,2]
[[6,5,5,3,1],[5,4,3,1]]=>[6,1]
[[4,3,2,2,1],[3,2]]=>[4,2,1]
[[5,4,3,3,1],[4,3,1,1]]=>[5,2]
[[5,4,3,2,1],[4,3,1]]=>[5,2]
[[6,5,4,3,1],[5,4,2,1]]=>[6,1]
[[6,5,4,2,1],[5,4,2]]=>[6,1]
[[7,6,5,3,1],[6,5,3,1]]=>[7]
[[3,3,3,2,2],[2,2,1,1]]=>[3,2,2]
[[4,4,4,3,2],[3,3,2,2]]=>[4,2,1]
[[4,4,4,2,2],[3,3,2,1]]=>[4,2,1]
[[5,5,5,3,2],[4,4,3,2]]=>[5,1,1]
[[4,4,3,2,2],[3,3,1,1]]=>[4,2,1]
[[5,5,4,3,2],[4,4,2,2]]=>[5,2]
[[5,5,4,2,2],[4,4,2,1]]=>[5,2]
[[6,6,5,3,2],[5,5,3,2]]=>[6,1]
[[4,3,3,2,2],[3,2,1,1]]=>[4,2,1]
[[5,4,4,3,2],[4,3,2,2]]=>[5,2]
[[5,4,4,2,2],[4,3,2,1]]=>[5,2]
[[6,5,5,3,2],[5,4,3,2]]=>[6,1]
[[5,4,3,2,2],[4,3,1,1]]=>[5,1,1]
[[6,5,4,3,2],[5,4,2,2]]=>[6,1]
[[6,5,4,2,2],[5,4,2,1]]=>[6,1]
[[7,6,5,3,2],[6,5,3,2]]=>[7]
[[2,2,2,1,1,1],[1,1]]=>[2,2,2,1]
[[3,3,3,2,2,1],[2,2,1,1,1]]=>[3,2,2]
[[3,3,3,2,1,1],[2,2,1,1]]=>[3,3,1]
[[4,4,4,3,2,1],[3,3,2,2,1]]=>[4,2,1]
[[3,3,3,1,1,1],[2,2,1]]=>[3,2,2]
[[4,4,4,2,2,1],[3,3,2,1,1]]=>[4,2,1]
[[4,4,4,2,1,1],[3,3,2,1]]=>[4,2,1]
[[5,5,5,3,2,1],[4,4,3,2,1]]=>[5,1,1]
[[3,3,2,1,1,1],[2,2]]=>[3,2,1,1]
[[4,4,3,2,2,1],[3,3,1,1,1]]=>[4,2,1]
[[4,4,3,2,1,1],[3,3,1,1]]=>[4,3]
[[5,5,4,3,2,1],[4,4,2,2,1]]=>[5,2]
[[4,4,3,1,1,1],[3,3,1]]=>[4,2,1]
[[5,5,4,2,2,1],[4,4,2,1,1]]=>[5,2]
[[5,5,4,2,1,1],[4,4,2,1]]=>[5,2]
[[6,6,5,3,2,1],[5,5,3,2,1]]=>[6,1]
[[3,2,2,1,1,1],[2,1]]=>[3,2,1,1]
[[4,3,3,2,2,1],[3,2,1,1,1]]=>[4,2,1]
[[4,3,3,2,1,1],[3,2,1,1]]=>[4,3]
[[5,4,4,3,2,1],[4,3,2,2,1]]=>[5,2]
[[4,3,3,1,1,1],[3,2,1]]=>[4,2,1]
[[5,4,4,2,2,1],[4,3,2,1,1]]=>[5,2]
[[5,4,4,2,1,1],[4,3,2,1]]=>[5,2]
[[6,5,5,3,2,1],[5,4,3,2,1]]=>[6,1]
[[4,3,2,1,1,1],[3,2]]=>[4,1,1,1]
[[5,4,3,2,2,1],[4,3,1,1,1]]=>[5,1,1]
[[5,4,3,2,1,1],[4,3,1,1]]=>[5,2]
[[6,5,4,3,2,1],[5,4,2,2,1]]=>[6,1]
[[5,4,3,1,1,1],[4,3,1]]=>[5,1,1]
[[6,5,4,2,2,1],[5,4,2,1,1]]=>[6,1]
[[6,5,4,2,1,1],[5,4,2,1]]=>[6,1]
[[7,6,5,3,2,1],[6,5,3,2,1]]=>[7]
[[4,4,4,4],[3,3,3]]=>[4,1,1,1]
[[5,5,5,4],[4,4,4]]=>[5,1,1]
[[5,5,4,4],[4,4,3]]=>[5,2]
[[6,6,5,4],[5,5,4]]=>[6,1]
[[5,4,4,4],[4,3,3]]=>[5,1,1]
[[6,5,5,4],[5,4,4]]=>[6,1]
[[6,5,4,4],[5,4,3]]=>[6,1]
[[7,6,5,4],[6,5,4]]=>[7]
[[3,3,3,3,1],[2,2,2]]=>[3,2,1,1]
[[4,4,4,4,1],[3,3,3,1]]=>[4,1,1,1]
[[4,4,4,3,1],[3,3,3]]=>[4,2,1]
[[5,5,5,4,1],[4,4,4,1]]=>[5,1,1]
[[4,4,3,3,1],[3,3,2]]=>[4,3]
[[5,5,4,4,1],[4,4,3,1]]=>[5,2]
[[5,5,4,3,1],[4,4,3]]=>[5,2]
[[6,6,5,4,1],[5,5,4,1]]=>[6,1]
[[4,3,3,3,1],[3,2,2]]=>[4,2,1]
[[5,4,4,4,1],[4,3,3,1]]=>[5,1,1]
[[5,4,4,3,1],[4,3,3]]=>[5,2]
[[6,5,5,4,1],[5,4,4,1]]=>[6,1]
[[5,4,3,3,1],[4,3,2]]=>[5,2]
[[6,5,4,4,1],[5,4,3,1]]=>[6,1]
[[6,5,4,3,1],[5,4,3]]=>[6,1]
[[7,6,5,4,1],[6,5,4,1]]=>[7]
