Identifier
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
Images
=>
Cc0002;cc-rep-0Cc0002;cc-rep-1Cc0005;cc-rep-2Cc0005;cc-rep-3
[1]=>[1]=>[1,0]=>[1,0] [2]=>[1,1]=>[1,1,0,0]=>[1,1,0,0] [1,1]=>[2]=>[1,0,1,0]=>[1,0,1,0] [3]=>[1,1,1]=>[1,1,0,1,0,0]=>[1,1,0,1,0,0] [2,1]=>[2,1]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0] [1,1,1]=>[3]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0] [4]=>[1,1,1,1]=>[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0] [3,1]=>[2,1,1]=>[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0] [2,2]=>[2,2]=>[1,1,1,0,0,0]=>[1,1,1,0,0,0] [2,1,1]=>[3,1]=>[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0] [1,1,1,1]=>[4]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0] [5]=>[1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0] [4,1]=>[2,1,1,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0] [3,2]=>[2,2,1]=>[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0] [3,1,1]=>[3,1,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0] [2,2,1]=>[3,2]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0] [2,1,1,1]=>[4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0] [1,1,1,1,1]=>[5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0] [6]=>[1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0] [5,1]=>[2,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0] [4,2]=>[2,2,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0] [4,1,1]=>[3,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0] [3,3]=>[2,2,2]=>[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0] [3,2,1]=>[3,2,1]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0] [3,1,1,1]=>[4,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0] [2,2,2]=>[3,3]=>[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0] [2,2,1,1]=>[4,2]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0] [2,1,1,1,1]=>[5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1]=>[6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0] [7]=>[1,1,1,1,1,1,1]=>[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] [6,1]=>[2,1,1,1,1,1]=>[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] [5,2]=>[2,2,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0] [5,1,1]=>[3,1,1,1,1]=>[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] [4,3]=>[2,2,2,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0] [4,2,1]=>[3,2,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0] [4,1,1,1]=>[4,1,1,1]=>[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] [3,3,1]=>[3,2,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0] [3,2,2]=>[3,3,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0] [3,2,1,1]=>[4,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0] [3,1,1,1,1]=>[5,1,1]=>[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] [2,2,2,1]=>[4,3]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0] [2,2,1,1,1]=>[5,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0] [2,1,1,1,1,1]=>[6,1]=>[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] [1,1,1,1,1,1,1]=>[7]=>[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] [8]=>[1,1,1,1,1,1,1,1]=>[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] [7,1]=>[2,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [6,2]=>[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] [6,1,1]=>[3,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] [5,3]=>[2,2,2,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0] [5,2,1]=>[3,2,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0] [5,1,1,1]=>[4,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] [4,4]=>[2,2,2,2]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0] [4,3,1]=>[3,2,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0] [4,2,2]=>[3,3,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0] [4,2,1,1]=>[4,2,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0] [4,1,1,1,1]=>[5,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] [3,3,2]=>[3,3,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0] [3,3,1,1]=>[4,2,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0] [3,2,2,1]=>[4,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0] [3,2,1,1,1]=>[5,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0] [3,1,1,1,1,1]=>[6,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] [2,2,2,2]=>[4,4]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0] [2,2,2,1,1]=>[5,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0] [2,2,1,1,1,1]=>[6,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0] [2,1,1,1,1,1,1]=>[7,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1]=>[8]=>[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] [9]=>[1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] [8,1]=>[2,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [7,2]=>[2,2,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] [7,1,1]=>[3,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] [6,3]=>[2,2,2,1,1,1]=>[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] [6,2,1]=>[3,2,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] [6,1,1,1]=>[4,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] [5,4]=>[2,2,2,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0] [5,3,1]=>[3,2,2,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0] [5,2,2]=>[3,3,1,1,1]=>[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] [5,2,1,1]=>[4,2,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] [5,1,1,1,1]=>[5,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] [4,4,1]=>[3,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0] [4,3,2]=>[3,3,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0] [4,3,1,1]=>[4,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0] [4,2,2,1]=>[4,3,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0] [4,2,1,1,1]=>[5,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] [4,1,1,1,1,1]=>[6,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] [3,3,3]=>[3,3,