Identifier
Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00186: Skew partitions —dominating partition⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0028;cc-rep-2Cc0002;cc-rep-3
[1,0]=>[1,0]=>[[1],[]]=>[1] [1,0,1,0]=>[1,0,1,0]=>[[1,1],[]]=>[1,1] [1,1,0,0]=>[1,1,0,0]=>[[2],[]]=>[2] [1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[[1,1,1],[]]=>[1,1,1] [1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[[2,2],[1]]=>[2,1] [1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[[2,1],[]]=>[2,1] [1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[[3],[]]=>[3] [1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[[2,2],[]]=>[2,2] [1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[1,1,1,1],[]]=>[1,1,1,1] [1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[[2,2,2],[1,1]]=>[2,1,1] [1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[[2,2,1],[1]]=>[2,2] [1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[[3,3],[2]]=>[3,1] [1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[[2,2,2],[1]]=>[2,2,1] [1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[[2,1,1],[]]=>[2,1,1] [1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[[3,2],[1]]=>[3,1] [1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[[3,1],[]]=>[3,1] [1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[[4],[]]=>[4] [1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[[3,2],[]]=>[3,2] [1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[[2,2,1],[]]=>[2,2,1] [1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[[3,3],[1]]=>[3,2] [1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[[2,2,2],[]]=>[2,2,2] [1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[[3,3],[]]=>[3,3] [1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1],[]]=>[1,1,1,1,1] [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2],[1,1,1]]=>[2,1,1,1] [1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1],[1,1]]=>[2,2,1] [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[[3,3,3],[2,2]]=>[3,1,1] [1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[[2,2,2,2],[1,1]]=>[2,2,1,1] [1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1],[1]]=>[2,2,1] [1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[[3,3,2],[2,1]]=>[3,2] [1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[[3,3,1],[2]]=>[3,2] [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[[4,4],[3]]=>[4,1] [1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[[3,3,2],[2]]=>[3,3] [1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[[2,2,2,1],[1]]=>[2,2,2] [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[[3,3,3],[2,1]]=>[3,2,1] [1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[[2,2,2,2],[1]]=>[2,2,2,1] [1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[[3,3,3],[2]]=>[3,3,1] [1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1],[]]=>[2,1,1,1] [1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[[3,2,2],[1,1]]=>[3,1,1] [1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[[3,2,1],[1]]=>[3,2] [1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[[4,3],[2]]=>[4,1] [1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[[3,2,2],[1]]=>[3,2,1] [1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[[3,1,1],[]]=>[3,1,1] [1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[[4,2],[1]]=>[4,1] [1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[[4,1],[]]=>[4,1] [1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[[5],[]]=>[5] [1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[[4,2],[]]=>[4,2] [1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[[3,2,1],[]]=>[3,2,1] [1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[[4,3],[1]]=>[4,2] [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[[3,2,2],[]]=>[3,2,2] [1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[[4,3],[]]=>[4,3] [1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1],[]]=>[2,2,1,1] [1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[[3,3,2],[1,1]]=>[3,2,1] [1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[[3,3,1],[1]]=>[3,3] [1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[[4,4],[2]]=>[4,2] [1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[[3,3,2],[1]]=>[3,3,1] [1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1],[]]=>[2,2,2,1] [1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[[3,3,3],[1,1]]=>[3,2,2] [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[[2,2,2,2],[]]=>[2,2,2,2] [1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[[3,3,3],[1]]=>[3,3,2] [1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[[3,3,1],[]]=>[3,3,1] [1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[[4,4],[1]]=>[4,3] [1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[[3,3,2],[]]=>[3,3,2] [1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[[4,4],[]]=>[4,4] [1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[[3,3,3],[]]=>[3,3,3] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1],[]]=>[1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2],[1,1,1,1]]=>[2,1,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2,1],[1,1,1]]=>[2,2,1,1] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3],[2,2,2]]=>[3,1,1,1] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[2,2,2,2,2],[1,1,1]]=>[2,2,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1,1],[1,1]]=>[2,2,2] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2],[2,2,1]]=>[3,2,1] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[3,3,3,1],[2,2]]=>[3,2,1] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