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Identifier
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Images
=>
[1]=>[1] [1,1]=>[2] [2]=>[1] [1,1,1]=>[3] [1,2]=>[1,1] [2,1]=>[1,1] [3]=>[1] [1,1,1,1]=>[4] [1,1,2]=>[2,1] [1,2,1]=>[1,1,1] [1,3]=>[1,1] [2,1,1]=>[1,2] [2,2]=>[2] [3,1]=>[1,1] [4]=>[1] [1,1,1,1,1]=>[5] [1,1,1,2]=>[3,1] [1,1,2,1]=>[2,1,1] [1,1,3]=>[2,1] [1,2,1,1]=>[1,1,2] [1,2,2]=>[1,2] [1,3,1]=>[1,1,1] [1,4]=>[1,1] [2,1,1,1]=>[1,3] [2,1,2]=>[1,1,1] [2,2,1]=>[2,1] [2,3]=>[1,1] [3,1,1]=>[1,2] [3,2]=>[1,1] [4,1]=>[1,1] [5]=>[1] [1,1,1,1,1,1]=>[6] [1,1,1,1,2]=>[4,1] [1,1,1,2,1]=>[3,1,1] [1,1,1,3]=>[3,1] [1,1,2,1,1]=>[2,1,2] [1,1,2,2]=>[2,2] [1,1,3,1]=>[2,1,1] [1,1,4]=>[2,1] [1,2,1,1,1]=>[1,1,3] [1,2,1,2]=>[1,1,1,1] [1,2,2,1]=>[1,2,1] [1,2,3]=>[1,1,1] [1,3,1,1]=>[1,1,2] [1,3,2]=>[1,1,1] [1,4,1]=>[1,1,1] [1,5]=>[1,1] [2,1,1,1,1]=>[1,4] [2,1,1,2]=>[1,2,1] [2,1,2,1]=>[1,1,1,1] [2,1,3]=>[1,1,1] [2,2,1,1]=>[2,2] [2,2,2]=>[3] [2,3,1]=>[1,1,1] [2,4]=>[1,1] [3,1,1,1]=>[1,3] [3,1,2]=>[1,1,1] [3,2,1]=>[1,1,1] [3,3]=>[2] [4,1,1]=>[1,2] [4,2]=>[1,1] [5,1]=>[1,1] [6]=>[1] [1,1,1,1,1,1,1]=>[7] [1,1,1,1,1,2]=>[5,1] [1,1,1,1,2,1]=>[4,1,1] [1,1,1,1,3]=>[4,1] [1,1,1,2,1,1]=>[3,1,2] [1,1,1,2,2]=>[3,2] [1,1,1,3,1]=>[3,1,1] [1,1,1,4]=>[3,1] [1,1,2,1,1,1]=>[2,1,3] [1,1,2,1,2]=>[2,1,1,1] [1,1,2,2,1]=>[2,2,1] [1,1,2,3]=>[2,1,1] [1,1,3,1,1]=>[2,1,2] [1,1,3,2]=>[2,1,1] [1,1,4,1]=>[2,1,1] [1,1,5]=>[2,1] [1,2,1,1,1,1]=>[1,1,4] [1,2,1,1,2]=>[1,1,2,1] [1,2,1,2,1]=>[1,1,1,1,1] [1,2,1,3]=>[1,1,1,1] [1,2,2,1,1]=>[1,2,2] [1,2,2,2]=>[1,3] [1,2,3,1]=>[1,1,1,1] [1,2,4]=>[1,1,1] [1,3,1,1,1]=>[1,1,3] [1,3,1,2]=>[1,1,1,1] [1,3,2,1]=>[1,1,1,1] [1,3,3]=>[1,2] [1,4,1,1]=>[1,1,2] [1,4,2]=>[1,1,1] [1,5,1]=>[1,1,1] [1,6]=>[1,1] [2,1,1,1,1,1]=>[1,5] [2,1,1,1,2]=>[1,3,1] [2,1,1,2,1]=>[1,2,1,1] [2,1,1,3]=>[1,2,1] [2,1,2,1,1]=>[1,1,1,2] [2,1,2,2]=>[1,1,2] [2,1,3,1]=>[1,1,1,1] [2,1,4]=>[1,1,1] [2,2,1,1,1]=>[2,3] [2,2,1,2]=>[2,1,1] [2,2,2,1]=>[3,1] [2,2,3]=>[2,1] [2,3,1,1]=>[1,1,2] [2,3,2]=>[1,1,1] [2,4,1]=>[1,1,1] [2,5]=>[1,1] [3,1,1,1,1]=>[1,4] [3,1,1,2]=>[1,2,1] [3,1,2,1]=>[1,1,1,1] [3,1,3]=>[1,1,1] [3,2,1,1]=>[1,1,2] [3,2,2]=>[1,2] [3,3,1]=>[2,1] [3,4]=>[1,1] [4,1,1,1]=>[1,3] [4,1,2]=>[1,1,1] [4,2,1]=>[1,1,1] [4,3]=>[1,1] [5,1,1]=>[1,2] [5,2]=>[1,1] [6,1]=>[1,1] [7]=>[1] [1,1,1,1,1,1,1,1]=>[8] [1,1,1,1,1,1,2]=>[6,1] [1,1,1,1,1,2,1]=>[5,1,1] [1,1,1,1,1,3]=>[5,1] [1,1,1,1,2,1,1]=>[4,1,2] [1,1,1,1,2,2]=>[4,2] [1,1,1,1,3,1]=>[4,1,1] [1,1,1,1,4]=>[4,1] [1,1,1,2,1,1,1]=>[3,1,3] [1,1,1,2,1,2]=>[3,1,1,1] [1,1,1,2,2,1]=>[3,2,1] [1,1,1,2,3]=>[3,1,1] [1,1,1,3,1,1]=>[3,1,2] [1,1,1,3,2]=>[3,1,1] [1,1,1,4,1]=>[3,1,1] [1,1,1,5]=>[3,1] [1,1,2,1,1,1,1]=>[2,1,4] [1,1,2,1,1,2]=>[2,1,2,1] [1,1,2,1,2,1]=>[2,1,1,1,1] [1,1,2,1,3]=>[2,1,1,1] [1,1,2,2,1,1]=>[2,2,2] [1,1,2,2,2]=>[2,3] [1,1,2,3,1]=>[2,1,1,1] [1,1,2,4]=>[2,1,1] [1,1,3,1,1,1]=>[2,1,3] [1,1,3,1,2]=>[2,1,1,1] [1,1,3,2,1]=>[2,1,1,1] [1,1,3,3]=>[2,2] [1,1,4,1,1]=>[2,1,2] [1,1,4,2]=>[2,1,1] [1,1,5,1]=>[2,1,1] [1,1,6]=>[2,1] [1,2,1,1,1,1,1]=>[1,1,5] [1,2,1,1,1,2]=>[1,1,3,1] [1,2,1,1,2,1]=>[1,1,2,1,1] [1,2,1,1,3]=>[1,1,2,1] [1,2,1,2,1,1]=>[1,1,1,1,2] [1,2,1,2,2]=>[1,1,1,2] [1,2,1,3,1]=>[1,1,1,1,1] [1,2,1,4]=>[1,1,1,1] [1,2,2,1,1,1]=>[1,2,3] [1,2,2,1,2]=>[1,2,1,1] [1,2,2,2,1]=>[1,3,1] [1,2,2,3]=>[1,2,1] [1,2,3,1,1]=>[1,1,1,2] [1,2,3,2]=>[1,1,1,1] [1,2,4,1]=>[1,1,1,1] [1,2,5]=>[1,1,1] [1,3,1,1,1,1]=>[1,1,4] [1,3,1,1,2]=>[1,1,2,1] [1,3,1,2,1]=>[1,1,1,1,1] [1,3,1,3]=>[1,1,1,1] [1,3,2,1,1]=>[1,1,1,2] [1,3,2,2]=>[1,1,2] [1,3,3,1]=>[1,2,1] [1,3,4]=>[1,1,1] [1,4,1,1,1]=>[1,1,3] [1,4,1,2]=>[1,1,1,1] [1,4,2,1]=>[1,1,1,1] [1,4,3]=>[1,1,1] [1,5,1,1]=>[1,1,2] [1,5,2]=>[1,1,1] [1,6,1]=>[1,1,1] [1,7]=>[1,1] [2,1,1,1,1,1,1]=>[1,6] [2,1,1,1,1,2]=>[1,4,1] [2,1,1,1,2,1]=>[1,3,1,1] [2,1,1,1,3]=>[1,3,1] [2,1,1,2,1,1]=>[1,2,1,2] [2,1,1,2,2]=>[1,2,2] [2,1,1,3,1]=>[1,2,1,1] [2,1,1,4]=>[1,2,1] [2,1,2,1,1,1]=>[1,1,1,3] [2,1,2,1,2]=>[1,1,1,1,1] [2,1,2,2,1]=>[1,1,2,1] [2,1,2,3]=>[1,1,1,1] [2,1,3,1,1]=>[1,1,1,2] [2,1,3,2]=>[1,1,1,1] [2,1,4,1]=>[1,1,1,1] [2,1,5]=>[1,1,1] [2,2,1,1,1,1]=>[2,4] [2,2,1,1,2]=>[2,2,1] [2,2,1,2,1]=>[2,1,1,1] [2,2,1,3]=>[2,1,1] [2,2,2,1,1]=>[3,2] [2,2,2,2]=>[4] [2,2,3,1]=>[2,1,1] [2,2,4]=>[2,1] [2,3,1,1,1]=>[1,1,3] [2,3,1,2]=>[1,1,1,1] [2,3,2,1]=>[1,1,1,1] [2,3,3]=>[1,2] [2,4,1,1]=>[1,1,2] [2,4,2]=>[1,1,1] [2,5,1]=>[1,1,1] [2,6]=>[1,1] [3,1,1,1,1,1]=>[1,5] [3,1,1,1,2]=>[1,3,1] [3,1,1,2,1]=>[1,2,1,1] [3,1,1,3]=>[1,2,1] [3,1,2,1,1]=>[1,1,1,2] [3,1,2,2]=>[1,1,2] [3,1,3,1]=>[1,1,1,1] [3,1,4]=>[1,1,1] [3,2,1,1,1]=>[1,1,3] [3,2,1,2]=>[1,1,1,1] [3,2,2,1]=>[1,2,1] [3,2,3]=>[1,1,1] [3,3,1,1]=>[2,2] [3,3,2]=>[2,1] [3,4,1]=>[1,1,1] [3,5]=>[1,1] [4,1,1,1,1]=>[1,4] [4,1,1,2]=>[1,2,1] [4,1,2,1]=>[1,1,1,1] [4,1,3]=>[1,1,1] [4,2,1,1]=>[1,1,2] [4,2,2]=>[1,2] [4,3,1]=>[1,1,1] [4,4]=>[2] [5,1,1,1]=>[1,3] [5,1,2]=>[1,1,1] [5,2,1]=>[1,1,1] [5,3]=>[1,1] [6,1,1]=>[1,2] [6,2]=>[1,1] [7,1]=>[1,1] [8]=>[1] [1,1,1,1,1,1,1,1,1]=>[9] [1,1,1,1,1,1,1,2]=>[7,1] [1,1,1,1,1,1,2,1]=>[6,1,1] [1,1,1,1,1,1,3]=>[6,1] [1,1,1,1,1,2,1,1]=>[5,1,2] [1,1,1,1,1,2,2]=>[5,2] [1,1,1,1,1,3,1]=>[5,1,1] [1,1,1,1,1,4]=>[5,1] [1,1,1,1,2,1,1,1]=>[4,1,3] [1,1,1,1,2,1,2]=>[4,1,1,1] [1,1,1,1,2,2,1]=>[4,2,1] [1,1,1,1,2,3]=>[4,1,1] [1,1,1,1,3,1,1]=>[4,1,2] [1,1,1,1,3,2]=>[4,1,1] [1,1,1,1,4,1]=>[4,1,1] [1,1,1,1,5]=>[4,1] [1,1,1,2,1,1,1,1]=>[3,1,4] [1,1,1,2,1,1,2]=>[3,1,2,1] [1,1,1,2,1,2,1]=>[3,1,1,1,1] [1,1,1,2,1,3]=>[3,1,1,1] [1,1,1,2,2,1,1]=>[3,2,2] [1,1,1,2,2,2]=>[3,3] [1,1,1,2,3,1]=>[3,1,1,1] [1,1,1,2,4]=>[3,1,1] [1,1,1,3,1,1,1]=>[3,1,3] [1,1,1,3,1,2]=>[3,1,1,1] [1,1,1,3,2,1]=>[3,1,1,1] [1,1,1,3,3]=>[3,2] [1,1,1,4,1,1]=>[3,1,2] [1,1,1,4,2]=>[3,1,1] [1,1,1,5,1]=>[3,1,1] [1,1,1,6]=>[3,1] [1,1,2,1,1,1,1,1]=>[2,1,5] [1,1,2,1,1,1,2]=>[2,1,3,1] [1,1,2,1,1,2,1]=>[2,1,2,1,1] [1,1,2,1,1,3]=>[2,1,2,1] [1,1,2,1,2,1,1]=>[2,1,1,1,2] [1,1,2,1,2,2]=>[2,1,1,2] [1,1,2,1,3,1]=>[2,1,1,1,1] [1,1,2,1,4]=>[2,1,1,1] [1,1,2,2,1,1,1]=>[2,2,3] [1,1,2,2,1,2]=>[2,2,1,1] [1,1,2,2,2,1]=>[2,3,1] [1,1,2,2,3]=>[2,2,1] [1,1,2,3,1,1]=>[2,1,1,2] [1,1,2,3,2]=>[2,1,1,1] [1,1,2,4,1]=>[2,1,1,1] [1,1,2,5]=>[2,1,1] [1,1,3,1,1,1,1]=>[2,1,4] [1,1,3,1,1,2]=>[2,1,2,1] [1,1,3,1,2,1]=>[2,1,1,1,1] [1,1,3,1,3]=>[2,1,1,1] [1,1,3,2,1,1]=>[2,1,1,2] [1,1,3,2,2]=>[2,1,2] [1,1,3,3,1]=>[2,2,1] [1,1,3,4]=>[2,1,1] [1,1,4,1,1,1]=>[2,1,3] [1,1,4,1,2]=>[2,1,1,1] [1,1,4,2,1]=>[2,1,1,1] [1,1,4,3]=>[2,1,1] [1,1,5,1,1]=>[2,1,2] [1,1,5,2]=>[2,1,1] [1,1,6,1]=>[2,1,1] [1,1,7]=>[2,1] [1,2,1,1,1,1,1,1]=>[1,1,6] [1,2,1,1,1,1,2]=>[1,1,4,1] [1,2,1,1,1,2,1]=>[1,1,3,1,1] [1,2,1,1,1,3]=>[1,1,3,1] [1,2,1,1,2,1,1]=>[1,1,2,1,2] [1,2,1,1,2,2]=>[1,1,2,2] [1,2,1,1,3,1]=>[1,1,2,1,1] [1,2,1,1,4]=>[1,1,2,1] [1,2,1,2,1,1,1]=>[1,1,1,1,3] [1,2,1,2,1,2]=>[1,1,1,1,1,1] [1,2,1,2,2,1]=>[1,1,1,2,1] [1,2,1,2,3]=>[1,1,1,1,1] [1,2,1,3,1,1]=>[1,1,1,1,2] [1,2,1,3,2]=>[1,1,1,1,1] [1,2,1,4,1]=>[1,1,1,1,1] [1,2,1,5]=>[1,1,1,1] [1,2,2,1,1,1,1]=>[1,2,4] [1,2,2,1,1,2]=>[1,2,2,1] [1,2,2,1,2,1]=>[1,2,1,1,1] [1,2,2,1,3]=>[1,2,1,1] [1,2,2,2,1,1]=>[1,3,2] [1,2,2,2,2]=>[1,4] [1,2,2,3,1]=>[1,2,1,1] [1,2,2,4]=>[1,2,1] [1,2,3,1,1,1]=>[1,1,1,3] [1,2,3,1,2]=>[1,1,1,1,1] [1,2,3,2,1]=>[1,1,1,1,1] [1,2,3,3]=>[1,1,2] [1,2,4,1,1]=>[1,1,1,2] [1,2,4,2]=>[1,1,1,1] [1,2,5,1]=>[1,1,1,1] [1,2,6]=>[1,1,1] [1,3,1,1,1,1,1]=>[1,1,5] [1,3,1,1,1,2]=>[1,1,3,1] [1,3,1,1,2,1]=>[1,1,2,1,1] [1,3,1,1,3]=>[1,1,