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Identifier
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Images
=>
[1]=>[1] [1,1]=>[2] [2]=>[1,1] [1,1,1]=>[3] [1,2]=>[1,2] [2,1]=>[2,1] [3]=>[1,1,1] [1,1,1,1]=>[4] [1,1,2]=>[1,3] [1,2,1]=>[2,2] [1,3]=>[1,1,2] [2,1,1]=>[3,1] [2,2]=>[1,2,1] [3,1]=>[2,1,1] [4]=>[1,1,1,1] [1,1,1,1,1]=>[5] [1,1,1,2]=>[1,4] [1,1,2,1]=>[2,3] [1,1,3]=>[1,1,3] [1,2,1,1]=>[3,2] [1,2,2]=>[1,2,2] [1,3,1]=>[2,1,2] [1,4]=>[1,1,1,2] [2,1,1,1]=>[4,1] [2,1,2]=>[1,3,1] [2,2,1]=>[2,2,1] [2,3]=>[1,1,2,1] [3,1,1]=>[3,1,1] [3,2]=>[1,2,1,1] [4,1]=>[2,1,1,1] [5]=>[1,1,1,1,1] [1,1,1,1,1,1]=>[6] [1,1,1,1,2]=>[1,5] [1,1,1,2,1]=>[2,4] [1,1,1,3]=>[1,1,4] [1,1,2,1,1]=>[3,3] [1,1,2,2]=>[1,2,3] [1,1,3,1]=>[2,1,3] [1,1,4]=>[1,1,1,3] [1,2,1,1,1]=>[4,2] [1,2,1,2]=>[1,3,2] [1,2,2,1]=>[2,2,2] [1,2,3]=>[1,1,2,2] [1,3,1,1]=>[3,1,2] [1,3,2]=>[1,2,1,2] [1,4,1]=>[2,1,1,2] [1,5]=>[1,1,1,1,2] [2,1,1,1,1]=>[5,1] [2,1,1,2]=>[1,4,1] [2,1,2,1]=>[2,3,1] [2,1,3]=>[1,1,3,1] [2,2,1,1]=>[3,2,1] [2,2,2]=>[1,2,2,1] [2,3,1]=>[2,1,2,1] [2,4]=>[1,1,1,2,1] [3,1,1,1]=>[4,1,1] [3,1,2]=>[1,3,1,1] [3,2,1]=>[2,2,1,1] [3,3]=>[1,1,2,1,1] [4,1,1]=>[3,1,1,1] [4,2]=>[1,2,1,1,1] [5,1]=>[2,1,1,1,1] [6]=>[1,1,1,1,1,1] [1,1,1,1,1,1,1]=>[7] [1,1,1,1,1,2]=>[1,6] [1,1,1,1,2,1]=>[2,5] [1,1,1,1,3]=>[1,1,5] [1,1,1,2,1,1]=>[3,4] [1,1,1,2,2]=>[1,2,4] [1,1,1,3,1]=>[2,1,4] [1,1,1,4]=>[1,1,1,4] [1,1,2,1,1,1]=>[4,3] [1,1,2,1,2]=>[1,3,3] [1,1,2,2,1]=>[2,2,3] [1,1,2,3]=>[1,1,2,3] [1,1,3,1,1]=>[3,1,3] [1,1,3,2]=>[1,2,1,3] [1,1,4,1]=>[2,1,1,3] [1,1,5]=>[1,1,1,1,3] [1,2,1,1,1,1]=>[5,2] [1,2,1,1,2]=>[1,4,2] [1,2,1,2,1]=>[2,3,2] [1,2,1,3]=>[1,1,3,2] [1,2,2,1,1]=>[3,2,2] [1,2,2,2]=>[1,2,2,2] [1,2,3,1]=>[2,1,2,2] [1,2,4]=>[1,1,1,2,2] [1,3,1,1,1]=>[4,1,2] [1,3,1,2]=>[1,3,1,2] [1,3,2,1]=>[2,2,1,2] [1,3,3]=>[1,1,2,1,2] [1,4,1,1]=>[3,1,1,2] [1,4,2]=>[1,2,1,1,2] [1,5,1]=>[2,1,1,1,2] [1,6]=>[1,1,1,1,1,2] [2,1,1,1,1,1]=>[6,1] [2,1,1,1,2]=>[1,5,1] [2,1,1,2,1]=>[2,4,1] [2,1,1,3]=>[1,1,4,1] [2,1,2,1,1]=>[3,3,1] [2,1,2,2]=>[1,2,3,1] [2,1,3,1]=>[2,1,3,1] [2,1,4]=>[1,1,1,3,1] [2,2,1,1,1]=>[4,2,1] [2,2,1,2]=>[1,3,2,1] [2,2,2,1]=>[2,2,2,1] [2,2,3]=>[1,1,2,2,1] [2,3,1,1]=>[3,1,2,1] [2,3,2]=>[1,2,1,2,1] [2,4,1]=>[2,1,1,2,1] [2,5]=>[1,1,1,1,2,1] [3,1,1,1,1]=>[5,1,1] [3,1,1,2]=>[1,4,1,1] [3,1,2,1]=>[2,3,1,1] [3,1,3]=>[1,1,3,1,1] [3,2,1,1]=>[3,2,1,1] [3,2,2]=>[1,2,2,1,1] [3,3,1]=>[2,1,2,1,1] [3,4]=>[1,1,1,2,1,1] [4,1,1,1]=>[4,1,1,1] [4,1,2]=>[1,3,1,1,1] [4,2,1]=>[2,2,1,1,1] [4,3]=>[1,1,2,1,1,1] [5,1,1]=>[3,1,1,1,1] [5,2]=>[1,2,1,1,1,1] [6,1]=>[2,1,1,1,1,1] [7]=>[1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1]=>[8] [1,1,1,1,1,1,2]=>[1,7] [1,1,1,1,1,2,1]=>[2,6] [1,1,1,1,1,3]=>[1,1,6] [1,1,1,1,2,1,1]=>[3,5] [1,1,1,1,2,2]=>[1,2,5] [1,1,1,1,3,1]=>[2,1,5] [1,1,1,1,4]=>[1,1,1,5] [1,1,1,2,1,1,1]=>[4,4] [1,1,1,2,1,2]=>[1,3,4] [1,1,1,2,2,1]=>[2,2,4] [1,1,1,2,3]=>[1,1,2,4] [1,1,1,3,1,1]=>[3,1,4] [1,1,1,3,2]=>[1,2,1,4] [1,1,1,4,1]=>[2,1,1,4] [1,1,1,5]=>[1,1,1,1,4] [1,1,2,1,1,1,1]=>[5,3] [1,1,2,1,1,2]=>[1,4,3] [1,1,2,1,2,1]=>[2,3,3] [1,1,2,1,3]=>[1,1,3,3] [1,1,2,2,1,1]=>[3,2,3] [1,1,2,2,2]=>[1,2,2,3] [1,1,2,3,1]=>[2,1,2,3] [1,1,2,4]=>[1,1,1,2,3] [1,1,3,1,1,1]=>[4,1,3] [1,1,3,1,2]=>[1,3,1,3] [1,1,3,2,1]=>[2,2,1,3] [1,1,3,3]=>[1,1,2,1,3] [1,1,4,1,1]=>[3,1,1,3] [1,1,4,2]=>[1,2,1,1,3] [1,1,5,1]=>[2,1,1,1,3] [1,1,6]=>[1,1,1,1,1,3] [1,2,1,1,1,1,1]=>[6,2] [1,2,1,1,1,2]=>[1,5,2] [1,2,1,1,2,1]=>[2,4,2] [1,2,1,1,3]=>[1,1,4,2] [1,2,1,2,1,1]=>[3,3,2] [1,2,1,2,2]=>[1,2,3,2] [1,2,1,3,1]=>[2,1,3,2] [1,2,1,4]=>[1,1,1,3,2] [1,2,2,1,1,1]=>[4,2,2] [1,2,2,1,2]=>[1,3,2,2] [1,2,2,2,1]=>[2,2,2,2] [1,2,2,3]=>[1,1,2,2,2] [1,2,3,1,1]=>[3,1,2,2] [1,2,3,2]=>[1,2,1,2,2] [1,2,4,1]=>[2,1,1,2,2] [1,2,5]=>[1,1,1,1,2,2] [1,3,1,1,1,1]=>[5,1,2] [1,3,1,1,2]=>[1,4,1,2] [1,3,1,2,1]=>[2,3,1,2] [1,3,1,3]=>[1,1,3,1,2] [1,3,2,1,1]=>[3,2,1,2] [1,3,2,2]=>[1,2,2,1,2] [1,3,3,1]=>[2,1,2,1,2] [1,3,4]=>[1,1,1,2,1,2] [1,4,1,1,1]=>[4,1,1,2] [1,4,1,2]=>[1,3,1,1,2] [1,4,2,1]=>[2,2,1,1,2] [1,4,3]=>[1,1,2,1,1,2] [1,5,1,1]=>[3,1,1,1,2] [1,5,2]=>[1,2,1,1,1,2] [1,6,1]=>[2,1,1,1,1,2] [1,7]=>[1,1,1,1,1,1,2] [2,1,1,1,1,1,1]=>[7,1] [2,1,1,1,1,2]=>[1,6,1] [2,1,1,1,2,1]=>[2,5,1] [2,1,1,1,3]=>[1,1,5,1] [2,1,1,2,1,1]=>[3,4,1] [2,1,1,2,2]=>[1,2,4,1] [2,1,1,3,1]=>[2,1,4,1] [2,1,1,4]=>[1,1,1,4,1] [2,1,2,1,1,1]=>[4,3,1] [2,1,2,1,2]=>[1,3,3,1] [2,1,2,2,1]=>[2,2,3,1] [2,1,2,3]=>[1,1,2,3,1] [2,1,3,1,1]=>[3,1,3,1] [2,1,3,2]=>[1,2,1,3,1] [2,1,4,1]=>[2,1,1,3,1] [2,1,5]=>[1,1,1,1,3,1] [2,2,1,1,1,1]=>[5,2,1] [2,2,1,1,2]=>[1,4,2,1] [2,2,1,2,1]=>[2,3,2,1] [2,2,1,3]=>[1,1,3,2,1] [2,2,2,1,1]=>[3,2,2,1] [2,2,2,2]=>[1,2,2,2,1] [2,2,3,1]=>[2,1,2,2,1] [2,2,4]=>[1,1,1,2,2,1] [2,3,1,1,1]=>[4,1,2,1] [2,3,1,2]=>[1,3,1,2,1] [2,3,2,1]=>[2,2,1,2,1] [2,3,3]=>[1,1,2,1,2,1] [2,4,1,1]=>[3,1,1,2,1] [2,4,2]=>[1,2,1,1,2,1] [2,5,1]=>[2,1,1,1,2,1] [2,6]=>[1,1,1,1,1,2,1] [3,1,1,1,1,1]=>[6,1,1] [3,1,1,1,2]=>[1,5,1,1] [3,1,1,2,1]=>[2,4,1,1] [3,1,1,3]=>[1,1,4,1,1] [3,1,2,1,1]=>[3,3,1,1] [3,1,2,2]=>[1,2,3,1,1] [3,1,3,1]=>[2,1,3,1,1] [3,1,4]=>[1,1,1,3,1,1] [3,2,1,1,1]=>[4,2,1,1] [3,2,1,2]=>[1,3,2,1,1] [3,2,2,1]=>[2,2,2,1,1] [3,2,3]=>[1,1,2,2,1,1] [3,3,1,1]=>[3,1,2,1,1] [3,3,2]=>[1,2,1,2,1,1] [3,4,1]=>[2,1,1,2,1,1] [3,5]=>[1,1,1,1