[4,4,4],[3,3]]=>[4,1,1] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[[3,3,3,2],[2,2]]=>[3,3,1] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[2,2,2,2,1],[1,1]]=>[2,2,2,1] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[[3,3,3,3],[2,2,1]]=>[3,2,1,1] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[[2,2,2,2,2],[1,1]]=>[2,2,2,1,1] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[3,3,3,3],[2,2]]=>[3,3,1,1] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1,1],[1]]=>[2,2,1,1] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2],[2,1,1]]=>[3,2,1] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[3,3,2,1],[2,1]]=>[3,3] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[4,4,3],[3,2]]=>[4,2] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[3,3,2,2],[2,1]]=>[3,3,1] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[3,3,1,1],[2]]=>[3,2,1] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[4,4,2],[3,1]]=>[4,2] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[4,4,1],[3]]=>[4,2] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[5,5],[4]]=>[5,1] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[[4,4,2],[3]]=>[4,3] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[3,3,2,1],[2]]=>[3,3,1] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[[4,4,3],[3,1]]=>[4,3] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[[3,3,2,2],[2]]=>[3,3,2] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[[4,4,3],[3]]=>[4,4] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[2,2,2,1,1],[1]]=>[2,2,2,1] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[3,3,3,2],[2,1,1]]=>[3,2,2] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[3,3,3,1],[2,1]]=>[3,3,1] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[4,4,4],[3,2]]=>[4,2,1] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[[3,3,3,2],[2,1]]=>[3,3,2] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[2,2,2,2,1],[1]]=>[2,2,2,2] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[[3,3,3,3],[2,1,1]]=>[3,2,2,1] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[[2,2,2,2,2],[1]]=>[2,2,2,2,1] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[[3,3,3,3],[2,1]]=>[3,3,2,1] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[3,3,3,1],[2]]=>[3,3,2] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[[4,4,4],[3,1]]=>[4,3,1] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[[3,3,3,2],[2]]=>[3,3,3] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[[4,4,4],[3]]=>[4,4,1] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[3,3,3,3],[2]]=>[3,3,3,1] [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1],[]]=>[2,1,1,1,1] [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2],[1,1,1]]=>[3,1,1,1] [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[3,2,2,1],[1,1]]=>[3,2,1] [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[4,3,3],[2,2]]=>[4,1,1] [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[3,2,2,2],[1,1]]=>[3,2,1,1] [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[3,2,1,1],[1]]=>[3,2,1] [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2],[2,1]]=>[4,2] [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[4,3,1],[2]]=>[4,2] [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[5,4],[3]]=>[5,1] [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[[4,3,2],[2]]=>[4,3] [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[3,2,2,1],[1]]=>[3,2,2] [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[[4,3,3],[2,1]]=>[4,2,1] [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[[3,2,2,2],[1]]=>[3,2,2,1] [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[4,3,3],[2]]=>[4,3,1] [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1],[]]=>[3,1,1,1] [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[4,2,2],[1,1]]=>[4,1,1] [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[4,2,1],[1]]=>[4,2] [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[5,3],[2]]=>[5,1] [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[[4,2,2],[1]]=>[4,2,1] [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1],[]]=>[4,1,1] [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[5,2],[1]]=>[5,1] [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1],[]]=>[5,1] [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[[6],[]]=>[6] [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[[5,2],[]]=>[5,2] [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[[4,2,1],[]]=>[4,2,1] [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[[5,3],[1]]=>[5,2] [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2],[]]=>[4,2,2] [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[[5,3],[]]=>[5,3] [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[[3,2,1,1],[]]=>[3,2,1,1] [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[[4,3,2],[1,1]]=>[4,2,1] [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[[4,3,1],[1]]=>[4,3] [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[[5,4],[2]]=>[5,2] [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[[4,3,2],[1]]=>[4,3,1] [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[[3,2,2,1],[]]=>[3,2,2,1] [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[[4,3,3],[1,1]]=>[4,2,2] [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2],[]]=>[3,2,2,2] [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[[4,3,3],[1]]=>[4,3,2] [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[[4,3,1],[]]=>[4,3,1] [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[[5,4],[1]]=>[5,3] [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2],[]]=>[4,3,2] [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[[5,4],[]]=>[5,4] [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3],[]]=>[4,3,3] [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1],[]]=>[2,2,1,1,1] [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[3,3,2,2],[1,1,1]]=>[3,2,1,1] [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[3,3,2,1],[1,1]]=>[3,3,1] [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[[4,4,3],[2,2]]=>[4,2,1] [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[3,3,2,2],[1,1]]=>[3,3,1,1] [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[3,3,1,1],[1]]=>[3,3,1] [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[[4,4,2],[2,1]]=>[4,3] [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[4,4,1],[2]]=>[4,3] [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[[5,5],[3]]=>[5,2] [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[[4,4,2],[2]]=>[4,4] [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[[3,3,2,1],[1]]=>[3,3,2] [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[[4,4,3],[2,1]]=>[4,3,1] [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[[3,3,2,2],[1]]=>[3,3,2,1] [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[[4,4,3],[2]]=>[4,4,1] [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1,1],[]]=>[2,2,2,1,1] [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[[3,3,3,2],[1,1,1]]=>[3,2,2,1] [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[3,3,3,1],[1,1]]=>[3,3,2] [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[[4,4,4],[2,2]]=>[4,2,2] [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[[3,3,3,2],[1,1]]=>[3,3,2,1] [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[2,2,2,2,1],[]]=>[2,2,2,2,1] [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3],[1,1,1]]=>[3,2,2,2] [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2],[]]=>[2,2,2,2,2] [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[[3,3,3,3],[1,1]]=>[3,3,2,2] [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[[3,3,3,1],[1]]=>[3,3,3] [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[[4,4,4],[2,1]]=>[4,3,2] [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[[3,3,3,2],[1]]=>[3,3,3,1] [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4],[2]]=>[4,4,2] [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3],[1]]=>[3,3,3,2] [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[3,3,1,1],[]]=>[3,3,1,1] [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[4,4,2],[1,1]]=>[4,3,1] [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[4,4,1],[1]]=>[4,4] [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[[5,5],[2]]=>[5,3] [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[[4,4,2],[1]]=>[4,4,1] [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[3,3,2,1],[]]=>[3,3,2,1] [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[[4,4,3],[1,1]]=>[4,3,2] [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[[3,3,2,2],[]]=>[3,3,2,2] [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3],[1]]=>[4,4,2] [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[4,4,1],[]]=>[4,4,1] [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[[5,5],[1]]=>[5,4] [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2],[]]=>[4,4,2] [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[[5,5],[]]=>[5,5] [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3],[]]=>[4,4,3] [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[3,3,3,1],[]]=>[3,3,3,1] [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4],[1,1]]=>[4,3,3] [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2],[]]=>[3,3,3,2] [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4],[1]]=>[4,4,3] [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3],[]]=>[3,3,3,3] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4],[]]=>[4,4,4] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[2,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[2,2,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[3,3,3,3,3],[2,2,2,2]]=>[3,1,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[2,2,2,2,1,1],[1,1,1]]=>[2,2,2,1] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,2],[2,2,2,1]]=>[3,2,1,1] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[3,3,3,3,1],[2,2,2]]=>[3,2,1,1] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[4,4,4,4],[3,3,3]]=>[4,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[2,2,2,1,1,1],[1,1]]=>[2,2,2,1] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,2],[2,2,1,1]]=>[3,2,2] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[3,3,3,2,1],[2,2,1]]=>[3,3,1] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[4,4,4,3],[3,3,2]]=>[4,2,1] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[3,3,3,1,1],[2,2]]=>[3,2,2] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[4,4,4,2],[3,3,1]]=>[4,2,1] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[4,4,4,1],[3,3]]=>[4,2,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[5,5,5],[4,4]]=>[5,1,1] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[2,2,1,1,1,1],[1]]=>[2,2,1,1,1] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,2],[2,1,1,1]]=>[3,2,1,1] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[3,3,2,2,1],[2,1,1]]=>[3,3,1] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[4,4,3,3],[3,2,2]]=>[4,2,1] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[3,3,2,1,1],[2,1]]=>[3,3,1] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[4,4,3,2],[3,2,1]]=>[4,3] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[4,4,3,1],[3,2]]=>[4,3] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[5,5,4],[4,3]]=>[5,2] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[3,3,1,1,1],[2]]=>[3,2,1,1] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[4,4,2,2],[3,1,1]]=>[4,2,1] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[4,4,2,1],[3,1]]=>[4,3] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[5,5,3],[4,2]]=>[5,2] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[4,4,1,1],[3]]=>[4,2,1] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[5,5,2],[4,1]]=>[5,2] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[5,5,1],[4]]=>[5,2] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[6,6],[5]]=>[6,1] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[4,4,3,3],[3]]=>[4,4,3] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[4,4,4,4],[3,2]]=>[4,4,2,1] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[3,3,3,3,3],[2,1]]=>[3,3,3,2,1] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[4,4,4,3],[3,1]]=>[4,4,3] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[4,4,4,2],[3]]=>[4,4,3] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[5,5,5],[4]]=>[5,5,1] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[4,4,4,3],[3]]=>[4,4,4] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4],[3,1,1]]=>[4,3,3,1] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[3,3,3,3,2],[2]]=>[3,3,3,3] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[4,4,4,4],[3,1]]=>[4,4,3,1] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[3,3,3,3,3],[2]]=>[3,3,3,3,1] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[4,4,4,4],[3]]=>[4,4,4,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1],[]]=>[2,1,1,1,1,1] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,2],[1,1,1,1]]=>[3,1,1,1,1] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[3,2,2,2,1],[1,1,1]]=>[3,2,1,1] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[4,3,3,3],[2,2,2]]=>[4,1,1,1] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[3,2,2,1,1],[1,1]]=>[3,2,2] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[4,3,3,2],[2,2,1]]=>[4,2,1] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[4,3,3,1],[2,2]]=>[4,2,1] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[5,4,4],[3,3]]=>[5,1,1] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[3,2,1,1,1],[1]]=>[3,2,1,1] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[4,3,2,2],[2,1,1]]=>[4,2,1] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[4,3,2,1],[2,1]]=>[4,3] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[5,4,3],[3,2]]=>[5,2] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[4,3,1,1],[2]]=>[4,2,1] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[5,4,2],[3,1]]=>[5,2] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[5,4,1],[3]]=>[5,2] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[6,5],[4]]=>[6,1] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[4,3,3,3],[2]]=>[4,3,3,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1],[]]=>[3,1,1,1,1] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[4,2,2,2],[1,1,1]]=>[4,1,1,1] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[4,2,2,1],[1,1]]=>[4,2,1] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[5,3,3],[2,2]]=>[5,1,1] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[4,2,1,1],[1]]=>[4,2,1] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[5,3,2],[2,1]]=>[5,2] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[5,3,1],[2]]=>[5,2] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[6,4],[3]]=>[6,1] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1,1],[]]=>[4,1,1,1] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[5,2,2],[1,1]]=>[5,1,1] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[5,2,1],[1]]=>[5,2] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[6,3],[2]]=>[6,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1,1],[]]=>[5,1,1] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[6,2],[1]]=>[6,1] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[6,1],[]]=>[6,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7],[]]=>[7] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2],[]]=>[6,2] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[5,2,1],[]]=>[5,2,1] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[6,3],[1]]=>[6,2] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[5,2,2],[]]=>[5,2,2] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[6,3],[]]=>[6,3] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[4,2,1,1],[]]=>[4,2,1,1] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[6,4],[2]]=>[6,2] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[5,3,2],[1]]=>[5,3,1] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,1],[]]=>[4,2,2,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[5,3,3],[1,1]]=>[5,2,2] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,2],[]]=>[4,2,2,2] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[5,3,3],[1]]=>[5,3,2] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[5,3,1],[]]=>[5,3,1] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[6,4],[1]]=>[6,3] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[5,3,2],[]]=>[5,3,2] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[6,4],[]]=>[6,4] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[5,3,3],[]]=>[5,3,3] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[3,2,1,1,1],[]]=>[3,2,1,1,1] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[6,5],[3]]=>[6,2] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[5,4,2],[2]]=>[5,4] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[5,4,3],[2,1]]=>[5,3,1] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[4,3,2,2],[1]]=>[4,3,2,1] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[5,4,3],[2]]=>[5,4,1] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[3,2,2,1,1],[]]=>[3,2,2,1,1] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[5,4,4],[2,2]]=>[5,2,2] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[4,3,3,2],[1,1]]=>[4,3,2,1] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,1],[]]=>[3,2,2,2,1] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3],[1,1,1]]=>[4,2,2,2] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[3,2,2,2,2],[]]=>[3,2,2,2,2] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[4,3,3,3],[1,1]]=>[4,3,2,2] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[5,4,4],[2,1]]=>[5,3,2] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[4,3,3,2],[1]]=>[4,3,3,1] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[5,4,4],[2]]=>[5,4,2] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[4,3,3,3],[1]]=>[4,3,3,2] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[4,3,1,1],[]]=>[4,3,1,1] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[6,5],[2]]=>[6,3] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[5,4,2],[1]]=>[5,4,1] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2,1],[]]=>[4,3,2,1] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[5,4,3],[1,1]]=>[5,3,2] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[4,3,2,2],[]]=>[4,3,2,2] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[5,4,3],[1]]=>[5,4,2] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[5,4,1],[]]=>[5,4,1] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[6,5],[1]]=>[6,4] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[5,4,2],[]]=>[5,4,2] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[6,5],[]]=>[6,5] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[5,4,3],[]]=>[5,4,3] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3,1],[]]=>[4,3,3,1] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[5,4,4],[1,1]]=>[5,3,3] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[4,3,3,2],[]]=>[4,3,3,2] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[5,4,4],[1]]=>[5,4,3] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[4,3,3,3],[]]=>[4,3,3,3] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[5,4,4],[]]=>[5,4,4] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1,1],[]]=>[2,2,1,1,1,1] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[6,6],[4]]=>[6,2] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[5,5,2],[3]]=>[5,4] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[5,5,3],[3,1]]=>[5,4] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[4,4,2,2],[2]]=>[4,4,2] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[5,5,3],[3]]=>[5,5] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[5,5,4],[3,2]]=>[5,3,1] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[4,4,3,2],[2,1]]=>[4,4,2] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3],[2,1,1]]=>[4,3,2,1] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[3,3,2,2,2],[1]]=>[3,3,2,2,1] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[4,4,3,3],[2,1]]=>[4,4,2,1] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[5,5,4],[3,1]]=>[5,4,1] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[4,4,3,2],[2]]=>[4,4,3] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[5,5,4],[3]]=>[5,5,1] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[4,4,3,3],[2]]=>[4,4,3,1] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1,1,1],[]]=>[2,2,2,1,1,1] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[5,5,5],[3,3]]=>[5,2,2] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[4,4,4,2],[2,2]]=>[4,4,2] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3],[2,2,1]]=>[4,3,2,1] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[3,3,3,2,2],[1,1]]=>[3,3,3,1,1] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[4,4,4,3],[2,2]]=>[4,4,2,1] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[2,2,2,2,1,1],[]]=>[2,2,2,2,1,1] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[4,4,4,4],[2,2,2]]=>[4,2,2,2] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[3,3,3,3,2],[1,1,1]]=>[3,3,2,2,1] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3],[1,1,1,1]]=>[3,2,2,2,2] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[2,2,2,2,2,2],[]]=>[2,2,2,2,2,2] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[3,3,3,3,3],[1,1,1]]=>[3,3,2,2,2] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4],[2,2,1]]=>[4,3,2,2] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[3,3,3,3,2],[1,1]]=>[3,3,3,2,1] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[4,4,4,4],[2,2]]=>[4,4,2,2] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[3,3,3,3,3],[1,1]]=>[3,3,3,2,2] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[5,5,5],[3,2]]=>[5,3,2] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[4,4,4,2],[2,1]]=>[4,4,3] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3],[2,1,1]]=>[4,3,3,1] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[3,3,3,2,2],[1]]=>[3,3,3,2,1] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[4,4,4,3],[2,1]]=>[4,4,3,1] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4,1],[2]]=>[4,4,3] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[5,5,5],[3,1]]=>[5,4,2] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[4,4,4,2],[2]]=>[4,4,4] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[5,5,5],[3]]=>[5,5,2] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[4,4,4,3],[2]]=>[4,4,4,1] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3,1],[1]]=>[3,3,3,3] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4],[2,1,1]]=>[4,3,3,2] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[3,3,3,3,2],[1]]=>[3,3,3,3,1] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[4,4,4,4],[2,1]]=>[4,4,3,2] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[3,3,3,3,3],[1]]=>[3,3,3,3,2] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[4,4,4,4],[2]]=>[4,4,4,2] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[3,3,1,1,1],[]]=>[3,3,1,1,1] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[6,6],[3]]=>[6,3] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[5,5,2],[2]]=>[5,5] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[5,5,3],[2,1]]=>[5,4,1] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[4,4,2,2],[1]]=>[4,4,2,1] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[5,5,3],[2]]=>[5,5,1] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[3,3,2,1,1],[]]=>[3,3,2,1,1] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[5,5,4],[2,2]]=>[5,3,2] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[4,4,3,2],[1,1]]=>[4,4,2,1] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3],[1,1,1]]=>[4,3,2,2] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[3,3,2,2,2],[]]=>[3,3,2,2,2] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[4,4,3,3],[1,1]]=>[4,4,2,2] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3,1],[1]]=>[4,4,3] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[5,5,4],[2,1]]=>[5,4,2] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[4,4,3,2],[1]]=>[4,4,3,1] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[5,5,4],[2]]=>[5,5,2] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[4,4,3,3],[1]]=>[4,4,3,2] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[4,4,1,1],[]]=>[4,4,1,1] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[6,6],[2]]=>[6,4] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[5,5,2],[1]]=>[5,5,1] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2,1],[]]=>[4,4,2,1] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[5,5,3],[1,1]]=>[5,4,2] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[4,4,2,2],[]]=>[4,4,2,2] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[5,5,3],[1]]=>[5,5,2] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[5,5,1],[]]=>[5,5,1] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[6,6],[1]]=>[6,5] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[5,5,2],[]]=>[5,5,2] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[6,6],[]]=>[6,6] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[5,5,3],[]]=>[5,5,3] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3,1],[]]=>[4,4,3,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[5,5,4],[1,1]]=>[5,4,3] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[4,4,3,2],[]]=>[4,4,3,2] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[5,5,4],[1]]=>[5,5,3] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[4,4,3,3],[]]=>[4,4,3,3] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[5,5,4],[]]=>[5,5,4] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2],[1,1,1]]=>[4,3,3,1] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4,1],[1,1]]=>[4,4,3] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[5,5,5],[2,2]]=>[5,3,3] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[4,4,4,2],[1,1]]=>[4,4,3,1] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2,1],[]]=>[3,3,3,2,1] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3],[1,1,1]]=>[4,3,3,2] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[3,3,3,2,2],[]]=>[3,3,3,2,2] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[4,4,4,3],[1,1]]=>[4,4,3,2] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4,1],[1]]=>[4,4,4] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[5,5,5],[2,1]]=>[5,4,3] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[4,4,4,2],[1]]=>[4,4,4,1] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[5,5,5],[2]]=>[5,5,3] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[4,4,4,3],[1]]=>[4,4,4,2] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3,1],[]]=>[3,3,3,3,1] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4],[1,1,1]]=>[4,3,3,3] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[3,3,3,3,2],[]]=>[3,3,3,3,2] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[4,4,4,4],[1,1]]=>[4,4,3,3] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[3,3,3,3,3],[]]=>[3,3,3,3,3] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[4,4,4,4],[1]]=>[4,4,4,3] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,1],[]]=>[4,4,4,1] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[5,5,5],[1,1]]=>[5,4,4] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[4,4,4,2],[]]=>[4,4,4,2] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[5,5,5],[1]]=>[5,5,4] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3],[]]=>[4,4,4,3] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[5,5,5],[]]=>[5,5,5] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[4,4,4,4],[]]=>[4,4,4,4] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1] [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[5,5,5,4],[4]]=>[5,5,5] [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[3,3,3,3,3,3],[2]]=>[3,3,3,3,3,1] [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[4,4,4,4,4],[3,1]]=>[4,4,4,3,1] [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5],[4,1]]=>[5,5,4,1] [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[4,4,4,4,3],[3]]=>[4,4,4,4] [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5],[4]]=>[5,5,5,1] [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[4,4,4,4,4],[3]]=>[4,4,4,4,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1,1],[]]=>[3,1,1,1,1,1] [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1,1,1],[]]=>[4,1,1,1,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1,1,1],[]]=>[5,1,1,1] [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[6,1,1],[]]=>[6,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,1],[]]=>[7,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8],[]]=>[8] [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,2],[]]=>[7,2] [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2,1],[]]=>[6,2,1] [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2,2],[]]=>[6,2,2] [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[7,3],[]]=>[7,3] [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[5,2,1,1],[]]=>[5,2,1,1] [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[5,2,2,1],[]]=>[5,2,2,1] [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[6,3,1],[]]=>[6,3,1] [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[4,2,1,1,1],[]]=>[4,2,1,1,1] [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[4,2,2,1,1],[]]=>[4,2,2,1,1] [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[5,3,1,1],[]]=>[5,3,1,1] [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[3,2,1,1,1,1],[]]=>[3,2,1,1,1,1] [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[3,2,2,1,1,1],[]]=>[3,2,2,1,1,1] [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[4,3,1,1,1],[]]=>[4,3,1,1,1] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1,1,1],[]]=>[2,2,1,1,1,1,1] [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[2,2,2,1,1,1,1],[]]=>[2,2,2,1,1,1,1] [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[3,3,1,1,1,1],[]]=>[3,3,1,1,1,1] [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[5,5,4,1],[]]=>[5,5,4,1] [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[3,3,3,3,3,1],[]]=>[3,3,3,3,3,1] [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[4,4,4,4,1],[1]]=>[4,4,4,4] [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[5,5,5,1],[1]]=>[5,5,5] [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[4,4,4,3,1],[]]=>[4,4,4,3,1] [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[5,5,5,1],[]]=>[5,5,5,1] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[4,4,4,4,1],[]]=>[4,4,4,4,1] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[5,5,5,5,1],[]]=>[5,5,5,5,1] [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5],[4]]=>[5,5,5,5,1] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[5,5,5,5,5,1],[]]=>[5,5,5,5,5,1] [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[4,4,4,4,4,1],[]]=>[4,4,4,4,4,1] [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[4,4,4,4,4,4],[3]]=>[4,4,4,4,4,1] [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5,5],[4]]=>[5,5,5,5,5,1] [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[6,6,6,6,6,1],[]]=>[6,6,6,6,6,1] [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[6,6,6,6,1],[]]=>[6,6,6,6,1] [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[5,5,5,5,1],[1]]=>[5,5,5,5] [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[5,5,5,4,1],[]]=>[5,5,5,4,1] [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[5,5,5,5,5],[4,1]]=>[5,5,5,4,1] [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[5,5,5,5,4],[4]]=>[5,5,5,5] [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[6,6,6,6,6],[5]]=>[6,6,6,6,1] [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[6,6,6,6,6,6],[5]]=>[6,6,6,6,6,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[9],[]]=>[9] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,2],[]]=>[8,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,1,1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[10],[]]=>[10] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[2,2,1,1,1,1,1,1],[]]=>[2,2,1,1,1,1,1,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[2,1,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1] [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1,1,1,1],[]]=>[4,1,1,1,1,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1,1,1,1],[]]=>[5,1,1,1,1] [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[6,1,1,1],[]]=>[6,1,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,1,1],[]]=>[7,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,1],[]]=>[8,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[3,1,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1,1] [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[3,2,1,1,1,1,1],[]]=>[3,2,1,1,1,1,1] [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[4,1,1,1,1,1,1],[]]=>[4,1,1,1,1,1,1] [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[4,2,1,1,1,1],[]]=>[4,2,1,1,1,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[5,1,1,1,1,1],[]]=>[5,1,1,1,1,1] [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[5,2,1,1,1],[]]=>[5,2,1,1,1] [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[6,1,1,1,1],[]]=>[6,1,1,1,1] [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[6,2,1,1],[]]=>[6,2,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,1,1,1],[]]=>[7,1,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[7,2,1],[]]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[8,1,1],[]]=>[8,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[9,1],[]]=>[9,1]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Map
dominating partition
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 $311$.