[[2,2,2,2,2],[1,1,1]]=>[2,2,1,1,1]
[[3,3,3,3,2],[2,2,2,1]]=>[3,2,1,1]
[[4,4,4,4,2],[3,3,3,2]]=>[4,1,1,1]
[[3,3,3,2,2],[2,2,2]]=>[3,3,1]
[[4,4,4,3,2],[3,3,3,1]]=>[4,2,1]
[[5,5,5,4,2],[4,4,4,2]]=>[5,1,1]
[[3,3,2,2,2],[2,2,1]]=>[3,3,1]
[[4,4,3,3,2],[3,3,2,1]]=>[4,3]
[[5,5,4,4,2],[4,4,3,2]]=>[5,2]
[[4,4,3,2,2],[3,3,2]]=>[4,3]
[[5,5,4,3,2],[4,4,3,1]]=>[5,2]
[[6,6,5,4,2],[5,5,4,2]]=>[6,1]
[[3,2,2,2,2],[2,1,1]]=>[3,2,1,1]
[[4,3,3,3,2],[3,2,2,1]]=>[4,2,1]
[[5,4,4,4,2],[4,3,3,2]]=>[5,1,1]
[[4,3,3,2,2],[3,2,2]]=>[4,3]
[[5,4,4,3,2],[4,3,3,1]]=>[5,2]
[[6,5,5,4,2],[5,4,4,2]]=>[6,1]
[[4,3,2,2,2],[3,2,1]]=>[4,2,1]
[[5,4,3,3,2],[4,3,2,1]]=>[5,2]
[[6,5,4,4,2],[5,4,3,2]]=>[6,1]
[[5,4,3,2,2],[4,3,2]]=>[5,2]
[[6,5,4,3,2],[5,4,3,1]]=>[6,1]
[[7,6,5,4,2],[6,5,4,2]]=>[7]
[[2,2,2,2,1,1],[1,1,1]]=>[2,2,2,1]
[[3,3,3,3,2,1],[2,2,2,1,1]]=>[3,2,1,1]
[[3,3,3,3,1,1],[2,2,2,1]]=>[3,2,1,1]
[[4,4,4,4,2,1],[3,3,3,2,1]]=>[4,1,1,1]
[[3,3,3,2,1,1],[2,2,2]]=>[3,2,2]
[[4,4,4,3,2,1],[3,3,3,1,1]]=>[4,2,1]
[[4,4,4,3,1,1],[3,3,3,1]]=>[4,2,1]
[[5,5,5,4,2,1],[4,4,4,2,1]]=>[5,1,1]
[[3,3,2,2,1,1],[2,2,1]]=>[3,3,1]
[[4,4,3,3,2,1],[3,3,2,1,1]]=>[4,3]
[[4,4,3,3,1,1],[3,3,2,1]]=>[4,3]
[[5,5,4,4,2,1],[4,4,3,2,1]]=>[5,2]
[[4,4,3,2,1,1],[3,3,2]]=>[4,2,1]
[[5,5,4,3,2,1],[4,4,3,1,1]]=>[5,2]
[[5,5,4,3,1,1],[4,4,3,1]]=>[5,2]
[[6,6,5,4,2,1],[5,5,4,2,1]]=>[6,1]
[[3,2,2,2,1,1],[2,1,1]]=>[3,2,2]
[[4,3,3,3,2,1],[3,2,2,1,1]]=>[4,2,1]
[[4,3,3,3,1,1],[3,2,2,1]]=>[4,2,1]
[[5,4,4,4,2,1],[4,3,3,2,1]]=>[5,1,1]
[[4,3,3,2,1,1],[3,2,2]]=>[4,2,1]
[[5,4,4,3,2,1],[4,3,3,1,1]]=>[5,2]
[[5,4,4,3,1,1],[4,3,3,1]]=>[5,2]
[[6,5,5,4,2,1],[5,4,4,2,1]]=>[6,1]
[[4,3,2,2,1,1],[3,2,1]]=>[4,2,1]
[[5,4,3,3,2,1],[4,3,2,1,1]]=>[5,2]
[[5,4,3,3,1,1],[4,3,2,1]]=>[5,2]
[[6,5,4,4,2,1],[5,4,3,2,1]]=>[6,1]
[[5,4,3,2,1,1],[4,3,2]]=>[5,1,1]
[[6,5,4,3,2,1],[5,4,3,1,1]]=>[6,1]
[[6,5,4,3,1,1],[5,4,3,1]]=>[6,1]
[[7,6,5,4,2,1],[6,5,4,2,1]]=>[7]
[[3,3,3,3,3],[2,2,2,2]]=>[3,1,1,1,1]
[[4,4,4,4,3],[3,3,3,3]]=>[4,1,1,1]
[[4,4,4,3,3],[3,3,3,2]]=>[4,2,1]
[[5,5,5,4,3],[4,4,4,3]]=>[5,1,1]
[[4,4,3,3,3],[3,3,2,2]]=>[4,2,1]
[[5,5,4,4,3],[4,4,3,3]]=>[5,2]
[[5,5,4,3,3],[4,4,3,2]]=>[5,2]
[[6,6,5,4,3],[5,5,4,3]]=>[6,1]
[[4,3,3,3,3],[3,2,2,2]]=>[4,1,1,1]
[[5,4,4,4,3],[4,3,3,3]]=>[5,1,1]
[[5,4,4,3,3],[4,3,3,2]]=>[5,2]
[[6,5,5,4,3],[5,4,4,3]]=>[6,1]
[[5,4,3,3,3],[4,3,2,2]]=>[5,1,1]
[[6,5,4,4,3],[5,4,3,3]]=>[6,1]
[[6,5,4,3,3],[5,4,3,2]]=>[6,1]
[[7,6,5,4,3],[6,5,4,3]]=>[7]
[[2,2,2,2,2,1],[1,1,1,1]]=>[2,2,1,1,1]
[[3,3,3,3,3,1],[2,2,2,2,1]]=>[3,1,1,1,1]
[[3,3,3,3,2,1],[2,2,2,2]]=>[3,2,1,1]
[[4,4,4,4,3,1],[3,3,3,3,1]]=>[4,1,1,1]