,2,1,1] [4,1,1,1,1]=>[5,1,1,1] [4,1,1,2]=>[1,4,1,1,1] [4,1,2,1]=>[2,3,1,1,1] [4,1,3]=>[1,1,3,1,1,1] [4,2,1,1]=>[3,2,1,1,1] [4,2,2]=>[1,2,2,1,1,1] [4,3,1]=>[2,1,2,1,1,1] [4,4]=>[1,1,1,2,1,1,1] [5,1,1,1]=>[4,1,1,1,1] [5,1,2]=>[1,3,1,1,1,1] [5,2,1]=>[2,2,1,1,1,1] [5,3]=>[1,1,2,1,1,1,1] [6,1,1]=>[3,1,1,1,1,1] [6,2]=>[1,2,1,1,1,1,1] [7,1]=>[2,1,1,1,1,1,1] [8]=>[1,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1]=>[9] [1,1,1,1,1,1,1,2]=>[1,8] [1,1,1,1,1,1,2,1]=>[2,7] [1,1,1,1,1,1,3]=>[1,1,7] [1,1,1,1,1,2,1,1]=>[3,6] [1,1,1,1,1,2,2]=>[1,2,6] [1,1,1,1,1,3,1]=>[2,1,6] [1,1,1,1,1,4]=>[1,1,1,6] [1,1,1,1,2,1,1,1]=>[4,5] [1,1,1,1,2,1,2]=>[1,3,5] [1,1,1,1,2,2,1]=>[2,2,5] [1,1,1,1,2,3]=>[1,1,2,5] [1,1,1,1,3,1,1]=>[3,1,5] [1,1,1,1,3,2]=>[1,2,1,5] [1,1,1,1,4,1]=>[2,1,1,5] [1,1,1,1,5]=>[1,1,1,1,5] [1,1,1,2,1,1,1,1]=>[5,4] [1,1,1,2,1,1,2]=>[1,4,4] [1,1,1,2,1,2,1]=>[2,3,4] [1,1,1,2,1,3]=>[1,1,3,4] [1,1,1,2,2,1,1]=>[3,2,4] [1,1,1,2,2,2]=>[1,2,2,4] [1,1,1,2,3,1]=>[2,1,2,4] [1,1,1,2,4]=>[1,1,1,2,4] [1,1,1,3,1,1,1]=>[4,1,4] [1,1,1,3,1,2]=>[1,3,1,4] [1,1,1,3,2,1]=>[2,2,1,4] [1,1,1,3,3]=>[1,1,2,1,4] [1,1,1,4,1,1]=>[3,1,1,4] [1,1,1,4,2]=>[1,2,1,1,4] [1,1,1,5,1]=>[2,1,1,1,4] [1,1,1,6]=>[1,1,1,1,1,4] [1,1,2,1,1,1,1,1]=>[6,3] [1,1,2,1,1,1,2]=>[1,5,3] [1,1,2,1,1,2,1]=>[2,4,3] [1,1,2,1,1,3]=>[1,1,4,3] [1,1,2,1,2,1,1]=>[3,3,3] [1,1,2,1,2,2]=>[1,2,3,3] [1,1,2,1,3,1]=>[2,1,3,3] [1,1,2,1,4]=>[1,1,1,3,3] [1,1,2,2,1,1,1]=>[4,2,3] [1,1,2,2,1,2]=>[1,3,2,3] [1,1,2,2,2,1]=>[2,2,2,3] [1,1,2,2,3]=>[1,1,2,2,3] [1,1,2,3,1,1]=>[3,1,2,3] [1,1,2,3,2]=>[1,2,1,2,3] [1,1,2,4,1]=>[2,1,1,2,3] [1,1,2,5]=>[1,1,1,1,2,3] [1,1,3,1,1,1,1]=>[5,1,3] [1,1,3,1,1,2]=>[1,4,1,3] [1,1,3,1,2,1]=>[2,3,1,3] [1,1,3,1,3]=>[1,1,3,1,3] [1,1,3,2,1,1]=>[3,2,1,3] [1,1,3,2,2]=>[1,2,2,1,3] [1,1,3,3,1]=>[2,1,2,1,3] [1,1,3,4]=>[1,1,1,2,1,3] [1,1,4,1,1,1]=>[4,1,1,3] [1,1,4,1,2]=>[1,3,1,1,3] [1,1,4,2,1]=>[2,2,1,1,3] [1,1,4,3]=>[1,1,2,1,1,3] [1,1,5,1,1]=>[3,1,1,1,3] [1,1,5,2]=>[1,2,1,1,1,3] [1,1,6,1]=>[2,1,1,1,1,3] [1,1,7]=>[1,1,1,1,1,1,3] [1,2,1,1,1,1,1,1]=>[7,2] [1,2,1,1,1,1,2]=>[1,6,2] [1,2,1,1,1,2,1]=>[2,5,2] [1,2,1,1,1,3]=>[1,1,5,2] [1,2,1,1,2,1,1]=>[3,4,2] [1,2,1,1,2,2]=>[1,2,4,2] [1,2,1,1,3,1]=>[2,1,4,2] [1,2,1,1,4]=>[1,1,1,4,2] [1,2,1,2,1,1,1]=>[4,3,2] [1,2,1,2,1,2]=>[1,3,3,2] [1,2,1,2,2,1]=>[2,2,3,2] [1,2,1,2,3]=>[1,1,2,3,2] [1,2,1,3,1,1]=>[3,1,3,2] [1,2,1,3,2]=>[1,2,1,3,2] [1,2,1,4,1]=>[2,1,1,3,2] [1,2,1,5]=>[1,1,1,1,3,2] [1,2,2,1,1,1,1]=>[5,2,2] [1,2,2,1,1,2]=>[1,4,2,2] [1,2,2,1,2,1]=>[2,3,2,2] [1,2,2,1,3]=>[1,1,3,2,2] [1,2,2,2,1,1]=>[3,2,2,2] [1,2,2,2,2]=>[1,2,2,2,2] [1,2,2,3,1]=>[2,1,2,2,2] [1,2,2,4]=>[1,1,1,2,2,2] [1,2,3,1,1,1]=>[4,1,2,2] [1,2,3,1,2]=>[1,3,1,2,2] [1,2,3,2,1]=>[2,2,1,2,2] [1,2,3,3]=>[1,1,2,1,2,2] [1,2,4,1,1]=>[3,1,1,2,2] [1,2,4,2]=>[1,2,1,1,2,2] [1,2,5,1]=>[2,1,1,1,2,2] [1,2,6]=>[1,1,1,1,1,2,2] [1,3,1,1,1,1,1]=>[6,1,2] [1,3,1,1,1,2]=>[1,5,1,2] [1,3,1,1,2,1]=>[2,4,1,2] [1,3,1,1,3]=>[1,1,4,1,2] [1,3,1,2,1,1]=>[3,3,1,2] [1,3,1,2,2]=>[1,2,3,1,2] [1,3,1,3,1]=>[2,1,3,1,2] [1,3,1,4]=>[1,1,1,3,1,2] [1,3,2,1,1,1]=>[4,2,1,2] [1,3,2,1,2]=>[1,3,2,1,2] [1,3,2,2,1]=>[2,2,2,1,2] [1,3,2,3]=>[1,1,2,2,1,2] [1,3,3,1,1]=>[3,1,2,1,2] [1,3,3,2]=>[1,2,1,2,1,2] [1,3,4,1]=>[2,1,1,2,1,2] [1,3,5]=>[1,1,1,1,2,1,2] [1,4,1,1,1,1]=>[5,1,1,2] [1,4,1,1,2]=>[1,4,1,1,2] [1,4,1,2,1]=>[2,3,1,1,2] [1,4,1,3]=>[1,1,3,1,1,2] [1,4,2,1,1]=>[3,2,1,1,2] [1,4,2,2]=>[1,2,2,1,1,2] [1,4,3,1]=>[2,1,2,1,1,2] [1,4,4]=>[1,1,1,2,1,1,2] [1,5,1,1,1]=>[4,1,1,1,2] [1,5,1,2]=>[1,3,1,1,1,2] [1,5,2,1]=>[2,2,1,1,1,2] [1,5,3]=>[1,1,2,1,1,1,2] [1,6,1,1]=>[3,1,1,1,1,2] [1,6,2]=>[1,2,1,1,1,1,2] [1,7,1]=>[2,1,1,1,1,1,2] [1,8]=>[1,1,1,1,1,1,1,2] [2,1,1,1,1,1,1,1]=>[8,1] [2,1,1,1,1,1,2]=>[1,7,1] [2,1,1,1,1,2,1]=>[2,6,1] [2,1,1,1,1,3]=>[1,1,6,1] [2,1,1,1,2,1,1]=>[3,5,1] [2,1,1,1,2,2]=>[1,2,5,1] [2,1,1,1,3,1]=>[2,1,5,1] [2,1,1,1,4]=>[1,1,1,5,1] [2,1,1,2,1,1,1]=>[4,4,1] [2,1,1,2,1,2]=>[1,3,4,1] [2,1,1,2,2,1]=>[2,2,4,1] [2,1,1,2,3]=>[1,1,2,4,1] [2,1,1,3,1,1]=>[3,1,4,1] [2,1,1,3,2]=>[1,2,1,4,1] [2,1,1,4,1]=>[2,1,1,4,1] [2,1,1,5]=>[1,1,1,1,4,1] [2,1,2,1,1,1,1]=>[5,3,1] [2,1,2,1,1,2]=>[1,4,3,1] [2,1,2,1,2,1]=>[2,3,3,1] [2,1,2,1,3]=>[1,1,3,3,1] [2,1,2,2,1,1]=>[3,2,3,1] [2,1,2,2,2]=>[1,2,2,3,1] [2,1,2,3,1]=>[2,1,2,3,1] [2,1,2,4]=>[1,1,1,2,3,1] [2,1,3,1,1,1]=>[4,1,3,1] [2,1,3,1,2]=>[1,3,1,3,1] [2,1,3,2,1]=>[2,2,1,3,1] [2,1,3,3]=>[1,1,2,1,3,1] [2,1,4,1,1]=>[3,1,1,3,1] [2,1,4,2]=>[1,2,1,1,3,1] [2,1,5,1]=>[2,1,1,1,3,1] [2,1,6]=>[1,1,1,1,1,3,1] [2,2,1,1,1,1,1]=>[6,2,1] [2,2,1,1,1,2]=>[1,5,2,1] [2,2,1,1,2,1]=>[2,4,2,1] [2,2,1,1,3]=>[1,1,4,2,1] [2,2,1,2,1,1]=>[3,3,2,1] [2,2,1,2,2]=>[1,2,3,2,1] [2,2,1,3,1]=>[2,1,3,2,1] [2,2,1,4]=>[1,1,1,3,2,1] [2,2,2,1,1,1]=>[4,2,2,1] [2,2,2,1,2]=>[1,3,2,2,1] [2,2,2,2,1]=>[2,2,2,2,1] [2,2,2,3]=>[1,1,2,2,2,1] [2,2,3,1,1]=>[3,1,2,2,1] [2,2,3,2]=>[1,2,1,2,2,1] [2,2,4,1]=>[2,1,1,2,2,1] [2,2,5]=>[1,1,1,1,2,2,1] [2,3,1,1,1,1]=>[5,1,2,1] [2,3,1,1,2]=>[1,4,1,2,1] [2,3,1,2,1]=>[2,3,1,2,1] [2,3,1,3]=>[1,1,3,1,2,1] [2,3,2,1,1]=>[3,2,1,2,1] [2,3,2,2]=>[1,2,2,1,2,1] [2,3,3,1]=>[2,1,2,1,2,1] [2,3,4]=>[1,1,1,2,1,2,1] [2,4,1,1,1]=>[4,1,1,2,1] [2,4,1,2]=>[1,3,1,1,2,1] [2,4,2,1]=>[2,2,1,1,2,1] [2,4,3]=>[1,1,2,1,1,2,1] [2,5,1,1]=>[3,1,1,1,2,1] [2,5,2]=>[1,2,1,1,1,2,1] [2,6,1]=>[2,1,1,1,1,2,1] [2,7]=>[1,1,1,1,1,1,2,1] [3,1,1,1,1,1,1]=>[7,1,1] [3,1,1,1,1,2]=>[1,6,1,1] [3,1,1,1,2,1]=>[2,5,1,1] [3,1,1,1,3]=>[1,1,5,1,1] [3,1,1,2,1,1]=>[3,4,1,1] [3,1,1,2,2]=>[1,2,4,1,1] [3,1,1,3,1]=>[2,1,4,1,1] [3,1,1,4]=>[1,1,1,4,1,1] [3,1,2,1,1,1]=>[4,3,1,1] [3,1,2,1,2]=>[1,3,3,1,1] [3,1,2,2,1]=>[2,2,3,1,1] [3,1,2,3]=>[1,1,2,3,1,1] [3,1,3,1,1]=>[3,1,3,1,1] [3,1,3,2]=>[1,2,1,3,1,1] [3,1,4,1]=>[2,1,1,3,1,1] [3,1,5]=>[1,1,1,1,3,1,1] [3,2,1,1,1,1]=>[5,2,1,1] [3,2,1,1,2]=>[1,4,2,1,1] [3,2,1,2,1]=>[2,3,2,1,1] [3,2,1,3]=>[1,1,3,2,1,1] [3,2,2,1,1]=>[3,2,2,1,1] [3,2,2,2]=>[1,2,2,2,1,1] [3,2,3,1]=>[2,1,2,2,1,1] [3,2,4]=>[1,1,1,2,2,1,1] [3,3,1,1,1]=>[4,1,2,1,1] [3,3,1,2]=>[1,3,1,2,1,1] [3,3,2,1]=>[2,2,1,2,1,1] [3,3,3]=>[1,1,2,1,2,1,1] [3,4,1,1]=>[3,1,1,2,1,1] [3,4,2]=>[1,2,1,1,2,1,1] [3,5,1]=>[2,1,1,1,2,1,1] [3,6]=>[1,1,1,1,1,2,1,1] [4,1,1,1,1,1]=>[6,1,1,1] [4,1,1,1,2]=>[1,5,1,1,1] [4,1,1,2,1]=>[2,4,1,1,1] [4,1,1,3]=>[1,1,4,1,1,1] [4,1,2,1,1]=>[3,3,1,1,1] [4,1,2,2]=>[1,2,3,1,1,1] [4,1,3,1]=>[2,1,3,1,1,1] [4,1,4]=>[1,1,1,3,1,1,1] [4,2,1,1,1]=>[4,2,1,1,1] [4,2,1,2]=>[1,3,2,1,1,1] [4,2,2,1]=>[2,2,2,1,1,1] [4,2,3]=>[1,1,2,2,1,1,1] [4,3,1,1]=>[3,1,2,1,1,1] [4,3,2]=>[1,2,1,2,1,1,1] [4,4,1]=>[2,1,1,2,1,1,1] [4,5]=>[1,1,1,1,2,1,1,1] [5,1,1,1,1]=>[5,1,1,1,1] [5,1,1,2]=>[1,4,1,1,1,1] [5,1,2,1]=>[2,3,1,1,1,1] [5,1,3]=>[1,1,3,1,1,1,1] [5,2,1,1]=>[3,2,1,1,1,1] [5,2,2]=>[1,2,2,1,1,1,1] [5,3,1]=>[2,1,2,1,1,1,1] [5,4]=>[1,1,1,2,1,1,1,1] [6,1,1,1]=>[4,1,1,1,1,1] [6,1,2]=>[1,3,1,1,1,1,1] [6,2,1]=>[2,2,1,1,1,1,1] [6,3]=>[1,1,2,1,1,1,1,1] [7,1,1]=>[3,1,1,1,1,1,1] [7,2]=>[1,2,1,1,1,1,1,1] [8,1]=>[2,1,1,1,1,1,1,1] [9]=>[1,1,1,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,1,1]=>[10] [1,1,1,1,1,1,1,1,2]=>[1,9] [1,1,1,1,1,1,1,2,1]=>[2,8] [1,1,1,1,1,1,1,3]=>[1,1,8] [1,1,1,1,1,1,2,1,1]=>[3,7] [1,1,1,1,1,1,2,2]=>[1,2,7] [1,1,1,1,1,1,3,1]=>[2,1,7] [1,1,1,1,1,1,4]=>[1,1,1,7] [1,1,1,1,1,2,1,1,1]=>[4,6] [1,1,1,1,1,2,1,2]=>[1,3,6] [1,1,1,1,1,2,2,1]=>[2,2,6] [1,1,1,1,1,2,3]=>[1,1,2,6] [1,1,1,1,1,3,1,1]=>[3,1,6] [1,1,1,1,1,3,2]=>[1,2,1,6] [1,1,1,1,1,4,1]=>[2,1,1,6] [1,1,1,1,1,5]=>[1,1,1,1,6] [1,1,1,1,2,1,1,1,1]=>[5,5] [1,1,1,1,2,1,1,2]=>[1,4,5] [1,1,1,1,2,1,2,1]=>[2,3,5] [1,1,1,1,2,1,3]=>[1,1,3,5] [1,1,1,1,2,2,1,1]=>[3,2,5] [1,1,1,1,2,2,2]=>[1,2,2,5] [1,1,1,1,2,3,1]=>[2,1,2,5] [1,1,1,1,2,4]=>[1,1,1,2,5] [1,1,1,1,3,1,1,1]=>[4,1,5] [1,1,1,1,3,1,2]=>[1,3,1,5] [1,1,1,1,3,2,1]=>[2,2,1,5] [1,1,1,1,3,3]=>[1,1,2,1,5] [1,1,1,1,4,1,1]=>[3,1,1,5] [1,1,1,1,4,2]=>[1,2,1,1,5] [1,1,1,1,5,1]=>[2,1,1,1,5] [1,1,1,1,6]=>[1,1,1,1,1,5] [1,1,1,2,1,1,1,1,1]=>[6,4] [1,1,1,2,1,1,1,2]=>[1,5,4] [1,1,1,2,1,1,2,1]=>[2,4,4] [1,1,1,2,1,1,3]=>[1,1,4,4] [1,1,1,2,1,2,1,1]=>[3,3,4] [1,1,1,2,1,2,2]=>[1,2,3,4] [1,1,1,2,1,3,1]=>[2,1,3,4] [1,1,1,2,1,4]=>[1,1,1,3,4] [1,1,1,2,2,1,1,1]=>[4,2,4] [1,1,1,2,2,1,2]=>[1,3,2,4] [1,1,1,2,2,2,1]=>[2,2,2,4] [1,1,1,2,2,3]=>[1,1,2,2,4] [1,1,1,2,3,1,1]=>[3,1,2,4] [1,1,1,2,3,2]=>[1,2,1,2,4] [1,1,1,2,4,1]=>[2,1,1,2,4] [1,1,1,2,5]=>[1,1,1,1,2,4] [1,1,1,3,1,1,1,1]=>[5,1,4] [1,1,1,3,1,1,2]=>[1,4,1,4] [1,1,1,3,1,2,1]=>[2,3,1,4] [1,1,1,3,1,3]=>[1,1,3,1,4] [1,1,1,3,2,1,1]=>[3,2,1,4] [1,1,1,3,2,2]=>[1,2,2,1,4] [1,1,1,3,3,1]=>[2,1,2,1,4] [1,1,1,3,4]=>[1,1,1,2,1,4] [1,1,1,4,1,1,1]=>[4,1,1,4] [1,1,1,4,1,2]=>[1,3,1,1,4] [1,1,1,4,2,1]=>[2,2,1,1,4] [1,1,1,4,3]=>[1,1,2,1,1,4] [1,1,1,5,1,1]=>[3,1,1,1,4] [1,1,1,5,2]=>[1,2,1,1,1,4] [1,1,1,6,1]=>[2,1,1,1,1,4] [1,1,1,7]=>[1,1,1,1,1,1,4] [1,1,2,1,1,1,1,1,1]=>[7,3] [1,1,2,1,1,1,1,2]=>[1,6,3] [1,1,2,1,1,1,2,1]=>[2,5,3] [1,1,2,1,1,1,3]=>[1,1,5,3] [1,1,2,1,1,2,1,1]=>[3,4,3] [1,1,2,1,1,2,2]=>[1,2,4,3] [1,1,2,1,1,3,1]=>[2,1,4,3] [1,1,2,1,1,4]=>[1,1,1,4,3] [1,1,2,1,2,1,1,1]=>[4,3,3] [1,1,2,1,2,1,2]=>[1,3,3,3] [1,1,2,1,2,2,1]=>[2,2,3,3] [1,1,2,1,2,3]=>[1,1,2,3,3] [1,1,2,1,3,1,1]=>[3,1,3,3] [1,1,2,1,3,2]=>[1,2,1,3,3] [1,1,2,1,4,1]=>[2,1,1,3,3] [1,1,2,1,5]=>[1,1,1,1,3,3] [1,1,2,2,1,1,1,1]=>[5,2,3] [1,1,2,2,1,1,2]=>[1,4,2,3] [1,1,2,2,1,2,1]=>[2,3,2,3] [1,1,2,2,1,3]=>[1,1,3,2,3] [1,1,2,2,2,1,1]=>[3,2,2,3] [1,1,2,2,2,2]=>[1,2,2,2,3] [1,1,2,2,3,1]=>[2,1,2,2,3] [1,1,2,2,4]=>[1,1,1,2,2,3] [1,1,2,3,1,1,1]=>[4,1,2,3] [1,1,2,3,1,2]=>[1,3,1,2,3] [1,1,2,3,2,1]=>[2,2,1,2,3] [1,1,2,3,3]=>[1,1,2,1,2,3] [1,1,2,4,1,1]=>[3,1,1,2,3] [1,1,2,4,2]=>[1,2,1,1,2,3] [1,1,2,5,1]=>[2,1,1,1,2,3] [1,1,2,6]=>[1,1,1,1,1,2,3] [1,1,3,1,1,1,1,1]=>[6,1,3] [1,1,3,1,1,1,2]=>[1,5,1,3] [1,1,3,1,1,2,1]=>[2,4,1,3] [1,1,3,1,1,3]=>[1,1,4,1,3] [1,1,3,1,2,1,1]=>[3,3,1,3] [1,1,3,1,2,2]=>[1,2,3,1,3] [1,1,3,1,3,1]=>[2,1,3,1,3] [1,1,3,1,4]=>[1,1,1,3,1,3] [1,1,3,2,1,1,1]=>[4,2,1,3] [1,1,3,2,1,2]=>[1,3,2,1,3] [1,1,3,2,2,1]=>[2,2,2,1,3] [1,1,3,2,3]=>[1,1,2,2,1,3] [1,1,3,3,1,1]=>[3,1,2,1,3] [1,1,3,3,2]=>[1,2,1,2,1,3] [1,1,3,4,1]=>[2,1,1,2,1,3] [1,1,3,5]=>[1,1,1,1,2,1,3] [1,1,4,1,1,1,1]=>[5,1,1,3] [1,1,4,1,1,2]=>[1,4,1,1,3] [1,1,4,1,2,1]=>[2,3,1,1,3] [1,1,4,1,3]=>[1,1,3,1,1,3] [1,1,4,2,1,1]=>[3,2,1,1,3] [1,1,4,2,2]=>[1,2,2,1,1,3] [1,1,4,3,1]=>[2,1,2,1,1,3] [1,1,4,4]=>[1,1,1,2,1,1,3] [1,1,5,1,1,1]=>[4,1,1,1,3] [1,1,5,1,2]=>[1,3,1,1,1,3] [1,1,5,2,1]=>[2,2,1,1,1,3] [1,1,5,3]=>[1,1,2,1,1,1,3] [1,1,6,1,1]=>[3,1,1,1,1,3] [1,1,6,2]=>[1,2,1,1,1,1,3] [1,1,7,1]=>[2,1,1,1,1,1,3] [1,1,8]=>[1,1,1,1,1,1,1,3] [1,2,1,1,1,1,1,