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0] [3,3,2,1]=>[4,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0] [3,3,1,1,1]=>[5,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0] [3,2,2,2]=>[4,4,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0] [3,2,2,1,1]=>[5,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0] [3,2,1,1,1,1]=>[6,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] [3,1,1,1,1,1,1]=>[7,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,2,2,2,1]=>[5,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0] [2,2,2,1,1,1]=>[6,3]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0] [2,2,1,1,1,1,1]=>[7,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [2,1,1,1,1,1,1,1]=>[8,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,1]=>[9]=>[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] [10]=>[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] [9,1]=>[2,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [8,2]=>[2,2,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] [8,1,1]=>[3,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] [7,3]=>[2,2,2,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] [7,2,1]=>[3,2,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] [7,1,1,1]=>[4,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] [6,4]=>[2,2,2,2,1,1]=>[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] [6,3,1]=>[3,2,2,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] [6,2,2]=>[3,3,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] [6,2,1,1]=>[4,2,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] [6,1,1,1,1]=>[5,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] [5,5]=>[2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0] [5,4,1]=>[3,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0] [5,3,2]=>[3,3,2,1,1]=>[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] [5,3,1,1]=>[4,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] [5,2,2,1]=>[4,3,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] [5,2,1,1,1]=>[5,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] [5,1,1,1,1,1]=>[6,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] [4,4,2]=>[3,3,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0] [4,4,1,1]=>[4,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0] [4,3,3]=>[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] [4,3,2,1]=>[4,3,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0] [4,3,1,1,1]=>[5,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] [4,2,2,2]=>[4,4,1,1]=>[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] [4,2,2,1,1]=>[5,3,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] [4,2,1,1,1,1]=>[6,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] [4,1,1,1,1,1,1]=>[7,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [3,3,3,1]=>[4,3,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0] [3,3,2,2]=>[4,4,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0] [3,3,2,1,1]=>[5,3,2]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0] [3,3,1,1,1,1]=>[6,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] [3,2,2,2,1]=>[5,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0] [3,2,2,1,1,1]=>[6,3,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] [3,2,1,1,1,1,1]=>[7,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [3,1,1,1,1,1,1,1]=>[8,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,2,2,2,2]=>[5,5]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0] [2,2,2,2,1,1]=>[6,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0] [2,2,2,1,1,1,1]=>[7,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] [2,2,1,1,1,1,1,1]=>[8,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,1,1,1,1,1,1,1,1]=>[9,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,1,1]=>[10]=>[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] [11]=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] [10,1]=>[2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [9,2]=>[2,2,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] [9,1,1]=>[3,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] [8,3]=>[2,2,2,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] [8,2,1]=>[3,2,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] [7,4]=>[2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] [7,3,1]=>[3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] [7,2,2]=>[3,3,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] [7,2,1,1]=>[4,2,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] [7,1,1,1,1]=>[5,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] [6,5]=>[2,2,2,2,2,1]=>[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] [6,4,1]=>[3,2,2,2,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] [6,3,2]=>[3,3,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] [6,3,1,1]=>[4,2,2,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] [6,2,2,1]=>[4,3,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] [6,2,1,1,1]=>[5,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] [6,1,1,1,1,1]=>[6,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] [5,5,1]=>[3,2,2,2,2]=>[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] [5,4,2]=>[3,3,2,2,1]=>[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] [5,4,1,1]=>[4,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] [5,3,3]=>[3,3,3,1,1]=>[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] [5,3,2,1]=>[4,3,2,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] [5,3,1,1,1]=>[5,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] [5,2,2,2]=>[4,4,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] [5,2,2,1,1]=>[5,3,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] [5,2,1,1,1,1]=>[6,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] [5,1,1,1,1,1,1]=>[7,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [4,4,3]=>[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] [4,4,2,1]=>[4,3,2,2]=>[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] [4,4,1,1,1]=>[5,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] [4,3,3,1]=>[4,3,3,1]=>[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] [4,3,2,2]=>[4,4,2,1]=>[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] [4,3,2,1,1]=>[5,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] [4,3,1,1,1,1]=>[6,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] [4,2,2,2,1]=>[5,4,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] [4,2,2,1,1,1]=>[6,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] [4,2,1,1,1,1,1]=>[7,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [4,1,1,1,1,1,1,1]=>[8,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [3,3,3,2]=>[4,4,3]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0] [3,3,3,1,1]=>[5,3,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0] [3,3,2,2,1]=>[5,4,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0] [3,3,2,1,1,1]=>[6,3,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] [3,3,1,1,1,1,1]=>[7,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] [3,2,2,2,2]=>[5,5,1]=>[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] [3,2,2,2,1,1]=>[6,4,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] [3,2,2,1,1,1,1]=>[7,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] [3,2,1,1,1,1,1,1]=>[8,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [3,1,1,1,1,1,1,1,1]=>[9,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,2,2,2,2,1]=>[6,5]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0] [2,2,2,2,1,1,1]=>[7,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] [2,2,2,1,1,1,1,1]=>[8,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [2,2,1,1,1,1,1,1,1]=>[9,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,1,1,1,1,1,1,1,1,1]=>[10,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,1,1,1]=>[11]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] [11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [10,2]=>[2,2,1,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] [9,3]=>[2,2,2,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] [8,4]=>[2,2,2,2,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] [8,3,1]=>[3,2,2,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] [8,2,2]=>[3,3,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] [7,5]=>[2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] [7,4,1]=>[3,2,2,2,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] [7,3,2]=>[3,3,2,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] [7,3,1,1]=>[4,2,2,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] [7,2,2,1]=>[4,3,1,1,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] [6,6]=>[2,2,2,2,2,2]=>[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] [6,5,1]=>[3,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] [6,4,2]=>[3,3,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] [6,4,1,1]=>[4,2,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] [6,3,3]=>[3,3,3,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] [6,3,1,1,1]=>[5,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] [6,2,2,2]=>[4,4,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] [5,5,2]=>[3,3,2,2,2]=>[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] [5,5,1,1]=>[4,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] [5,4,3]=>[3,3,3,2,1]=>[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] [5,4,2,1]=>[4,3,2,2,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] [5,4,1,1,1]=>[5,2,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] [5,3,3,1]=>[4,3,3,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] [5,3,2,2]=>[4,4,2,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] [5,3,2,1,1]=>[5,3,2,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] [5,3,1,1,1,1]=>[6,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] [5,2,2,2,1]=>[5,4,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] [5,2,2,1,1,1]=>[6,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] [4,4,4]=>[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] [4,4,3,1]=>[4,3,3,2]=>[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] [4,4,2,2]=>[4,4,2,2]=>[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] [4,4,2,1,1]=>[5,3,2,2]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] [4,4,1,1,1,1]=>[6,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] [4,3,3,2]=>[4,4,3,1]=>[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] [4,3,3,1,1]=>[5,3,3,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] [4,3,2,2,1]=>[5,4,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] [4,3,2,1,1,1]=>[6,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] [4,3,1,1,1,1,1]=>[7,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] [4,2,2,2,2]=>[5,5,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] [4,2,2,2,1,1]=>[6,4,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] [3,3,3,3]=>[4,4,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0] [3,3,3,2,1]=>[5,4,3]=>[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] [3,3,3,1,1,1]=>[6,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] [3,3,2,2,2]=>[5,5,2]=>[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] [3,3,2,2,1,1]=>[6,4,2]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] [3,3,2,1,1,1,1]=>[7,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0] [3,3,1,1,1,1,1,1]=>[8,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [3,2,2,2,2,1]=>[6,5,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] [3,2,2,2,1,1,1]=>[7,4,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] [3,2,1,1,1,1,1,1,1]=>[9,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,2,2,2,2,2]=>[6,6]=>[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] [2,2,2,2,2,1,1]=>[7,5]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] [2,2,2,2,1,1,1,1]=>[8,4]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] [2,2,2,1,1,1,1,1,1]=>[9,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,2,1,1,1,1,1,1,1,1]=>[10,