2,1] [1,3,1,2,1,1]=>[1,1,1,1,2] [1,3,1,2,2]=>[1,1,1,2] [1,3,1,3,1]=>[1,1,1,1,1] [1,3,1,4]=>[1,1,1,1] [1,3,2,1,1,1]=>[1,1,1,3] [1,3,2,1,2]=>[1,1,1,1,1] [1,3,2,2,1]=>[1,1,2,1] [1,3,2,3]=>[1,1,1,1] [1,3,3,1,1]=>[1,2,2] [1,3,3,2]=>[1,2,1] [1,3,4,1]=>[1,1,1,1] [1,3,5]=>[1,1,1] [1,4,1,1,1,1]=>[1,1,4] [1,4,1,1,2]=>[1,1,2,1] [1,4,1,2,1]=>[1,1,1,1,1] [1,4,1,3]=>[1,1,1,1] [1,4,2,1,1]=>[1,1,1,2] [1,4,2,2]=>[1,1,2] [1,4,3,1]=>[1,1,1,1] [1,4,4]=>[1,2] [1,5,1,1,1]=>[1,1,3] [1,5,1,2]=>[1,1,1,1] [1,5,2,1]=>[1,1,1,1] [1,5,3]=>[1,1,1] [1,6,1,1]=>[1,1,2] [1,6,2]=>[1,1,1] [1,7,1]=>[1,1,1] [1,8]=>[1,1] [2,1,1,1,1,1,1,1]=>[1,7] [2,1,1,1,1,1,2]=>[1,5,1] [2,1,1,1,1,2,1]=>[1,4,1,1] [2,1,1,1,1,3]=>[1,4,1] [2,1,1,1,2,1,1]=>[1,3,1,2] [2,1,1,1,2,2]=>[1,3,2] [2,1,1,1,3,1]=>[1,3,1,1] [2,1,1,1,4]=>[1,3,1] [2,1,1,2,1,1,1]=>[1,2,1,3] [2,1,1,2,1,2]=>[1,2,1,1,1] [2,1,1,2,2,1]=>[1,2,2,1] [2,1,1,2,3]=>[1,2,1,1] [2,1,1,3,1,1]=>[1,2,1,2] [2,1,1,3,2]=>[1,2,1,1] [2,1,1,4,1]=>[1,2,1,1] [2,1,1,5]=>[1,2,1] [2,1,2,1,1,1,1]=>[1,1,1,4] [2,1,2,1,1,2]=>[1,1,1,2,1] [2,1,2,1,2,1]=>[1,1,1,1,1,1] [2,1,2,1,3]=>[1,1,1,1,1] [2,1,2,2,1,1]=>[1,1,2,2] [2,1,2,2,2]=>[1,1,3] [2,1,2,3,1]=>[1,1,1,1,1] [2,1,2,4]=>[1,1,1,1] [2,1,3,1,1,1]=>[1,1,1,3] [2,1,3,1,2]=>[1,1,1,1,1] [2,1,3,2,1]=>[1,1,1,1,1] [2,1,3,3]=>[1,1,2] [2,1,4,1,1]=>[1,1,1,2] [2,1,4,2]=>[1,1,1,1] [2,1,5,1]=>[1,1,1,1] [2,1,6]=>[1,1,1] [2,2,1,1,1,1,1]=>[2,5] [2,2,1,1,1,2]=>[2,3,1] [2,2,1,1,2,1]=>[2,2,1,1] [2,2,1,1,3]=>[2,2,1] [2,2,1,2,1,1]=>[2,1,1,2] [2,2,1,2,2]=>[2,1,2] [2,2,1,3,1]=>[2,1,1,1] [2,2,1,4]=>[2,1,1] [2,2,2,1,1,1]=>[3,3] [2,2,2,1,2]=>[3,1,1] [2,2,2,2,1]=>[4,1] [2,2,2,3]=>[3,1] [2,2,3,1,1]=>[2,1,2] [2,2,3,2]=>[2,1,1] [2,2,4,1]=>[2,1,1] [2,2,5]=>[2,1] [2,3,1,1,1,1]=>[1,1,4] [2,3,1,1,2]=>[1,1,2,1] [2,3,1,2,1]=>[1,1,1,1,1] [2,3,1,3]=>[1,1,1,1] [2,3,2,1,1]=>[1,1,1,2] [2,3,2,2]=>[1,1,2] [2,3,3,1]=>[1,2,1] [2,3,4]=>[1,1,1] [2,4,1,1,1]=>[1,1,3] [2,4,1,2]=>[1,1,1,1] [2,4,2,1]=>[1,1,1,1] [2,4,3]=>[1,1,1] [2,5,1,1]=>[1,1,2] [2,5,2]=>[1,1,1] [2,6,1]=>[1,1,1] [2,7]=>[1,1] [3,1,1,1,1,1,1]=>[1,6] [3,1,1,1,1,2]=>[1,4,1] [3,1,1,1,2,1]=>[1,3,1,1] [3,1,1,1,3]=>[1,3,1] [3,1,1,2,1,1]=>[1,2,1,2] [3,1,1,2,2]=>[1,2,2] [3,1,1,3,1]=>[1,2,1,1] [3,1,1,4]=>[1,2,1] [3,1,2,1,1,1]=>[1,1,1,3] [3,1,2,1,2]=>[1,1,1,1,1] [3,1,2,2,1]=>[1,1,2,1] [3,1,2,3]=>[1,1,1,1] [3,1,3,1,1]=>[1,1,1,2] [3,1,3,2]=>[1,1,1,1] [3,1,4,1]=>[1,1,1,1] [3,1,5]=>[1,1,1] [3,2,1,1,1,1]=>[1,1,4] [3,2,1,1,2]=>[1,1,2,1] [3,2,1,2,1]=>[1,1,1,1,1] [3,2,1,3]=>[1,1,1,1] [3,2,2,1,1]=>[1,2,2] [3,2,2,2]=>[1,3] [3,2,3,1]=>[1,1,1,1] [3,2,4]=>[1,1,1] [3,3,1,1,1]=>[2,3] [3,3,1,2]=>[2,1,1] [3,3,2,1]=>[2,1,1] [3,3,3]=>[3] [3,4,1,1]=>[1,1,2] [3,4,2]=>[1,1,1] [3,5,1]=>[1,1,1] [3,6]=>[1,1] [4,1,1,1,1,1]=>[1,5] [4,1,1,1,2]=>[1,3,1] [4,1,1,2,1]=>[1,2,1,1] [4,1,1,3]=>[1,2,1] [4,1,2,1,1]=>[1,1,1,2] [4,1,2,2]=>[1,1,2] [4,1,3,1]=>[1,1,1,1] [4,1,4]=>[1,1,1] [4,2,1,1,1]=>[1,1,3] [4,2,1,2]=>[1,1,1,1] [4,2,2,1]=>[1,2,1] [4,2,3]=>[1,1,1] [4,3,1,1]=>[1,1,2] [4,3,2]=>[1,1,1] [4,4,1]=>[2,1] [4,5]=>[1,1] [5,1,1,1,1]=>[1,4] [5,1,1,2]=>[1,2,1] [5,1,2,1]=>[1,1,1,1] [5,1,3]=>[1,1,1] [5,2,1,1]=>[1,1,2] [5,2,2]=>[1,2] [5,3,1]=>[1,1,1] [5,4]=>[1,1] [6,1,1,1]=>[1,3] [6,1,2]=>[1,1,1] [6,2,1]=>[1,1,1] [6,3]=>[1,1] [7,1,1]=>[1,2] [7,2]=>[1,1] [8,1]=>[1,1] [9]=>[1] [1,1,1,1,1,1,1,1,1,1]=>[10] [1,1,1,1,1,1,1,1,2]=>[8,1] [1,1,1,1,1,1,1,2,1]=>[7,1,1] [1,1,1,1,1,1,1,3]=>[7,1] [1,1,1,1,1,1,2,1,1]=>[6,1,2] [1,1,1,1,1,1,2,2]=>[6,2] [1,1,1,1,1,1,3,1]=>[6,1,1] [1,1,1,1,1,1,4]=>[6,1] [1,1,1,1,1,2,1,1,1]=>[5,1,3] [1,1,1,1,1,2,1,2]=>[5,1,1,1] [1,1,1,1,1,2,2,1]=>[5,2,1] [1,1,1,1,1,2,3]=>[5,1,1] [1,1,1,1,1,3,1,1]=>[5,1,2] [1,1,1,1,1,3,2]=>[5,1,1] [1,1,1,1,1,4,1]=>[5,1,1] [1,1,1,1,1,5]=>[5,1] [1,1,1,1,2,1,1,1,1]=>[4,1,4] [1,1,1,1,2,1,1,2]=>[4,1,2,1] [1,1,1,1,2,1,2,1]=>[4,1,1,1,1] [1,1,1,1,2,1,3]=>[4,1,1,1] [1,1,1,1,2,2,1,1]=>[4,2,2] [1,1,1,1,2,2,2]=>[4,3] [1,1,1,1,2,3,1]=>[4,1,1,1] [1,1,1,1,2,4]=>[4,1,1] [1,1,1,1,3,1,1,1]=>[4,1,3] [1,1,1,1,3,1,2]=>[4,1,1,1] [1,1,1,1,3,2,1]=>[4,1,1,1] [1,1,1,1,3,3]=>[4,2] [1,1,1,1,4,1,1]=>[4,1,2] [1,1,1,1,4,2]=>[4,1,1] [1,1,1,1,5,1]=>[4,1,1] [1,1,1,1,6]=>[4,1] [1,1,1,2,1,1,1,1,1]=>[3,1,5] [1,1,1,2,1,1,1,2]=>[3,1,3,1] [1,1,1,2,1,1,2,1]=>[3,1,2,1,1] [1,1,1,2,1,1,3]=>[3,1,2,1] [1,1,1,2,1,2,1,1]=>[3,1,1,1,2] [1,1,1,2,1,2,2]=>[3,1,1,2] [1,1,1,2,1,3,1]=>[3,1,1,1,1] [1,1,1,2,1,4]=>[3,1,1,1] [1,1,1,2,2,1,1,1]=>[3,2,3] [1,1,1,2,2,1,2]=>[3,2,1,1] [1,1,1,2,2,2,1]=>[3,3,1] [1,1,1,2,2,3]=>[3,2,1] [1,1,1,2,3,1,1]=>[3,1,1,2] [1,1,1,2,3,2]=>[3,1,1,1] [1,1,1,2,4,1]=>[3,1,1,1] [1,1,1,2,5]=>[3,1,1] [1,1,1,3,1,1,1,1]=>[3,1,4] [1,1,1,3,1,1,2]=>[3,1,2,1] [1,1,1,3,1,2,1]=>[3,1,1,1,1] [1,1,1,3,1,3]=>[3,1,1,1] [1,1,1,3,2,1,1]=>[3,1,1,2] [1,1,1,3,2,2]=>[3,1,2] [1,1,1,3,3,1]=>[3,2,1] [1,1,1,3,4]=>[3,1,1] [1,1,1,4,1,1,1]=>[3,1,3] [1,1,1,4,1,2]=>[3,1,1,1] [1,1,1,4,2,1]=>[3,1,1,1] [1,1,1,4,3]=>[3,1,1] [1,1,1,5,1,1]=>[3,1,2] [1,1,1,5,2]=>[3,1,1] [1,1,1,6,1]=>[3,1,1] [1,1,1,7]=>[3,1] [1,1,2,1,1,1,1,1,1]=>[2,1,6] [1,1,2,1,1,1,1,2]=>[2,1,4,1] [1,1,2,1,1,1,2,1]=>[2,1,3,1,1] [1,1,2,1,1,1,3]=>[2,1,3,1] [1,1,2,1,1,2,1,1]=>[2,1,2,1,2] [1,1,2,1,1,2,2]=>[2,1,2,2] [1,1,2,1,1,3,1]=>[2,1,2,1,1] [1,1,2,1,1,4]=>[2,1,2,1] [1,1,2,1,2,1,1,1]=>[2,1,1,1,3] [1,1,2,1,2,1,2]=>[2,1,1,1,1,1] [1,1,2,1,2,2,1]=>[2,1,1,2,1] [1,1,2,1,2,3]=>[2,1,1,1,1] [1,1,2,1,3,1,1]=>[2,1,1,1,2] [1,1,2,1,3,2]=>[2,1,1,1,1] [1,1,2,1,4,1]=>[2,1,1,1,1] [1,1,2,1,5]=>[2,1,1,1] [1,1,2,2,1,1,1,1]=>[2,2,4] [1,1,2,2,1,1,2]=>[2,2,2,1] [1,1,2,2,1,2,1]=>[2,2,1,1,1] [1,1,2,2,1,3]=>[2,2,1,1] [1,1,2,2,2,1,1]=>[2,3,2] [1,1,2,2,2,2]=>[2,4] [1,1,2,2,3,1]=>[2,2,1,1] [1,1,2,2,4]=>[2,2,1] [1,1,2,3,1,1,1]=>[2,1,1,3] [1,1,2,3,1,2]=>[2,1,1,1,1] [1,1,2,3,2,1]=>[2,1,1,1,1] [1,1,2,3,3]=>[2,1,2] [1,1,2,4,1,1]=>[2,1,1,2] [1,1,2,4,2]=>[2,1,1,1] [1,1,2,5,1]=>[2,1,1,1] [1,1,2,6]=>[2,1,1] [1,1,3,1,1,1,1,1]=>[2,1,5] [1,1,3,1,1,1,2]=>[2,1,3,1] [1,1,3,1,1,2,1]=>[2,1,2,1,1] [1,1,3,1,1,3]=>[2,1,2,1] [1,1,3,1,2,1,1]=>[2,1,1,1,2] [1,1,3,1,2,2]=>[2,1,1,2] [1,1,3,1,3,1]=>[2,1,1,1,1] [1,1,3,1,4]=>[2,1,1,1] [1,1,3,2,1,1,1]=>[2,1,1,3] [1,1,3,2,1,2]=>[2,1,1,1,1] [1,1,3,2,2,1]=>[2,1,2,1] [1,1,3,2,3]=>[2,1,1,1] [1,1,3,3,1,1]=>[2,2,2] [1,1,3,3,2]=>[2,2,1] [1,1,3,4,1]=>[2,1,1,1] [1,1,3,5]=>[2,1,1] [1,1,4,1,1,1,1]=>[2,1,4] [1,1,4,1,1,2]=>[2,1,2,1] [1,1,4,1,2,1]=>[2,1,1,1,1] [1,1,4,1,3]=>[2,1,1,1] [1,1,4,2,1,1]=>[2,1,1,2] [1,1,4,2,2]=>[2,1,2] [1,1,4,3,1]=>[2,1,1,1] [1,1,4,4]=>[2,2] [1,1,5,1,1,1]=>[2,1,3] [1,1,5,1,2]=>[2,1,1,1] [1,1,5,2,1]=>[2,1,1,1] [1,1,5,3]=>[2,1,1] [1,1,6,1,1]=>[2,1,2] [1,1,6,2]=>[2,1,1] [1,1,7,1]=>[2,1,1] [1,1,8]=>[2,1] [1,2,1,1,1,1,1,1,1]=>[1,1,7] [1,2,1,1,1,1,1,2]=>[1,1,5,1] [1,2,1,1,1,1,2,1]=>[1,1,4,1,1] [1,2,1,1,1,1,3]=>[1,1,4,1] [1,2,1,1,1,2,1,1]=>[1,1,3,1,2] [1,2,1,1,1,2,2]=>[1,1,3,2] [1,2,1,1,1,3,1]=>[1,1,3,1,1] [1,2,1,1,1,4]=>[1,1,3,1] [1,2,1,1,2,1,1,1]=>[1,1,2,1,3] [1,2,1,1,2,1,2]=>[1,1,2,1,1,1] [1,2,1,1,2,2,1]=>[1,1,2,2,1] [1,2,1,1,2,3]=>[1,1,2,1,1] [1,2,1,1,3,1,1]=>[1,1,2,1,2] [1,2,1,1,3,2]=>[1,1,2,1,1] [1,2,1,1,4,1]=>[1,1,2,1,1] [1,2,1,1,5]=>[1,1,2,1] [1,2,1,2,1,1,1,1]=>[1,1,1,1,4] [1,2,1,2,1,1,2]=>[1,1,1,1,2,1] [1,2,1,2,1,2,1]=>[1,1,1,1,1,1,1] [1,2,1,2,1,3]=>[1,1,1,1,1,1] [1,2,1,2,2,1,1]=>[1,1,1,2,2] [1,2,1,2,2,2]=>[1,1,1,3] [1,2,1,2,3,1]=>[1,1,1,1,1,1] [1,2,1,2,4]=>[1,1,1,1,1] [1,2,1,3,1,1,1]=>[1,1,1,1,3] [1,2,1,3,1,2]=>[1,1,1,1,1,1] [1,2,1,3,2,1]=>[1,1,1,1,1,1] [1,2,1,3,3]=>[1,1,1,2] [1,2,1,4,1,1]=>[1,1,1,1,2] [1,2,1,4,2]=>[1,1,1,1,1] [1,2,1,5,1]=>[1,1,1,1,1] [1,2,1,6]=>[1,1,1,1] [1,2,2,1,1,1,1,1]=>[1,2,5] [1,2,2,1,1,1,2]=>[1,2,3,1] [1,2,2,1,1,2,1]=>[1,2,2,1,1] [1,2,2,1,1,3]=>[1,2,2,1] [1,2,2,1,2,1,1]=>[1,2,1,1,2] [1,2,2,1,2,2]=>[1,2,1,2] [1,2,2,1,3,1]=>[1,2,1,1,1] [1,2,2,1,4]=>[1,2,1,1] [1,2,2,2,1,1,1]=>[1,3,3] [1,2,2,2,1,2]=>[1,3,1,1] [1,2,2,2,2,1]=>[1,4,1] [1,2,2,2,3]=>[1,3,1] [1,2,2,3,1,1]=>[1,2,1,2] [1,2,2,3,2]=>[1,2,1,1] [1,2,2,4,1]=>[1,2,1,1] [1,2,2,5]=>[1,2,1] [1,2,3,1,1,1,1]=>[1,1,1,4] [1,2,3,1,1,2]=>[1,1,1,2,1] [1,2,3,1,2,1]=>[1,1,1,1,1,1] [1,2,3,1,3]=>[1,1,1,1,1] [1,2,3,2,1,1]=>[1,1,1,1,2] [1,2,3,2,2]=>[1,1,1,2] [1,2,3,3,1]=>[1,1,2,1] [1,2,3,4]=>[1,1,1,1] [1,2,4,1,1,1]=>[1,1,1,3] [1,2,4,1,2]=>[1,1,1,1,1] [1,2,4,2,1]=>[1,1,1,1,1] [1,2,4,3]=>[1,1,1,1] [1,2,5,1,1]=>[1,1,1,2] [1,2,5,2]=>[1,1,1,1] [1,2,6,1]=>[1,1,1,1] [1,2,7]=>[1,1,1] [1,3,1,1,1,1,1,1]=>[1,1,6] [1,3,1,1,1,1,2]=>[1,1,4,1] [1,3,1,1,1,2,1]=>[1,1,3,1,1] [1,3,1,1,1,3]=>[1,1,3,1] [1,3,1,1,2,1,1]=>[1,1,2,1,2] [1,3,1,1,2,2]=>[1,1,2,2] [1,3,1,1,3,1]=>[1,1,2,1,1] [1,3,1,1,4]=>[1,1,2,1] [1,3,1,2,1,1,1]=>[1,1,1,1,3] [1,3,1,2,1,2]=>[1,1,1,1,1,1] [1,3,1,2,2,1]=>[1,1,1,2,1] [1,3,1,2,3]=>[1,1,1,1,1] [1,3,1,3,1,1]=>[1,1,1,1,2] [1,3,1,3,2]=>[1,1,1,1,1] [1,3,1,4,1]=>[1,1,1,1,1] [1,3,1,5]=>[1,1,1,1] [1,3,2,1,1,1,1]=>[1,1,1,4] [1,3,2,1,1,2]=>[1,1,1,2,1] [1,3,2,1,2,1]=>[1,1,1,1,1,1] [1,3,2,1,3]=>[1,1,1,1,1] [1,3,2,2,1,1]=>[1,1,2,2] [1,3,2,2,2]=>[1,1,3] [1,3,2,3,1]=>[1,1,1,1,1] [1,3,2,4]=>[1,1,1,1] [1,3,3,1,1,1]=>[1,2,3] [1,3,3,1,2]=>[1,2,1,1] [1,3,3,2,1]=>[1,2,1,1] [1,3,3,3]=>[1,3] [1,3,4,1,1]=>[1,1,1,2] [1,3,4,2]=>[1,1,1,1] [1,3,5,1]=>[1,1,1,1] [1,3,6]=>[1,1,1] [1,4,1,1,1,1,1]=>[1,1,5] [1,4,1,1,1,2]=>[1,1,3,1] [1,4,1,1,2,1]=>[1,1,2,1,1] [1,4,1,1,3]=>[1,1,2,1] [1,4,1,2,1,1]=>[1,1,1,1,2] [1,4,1,2,2]=>[1,1,1,2] [1,4,1,3,1]=>[1,1,1,1,1] [1,4,1,4]=>[1,1,1,1] [1,4,2,1,1,1]=>[1,1,1,3] [1,4,2,1,2]=>[1,1,1,1,1] [1,4,2,2,1]=>[1,1,2,1] [1,4,2,3]=>[1,1,1,1] [1,4,3,1,1]=>[1,1,1,2] [1,4,3,2]=>[1,1,1,1] [1,4,4,1]=>[1,2,1] [1,4,5]=>[1,1,1] [1,5,1,1,1,1]=>[1,1,4] [1,5,1,1,2]=>[1,1,2,1] [1,5,1,2,1]=>[1,1,1,1,1] [1,5,1,3]=>[1,1,1,1] [1,5,2,1,1]=>[1,1,1,2] [1,5,2,2]=>[1,1,2] [1,5,3,1]=>[1,1,1,1] [1,5,4]=>[1,1,1] [1,6,1,1,1]=>[1,1,3] [1,6,1,2]=>[1,1,1,1] [1,6,2,1]=>[1,1,1,1] [1,6,3]=>[1,1,1] [1,7,1,1]=>[1,1,2] [1,7,2]=>[1,1,1] [1,8,1]=>[1,1,1] [1,9]=>[1,1] [2,1,1,1,1,1,1,1,1]=>[1,8] [2,1,1,1,1,1,1,2]=>[1,6,1] [2,1,1,1,1,1,2,1]=>[1,5,1,1] [2,1,1,1,1,1,3]=>[1,5,1] [2,1,1,1,1,2,1,1]=>[1,4,1,2] [2,1,1,1,1,2,2]=>[1,4,2] [2,1,1,1,1,3,1]=>[1,4,1,1] [2,1,1,1,1,4]=>[1,4,1] [2,1,1,1,2,1,1,1]=>[1,3,1,3] [2,1,1,1,2,1,2]=>[1,3,1,1,1] [2,1,1,1,2,2,1]=>[1,3,2,1] [2,1,1,1,2,3]=>[1,3,1,1] [2,1,1,1,3,1,1]=>[1,3,1,2] [2,1,1,1,3,2]=>[1,3,1,1] [2,1,1,1,4,1]=>[1,3,1,1] [2,1,1,1,5]=>[1,3,1] [2,1,1,2,1,1,1,1]=>[1,2,1,4] [2,1,1,2,1,1,2]=>[1,2,1,2,1] [2,1,1,2,1,2,1]=>[1,2,1,1,1,1] [2,1,1,2,1,3]=>[1,2,1,1,1] [2,1,1,2,2,1,1]=>[1,2,2,2] [2,1,1,2,2,2]=>[1,2,3] [2,1,1,2,3,1]=>[1,2,1,1,1] [2,1,1,2,4]=>[1,2,1,1] [2,1,1,3,1,1,1]=>[1,2,1,3] [2,1,1,3,1,2]=>[1,2,1,1,1] [2,1,1,3,2,1]=>[1,2,1,1,1] [2,1,1,3,3]=>[1,2,2] [2,1,1,4,1,1]=>[1,2,1,2] [2,1,1,4,2]=>[1,2,1,1] [2,1,1,5,1]=>[1,2,1,1] [2,1,1,6]=>[1,2,1] [2,1,2,1,1,1,1,1]=>[1,1,1,5] [2,1,2,1,1,1,2]=>[1,1,1,3,1] [2,1,2,1,1,2,1]=>[1,1,1,2,1,1] [2,1,2,1,1,3]=>[1,1,1,2,1] [2,1,2,1,2,1,1]=>[1,1,1,1,1,2] [2,1,2,1,2,2]=>[1,1,1,1,2] [2,1,2,1,3,1]=>[1,1,1,1,1,1] [2,1,2,1,4]=>[1,1,1,1,1] [2,1,2,2,1,1,1]=>[1,1,2,3] [2,1,2,2,1,2]=>[1,1,2,1,1] [2,1,2,2,2,1]=>[1,1,3,1] [2,1,2,2,3]=>[1,1,2,1] [2,1,2,3,1,1]=>[1,1,1,1,2] [2,1,2,3,2]=>[1,1,1,1,1] [2,1,2,4,1]=>[1,1,1,1,1] [2,1,2,5]=>[1,1,1,1] [2,1,3,1,1,1,1]=>[1,1,1,4] [2,1,3,1,1,2]=>[1,1,1,2,1] [2,1,3,1,2,1]=>[1,1,1,1,1,1] [2,1,3,1,3]=>[1,1,1,1,1] [2,1,3,2,1,1]=>[1,1,1,1,2] [2,1,3,2,2]=>[1,1,1,2] [2,1,3,3,1]=>[1,1,2,1] [2,1,3,4]=>[1,1,1,1] [2,1,4,1,1,1]=>[1,1,1,3] [2,1,4,1,2]=>[1,1,1,1,1] [2,1,4,2,1]=>[1,1,1,1,1] [2,1,4,3]=>[1,1,1,1] [2,1,5,1,1]=>[1,1,1,2] [2,1,5,2]=>[1,1,1,1] [2,1,6,1]=>[1,1,1,1] [2,1,7]=>[1,1,1] [2,2,1,1,1,1,1,1]=>[2,6] [2,2,1,1,1,1,2]=>[2,4,1] [2,2,1,1,1,2,1]=>[2,3,1,1] [2,2,1,1,1,3]=>[2,3,1] [2,2,1,1,2,1,1]=>[2,2,1,2] [2,2,1,1,2,2]=>[2,2,2] [2,2,1,1,3,1]=>[2,2,1,1] [2,2,1,1,4]=>[2,2,1] [2,2,1,2,1,1,1]=>[2,1,1,3] [2,2,1,2,1,2]=>[2,1,1,1,1] [2,2,1,2,2,1]=>[2,1,2,1] [2,2,1,2,3]=>[2,1,1,1] [2,2,1,3,1,1]=>[2,1,1,2] [2,2,1,3,2]=>[2,1,1,1] [2,2,1,4,1]=>[2,1,1,1] [2,2,1,5]=>[2,1,1] [2,2,2,1,1,1,1]=>[3,4] [2,2,2,1,1,2]=>[3,2,1] [2,2,2,1,2,1]=>[3,1,1,1] [2,2,2,1,3]=>[3,1,1] [2,2,2,2,1,1]=>[4,2] [2,2,2,2,2]=>[5] [2,2,2,3,1]=>[3,1,1] [2,2,2,4]=>[3,1] [2,2,3,1,1,1]=>[2,1,3] [2,2,3,1,2]=>[2,1,1,1] [2,2,3,2,1]=>[2,1,1,1] [2,2,3,3]=>[2,2] [2,2,4,1,1]=>[2,1,2] [2,2,4,2]=>[2,1,1] [2,2,5,1]=>[2,1,1] [2,2,6]=>[2,1] [2,3,1,1,1,1,1]=>[1,1,5] [2,3,1,1,1,2]=>[1,1,3,1] [2,3,1,1,2,1]=>[1,1,2,1,1] [2,3,1,1,3]=>[1,1,2,1] [2,3,1,2,1,1]=>[1,1,1,1,2] [2,3,1,2,2]=>[1,1,1,2] [2,3,1,3,1]=>[1,1,1,1,1] [2,3,1,4]=>[1,1,1,1] [2,3,2,1,1,1]=>[1,1,1,3] [2,3,2,1,2]=>[1,1,1,1,1] [2,3,2,2,1]=>[1,1,2,1] [2,3,2,3]=>[1,1,1,1] [2,3,3,1,1]=>[1,2,2] [2,3,3,2]=>[1,2,1] [2,3,4,1]=>[1,1,1,1] [2,3,5]=>[1,1,1] [2,4,1,1,1,1]=>[1,1,4] [2,4,1,1,2]=>[1,1,2,1] [2,4,1,2,1]=>[1,1,1,1,1] [2,4,1,3]=>[1,1,1,1] [2,4,2,1,1]=>[1,1,1,2] [2,4,2,2]=>[1,1,2] [2,4,3,1]=>[1,1,1,1] [2,4,4]=>[1,2] [2,5,1,1,1]=>[1,1,3] [2,5,1,2]=>[1,1,1,1] [2,5,2,1]=>[1,1,1,1] [2,5,3]=>[1,1,1] [2,6,1,1]=>[1,1,2] [2,6,2]=>[1,1,1] [2,7,1]=>[1,1,1] [2,8]=>[1,1] [3,1,1,1,1,1,1,1]=>[1,7] [3,1,1,1,1,1,2]=>[1,5,1] [3,1,1,1,1,2,1]=>[1,4,1,1] [3,1,1,1,1,3]=>[1,4,1] [3,1,1,1,2,1,1]=>[1,3,1,2] [3,1,1,1,2,2]=>[1,3,2] [3,1,1,1,3,1]=>[1,3,1,1] [3,1,1,1,4]=>[1,3,1] [3,1,1,2,1,1,1]=>[1,2,1,3] [3,1,1,2,1,2]=>[1,2,1,1,1] [3,1,1,2,2,1]=>[1,2,2,1] [3,1,1,2,3]=>[1,2,1,1] [3,1,1,3,1,1]=>[1,2,1,2] [3,1,1,3,2]=>[1,2,1,1] [3,1,1,4,1]=>[1,2,1,1] [3,1,1,5]=>[1,2,1] [3,1,2,1,1,1,1]=>[1,1,1,4] [3,1,2,1,1,2]=>[1,1,1,2,1] [3,1,2,1,2,1]=>[1,1,1,1,1,1] [3,1,2,1,3]=>[1,1,1,1,1] [3,1,2,2,1,1]=>[1,1,2,2] [3,1,2,2,2]=>[1,1,3] [3,1,2,3,1]=>[1,1,1,1,1] [3,1,2,4]=>[1,1,1,1] [3,1,3,1,1,1]=>[1,1,1,3] [3,1,3,1,2]=>[1,1,1,1,1] [3,1,3,2,1]=>[1,1,1,1,1] [3,1,3,3]=>[1,1,2] [3,1,4,1,1]=>[1,1,1,2] [3,1,4,2]=>[1,1,1,1] [3,1,5,1]=>[1,1,1,1] [3,1,6]=>[1,1,1] [3,2,1,1,1,1,1]=>[1,1,5] [3,2,1,1,1,2]=>[1,1,3,1] [3,2,1,1,2,1]=>[1,1,2,1,1] [3,2,1,1,3]=>[1,1,2,1] [3,2,1,2,1,1]=>[1,1,1,1,2] [3,2,1,2,2]=>[1,1,1,2] [3,2,1,3,1]=>[1,1,1,1,1] [3,2,1,4]=>[1,1,1,1] [3,2,2,1,1,1]=>[1,2,3] [3,2,2,1,2]=>[1,2,1,1] [3,2,2,2,1]=>[1,3,1] [3,2,2,3]=>[1,2,1] [3,2,3,1,1]=>[1,1,1,2] [3,2,3,2]=>[1,1,1,1] [3,2,4,1]=>[1,1,1,1] [3,2,5]=>[1,1,1] [3,3,1,1,1,1]=>[2,4] [3,3,1,1,2]=>[2,2,1] [3,3,1,2,1]=>[2,1,1,1] [3,3,1,3]=>[2,1,1] [3,3,2,1,1]=>[2,1,2] [3,3,2,2]=>[2,2] [3,3,3,1]=>[3,1] [3,3,4]=>[2,1] [3,4,1,1,1]=>[1,1,3] [3,4,1,2]=>[1,1,1,1] [3,4,2,1]=>[1,1,1,1] [3,4,3]=>[1,1,1] [3,5,1,1]=>[1,1,2] [3,5,2]=>[1,1,1] [3,6,1]=>[1,1,1] [3,7]=>[1,1] [4,1,1,1,1,1,1]=>[1,6] [4,1,1,1,1,2]=>[1,4,1] [4,1,1,1,2,1]=>[1,3,1,1] [4,1,1,1,3]=>[1,3,1] [4,1,1,2,1,1]=>[1,2,1,2] [4,1,1,2,2]=>[1,2,2] [4,1,1,3,1]=>[1,2,1,1] [4,1,1,4]=>[1,2,1] [4,1,2,1,1,1]=>[1,1,1,3] [4,1,2,1,2]=>[1,1,1,1,1] [4,1,2,2,1]=>[1,1,2,1] [4,1,2,3]=>[1,1,1,1] [4,1,3,1,1]=>[1,1,1,2] [4,1,3,2]=>[1,1,1,1] [4,1,4,1]=>[1,1,1,1] [4,1,5]=>[1,1,1] [4,2,1,1,1,1]=>[1,1,4] [4,2,1,1,2]=>[1,1,2,1] [4,2,1,2,1]=>[1,1,1,1,1] [4,2,1,3]=>[1,1,1,1] [4,2,2,1,1]=>[1,2,2] [4,2,2,2]=>[1,3] [4,2,3,1]=>[1,1,1,1] [4,2,4]=>[1,1,1] [4,3,1,1,1]=>[1,1,3] [4,3,1,2]=>[1,1,1,1] [4,3,2,1]=>[1,1,1,1] [4,3,3]=>[1,2] [4,4,1,1]=>[2,2] [4,4,2]=>[2,1] [4,5,1]=>[1,1,1] [4,6]=>[1,1] [5,1,1,1,1,1]=>[1,5] [5,1,1,1,2]=>[1,3,1] [5,1,1,2,1]=>[1,2,1,1] [5,1,1,3]=>[1,2,1] [5,1,2,1,1]=>[1,1,1,2] [5,1,2,2]=>[1,1,2] [5,1,3,1]=>[1,1,1,1] [5,1,4]=>[1,1,1] [5,2,1,1,1]=>[1,1,3] [5,2,1,2]=>[1,1,1,1] [5,2,2,1]=>[1,2,1] [5,2,3]=>[1,1,1] [5,3,1,1]=>[1,1,2] [5,3,2]=>[1,1,1] [5,4,1]=>[1,1,1] [5,5]=>[2] [6,1,1,1,1]=>[1,4] [6,1,1,2]=>[1,2,1] [6,1,2,1]=>[1,1,1,1] [6,1,3]=>[1,1,1] [6,2,1,1]=>[1,1,2] [6,2,2]=>[1,2] [6,3,1]=>[1,1,1] [6,4]=>[1,1] [7,1,1,1]=>[1,3] [7,1,2]=>[1,1,1] [7,2,1]=>[1,1,1] [7,3]=>[1,1] [8,1,1]=>[1,2] [8,2]=>[1,1] [9,1]=>[1,1] [10]=>[1] [1,10]=>[1,1] [1,8,1,1]=>[1,1,2] [1,7,2,1]=>[1,1,1,1] [1,6,3,1]=>[1,1,1,1] [1,5,4,1]=>[1,1,1,1] [1,4,5,1]=>[1,1,1,1] [1,3,6,1]=>[1,1,1,1] [1,2,7,1]=>[1,1,1,1] [1,1,8,1]=>[2,1,1] [10,1]=>[1,1] [1,8,2]=>[1,1,1] [1,7,1,2]=>[1,1,1,1] [1,6,1,1,2]=>[1,1,2,1] [1,5,1,1,1,2]=>[1,1,3,1] [1,4,1,1,1,1,2]=>[1,1,4,1] [1,3,1,1,1,1,1,2]=>[1,1,5,1] [1,2,1,1,1,1,1,1,2]=>[1,1,6,1] [1,1,1,1,1,1,1,1,1,2]=>[9,1] [1,7,3]=>[1,1,1] [1,6,2,2]=>[1,1,2] [1,5,2,1,2]=>[1,1,1,1,1] [1,4,2,1,1,2]=>[1,1,1,2,1] [1,3,2,1,1,1,2]=>[1,1,1,3,1] [1,2,2,1,1,1,1,2]=>[1,2,4,1] [1,1,2,1,1,1,1,1,2]=>[2,1,5,1] [1,2,2,2,2,2]=>[1,5] [1,2,2,2,1,3]=>[1,3,1,1] [1,2,2,1,3,2]=>[1,2,1,1,1] [1,2,2,1,2,3]=>[1,2,1,1,1] [1,2,2,1,1,4]=>[1,2,2,1] [1,2,1,3,2,2]=>[1,1,1,1,2] [1,2,1,3,1,3]=>[1,1,1,1,1,1] [1,2,1,2,3,2]=>[1,1,1,1,1,1] [1,2,1,2,2,3]=>[1,1,1,2,1] [1,2,1,2,1,4]=>[1,1,1,1,1,1] [1,2,1,1,4,2]=>[1,1,2,1,1] [1,2,1,1,3,3]=>[1,1,2,2] [1,2,1,1,2,4]=>[1,1,2,1,1] [1,2,1,1,1,5]=>[1,1,3,1] [1,1,3,2,2,2]=>[2,1,3] [1,1,3,2,1,3]=>[2,1,1,1,1] [1,1,3,1,3,2]=>[2,1,1,1,1] [1,1,3,1,2,3]=>[2,1,1,1,1] [1,1,3,1,1,4]=>[2,1,2,1] [1,1,2,3,2,2]=>[2,1,1,2] [1,1,2,3,1,3]=>[2,1,1,1,1] [1,1,2,2,3,2]=>[2,2,1,1] [1,1,2,2,2,3]=>[2,3,1] [1,1,2,2,1,4]=>[2,2,1,1] [1,1,2,1,4,2]=>[2,1,1,1,1] [1,1,2,1,3,3]=>[2,1,1,2] [1,1,2,1,2,4]=>[2,1,1,1,1] [1,1,2,1,1,5]=>[2,1,2,1] [1,1,1,4,2,2]=>[3,1,2] [1,1,1,4,1,3]=>[3,1,1,1] [1,1,1,3,3,2]=>[3,2,1] [1,1,1,3,2,3]=>[3,1,1,1] [1,1,1,3,1,4]=>[3,1,1,1] [1,1,1,2,4,2]=>[3,1,1,1] [1,1,1,2,3,3]=>[3,1,2] [1,1,1,2,2,4]=>[3,2,1] [1,1,1,2,1,5]=>[3,1,1,1] [1,1,1,1,5,2]=>[4,1,1] [1,1,1,1,4,3]=>[4,1,1] [1,1,1,1,3,4]=>[4,1,1] [1,1,1,1,2,5]=>[4,1,1] [1,1,1,1,1,6]=>[5,1] [3,3,3,2]=>[3,1] [3,4,4]=>[1,2] [2,3,3,3]=>[1,3] [4,4,3]=>[2,1] [2,1,1,1,1,1,1,1,1,1]=>[1,9] [2,8,1]=>[1,1,1] [2,1,7,1]=>[1,1,1,1] [2,1,1,6,1]=>[1,2,1,1] [2,1,1,1,5,1]=>[1,3,1,1] [2,1,1,1,1,4,1]=>[1,4,1,1] [2,1,1,1,1,1,3,1]=>[1,5,1,1] [2,1,1,1,1,1,1,2,1]=>[1,6,1,1] [3,7,1]=>[1,1,1] [2,2,6,1]=>[2,1,1] [2,1,2,5,1]=>[1,1,1,1,1] [2,1,1,2,4,1]=>[1,2,1,1,1] [2,1,1,1,2,3,1]=>[1,3,1,1,1] [2,1,1,1,1,2,2,1]=>[1,4,2,1] [2,1,1,1,1,1,2,1,1]=>[1,5,1,2] [2,2,2,2,2,1]=>[5,1] [3,1,2,2,2,1]=>[1,1,3,1] [2,3,1,2,2,1]=>[1,1,1,2,1] [3,2,1,2,2,1]=>[1,1,1,2,1] [4,1,1,2,2,1]=>[1,2,2,1] [2,2,3,1,2,1]=>[2,1,1,1,1] [3,1,3,1,2,1]=>[1,1,1,1,1,1] [2,3,2,1,2,1]=>[1,1,1,1,1,1] [3,2,2,1,2,1]=>[1,2,1,1,1] [4,1,2,1,2,1]=>[1,1,1,1,1,1] [2,4,1,1,2,1]=>[1,1,2,1,1] [3,3,1,1,2,1]=>[2,2,1,1] [4,2,1,1,2,1]=>[1,1,2,1,1] [5,1,1,1,2,1]=>[1,3,1,1] [2,2,2,3,1,1]=>[3,1,2] [3,1,2,3,1,1]=>[1,1,1,1,2] [2,3,1,3,1,1]=>[1,1,1,1,2] [3,2,1,3,1,1]=>[1,1,1,1,2] [4,1,1,3,1,1]=>[1,2,1,2] [2,2,3,2,1,1]=>[2,1,1,2] [3,1,3,2,1,1]=>[1,1,1,1,2] [2,3,2,2,1,1]=>[1,1,2,2] [3,2,2,2,1,1]=>[1,3,2] [4,1,2,2,1,1]=>[1,1,2,2] [2,4,1,2,1,1]=>[1,1,1,1,2] [3,3,1,2,1,1]=>[2,1,1,2] [4,2,1,2,1,1]=>[1,1,1,1,2] [5,1,1,2,1,1]=>[1,2,1,2] [2,2,4,1,1,1]=>[2,1,3] [3,1,4,1,1,1]=>[1,1,1,3] [2,3,3,1,1,1]=>[1,2,3] [3,2,3,1,1,1]=>[1,1,1,3] [4,1,3,1,1,1]=>[1,1,1,3] [2,4,2,1,1,1]=>[1,1,1,3] [3,3,2,1,1,1]=>[2,1,3] [4,2,2,1,1,1]=>[1,2,3] [5,1,2,1,1,1]=>[1,1,1,3] [2,5,1,1,1,1]=>[1,1,4] [3,4,1,1,1,1]=>[1,1,4] [4,3,1,1,1,1]=>[1,1,4] [5,2,1,1,1,1]=>[1,1,4] [6,1,1,1,1,1]=>[1,5] [2,1,1,1,1,1,1,3]=>[1,6,1] [2,1,1,1,1,1,2,2]=>[1,5,2] [2,1,1,1,1,2,1,2]=>[1,4,1,1,1] [2,1,1,1,2,1,1,2]=>[1,3,1,2,1] [2,1,1,2,1,1,1,2]=>[1,2,1,3,1] [2,1,2,1,1,1,1,2]=>[1,1,1,4,1] [2,2,1,1,1,1,1,2]=>[2,5,1] [3,1,1,1,1,1,1,2]=>[1,6,1] [9,2]=>[1,1] [1,9,1]=>[1,1,1] [11]=>[1] [2,9]=>[1,1] [1,1,2,2,4,1]=>[2,2,1,1] [5,1,1,1,1,2]=>[1,4,1] [1,1,1,1,1,1,1,1,2,1]=>[8,1,1] [1,2,1,1,1,1,1,2,1]=>[1,1,5,1,1] [1,1,1,1,1,1,1,1,1,1,1]=>[11] [1,1,1,1,1,1,1,3,1]=>[7,1,1] [1,1,1,1,1,3,1,1,1]=>[5,1,3] [1,1,1,1,1,5,1]=>[5,1,1] [1,1,1,1,1,2,1,2,1]=>[5,1,1,1,1] [1,1,1,3,1,1,1,1,1]=>[3,1,5] [1,1,1,3,1,3,1]=>[3,1,1,1,1] [1,1,1,5,1,1,1]=>[3,1,3] [1,1,1,7,1]=>[3,1,1] [1,1,1,4,1,2,1]=>[3,1,1,1,1] [1,1,1,2,1,2,1,1,1]=>[3,1,1,1,3] [1,1,1,2,1,4,1]=>[3,1,1,1,1] [1,1,1,2,1,1,1,2,1]=>[3,1,3,1,1] [1,1,1,2,3,2,1]=>[3,1,1,1,1] [1,3,1,1,1,1,1,1,1]=>[1,1,7] [1,3,1,1,1,3,1]=>[1,1,3,1,1] [1,3,1,3,1,1,1]=>[1,1,1,1,3] [1,3,1,5,1]=>[1,1,1,1,1] [1,3,1,2,1,2,1]=>[1,1,1,1,1,1,1] [1,5,1,1,1,1,1]=>[1,1,5] [1,5,1,3,1]=>[1,1,1,1,1] [1,7,1,1,1]=>[1,1,3] [1,6,1,2,1]=>[1,1,1,1,1] [1,4,1,2,1,1,1]=>[1,1,1,1,3] [1,4,1,4,1]=>[1,1,1,1,1] [1,4,1,1,1,2,1]=>[1,1,3,1,1] [1,4,3,2,1]=>[1,1,1,1,1] [1,2,1,2,1,1,1,1,1]=>[1,1,1,1,5] [1,2,1,2,1,3,1]=>[1,1,1,1,1,1,1] [1,2,1,4,1,1,1]=>[1,1,1,1,3] [1,2,1,6,1]=>[1,1,1,1,1] [1,2,1,3,1,2,1]=>[1,1,1,1,1,1,1] [1,2,1,1,1,2,1,1,1]=>[1,1,3,1,3] [1,2,1,1,1,4,1]=>[1,1,3,1,1] [1,2,1,1,3,2,1]=>[1,1,2,1,1,1] [1,2,3,2,1,1,1]=>[1,1,1,1,3] [1,2,3,4,1]=>[1,1,1,1,1] [1,2,3,1,1,2,1]=>[1,1,1,2,1,1] [1,2,5,2,1]=>[1,1,1,1,1] [1,2,2,1,2,2,1]=>[1,2,1,2,1] [1,1,9]=>[2,1] [1,1,1,1,1,1,1,1,3]=>[8,1] [1,6,4]=>[1,1,1] [1,5,5]=>[1,2] [1,4,6]=>[1,1,1] [1,3,7]=>[1,1,1] [1,2,8]=>[1,1,1] [1,1,2,1,1,1,2,1,1]=>[2,1,3,1,2] [1,1,2,2,2,2,1]=>[2,4,1] [1,1,2,2,2,1,1,1]=>[2,3,3] [1,1,2,2,3,1,1]=>[2,2,1,2] [1,1,2,2,1,2,1,1]=>[2,2,1,1,2] [1,1,2,3,2,1,1]=>[2,1,1,1,2] [1,1,2,1,2,2,1,1]=>[2,1,1,2,2] [1,1,3,2,2,1,1]=>[2,1,2,2] [1,1,1,2,2,2,1,1]=>[3,3,2] [1,2,2,2,2,1,1]=>[1,4,2] [1,1,2,2,1,1,1,1,1]=>[2,2,5] [1,1,2,5,1,1]=>[2,1,1,2] [1,1,5,2,1,1]=>[2,1,1,2] [1,1,1,1,1,2,2,1,1]=>[5,2,2] [1,4,2,2,1,1]=>[1,1,2,2] [1,1,1,1,1,1,1,1,1,1,1,1]=>[12] [1,1,1,1,1,1,1,1,2,2]=>[8,2] [1,1,1,1,1,1,2,2,1,1]=>[6,2,2] [1,1,1,1,1,1,2,1,1,2]=>[6,1,2,1] [1,1,1,1,1,1,3,3]=>[6,2] [1,1,1,1,2,2,1,1,1,1]=>[4,2,4] [1,1,1,1,2,2,2,2]=>[4,4] [1,1,1,1,2,1,1,2,1,1]=>[4,1,2,1,2] [1,1,1,1,2,1,1,1,1,2]=>[4,1,4,1] [1,1,1,1,2,1,2,3]=>[4,1,1,1,1] [1,1,1,1,3,3,1,1]=>[4,2,2] [1,1,1,1,3,2,1,2]=>[4,1,1,1,1] [1,1,1,1,3,1,1,3]=>[4,1,2,1] [1,1,1,1,4,4]=>[4,2] [1,1,2,2,1,1,1,1,1,1]=>[2,2,6] [1,1,2,2,1,1,2,2]=>[2,2,2,2] [1,1,2,2,2,2,1,1]=>[2,4,2] [1,1,2,2,2,1,1,2]=>[2,3,2,1] [1,1,2,2,3,3]=>[2,2,2] [1,1,2,1,1,2,1,1,1,1]=>[2,1,2,1,4] [1,1,2,1,1,2,2,2]=>[2,1,2,3] [1,1,2,1,1,1,1,2,1,1]=>[2,1,4,1,2] [1,1,2,1,1,1,1,1,1,2]=>[2,1,6,1] [1,1,2,1,1,1,2,3]=>[2,1,3,1,1] [1,1,2,1,2,3,1,1]=>[2,1,1,1,1,2] [1,1,2,1,2,2,1,2]=>[2,1,1,2,1,1] [1,1,2,1,2,1,1,3]=>[2,1,1,1,2,1] [1,1,2,1,3,4]=>[2,1,1,1,1] [1,1,3,3,1,1,1,1]=>[2,2,4] [1,1,3,3,2,2]=>[2,2,2] [1,1,3,2,1,2,1,1]=>[2,1,1,1,1,2] [1,1,3,2,1,1,1,2]=>[2,1,1,3,1] [1,1,3,2,2,3]=>[2,1,2,1] [1,1,3,1,1,3,1,1]=>[2,1,2,1,2] [1,1,3,1,1,2,1,2]=>[2,1,2,1,1,1] [1,1,3,1,1,1,1,3]=>[2,1,4,1] [1,1,3,1,2,4]=>[2,1,1,1,1] [1,1,4,4,1,1]=>[2,2,2] [1,1,4,3,1,2]=>[2,1,1,1,1] [1,1,4,2,1,3]=>[2,1,1,1,1] [1,1,4,1,1,4]=>[2,1,2,1] [1,1,5,5]=>[2,2] [2,2,1,1,1,1,1,1,1,1]=>[2,8] [2,2,1,1,1,1,2,2]=>[2,4,2] [2,2,1,1,2,2,1,1]=>[2,2,2,2] [2,2,1,1,2,1,1,2]=>[2,2,1,2,1] [2,2,1,1,3,3]=>[2,2,2] [2,2,2,2,1,1,1,1]=>[4,4] [2,2,2,2,2,2]=>[6] [2,2,2,1,1,2,1,1]=>[3,2,1,2] [2,2,2,1,1,1,1,2]=>[3,4,1] [2,2,2,1,2,3]=>[3,1,1,1] [2,2,3,3,1,1]=>[2,2,2] [2,2,3,2,1,2]=>[2,1,1,1,1] [2,2,3,1,1,3]=>[2,1,2,1] [2,2,4,4]=>[2,2] [2,1,1,2,1,1,1,1,1,1]=>[1,2,1,6] [2,1,1,2,1,1,2,2]=>[1,2,1,2,2] [2,1,1,2,2,2,1,1]=>[1,2,3,2] [2,1,1,2,2,1,1,2]=>[1,2,2,2,1] [2,1,1,2,3,3]=>[1,2,1,2] [2,1,1,1,1,2,1,1,1,1]=>[1,4,1,4] [2,1,1,1,1,2,2,2]=>[1,4,3] [2,1,1,1,1,1,1,2,1,1]=>[1,6,1,2] [2,1,1,1,1,1,1,1,1,2]=>[1,8,1] [2,1,1,1,1,1,2,3]=>[1,5,1,1] [2,1,1,1,2,3,1,1]=>[1,3,1,1,2] [2,1,1,1,2,2,1,2]=>[1,3,2,1,1] [2,1,1,1,2,1,1,3]=>[1,3,1,2,1] [2,1,1,1,3,4]=>[1,3,1,1] [2,1,2,3,1,1,1,1]=>[1,1,1,1,4] [2,1,2,3,2,2]=>[1,1,1,1,2] [2,1,2,2,1,2,1,1]=>[1,1,2,1,1,2] [2,1,2,2,1,1,1,2]=>[1,1,2,3,1] [2,1,2,2,2,3]=>[1,1,3,1] [2,1,2,1,1,3,1,1]=>[1,1,1,2,1,2] [2,1,2,1,1,2,1,2]=>[1,1,1,2,1,1,1] [2,1,2,1,1,1,1,3]=>[1,1,1,4,1] [2,1,2,1,2,4]=>[1,1,1,1,1,1] [2,1,3,4,1,1]=>[1,1,1,1,2] [2,1,3,3,1,2]=>[1,1,2,1,1] [2,1,3,2,1,3]=>[1,1,1,1,1,1] [2,1,3,1,1,4]=>[1,1,1,2,1] [2,1,4,5]=>[1,1,1,1] [3,3,1,1,1,1,1,1]=>[2,6] [3,3,1,1,2,2]=>[2,2,2] [3,3,2,2,1,1]=>[2,2,2] [3,3,2,1,1,2]=>[2,1,2,1] [3,3,3,3]=>[4] [3,2,1,2,1,1,1,1]=>[1,1,1,1,4] [3,2,1,2,2,2]=>[1,1,1,3] [3,2,1,1,1,2,1,1]=>[1,1,3,1,2] [3,2,1,1,1,1,1,2]=>[1,1,5,1] [3,2,1,1,2,3]=>[1,1,2,1,1] [3,2,2,3,1,1]=>[1,2,1,2] [3,2,2,2,1,2]=>[1,3,1,1] [3,2,2,1,1,3]=>[1,2,2,1] [3,2,3,4]=>[1,1,1,1] [3,1,1,3,1,1,1,1]=>[1,2,1,4] [3,1,1,3,2,2]=>[1,2,1,2] [3,1,1,2,1,2,1,1]=>[1,2,1,1,1,2] [3,1,1,2,1,1,1,2]=>[1,2,1,3,1] [3,1,1,2,2,3]=>[1,2,2,1] [3,1,1,1,1,3,1,1]=>[1,4,1,2] [3,1,1,1,1,2,1,2]=>[1,4,1,1,1] [3,1,1,1,1,1,1,3]=>[1,6,1] [3,1,1,1,2,4]=>[1,3,1,1] [3,1,2,4,1,1]=>[1,1,1,1,2] [3,1,2,3,1,2]=>[1,1,1,1,1,1] [3,1,2,2,1,3]=>[1,1,2,1,1] [3,1,2,1,1,4]=>[1,1,1,2,1] [3,1,3,5]=>[1,1,1,1] [4,4,1,1,1,1]=>[2,4] [4,4,2,2]=>[2,2] [4,3,1,2,1,1]=>[1,1,1,1,2] [4,3,1,1,1,2]=>[1,1,3,1] [4,3,2,3]=>[1,1,1,1] [4,2,1,3,1,1]=>[1,1,1,1,2] [4,2,1,2,1,2]=>[1,1,1,1,1,1] [4,2,1,1,1,3]=>[1,1,3,1] [4,2,2,4]=>[1,2,1] [4,1,1,4,1,1]=>[1,2,1,2] [4,1,1,3,1,2]=>[1,2,1,1,1] [4,1,1,2,1,3]=>[1,2,1,1,1] [4,1,1,1,1,4]=>[1,4,1] [4,1,2,5]=>[1,1,1,1] [5,5,1,1]=>[2,2] [5,4,1,2]=>[1,1,1,1] [5,3,1,3]=>[1,1,1,1] [5,2,1,4]=>[1,1,1,1] [5,1,1,5]=>[1,2,1] [6,6]=>[2] [1,2,2,2,2,2,1]=>[1,5,1] [1,2,2,2,3,2]=>[1,3,1,1] [1,2,2,3,3,1]=>[1,2,2,1] [1,2,2,3,2,2]=>[1,2,1,2] [1,2,2,4,3]=>[1,2,1,1] [1,2,3,3,2,1]=>[1,1,2,1,1] [1,2,3,4,2]=>[1,1,1,1,1] [1,2,3,2,3,1]=>[1,1,1,1,1,1] [1,2,3,2,2,2]=>[1,1,1,3] [1,2,3,3,3]=>[1,1,3] [1,2,4,4,1]=>[1,1,2,1] [1,2,4,3,2]=>[1,1,1,1,1] [1,2,4,2,3]=>[1,1,1,1,1] [1,2,5,4]=>[1,1,1,1] [1,3,3,2,2,1]=>[1,2,2,1] [1,3,3,3,2]=>[1,3,1] [1,3,4,3,1]=>[1,1,1,1,1] [1,3,4,2,2]=>[1,1,1,2] [1,3,5,3]=>[1,1,1,1] [1,3,2,3,2,1]=>[1,1,1,1,1,1] [1,3,2,4,2]=>[1,1,1,1,1] [1,3,2,2,3,1]=>[1,1,2,1,1] [1,3,2,2,2,2]=>[1,1,4] [1,3,2,3,3]=>[1,1,1,2] [1,3,3,4,1]=>[1,2,1,1] [1,3,3,2,3]=>[1,2,1,1] [1,3,4,4]=>[1,1,2] [1,4,4,2,1]=>[1,2,1,1] [1,4,5,2]=>[1,1,1,1] [1,4,3,3,1]=>[1,1,2,1] [1,4,3,2,2]=>[1,1,1,2] [1,4,4,3]=>[1,2,1] [1,4,2,4,1]=>[1,1,1,1,1] [1,4,2,3,2]=>[1,1,1,1,1] [1,4,2,2,3]=>[1,1,2,1] [1,4,3,4]=>[1,1,1,1] [1,5,5,1]=>[1,2,1] [1,5,4,2]=>[1,1,1,1] [1,5,3,3]=>[1,1,2] [1,5,2,4]=>[1,1,1,1] [1,6,5]=>[1,1,1] [2,3,2,2,2,1]=>[1,1,3,1] [2,3,2,3,2]=>[1,1,1,1,1] [2,3,3,3,1]=>[1,3,1] [2,3,3,2,2]=>[1,2,2] [2,3,4,3]=>[1,1,1,1] [2,4,3,2,1]=>[1,1,1,1,1] [2,4,4,2]=>[1,2,1] [2,4,2,3,1]=>[1,1,1,1,1] [2,4,2,2,2]=>[1,1,3] [2,4,3,3]=>[1,1,2] [2,5,4,1]=>[1,1,1,1] [2,5,3,2]=>[1,1,1,1] [2,5,2,3]=>[1,1,1,1] [2,6,4]=>[1,1,1] [2,2,3,2,2,1]=>[2,1,2,1] [2,2,3,3,2]=>[2,2,1] [2,2,4,3,1]=>[2,1,1,1] [2,2,4,2,2]=>[2,1,2] [2,2,5,3]=>[2,1,1] [2,2,2,3,2,1]=>[3,1,1,1] [2,2,2,4,2]=>[3,1,1] [2,2,2,2,3,1]=>[4,1,1] [2,2,2,3,3]=>[3,2] [2,2,3,4,1]=>[2,1,1,1] [2,2,3,2,3]=>[2,1,1,1] [2,3,4,2,1]=>[1,1,1,1,1] [2,3,5,2]=>[1,1,1,1] [2,3,2,4,1]=>[1,1,1,1,1] [2,3,2,2,3]=>[1,1,2,1] [2,3,3,4]=>[1,2,1] [2,4,5,1]=>[1,1,1,1] [2,4,2,4]=>[1,1,1,1] [2,5,5]=>[1,2] [3,4,2,2,1]=>[1,1,2,1] [3,4,3,2]=>[1,1,1,1] [3,5,3,1]=>[1,1,1,1] [3,5,2,2]=>[1,1,2] [3,6,3]=>[1,1,1] [3,3,3,2,1]=>[3,1,1] [3,3,4,2]=>[2,1,1] [3,3,2,3,1]=>[2,1,1,1] [3,3,2,2,2]=>[2,3] [3,4,4,1]=>[1,2,1] [3,4,2,3]=>[1,1,1,1] [3,5,4]=>[1,1,1] [3,2,4,2,1]=>[1,1,1,1,1] [3,2,5,2]=>[1,1,1,1] [3,2,3,3,1]=>[1,1,2,1] [3,2,3,2,2]=>[1,1,1,2] [3,2,4,3]=>[1,1,1,1] [3,2,2,4,1]=>[1,2,1,1] [3,2,2,3,2]=>[1,2,1,1] [3,2,2,2,3]=>[1,3,1] [3,3,5,1]=>[2,1,1] [3,3,2,4]=>[2,1,1] [3,4,5]=>[1,1,1] [4,5,2,1]=>[1,1,1,1] [4,6,2]=>[1,1,1] [4,4,3,1]=>[2,1,1] [4,5,3]=>[1,1,1] [4,3,4,1]=>[1,1,1,1] [4,3,3,2]=>[1,2,1] [4,4,4]=>[3] [4,2,5,1]=>[1,1,1,1] [4,2,4,2]=>[1,1,1,1] [4,2,3,3]=>[1,1,2] [4,3,5]=>[1,1,1] [5,6,1]=>[1,1,1] [5,5,2]=>[2,1] [5,4,3]=>[1,1,1] [5,3,4]=>[1,1,1] [5,2,5]=>[1,1,1] [1,11]=>[1,1] [1,9,2]=>[1,1,1] [1,8,1,2]=>[1,1,1,1] [1,7,1,1,2]=>[1,1,2,1] [1,6,1,1,1,2]=>[1,1,3,1] [1,5,1,1,1,1,2]=>[1,1,4,1] [1,4,1,1,1,1,1,2]=>[1,1,5,1] [1,3,1,1,1,1,1,1,2]=>[1,1,6,1] [1,2,1,1,1,1,1,1,1,2]=>[1,1,7,1] [1,1,1,1,1,1,1,1,1,1,2]=>[10,1] [12]=>[1] [1,2,9]=>[1,1,1] [3,2,7]=>[1,1,1] [1,4,7]=>[1,1,1] [1,1,2,1,7]=>[2,1,1,1] [1,2,2,2,5]=>[1,3,1] [1,1,2,3,5]=>[2,1,1,1] [3,1,2,1,5]=>[1,1,1,1,1] [1,3,2,1,5]=>[1,1,1,1,1] [1,1,4,1,5]=>[2,1,1,1] [1,1,1,2,1,1,5]=>[3,1,2,1] [7,2,3]=>[1,1,1] [1,1,2,1,2,2,3]=>[2,1,1,2,1] [1,8,3]=>[1,1,1] [1,1,2,5,3]=>[2,1,1,1] [3,1,2,3,3]=>[1,1,1,2] [1,1,4,3,3]=>[2,1,2] [1,1,1,2,1,3,3]=>[3,1,1,2] [5,1,2,1,3]=>[1,1,1,1,1] [1,2,2,1,2,1,3]=>[1,2,1,1,1,1] [3,3,2,1,3]=>[2,1,1,1] [1,5,2,1,3]=>[1,1,1,1,1] [1,1,2,2,2,1,3]=>[2,3,1,1] [3,1,4,1,3]=>[1,1,1,1,1] [1,3,4,1,3]=>[1,1,1,1,1] [1,1,6,1,3]=>[2,1,1,1] [1,1,1,2,3,1,3]=>[3,1,1,1,1] [3,1,1,2,1,1,3]=>[1,2,1,2,1] [1,3,1,2,1,1,3]=>[1,1,1,1,2,1] [1,1,3,2,1,1,3]=>[2,1,1,2,1] [1,1,1,4,1,1,3]=>[3,1,2,1] [1,1,1,1,2,1,1,1,3]=>[4,1,3,1] [9,2,1]=>[1,1,1] [1,2,6,2,1]=>[1,1,1,1,1] [1,1,2,1,4,2,1]=>[2,1,1,1,1,1] [5,2,2,2,1]=>[1,3,1] [1,6,2,2,1]=>[1,1,2,1] [1,1,2,3,2,2,1]=>[2,1,1,2,1] [3,1,2,1,2,2,1]=>[1,1,1,1,2,1] [1,3,2,1,2,2,1]=>[1,1,1,1,2,1] [1,1,4,1,2,2,1]=>[2,1,1,2,1] [1,1,1,2,1,1,2,2,1]=>[3,1,2,2,1] [7,4,1]=>[1,1,1] [1,1,2,1,2,4,1]=>[2,1,1,1,1,1] [1,2,2,6,1]=>[1,2,1,1] [3,8,1]=>[1,1,1] [1,10,1]=>[1,1,1] [1,1,2,7,1]=>[2,1,1,1] [3,1,2,5,1]=>[1,1,1,1,1] [1,3,2,5,1]=>[1,1,1,1,1] [1,1,4,5,1]=>[2,1,1,1] [1,1,1,2,1,5,1]=>[3,1,1,1,1] [5,1,2,3,1]=>[1,1,1,1,1] [1,2,2,1,2,3,1]=>[1,2,1,1,1,1] [1,5,2,3,1]=>[1,1,1,1,1] [1,1,2,2,2,3,1]=>[2,3,1,1] [3,1,4,3,1]=>[1,1,1,1,1] [1,1,6,3,1]=>[2,1,1,1] [1,1,1,2,3,3,1]=>[3,1,2,1] [3,1,1,2,1,3,1]=>[1,2,1,1,1,1] [1,3,1,2,1,3,1]=>[1,1,1,1,1,1,1] [1,1,3,2,1,3,1]=>[2,1,1,1,1,1] [1,1,1,4,1,3,1]=>[3,1,1,1,1] [1,1,1,1,2,1,1,3,1]=>[4,1,2,1,1] [7,1,2,1,1]=>[1,1,1,2] [1,2,4,1,2,1,1]=>[1,1,1,1,1,2] [3,2,2,1,2,1,1]=>[1,2,1,1,2] [1,4,2,1,2,1,1]=>[1,1,1,1,1,2] [1,1,2,1,2,1,2,1,1]=>[2,1,1,1,1,1,2] [5,3,2,1,1]=>[1,1,1,2] [1,2,2,3,2,1,1]=>[1,2,1,1,2] [3,5,2,1,1]=>[1,1,1,2] [1,7,2,1,1]=>[1,1,1,2] [1,1,2,4,2,1,1]=>[2,1,1,1,2] [3,1,2,2,2,1,1]=>[1,1,3,2] [1,3,2,2,2,1,1]=>[1,1,3,2] [1,1,4,2,2,1,1]=>[2,1,2,2] [1,1,1,2,1,2,2,1,1]=>[3,1,1,2,2] [5,1,4,1,1]=>[1,1,1,2] [1,2,2,1,4,1,1]=>[1,2,1,1,2] [3,3,4,1,1]=>[2,1,2] [1,5,4,1,1]=>[1,1,1,2] [1,1,2,2,4,1,1]=>[2,2,1,2] [3,1,6,1,1]=>[1,1,1,2] [1,3,6,1,1]=>[1,1,1,2] [1,1,8,1,1]=>[2,1,2] [1,1,1,2,5,1,1]=>[3,1,1,2] [3,1,1,2,3,1,1]=>[1,2,1,1,2] [1,3,1,2,3,1,1]=>[1,1,1,1,1,2] [1,1,3,2,3,1,1]=>[2,1,1,1,2] [1,1,1,4,3,1,1]=>[3,1,1,2] [1,1,1,1,2,1,3,1,1]=>[4,1,1,1,2] [5,1,1,2,1,1,1]=>[1,2,1,3] [1,2,2,1,1,2,1,1,1]=>[1,2,2,1,3] [3,3,1,2,1,1,1]=>[2,1,1,3] [1,5,1,2,1,1,1]=>[1,1,1,1,3] [1,1,2,2,1,2,1,1,1]=>[2,2,1,1,3] [3,1,3,2,1,1,1]=>[1,1,1,1,3] [1,3,3,2,1,1,1]=>[1,2,1,3] [1,1,5,2,1,1,1]=>[2,1,1,3] [1,1,1,2,2,2,1,1,1]=>[3,3,3] [3,1,1,4,1,1,1]=>[1,2,1,3] [1,3,1,4,1,1,1]=>[1,1,1,1,3] [1,1,3,4,1,1,1]=>[2,1,1,3] [1,1,1,6,1,1,1]=>[3,1,3] [1,1,1,1,2,3,1,1,1]=>[4,1,1,3] [3,1,1,1,2,1,1,1,1]=>[1,3,1,4] [1,3,1,1,2,1,1,1,1]=>[1,1,2,1,4] [1,1,3,1,2,1,1,1,1]=>[2,1,1,1,4] [1,1,1,3,2,1,1,1,1]=>[3,1,1,4] [1,1,1,1,4,1,1,1,1]=>[4,1,4] [1,1,1,1,1,2,1,1,1,1,1]=>[5,1,5] [2,2,2,2,1,2,1]=>[4,1,1,1] [2,2,2,1,2,1,2]=>[3,1,1,1,1] [2,2,2,1,2,2,1]=>[3,1,2,1] [2,2,2,1,1,2,2]=>[3,2,2] [2,2,1,2,1,2,2]=>[2,1,1,1,2] [2,2,1,2,1,1,2,1]=>[2,1,1,2,1,1] [2,2,1,2,2,1,2]=>[2,1,2,1,1] [2,2,1,2,2,2,1]=>[2,1,3,1] [2,2,1,1,2,2,2]=>[2,2,3] [2,2,1,1,2,1,2,1]=>[2,2,1,1,1,1] [2,2,1,1,1,2,2,1]=>[2,3,2,1] [2,1,2,1,2,2,2]=>[1,1,1,1,3] [2,1,2,1,2,1,2,1]=>[1,1,1,1,1,1,1,1] [2,1,2,1,1,2,2,1]=>[1,1,1,2,2,1] [2,1,2,1,1,1,2,2]=>[1,1,1,3,2] [2,1,2,2,1,2,2]=>[1,1,2,1,2] [2,1,2,2,1,1,2,1]=>[1,1,2,2,1,1] [2,1,2,2,2,1,2]=>[1,1,3,1,1] [2,1,2,2,2,2,1]=>[1,1,4,1] [2,1,1,2,2,2,2]=>[1,2,4] [2,1,1,2,2,1,2,1]=>[1,2,2,1,1,1] [2,1,1,2,1,2,1,2]=>[1,2,1,1,1,1,1] [2,1,1,2,1,2,2,1]=>[1,2,1,1,2,1] [2,1,1,1,2,2,2,1]=>[1,3,3,1] [2,1,1,1,2,1,2,2]=>[1,3,1,1,2] [1,2,1,2,2,2,2]=>[1,1,1,4] [1,2,1,2,2,1,2,1]=>[1,1,1,2,1,1,1] [1,2,1,2,1,2,1,2]=>[1,1,1,1,1,1,1,1] [1,2,1,2,1,2,2,1]=>[1,1,1,1,1,2,1] [1,2,1,2,1,1,2,2]=>[1,1,1,1,2,2] [1,2,1,1,2,1,2,2]=>[1,1,2,1,1,2] [1,2,1,1,2,1,1,2,1]=>[1,1,2,1,2,1,1] [1,2,1,1,2,2,1,2]=>[1,1,2,2,1,1] [1,2,1,1,2,2,2,1]=>[1,1,2,3,1] [1,2,1,1,1,2,2,2]=>[1,1,3,3] [1,2,1,1,1,2,1,2,1]=>[1,1,3,1,1,1,1] [1,2,1,1,1,1,2,2,1]=>[1,1,4,2,1] [1,2,2,1,2,2,2]=>[1,2,1,3] [1,2,2,1,2,1,2,1]=>[1,2,1,1,1,1,1] [1,2,2,1,1,2,1,2]=>[1,2,2,1,1,1] [1,2,2,1,1,2,2,1]=>[1,2,2,2,1] [1,2,2,1,1,1,2,2]=>[1,2,3,2] [1,2,2,2,1,2,2]=>[1,3,1,2] [1,2,2,2,1,1,2,1]=>[1,3,2,1,1] [1,2,2,2,2,1,2]=>[1,4,1,1] [1,1,2,2,2,2,2]=>[2,5] [1,1,2,2,2,1,2,1]=>[2,3,1,1,1] [1,1,2,2,1,2,1,2]=>[2,2,1,1,1,1] [1,1,2,2,1,2,2,1]=>[2,2,1,2,1] [1,1,2,1,2,1,2,2]=>[2,1,1,1,1,2] [1,1,2,1,2,1,1,2,1]=>[2,1,1,1,2,1,1] [1,1,2,1,2,2,2,1]=>[2,1,1,3,1] [1,1,2,1,1,2,1,2,1]=>[2,1,2,1,1,1,1] [1,1,2,1,1,1,2,2,1]=>[2,1,3,2,1] [1,1,1,2,2,1,2,2]=>[3,2,1,2] [1,1,1,2,2,1,1,2,1]=>[3,2,2,1,1] [1,1,1,2,2,2,1,2]=>[3,3,1,1] [1,1,1,2,2,2,2,1]=>[3,4,1] [1,1,1,2,1,2,2,2]=>[3,1,1,3] [1,1,1,2,1,2,1,2,1]=>[3,1,1,1,1,1,1] [1,1,1,1,2,2,1,2,1]=>[4,2,1,1,1] [1,1,1,1,2,1,2,2,1]=>[4,1,1,2,1] [1,1,1,1,1,2,2,2,1]=>[5,3,1] [3,2,2,2,2,1]=>[1,4,1] [4,3,2,2,1]=>[1,1,2,1] [4,2,3,2,1]=>[1,1,1,1,1] [4,2,2,3,1]=>[1,2,1,1] [4,2,2,2,2]=>[1,4] [5,4,2,1]=>[1,1,1,1] [5,3,3,1]=>[1,2,1] [5,3,2,2]=>[1,1,2] [5,2,4,1]=>[1,1,1,1] [5,2,3,2]=>[1,1,1,1] [5,2,2,3]=>[1,2,1] [6,5,1]=>[1,1,1] [6,4,2]=>[1,1,1] [6,3,3]=>[1,2] [6,2,4]=>[1,1,1] [7,5]=>[1,1] [11,1]=>[1,1] [2,9,1]=>[1,1,1] [2,1,8,1]=>[1,1,1,1] [2,1,1,7,1]=>[1,2,1,1] [2,1,1,1,6,1]=>[1,3,1,1] [2,1,1,1,1,5,1]=>[1,4,1,1] [2,1,1,1,1,1,4,1]=>[1,5,1,1] [2,1,1,1,1,1,1,3,1]=>[1,6,1,1] [2,1,1,1,1,1,1,1,2,1]=>[1,7,1,1] [2,1,1,1,1,1,1,1,1,1,1]=>[1,10] [2,2,1,2,1,2,1,1]=>[2,1,1,1,1,2] [2,2,1,1,1,2,1,1,1]=>[2,3,1,3] [2,1,2,1,1,1,2,1,1]=>[1,1,1,3,1,2] [2,1,2,1,2,1,1,2]=>[1,1,1,1,1,2,1] [2,1,2,1,2,2,1,1]=>[1,1,1,1,2,2] [2,1,2,1,1,2,1,1,1]=>[1,1,1,2,1,3] [2,1,1,2,1,1,1,2,1]=>[1,2,1,3,1,1] [2,1,1,2,1,1,2,1,1]=>[1,2,1,2,1,2] [2,1,1,2,1,2,1,1,1]=>[1,2,1,1,1,3] [2,1,1,1,2,1,1,1,2]=>[1,3,1,3,1] [2,1,1,1,2,1,1,2,1]=>[1,3,1,2,1,1] [2,1,1,1,2,1,2,1,1]=>[1,3,1,1,1,2] [2,1,1,1,2,2,1,1,1]=>[1,3,2,3] [1,2,1,2,1,1,2,1,1]=>[1,1,1,1,2,1,2] [1,2,1,1,2,1,2,1,1]=>[1,1,2,1,1,1,2] [1,2,1,1,1,2,1,1,2]=>[1,1,3,1,2,1] [1,2,1,1,1,2,2,1,1]=>[1,1,3,2,2] [1,2,1,1,1,1,2,1,1,1]=>[1,1,4,1,3] [1,2,2,1,1,1,2,1,1]=>[1,2,3,1,2] [1,2,2,2,1,2,1,1]=>[1,3,1,1,2] [1,2,2,1,2,1,1,2]=>[1,2,1,1,2,1] [1,2,2,1,2,2,1,1]=>[1,2,1,2,2] [1,2,1,2,1,1,1,2,1]=>[1,1,1,1,3,1,1] [1,2,1,2,2,1,1,2]=>[1,1,1,2,2,1] [1,2,1,2,2,2,1,1]=>[1,1,1,3,2] [1,2,1,2,1,2,1,1,1]=>[1,1,1,1,1,1,3] [1,2,1,1,2,1,1,1,2]=>[1,1,2,1,3,1] [1,2,1,1,2,2,1,1,1]=>[1,1,2,2,3] [1,2,1,1,1,2,1,1,1,1]=>[1,1,3,1,4] [1,1,2,1,1,1,2,1,2]=>[2,1,3,1,1,1] [1,1,2,1,1,2,1,1,2]=>[2,1,2,1,2,1] [1,1,2,1,1,2,2,1,1]=>[2,1,2,2,2] [1,1,2,1,1,1,2,1,1,1]=>[2,1,3,1,3] [1,1,2,2,1,1,1,2,1]=>[2,2,3,1,1] [1,1,2,2,1,1,2,1,1]=>[2,2,2,1,2] [1,1,2,1,2,1,1,1,2]=>[2,1,1,1,3,1] [1,1,2,1,2,2,1,1,1]=>[2,1,1,2,3] [1,1,1,2,1,1,1,2,2]=>[3,1,3,2] [1,1,1,2,1,1,1,1,2,1]=>[3,1,4,1,1] [1,1,1,2,1,1,2,1,2]=>[3,1,2,1,1,1] [1,1,1,2,1,1,1,2,1,1]=>[3,1,3,1,2] [1,1,1,2,1,2,1,1,2]=>[3,1,1,1,2,1] [1,1,1,2,1,1,2,1,1,1]=>[3,1,2,1,3] [1,1,1,2,2,1,1,1,2]=>[3,2,3,1] [1,1,1,2,2,1,2,1,1]=>[3,2,1,1,2] [1,1,1,2,1,2,1,1,1,1]=>[3,1,1,1,4] [1,1,1,1,2,1,1,1,2,1]=>[4,1,3,1,1] [1,1,1,1,2,1,2,1,1,1]=>[4,1,1,1,3] [1,2,2,4,2,1]=>[1,2,1,1,1] [1,2,4,2,2,1]=>[1,1,1,2,1] [1,2,5,2,2]=>[1,1,1,2] [1,3,5,2,1]=>[1,1,1,1,1] [1,4,2,2,2,1]=>[1,1,3,1] [1,5,2,2,2]=>[1,1,3] [1,5,3,2,1]=>[1,1,1,1,1] [2,5,2,2,1]=>[1,1,2,1] [2,6,2,2]=>[1,1,2] [2,2,5,2,1]=>[2,1,1,1] [6,2,2,2]=>[1,3] [2,2,2,2,2,1,1]=>[5,2] [2,2,2,1,2,1,1,1]=>[3,1,1,3] [2,2,1,2,2,1,1,1]=>[2,1,2,3] [2,1,2,2,2,1,1,1]=>[1,1,3,3] [1,2,2,2,2,1,1,1]=>[1,4,3] [1,2,2,1,2,1,1,1,1]=>[1,2,1,1,4] [1,2,1,2,2,1,1,1,1]=>[1,1,1,2,4] [1,1,2,2,2,1,1,1,1]=>[2,3,4] [1,2,1,1,2,1,1,1,1,1]=>[1,1,2,1,5] [1,1,2,1,2,1,1,1,1,1]=>[2,1,1,1,5] [1,1,1,2,2,1,1,1,1,1]=>[3,2,5] [1,1,1,1,2,1,1,1,1,1,1]=>[4,1,6] [10,2]=>[1,1] [1,1,1,1,1,1,1,2,2,1]=>[7,2,1] [1,1,1,1,1,2,2,1,1,1]=>[5,2,3] [1,1,1,1,1,2,1,1,2,1]=>[5,1,2,1,1] [1,2,2,1,1,1,1,1,1,1]=>[1,2,7] [1,2,1,1,1,1,1,1,2,1]=>[1,1,6,1,1] [1,2,2,2,3,1,1]=>[1,3,1,2] [1,2,2,3,1,2,1]=>[1,2,1,1,1,1] [1,2,2,4,1,1,1]=>[1,2,1,3] [1,2,3,1,2,2,1]=>[1,1,1,1,2,1] [1,2,3,1,3,1,1]=>[1,1,1,1,1,2] [1,2,3,2,1,2,1]=>[1,1,1,1,1,1,1] [1,2,4,1,1,2,1]=>[1,1,1,2,1,1] [1,2,3,2,2,1,1]=>[1,1,1,2,2] [1,2,3,3,1,1,1]=>[1,1,2,3] [1,2,4,2,1,1,1]=>[1,1,1,1,3] [1,2,5,1,1,1,1]=>[1,1,1,4] [1,3,1,2,2,2,1]=>[1,1,1,3,1] [1,3,1,3,1,2,1]=>[1,1,1,1,1,1,1] [1,3,1,3,2,1,1]=>[1,1,1,1,1,2] [1,3,2,1,3,1,1]=>[1,1,1,1,1,2] [1,4,1,1,2,2,1]=>[1,1,2,2,1] [1,4,1,1,3,1,1]=>[1,1,2,1,2] [1,3,2,2,1,2,1]=>[1,1,2,1,1,1] [1,3,3,1,1,2,1]=>[1,2,2,1,1] [1,4,1,2,1,2,1]=>[1,1,1,1,1,1,1] [1,4,2,1,1,2,1]=>[1,1,1,2,1,1] [1,5,1,1,1,2,1]=>[1,1,3,1,1] [1,3,2,3,1,1,1]=>[1,1,1,1,3] [1,3,3,1,2,1,1]=>[1,2,1,1,2] [1,3,4,1,1,1,1]=>[1,1,1,4] [1,4,1,2,2,1,1]=>[1,1,1,2,2] [1,4,1,3,1,1,1]=>[1,1,1,1,3] [1,5,1,1,2,1,1]=>[1,1,2,1,2] [1,4,2,2,1,1,1]=>[1,1,2,3] [1,4,3,1,1,1,1]=>[1,1,1,4] [1,5,2,1,1,1,1]=>[1,1,1,4] [1,6,1,1,1,1,1]=>[1,1,5] [2,1,2,2,3,1,1]=>[1,1,2,1,2] [2,1,2,3,1,2,1]=>[1,1,1,1,1,1,1] [2,1,2,3,2,1,1]=>[1,1,1,1,1,2] [2,1,2,4,1,1,1]=>[1,1,1,1,3] [2,1,3,1,2,2,1]=>[1,1,1,1,2,1] [2,1,3,1,3,1,1]=>[1,1,1,1,1,2] [2,1,3,2,1,2,1]=>[1,1,1,1,1,1,1] [2,1,4,1,1,2,1]=>[1,1,1,2,1,1] [2,1,3,2,2,1,1]=>[1,1,1,2,2] [2,1,3,3,1,1,1]=>[1,1,2,3] [2,1,4,1,2,1,1]=>[1,1,1,1,1,2] [2,1,4,2,1,1,1]=>[1,1,1,1,3] [2,1,5,1,1,1,1]=>[1,1,1,4] [2,2,1,2,3,1,1]=>[2,1,1,1,2] [2,2,1,3,1,2,1]=>[2,1,1,1,1,1] [2,2,1,3,2,1,1]=>[2,1,1,1,2] [2,2,1,4,1,1,1]=>[2,1,1,3] [3,1,1,2,2,2,1]=>[1,2,3,1] [3,1,1,3,1,2,1]=>[1,2,1,1,1,1] [3,1,1,3,2,1,1]=>[1,2,1,1,2] [2,2,2,1,3,1,1]=>[3,1,1,2] [2,3,1,1,2,2,1]=>[1,1,2,2,1] [2,3,1,1,3,1,1]=>[1,1,2,1,2] [3,1,2,1,3,1,1]=>[1,1,1,1,1,2] [3,2,1,1,2,2,1]=>[1,1,2,2,1] [3,2,1,1,3,1,1]=>[1,1,2,1,2] [4,1,1,1,2,2,1]=>[1,3,2,1] [4,1,1,1,3,1,1]=>[1,3,1,2] [2,2,3,1,1,2,1]=>[2,1,2,1,1] [2,3,1,2,1,2,1]=>[1,1,1,1,1,1,1] [2,3,2,1,1,2,1]=>[1,1,1,2,1,1] [2,4,1,1,1,2,1]=>[1,1,3,1,1] [3,1,2,2,1,2,1]=>[1,1,2,1,1,1] [3,1,3,1,1,2,1]=>[1,1,1,2,1,1] [3,2,1,2,1,2,1]=>[1,1,1,1,1,1,1] [4,1,1,2,1,2,1]=>[1,2,1,1,1,1] [3,2,2,1,1,2,1]=>[1,2,2,1,1] [3,3,1,1,1,2,1]=>[2,3,1,1] [4,1,2,1,1,2,1]=>[1,1,1,2,1,1] [4,2,1,1,1,2,1]=>[1,1,3,1,1] [5,1,1,1,1,2,1]=>[1,4,1,1] [2,2,2,3,1,1,1]=>[3,1,3] [2,2,3,1,2,1,1]=>[2,1,1,1,2] [2,2,3,2,1,1,1]=>[2,1,1,3] [2,2,4,1,1,1,1]=>[2,1,4] [2,3,1,2,2,1,1]=>[1,1,1,2,2] [2,3,1,3,1,1,1]=>[1,1,1,1,3] [2,3,2,1,2,1,1]=>[1,1,1,1,1,2] [2,4,1,1,2,1,1]=>[1,1,2,1,2] [2,3,2,2,1,1,1]=>[1,1,2,3] [2,3,3,1,1,1,1]=>[1,2,4] [2,4,1,2,1,1,1]=>[1,1,1,1,3] [2,4,2,1,1,1,1]=>[1,1,1,4] [2,5,1,1,1,1,1]=>[1,1,5] [3,1,2,3,1,1,1]=>[1,1,1,1,3] [3,1,3,1,2,1,1]=>[1,1,1,1,1,2] [3,1,4,1,1,1,1]=>[1,1,1,4] [3,2,1,2,2,1,1]=>[1,1,1,2,2] [3,2,1,3,1,1,1]=>[1,1,1,1,3] [4,1,1,2,2,1,1]=>[1,2,2,2] [4,1,1,3,1,1,1]=>[1,2,1,3] [3,3,1,1,2,1,1]=>[2,2,1,2] [4,1,2,1,2,1,1]=>[1,1,1,1,1,2] [4,2,1,1,2,1,1]=>[1,1,2,1,2] [5,1,1,1,2,1,1]=>[1,3,1,2] [3,2,2,2,1,1,1]=>[1,3,3] [3,2,3,1,1,1,1]=>[1,1,1,4] [3,3,2,1,1,1,1]=>[2,1,4] [3,4,1,1,1,1,1]=>[1,1,5] [4,1,2,2,1,1,1]=>[1,1,2,3] [4,1,3,1,1,1,1]=>[1,1,1,4] [4,2,1,2,1,1,1]=>[1,1,1,1,3] [4,2,2,1,1,1,1]=>[1,2,4] [4,3,1,1,1,1,1]=>[1,1,5] [5,1,2,1,1,1,1]=>[1,1,1,4] [5,2,1,1,1,1,1]=>[1,1,5] [6,1,1,1,1,1,1]=>[1,6] [1,2,1,1,1,1,1,1,1,1,1]=>[1,1,9] [1,2,2,2,1,1,1,1,1]=>[1,3,5] [1,2,2,1,1,1,1,2,1]=>[1,2,4,1,1] [1,1,1,2,1,1,1,1,1,1,1]=>[3,1,7] [1,1,1,1,1,1,1,2,1,1,1]=>[7,1,3] [1,1,1,1,1,1,1,1,1,2,1]=>[9,1,1] [1,1,2,3,2,3]=>[2,1,1,1,1] [2,2,2,2,4]=>[4,1] [1,2,2,2,2,3]=>[1,4,1] [1,2,2,3,4]=>[1,2,1,1] [2,2,3,5]=>[2,1,1] [1,2,3,2,4]=>[1,1,1,1,1] [2,3,2,5]=>[1,1,1,1] [1,3,2,2,4]=>[1,1,2,1] [2,2,2,2,1,1,2]=>[4,2,1] [1,1,2,1,1,1,1,1,1,1,1]=>[2,1,8] [1,1,2,2,1,2,3]=>[2,2,1,1,1] [1,1,1,1,2,2,2,1,1]=>[4,3,2] [1,1,1,1,1,1,2,1,1,1,1]=>[6,1,4] [1,1,1,1,1,1,1,1,2,1,1]=>[8,1,2] [1,1,1,2,2,2,3]=>[3,3,1] [2,2,2,6]=>[3,1] [2,2,6,2]=>[2,1,1] [1,2,1,2,1,1,1,1,1,1]=>[1,1,1,1,6] [1,2,1,1,1,1,1,2,1,1]=>[1,1,5,1,2] [1,1,2,1,1,1,1,1,2,1]=>[2,1,5,1,1] [1,1,1,1,1,2,1,2,1,1]=>[5,1,1,1,2] [1,1,1,1,1,1,2,1,2,1]=>[6,1,1,1,1] [1,2,5,3,1]=>[1,1,1,1,1] [1,2,2,2,4,1]=>[1,3,1,1] [2,2,2,5,1]=>[3,1,1] [1,2,3,5,1]=>[1,1,1,1,1] [1,2,2,5,2]=>[1,2,1,1] [1,1,2,2,2,4]=>[2,3,1] [2,2,1,1,1,2,1,2]=>[2,3,1,1,1] [1,2,2,2,1,1,1,2]=>[1,3,3,1] [2,2,1,2,1,1,1,2]=>[2,1,1,3,1] [2,2,2,1,1,1,2,1]=>[3,3,1,1] [1,2,2,2,2,2,2]=>[1,6] [1,2,2,2,2,1,3]=>[1,4,1,1] [1,2,2,2,1,3,2]=>[1,3,1,1,1] [1,2,2,2,1,2,3]=>[1,3,1,1,1] [1,2,2,2,1,1,4]=>[1,3,2,1] [1,2,2,1,3,2,2]=>[1,2,1,1,2] [1,2,2,1,3,1,3]=>[1,2,1,1,1,1] [1,2,2,1,2,3,2]=>[1,2,1,1,1,1] [1,2,2,1,2,2,3]=>[1,2,1,2,1] [1,2,2,1,2,1,4]=>[1,2,1,1,1,1] [1,2,2,1,1,4,2]=>[1,2,2,1,1] [1,2,2,1,1,3,3]=>[1,2,2,2] [1,2,2,1,1,2,4]=>[1,2,2,1,1] [1,2,2,1,1,1,5]=>[1,2,3,1] [1,2,1,3,2,2,2]=>[1,1,1,1,3] [1,2,1,3,2,1,3]=>[1,1,1,1,1,1,1] [1,2,1,3,1,3,2]=>[1,1,1,1,1,1,1] [1,2,1,3,1,2,3]=>[1,1,1,1,1,1,1] [1,2,1,3,1,1,4]=>[1,1,1,1,2,1] [1,2,1,2,3,2,2]=>[1,1,1,1,1,2] [1,2,1,2,3,1,3]=>[1,1,1,1,1,1,1] [1,2,1,2,2,3,2]=>[1,1,1,2,1,1] [1,2,1,2,2,2,3]=>[1,1,1,3,1] [1,2,1,2,2,1,4]=>[1,1,1,2,1,1] [1,2,1,2,1,4,2]=>[1,1,1,1,1,1,1] [1,2,1,2,1,3,3]=>[1,1,1,1,1,2] [1,2,1,2,1,2,4]=>[1,1,1,1,1,1,1] [1,2,1,2,1,1,5]=>[1,1,1,1,2,1] [1,2,1,1,4,2,2]=>[1,1,2,1,2] [1,2,1,1,4,1,3]=>[1,1,2,1,1,1] [1,2,1,1,3,3,2]=>[1,1,2,2,1] [1,2,1,1,3,2,3]=>[1,1,2,1,1,1] [1,2,1,1,3,1,4]=>[1,1,2,1,1,1] [1,2,1,1,2,4,2]=>[1,1,2,1,1,1] [1,2,1,1,2,3,3]=>[1,1,2,1,2] [1,2,1,1,2,2,4]=>[1,1,2,2,1] [1,2,1,1,2,1,5]=>[1,1,2,1,1,1] [1,2,1,1,1,5,2]=>[1,1,3,1,1] [1,2,1,1,1,4,3]=>[1,1,3,1,1] [1,2,1,1,1,3,4]=>[1,1,3,1,1] [1,2,1,1,1,2,5]=>[1,1,3,1,1] [1,2,1,1,1,1,6]=>[1,1,4,1] [1,1,3,2,2,2,2]=>[2,1,4] [1,1,3,2,2,1,3]=>[2,1,2,1,1] [1,1,3,2,1,3,2]=>[2,1,1,1,1,1] [1,1,3,2,1,2,3]=>[2,1,1,1,1,1] [1,1,3,2,1,1,4]=>[2,1,1,2,1] [1,1,3,1,3,2,2]=>[2,1,1,1,2] [1,1,3,1,3,1,3]=>[2,1,1,1,1,1] [1,1,3,1,2,3,2]=>[2,1,1,1,1,1] [1,1,3,1,2,2,3]=>[2,1,1,2,1] [1,1,3,1,2,1,4]=>[2,1,1,1,1,1] [1,1,3,1,1,4,2]=>[2,1,2,1,1] [1,1,3,1,1,3,3]=>[2,1,2,2] [1,1,3,1,1,2,4]=>[2,1,2,1,1] [1,1,3,1,1,1,5]=>[2,1,3,1] [1,1,2,3,2,2,2]=>[2,1,1,3] [1,1,2,3,2,1,3]=>[2,1,1,1,1,1] [1,1,2,3,1,3,2]=>[2,1,1,1,1,1] [1,1,2,3,1,2,3]=>[2,1,1,1,1,1] [1,1,2,3,1,1,4]=>[2,1,1,2,1] [1,1,2,2,3,2,2]=>[2,2,1,2] [1,1,2,2,3,1,3]=>[2,2,1,1,1] [1,1,2,2,2,3,2]=>[2,3,1,1] [1,1,2,2,2,2,3]=>[2,4,1] [1,1,2,2,2,1,4]=>[2,3,1,1] [1,1,2,2,1,4,2]=>[2,2,1,1,1] [1,1,2,2,1,3,3]=>[2,2,1,2] [1,1,2,2,1,2,4]=>[2,2,1,1,1] [1,1,2,2,1,1,5]=>[2,2,2,1] [1,1,2,1,4,2,2]=>[2,1,1,1,2] [1,1,2,1,4,1,3]=>[2,1,1,1,1,1] [1,1,2,1,3,3,2]=>[2,1,1,2,1] [1,1,2,1,3,2,3]=>[2,1,1,1,1,1] [1,1,2,1,3,1,4]=>[2,1,1,1,1,1] [1,1,2,1,2,4,2]=>[2,1,1,1,1,1] [1,1,2,1,2,3,3]=>[2,1,1,1,2] [1,1,2,1,2,2,4]=>[2,1,1,2,1] [1,1,2,1,2,1,5]=>[2,1,1,1,1,1] [1,1,2,1,1,5,2]=>[2,1,2,1,1] [1,1,2,1,1,4,3]=>[2,1,2,1,1] [1,1,2,1,1,3,4]=>[2,1,2,1,1] [1,1,2,1,1,2,5]=>[2,1,2,1,1] [1,1,2,1,1,1,6]=>[2,1,3,1] [1,1,1,4,2,2,2]=>[3,1,3] [1,1,1,4,2,1,3]=>[3,1,1,1,1] [1,1,1,4,1,3,2]=>[3,1,1,1,1] [1,1,1,4,1,2,3]=>[3,1,1,1,1] [1,1,1,4,1,1,4]=>[3,1,2,1] [1,1,1,3,3,2,2]=>[3,2,2] [1,1,1,3,3,1,3]=>[3,2,1,1] [1,1,1,3,2,3,2]=>[3,1,1,1,1] [1,1,1,3,2,2,3]=>[3,1,2,1] [1,1,1,3,2,1,4]=>[3,1,1,1,1] [1,1,1,3,1,4,2]=>[3,1,1,1,1] [1,1,1,3,1,3,3]=>[3,1,1,2] [1,1,1,3,1,2,4]=>[3,1,1,1,1] [1,1,1,3,1,1,5]=>[3,1,2,1] [1,1,1,2,4,2,2]=>[3,1,1,2] [1,1,1,2,4,1,3]=>[3,1,1,1,1] [1,1,1,2,3,3,2]=>[3,1,2,1] [1,1,1,2,3,2,3]=>[3,1,1,1,1] [1,1,1,2,3,1,4]=>[3,1,1,1,1] [1,1,1,2,2,4,2]=>[3,2,1,1] [1,1,1,2,2,3,3]=>[3,2,2] [1,1,1,2,2,2,4]=>[3,3,1] [1,1,1,2,2,1,5]=>[3,2,1,1] [1,1,1,2,1,5,2]=>[3,1,1,1,1] [1,1,1,2,1,4,3]=>[3,1,1,1,1] [1,1,1,2,1,3,4]=>[3,1,1,1,1] [1,1,1,2,1,2,5]=>[3,1,1,1,1] [1,1,1,2,1,1,6]=>[3,1,2,1] [1,1,1,1,5,2,2]=>[4,1,2] [1,1,1,1,5,1,3]=>[4,1,1,1] [1,1,1,1,4,3,2]=>[4,1,1,1] [1,1,1,1,4,2,3]=>[4,1,1,1] [1,1,1,1,4,1,4]=>[4,1,1,1] [1,1,1,1,3,4,2]=>[4,1,1,1] [1,1,1,1,3,3,3]=>[4,3] [1,1,1,1,3,2,4]=>[4,1,1,1] [1,1,1,1,3,1,5]=>[4,1,1,1] [1,1,1,1,2,5,2]=>[4,1,1,1] [1,1,1,1,2,4,3]=>[4,1,1,1] [1,1,1,1,2,3,4]=>[4,1,1,1] [1,1,1,1,2,2,5]=>[4,2,1] [1,1,1,1,2,1,6]=>[4,1,1,1] [1,1,1,1,1,6,2]=>[5,1,1] [1,1,1,1,1,5,3]=>[5,1,1] [1,1,1,1,1,4,4]=>[5,2] [1,1,1,1,1,3,5]=>[5,1,1] [1,1,1,1,1,2,6]=>[5,1,1] [1,1,1,1,1,1,7]=>[6,1] [2,2,2,2,2,2,1]=>[6,1] [3,1,2,2,2,2,1]=>[1,1,4,1] [2,3,1,2,2,2,1]=>[1,1,1,3,1] [3,2,1,2,2,2,1]=>[1,1,1,3,1] [4,1,1,2,2,2,1]=>[1,2,3,1] [2,2,3,1,2,2,1]=>[2,1,1,2,1] [3,1,3,1,2,2,1]=>[1,1,1,1,2,1] [2,3,2,1,2,2,1]=>[1,1,1,1,2,1] [3,2,2,1,2,2,1]=>[1,2,1,2,1] [4,1,2,1,2,2,1]=>[1,1,1,1,2,1] [2,4,1,1,2,2,1]=>[1,1,2,2,1] [3,3,1,1,2,2,1]=>[2,2,2,1] [4,2,1,1,2,2,1]=>[1,1,2,2,1] [5,1,1,1,2,2,1]=>[1,3,2,1] [2,2,2,3,1,2,1]=>[3,1,1,1,1] [3,1,2,3,1,2,1]=>[1,1,1,1,1,1,1] [2,3,1,3,1,2,1]=>[1,1,1,1,1,1,1] [3,2,1,3,1,2,1]=>[1,1,1,1,1,1,1] [4,1,1,3,1,2,1]=>[1,2,1,1,1,1] [2,2,3,2,1,2,1]=>[2,1,1,1,1,1] [3,1,3,2,1,2,1]=>[1,1,1,1,1,1,1] [2,3,2,2,1,2,1]=>[1,1,2,1,1,1] [3,2,2,2,1,2,1]=>[1,3,1,1,1] [4,1,2,2,1,2,1]=>[1,1,2,1,1,1] [2,4,1,2,1,2,1]=>[1,1,1,1,1,1,1] [3,3,1,2,1,2,1]=>[2,1,1,1,1,1] [4,2,1,2,1,2,1]=>[1,1,1,1,1,1,1] [5,1,1,2,1,2,1]=>[1,2,1,1,1,1] [2,2,4,1,1,2,1]=>[2,1,2,1,1] [3,1,4,1,1,2,1]=>[1,1,1,2,1,1] [2,3,3,1,1,2,1]=>[1,2,2,1,1] [3,