1,1]=>[8,2] [1,2,1,1,1,1,1,2]=>[1,7,2] [1,2,1,1,1,1,2,1]=>[2,6,2] [1,2,1,1,1,1,3]=>[1,1,6,2] [1,2,1,1,1,2,1,1]=>[3,5,2] [1,2,1,1,1,2,2]=>[1,2,5,2] [1,2,1,1,1,3,1]=>[2,1,5,2] [1,2,1,1,1,4]=>[1,1,1,5,2] [1,2,1,1,2,1,1,1]=>[4,4,2] [1,2,1,1,2,1,2]=>[1,3,4,2] [1,2,1,1,2,2,1]=>[2,2,4,2] [1,2,1,1,2,3]=>[1,1,2,4,2] [1,2,1,1,3,1,1]=>[3,1,4,2] [1,2,1,1,3,2]=>[1,2,1,4,2] [1,2,1,1,4,1]=>[2,1,1,4,2] [1,2,1,1,5]=>[1,1,1,1,4,2] [1,2,1,2,1,1,1,1]=>[5,3,2] [1,2,1,2,1,1,2]=>[1,4,3,2] [1,2,1,2,1,2,1]=>[2,3,3,2] [1,2,1,2,1,3]=>[1,1,3,3,2] [1,2,1,2,2,1,1]=>[3,2,3,2] [1,2,1,2,2,2]=>[1,2,2,3,2] [1,2,1,2,3,1]=>[2,1,2,3,2] [1,2,1,2,4]=>[1,1,1,2,3,2] [1,2,1,3,1,1,1]=>[4,1,3,2] [1,2,1,3,1,2]=>[1,3,1,3,2] [1,2,1,3,2,1]=>[2,2,1,3,2] [1,2,1,3,3]=>[1,1,2,1,3,2] [1,2,1,4,1,1]=>[3,1,1,3,2] [1,2,1,4,2]=>[1,2,1,1,3,2] [1,2,1,5,1]=>[2,1,1,1,3,2] [1,2,1,6]=>[1,1,1,1,1,3,2] [1,2,2,1,1,1,1,1]=>[6,2,2] [1,2,2,1,1,1,2]=>[1,5,2,2] [1,2,2,1,1,2,1]=>[2,4,2,2] [1,2,2,1,1,3]=>[1,1,4,2,2] [1,2,2,1,2,1,1]=>[3,3,2,2] [1,2,2,1,2,2]=>[1,2,3,2,2] [1,2,2,1,3,1]=>[2,1,3,2,2] [1,2,2,1,4]=>[1,1,1,3,2,2] [1,2,2,2,1,1,1]=>[4,2,2,2] [1,2,2,2,1,2]=>[1,3,2,2,2] [1,2,2,2,2,1]=>[2,2,2,2,2] [1,2,2,2,3]=>[1,1,2,2,2,2] [1,2,2,3,1,1]=>[3,1,2,2,2] [1,2,2,3,2]=>[1,2,1,2,2,2] [1,2,2,4,1]=>[2,1,1,2,2,2] [1,2,2,5]=>[1,1,1,1,2,2,2] [1,2,3,1,1,1,1]=>[5,1,2,2] [1,2,3,1,1,2]=>[1,4,1,2,2] [1,2,3,1,2,1]=>[2,3,1,2,2] [1,2,3,1,3]=>[1,1,3,1,2,2] [1,2,3,2,1,1]=>[3,2,1,2,2] [1,2,3,2,2]=>[1,2,2,1,2,2] [1,2,3,3,1]=>[2,1,2,1,2,2] [1,2,3,4]=>[1,1,1,2,1,2,2] [1,2,4,1,1,1]=>[4,1,1,2,2] [1,2,4,1,2]=>[1,3,1,1,2,2] [1,2,4,2,1]=>[2,2,1,1,2,2] [1,2,4,3]=>[1,1,2,1,1,2,2] [1,2,5,1,1]=>[3,1,1,1,2,2] [1,2,5,2]=>[1,2,1,1,1,2,2] [1,2,6,1]=>[2,1,1,1,1,2,2] [1,2,7]=>[1,1,1,1,1,1,2,2] [1,3,1,1,1,1,1,1]=>[7,1,2] [1,3,1,1,1,1,2]=>[1,6,1,2] [1,3,1,1,1,2,1]=>[2,5,1,2] [1,3,1,1,1,3]=>[1,1,5,1,2] [1,3,1,1,2,1,1]=>[3,4,1,2] [1,3,1,1,2,2]=>[1,2,4,1,2] [1,3,1,1,3,1]=>[2,1,4,1,2] [1,3,1,1,4]=>[1,1,1,4,1,2] [1,3,1,2,1,1,1]=>[4,3,1,2] [1,3,1,2,1,2]=>[1,3,3,1,2] [1,3,1,2,2,1]=>[2,2,3,1,2] [1,3,1,2,3]=>[1,1,2,3,1,2] [1,3,1,3,1,1]=>[3,1,3,1,2] [1,3,1,3,2]=>[1,2,1,3,1,2] [1,3,1,4,1]=>[2,1,1,3,1,2] [1,3,1,5]=>[1,1,1,1,3,1,2] [1,3,2,1,1,1,1]=>[5,2,1,2] [1,3,2,1,1,2]=>[1,4,2,1,2] [1,3,2,1,2,1]=>[2,3,2,1,2] [1,3,2,1,3]=>[1,1,3,2,1,2] [1,3,2,2,1,1]=>[3,2,2,1,2] [1,3,2,2,2]=>[1,2,2,2,1,2] [1,3,2,3,1]=>[2,1,2,2,1,2] [1,3,2,4]=>[1,1,1,2,2,1,2] [1,3,3,1,1,1]=>[4,1,2,1,2] [1,3,3,1,2]=>[1,3,1,2,1,2] [1,3,3,2,1]=>[2,2,1,2,1,2] [1,3,3,3]=>[1,1,2,1,2,1,2] [1,3,4,1,1]=>[3,1,1,2,1,2] [1,3,4,2]=>[1,2,1,1,2,1,2] [1,3,5,1]=>[2,1,1,1,2,1,2] [1,3,6]=>[1,1,1,1,1,2,1,2] [1,4,1,1,1,1,1]=>[6,1,1,2] [1,4,1,1,1,2]=>[1,5,1,1,2] [1,4,1,1,2,1]=>[2,4,1,1,2] [1,4,1,1,3]=>[1,1,4,1,1,2] [1,4,1,2,1,1]=>[3,3,1,1,2] [1,4,1,2,2]=>[1,2,3,1,1,2] [1,4,1,3,1]=>[2,1,3,1,1,2] [1,4,1,4]=>[1,1,1,3,1,1,2] [1,4,2,1,1,1]=>[4,2,1,1,2] [1,4,2,1,2]=>[1,3,2,1,1,2] [1,4,2,2,1]=>[2,2,2,1,1,2] [1,4,2,3]=>[1,1,2,2,1,1,2] [1,4,3,1,1]=>[3,1,2,1,1,2] [1,4,3,2]=>[1,2,1,2,1,1,2] [1,4,4,1]=>[2,1,1,2,1,1,2] [1,4,5]=>[1,1,1,1,2,1,1,2] [1,5,1,1,1,1]=>[5,1,1,1,2] [1,5,1,1,2]=>[1,4,1,1,1,2] [1,5,1,2,1]=>[2,3,1,1,1,2] [1,5,1,3]=>[1,1,3,1,1,1,2] [1,5,2,1,1]=>[3,2,1,1,1,2] [1,5,2,2]=>[1,2,2,1,1,1,2] [1,5,3,1]=>[2,1,2,1,1,1,2] [1,5,4]=>[1,1,1,2,1,1,1,2] [1,6,1,1,1]=>[4,1,1,1,1,2] [1,6,1,2]=>[1,3,1,1,1,1,2] [1,6,2,1]=>[2,2,1,1,1,1,2] [1,6,3]=>[1,1,2,1,1,1,1,2] [1,7,1,1]=>[3,1,1,1,1,1,2] [1,7,2]=>[1,2,1,1,1,1,1,2] [1,8,1]=>[2,1,1,1,1,1,1,2] [1,9]=>[1,1,1,1,1,1,1,1,2] [2,1,1,1,1,1,1,1,1]=>[9,1] [2,1,1,1,1,1,1,2]=>[1,8,1] [2,1,1,1,1,1,2,1]=>[2,7,1] [2,1,1,1,1,1,3]=>[1,1,7,1] [2,1,1,1,1,2,1,1]=>[3,6,1] [2,1,1,1,1,2,2]=>[1,2,6,1] [2,1,1,1,1,3,1]=>[2,1,6,1] [2,1,1,1,1,4]=>[1,1,1,6,1] [2,1,1,1,2,1,1,1]=>[4,5,1] [2,1,1,1,2,1,2]=>[1,3,5,1] [2,1,1,1,2,2,1]=>[2,2,5,1] [2,1,1,1,2,3]=>[1,1,2,5,1] [2,1,1,1,3,1,1]=>[3,1,5,1] [2,1,1,1,3,2]=>[1,2,1,5,1] [2,1,1,1,4,1]=>[2,1,1,5,1] [2,1,1,1,5]=>[1,1,1,1,5,1] [2,1,1,2,1,1,1,1]=>[5,4,1] [2,1,1,2,1,1,2]=>[1,4,4,1] [2,1,1,2,1,2,1]=>[2,3,4,1] [2,1,1,2,1,3]=>[1,1,3,4,1] [2,1,1,2,2,1,1]=>[3,2,4,1] [2,1,1,2,2,2]=>[1,2,2,4,1] [2,1,1,2,3,1]=>[2,1,2,4,1] [2,1,1,2,4]=>[1,1,1,2,4,1] [2,1,1,3,1,1,1]=>[4,1,4,1] [2,1,1,3,1,2]=>[1,3,1,4,1] [2,1,1,3,2,1]=>[2,2,1,4,1] [2,1,1,3,3]=>[1,1,2,1,4,1] [2,1,1,4,1,1]=>[3,1,1,4,1] [2,1,1,4,2]=>[1,2,1,1,4,1] [2,1,1,5,1]=>[2,1,1,1,4,1] [2,1,1,6]=>[1,1,1,1,1,4,1] [2,1,2,1,1,1,1,1]=>[6,3,1] [2,1,2,1,1,1,2]=>[1,5,3,1] [2,1,2,1,1,2,1]=>[2,4,3,1] [2,1,2,1,1,3]=>[1,1,4,3,1] [2,1,2,1,2,1,1]=>[3,3,3,1] [2,1,2,1,2,2]=>[1,2,3,3,1] [2,1,2,1,3,1]=>[2,1,3,3,1] [2,1,2,1,4]=>[1,1,1,3,3,1] [2,1,2,2,1,1,1]=>[4,2,3,1] [2,1,2,2,1,2]=>[1,3,2,3,1] [2,1,2,2,2,1]=>[2,2,2,3,1] [2,1,2,2,3]=>[1,1,2,2,3,1] [2,1,2,3,1,1]=>[3,1,2,3,1] [2,1,2,3,2]=>[1,2,1,2,3,1] [2,1,2,4,1]=>[2,1,1,2,3,1] [2,1,2,5]=>[1,1,1,1,2,3,1] [2,1,3,1,1,1,1]=>[5,1,3,1] [2,1,3,1,1,2]=>[1,4,1,3,1] [2,1,3,1,2,1]=>[2,3,1,3,1] [2,1,3,1,3]=>[1,1,3,1,3,1] [2,1,3,2,1,1]=>[3,2,1,3,1] [2,1,3,2,2]=>[1,2,2,1,3,1] [2,1,3,3,1]=>[2,1,2,1,3,1] [2,1,3,4]=>[1,1,1,2,1,3,1] [2,1,4,1,1,1]=>[4,1,1,3,1] [2,1,4,1,2]=>[1,3,1,1,3,1] [2,1,4,2,1]=>[2,2,1,1,3,1] [2,1,4,3]=>[1,1,2,1,1,3,1] [2,1,5,1,1]=>[3,1,1,1,3,1] [2,1,5,2]=>[1,2,1,1,1,3,1] [2,1,6,1]=>[2,1,1,1,1,3,1] [2,1