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,1,1,1,1]=>[12]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [13]=>[1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] [9,4]=>[2,2,2,2,1,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] [8,5]=>[2,2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] [8,3,2]=>[3,3,2,1,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] [7,6]=>[2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] [7,3,3]=>[3,3,3,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] [7,2,2,2]=>[4,4,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] [6,6,1]=>[3,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] [6,5,2]=>[3,3,2,2,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] [6,5,1,1]=>[4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] [6,4,3]=>[3,3,3,2,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] [6,3,3,1]=>[4,3,3,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] [6,3,2,2]=>[4,4,2,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] [6,3,2,1,1]=>[5,3,2,1,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] [6,2,2,2,1]=>[5,4,1,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] [5,5,3]=>[3,3,3,2,2]=>[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] [5,5,2,1]=>[4,3,2,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] [5,5,1,1,1]=>[5,2,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] [5,4,4]=>[3,3,3,3,1]=>[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] [5,4,3,1]=>[4,3,3,2,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] [5,4,2,2]=>[4,4,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] [5,4,2,1,1]=>[5,3,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] [5,4,1,1,1,1]=>[6,2,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] [5,3,3,2]=>[4,4,3,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] [5,3,3,1,1]=>[5,3,3,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] [5,3,2,2,1]=>[5,4,2,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] [5,3,2,1,1,1]=>[6,3,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] [5,2,2,2,2]=>[5,5,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] [4,4,4,1]=>[4,3,3,3]=>[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] [4,4,3,2]=>[4,4,3,2]=>[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] [4,4,3,1,1]=>[5,3,3,2]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] [4,4,2,2,1]=>[5,4,2,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] [4,4,2,1,1,1]=>[6,3,2,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0] [4,4,1,1,1,1,1]=>[7,2,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] [4,3,3,3]=>[4,4,4,1]=>[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] [4,3,3,2,1]=>[5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] [4,3,3,1,1,1]=>[6,3,3,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] [4,3,2,2,2]=>[5,5,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] [4,2,2,2,2,1]=>[6,5,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] [3,3,3,3,1]=>[5,4,4]=>[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] [3,3,3,2,2]=>[5,5,3]=>[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] [3,3,3,2,1,1]=>[6,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] [3,3,3,1,1,1,1]=>[7,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] [3,3,2,2,2,1]=>[6,5,2]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] [3,3,2,2,1,1,1]=>[7,4,2]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0] [3,3,2,1,1,1,1,1]=>[8,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [3,3,1,1,1,1,1,1,1]=>[9,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [3,2,2,2,2,2]=>[6,6,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] [3,2,2,2,2,1,1]=>[7,5,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] [2,2,2,2,2,2,1]=>[7,6]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] [2,2,2,2,2,1,1,1]=>[8,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] [2,2,2,2,1,1,1,1,1]=>[9,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [2,2,2,1,1,1,1,1,1,1]=>[10,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,1,1,1,1,1]=>[13]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [14]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] [9,5]=>[2,2,2,2,2,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] [8,6]=>[2,2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] [8,3,3]=>[3,3,3,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] [7,7]=>[2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] [7,6,1]=>[3,2,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] [7,4,3]=>[3,3,3,2,1,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] [6,6,2]=>[3,3,2,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] [6,6,1,1]=>[4,2,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] [6,5,3]=>[3,3,3,2,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] [6,5,2,1]=>[4,3,2,2,2,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] [6,5,1,1,1]=>[5,2,2,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] [6,4,4]=>[3,3,3,3,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] [6,4,2,2]=>[4,4,2,2,1,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] [6,3,2,2,1]=>[5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] [6,2,2,2,2]=>[5,5,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] [5,5,4]=>[3,3,3,3,2]=>[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] [5,5,3,1]=>[4,3,3,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] [5,5,2,2]=>[4,4,2,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] [5,5,2,1,1]=>[5,3,2,2,2]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] [5,5,1,1,1,1]=>[6,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] [5,4,4,1]=>[4,3,3,3,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] [5,4,3,2]=>[4,4,3,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] [5,4,3,1,1]=>[5,3,3,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] [5,4,2,2,1]=>[5,4,2,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] [5,4,2,1,1,1]=>[6,3,2,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0] [5,3,3,3]=>[4,4,4,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] [5,3,3,2,1]=>[5,4,3,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] [5,3,2,2,2]=>[5,5,2,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] [5,2,2,2,2,1]=>[6,5,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] [4,4,4,2]=>[4,4,3,3]=>[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] [4,4,4,1,1]=>[5,3,3,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] [4,4,3,3]=>[4,4,4,2]=>[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] [4,4,3,2,1]=>[5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] [4,4,3,1,1,1]=>[6,3,3,2]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0] [4,4,2,2,2]=>[5,5,2,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] [4,4,2,1,1,1,1]=>[7,3,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0] [4,3,3,3,1]=>[5,4,4,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] [4,3,3,2,2]=>[5,5,3,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] [4,3,3,2,1,1]=>[6,4,3,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] [4,3,3,1,1,1,1]=>[7,3,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] [4,3,2,2,2,1]=>[6,5,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] [4,2,2,2,2,2]=>[6,6,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] [3,3,3,3,2]=>[5,5,4]=>[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] [3,3,3,3,1,1]=>[6,4,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] [3,3,3,2,2,1]=>[6,5,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] [3,3,3,2,1,1,1]=>[7,4,3]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] [3,3,3,1,1,1,1,1]=>[8,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] [3,3,2,2,2,2]=>[6,6,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] [3,3,2,2,2,1,1]=>[7,5,2]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] [3,3,2,2,1,1,1,1]=>[8,4,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] [3,2,2,2,2,2,1]=>[7,6,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] [2,2,2,2,2,2,2]=>[7,7]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] [2,2,2,2,2,2,1,1]=>[8,6]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] [2,2,2,2,2,1,1,1,1]=>[9,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[14]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [15]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] [9,6]=>[2,2,2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] [8,7]=>[2,2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] [7,7,1]=>[3,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] [7,6,2]=>[3,3,2,2,2,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] [7,4,4]=>[3,3,3,3,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] [6,6,3]=>[3,3,3,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] [6,6,2,1]=>[4,3,2,2,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0] [6,6,1,1,1]=>[5,2,2,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] [6,5,4]=>[3,3,3,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] [6,5,2,2]=>[4,4,2,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] [6,5,2,1,1]=>[5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] [6,4,4,1]=>[4,3,3,3,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] [6,3,3,3]=>[4,4,4,1,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] [6,3,3,2,1]=>[5,4,3,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] [6,3,2,2,2]=>[5,5,2,1,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] [5,5,5]=>[3,3,3,3,3]=>[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] [5,5,4,1]=>[4,3,3,3,2]=>[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] [5,5,3,2]=>[4,4,3,2,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] [5,5,3,1,1]=>[5,3,3,2,2]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0,1,0] [5,5,2,2,1]=>[5,4,2,2,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] [5,4,4,2]=>[4,4,3,3,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] [5,4,4,1,1]=>[5,3,3,3,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] [5,4,3,3]=>[4,4,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] [5,4,3,2,1]=>[5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] [5,4,3,1,1,1]=>[6,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0] [5,4,2,2,2]=>[5,5,2,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] [5,3,3,3,1]=>[5,4,4,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] [5,3,3,2,2]=>[5,5,3,1,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] [5,3,2,2,2,1]=>[6,5,2,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] [4,4,4,3]=>[4,4,4,3]=>[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] [4,4,4,2,1]=>[5,4,3,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] [4,4,4,1,1,1]=>[6,3,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] [4,4,3,3,1]=>[5,4,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] [4,4,3,2,2]=>[5,5,3,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] [4,4,3,2,1,1]=>[6,4,3,2]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] [4,4,3,1,1,1,1]=>[7,3,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] [4,3,3,3,2]=>[5,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] [4,3,3,3,1,1]=>[6,4,4,1]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] [4,3,2,2,2,2]=>[6,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] [3,3,3,3,3]=>[5,5,5]=>[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] [3,3,3,3,2,1]=>[6,5,4]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] [3,3,3,3,1,1,1]=>[7,4,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] [3,3,3,2,2,2]=>[6,6,3]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] [3,3,3,2,2,1,1]=>[7,5,3]=>[1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0] [3,3,3,2,1,1,1,1]=>[8,4,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0] [3,3,3,1,1,1,1,1,1]=>[9,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [3,3,2,2,2,2,1]=>[7,6,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