2,3,1,1,2,1]=>[1,1,1,2,1,1] [4,1,3,1,1,2,1]=>[1,1,1,2,1,1] [2,4,2,1,1,2,1]=>[1,1,1,2,1,1] [3,3,2,1,1,2,1]=>[2,1,2,1,1] [4,2,2,1,1,2,1]=>[1,2,2,1,1] [5,1,2,1,1,2,1]=>[1,1,1,2,1,1] [2,5,1,1,1,2,1]=>[1,1,3,1,1] [3,4,1,1,1,2,1]=>[1,1,3,1,1] [4,3,1,1,1,2,1]=>[1,1,3,1,1] [5,2,1,1,1,2,1]=>[1,1,3,1,1] [6,1,1,1,1,2,1]=>[1,4,1,1] [2,2,2,2,3,1,1]=>[4,1,2] [3,1,2,2,3,1,1]=>[1,1,2,1,2] [2,3,1,2,3,1,1]=>[1,1,1,1,1,2] [3,2,1,2,3,1,1]=>[1,1,1,1,1,2] [4,1,1,2,3,1,1]=>[1,2,1,1,2] [2,2,3,1,3,1,1]=>[2,1,1,1,2] [3,1,3,1,3,1,1]=>[1,1,1,1,1,2] [2,3,2,1,3,1,1]=>[1,1,1,1,1,2] [3,2,2,1,3,1,1]=>[1,2,1,1,2] [4,1,2,1,3,1,1]=>[1,1,1,1,1,2] [2,4,1,1,3,1,1]=>[1,1,2,1,2] [3,3,1,1,3,1,1]=>[2,2,1,2] [4,2,1,1,3,1,1]=>[1,1,2,1,2] [5,1,1,1,3,1,1]=>[1,3,1,2] [2,2,2,3,2,1,1]=>[3,1,1,2] [3,1,2,3,2,1,1]=>[1,1,1,1,1,2] [2,3,1,3,2,1,1]=>[1,1,1,1,1,2] [3,2,1,3,2,1,1]=>[1,1,1,1,1,2] [4,1,1,3,2,1,1]=>[1,2,1,1,2] [2,2,3,2,2,1,1]=>[2,1,2,2] [3,1,3,2,2,1,1]=>[1,1,1,2,2] [2,3,2,2,2,1,1]=>[1,1,3,2] [3,2,2,2,2,1,1]=>[1,4,2] [4,1,2,2,2,1,1]=>[1,1,3,2] [2,4,1,2,2,1,1]=>[1,1,1,2,2] [3,3,1,2,2,1,1]=>[2,1,2,2] [4,2,1,2,2,1,1]=>[1,1,1,2,2] [5,1,1,2,2,1,1]=>[1,2,2,2] [2,2,4,1,2,1,1]=>[2,1,1,1,2] [3,1,4,1,2,1,1]=>[1,1,1,1,1,2] [2,3,3,1,2,1,1]=>[1,2,1,1,2] [3,2,3,1,2,1,1]=>[1,1,1,1,1,2] [4,1,3,1,2,1,1]=>[1,1,1,1,1,2] [2,4,2,1,2,1,1]=>[1,1,1,1,1,2] [3,3,2,1,2,1,1]=>[2,1,1,1,2] [4,2,2,1,2,1,1]=>[1,2,1,1,2] [5,1,2,1,2,1,1]=>[1,1,1,1,1,2] [2,5,1,1,2,1,1]=>[1,1,2,1,2] [3,4,1,1,2,1,1]=>[1,1,2,1,2] [4,3,1,1,2,1,1]=>[1,1,2,1,2] [5,2,1,1,2,1,1]=>[1,1,2,1,2] [6,1,1,1,2,1,1]=>[1,3,1,2] [2,2,2,4,1,1,1]=>[3,1,3] [3,1,2,4,1,1,1]=>[1,1,1,1,3] [2,3,1,4,1,1,1]=>[1,1,1,1,3] [3,2,1,4,1,1,1]=>[1,1,1,1,3] [4,1,1,4,1,1,1]=>[1,2,1,3] [2,2,3,3,1,1,1]=>[2,2,3] [3,1,3,3,1,1,1]=>[1,1,2,3] [2,3,2,3,1,1,1]=>[1,1,1,1,3] [3,2,2,3,1,1,1]=>[1,2,1,3] [4,1,2,3,1,1,1]=>[1,1,1,1,3] [2,4,1,3,1,1,1]=>[1,1,1,1,3] [3,3,1,3,1,1,1]=>[2,1,1,3] [4,2,1,3,1,1,1]=>[1,1,1,1,3] [5,1,1,3,1,1,1]=>[1,2,1,3] [2,2,4,2,1,1,1]=>[2,1,1,3] [3,1,4,2,1,1,1]=>[1,1,1,1,3] [2,3,3,2,1,1,1]=>[1,2,1,3] [3,2,3,2,1,1,1]=>[1,1,1,1,3] [4,1,3,2,1,1,1]=>[1,1,1,1,3] [2,4,2,2,1,1,1]=>[1,1,2,3] [3,3,2,2,1,1,1]=>[2,2,3] [4,2,2,2,1,1,1]=>[1,3,3] [5,1,2,2,1,1,1]=>[1,1,2,3] [2,5,1,2,1,1,1]=>[1,1,1,1,3] [3,4,1,2,1,1,1]=>[1,1,1,1,3] [4,3,1,2,1,1,1]=>[1,1,1,1,3] [5,2,1,2,1,1,1]=>[1,1,1,1,3] [6,1,1,2,1,1,1]=>[1,2,1,3] [2,2,5,1,1,1,1]=>[2,1,4] [3,1,5,1,1,1,1]=>[1,1,1,4] [2,3,4,1,1,1,1]=>[1,1,1,4] [3,2,4,1,1,1,1]=>[1,1,1,4] [4,1,4,1,1,1,1]=>[1,1,1,4] [2,4,3,1,1,1,1]=>[1,1,1,4] [3,3,3,1,1,1,1]=>[3,4] [4,2,3,1,1,1,1]=>[1,1,1,4] [5,1,3,1,1,1,1]=>[1,1,1,4] [2,5,2,1,1,1,1]=>[1,1,1,4] [3,4,2,1,1,1,1]=>[1,1,1,4] [4,3,2,1,1,1,1]=>[1,1,1,4] [5,2,2,1,1,1,1]=>[1,2,4] [6,1,2,1,1,1,1]=>[1,1,1,4] [2,6,1,1,1,1,1]=>[1,1,5] [3,5,1,1,1,1,1]=>[1,1,5] [4,4,1,1,1,1,1]=>[2,5] [5,3,1,1,1,1,1]=>[1,1,5] [6,2,1,1,1,1,1]=>[1,1,5] [7,1,1,1,1,1,1]=>[1,6] [1,3,1,3,1,3,1]=>[1,1,1,1,1,1,1] [1,3,1,2,3,2,1]=>[1,1,1,1,1,1,1] [1,3,1,2,1,4,1]=>[1,1,1,1,1,1,1] [1,3,1,1,1,5,1]=>[1,1,3,1,1] [1,2,3,2,1,3,1]=>[1,1,1,1,1,1,1] [1,2,3,1,3,2,1]=>[1,1,1,1,1,1,1] [1,2,3,1,1,4,1]=>[1,1,1,2,1,1] [1,2,2,3,2,2,1]=>[1,2,1,2,1] [1,2,2,1,4,2,1]=>[1,2,1,1,1,1] [1,2,2,1,2,4,1]=>[1,2,1,1,1,1] [1,2,1,4,1,3,1]=>[1,1,1,1,1,1,1] [1,2,1,3,3,2,1]=>[1,1,1,2,1,1] [1,2,1,3,1,4,1]=>[1,1,1,1,1,1,1] [1,2,1,2,1,5,1]=>[1,1,1,1,1,1,1] [1,2,1,1,5,2,1]=>[1,1,2,1,1,1] [1,2,1,1,3,4,1]=>[1,1,2,1,1,1] [1,2,1,1,1,6,1]=>[1,1,3,1,1] [1,1,1,5,1,3,1]=>[3,1,1,1,1] [1,1,1,4,3,2,1]=>[3,1,1,1,1] [1,1,1,4,1,4,1]=>[3,1,1,1,1] [1,1,1,3,1,5,1]=>[3,1,1,1,1] [1,1,1,2,5,2,1]=>[3,1,1,1,1] [1,1,1,2,3,4,1]=>[3,1,1,1,1] [1,1,1,2,1,6,1]=>[3,1,1,1,1] [1,1,1,1,1,7,1]=>[5,1,1] [1,1,1,1,1,1,1,1,1,1,1,1,1]=>[13] [1,1,1,1,1,1,1,1,1,3,1]=>[9,1,1] [1,1,1,1,1,1,1,3,1,1,1]=>[7,1,3] [1,1,1,1,1,1,1,5,1]=>[7,1,1] [1,1,1,1,1,1,1,2,1,2,1]=>[7,1,1,1,1] [1,1,1,1,1,3,1,1,1,1,1]=>[5,1,5] [1,1,1,1,1,3,1,3,1]=>[5,1,1,1,1] [1,1,1,1,1,5,1,1,1]=>[5,1,3] [1,1,1,1,1,4,1,2,1]=>[5,1,1,1,1] [1,1,1,1,1,2,1,2,1,1,1]=>[5,1,1,1,3] [1,1,1,1,1,2,1,4,1]=>[5,1,1,1,1] [1,1,1,1,1,2,1,1,1,2,1]=>[5,1,3,1,1] [1,1,1,1,1,2,3,2,1]=>[5,1,1,1,1] [1,1,1,3,1,1,1,1,1,1,1]=>[3,1,7] [1,1,1,3,1,1,1,3,1]=>[3,1,3,1,1] [1,1,1,3,1,3,1,1,1]=>[3,1,1,1,3] [1,1,1,3,1,2,1,2,1]=>[3,1,1,1,1,1,1] [1,1,1,5,1,1,1,1,1]=>[3,1,5] [1,1,1,7,1,1,1]=>[3,1,3] [1,1,1,9,1]=>[3,1,1] [1,1,1,6,1,2,1]=>[3,1,1,1,1] [1,1,1,4,1,2,1,1,1]=>[3,1,1,1,3] [1,1,1,4,1,1,1,2,1]=>[3,1,3,1,1] [1,1,1,2,1,2,1,1,1,1,1]=>[3,1,1,1,5] [1,1,1,2,1,2,1,3,1]=>[3,1,1,1,1,1,1] [1,1,1,2,1,4,1,1,1]=>[3,1,1,1,3] [1,1,1,2,1,3,1,2,1]=>[3,1,1,1,1,1,1] [1,1,1,2,1,1,1,2,1,1,1]=>[3,1,3,1,3] [1,1,1,2,1,1,1,4,1]=>[3,1,3,1,1] [1,1,1,2,1,1,1,1,1,2,1]=>[3,1,5,1,1] [1,1,1,2,1,1,3,2,1]=>[3,1,2,1,1,1] [1,1,1,2,3,2,1,1,1]=>[3,1,1,1,3] [1,1,1,2,3,1,1,2,1]=>[3,1,1,2,1,1] [1,1,1,2,2,1,2,2,1]=>[3,2,1,2,1] [1,3,1,1,1,1,1,1,1,1,1]=>[1,1,9] [1,3,1,1,1,1,1,3,1]=>[1,1,5,1,1] [1,3,1,1,1,3,1,1,1]=>[1,1,3,1,3] [1,3,1,1,1,2,1,2,1]=>[1,1,3,1,1,1,1] [1,3,1,3,1,1,1,1,1]=>[1,1,1,1,5] [1,3,1,5,1,1,1]=>[1,1,1,1,3] [1,3,1,7,1]=>[1,1,1,1,1] [1,3,1,4,1,2,1]=>[1,1,1,1,1,1,1] [1,3,1,2,1,2,1,1,1]=>[1,1,1,1,1,1,3] [1,3,1,2,1,1,1,2,1]=>[1,1,1,1,3,1,1] [1,5,1,1,1,1,1,1,1]=>[1,1,7] [1,5,1,1,1,3,1]=>[1,1,3,1,1] [1,5,1,3,1,1,1]=>[1,1,1,1,3] [1,5,1,5,1]=>[1,1,1,1,1] [1,5,1,2,1,2,1]=>[1,1,1,1,1,1,1] [1,7,1,1,1,1,1]=>[1,1,5] [1,7,1,3,1]=>[1,1,1,1,1] [1,9,1,1,1]=>[1,1,3] [1,11,1]=>[1,1,1] [1,8,1,2,1]=>[1,1,1,1,1] [1,6,1,2,1,1,1]=>[1,1,1,1,3] [1,6,1,4,1]=>[1,1,1,1,1] [1,6,1,1,1,2,1]=>[1,1,3,1,1] [1,6,3,2,1]=>[1,1,1,1,1] [1,4,1,2,1,1,1,1,1]=>[1,1,1,1,5] [1,4,1,2,1,3,1]=>[1,1,1,1,1,1,1] [1,4,1,4,1,1,1]=>[1,1,1,1,3] [1,4,1,6,1]=>[1,1,1,1,1] [1,4,1,3,1,2,1]=>[1,1,1,1,1,1,1] [1,4,1,1,1,2,1,1,1]=>[1,1,3,1,3] [1,4,1,1,1,4,1]=>[1,1,3,1,1] [1,4,1,1,1,1,1,2,1]=>[1,1,5,1,1] [1,4,1,1,3,2,1]=>[1,1,2,1,1,1] [1,4,3,2,1,1,1]=>[1,1,1,1,3] [1,4,3,4,1]=>[1,1,1,1,1] [1,4,3,1,1,2,1]=>[1,1,1,2,1,1] [1,4,5,2,1]=>[1,1,1,1,1] [1,4,2,1,2,2,1]=>[1,1,1,1,2,1] [1,2,1,2,1,1,1,1,1,1,1]=>[1,1,1,1,7] [1,2,1,2,1,1,1,3,1]=>[1,1,1,1,3,1,1] [1,2,1,2,1,3,1,1,1]=>[1,1,1,1,1,1,3] [1,2,1,2,1,2,1,2,1]=>[1,1,1,1,1,1,1,1,1] [1,2,1,4,1,1,1,1,1]=>[1,1,1,1,5] [1,2,1,6,1,1,1]=>[1,1,1,1,3] [1,2,1,8,1]=>[1,1,1,1,1] [1,2,1,5,1,2,1]=>[1,1,1,1,1,1,1] [1,2,1,3,1,2,1,1,1]=>[1,1,1,1,1,1,3] [1,2,1,3,1,1,1,2,1]=>[1,1,1,1,3,1,1] [1,2,1,1,1,2,1,1,1,1,1]=>[1,1,3,1,5] [1,2,1,1,1,2,1,3,1]=>[1,1,3,1,1,1,1] [1,2,1,1,1,4,1,1,1]=>[1,1,3,1,3] [1,2,1,1,1,3,1,2,1]=>[1,1,3,1,1,1,1] [1,2,1,1,1,1,1,2,1,1,1]=>[1,1,5,1,3] [1,2,1,1,1,1,1,4,1]=>[1,1,5,1,1] [1,2,1,1,1,1,1,1,1,2,1]=>[1,1,7,1,1] [1,2,1,1,1,1,3,2,1]=>[1,1,4,1,1,1] [1,2,1,1,3,2,1,1,1]=>[1,1,2,1,1,3] [1,2,1,1,3,1,1,2,1]=>[1,1,2,1,2,1,1] [1,2,1,1,2,1,2,2,1]=>[1,1,2,1,1,2,1] [1,2,3,2,1,1,1,1,1]=>[1,1,1,1,5] [1,2,3,4,1,1,1]=>[1,1,1,1,3] [1,2,3,6,1]=>[1,1,1,1,1] [1,2,3,3,1,2,1]=>[1,1,2,1,1,1] [1,2,3,1,1,2,1,1,1]=>[1,1,1,2,1,3] [1,2,3,1,1,1,1,2,1]=>[1,1,1,4,1,1] [1,2,5,2,1,1,1]=>[1,1,1,1,3] [1,2,5,4,1]=>[1,1,1,1,1] [1,2,5,1,1,2,1]=>[1,1,1,2,1,1] [1,2,7,2,1]=>[1,1,1,1,1] [1,2,4,1,2,2,1]=>[1,1,1,1,2,1] [1,2,2,1,2,2,1,1,1]=>[1,2,1,2,3] [1,2,2,1,2,1,1,2,1]=>[1,2,1,1,2,1,1] [1,2,2,1,1,1,2,2,1]=>[1,2,3,2,1]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Properties
surjective
Sage code
def mapping(X):
    return Composition(Word(X).delta())
Weight
26
Created
Jan 29, 2020 at 13:27 by FindStatCrew
Updated
Jan 29, 2020 at 13:27 by Martin Rubey