,7]=>[1,1,1,1,1,1,3,1] [2,2,1,1,1,1,1,1]=>[7,2,1] [2,2,1,1,1,1,2]=>[1,6,2,1] [2,2,1,1,1,2,1]=>[2,5,2,1] [2,2,1,1,1,3]=>[1,1,5,2,1] [2,2,1,1,2,1,1]=>[3,4,2,1] [2,2,1,1,2,2]=>[1,2,4,2,1] [2,2,1,1,3,1]=>[2,1,4,2,1] [2,2,1,1,4]=>[1,1,1,4,2,1] [2,2,1,2,1,1,1]=>[4,3,2,1] [2,2,1,2,1,2]=>[1,3,3,2,1] [2,2,1,2,2,1]=>[2,2,3,2,1] [2,2,1,2,3]=>[1,1,2,3,2,1] [2,2,1,3,1,1]=>[3,1,3,2,1] [2,2,1,3,2]=>[1,2,1,3,2,1] [2,2,1,4,1]=>[2,1,1,3,2,1] [2,2,1,5]=>[1,1,1,1,3,2,1] [2,2,2,1,1,1,1]=>[5,2,2,1] [2,2,2,1,1,2]=>[1,4,2,2,1] [2,2,2,1,2,1]=>[2,3,2,2,1] [2,2,2,1,3]=>[1,1,3,2,2,1] [2,2,2,2,1,1]=>[3,2,2,2,1] [2,2,2,2,2]=>[1,2,2,2,2,1] [2,2,2,3,1]=>[2,1,2,2,2,1] [2,2,2,4]=>[1,1,1,2,2,2,1] [2,2,3,1,1,1]=>[4,1,2,2,1] [2,2,3,1,2]=>[1,3,1,2,2,1] [2,2,3,2,1]=>[2,2,1,2,2,1] [2,2,3,3]=>[1,1,2,1,2,2,1] [2,2,4,1,1]=>[3,1,1,2,2,1] [2,2,4,2]=>[1,2,1,1,2,2,1] [2,2,5,1]=>[2,1,1,1,2,2,1] [2,2,6]=>[1,1,1,1,1,2,2,1] [2,3,1,1,1,1,1]=>[6,1,2,1] [2,3,1,1,1,2]=>[1,5,1,2,1] [2,3,1,1,2,1]=>[2,4,1,2,1] [2,3,1,1,3]=>[1,1,4,1,2,1] [2,3,1,2,1,1]=>[3,3,1,2,1] [2,3,1,2,2]=>[1,2,3,1,2,1] [2,3,1,3,1]=>[2,1,3,1,2,1] [2,3,1,4]=>[1,1,1,3,1,2,1] [2,3,2,1,1,1]=>[4,2,1,2,1] [2,3,2,1,2]=>[1,3,2,1,2,1] [2,3,2,2,1]=>[2,2,2,1,2,1] [2,3,2,3]=>[1,1,2,2,1,2,1] [2,3,3,1,1]=>[3,1,2,1,2,1] [2,3,3,2]=>[1,2,1,2,1,2,1] [2,3,4,1]=>[2,1,1,2,1,2,1] [2,3,5]=>[1,1,1,1,2,1,2,1] [2,4,1,1,1,1]=>[5,1,1,2,1] [2,4,1,1,2]=>[1,4,1,1,2,1] [2,4,1,2,1]=>[2,3,1,1,2,1] [2,4,1,3]=>[1,1,3,1,1,2,1] [2,4,2,1,1]=>[3,2,1,1,2,1] [2,4,2,2]=>[1,2,2,1,1,2,1] [2,4,3,1]=>[2,1,2,1,1,2,1] [2,4,4]=>[1,1,1,2,1,1,2,1] [2,5,1,1,1]=>[4,1,1,1,2,1] [2,5,1,2]=>[1,3,1,1,1,2,1] [2,5,2,1]=>[2,2,1,1,1,2,1] [2,5,3]=>[1,1,2,1,1,1,2,1] [2,6,1,1]=>[3,1,1,1,1,2,1] [2,6,2]=>[1,2,1,1,1,1,2,1] [2,7,1]=>[2,1,1,1,1,1,2,1] [2,8]=>[1,1,1,1,1,1,1,2,1] [3,1,1,1,1,1,1,1]=>[8,1,1] [3,1,1,1,1,1,2]=>[1,7,1,1] [3,1,1,1,1,2,1]=>[2,6,1,1] [3,1,1,1,1,3]=>[1,1,6,1,1] [3,1,1,1,2,1,1]=>[3,5,1,1] [3,1,1,1,2,2]=>[1,2,5,1,1] [3,1,1,1,3,1]=>[2,1,5,1,1] [3,1,1,1,4]=>[1,1,1,5,1,1] [3,1,1,2,1,1,1]=>[4,4,1,1] [3,1,1,2,1,2]=>[1,3,4,1,1] [3,1,1,2,2,1]=>[2,2,4,1,1] [3,1,1,2,3]=>[1,1,2,4,1,1] [3,1,1,3,1,1]=>[3,1,4,1,1] [3,1,1,3,2]=>[1,2,1,4,1,1] [3,1,1,4,1]=>[2,1,1,4,1,1] [3,1,1,5]=>[1,1,1,1,4,1,1] [3,1,2,1,1,1,1]=>[5,3,1,1] [3,1,2,1,1,2]=>[1,4,3,1,1] [3,1,2,1,2,1]=>[2,3,3,1,1] [3,1,2,1,3]=>[1,1,3,3,1,1] [3,1,2,2,1,1]=>[3,2,3,1,1] [3,1,2,2,2]=>[1,2,2,3,1,1] [3,1,2,3,1]=>[2,1,2,3,1,1] [3,1,2,4]=>[1,1,1,2,3,1,1] [3,1,3,1,1,1]=>[4,1,3,1,1] [3,1,3,1,2]=>[1,3,1,3,1,1] [3,1,3,2,1]=>[2,2,1,3,1,1] [3,1,3,3]=>[1,1,2,1,3,1,1] [3,1,4,1,1]=>[3,1,1,3,1,1] [3,1,4,2]=>[1,2,1,1,3,1,1] [3,1,5,1]=>[2,1,1,1,3,1,1] [3,1,6]=>[1,1,1,1,1,3,1,1] [3,2,1,1,1,1,1]=>[6,2,1,1] [3,2,1,1,1,2]=>[1,5,2,1,1] [3,2,1,1,2,1]=>[2,4,2,1,1] [3,2,1,1,3]=>[1,1,4,2,1,1] [3,2,1,2,1,1]=>[3,3,2,1,1] [3,2,1,2,2]=>[1,2,3,2,1,1] [3,2,1,3,1]=>[2,1,3,2,1,1] [3,2,1,4]=>[1,1,1,3,2,1,1] [3,2,2,1,1,1]=>[4,2,2,1,1] [3,2,2,1,2]=>[1,3,2,2,1,1] [3,2,2,2,1]=>[2,2,2,2,1,1] [3,2,2,3]=>[1,1,2,2,2,1,1] [3,2,3,1,1]=>[3,1,2,2,1,1] [3,2,3,2]=>[1,2,1,2,2,1,1] [3,2,4,1]=>[2,1,1,2,2,1,1] [3,2,5]=>[1,1,1,1,2,2,1,1] [3,3,1,1,1,1]=>[5,1,2,1,1] [3,3,1,1,2]=>[1,4,1,2,1,1] [3,3,1,2,1]=>[2,3,1,2,1,1] [3,3,1,3]=>[1,1,3,1,2,1,1] [3,3,2,1,1]=>[3,2,1,2,1,1] [3,3,2,2]=>[1,2,2,1,2,1,1] [3,3,3,1]=>[2,1,2,1,2,1,1] [3,3,4]=>[1,1,1,2,1,2,1,1] [3,4,1,1,1]=>[4,1,1,2,1,1] [3,4,1,2]=>[1,3,1,1,2,1,1] [3,4,2,1]=>[2,2,1,1,2,1,1] [3,4,3]=>[1,1,2,1,1,2,1,1] [3,5,1,1]=>[3,1,1,1,2,1,1] [3,5,2]=>[1,2,1,1,1,2,1,1] [3,6,1]=>[2,1,1,1,1,2,1,1] [3,7]=>[1,1,1,1,1,1,2,1,1] [4,1,1,1,1,1,1]=>[7,1,1,1] [4,1,1,1,1,2]=>[1,6,1,1,1] [4,1,1,1,2,1]=>[2,5,1,1,1] [4,1,1,1,3]=>[1,1,5,1,1,1] [4,1,1,2,1,1]=>[3,4,1,1,1] [4,1,1,2,2]=>[1,2,4,1,1,1] [4,1,1,3,1]=>[2,1,4,1,1,1] [4,1,1,4]=>[1,1,1,4,1,1,1] [4,1,2,1,1,1]=>[4,3,1,1,1] [4,1,2,1,2]=>[1,3,3,1,1,1] [4,1,2,2,1]=>[2,2,3,1,1,1] [4,1,2,3]=>[1,1,2,3,1,1,1] [4,1,3,1,1]=>[3,1,3,1,1,1] [4,1,3,2]=>[1,2,1,3,1,1,1] [4,1,4,1]=>[2,1,1,3,1,1,1] [4,1,5]=>[1,1,1,1,3,1,1,1] [4,2,1,1,1,1]=>[5,2,1,1,1] [4,2,1,1,2]=>[1,4,2,1,1,1] [4,2,1,2,1]=>[2,3,2,1,1,1] [4,2,1,3]=>[1,1,3,2,1,1,1] [4,2,2,1,1]=>[3,2,2,1,1,1] [4,2,2,2]=>[1,2,2,2,1,1,1] [4,2,3,1]=>[2,1,2,2,1,1,1] [4,2,4]=>[1,1,1,2,2,1,1,1] [4,3,1,1,1]=>[4,1,2,1,1,1] [4,3,1,2]=>[1,3,1,2,1,1,1] [4,3,2,1]=>[2,2,1,2,1,1,1] [4,3,3]=>[1,1,2,1,2,1,1,1] [4,4,1,1]=>[3,1,1,2,1,1,1] [4,4,2]=>[1,2,1,1,2,1,1,1] [4,5,1]=>[2,1,1,1,2,1,1,1] [4,6]=>[1,1,1,1,1,2,1,1,1] [5,1,1,1,1,1]=>[6,1,1,1,1] [5,1,1,1,2]=>[1,5,1,1,1,1] [5,1,1,2,1]=>[2,4,1,1,1,1] [5,1,1,3]=>[1,1,4,1,1,1,1] [5,1,2,1,1]=>[3,3,1,1,1,1] [5,1,2,2]=>[1,2,3,1,1,1,1] [5,1,3,1]=>[2,1,3,1,1,1,1] [5,1,4]=>[1,1,1,3,1,1,1,1] [5,2,1,1,1]=>[4,2,1,1,1,1] [5,2,1,2]=>[1,3,2,1,1,1,1] [5,2,2,1]=>[2,2,2,1,1,1,1] [5,2,3]=>[1,1,2,2,1,1,1,1] [5,3,1,1]=>[3,1,2,1,1,1,1] [5,3,2]=>[1,2,1,2,1,1,1,1] [5,4,1]=>[2,1,1,2,1,1,1,1] [5,5]=>[1,1,1,1,2,1,1,1,1] [6,1,1,1,1]=>[5,1,1,1,1,1] [6,1,1,2]=>[1,4,1,1,1,1,1] [6,1,2,1]=>[2,3,1,1,1,1,1] [6,1,3]=>[1,1,3,1,1,1,1,1] [6,2,1,1]=>[3,2,1,1,1,1,1] [6,2,2]=>[1,2,2,1,1,1,1,1] [6,3,1]=>[2,1,2,1,1,1,1,1] [6,4]=>[1,1,1,2,1,1,1,1,1] [7,1,1,1]=>[4,1,1,1,1,1,1] [7,1,2]=>[1,3,1,1,1,1,1,1] [7,2,1]=>[2,2,1,1,1,1,1,1] [7,3]=>[1,1,2,1,1,1,1,1,1] [8,1,1]=>[3,1,1,1,1,1,1,1] [8,2]=>[1,2,1,1,1,1,