] [3,3,2,2,2,1,1,1]=>[8,5,2]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] [3,2,2,2,2,2,2]=>[7,7,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] [2,2,2,2,2,2,2,1]=>[8,7]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] [2,2,2,2,2,2,1,1,1]=>[9,6]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[15]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [12,4]=>[2,2,2,2,1,1,1,1,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] [10,6]=>[2,2,2,2,2,2,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] [9,7]=>[2,2,2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] [8,8]=>[2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] [8,4,4]=>[3,3,3,3,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] [7,7,2]=>[3,3,2,2,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] [7,7,1,1]=>[4,2,2,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] [7,5,3,1]=>[4,3,3,2,2,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] [7,3,3,3]=>[4,4,4,1,1,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] [6,6,4]=>[3,3,3,3,2,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] [6,6,3,1]=>[4,3,3,2,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] [6,6,2,2]=>[4,4,2,2,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] [6,5,5]=>[3,3,3,3,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] [6,5,4,1]=>[4,3,3,3,2,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] [6,5,3,2]=>[4,4,3,2,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] [6,5,2,2,1]=>[5,4,2,2,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] [6,4,4,2]=>[4,4,3,3,1,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] [6,4,3,2,1]=>[5,4,3,2,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] [5,5,5,1]=>[4,3,3,3,3]=>[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] [5,5,4,2]=>[4,4,3,3,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] [5,5,4,1,1]=>[5,3,3,3,2]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,1,0] [5,5,3,3]=>[4,4,4,2,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] [5,5,2,2,2]=>[5,5,2,2,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] [5,4,4,3]=>[4,4,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] [5,4,4,2,1]=>[5,4,3,3,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] [5,4,4,1,1,1]=>[6,3,3,3,1]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] [5,4,3,2,1,1]=>[6,4,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] [5,4,2,2,2,1]=>[6,5,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,1,0] [4,4,4,4]=>[4,4,4,4]=>[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] [4,4,4,3,1]=>[5,4,4,3]=>[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] [4,4,4,2,2]=>[5,5,3,3]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] [4,4,4,2,1,1]=>[6,4,3,3]=>[1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] [4,4,4,1,1,1,1]=>[7,3,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] [4,4,3,3,2]=>[5,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] [4,4,3,1,1,1,1,1]=>[8,3,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] [4,4,2,2,2,2]=>[6,6,2,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] [4,3,3,3,3]=>[5,5,5,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] [4,3,3,3,2,1]=>[6,5,4,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] [4,3,3,2,2,2]=>[6,6,3,1]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] [4,3,3,2,2,1,1]=>[7,5,3,1]=>[1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0] [3,3,3,3,3,1]=>[6,5,5]=>[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] [3,3,3,3,2,2]=>[6,6,4]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] [3,3,3,3,2,1,1]=>[7,5,4]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0] [3,3,3,3,1,1,1,1]=>[8,4,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] [3,3,3,2,2,1,1,1]=>[8,5,3]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0,1,0] [3,3,2,2,2,2,2]=>[7,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] [3,3,2,2,2,2,1,1]=>[8,6,2]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] [3,2,2,2,2,2,2,1]=>[8,7,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] [2,2,2,2,2,2,2,2]=>[8,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] [2,2,2,2,2,2,2,1,1]=>[9,7]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] [2,2,2,2,2,2,1,1,1,1]=>[10,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] [2,2,2,2,1,1,1,1,1,1,1,1]=>[12,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [9,8]=>[2,2,2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] [9,4,4]=>[3,3,3,3,1,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] [8,8,1]=>[3,2,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] [7,7,3]=>[3,3,3,2,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] [7,5,5]=>[3,3,3,3,3,1,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] [6,6,5]=>[3,3,3,3,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] [6,6,4,1]=>[4,3,3,3,2,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0] [6,5,5,1]=>[4,3,3,3,3,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] [6,5,4,1,1]=>[5,3,3,3,2,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,1,0] [6,5,3,2,1]=>[5,4,3,2,2,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0] [6,4,4,3]=>[4,4,4,3,1,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] [5,5,5,2]=>[4,4,3,3,3]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] [5,5,5,1,1]=>[5,3,3,3,3]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] [5,5,4,3]=>[4,4,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] [5,5,4,2,1]=>[5,4,3,3,2]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0] [5,5,3,3,1]=>[5,4,4,2,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,1,0] [5,4,4,4]=>[4,4,4,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] [5,4,4,3,1]=>[5,4,4,3,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] [5,4,4,2,2]=>[5,5,3,3,1]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] [5,4,3,2,2,1]=>[6,5,3,2,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0] [5,3,3,3,2,1]=>[6,5,4,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] [4,4,4,4,1]=>[5,4,4,4]=>[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] [4,4,4,3,2]=>[5,5,4,3]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] [4,4,4,3,1,1]=>[6,4,4,3]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] [4,4,4,2,2,1]=>[6,5,3,3]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] [4,4,4,2,1,1,1]=>[7,4,3,3]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0] [4,4,3,3,3]=>[5,5,5,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] [4,3,2,2,2,2,2]=>[7,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] [3,3,3,3,3,2]=>[6,6,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] [3,3,3,3,3,1,1]=>[7,5,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0] [3,3,3,3,2,2,1]=>[7,6,4]=>[1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0] [3,3,3,3,1,1,1,1,1]=>[9,4,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] [3,3,3,2,2,2,2]=>[7,7,3]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] [3,3,2,2,2,2,2,1]=>[8,7,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] [3,2,2,2,2,2,2,2]=>[8,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] [2,2,2,2,2,2,2,2,1]=>[9,8]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] []=>[]=>[]=>[] [6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0] [5,5,4,3,2,1]=>[6,5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0] [5,4,4,3,2,1]=>[6,5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0] [4,4,4,3,2,1]=>[6,5,4,3]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0] [5,4,3,3,2,1]=>[6,5,4,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] [6,5,4,3,2]=>[5,5,4,3,2,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] [5,5,4,3,2]=>[5,5,4,3,2]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] [5,4,4,3,2]=>[5,5,4,3,1]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] [6,4,3,3,2]=>[5,5,4,2,1,1]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] [5,5,4,2,2]=>[5,5,3,3,2]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] [6,5,4,3,1]=>[5,4,4,3,2,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0] [5,5,4,3,1]=>[5,4,4,3,2]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0] [6,5,4,2,1]=>[5,4,3,3,2,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0] [6,5,4,3]=>[4,4,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] [7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [6,6,5,4,3,2,1]=>[7,6,5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [6,5,5,4,3,2,1]=>[7,6,5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [5,5,5,4,3,2,1]=>[7,6,5,4,3]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [6,5,4,4,3,2,1]=>[7,6,5,4,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [6,4,4,4,3,2,1]=>[7,6,5,4,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [5,4,4,4,3,2,1]=>[7,6,5,4,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [4,4,4,4,3,2,1]=>[7,6,5,4]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [6,5,4,3,3,2,1]=>[7,6,5,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0,1,0] [6,5,3,3,3,2,1]=>[7,6,5,2,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] [6,4,3,3,3,2,1]=>[7,6,5,2,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] [6,3,3,3,3,2,1]=>[7,6,5,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] [3,3,3,3,3,2,1]=>[7,6,5]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] [6,5,4,3,2,2,1]=>[7,6,4,3,2,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0] [6,5,4,2,2,2,1]=>[7,6,3,3,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,0] [6,5,3,2,2,2,1]=>[7,6,3,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0,0,1,0] [6,5,2,2,2,2,1]=>[7,6,2,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] [6,5,4,3,2,1,1]=>[7,5,4,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0] [6,5,4,3,1,1,1]=>[7,4,4,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,0] [6,5,4,2,1,1,1]=>[7,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0] [5,5,5,1,1,1,1]=>[7,3,3,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] [6,5,4,1,1,1,1]=>[7,3,3,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] [7,6,5,4,3,2]=>[6,6,5,4,3,2,1]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] [5,5,5,4,3,2]=>[6,6,5,4,3]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] [6,6,2,2,2,2]=>[6,6,2,2,2,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] [7,6,5,4,3,1]=>[6,5,5,4,3,2,1]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0] [4,4,4,4,3,1]=>[6,5,5,4]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] [7,6,5,4,2,1]=>[6,5,4,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0,1,0] [7,6,5,3,2,1]=>[6,5,4,3,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,4,3,2,1]=>[6,5,4,3,2,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0] [7,5,4,3,2,1]=>[6,5,4,3,2,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0] [7,4,4,3,2,1]=>[6,5,4,3,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,3,3,2,1]=>[6,5,4,2,2,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] [7,3,3,3,2,1]=>[6,5,4,1,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] [7,6,5,2,2,1]=>[6,5,3,3,3,2,1]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,1,0] [7,6,2,2,2,1]=>[6,5,2,2,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,1,0] [7,6,5,4,1,1]=>[6,4,4,4,3,2,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,1,0] [7,6,5,1,1,1]=>[6,3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] [7,6,5,4,3]=>[5,5,5,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] [7,6,5,4,1]=>[5,4,4,4,3,2,1]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] [7,5,4,3,1]=>[5,4,4,3,2,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0] [7,6,5,4]=>[4,4,4,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] [6,5,4,4]=>[4,4,4,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] [5,5,4,4]=>[4,4,4,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] [2,2,2,2,2,2,2,2,2]=>[9,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] [3,3,3,3,3,3]=>[6,6,6]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] [3,3,3,3,3,3,3,3]=>[8,8,8]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] [3,3,3,3,3,3,1]=>[7,6,6]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] [3,3,3,3,3,3,3]=>[7,7,7]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] [4,3,3,3,3,3]=>[6,6,6,1]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] [4,4,4,4,4]=>[5,5,5,5]=>[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] [4,4,4,4,4,4]=>[6,6,6,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] [5,5,5,5]=>[4,4,4,4,4]=>[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] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>[16,16]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] [6,6,6,6]=>[4,4,4,4,4,4]=>[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] [6,2,2,2,2,2,2]=>[7,7,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] [6,6,6]=>[3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] [7,6,6]=>[3,3,3,3,3,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] [10,4,4]=>[3,3,3,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] [10,10]=>[2,2,2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] [6,6,6,6,6]=>[5,5,5,5,5,5]=>[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] [10,10,10,10]=>[4,4,4,4,4,4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0] [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>[24,24,24,24,24]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0] [5,5,5,5,5,5,5,5,5,5,5,5]=>[12,12,12,12,12]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0] [15,15]=>[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] [5,5,5,5,5,5]=>[6,6,6,6,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] [15,5,5]=>[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] [7,7,7]=>[3,3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] [11,7,5,1]=>[4,3,3,3,3,2,2,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] [9,7,5,3,1]=>[5,4,4,3,3,2,2,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] [11,9,7,5,3,1]=>[6,5,5,4,4,3,3,2,2,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] [9,7,5,5,3,1]=>[6,5,5,4,4,2,2,1,1]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] [11,8,7,5,4,1]=>[6,5,5,5,4,3,3,2,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] [8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,6,5,4,3,2,1]=>[8,7,6,5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,5,5,4,3,2,1]=>[8,7,6,5,4,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,5,4,4,3,2,1]=>[8,7,6,5,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,5,4,3,3,2,1]=>[8,7,6,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0] [7,6,5,4,3,2,2,1]=>[8,7,5,4,3,2,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0] [7,6,5,4,3,2,1,1]=>[8,6,5,4,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0] [9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [8,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [6,6,6,5,4,3,2,1]=>[8,7,6,5,4,3]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [8,7,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,5,5,5,4,3,2,1]=>[8,7,6,5,4,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [8,7,6,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,4,4,4,3,2,1]=>[8,7,6,5,2,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [8,7,6,5,5,4,3,2,1]=>[9,8,7,6,5,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,5,3,3,3,2,1]=>[8,7,6,3,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0] [8,7,6,5,4,4,3,2,1]=>[9,8,7,6,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [7,6,5,4,2,2,2,1]=>[8,7,4,4,3,2,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0,0,0,1,0] [8,7,6,5,4,3,3,2,1]=>[9,8,7,5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0] [7,6,5,4,3,1,1,1]=>[8,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0,1,0] [8,7,6,5,4,3,2,2,1]=>[9,8,6,5,4,3,2,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0] [8,7,6,5,4,3,2,1,1]=>[9,7,6,5,4,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0] [8,7,6,5,4,3,2]=>[7,7,6,5,4,3,2,1]=>[1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0] [8,7,6,5,4,3,1]=>[7,6,6,5,4,3,2,1]=>[1,0,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,1,0] [8,7,6,5,4,2,1]=>[7,6,5,5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,1,0] [8,7,6,5,3,2,1]=>[7,6,5,4,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0,1,0] [8,7,6,4,3,2,1]=>[7,6,5,4,3,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [8,7,5,4,3,2,1]=>[7,6,5,4,3,2,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [8,6,5,4,3,2,1]=>[7,6,5,4,3,2,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [9,8,7,6,5,4,3,2]=>[8,8,7,6,5,4,3,2,1]=>[1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0] [8,7,6,5,4,3]=>[6,6,6,5,4,3,2,1]=>[1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0] [8,7,6,5,4,1,1]=>[7,5,5,5,4,3,2,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0] [8,7,6,5,2,2,1]=>[7,6,4,4,4,3,2,1]=>[1,0,1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0,1,0] [8,7,6,3,3,2,1]=>[7,6,5,3,3,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0,0,0,1,0] [8,7,4,4,3,2,1]=>[7,6,5,4,2,2,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [8,5,5,4,3,2,1]=>[7,6,5,4,3,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [9,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0] [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>[15,15]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] [5,5,5,5,5]=>[5,5,5,5,5]=>[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] [7,7,1,1,1,1]=>[6,2,2,2,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] [6,5,5,5]=>[4,4,4,4,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [5,4,4,4,4]=>[5,5,5,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] [4,4,4,4,4,1]=>[6,5,5,5]=>[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] [5,5,5,5,1]=>[5,4,4,4,4]=>[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] [6,6,6,1]=>[4,3,3,3,3,3]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.