[[3,3,3,2,2,1],[2,2,2,1]]=>[3,3,1]
[[4,4,4,3,3,1],[3,3,3,2,1]]=>[4,2,1]
[[4,4,4,3,2,1],[3,3,3,2]]=>[4,2,1]
[[5,5,5,4,3,1],[4,4,4,3,1]]=>[5,1,1]
[[3,3,2,2,2,1],[2,2,1,1]]=>[3,3,1]
[[4,4,3,3,3,1],[3,3,2,2,1]]=>[4,2,1]
[[4,4,3,3,2,1],[3,3,2,2]]=>[4,3]
[[5,5,4,4,3,1],[4,4,3,3,1]]=>[5,2]
[[4,4,3,2,2,1],[3,3,2,1]]=>[4,3]
[[5,5,4,3,3,1],[4,4,3,2,1]]=>[5,2]
[[5,5,4,3,2,1],[4,4,3,2]]=>[5,2]
[[6,6,5,4,3,1],[5,5,4,3,1]]=>[6,1]
[[3,2,2,2,2,1],[2,1,1,1]]=>[3,2,1,1]
[[4,3,3,3,3,1],[3,2,2,2,1]]=>[4,1,1,1]
[[4,3,3,3,2,1],[3,2,2,2]]=>[4,2,1]
[[5,4,4,4,3,1],[4,3,3,3,1]]=>[5,1,1]
[[4,3,3,2,2,1],[3,2,2,1]]=>[4,3]
[[5,4,4,3,3,1],[4,3,3,2,1]]=>[5,2]
[[5,4,4,3,2,1],[4,3,3,2]]=>[5,2]
[[6,5,5,4,3,1],[5,4,4,3,1]]=>[6,1]
[[4,3,2,2,2,1],[3,2,1,1]]=>[4,2,1]
[[5,4,3,3,3,1],[4,3,2,2,1]]=>[5,1,1]
[[5,4,3,3,2,1],[4,3,2,2]]=>[5,2]
[[6,5,4,4,3,1],[5,4,3,3,1]]=>[6,1]
[[5,4,3,2,2,1],[4,3,2,1]]=>[5,2]
[[6,5,4,3,3,1],[5,4,3,2,1]]=>[6,1]
[[6,5,4,3,2,1],[5,4,3,2]]=>[6,1]
[[7,6,5,4,3,1],[6,5,4,3,1]]=>[7]
[[2,2,2,2,2,2],[1,1,1,1,1]]=>[2,1,1,1,1,1]
[[3,3,3,3,3,2],[2,2,2,2,2]]=>[3,1,1,1,1]
[[3,3,3,3,2,2],[2,2,2,2,1]]=>[3,2,1,1]
[[4,4,4,4,3,2],[3,3,3,3,2]]=>[4,1,1,1]
[[3,3,3,2,2,2],[2,2,2,1,1]]=>[3,2,2]
[[4,4,4,3,3,2],[3,3,3,2,2]]=>[4,2,1]
[[4,4,4,3,2,2],[3,3,3,2,1]]=>[4,2,1]
[[5,5,5,4,3,2],[4,4,4,3,2]]=>[5,1,1]
[[3,3,2,2,2,2],[2,2,1,1,1]]=>[3,2,1,1]
[[4,4,3,3,3,2],[3,3,2,2,2]]=>[4,2,1]
[[4,4,3,3,2,2],[3,3,2,2,1]]=>[4,3]
[[5,5,4,4,3,2],[4,4,3,3,2]]=>[5,2]
[[4,4,3,2,2,2],[3,3,2,1,1]]=>[4,2,1]
[[5,5,4,3,3,2],[4,4,3,2,2]]=>[5,2]
[[5,5,4,3,2,2],[4,4,3,2,1]]=>[5,2]
[[6,6,5,4,3,2],[5,5,4,3,2]]=>[6,1]
[[3,2,2,2,2,2],[2,1,1,1,1]]=>[3,1,1,1,1]
[[4,3,3,3,3,2],[3,2,2,2,2]]=>[4,1,1,1]
[[4,3,3,3,2,2],[3,2,2,2,1]]=>[4,2,1]
[[5,4,4,4,3,2],[4,3,3,3,2]]=>[5,1,1]
[[4,3,3,2,2,2],[3,2,2,1,1]]=>[4,2,1]
[[5,4,4,3,3,2],[4,3,3,2,2]]=>[5,2]
[[5,4,4,3,2,2],[4,3,3,2,1]]=>[5,2]
[[6,5,5,4,3,2],[5,4,4,3,2]]=>[6,1]
[[4,3,2,2,2,2],[3,2,1,1,1]]=>[4,1,1,1]
[[5,4,3,3,3,2],[4,3,2,2,2]]=>[5,1,1]
[[5,4,3,3,2,2],[4,3,2,2,1]]=>[5,2]
[[6,5,4,4,3,2],[5,4,3,3,2]]=>[6,1]
[[5,4,3,2,2,2],[4,3,2,1,1]]=>[5,1,1]
[[6,5,4,3,3,2],[5,4,3,2,2]]=>[6,1]
[[6,5,4,3,2,2],[5,4,3,2,1]]=>[6,1]
[[7,6,5,4,3,2],[6,5,4,3,2]]=>[7]
[[1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1]
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]]=>[2,1,1,1,1,1]
[[2,2,2,2,2,1,1],[1,1,1,1,1]]=>[2,2,1,1,1]
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]]=>[3,1,1,1,1]
[[2,2,2,2,1,1,1],[1,1,1,1]]=>[2,2,2,1]
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]]=>[3,2,1,1]
[[3,3,3,3,2,1,1],[2,2,2,2,1]]=>[3,2,1,1]
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]]=>[4,1,1,1]
[[2,2,2,1,1,1,1],[1,1,1]]=>[2,2,2,1]
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]]=>[3,2,2]
[[3,3,3,2,2,1,1],[2,2,2,1,1]]=>[3,3,1]
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]]=>[4,2,1]
[[3,3,3,2,1,1,1],[2,2,2,1]]=>[3,2,2]
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]]=>[4,2,1]
[[4,4,4,3,2,1,1],[3,3,3,2,1]]=>[4,2,1]
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]]=>[5,1,1]
[[2,2,1,1,1,1,1],[1,1]]=>[2,2,1,1,1]
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]]=>[3,2,1,1]
[[3,3,2,2,2,1,1],[2,2,1,1,1]]=>[3,3,1]
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]]=>[4,2,1]
[[3,3,2,2,1,1,1],[2,2,1,1]]=>[3,3,1]
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]]=>[4,3]
[[4,4,3,3,2,1,1],[3,3,2,2,1]]=>[4,3]
[[5,5,4,4,3,2,1],[4,4,3,3,2,1]]=>[5,2]
[[3,3,2,1,1,1,1],[2,2,1]]=>[3,2,1,1]
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]]=>[4,2,1]
[[4,4,3,2,2,1,1],[3,3,2,1,1]]=>[4,3]
[[5,5,4,3,3,2,1],[4,4,3,2,2,1]]=>[5,2]
[[4,4,3,2,1,1,1],[3,3,2,1]]=>[4,2,1]
[[5,5,4,3,2,2,1],[4,4,3,2,1,1]]=>[5,2]
[[5,5,4,3,2,1,1],[4,4,3,2,1]]=>[5,2]
[[6,6,5,4,3,2,1],[5,5,4,3,2,1]]=>[6,1]
[[2,1,1,1,1,1,1],[1]]=>[2,1,1,1,1,1]
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]]=>[3,1,1,1,1]
[[3,2,2,2,2,1,1],[2,1,1,1,1]]=>[3,2,1,1]
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]]=>[4,1,1,1]
[[3,2,2,2,1,1,1],[2,1,1,1]]=>[3,2,2]
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]]=>[4,2,1]
[[4,3,3,3,2,1,1],[3,2,2,2,1]]=>[4,2,1]
[[5,4,4,4,3,2,1],[4,3,3,3,2,1]]=>[5,1,1]
[[3,2,2,1,1,1,1],[2,1,1]]=>[3,2,1,1]
[[4,3,3,2,2,2,1],[3,2,2,1,1,1]]=>[4,2,1]
[[4,3,3,2,2,1,1],[3,2,2,1,1]]=>[4,3]
[[5,4,4,3,3,2,1],[4,3,3,2,2,1]]=>[5,2]
[[4,3,3,2,1,1,1],[3,2,2,1]]=>[4,2,1]
[[5,4,4,3,2,2,1],[4,3,3,2,1,1]]=>[5,2]
[[5,4,4,3,2,1,1],[4,3,3,2,1]]=>[5,2]
[[6,5,5,4,3,2,1],[5,4,4,3,2,1]]=>[6,1]
[[3,2,1,1,1,1,1],[2,1]]=>[3,1,1,1,1]
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]]=>[4,1,1,1]
[[4,3,2,2,2,1,1],[3,2,1,1,1]]=>[4,2,1]
[[5,4,3,3,3,2,1],[4,3,2,2,2,1]]=>[5,1,1]
[[4,3,2,2,1,1,1],[3,2,1,1]]=>[4,2,1]
[[5,4,3,3,2,2,1],[4,3,2,2,1,1]]=>[5,2]
[[5,4,3,3,2,1,1],[4,3,2,2,1]]=>[5,2]
[[6,5,4,4,3,2,1],[5,4,3,3,2,1]]=>[6,1]
[[4,3,2,1,1,1,1],[3,2,1]]=>[4,1,1,1]
[[5,4,3,2,2,2,1],[4,3,2,1,1,1]]=>[5,1,1]
[[5,4,3,2,2,1,1],[4,3,2,1,1]]=>[5,2]
[[6,5,4,3,3,2,1],[5,4,3,2,2,1]]=>[6,1]
[[5,4,3,2,1,1,1],[4,3,2,1]]=>[5,1,1]
[[6,5,4,3,2,2,1],[5,4,3,2,1,1]]=>[6,1]
[[6,5,4,3,2,1,1],[5,4,3,2,1]]=>[6,1]
[[7,6,5,4,3,2,1],[6,5,4,3,2,1]]=>[7]
[[8],[]]=>[8]
[[7,1],[]]=>[7,1]
[[6,2],[]]=>[6,2]
[[6,1,1],[]]=>[6,1,1]
[[5,3],[]]=>[5,3]
[[5,2,1],[]]=>[5,2,1]
[[5,1,1,1],[]]=>[5,1,1,1]
[[4,4],[]]=>[4,4]
[[4,3,1],[]]=>[4,3,1]
[[4,2,2],[]]=>[4,2,2]
[[4,2,1,1],[]]=>[4,2,1,1]
[[4,1,1,1,1],[]]=>[4,1,1,1,1]
[[3,3,2],[]]=>[3,3,2]
[[3,3,1,1],[]]=>[3,3,1,1]
[[3,2,2,1],[]]=>[3,2,2,1]
[[3,2,1,1,1],[]]=>[3,2,1,1,1]
[[3,1,1,1,1,1],[]]=>[3,1,1,1,1,1]
[[2,2,2,2],[]]=>[2,2,2,2]
[[2,2,2,1,1],[]]=>[2,2,2,1,1]
[[2,2,1,1,1,1],[]]=>[2,2,1,1,1,1]
[[2,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1]
[[1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1]
[[3,3,3],[1]]=>[3,3,2]
[[3,3,3,1],[1,1]]=>[3,3,2]
[[4,4,1],[1]]=>[4,4]
[[3,3,2,1],[1]]=>[3,3,2]
[[2,2,2,2,1],[1]]=>[2,2,2,2]
[[3,3,3,1],[2]]=>[3,3,2]
[[3,3,3,2],[1,1,1]]=>[3,2,2,1]
[[4,4,2],[1,1]]=>[4,3,1]
[[4,4,4],[2,2]]=>[4,2,2]
[[5,5],[2]]=>[5,3]
[[4,4,3],[2,1]]=>[4,3,1]
[[3,3,3,3],[2,1,1]]=>[3,2,2,1]
[[4,3,3],[1,1]]=>[4,2,2]
[[4,4,4],[3,1]]=>[4,3,1]
[[5,4],[1]]=>[5,3]
[[3,3,2,2],[1,1]]=>[3,3,1,1]
[[4,4,2],[2]]=>[4,4]
[[3,3,3,2],[2,1]]=>[3,3,2]
[[4,3,2],[1]]=>[4,3,1]
[[2,2,2,2,2],[1,1]]=>[2,2,2,1,1]
[[3,2,2,2],[1]]=>[3,2,2,1]
[[3,3,2,2],[2]]=>[3,3,2]
[[3,3,3,3],[2,2]]=>[3,3,1,1]
[[4,3,3],[2]]=>[4,3,1]
[[4,4,3],[3]]=>[4,4]
[[6,6],[4]]=>[6,2]
[[6,5],[3]]=>[6,2]
[[6,4],[2]]=>[6,2]
[[6,3],[1]]=>[6,2]
[[9],[]]=>[9]
[[8,1],[]]=>[8,1]
[[7,2],[]]=>[7,2]
[[7,1,1],[]]=>[7,1,1]
[[6,3],[]]=>[6,3]
[[6,2,1],[]]=>[6,2,1]
[[6,1,1,1],[]]=>[6,1,1,1]
[[5,4],[]]=>[5,4]
[[5,3,1],[]]=>[5,3,1]
[[5,2,2],[]]=>[5,2,2]
[[5,2,1,1],[]]=>[5,2,1,1]
[[5,1,1,1,1],[]]=>[5,1,1,1,1]
[[4,4,1],[]]=>[4,4,1]
[[4,3,2],[]]=>[4,3,2]
[[4,3,1,1],[]]=>[4,3,1,1]
[[4,2,2,1],[]]=>[4,2,2,1]
[[4,2,1,1,1],[]]=>[4,2,1,1,1]
[[4,1,1,1,1,1],[]]=>[4,1,1,1,1,1]
[[3,3,3],[]]=>[3,3,3]
[[3,3,2,1],[]]=>[3,3,2,1]
[[3,3,1,1,1],[]]=>[3,3,1,1,1]
[[3,2,2,2],[]]=>[3,2,2,2]
[[3,2,2,1,1],[]]=>[3,2,2,1,1]
[[3,2,1,1,1,1],[]]=>[3,2,1,1,1,1]
[[3,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1]
[[2,2,2,2,1],[]]=>[2,2,2,2,1]
[[2,2,2,1,1,1],[]]=>[2,2,2,1,1,1]
[[2,2,1,1,1,1,1],[]]=>[2,2,1,1,1,1,1]
[[2,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1]
[[1,1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1,1]
[[3,3,3,1],[1]]=>[3,3,3]
[[3,3,3,3],[1,1,1]]=>[3,2,2,2]
[[4,4,3],[1,1]]=>[4,3,2]
[[4,4,4],[2,1]]=>[4,3,2]
[[5,5],[1]]=>[5,4]
[[3,3,3,2],[1,1]]=>[3,3,2,1]
[[4,4,2],[1]]=>[4,4,1]
[[3,3,2,2],[1]]=>[3,3,2,1]
[[2,2,2,2,2],[1]]=>[2,2,2,2,1]
[[3,3,3,2],[2]]=>[3,3,3]
[[4,4,3],[2]]=>[4,4,1]
[[3,3,3,3],[2,1]]=>[3,3,2,1]
[[4,3,3],[1]]=>[4,3,2]
[[4,4,4],[3]]=>[4,4,1]
[[5,5,5],[3,3]]=>[5,2,2]
[[6,6],[3]]=>[6,3]
[[5,5,4],[3,2]]=>[5,3,1]
[[5,4,4],[2,2]]=>[5,2,2]
[[6,5],[2]]=>[6,3]
[[5,5,3],[3,1]]=>[5,4]
[[5,4,3],[2,1]]=>[5,3,1]
[[5,3,3],[1,1]]=>[5,2,2]
[[6,4],[1]]=>[6,3]
[[5,5,2],[3]]=>[5,4]
[[5,4,2],[2]]=>[5,4]
[[5,3,2],[1]]=>[5,3,1]
[[10],[]]=>[10]
[[9,1],[]]=>[9,1]
[[8,2],[]]=>[8,2]
[[8,1,1],[]]=>[8,1,1]
[[7,3],[]]=>[7,3]
[[7,2,1],[]]=>[7,2,1]
[[7,1,1,1],[]]=>[7,1,1,1]
[[6,4],[]]=>[6,4]
[[6,3,1],[]]=>[6,3,1]
[[6,2,2],[]]=>[6,2,2]
[[6,2,1,1],[]]=>[6,2,1,1]
[[6,1,1,1,1],[]]=>[6,1,1,1,1]
[[5,5],[]]=>[5,5]
[[5,4,1],[]]=>[5,4,1]
[[5,3,2],[]]=>[5,3,2]
[[5,3,1,1],[]]=>[5,3,1,1]
[[5,2,2,1],[]]=>[5,2,2,1]
[[5,2,1,1,1],[]]=>[5,2,1,1,1]
[[5,1,1,1,1,1],[]]=>[5,1,1,1,1,1]
[[4,4,2],[]]=>[4,4,2]
[[4,4,1,1],[]]=>[4,4,1,1]
[[4,3,3],[]]=>[4,3,3]
[[4,3,2,1],[]]=>[4,3,2,1]
[[4,3,1,1,1],[]]=>[4,3,1,1,1]
[[4,2,2,2],[]]=>[4,2,2,2]
[[4,2,2,1,1],[]]=>[4,2,2,1,1]
[[4,2,1,1,1,1],[]]=>[4,2,1,1,1,1]
[[4,1,1,1,1,1,1],[]]=>[4,1,1,1,1,1,1]
[[3,3,3,1],[]]=>[3,3,3,1]
[[3,3,2,2],[]]=>[3,3,2,2]
[[3,3,2,1,1],[]]=>[3,3,2,1,1]
[[3,3,1,1,1,1],[]]=>[3,3,1,1,1,1]
[[3,2,2,2,1],[]]=>[3,2,2,2,1]
[[3,2,2,1,1,1],[]]=>[3,2,2,1,1,1]
[[3,2,1,1,1,1,1],[]]=>[3,2,1,1,1,1,1]
[[3,1,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1,1]
[[2,2,2,2,2],[]]=>[2,2,2,2,2]
[[2,2,2,2,1,1],[]]=>[2,2,2,2,1,1]
[[2,2,2,1,1,1,1],[]]=>[2,2,2,1,1,1,1]
[[2,2,1,1,1,1,1,1],[]]=>[2,2,1,1,1,1,1,1]
[[2,1,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1,1]
[[1,1,1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1,1,1]
[[4,4,4],[1,1]]=>[4,3,3]
[[3,3,3,2],[1]]=>[3,3,3,1]
[[3,3,3,3],[1,1]]=>[3,3,2,2]
[[4,4,3],[1]]=>[4,4,2]
[[4,4,4],[2]]=>[4,4,2]
[[3,3,3,3],[2]]=>[3,3,3,1]
[[4,4,4,4],[2,2,2]]=>[4,2,2,2]
[[5,5,4],[2,2]]=>[5,3,2]
[[5,5,5],[3,2]]=>[5,3,2]
[[6,6],[2]]=>[6,4]
[[4,4,4,3],[2,2,1]]=>[4,3,2,1]
[[5,5,3],[2,1]]=>[5,4,1]
[[4,4,3,3],[2,1,1]]=>[4,3,2,1]
[[4,3,3,3],[1,1,1]]=>[4,2,2,2]
[[5,4,3],[1,1]]=>[5,3,2]
[[5,5,4],[3,1]]=>[5,4,1]
[[5,4,4],[2,1]]=>[5,3,2]
[[6,5],[1]]=>[6,4]
[[4,4,4,2],[2,2]]=>[4,4,2]
[[5,5,2],[2]]=>[5,5]
[[4,4,3,2],[2,1]]=>[4,4,2]
[[4,3,3,2],[1,1]]=>[4,3,2,1]
[[5,4,2],[1]]=>[5,4,1]
[[4,4,2,2],[2]]=>[4,4,2]
[[4,3,2,2],[1]]=>[4,3,2,1]
[[5,5,3],[3]]=>[5,5]
[[5,4,3],[2]]=>[5,4,1]
[[5,3,3],[1]]=>[5,3,2]
[[6,5],[]]=>[6,5]
[[5,5,1],[]]=>[5,5,1]
[[5,4,2],[]]=>[5,4,2]
[[5,3,3],[]]=>[5,3,3]
[[4,4,3],[]]=>[4,4,3]
[[4,4,2,1],[]]=>[4,4,2,1]
[[4,3,3,1],[]]=>[4,3,3,1]
[[4,3,2,2],[]]=>[4,3,2,2]
[[3,3,3,2],[]]=>[3,3,3,2]
[[3,2,2,2,2],[]]=>[3,2,2,2,2]
[[4,4,4],[1]]=>[4,4,3]
[[3,3,3,3],[1]]=>[3,3,3,2]
[[4,4,4,1],[1,1]]=>[4,4,3]
[[4,4,3,1],[1]]=>[4,4,3]
[[4,4,4,1],[2]]=>[4,4,3]
[[4,4,4,2],[1,1,1]]=>[4,3,3,1]
[[5,5,5],[2,2]]=>[5,3,3]
[[3,3,3,3,3],[1,1,1,1]]=>[3,2,2,2,2]
[[4,4,3,3],[1,1,1]]=>[4,3,2,2]
[[4,4,4,3],[2,1,1]]=>[4,3,3,1]
[[5,5,3],[1,1]]=>[5,4,2]
[[4,4,4,4],[2,2,1]]=>[4,3,2,2]
[[5,5,4],[2,1]]=>[5,4,2]
[[5,5,5],[3,1]]=>[5,4,2]
[[6,6],[1]]=>[6,5]
[[4,4,4,4],[3,1,1]]=>[4,3,3,1]
[[5,4,4],[1,1]]=>[5,3,3]
[[3,3,3,3,2],[1,1,1]]=>[3,3,2,2,1]
[[4,4,3,2],[1,1]]=>[4,4,2,1]
[[4,4,4,2],[2,1]]=>[4,4,3]
[[5,5,2],[1]]=>[5,5,1]
[[3,3,3,2,2],[1,1]]=>[3,3,3,1,1]
[[4,4,2,2],[1]]=>[4,4,2,1]
[[3,3,2,2,2],[1]]=>[3,3,2,2,1]
[[4,4,3,2],[2]]=>[4,4,3]
[[4,3,3,2],[1]]=>[4,3,3,1]
[[4,4,4,2],[3]]=>[4,4,3]
[[4,4,4,3],[2,2]]=>[4,4,2,1]
[[5,5,3],[2]]=>[5,5,1]
[[4,4,3,3],[2,1]]=>[4,4,2,1]
[[4,3,3,3],[1,1]]=>[4,3,2,2]
[[4,4,4,3],[3,1]]=>[4,4,3]
[[5,4,3],[1]]=>[5,4,2]
[[5,5,4],[3]]=>[5,5,1]
[[4,4,4,4],[3,2]]=>[4,4,2,1]
[[5,4,4],[2]]=>[5,4,2]
[[5,5,5],[4]]=>[5,5,1]
[[4,3,3,3],[2]]=>[4,3,3,1]
[[4,4,3,3],[3]]=>[4,4,3]
[[6,6],[]]=>[6,6]
[[5,5,2],[]]=>[5,5,2]
[[5,4,3],[]]=>[5,4,3]
[[4,4,4],[]]=>[4,4,4]
[[4,4,3,1],[]]=>[4,4,3,1]
[[4,4,2,2],[]]=>[4,4,2,2]
[[4,3,3,2],[]]=>[4,3,3,2]
[[3,3,3,3],[]]=>[3,3,3,3]
[[3,3,3,2,1],[]]=>[3,3,3,2,1]
[[3,3,2,2,2],[]]=>[3,3,2,2,2]
[[2,2,2,2,2,2],[]]=>[2,2,2,2,2,2]
[[4,4,4,1],[1]]=>[4,4,4]
[[3,3,3,3,1],[1]]=>[3,3,3,3]
[[4,4,4,3],[1,1,1]]=>[4,3,3,2]
[[5,5,5],[2,1]]=>[5,4,3]
[[4,4,4,4],[2,1,1]]=>[4,3,3,2]
[[5,5,4],[1,1]]=>[5,4,3]
[[4,4,4,2],[1,1]]=>[4,4,3,1]
[[3,3,3,2,2],[1]]=>[3,3,3,2,1]
[[3,3,3,3,2],[1,1]]=>[3,3,3,2,1]
[[4,4,3,2],[1]]=>[4,4,3,1]
[[4,4,4,2],[2]]=>[4,4,4]
[[3,3,3,3,2],[2]]=>[3,3,3,3]
[[3,3,3,3,3],[1,1,1]]=>[3,3,2,2,2]
[[4,4,3,3],[1,1]]=>[4,4,2,2]
[[4,4,4,3],[2,1]]=>[4,4,3,1]
[[5,5,3],[1]]=>[5,5,2]
[[4,4,4,4],[2,2]]=>[4,4,2,2]
[[5,5,4],[2]]=>[5,5,2]
[[5,5,5],[3]]=>[5,5,2]
[[4,4,4,4],[3,1]]=>[4,4,3,1]
[[5,4,4],[1]]=>[5,4,3]
[[4,4,3,3],[2]]=>[4,4,3,1]
[[3,3,3,3,3],[2,1]]=>[3,3,3,2,1]
[[4,3,3,3],[1]]=>[4,3,3,2]
[[4,4,4,3],[3]]=>[4,4,4]
[[5,5,3],[]]=>[5,5,3]
[[5,4,4],[]]=>[5,4,4]
[[4,4,4,1],[]]=>[4,4,4,1]
[[4,4,3,2],[]]=>[4,4,3,2]
[[4,3,3,3],[]]=>[4,3,3,3]
[[3,3,3,3,1],[]]=>[3,3,3,3,1]
[[3,3,3,2,2],[]]=>[3,3,3,2,2]
[[4,4,4,4],[1,1,1]]=>[4,3,3,3]
[[5,5,5],[1,1]]=>[5,4,4]
[[4,4,4,2],[1]]=>[4,4,4,1]
[[3,3,3,3,2],[1]]=>[3,3,3,3,1]
[[4,4,4,3],[1,1]]=>[4,4,3,2]
[[5,5,5],[2]]=>[5,5,3]
[[4,4,4,4],[2,1]]=>[4,4,3,2]
[[5,5,4],[1]]=>[5,5,3]
[[3,3,3,3,3],[1,1]]=>[3,3,3,2,2]
[[4,4,3,3],[1]]=>[4,4,3,2]
[[4,4,4,3],[2]]=>[4,4,4,1]
[[3,3,3,3,3],[2]]=>[3,3,3,3,1]
[[4,4,4,4],[3]]=>[4,4,4,1]
[[5,5,4],[]]=>[5,5,4]
[[4,4,4,2],[]]=>[4,4,4,2]
[[4,4,3,3],[]]=>[4,4,3,3]
[[3,3,3,3,2],[]]=>[3,3,3,3,2]
[[4,4,4,4],[1,1]]=>[4,4,3,3]
[[5,5,5],[1]]=>[5,5,4]
[[4,4,4,3],[1]]=>[4,4,4,2]
[[3,3,3,3,3],[1]]=>[3,3,3,3,2]
[[4,4,4,4],[2]]=>[4,4,4,2]
[[5,5,5],[]]=>[5,5,5]
[[5,5,4,1],[]]=>[5,5,4,1]
[[4,4,4,3],[]]=>[4,4,4,3]
[[3,3,3,3,3],[]]=>[3,3,3,3,3]
[[4,4,4,4],[1]]=>[4,4,4,3]
[[5,5,5,1],[1]]=>[5,5,5]
[[5,5,5,5],[4,1]]=>[5,5,4,1]
[[5,5,5,4],[4]]=>[5,5,5]
[[5,5,5,1],[]]=>[5,5,5,1]
[[4,4,4,4],[]]=>[4,4,4,4]
[[4,4,4,3,1],[]]=>[4,4,4,3,1]
[[3,3,3,3,3,1],[]]=>[3,3,3,3,3,1]
[[4,4,4,4,1],[1]]=>[4,4,4,4]
[[3,3,3,3,3,3],[2]]=>[3,3,3,3,3,1]
[[4,4,4,4,3],[3]]=>[4,4,4,4]
[[4,4,4,4,4],[3,1]]=>[4,4,4,3,1]
[[5,5,5,5],[4]]=>[5,5,5,1]
[[4,4,4,4,1],[]]=>[4,4,4,4,1]
[[4,4,4,4,4],[3]]=>[4,4,4,4,1]
[[5,5,5,5,4],[4]]=>[5,5,5,5]
[[5,5,5,5,5],[4,1]]=>[5,5,5,4,1]
[[5,5,5,4,1],[]]=>[5,5,5,4,1]
[[5,5,5,5,1],[1]]=>[5,5,5,5]
[[5,5,5,5,5],[4]]=>[5,5,5,5,1]
[[5,5,5,5,1],[]]=>[5,5,5,5,1]
[[4,4,4,4,4,4],[3]]=>[4,4,4,4,4,1]
[[4,4,4,4,4,1],[]]=>[4,4,4,4,4,1]
[[6,6,6,6,6],[5]]=>[6,6,6,6,1]
[[6,6,6,6,1],[]]=>[6,6,6,6,1]
[[5,5,5,5,5,5],[4]]=>[5,5,5,5,5,1]
[[5,5,5,5,5,1],[]]=>[5,5,5,5,5,1]
[[6,6,6,6,6,6],[5]]=>[6,6,6,6,6,1]
[[6,6,6,6,6,1],[]]=>[6,6,6,6,6,1]
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
The dominating partition in the Schur expansion.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a sublattice of the dominance order and that its top element is the conjugate of the partition formed by sorting the column lengths of $\lambda / \mu$ into decreasing order.
This map returns the largest partition $\nu$ in dominance order for which $c^\lambda_{\mu, \nu}$ is positive.
For example,
$$ s_{331/2} = s_{311} + s_{32}, $$
and the partition $32$ dominates $311$.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a sublattice of the dominance order and that its top element is the conjugate of the partition formed by sorting the column lengths of $\lambda / \mu$ into decreasing order.
This map returns the largest partition $\nu$ in dominance order for which $c^\lambda_{\mu, \nu}$ is positive.
For example,
$$ s_{331/2} = s_{311} + s_{32}, $$
and the partition $32$ dominates $311$.
References
[1] Azenhas, O. The admissible interval for the invariant factors of a product of matrices MathSciNet:1712853
Properties
surjective, graded
Sage code
def mapping(la):
return Partition(sorted(la.column_lengths(), reverse=True)).conjugate()
Weight
40
Created
Sep 27, 2020 at 14:56 by Martin Rubey
Updated
Sep 08, 2023 at 21:38 by Martin Rubey
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