1,1,1] [9,1]=>[2,1,1,1,1,1,1,1,1] [10]=>[1,1,1,1,1,1,1,1,1,1] [1,10]=>[1,1,1,1,1,1,1,1,1,2] [1,8,1,1]=>[3,1,1,1,1,1,1,2] [1,7,2,1]=>[2,2,1,1,1,1,1,2] [1,6,3,1]=>[2,1,2,1,1,1,1,2] [1,5,4,1]=>[2,1,1,2,1,1,1,2] [1,4,5,1]=>[2,1,1,1,2,1,1,2] [1,3,6,1]=>[2,1,1,1,1,2,1,2] [1,2,7,1]=>[2,1,1,1,1,1,2,2] [1,1,8,1]=>[2,1,1,1,1,1,1,3] [10,1]=>[2,1,1,1,1,1,1,1,1,1] [1,8,2]=>[1,2,1,1,1,1,1,1,2] [1,7,1,2]=>[1,3,1,1,1,1,1,2] [1,6,1,1,2]=>[1,4,1,1,1,1,2] [1,5,1,1,1,2]=>[1,5,1,1,1,2] [1,4,1,1,1,1,2]=>[1,6,1,1,2] [1,3,1,1,1,1,1,2]=>[1,7,1,2] [1,2,1,1,1,1,1,1,2]=>[1,8,2] [1,1,1,1,1,1,1,1,1,2]=>[1,10] [1,7,3]=>[1,1,2,1,1,1,1,1,2] [1,6,2,2]=>[1,2,2,1,1,1,1,2] [1,5,2,1,2]=>[1,3,2,1,1,1,2] [1,4,2,1,1,2]=>[1,4,2,1,1,2] [1,3,2,1,1,1,2]=>[1,5,2,1,2] [1,2,2,1,1,1,1,2]=>[1,6,2,2] [1,1,2,1,1,1,1,1,2]=>[1,7,3] [1,2,2,2,2,2]=>[1,2,2,2,2,2] [1,2,2,2,1,3]=>[1,1,3,2,2,2] [1,2,2,1,3,2]=>[1,2,1,3,2,2] [1,2,2,1,2,3]=>[1,1,2,3,2,2] [1,2,2,1,1,4]=>[1,1,1,4,2,2] [1,2,1,3,2,2]=>[1,2,2,1,3,2] [1,2,1,3,1,3]=>[1,1,3,1,3,2] [1,2,1,2,3,2]=>[1,2,1,2,3,2] [1,2,1,2,2,3]=>[1,1,2,2,3,2] [1,2,1,2,1,4]=>[1,1,1,3,3,2] [1,2,1,1,4,2]=>[1,2,1,1,4,2] [1,2,1,1,3,3]=>[1,1,2,1,4,2] [1,2,1,1,2,4]=>[1,1,1,2,4,2] [1,2,1,1,1,5]=>[1,1,1,1,5,2] [1,1,3,2,2,2]=>[1,2,2,2,1,3] [1,1,3,2,1,3]=>[1,1,3,2,1,3] [1,1,3,1,3,2]=>[1,2,1,3,1,3] [1,1,3,1,2,3]=>[1,1,2,3,1,3] [1,1,3,1,1,4]=>[1,1,1,4,1,3] [1,1,2,3,2,2]=>[1,2,2,1,2,3] [1,1,2,3,1,3]=>[1,1,3,1,2,3] [1,1,2,2,3,2]=>[1,2,1,2,2,3] [1,1,2,2,2,3]=>[1,1,2,2,2,3] [1,1,2,2,1,4]=>[1,1,1,3,2,3] [1,1,2,1,4,2]=>[1,2,1,1,3,3] [1,1,2,1,3,3]=>[1,1,2,1,3,3] [1,1,2,1,2,4]=>[1,1,1,2,3,3] [1,1,2,1,1,5]=>[1,1,1,1,4,3] [1,1,1,4,2,2]=>[1,2,2,1,1,4] [1,1,1,4,1,3]=>[1,1,3,1,1,4] [1,1,1,3,3,2]=>[1,2,1,2,1,4] [1,1,1,3,2,3]=>[1,1,2,2,1,4] [1,1,1,3,1,4]=>[1,1,1,3,1,4] [1,1,1,2,4,2]=>[1,2,1,1,2,4] [1,1,1,2,3,3]=>[1,1,2,1,2,4] [1,1,1,2,2,4]=>[1,1,1,2,2,4] [1,1,1,2,1,5]=>[1,1,1,1,3,4] [1,1,1,1,5,2]=>[1,2,1,1,1,5] [1,1,1,1,4,3]=>[1,1,2,1,1,5] [1,1,1,1,3,4]=>[1,1,1,2,1,5] [1,1,1,1,2,5]=>[1,1,1,1,2,5] [1,1,1,1,1,6]=>[1,1,1,1,1,6] [11]=>[1,1,1,1,1,1,1,1,1,1,1] [2,9]=>[1,1,1,1,1,1,1,1,2,1] [1,1,1,1,1,1,1,1,1,1,1,1]=>[12] [1,1,1,1,1,1,1,1,2,2]=>[1,2,9] [1,1,1,1,1,1,2,2,1,1]=>[3,2,7] [1,1,1,1,1,1,2,1,1,2]=>[1,4,7] [1,1,1,1,1,1,3,3]=>[1,1,2,1,7] [1,1,1,1,2,2,1,1,1,1]=>[5,2,5] [1,1,1,1,2,2,2,2]=>[1,2,2,2,5] [1,1,1,1,2,1,1,2,1,1]=>[3,4,5] [1,1,1,1,2,1,1,1,1,2]=>[1,6,5] [1,1,1,1,2,1,2,3]=>[1,1,2,3,5] [1,1,1,1,3,3,1,1]=>[3,1,2,1,5] [1,1,1,1,3,2,1,2]=>[1,3,2,1,5] [1,1,1,1,3,1,1,3]=>[1,1,4,1,5] [1,1,1,1,4,4]=>[1,1,1,2,1,1,5] [1,1,2,2,1,1,1,1,1,1]=>[7,2,3] [1,1,2,2,1,1,2,2]=>[1,2,4,2,3] [1,1,2,2,2,2,1,1]=>[3,2,2,2,3] [1,1,2,2,2,1,1,2]=>[1,4,2,2,3] [1,1,2,2,3,3]=>[1,1,2,1,2,2,3] [1,1,2,1,1,2,1,1,1,1]=>[5,4,3] [1,1,2,1,1,2,2,2]=>[1,2,2,4,3] [1,1,2,1,1,1,1,2,1,1]=>[3,6,3] [1,1,2,1,1,1,1,1,1,2]=>[1,8,3] [1,1,2,1,1,1,2,3]=>[1,1,2,5,3] [1,1,2,1,2,3,1,1]=>[3,1,2,3,3] [1,1,2,1,2,2,1,2]=>[1,3,2,3,3] [1,1,2,1,2,1,1,3]=>[1,1,4,3,3] [1,1,2,1,3,4]=>[1,1,1,2,1,3,3] [1,1,3,3,1,1,1,1]=>[5,1,2,1,3] [1,1,3,3,2,2]=>[1,2,2,1,2,1,3] [1,1,3,2,1,2,1,1]=>[3,3,2,1,3] [1,1,3,2,1,1,1,2]=>[1,5,2,1,3] [1,1,3,2,2,3]=>[1,1,2,2,2,1,3] [1,1,3,1,1,3,1,1]=>[3,1,4,1,3] [1,1,3,1,1,2,1,2]=>[1,3,4,1,3] [1,1,3,1,1,1,1,3]=>[1,1,6,1,3] [1,1,3,1,2,4]=>[1,1,1,2,3,1,3] [1,1,4,4,1,1]=>[3,1,1,2,1,1,3] [1,1,4,3,1,2]=>[1,3,1,2,1,1,3] [1,1,4,2,1,3]=>[1,1,3,2,1,1,3] [1,1,4,1,1,4]=>[1,1,1,4,1,1,3] [1,1,5,5]=>[1,1,1,1,2,1,1,1,3] [2,2,1,1,1,1,1,1,1,1]=>[9,2,1] [2,2,1,1,1,1,2,2]=>[1,2,6,2,1] [2,2,1,1,2,2,1,1]=>[3,2,4,2,1] [2,2,1,1,2,1,1,2]=>[1,4,4,2,1] [2,2,1,1,3,3]=>[1,1,2,1,4,2,1] [2,2,2,2,1,1,1,1]=>[5,2,2,2,1] [2,2,2,2,2,2]=>[1,2,2,2,2,2,1] [2,2,2,1,1,2,1,1]=>[3,4,2,2,1] [2,2,2,1,1,1,1,2]=>[1,6,2,2,1] [2,2,2,1,2,3]=>[1,1,2,3,2,2,1] [2,2,3,3,1,1]=>[3,1,2,1,2,2,1] [2,2,3,2,1,2]=>[1,3,2,1,2,2,1] [2,2,3,1,1,3]=>[1,1,4,1,2,2,1] [2,2,4,4]=>[1,1,1,2,1,1,2,2,1] [2,1,1,2,1,1,1,1,1,1]=>[7,4,1] [2,1,1,2,1,1,2,2]=>[1,2,4,4,1] [2,1,1,2,2,2,1,1]=>[3,2,2,4,1] [2,1,1,2,2,1,1,2]=>[1,4,2,4,1] [2,1,1,2,3,3]=>[1,1,2,1,2,4,1] [2,1,1,1,1,2,1,1,1,1]=>[5,6,1] [2,1,1,1,1,2,2,2]=>[1,2,2,6,1] [2,1,1,1,1,1,1,2,1,1]=>[3,8,1] [2,1,1,1,1,1,1,1,1,2]=>[1,10,1] [2,1,1,1,1,1,2,3]=>[1,1,2,7,1] [2,1,1,1,2,3,1,1]=>[3,1,2,5,1] [2,1,1,1,2,2,1,2]=>[1,3,2,5,1] [2,1,1,1,2,1,1,3]=>[1,1,4,5,1] [2,1,1,1,3,4]=>[1,1,1,2,1,5,1] [2,1,2,3,1,1,1,1]=>[5,1,2,3,1] [2,1,2,3,2,2]=>[1,2,2,1,2,3,1] [2,1,2,2,1,2,1,1]=>[3,3,2,3,1] [2,1,2,2,1,1,1,2]=>[1,5,2,3,1] [2,1,2,2,2,3]=>[1,1,2,2,2,3,1] [2,1,2,1,1,3,1,1]=>[3,1,4,3,1] [2,1,2,1,1,2,1,2]=>[1,3,4,3,1] [2,1,2,1,1,1,1,3]=>[1,1,6,3,1] [2,1,2,1,2,4]=>[1,1,1,2,3,3,1] [2,1,3,4,1,1]=>[3,1,1,2,1,3,1] [2,1,3,3,1,2]=>[1,3,1,2,1,3,1] [2,1,3,2,1,3]=>[1,1,3,2,1,3,1] [2,1,3,1,1,4]=>[1,1,1,4,1,3,1] [2,1,4,5]=>[1,1,1,1,2,1,1,3,1] [3,3,1,1,1,1,1,1]=>[7,1,2,1,1] [3,3,1,1,2,2]=>[1,2,4,1,2,1,1] [3,3,2,2,1,1]=>[3,2,2,1,2,1,1] [3,3,2,1,1,2]=>[1,4,2,1,2,1,1] [3,3,3,3]=>[1,1,2,1,2,1,2,1,1] [3,2,1,2,1,1,1,1]=>[5,3,2,1,1] [3,2,1,2,2,2]=>[1,2,2,3,2,1,1] [3,2,1,1,1,2,1,1]=>[3,5,2,1,1] [3,2,1,1,1,1,1,2]=>[1,7,2,1,1] [3,2,1,1,2,3]=>[1,1,2,4,2,1,1] [3,2,2,3,1,1]=>[3,1,2,2,2,1,1] [3,2,2,2,1,2]=>[1,3,2,2,2,1,1] [3,2,2,1,1,3]=>[1,1,4,2,2,1,1] [3,2,3,4]=>[1,1,1,2,1,2,2,1,1] [3,1,1,3,1,1,1,1]=>[5,1,4,1,1] [3,1,1,3,2,2]=>[1,2,2,1,4,1,1] [3,1,1,2,1,2,1,1]=>[3,3,4,1,1] [3,1,1,2,1,1,1,2]=>[1,5,4,1,1] [3,1,1,2,2,3]=>[1,1,2,2,4,1,1] [3,1,1,1,1,3,1,1]=>[3,1,6,1,1] [3,1,1,1,1,2,1,2]=>[1,3,6,1,1] [3,1,1,1,1,1,1,3]=>[1,1,8,1,1] [3,1,1,1,2,4]=>[1,1,1,2,5,1,1] [3,1,2,4,1,1]=>[3,1,1,2,3,1,1] [3,1,2,3,1,2]=>[1,3,1,2,3,1,1] [3,1,2,2,1,3]=>[1,1,3,2,3,1,1] [3,1,2,1,1,4]=>[1,1,1,4,3,1,1] [3,1,3,5]=>[1,1,1,1,2,1,3,1,1] [4,4,1,1,1,1]=>[5,1,1,2,1,1,1] [4,4,2,2]=>[1,2,2,1,1,2,1,1,1] [4,3,1,2,1,1]=>[3,3,1,2,1,1,1] [4,3,1,1,1,2]=>[1,5,1,2,1,1,1] [4,3,2,3]=>[1,1,2,2,1,2,1,1,1] [4,2,1,3,1,1]=>[3,1,3,2,1,1,1] [4,2,1,2,1,2]=>[1,3,3,2,1,1,1] [4,2,1,1,1,3]=>[1,1,5,2,1,1,1] [4,2,2,4]=>[1,1,1,2,2,2,1,1,1] [4,1,1,4,1,1]=>[3,1,1,4,1,1,1] [4,1,1,3,1,2]=>[1,3,1,4,1,1,1] [4,1,1,2,1,3]=>[1,1,3,4,1,1,1] [4,1,1,1,1,4]=>[1,1,1,6,1,1,1] [4,1,2,5]=>[1,1,1,1,2,3,1,1,1] [5,5,1,1]=>[3,1,1,1,2,1,1,1,1] [5,4,1,2]=>[1,3,1,1,2,1,1,1,1] [5,3,1,3]=>[1,1,3,1,2,1,1,1,1] [5,2,1,4]=>[1,1,1,3,2,1,1,1,1] [5,1,1,5]=>[1,1,1,1,4,1,1,1,1] [6,6]=>[1,1,1,1,1,2,1,1,1,1,1] [1,2,2,2,2,2,1]=>[2,2,2,2,2,2] [1,2,2,2,3,2]=>[1,2,1,2,2,2,2] [1,2,2,3,3,1]=>[2,1,2,1,2,2,2] [1,2,2,3,2,2]=>[1,2,2,1,2,2,2] [1,2,2,4,3]=>[1,1,2,1,1,2,2,2] [1,2,3,3,2,1]=>[2,2,1,2,1,2,2] [1,2,3,4,2]=>[1,2,1,1,2,1,2,2] [1,2,3,2,3,1]=>[2,1,2,2,1,2,2] [1,2,3,2,2,2]=>[1,2,2,2,1,2,2] [1,2,3,3,3]=>[1,1,2,1,2,1,2,2] [1,2,4,4,1]=>[2,1,1,2,1,1,2,2] [1,2,4,3,2]=>[1,2,1,2,1,1,2,2] [1,2,4,2,3]=>[1,1,2,2,1,1,2,2] [1,2,5,4]=>[1,1,1,2,1,1,1,2,2] [1,3,3,2,2,1]=>[2,2,2,1,2,1,2] [1,3,3,3,2]=>[1,2,1,2,1,2,1,2] [1,3,4,3,1]=>[2,1,2,1,1,2,1,2] [1,3,4,2,2]=>[1,2,2,1,1,2,1,2] [1,3,5,3]=>[1,1,2,1,1,1,2,1,2] [1,3,2,3,2,1]=>[2,2,1,2,2,1,2] [1,3,2,4,2]=>[1,2,1,1,2,2,1,2] [1,3,2,2,3,1]=>[2,1,2,2,2,1,2] [1,3,2,2,2,2]=>[1,2,2,2,2,1,2] [1,3,2,3,3]=>[1,1,2,1,2,2,1,2] [1,3,3,4,1]=>[2,1,1,2,1,2,1,2] [1,3,3,2,3]=>[1,1,2,2,1,2,1,2] [1,3,4,4]=>[1,1,1,2,1,1,2,1,2] [1,4,4,2,1]=>[2,2,1,1,2,1,1,2] [1,4,5,2]=>[1,2,1,1,1,2,1,1,2] [1,4,3,3,1]=>[2,1,2,1,2,1,1,2] [1,4,3,2,2]=>[1,2,2,1,2,1,1,2] [1,4,4,3]=>[1,1,2,1,1,2,1,1,2] [1,4,2,4,1]=>[2,1,1,2,2,1,1,2] [1,4,2,3,2]=>[1,2,1,2,2,1,1,2] [1,4,2,2,3]=>[1,1,2,2,2,1,1,2] [1,4,3,4]=>[1,1,1,2,1,2,1,1,2] [1,5,5,1]=>[2,1,1,1,2,1,1,1,2] [1,5,4,2]=>[1,2,1,1,2,1,1,1,2] [1,5,3,3]=>[1,1,2,1,2,1,1,1,2] [1,5,2,4]=>[1,1,1,2,2,1,1,1,2] [1,6,5]=>[1,1,1,1,2,1,1,1,1,2] [2,3,2,2,2,1]=>[2,2,2,2,1,2,1] [2,3,2,3,2]=>[1,2,1,2,2,1,2,1] [2,3,3,3,1]=>[2,1,2,1,2,1,2,1] [2,3,3,2,2]=>[1,2,2,1,2,1,2,1] [2,3,4,3]=>[1,1,2,1,1,2,1,2,1] [2,4,3,2,1]=>[2,2,1,2,1,1,2,1] [2,4,4,2]=>[1,2,1,1,2,1,1,2,1] [2,4,2,3,1]=>[2,1,2,2,1,1,2,1] [2,4,2,2,2]=>[1,2,2,2,1,1,2,1] [2,4,3,3]=>[1,1,2,1,2,1,1,2,1] [2,5,4,1]=>[2,1,1,2,1,1,1,2,1] [2,5,3,2]=>[1,2,1,2,1,1,1,2,1] [2,5,2,3]=>[1,1,2,2,1,1,1,2,1] [2,6,4]=>[1,1,1,2,1,1,1,1,2,1] [2,2,3,2,2,1]=>[2,2,2,1,2,2,1] [2,2,3,3,2]=>[1,2,1,2,1,2,2,1] [2,2,4,3,1]=>[2,1,2,1,1,2,2,1] [2,2,4,2,2]=>[1,2,2,1,1,2,2,1] [2,2,5,3]=>[1,1,2,1,1,1,2,2,1] [2,2,2,3,2,1]=>[2,2,1,2,2,2,1] [2,2,2,4,2]=>[1,2,1,1,2,2,2,1] [2,2,2,2,3,1]=>[2,1,2,2,2,2,1] [2,2,2,3,3]=>[1,1,2,1,2,2,2,1] [2,2,3,4,1]=>[2,1,1,2,1,2,2,1] [2,2,3,2,3]=>[1,1,2,2,1,2,2,1] [2,3,4,2,1]=>[2,2,1,1,2,1,2,1] [2,3,5,2]=>[1,2,1,1,1,2,1,2,1] [2,3,2,4,1]=>[2,1,1,2,2,1,2,1] [2,3,2,2,3]=>[1,1,2,2,2,1,2,1] [2,3,3,4]=>[1,1,1,2,1,2,1,2,1] [2,4,5,1]=>[2,1,1,1,2,1,1,2,1] [2,4,2,4]=>[1,1,1,2,2,1,1,2,1] [2,5,5]=>[1,1,1,1,2,1,1,1,2,1] [3,4,2,2,1]=>[2,2,2,1,1,2,1,1] [3,4,3,2]=>[1,2,1,2,1,1,2,1,1] [3,5,3,1]=>[2,1,2,1,1,1,2,1,1] [3,5,2,2]=>[1,2,2,1,1,1,2,1,1] [3,6,3]=>[1,1,2,1,1,1,1,2,1,1] [3,3,3,2,1]=>[2,2,1,2,1,2,1,1] [3,3,4,2]=>[1,2,1,1,2,1,2,1,1] [3,3,2,3,1]=>[2,1,2,2,1,2,1,1] [3,3,2,2,2]=>[1,2,2,2,1,2,1,1] [3,4,4,1]=>[2,1,1,2,1,1,2,1,1] [3,4,2,3]=>[1,1,2,2,1,1,2,1,1] [3,5,4]=>[1,1,1,2,1,1,1,2,1,1] [3,2,4,2,1]=>[2,2,1,1,2,2,1,1] [3,2,5,2]=>[1,2,1,1,1,2,2,1,1] [3,2,3,3,1]=>[2,1,2,1,2,2,1,1] [3,2,3,2,2]=>[1,2,2,1,2,2,1,1] [3,2,4,3]=>[1,1,2,1,1,2,2,1,1] [3,2,2,4,1]=>[2,1,1,2,2,2,1,1] [3,2,2,3,2]=>[1,2,1,2,2,2,1,1] [3,2,2,2,3]=>[1,1,2,2,2,2,1,1] [3,3,5,1]=>[2,1,1,1,2,1,2,1,1] [3,3,2,4]=>[1,1,1,2,2,1,2,1,1] [3,4,5]=>[1,1,1,1,2,1,1,2,1,1] [4,5,2,1]=>[2,2,1,1,1,2,1,1,1] [4,6,2]=>[1,2,1,1,1,1,2,1,1,1] [4,4,3,1]=>[2,1,2,1,1,2,1,1,1] [4,5,3]=>[1,1,2,1,1,1,2,1,1,1] [4,3,4,1]=>[2,1,1,2,1,2,1,1,1] [4,3,3,2]=>[1,2,1,2,1,2,1,1,1] [4,4,4]=>[1,1,1,2,1,1,2,1,1,1] [4,2,5,1]=>[2,1,1,1,2,2,1,1,1] [4,2,4,2]=>[1,2,1,1,2,2,1,1,1] [4,2,3,3]=>[1,1,2,1,2,2,1,1,1] [4,3,5]=>[1,1,1,1,2,1,2,1,1,1] [5,6,1]=>[2,1,1,1,1,2,1,1,1,1] [5,5,2]=>[1,2,1,1,1,2,1,1,1,1] [5,4,3]=>[1,1,2,1,1,2,1,1,1,1] [5,3,4]=>[1,1,1,2,1,2,1,1,1,1] [5,2,5]=>[1,1,1,1,2,2,1,1,1,1] [1,11]=>[1,1,1,1,1,1,1,1,1,1,2] [1,9,2]=>[1,2,1,1,1,1,1,1,1,2] [1,8,1,2]=>[1,3,1,1,1,1,1,1,2] [1,7,1,1,2]=>[1,4,1,1,1,1,1,2] [1,6,1,1,1,2]=>[1,5,1,1,1,1,2] [1,5,1,1,1,1,2]=>[1,6,1,1,1,2] [1,4,1,1,1,1,1,2]=>[1,7,1,1,2] [1,3,1,1,1,1,1,1,2]=>[1,8,1,2] [1,2,1,1,1,1,1,1,1,2]=>[1,9,2] [1,1,1,1,1,1,1,1,1,1,2]=>[1,11] [1,2,2,2,2,2,2]=>[1,2,2,2,2,2,2] [1,2,2,2,2,1,3]=>[1,1,3,2,2,2,2] [1,2,2,2,1,3,2]=>[1,2,1,3,2,2,2] [1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2] [1,2,2,2,1,1,4]=>[1,1,1,4,2,2,2] [1,2,2,1,3,2,2]=>[1,2,2,1,3,2,2] [1,2,2,1,3,1,3]=>[1,1,3,1,3,2,2] [1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] [1,2,2,1,2,2,3]=>[1,1,2,2,3,2,2] [1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2] [1,2,2,1,1,4,2]=>[1,2,1,1,4,2,2] [1,2,2,1,1,3,3]=>[1,1,2,1,4,2,2] [1,2,2,1,1,2,4]=>[1,1,1,2,4,2,2] [1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] [1,2,1,3,2,2,2]=>[1,2,2,2,1,3,2] [1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2] [1,2,1,3,1,3,2]=>[1,2,1,3,1,3,2] [1,2,1,3,1,2,3]=>[1,1,2,3,1,3,2] [1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] [1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] [1,2,1,2,3,1,3]=>[1,1,3,1,2,3,2] [1,2,1,2,2,3,2]=>[1,2,1,2,2,3,2] [1,2,1,2,2,2,3]=>[1,1,2,2,2,3,2] [1,2,1,2,2,1,4]=>[1,1,1,3,2,3,2] [1,2,1,2,1,4,2]=>[1,2,1,1,3,3,2] [1,2,1,2,1,3,3]=>[1,1,2,1,3,3,2] [1,2,1,2,1,2,4]=>[1,1,1,2,3,3,2] [1,2,1,2,1,1,5]=>[1,1,1,1,4,3,2] [1,2,1,1,4,2,2]=>[1,2,2,1,1,4,2] [1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2] [1,2,1,1,3,3,2]=>[1,2,1,2,1,4,2] [1,2,1,1,3,2,3]=>[1,1,2,2,1,4,2] [1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] [1,2,1,1,2,4,2]=>[1,2,1,1,2,4,2] [1,2,1,1,2,3,3]=>[1,1,2,1,2,4,2] [1,2,1,1,2,2,4]=>[1,1,1,2,2,4,2] [1,2,1,1,2,1,5]=>[1,1,1,1,3,4,2] [1,2,1,1,1,5,2]=>[1,2,1,1,1,5,2] [1,2,1,1,1,4,3]=>[1,1,2,1,1,5,2] [1,2,1,1,1,3,4]=>[1,1,1,2,1,5,2] [1,2,1,1,1,2,5]=>[1,1,1,1,2,5,2] [1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] [1,1,3,2,2,2,2]=>[1,2,2,2,2,1,3] [1,1,3,2,2,1,3]=>[1,1,3,2,2,1,3] [1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3] [1,1,3,2,1,2,3]=>[1,1,2,3,2,1,3] [1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] [1,1,3,1,3,2,2]=>[1,2,2,1,3,1,3] [1,1,3,1,3,1,3]=>[1,1,3,1,3,1,3] [1,1,3,1,2,3,2]=>[1,2,1,2,3,1,3] [1,1,3,1,2,2,3]=>[1,1,2,2,3,1,3] [1,1,3,1,2,1,4]=>[1,1,1,3,3,1,3] [1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3] [1,1,3,1,1,3,3]=>[1,1,2,1,4,1,3] [1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3] [1,1,3,1,1,1,5]=>[1,1,1,1,5,1,3] [1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3] [1,1,2,3,2,1,3]=>[1,1,3,2,1,2,3] [1,1,2,3,1,3,2]=>[1,2,1,3,1,2,3] [1,1,2,3,1,2,3]=>[1,1,2,3,1,2,3] [1,1,2,3,1,1,4]=>[1,1,1,4,1,2,3] [1,1,2,2,3,2,2]=>[1,2,2,1,2,2,3] [1,1,2,2,3,1,3]=>[1,1,3,1,2,2,3] [1,1,2,2,2,3,2]=>[1,2,1,2,2,2,3] [1,1,2,2,2,2,3]=>[1,1,2,2,2,2,3] [1,1,2,2,2,1,4]=>[1,1,1,3,2,2,3] [1,1,2,2,1,4,2]=>[1,2,1,1,3,2,3] [1,1,2,2,1,3,3]=>[1,1,2,1,3,2,3] [1,1,2,2,1,2,4]=>[1,1,1,2,3,2,3] [1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] [1,1,2,1,4,2,2]=>[1,2,2,1,1,3,3] [1,1,2,1,4,1,3]=>[1,1,3,1,1,3,3] [1,1,2,1,3,3,2]=>[1,2,1,2,1,3,3] [1,1,2,1,3,2,3]=>[1,1,2,2,1,3,3] [1,1,2,1,3,1,4]=>[1,1,1,3,1,3,3] [1,1,2,1,2,4,2]=>[1,2,1,1,2,3,3] [1,1,2,1,2,3,3]=>[1,1,2,1,2,3,3] [1,1,2,1,2,2,4]=>[1,1,1,2,2,3,3] [1,1,2,1,2,1,5]=>[1,1,1,1,3,3,3] [1,1,2,1,1,5,2]=>[1,2,1,1,1,4,3] [1,1,2,1,1,4,3]=>[1,1,2,1,1,4,3] [1,1,2,1,1,3,4]=>[1,1,1,2,1,4,3] [1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] [1,1,2,1,1,1,6]=>[1,1,1,1,1,5,3] [1,1,1,4,2,2,2]=>[1,2,2,2,1,1,4] [1,1,1,4,2,1,3]=>[1,1,3,2,1,1,4] [1,1,1,4,1,3,2]=>[1,2,1,3,1,1,4] [1,1,1,4,1,2,3]=>[1,1,2,3,1,1,4] [1,1,1,4,1,1,4]=>[1,1,1,4,1,1,4] [1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4] [1,1,1,3,3,1,3]=>[1,1,3,1,2,1,4] [1,1,1,3,2,3,2]=>[1,2,1,2,2,1,4] [1,1,1,3,2,2,3]=>[1,1,2,2,2,1,4] [1,1,1,3,2,1,4]=>[1,1,1,3,2,1,4] [1,1,1,3,1,4,2]=>[1,2,1,1,3,1,4] [1,1,1,3,1,3,3]=>[1,1,2,1,3,1,4] [1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] [1,1,1,3,1,1,5]=>[1,1,1,1,4,1,4] [1,1,1,2,4,2,2]=>[1,2,2,1,1,2,4] [1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4] [1,1,1,2,3,3,2]=>[1,2,1,2,1,2,4] [1,1,1,2,3,2,3]=>[1,1,2,2,1,2,4] [1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] [1,1,1,2,2,4,2]=>[1,2,1,1,2,2,4] [1,1,1,2,2,3,3]=>[1,1,2,1,2,2,4] [1,1,1,2,2,2,4]=>[1,1,1,2,2,2,4] [1,1,1,2,2,1,5]=>[1,1,1,1,3,2,4] [1,1,1,2,1,5,2]=>[1,2,1,1,1,3,4] [1,1,1,2,1,4,3]=>[1,1,2,1,1,3,4] [1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] [1,1,1,2,1,2,5]=>[1,1,1,1,2,3,4] [1,1,1,2,1,1,6]=>[1,1,1,1,1,4,4] [1,1,1,1,5,2,2]=>[1,2,2,1,1,1,5] [1,1,1,1,5,1,3]=>[1,1,3,1,1,1,5] [1,1,1,1,4,3,2]=>[1,2,1,2,1,1,5] [1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] [1,1,1,1,4,1,4]=>[1,1,1,3,1,1,5] [1,1,1,1,3,4,2]=>[1,2,1,1,2,1,5] [1,1,1,1,3,3,3]=>[1,1,2,1,2,1,5] [1,1,1,1,3,2,4]=>[1,1,1,2,2,1,5] [1,1,1,1,3,1,5]=>[1,1,1,1,3,1,5] [1,1,1,1,2,5,2]=>[1,2,1,1,1,2,5] [1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] [1,1,1,1,2,3,4]=>[1,1,1,2,1,2,5] [1,1,1,1,2,2,5]=>[1,1,1,1,2,2,5] [1,1,1,1,2,1,6]=>[1,1,1,1,1,3,5] [1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] [1,1,1,1,1,5,3]=>[1,1,2,1,1,1,6] [1,1,1,1,1,4,4]=>[1,1,1,2,1,1,6] [1,1,1,1,1,3,5]=>[1,1,1,1,2,1,6] [1,1,1,1,1,2,6]=>[1,1,1,1,1,2,6] [1,1,1,1,1,1,7]=>[1,1,1,1,1,1,7]
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Description
The conjugate of a composition.
The conjugate of a composition $C$ is defined as the complement (Mp00039complement) of the reversal (Mp00038reverse) of $C$.
Equivalently, the ribbon shape corresponding to the conjugate of $C$ is the conjugate of the ribbon shape of $C$.
Properties
bijective, graded, involutive
Sage code
def mapping(elt):
    return elt.conjugate()
Weight
11
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey