edit this map or download as text // json
Identifier
Mp00079: Set partitions —shape⟶ Integer partitions
Images
=>
Cc0009;cc-rep-0Cc0002;cc-rep-1
{{1}}=>[1] {{1,2}}=>[2] {{1},{2}}=>[1,1] {{1,2,3}}=>[3] {{1,2},{3}}=>[2,1] {{1,3},{2}}=>[2,1] {{1},{2,3}}=>[2,1] {{1},{2},{3}}=>[1,1,1] {{1,2,3,4}}=>[4] {{1,2,3},{4}}=>[3,1] {{1,2,4},{3}}=>[3,1] {{1,2},{3,4}}=>[2,2] {{1,2},{3},{4}}=>[2,1,1] {{1,3,4},{2}}=>[3,1] {{1,3},{2,4}}=>[2,2] {{1,3},{2},{4}}=>[2,1,1] {{1,4},{2,3}}=>[2,2] {{1},{2,3,4}}=>[3,1] {{1},{2,3},{4}}=>[2,1,1] {{1,4},{2},{3}}=>[2,1,1] {{1},{2,4},{3}}=>[2,1,1] {{1},{2},{3,4}}=>[2,1,1] {{1},{2},{3},{4}}=>[1,1,1,1] {{1,2,3,4,5}}=>[5] {{1,2,3,4},{5}}=>[4,1] {{1,2,3,5},{4}}=>[4,1] {{1,2,3},{4,5}}=>[3,2] {{1,2,3},{4},{5}}=>[3,1,1] {{1,2,4,5},{3}}=>[4,1] {{1,2,4},{3,5}}=>[3,2] {{1,2,4},{3},{5}}=>[3,1,1] {{1,2,5},{3,4}}=>[3,2] {{1,2},{3,4,5}}=>[3,2] {{1,2},{3,4},{5}}=>[2,2,1] {{1,2,5},{3},{4}}=>[3,1,1] {{1,2},{3,5},{4}}=>[2,2,1] {{1,2},{3},{4,5}}=>[2,2,1] {{1,2},{3},{4},{5}}=>[2,1,1,1] {{1,3,4,5},{2}}=>[4,1] {{1,3,4},{2,5}}=>[3,2] {{1,3,4},{2},{5}}=>[3,1,1] {{1,3,5},{2,4}}=>[3,2] {{1,3},{2,4,5}}=>[3,2] {{1,3},{2,4},{5}}=>[2,2,1] {{1,3,5},{2},{4}}=>[3,1,1] {{1,3},{2,5},{4}}=>[2,2,1] {{1,3},{2},{4,5}}=>[2,2,1] {{1,3},{2},{4},{5}}=>[2,1,1,1] {{1,4,5},{2,3}}=>[3,2] {{1,4},{2,3,5}}=>[3,2] {{1,4},{2,3},{5}}=>[2,2,1] {{1,5},{2,3,4}}=>[3,2] {{1},{2,3,4,5}}=>[4,1] {{1},{2,3,4},{5}}=>[3,1,1] {{1,5},{2,3},{4}}=>[2,2,1] {{1},{2,3,5},{4}}=>[3,1,1] {{1},{2,3},{4,5}}=>[2,2,1] {{1},{2,3},{4},{5}}=>[2,1,1,1] {{1,4,5},{2},{3}}=>[3,1,1] {{1,4},{2,5},{3}}=>[2,2,1] {{1,4},{2},{3,5}}=>[2,2,1] {{1,4},{2},{3},{5}}=>[2,1,1,1] {{1,5},{2,4},{3}}=>[2,2,1] {{1},{2,4,5},{3}}=>[3,1,1] {{1},{2,4},{3,5}}=>[2,2,1] {{1},{2,4},{3},{5}}=>[2,1,1,1] {{1,5},{2},{3,4}}=>[2,2,1] {{1},{2,5},{3,4}}=>[2,2,1] {{1},{2},{3,4,5}}=>[3,1,1] {{1},{2},{3,4},{5}}=>[2,1,1,1] {{1,5},{2},{3},{4}}=>[2,1,1,1] {{1},{2,5},{3},{4}}=>[2,1,1,1] {{1},{2},{3,5},{4}}=>[2,1,1,1] {{1},{2},{3},{4,5}}=>[2,1,1,1] {{1},{2},{3},{4},{5}}=>[1,1,1,1,1] {{1,2,3,4,5,6}}=>[6] {{1,2,3,4,5},{6}}=>[5,1] {{1,2,3,4,6},{5}}=>[5,1] {{1,2,3,4},{5,6}}=>[4,2] {{1,2,3,4},{5},{6}}=>[4,1,1] {{1,2,3,5,6},{4}}=>[5,1] {{1,2,3,5},{4,6}}=>[4,2] {{1,2,3,5},{4},{6}}=>[4,1,1] {{1,2,3,6},{4,5}}=>[4,2] {{1,2,3},{4,5,6}}=>[3,3] {{1,2,3},{4,5},{6}}=>[3,2,1] {{1,2,3,6},{4},{5}}=>[4,1,1] {{1,2,3},{4,6},{5}}=>[3,2,1] {{1,2,3},{4},{5,6}}=>[3,2,1] {{1,2,3},{4},{5},{6}}=>[3,1,1,1] {{1,2,4,5,6},{3}}=>[5,1] {{1,2,4,5},{3,6}}=>[4,2] {{1,2,4,5},{3},{6}}=>[4,1,1] {{1,2,4,6},{3,5}}=>[4,2] {{1,2,4},{3,5,6}}=>[3,3] {{1,2,4},{3,5},{6}}=>[3,2,1] {{1,2,4,6},{3},{5}}=>[4,1,1] {{1,2,4},{3,6},{5}}=>[3,2,1] {{1,2,4},{3},{5,6}}=>[3,2,1] {{1,2,4},{3},{5},{6}}=>[3,1,1,1] {{1,2,5,6},{3,4}}=>[4,2] {{1,2,5},{3,4,6}}=>[3,3] {{1,2,5},{3,4},{6}}=>[3,2,1] {{1,2,6},{3,4,5}}=>[3,3] {{1,2},{3,4,5,6}}=>[4,2] {{1,2},{3,4,5},{6}}=>[3,2,1] {{1,2,6},{3,4},{5}}=>[3,2,1] {{1,2},{3,4,6},{5}}=>[3,2,1] {{1,2},{3,4},{5,6}}=>[2,2,2] {{1,2},{3,4},{5},{6}}=>[2,2,1,1] {{1,2,5,6},{3},{4}}=>[4,1,1] {{1,2,5},{3,6},{4}}=>[3,2,1] {{1,2,5},{3},{4,6}}=>[3,2,1] {{1,2,5},{3},{4},{6}}=>[3,1,1,1] {{1,2,6},{3,5},{4}}=>[3,2,1] {{1,2},{3,5,6},{4}}=>[3,2,1] {{1,2},{3,5},{4,6}}=>[2,2,2] {{1,2},{3,5},{4},{6}}=>[2,2,1,1] {{1,2,6},{3},{4,5}}=>[3,2,1] {{1,2},{3,6},{4,5}}=>[2,2,2] {{1,2},{3},{4,5,6}}=>[3,2,1] {{1,2},{3},{4,5},{6}}=>[2,2,1,1] {{1,2,6},{3},{4},{5}}=>[3,1,1,1] {{1,2},{3,6},{4},{5}}=>[2,2,1,1] {{1,2},{3},{4,6},{5}}=>[2,2,1,1] {{1,2},{3},{4},{5,6}}=>[2,2,1,1] {{1,2},{3},{4},{5},{6}}=>[2,1,1,1,1] {{1,3,4,5,6},{2}}=>[5,1] {{1,3,4,5},{2,6}}=>[4,2] {{1,3,4,5},{2},{6}}=>[4,1,1] {{1,3,4,6},{2,5}}=>[4,2] {{1,3,4},{2,5,6}}=>[3,3] {{1,3,4},{2,5},{6}}=>[3,2,1] {{1,3,4,6},{2},{5}}=>[4,1,1] {{1,3,4},{2,6},{5}}=>[3,2,1] {{1,3,4},{2},{5,6}}=>[3,2,1] {{1,3,4},{2},{5},{6}}=>[3,1,1,1] {{1,3,5,6},{2,4}}=>[4,2] {{1,3,5},{2,4,6}}=>[3,3] {{1,3,5},{2,4},{6}}=>[3,2,1] {{1,3,6},{2,4,5}}=>[3,3] {{1,3},{2,4,5,6}}=>[4,2] {{1,3},{2,4,5},{6}}=>[3,2,1] {{1,3,6},{2,4},{5}}=>[3,2,1] {{1,3},{2,4,6},{5}}=>[3,2,1] {{1,3},{2,4},{5,6}}=>[2,2,2] {{1,3},{2,4},{5},{6}}=>[2,2,1,1] {{1,3,5,6},{2},{4}}=>[4,1,1] {{1,3,5},{2,6},{4}}=>[3,2,1] {{1,3,5},{2},{4,6}}=>[3,2,1] {{1,3,5},{2},{4},{6}}=>[3,1,1,1] {{1,3,6},{2,5},{4}}=>[3,2,1] {{1,3},{2,5,6},{4}}=>[3,2,1] {{1,3},{2,5},{4,6}}=>[2,2,2] {{1,3},{2,5},{4},{6}}=>[2,2,1,1] {{1,3,6},{2},{4,5}}=>[3,2,1] {{1,3},{2,6},{4,5}}=>[2,2,2] {{1,3},{2},{4,5,6}}=>[3,2,1] {{1,3},{2},{4,5},{6}}=>[2,2,1,1] {{1,3,6},{2},{4},{5}}=>[3,1,1,1] {{1,3},{2,6},{4},{5}}=>[2,2,1,1] {{1,3},{2},{4,6},{5}}=>[2,2,1,1] {{1,3},{2},{4},{5,6}}=>[2,2,1,1] {{1,3},{2},{4},{5},{6}}=>[2,1,1,1,1] {{1,4,5,6},{2,3}}=>[4,2] {{1,4,5},{2,3,6}}=>[3,3] {{1,4,5},{2,3},{6}}=>[3,2,1] {{1,4,6},{2,3,5}}=>[3,3] {{1,4},{2,3,5,6}}=>[4,2] {{1,4},{2,3,5},{6}}=>[3,2,1] {{1,4,6},{2,3},{5}}=>[3,2,1] {{1,4},{2,3,6},{5}}=>[3,2,1] {{1,4},{2,3},{5,6}}=>[2,2,2] {{1,4},{2,3},{5},{6}}=>[2,2,1,1] {{1,5,6},{2,3,4}}=>[3,3] {{1,5},{2,3,4,6}}=>[4,2] {{1,5},{2,3,4},{6}}=>[3,2,1] {{1,6},{2,3,4,5}}=>[4,2] {{1},{2,3,4,5,6}}=>[5,1] {{1},{2,3,4,5},{6}}=>[4,1,1] {{1,6},{2,3,4},{5}}=>[3,2,1] {{1},{2,3,4,6},{5}}=>[4,1,1] {{1},{2,3,4},{5,6}}=>[3,2,1] {{1},{2,3,4},{5},{6}}=>[3,1,1,1] {{1,5,6},{2,3},{4}}=>[3,2,1] {{1,5},{2,3,6},{4}}=>[3,2,1] {{1,5},{2,3},{4,6}}=>[2,2,2] {{1,5},{2,3},{4},{6}}=>[2,2,1,1] {{1,6},{2,3,5},{4}}=>[3,2,1] {{1},{2,3,5,6},{4}}=>[4,1,1] {{1},{2,3,5},{4,6}}=>[3,2,1] {{1},{2,3,5},{4},{6}}=>[3,1,1,1] {{1,6},{2,3},{4,5}}=>[2,2,2] {{1},{2,3,6},{4,5}}=>[3,2,1] {{1},{2,3},{4,5,6}}=>[3,2,1] {{1},{2,3},{4,5},{6}}=>[2,2,1,1] {{1,6},{2,3},{4},{5}}=>[2,2,1,1] {{1},{2,3,6},{4},{5}}=>[3,1,1,1] {{1},{2,3},{4,6},{5}}=>[2,2,1,1] {{1},{2,3},{4},{5,6}}=>[2,2,1,1] {{1},{2,3},{4},{5},{6}}=>[2,1,1,1,1] {{1,4,5,6},{2},{3}}=>[4,1,1] {{1,4,5},{2,6},{3}}=>[3,2,1] {{1,4,5},{2},{3,6}}=>[3,2,1] {{1,4,5},{2},{3},{6}}=>[3,1,1,1] {{1,4,6},{2,5},{3}}=>[3,2,1] {{1,4},{2,5,6},{3}}=>[3,2,1] {{1,4},{2,5},{3,6}}=>[2,2,2] {{1,4},{2,5},{3},{6}}=>[2,2,1,1] {{1,4,6},{2},{3,5}}=>[3,2,1] {{1,4},{2,6},{3,5}}=>[2,2,2] {{1,4},{2},{3,5,6}}=>[3,2,1] {{1,4},{2},{3,5},{6}}=>[2,2,1,1] {{1,4,6},{2},{3},{5}}=>[3,1,1,1] {{1,4},{2,6},{3},{5}}=>[2,2,1,1] {{1,4},{2},{3,6},{5}}=>[2,2,1,1] {{1,4},{2},{3},{5,6}}=>[2,2,1,1] {{1,4},{2},{3},{5},{6}}=>[2,1,1,1,1] {{1,5,6},{2,4},{3}}=>[3,2,1] {{1,5},{2,4,6},{3}}=>[3,2,1] {{1,5},{2,4},{3,6}}=>[2,2,2] {{1,5},{2,4},{3},{6}}=>[2,2,1,1] {{1,6},{2,4,5},{3}}=>[3,2,1] {{1},{2,4,5,6},{3}}=>[4,1,1] {{1},{2,4,5},{3,6}}=>[3,2,1] {{1},{2,4,5},{3},{6}}=>[3,1,1,1] {{1,6},{2,4},{3,5}}=>[2,2,2] {{1},{2,4,6},{3,5}}=>[3,2,1] {{1},{2,4},{3,5,6}}=>[3,2,1] {{1},{2,4},{3,5},{6}}=>[2,2,1,1] {{1,6},{2,4},{3},{5}}=>[2,2,1,1] {{1},{2,4,6},{3},{5}}=>[3,1,1,1] {{1},{2,4},{3,6},{5}}=>[2,2,1,1] {{1},{2,4},{3},{5,6}}=>[2,2,1,1] {{1},{2,4},{3},{5},{6}}=>[2,1,1,1,1] {{1,5,6},{2},{3,4}}=>[3,2,1] {{1,5},{2,6},{3,4}}=>[2,2,2] {{1,5},{2},{3,4,6}}=>[3,2,1] {{1,5},{2},{3,4},{6}}=>[2,2,1,1] {{1,6},{2,5},{3,4}}=>[2,2,2] {{1},{2,5,6},{3,4}}=>[3,2,1] {{1},{2,5},{3,4,6}}=>[3,2,1] {{1},{2,5},{3,4},{6}}=>[2,2,1,1] {{1,6},{2},{3,4,5}}=>[3,2,1] {{1},{2,6},{3,4,5}}=>[3,2,1] {{1},{2},{3,4,5,6}}=>[4,1,1] {{1},{2},{3,4,5},{6}}=>[3,1,1,1] {{1,6},{2},{3,4},{5}}=>[2,2,1,1] {{1},{2,6},{3,4},{5}}=>[2,2,1,1] {{1},{2},{3,4,6},{5}}=>[3,1,1,1] {{1},{2},{3,4},{5,6}}=>[2,2,1,1] {{1},{2},{3,4},{5},{6}}=>[2,1,1,1,1] {{1,5,6},{2},{3},{4}}=>[3,1,1,1] {{1,5},{2,6},{3},{4}}=>[2,2,1,1] {{1,5},{2},{3,6},{4}}=>[2,2,1,1] {{1,5},{2},{3},{4,6}}=>[2,2,1,1] {{1,5},{2},{3},{4},{6}}=>[2,1,1,1,1] {{1,6},{2,5},{3},{4}}=>[2,2,1,1] {{1},{2,5,6},{3},{4}}=>[3,1,1,1] {{1},{2,5},{3,6},{4}}=>[2,2,1,1] {{1},{2,5},{3},{4,6}}=>[2,2,1,1] {{1},{2,5},{3},{4},{6}}=>[2,1,1,1,1] {{1,6},{2},{3,5},{4}}=>[2,2,1,1] {{1},{2,6},{3,5},{4}}=>[2,2,1,1] {{1},{2},{3,5,6},{4}}=>[3,1,1,1] {{1},{2},{3,5},{4,6}}=>[2,2,1,1] {{1},{2},{3,5},{4},{6}}=>[2,1,1,1,1] {{1,6},{2},{3},{4,5}}=>[2,2,1,1] {{1},{2,6},{3},{4,5}}=>[2,2,1,1] {{1},{2},{3,6},{4,5}}=>[2,2,1,1] {{1},{2},{3},{4,5,6}}=>[3,1,1,1] {{1},{2},{3},{4,5},{6}}=>[2,1,1,1,1] {{1,6},{2},{3},{4},{5}}=>[2,1,1,1,1] {{1},{2,6},{3},{4},{5}}=>[2,1,1,1,1] {{1},{2},{3,6},{4},{5}}=>[2,1,1,1,1] {{1},{2},{3},{4,6},{5}}=>[2,1,1,1,1] {{1},{2},{3},{4},{5,6}}=>[2,1,1,1,1] {{1},{2},{3},{4},{5},{6}}=>[1,1,1,1,1,1] {{1,2,3,4,5,6,7}}=>[7] {{1,2,3,4,5,6},{7}}=>[6,1] {{1,2,3,4,5,7},{6}}=>[6,1] {{1,2,3,4,5},{6,7}}=>[5,2] {{1,2,3,4,5},{6},{7}}=>[5,1,1] {{1,2,3,4,6,7},{5}}=>[6,1] {{1,2,3,4,6},{5,7}}=>[5,2] {{1,2,3,4,6},{5},{7}}=>[5,1,1] {{1,2,3,4,7},{5,6}}=>[5,2] {{1,2,3,4},{5,6,7}}=>[4,3] {{1,2,3,4},{5,6},{7}}=>[4,2,1] {{1,2,3,4,7},{5},{6}}=>[5,1,1] {{1,2,3,4},{5,7},{6}}=>[4,2,1] {{1,2,3,4},{5},{6,7}}=>[4,2,1] {{1,2,3,4},{5},{6},{7}}=>[4,1,1,1] {{1,2,3,5,6,7},{4}}=>[6,1] {{1,2,3,5,6},{4,7}}=>[5,2] {{1,2,3,5,6},{4},{7}}=>[5,1,1] {{1,2,3,5,7},{4,6}}=>[5,2] {{1,2,3,5},{4,6,7}}=>[4,3] {{1,2,3,5},{4,6},{7}}=>[4,2,1] {{1,2,3,5,7},{4},{6}}=>[5,1,1] {{1,2,3,5},{4,7},{6}}=>[4,2,1] {{1,2,3,5},{4},{6,7}}=>[4,2,1] {{1,2,3,5},{4},{6},{7}}=>[4,1,1,1] {{1,2,3,6,7},{4,5}}=>[5,2] {{1,2,3,6},{4,5,7}}=>[4,3] {{1,2,3,6},{4,5},{7}}=>[4,2,1] {{1,2,3,7},{4,5,6}}=>[4,3] {{1,2,3},{4,5,6,7}}=>[4,3] {{1,2,3},{4,5,6},{7}}=>[3,3,1] {{1,2,3,7},{4,5},{6}}=>[4,2,1] {{1,2,3},{4,5,7},{6}}=>[3,3,1] {{1,2,3},{4,5},{6,7}}=>[3,2,2] {{1,2,3},{4,5},{6},{7}}=>[3,2,1,1] {{1,2,3,6,7},{4},{5}}=>[5,1,1] {{1,2,3,6},{4,7},{5}}=>[4,2,1] {{1,2,3,6},{4},{5,7}}=>[4,2,1] {{1,2,3,6},{4},{5},{7}}=>[4,1,1,1] {{1,2,3,7},{4,6},{5}}=>[4,2,1] {{1,2,3},{4,6,7},{5}}=>[3,3,1] {{1,2,3},{4,6},{5,7}}=>[3,2,2] {{1,2,3},{4,6},{5},{7}}=>[3,2,1,1] {{1,2,3,7},{4},{5,6}}=>[4,2,1] {{1,2,3},{4,7},{5,6}}=>[3,2,2] {{1,2,3},{4},{5,6,7}}=>[3,3,1] {{1,2,3},{4},{5,6},{7}}=>[3,2,1,1] {{1,2,3,7},{4},{5},{6}}=>[4,1,1,1] {{1,2,3},{4,7},{5},{6}}=>[3,2,1,1] {{1,2,3},{4},{5,7},{6}}=>[3,2,1,1] {{1,2,3},{4},{5},{6,7}}=>[3,2,1,1] {{1,2,3},{4},{5},{6},{7}}=>[3,1,1,1,1] {{1,2,4,5,6,7},{3}}=>[6,1] {{1,2,4,5,6},{3,7}}=>[5,2] {{1,2,4,5,6},{3},{7}}=>[5,1,1] {{1,2,4,5,7},{3,6}}=>[5,2] {{1,2,4,5},{3,6,7}}=>[4,3] {{1,2,4,5},{3,6},{7}}=>[4,2,1] {{1,2,4,5,7},{3},{6}}=>[5,1,1] {{1,2,4,5},{3,7},{6}}=>[4,2,1] {{1,2,4,5},{3},{6,7}}=>[4,2,1] {{1,2,4,5},{3},{6},{7}}=>[4,1,1,1] {{1,2,4,6,7},{3,5}}=>[5,2] {{1,2,4,6},{3,5,7}}=>[4,3] {{1,2,4,6},{3,5},{7}}=>[4,2,1] {{1,2,4,7},{3,5,6}}=>[4,3] {{1,2,4},{3,5,6,7}}=>[4,3] {{1,2,4},{3,5,6},{7}}=>[3,3,1] {{1,2,4,7},{3,5},{6}}=>[4,2,1] {{1,2,4},{3,5,7},{6}}=>[3,3,1] {{1,2,4},{3,5},{6,7}}=>[3,2,2] {{1,2,4},{3,5},{6},{7}}=>[3,2,1,1] {{1,2,4,6,7},{3},{5}}=>[5,1,1] {{1,2,4,6},{3,7},{5}}=>[4,2,1] {{1,2,4,6},{3},{5,7}}=>[4,2,1] {{1,2,4,6},{3},{5},{7}}=>[4,1,1,1] {{1,2,4,7},{3,6},{5}}=>[4,2,1] {{1,2,4},{3,6,7},{5}}=>[3,3,1] {{1,2,4},{3,6},{5,7}}=>[3,2,2] {{1,2,4},{3,6},{5},{7}}=>[3,2,1,1] {{1,2,4,7},{3},{5,6}}=>[4,2,1] {{1,2,4},{3,7},{5,6}}=>[3,2,2] {{1,2,4},{3},{5,6,7}}=>[3,3,1] {{1,2,4},{3},{5,6},{7}}=>[3,2,1,1] {{1,2,4,7},{3},{5},{6}}=>[4,1,1,1] {{1,2,4},{3,7},{5},{6}}=>[3,2,1,1] {{1,2,4},{3},{5,7},{6}}=>[3,2,1,1] {{1,2,4},{3},{5},{6,7}}=>[3,2,1,1] {{1,2,4},{3},{5},{6},{7}}=>[3,1,1,1,1] {{1,2,5,6,7},{3,4}}=>[5,2] {{1,2,5,6},{3,4,7}}=>[4,3] {{1,2,5,6},{3,4},{7}}=>[4,2,1] {{1,2,5,7},{3,4,6}}=>[4,3] {{1,2,5},{3,4,6,7}}=>[4,3] {{1,2,5},{3,4,6},{7}}=>[3,3,1] {{1,2,5,7},{3,4},{6}}=>[4,2,1] {{1,2,5},{3,4,7},{6}}=>[3,3,1] {{1,2,5},{3,4},{6,7}}=>[3,2,2] {{1,2,5},{3,4},{6},{7}}=>[3,2,1,1] {{1,2,6,7},{3,4,5}}=>[4,3] {{1,2,6},{3,4,5,7}}=>[4,3] {{1,2,6},{3,4,5},{7}}=>[3,3,1] {{1,2,7},{3,4,5,6}}=>[4,3] {{1,2},{3,4,5,6,7}}=>[5,2] {{1,2},{3,4,5,6},{7}}=>[4,2,1] {{1,2,7},{3,4,5},{6}}=>[3,3,1] {{1,2},{3,4,5,7},{6}}=>[4,2,1] {{1,2},{3,4,5},{6,7}}=>[3,2,2] {{1,2},{3,4,5},{6},{7}}=>[3,2,1,1] {{1,2,6,7},{3,4},{5}}=>[4,2,1] {{1,2,6},{3,4,7},{5}}=>[3,3,1] {{1,2,6},{3,4},{5,7}}=>[3,2,2] {{1,2,6},{3,4},{5},{7}}=>[3,2,1,1] {{1,2,7},{3,4,6},{5}}=>[3,3,1] {{1,2},{3,4,6,7},{5}}=>[4,2,1] {{1,2},{3,4,6},{5,7}}=>[3,2,2] {{1,2},{3,4,6},{5},{7}}=>[3,2,1,1] {{1,2,7},{3,4},{5,6}}=>[3,2,2] {{1,2},{3,4,7},{5,6}}=>[3,2,2] {{1,2},{3,4},{5,6,7}}=>[3,2,2] {{1,2},{3,4},{5,6},{7}}=>[2,2,2,1] {{1,2,7},{3,4},{5},{6}}=>[3,2,1,1] {{1,2},{3,4,7},{5},{6}}=>[3,2,1,1] {{1,2},{3,4},{5,7},{6}}=>[2,2,2,1] {{1,2},{3,4},{5},{6,7}}=>[2,2,2,1] {{1,2},{3,4},{5},{6},{7}}=>[2,2,1,1,1] {{1,2,5,6,7},{3},{4}}=>[5,1,1] {{1,2,5,6},{3,7},{4}}=>[4,2,1] {{1,2,5,6},{3},{4,7}}=>[4,2,1] {{1,2,5,6},{3},{4},{7}}=>[4,1,1,1] {{1,2,5,7},{3,6},{4}}=>[4,2,1] {{1,2,5},{3,6,7},{4}}=>[3,3,1] {{1,2,5},{3,6},{4,7}}=>[3,2,2] {{1,2,5},{3,6},{4},{7}}=>[3,2,1,1] {{1,2,5,7},{3},{4,6}}=>[4,2,1] {{1,2,5},{3,7},{4,6}}=>[3,2,2] {{1,2,5},{3},{4,6,7}}=>[3,3,1] {{1,2,5},{3},{4,6},{7}}=>[3,2,1,1] {{1,2,5,7},{3},{4},{6}}=>[4,1,1,1] {{1,2,5},{3,7},{4},{6}}=>[3,2,1,1] {{1,2,5},{3},{4,7},{6}}=>[3,2,1,1] {{1,2,5},{3},{4},{6,7}}=>[3,2,1,1] {{1,2,5},{3},{4},{6},{7}}=>[3,1,1,1,1] {{1,2,6,7},{3,5},{4}}=>[4,2,1] {{1,2,6},{3,5,7},{4}}=>[3,3,1] {{1,2,6},{3,5},{4,7}}=>[3,2,2] {{1,2,6},{3,5},{4},{7}}=>[3,2,1,1] {{1,2,7},{3,5,6},{4}}=>[3,3,1] {{1,2},{3,5,6,7},{4}}=>[4,2,1] {{1,2},{3,5,6},{4,7}}=>[3,2,2] {{1,2},{3,5,6},{4},{7}}=>[3,2,1,1] {{1,2,7},{3,5},{4,6}}=>[3,2,2] {{1,2},{3,5,7},{4,6}}=>[3,2,2] {{1,2},{3,5},{4,6,7}}=>[3,2,2] {{1,2},{3,5},{4,6},{7}}=>[2,2,2,1] {{1,2,7},{3,5},{4},{6}}=>[3,2,1,1] {{1,2},{3,5,7},{4},{6}}=>[3,2,1,1] {{1,2},{3,5},{4,7},{6}}=>[2,2,2,1] {{1,2},{3,5},{4},{6,7}}=>[2,2,2,1] {{1,2},{3,5},{4},{6},{7}}=>[2,2,1,1,1] {{1,2,6,7},{3},{4,5}}=>[4,2,1] {{1,2,6},{3,7},{4,5}}=>[3,2,2] {{1,2,6},{3},{4,5,7}}=>[3,3,1] {{1,2,6},{3},{4,5},{7}}=>[3,2,1,1] {{1,2,7},{3,6},{4,5}}=>[3,2,2] {{1,2},{3,6,7},{4,5}}=>[3,2,2] {{1,2},{3,6},{4,5,7}}=>[3,2,2] {{1,2},{3,6},{4,5},{7}}=>[2,2,2,1] {{1,2,7},{3},{4,5,6}}=>[3,3,1] {{1,2},{3,7},{4,5,6}}=>[3,2,2] {{1,2},{3},{4,5,6,7}}=>[4,2,1] {{1,2},{3},{4,5,6},{7}}=>[3,2,1,1] {{1,2,7},{3},{4,5},{6}}=>[3,2,1,1] {{1,2},{3,7},{4,5},{6}}=>[2,2,2,1] {{1,2},{3},{4,5,7},{6}}=>[3,2,1,1] {{1,2},{3},{4,5},{6,7}}=>[2,2,2,1] {{1,2},{3},{4,5},{6},{7}}=>[2,2,1,1,1] {{1,2,6,7},{3},{4},{5}}=>[4,1,1,1] {{1,2,6},{3,7},{4},{5}}=>[3,2,1,1] {{1,2,6},{3},{4,7},{5}}=>[3,2,1,1] {{1,2,6},{3},{4},{5,7}}=>[3,2,1,1] {{1,2,6},{3},{4},{5},{7}}=>[3,1,1,1,1] {{1,2,7},{3,6},{4},{5}}=>[3,2,1,1] {{1,2},{3,6,7},{4},{5}}=>[3,2,1,1] {{1,2},{3,6},{4,7},{5}}=>[2,2,2,1] {{1,2},{3,6},{4},{5,7}}=>[2,2,2,1] {{1,2},{3,6},{4},{5},{7}}=>[2,2,1,1,1] {{1,2,7},{3},{4,6},{5}}=>[3,2,1,1] {{1,2},{3,7},{4,6},{5}}=>[2,2,2,1] {{1,2},{3},{4,6,7},{5}}=>[3,2,1,1] {{1,2},{3},{4,6},{5,7}}=>[2,2,2,1] {{1,2},{3},{4,6},{5},{7}}=>[2,2,1,1,1] {{1,2,7},{3},{4},{5,6}}=>[3,2,1,1] {{1,2},{3,7},{4},{5,6}}=>[2,2,2,1] {{1,2},{3},{4,7},{5,6}}=>[2,2,2,1] {{1,2},{3},{4},{5,6,7}}=>[3,2,1,1] {{1,2},{3},{4},{5,6},{7}}=>[2,2,1,1,1] {{1,2,7},{3},{4},{5},{6}}=>[3,1,1,1,1] {{1,2},{3,7},{4},{5},{6}}=>[2,2,1,1,1] {{1,2},{3},{4,7},{5},{6}}=>[2,2,1,1,1] {{1,2},{3},{4},{5,7},{6}}=>[2,2,1,1,1] {{1,2},{3},{4},{5},{6,7}}=>[2,2,1,1,1] {{1,2},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1] {{1,3,4,5,6,7},{2}}=>[6,1] {{1,3,4,5,6},{2,7}}=>[5,2] {{1,3,4,5,6},{2},{7}}=>[5,1,1] {{1,3,4,5,7},{2,6}}=>[5,2] {{1,3,4,5},{2,6,7}}=>[4,3] {{1,3,4,5},{2,6},{7}}=>[4,2,1] {{1,3,4,5,7},{2},{6}}=>[5,1,1] {{1,3,4,5},{2,7},{6}}=>[4,2,1] {{1,3,4,5},{2},{6,7}}=>[4,2,1] {{1,3,4,5},{2},{6},{7}}=>[4,1,1,1] {{1,3,4,6,7},{2,5}}=>[5,2] {{1,3,4,6},{2,5,7}}=>[4,3] {{1,3,4,6},{2,5},{7}}=>[4,2,1] {{1,3,4,7},{2,5,6}}=>[4,3] {{1,3,4},{2,5,6,7}}=>[4,3] {{1,3,4},{2,5,6},{7}}=>[3,3,1] {{1,3,4,7},{2,5},{6}}=>[4,2,1] {{1,3,4},{2,5,7},{6}}=>[3,3,1] {{1,3,4},{2,5},{6,7}}=>[3,2,2] {{1,3,4},{2,5},{6},{7}}=>[3,2,1,1] {{1,3,4,6,7},{2},{5}}=>[5,1,1] {{1,3,4,6},{2,7},{5}}=>[4,2,1] {{1,3,4,6},{2},{5,7}}=>[4,2,1] {{1,3,4,6},{2},{5},{7}}=>[4,1,1,1] {{1,3,4,7},{2,6},{5}}=>[4,2,1] {{1,3,4},{2,6,7},{5}}=>[3,3,1] {{1,3,4},{2,6},{5,7}}=>[3,2,2] {{1,3,4},{2,6},{5},{7}}=>[3,2,1,1] {{1,3,4,7},{2},{5,6}}=>[4,2,1] {{1,3,4},{2,7},{5,6}}=>[3,2,2] {{1,3,4},{2},{5,6,7}}=>[3,3,1] {{1,3,4},{2},{5,6},{7}}=>[3,2,1,1] {{1,3,4,7},{2},{5},{6}}=>[4,1,1,1] {{1,3,4},{2,7},{5},{6}}=>[3,2,1,1] {{1,3,4},{2},{5,7},{6}}=>[3,2,1,1] {{1,3,4},{2},{5},{6,7}}=>[3,2,1,1] {{1,3,4},{2},{5},{6},{7}}=>[3,1,1,1,1] {{1,3,5,6,7},{2,4}}=>[5,2] {{1,3,5,6},{2,4,7}}=>[4,3] {{1,3,5,6},{2,4},{7}}=>[4,2,1] {{1,3,5,7},{2,4,6}}=>[4,3] {{1,3,5},{2,4,6,7}}=>[4,3] {{1,3,5},{2,4,6},{7}}=>[3,3,1] {{1,3,5,7},{2,4},{6}}=>[4,2,1] {{1,3,5},{2,4,7},{6}}=>[3,3,1] {{1,3,5},{2,4},{6,7}}=>[3,2,2] {{1,3,5},{2,4},{6},{7}}=>[3,2,1,1] {{1,3,6,7},{2,4,5}}=>[4,3] {{1,3,6},{2,4,5,7}}=>[4,3] {{1,3,6},{2,4,5},{7}}=>[3,3,1] {{1,3,7},{2,4,5,6}}=>[4,3] {{1,3},{2,4,5,6,7}}=>[5,2] {{1,3},{2,4,5,6},{7}}=>[4,2,1] {{1,3,7},{2,4,5},{6}}=>[3,3,1] {{1,3},{2,4,5,7},{6}}=>[4,2,1] {{1,3},{2,4,5},{6,7}}=>[3,2,2] {{1,3},{2,4,5},{6},{7}}=>[3,2,1,1] {{1,3,6,7},{2,4},{5}}=>[4,2,1] {{1,3,6},{2,4,7},{5}}=>[3,3,1] {{1,3,6},{2,4},{5,7}}=>[3,2,2] {{1,3,6},{2,4},{5},{7}}=>[3,2,1,1] {{1,3,7},{2,4,6},{5}}=>[3,3,1] {{1,3},{2,4,6,7},{5}}=>[4,2,1] {{1,3},{2,4,6},{5,7}}=>[3,2,2] {{1,3},{2,4,6},{5},{7}}=>[3,2,1,1] {{1,3,7},{2,4},{5,6}}=>[3,2,2] {{1,3},{2,4,7},{5,6}}=>[3,2,2] {{1,3},{2,4},{5,6,7}}=>[3,2,2] {{1,3},{2,4},{5,6},{7}}=>[2,2,2,1] {{1,3,7},{2,4},{5},{6}}=>[3,2,1,1] {{1,3},{2,4,7},{5},{6}}=>[3,2,1,1] {{1,3},{2,4},{5,7},{6}}=>[2,2,2,1] {{1,3},{2,4},{5},{6,7}}=>[2,2,2,1] {{1,3},{2,4},{5},{6},{7}}=>[2,2,1,1,1] {{1,3,5,6,7},{2},{4}}=>[5,1,1] {{1,3,5,6},{2,7},{4}}=>[4,2,1] {{1,3,5,6},{2},{4,7}}=>[4,2,1] {{1,3,5,6},{2},{4},{7}}=>[4,1,1,1] {{1,3,5,7},{2,6},{4}}=>[4,2,1] {{1,3,5},{2,6,7},{4}}=>[3,3,1] {{1,3,5},{2,6},{4,7}}=>[3,2,2] {{1,3,5},{2,6},{4},{7}}=>[3,2,1,1] {{1,3,5,7},{2},{4,6}}=>[4,2,1] {{1,3,5},{2,7},{4,6}}=>[3,2,2] {{1,3,5},{2},{4,6,7}}=>[3,3,1] {{1,3,5},{2},{4,6},{7}}=>[3,2,1,1] {{1,3,5,7},{2},{4},{6}}=>[4,1,1,1] {{1,3,5},{2,7},{4},{6}}=>[3,2,1,1] {{1,3,5},{2},{4,7},{6}}=>[3,2,1,1] {{1,3,5},{2},{4},{6,7}}=>[3,2,1,1] {{1,3,5},{2},{4},{6},{7}}=>[3,1,1,1,1] {{1,3,6,7},{2,5},{4}}=>[4,2,1] {{1,3,6},{2,5,7},{4}}=>[3,3,1] {{1,3,6},{2,5},{4,7}}=>[3,2,2] {{1,3,6},{2,5},{4},{7}}=>[3,2,1,1] {{1,3,7},{2,5,6},{4}}=>[3,3,1] {{1,3},{2,5,6,7},{4}}=>[4,2,1] {{1,3},{2,5,6},{4,7}}=>[3,2,2] {{1,3},{2,5,6},{4},{7}}=>[3,2,1,1] {{1,3,7},{2,5},{4,6}}=>[3,2,2] {{1,3},{2,5,7},{4,6}}=>[3,2,2] {{1,3},{2,5},{4,6,7}}=>[3,2,2] {{1,3},{2,5},{4,6},{7}}=>[2,2,2,1] {{1,3,7},{2,5},{4},{6}}=>[3,2,1,1] {{1,3},{2,5,7},{4},{6}}=>[3,2,1,1] {{1,3},{2,5},{4,7},{6}}=>[2,2,2,1] {{1,3},{2,5},{4},{6,7}}=>[2,2,2,1] {{1,3},{2,5},{4},{6},{7}}=>[2,2,1,1,1] {{1,3,6,7},{2},{4,5}}=>[4,2,1] {{1,3,6},{2,7},{4,5}}=>[3,2,2] {{1,3,6},{2},{4,5,7}}=>[3,3,1] {{1,3,6},{2},{4,5},{7}}=>[3,2,1,1] {{1,3,7},{2,6},{4,5}}=>[3,2,2] {{1,3},{2,6,7},{4,5}}=>[3,2,2] {{1,3},{2,6},{4,5,7}}=>[3,2,2] {{1,3},{2,6},{4,5},{7}}=>[2,2,2,1] {{1,3,7},{2},{4,5,6}}=>[3,3,1] {{1,3},{2,7},{4,5,6}}=>[3,2,2] {{1,3},{2},{4,5,6,7}}=>[4,2,1] {{1,3},{2},{4,5,6},{7}}=>[3,2,1,1] {{1,3,7},{2},{4,5},{6}}=>[3,2,1,1] {{1,3},{2,7},{4,5},{6}}=>[2,2,2,1] {{1,3},{2},{4,5,7},{6}}=>[3,2,1,1] {{1,3},{2},{4,5},{6,7}}=>[2,2,2,1] {{1,3},{2},{4,5},{6},{7}}=>[2,2,1,1,1] {{1,3,6,7},{2},{4},{5}}=>[4,1,1,1] {{1,3,6},{2,7},{4},{5}}=>[3,2,1,1] {{1,3,6},{2},{4,7},{5}}=>[3,2,1,1] {{1,3,6},{2},{4},{5,7}}=>[3,2,1,1] {{1,3,6},{2},{4},{5},{7}}=>[3,1,1,1,1] {{1,3,7},{2,6},{4},{5}}=>[3,2,1,1] {{1,3},{2,6,7},{4},{5}}=>[3,2,1,1] {{1,3},{2,6},{4,7},{5}}=>[2,2,2,1] {{1,3},{2,6},{4},{5,7}}=>[2,2,2,1] {{1,3},{2,6},{4},{5},{7}}=>[2,2,1,1,1] {{1,3,7},{2},{4,6},{5}}=>[3,2,1,1] {{1,3},{2,7},{4,6},{5}}=>[2,2,2,1] {{1,3},{2},{4,6,7},{5}}=>[3,2,1,1] {{1,3},{2},{4,6},{5,7}}=>[2,2,2,1] {{1,3},{2},{4,6},{5},{7}}=>[2,2,1,1,1] {{1,3,7},{2},{4},{5,6}}=>[3,2,1,1] {{1,3},{2,7},{4},{5,6}}=>[2,2,2,1] {{1,3},{2},{4,7},{5,6}}=>[2,2,2,1] {{1,3},{2},{4},{5,6,7}}=>[3,2,1,1] {{1,3},{2},{4},{5,6},{7}}=>[2,2,1,1,1] {{1,3,7},{2},{4},{5},{6}}=>[3,1,1,1,1] {{1,3},{2,7},{4},{5},{6}}=>[2,2,1,1,1] {{1,3},{2},{4,7},{5},{6}}=>[2,2,1,1,1] {{1,3},{2},{4},{5,7},{6}}=>[2,2,1,1,1] {{1,3},{2},{4},{5},{6,7}}=>[2,2,1,1,1] {{1,3},{2},{4},{5},{6},{7}}=>[2,1,1,1,1,1] {{1,4,5,6,7},{2,3}}=>[5,2] {{1,4,5,6},{2,3,7}}=>[4,3] {{1,4,5,6},{2,3},{7}}=>[4,2,1] {{1,4,5,7},{2,3,6}}=>[4,3] {{1,4,5},{2,3,6,7}}=>[4,3] {{1,4,5},{2,3,6},{7}}=>[3,3,1] {{1,4,5,7},{2,3},{6}}=>[4,2,1] {{1,4,5},{2,3,7},{6}}=>[3,3,1] {{1,4,5},{2,3},{6,7}}=>[3,2,2] {{1,4,5},{2,3},{6},{7}}=>[3,2,1,1] {{1,4,6,7},{2,3,5}}=>[4,3] {{1,4,6},{2,3,5,7}}=>[4,3] {{1,4,6},{2,3,5},{7}}=>[3,3,1] {{1,4,7},{2,3,5,6}}=>[4,3] {{1,4},{2,3,5,6,7}}=>[5,2] {{1,4},{2,3,5,6},{7}}=>[4,2,1] {{1,4,7},{2,3,5},{6}}=>[3,3,1] {{1,4},{2,3,5,7},{6}}=>[4,2,1] {{1,4},{2,3,5},{6,7}}=>[3,2,2] {{1,4},{2,3,5},{6},{7}}=>[3,2,1,1] {{1,4,6,7},{2,3},{5}}=>[4,2,1] {{1,4,6},{2,3,7},{5}}=>[3,3,1] {{1,4,6},{2,3},{5,7}}=>[3,2,2] {{1,4,6},{2,3},{5},{7}}=>[3,2,1,1] {{1,4,7},{2,3,6},{5}}=>[3,3,1] {{1,4},{2,3,6,7},{5}}=>[4,2,1] {{1,4},{2,3,6},{5,7}}=>[3,2,2] {{1,4},{2,3,6},{5},{7}}=>[3,2,1,1] {{1,4,7},{2,3},{5,6}}=>[3,2,2] {{1,4},{2,3,7},{5,6}}=>[3,2,2] {{1,4},{2,3},{5,6,7}}=>[3,2,2] {{1,4},{2,3},{5,6},{7}}=>[2,2,2,1] {{1,4,7},{2,3},{5},{6}}=>[3,2,1,1] {{1,4},{2,3,7},{5},{6}}=>[3,2,1,1] {{1,4},{2,3},{5,7},{6}}=>[2,2,2,1] {{1,4},{2,3},{5},{6,7}}=>[2,2,2,1] {{1,4},{2,3},{5},{6},{7}}=>[2,2,1,1,1] {{1,5,6,7},{2,3,4}}=>[4,3] {{1,5,6},{2,3,4,7}}=>[4,3] {{1,5,6},{2,3,4},{7}}=>[3,3,1] {{1,5,7},{2,3,4,6}}=>[4,3] {{1,5},{2,3,4,6,7}}=>[5,2] {{1,5},{2,3,4,6},{7}}=>[4,2,1] {{1,5,7},{2,3,4},{6}}=>[3,3,1] {{1,5},{2,3,4,7},{6}}=>[4,2,1] {{1,5},{2,3,4},{6,7}}=>[3,2,2] {{1,5},{2,3,4},{6},{7}}=>[3,2,1,1] {{1,6,7},{2,3,4,5}}=>[4,3] {{1,6},{2,3,4,5,7}}=>[5,2] {{1,6},{2,3,4,5},{7}}=>[4,2,1] {{1,7},{2,3,4,5,6}}=>[5,2] {{1},{2,3,4,5,6,7}}=>[6,1] {{1},{2,3,4,5,6},{7}}=>[5,1,1] {{1,7},{2,3,4,5},{6}}=>[4,2,1] {{1},{2,3,4,5,7},{6}}=>[5,1,1] {{1},{2,3,4,5},{6,7}}=>[4,2,1] {{1},{2,3,4,5},{6},{7}}=>[4,1,1,1] {{1,6,7},{2,3,4},{5}}=>[3,3,1] {{1,6},{2,3,4,7},{5}}=>[4,2,1] {{1,6},{2,3,4},{5,7}}=>[3,2,2] {{1,6},{2,3,4},{5},{7}}=>[3,2,1,1] {{1,7},{2,3,4,6},{5}}=>[4,2,1] {{1},{2,3,4,6,7},{5}}=>[5,1,1] {{1},{2,3,4,6},{5,7}}=>[4,2,1] {{1},{2,3,4,6},{5},{7}}=>[4,1,1,1] {{1,7},{2,3,4},{5,6}}=>[3,2,2] {{1},{2,3,4,7},{5,6}}=>[4,2,1] {{1},{2,3,4},{5,6,7}}=>[3,3,1] {{1},{2,3,4},{5,6},{7}}=>[3,2,1,1] {{1,7},{2,3,4},{5},{6}}=>[3,2,1,1] {{1},{2,3,4,7},{5},{6}}=>[4,1,1,1] {{1},{2,3,4},{5,7},{6}}=>[3,2,1,1] {{1},{2,3,4},{5},{6,7}}=>[3,2,1,1] {{1},{2,3,4},{5},{6},{7}}=>[3,1,1,1,1] {{1,5,6,7},{2,3},{4}}=>[4,2,1] {{1,5,6},{2,3,7},{4}}=>[3,3,1] {{1,5,6},{2,3},{4,7}}=>[3,2,2] {{1,5,6},{2,3},{4},{7}}=>[3,2,1,1] {{1,5,7},{2,3,6},{4}}=>[3,3,1] {{1,5},{2,3,6,7},{4}}=>[4,2,1] {{1,5},{2,3,6},{4,7}}=>[3,2,2] {{1,5},{2,3,6},{4},{7}}=>[3,2,1,1] {{1,5,7},{2,3},{4,6}}=>[3,2,2] {{1,5},{2,3,7},{4,6}}=>[3,2,2] {{1,5},{2,3},{4,6,7}}=>[3,2,2] {{1,5},{2,3},{4,6},{7}}=>[2,2,2,1] {{1,5,7},{2,3},{4},{6}}=>[3,2,1,1] {{1,5},{2,3,7},{4},{6}}=>[3,2,1,1] {{1,5},{2,3},{4,7},{6}}=>[2,2,2,1] {{1,5},{2,3},{4},{6,7}}=>[2,2,2,1] {{1,5},{2,3},{4},{6},{7}}=>[2,2,1,1,1] {{1,6,7},{2,3,5},{4}}=>[3,3,1] {{1,6},{2,3,5,7},{4}}=>[4,2,1] {{1,6},{2,3,5},{4,7}}=>[3,2,2] {{1,6},{2,3,5},{4},{7}}=>[3,2,1,1] {{1,7},{2,3,5,6},{4}}=>[4,2,1] {{1},{2,3,5,6,7},{4}}=>[5,1,1] {{1},{2,3,5,6},{4,7}}=>[4,2,1] {{1},{2,3,5,6},{4},{7}}=>[4,1,1,1] {{1,7},{2,3,5},{4,6}}=>[3,2,2] {{1},{2,3,5,7},{4,6}}=>[4,2,1] {{1},{2,3,5},{4,6,7}}=>[3,3,1] {{1},{2,3,5},{4,6},{7}}=>[3,2,1,1] {{1,7},{2,3,5},{4},{6}}=>[3,2,1,1] {{1},{2,3,5,7},{4},{6}}=>[4,1,1,1] {{1},{2,3,5},{4,7},{6}}=>[3,2,1,1] {{1},{2,3,5},{4},{6,7}}=>[3,2,1,1] {{1},{2,3,5},{4},{6},{7}}=>[3,1,1,1,1] {{1,6,7},{2,3},{4,5}}=>[3,2,2] {{1,6},{2,3,7},{4,5}}=>[3,2,2] {{1,6},{2,3},{4,5,7}}=>[3,2,2] {{1,6},{2,3},{4,5},{7}}=>[2,2,2,1] {{1,7},{2,3,6},{4,5}}=>[3,2,2] {{1},{2,3,6,7},{4,5}}=>[4,2,1] {{1},{2,3,6},{4,5,7}}=>[3,3,1] {{1},{2,3,6},{4,5},{7}}=>[3,2,1,1] {{1,7},{2,3},{4,5,6}}=>[3,2,2] {{1},{2,3,7},{4,5,6}}=>[3,3,1] {{1},{2,3},{4,5,6,7}}=>[4,2,1] {{1},{2,3},{4,5,6},{7}}=>[3,2,1,1] {{1,7},{2,3},{4,5},{6}}=>[2,2,2,1] {{1},{2,3,7},{4,5},{6}}=>[3,2,1,1] {{1},{2,3},{4,5,7},{6}}=>[3,2,1,1] {{1},{2,3},{4,5},{6,7}}=>[2,2,2,1] {{1},{2,3},{4,5},{6},{7}}=>[2,2,1,1,1] {{1,6,7},{2,3},{4},{5}}=>[3,2,1,1] {{1,6},{2,3,7},{4},{5}}=>[3,2,1,1] {{1,6},{2,3},{4,7},{5}}=>[2,2,2,1] {{1,6},{2,3},{4},{5,7}}=>[2,2,2,1] {{1,6},{2,3},{4},{5},{7}}=>[2,2,1,1,1] {{1,7},{2,3,6},{4},{5}}=>[3,2,1,1] {{1},{2,3,6,7},{4},{5}}=>[4,1,1,1] {{1},{2,3,6},{4,7},{5}}=>[3,2,1,1] {{1},{2,3,6},{4},{5,7}}=>[3,2,1,1] {{1},{2,3,6},{4},{5},{7}}=>[3,1,1,1,1] {{1,7},{2,3},{4,6},{5}}=>[2,2,2,1] {{1},{2,3,7},{4,6},{5}}=>[3,2,1,1] {{1},{2,3},{4,6,7},{5}}=>[3,2,1,1] {{1},{2,3},{4,6},{5,7}}=>[2,2,2,1] {{1},{2,3},{4,6},{5},{7}}=>[2,2,1,1,1] {{1,7},{2,3},{4},{5,6}}=>[2,2,2,1] {{1},{2,3,7},{4},{5,6}}=>[3,2,1,1] {{1},{2,3},{4,7},{5,6}}=>[2,2,2,1] {{1},{2,3},{4},{5,6,7}}=>[3,2,1,1] {{1},{2,3},{4},{5,6},{7}}=>[2,2,1,1,1] {{1,7},{2,3},{4},{5},{6}}=>[2,2,1,1,1] {{1},{2,3,7},{4},{5},{6}}=>[3,1,1,1,1] {{1},{2,3},{4,7},{5},{6}}=>[2,2,1,1,1] {{1},{2,3},{4},{5,7},{6}}=>[2,2,1,1,1] {{1},{2,3},{4},{5},{6,7}}=>[2,2,1,1,1] {{1},{2,3},{4},{5},{6},{7}}=>[2,1,1,1,1,1] {{1,4,5,6,7},{2},{3}}=>[5,1,1] {{1,4,5,6},{2,7},{3}}=>[4,2,1] {{1,4,5,6},{2},{3,7}}=>[4,2,1] {{1,4,5,6},{2},{3},{7}}=>[4,1,1,1] {{1,4,5,7},{2,6},{3}}=>[4,2,1] {{1,4,5},{2,6,7},{3}}=>[3,3,1] {{1,4,5},{2,6},{3,7}}=>[3,2,2] {{1,4,5},{2,6},{3},{7}}=>[3,2,1,1] {{1,4,5,7},{2},{3,6}}=>[4,2,1] {{1,4,5},{2,7},{3,6}}=>[3,2,2] {{1,4,5},{2},{3,6,7}}=>[3,3,1] {{1,4,5},{2},{3,6},{7}}=>[3,2,1,1] {{1,4,5,7},{2},{3},{6}}=>[4,1,1,1] {{1,4,5},{2,7},{3},{6}}=>[3,2,1,1] {{1,4,5},{2},{3,7},{6}}=>[3,2,1,1] {{1,4,5},{2},{3},{6,7}}=>[3,2,1,1] {{1,4,5},{2},{3},{6},{7}}=>[3,1,1,1,1] {{1,4,6,7},{2,5},{3}}=>[4,2,1] {{1,4,6},{2,5,7},{3}}=>[3,3,1] {{1,4,6},{2,5},{3,7}}=>[3,2,2] {{1,4,6},{2,5},{3},{7}}=>[3,2,1,1] {{1,4,7},{2,5,6},{3}}=>[3,3,1] {{1,4},{2,5,6,7},{3}}=>[4,2,1] {{1,4},{2,5,6},{3,7}}=>[3,2,2] {{1,4},{2,5,6},{3},{7}}=>[3,2,1,1] {{1,4,7},{2,5},{3,6}}=>[3,2,2] {{1,4},{2,5,7},{3,6}}=>[3,2,2] {{1,4},{2,5},{3,6,7}}=>[3,2,2] {{1,4},{2,5},{3,6},{7}}=>[2,2,2,1] {{1,4,7},{2,5},{3},{6}}=>[3,2,1,1] {{1,4},{2,5,7},{3},{6}}=>[3,2,1,1] {{1,4},{2,5},{3,7},{6}}=>[2,2,2,1] {{1,4},{2,5},{3},{6,7}}=>[2,2,2,1] {{1,4},{2,5},{3},{6},{7}}=>[2,2,1,1,1] {{1,4,6,7},{2},{3,5}}=>[4,2,1] {{1,4,6},{2,7},{3,5}}=>[3,2,2] {{1,4,6},{2},{3,5,7}}=>[3,3,1] {{1,4,6},{2},{3,5},{7}}=>[3,2,1,1] {{1,4,7},{2,6},{3,5}}=>[3,2,2] {{1,4},{2,6,7},{3,5}}=>[3,2,2] {{1,4},{2,6},{3,5,7}}=>[3,2,2] {{1,4},{2,6},{3,5},{7}}=>[2,2,2,1] {{1,4,7},{2},{3,5,6}}=>[3,3,1] {{1,4},{2,7},{3,5,6}}=>[3,2,2] {{1,4},{2},{3,5,6,7}}=>[4,2,1] {{1,4},{2},{3,5,6},{7}}=>[3,2,1,1] {{1,4,7},{2},{3,5},{6}}=>[3,2,1,1] {{1,4},{2,7},{3,5},{6}}=>[2,2,2,1] {{1,4},{2},{3,5,7},{6}}=>[3,2,1,1] {{1,4},{2},{3,5},{6,7}}=>[2,2,2,1] {{1,4},{2},{3,5},{6},{7}}=>[2,2,1,1,1] {{1,4,6,7},{2},{3},{5}}=>[4,1,1,1] {{1,4,6},{2,7},{3},{5}}=>[3,2,1,1] {{1,4,6},{2},{3,7},{5}}=>[3,2,1,1] {{1,4,6},{2},{3},{5,7}}=>[3,2,1,1] {{1,4,6},{2},{3},{5},{7}}=>[3,1,1,1,1] {{1,4,7},{2,6},{3},{5}}=>[3,2,1,1] {{1,4},{2,6,7},{3},{5}}=>[3,2,1,1] {{1,4},{2,6},{3,7},{5}}=>[2,2,2,1] {{1,4},{2,6},{3},{5,7}}=>[2,2,2,1] {{1,4},{2,6},{3},{5},{7}}=>[2,2,1,1,1] {{1,4,7},{2},{3,6},{5}}=>[3,2,1,1] {{1,4},{2,7},{3,6},{5}}=>[2,2,2,1] {{1,4},{2},{3,6,7},{5}}=>[3,2,1,1] {{1,4},{2},{3,6},{5,7}}=>[2,2,2,1] {{1,4},{2},{3,6},{5},{7}}=>[2,2,1,1,1] {{1,4,7},{2},{3},{5,6}}=>[3,2,1,1] {{1,4},{2,7},{3},{5,6}}=>[2,2,2,1] {{1,4},{2},{3,7},{5,6}}=>[2,2,2,1] {{1,4},{2},{3},{5,6,7}}=>[3,2,1,1] {{1,4},{2},{3},{5,6},{7}}=>[2,2,1,1,1] {{1,4,7},{2},{3},{5},{6}}=>[3,1,1,1,1] {{1,4},{2,7},{3},{5},{6}}=>[2,2,1,1,1] {{1,4},{2},{3,7},{5},{6}}=>[2,2,1,1,1] {{1,4},{2},{3},{5,7},{6}}=>[2,2,1,1,1] {{1,4},{2},{3},{5},{6,7}}=>[2,2,1,1,1] {{1,4},{2},{3},{5},{6},{7}}=>[2,1,1,1,1,1] {{1,5,6,7},{2,4},{3}}=>[4,2,1] {{1,5,6},{2,4,7},{3}}=>[3,3,1] {{1,5,6},{2,4},{3,7}}=>[3,2,2] {{1,5,6},{2,4},{3},{7}}=>[3,2,1,1] {{1,5,7},{2,4,6},{3}}=>[3,3,1] {{1,5},{2,4,6,7},{3}}=>[4,2,1] {{1,5},{2,4,6},{3,7}}=>[3,2,2] {{1,5},{2,4,6},{3},{7}}=>[3,2,1,1] {{1,5,7},{2,4},{3,6}}=>[3,2,2] {{1,5},{2,4,7},{3,6}}=>[3,2,2] {{1,5},{2,4},{3,6,7}}=>[3,2,2] {{1,5},{2,4},{3,6},{7}}=>[2,2,2,1] {{1,5,7},{2,4},{3},{6}}=>[3,2,1,1] {{1,5},{2,4,7},{3},{6}}=>[3,2,1,1] {{1,5},{2,4},{3,7},{6}}=>[2,2,2,1] {{1,5},{2,4},{3},{6,7}}=>[2,2,2,1] {{1,5},{2,4},{3},{6},{7}}=>[2,2,1,1,1] {{1,6,7},{2,4,5},{3}}=>[3,3,1] {{1,6},{2,4,5,7},{3}}=>[4,2,1] {{1,6},{2,4,5},{3,7}}=>[3,2,2] {{1,6},{2,4,5},{3},{7}}=>[3,2,1,1] {{1,7},{2,4,5,6},{3}}=>[4,2,1] {{1},{2,4,5,6,7},{3}}=>[5,1,1] {{1},{2,4,5,6},{3,7}}=>[4,2,1] {{1},{2,4,5,6},{3},{7}}=>[4,1,1,1] {{1,7},{2,4,5},{3,6}}=>[3,2,2] {{1},{2,4,5,7},{3,6}}=>[4,2,1] {{1},{2,4,5},{3,6,7}}=>[3,3,1] {{1},{2,4,5},{3,6},{7}}=>[3,2,1,1] {{1,7},{2,4,5},{3},{6}}=>[3,2,1,1] {{1},{2,4,5,7},{3},{6}}=>[4,1,1,1] {{1},{2,4,5},{3,7},{6}}=>[3,2,1,1] {{1},{2,4,5},{3},{6,7}}=>[3,2,1,1] {{1},{2,4,5},{3},{6},{7}}=>[3,1,1,1,1] {{1,6,7},{2,4},{3,5}}=>[3,2,2] {{1,6},{2,4,7},{3,5}}=>[3,2,2] {{1,6},{2,4},{3,5,7}}=>[3,2,2] {{1,6},{2,4},{3,5},{7}}=>[2,2,2,1] {{1,7},{2,4,6},{3,5}}=>[3,2,2] {{1},{2,4,6,7},{3,5}}=>[4,2,1] {{1},{2,4,6},{3,5,7}}=>[3,3,1] {{1},{2,4,6},{3,5},{7}}=>[3,2,1,1] {{1,7},{2,4},{3,5,6}}=>[3,2,2] {{1},{2,4,7},{3,5,6}}=>[3,3,1] {{1},{2,4},{3,5,6,7}}=>[4,2,1] {{1},{2,4},{3,5,6},{7}}=>[3,2,1,1] {{1,7},{2,4},{3,5},{6}}=>[2,2,2,1] {{1},{2,4,7},{3,5},{6}}=>[3,2,1,1] {{1},{2,4},{3,5,7},{6}}=>[3,2,1,1] {{1},{2,4},{3,5},{6,7}}=>[2,2,2,1] {{1},{2,4},{3,5},{6},{7}}=>[2,2,1,1,1] {{1,6,7},{2,4},{3},{5}}=>[3,2,1,1] {{1,6},{2,4,7},{3},{5}}=>[3,2,1,1] {{1,6},{2,4},{3,7},{5}}=>[2,2,2,1] {{1,6},{2,4},{3},{5,7}}=>[2,2,2,1] {{1,6},{2,4},{3},{5},{7}}=>[2,2,1,1,1] {{1,7},{2,4,6},{3},{5}}=>[3,2,1,1] {{1},{2,4,6,7},{3},{5}}=>[4,1,1,1] {{1},{2,4,6},{3,7},{5}}=>[3,2,1,1] {{1},{2,4,6},{3},{5,7}}=>[3,2,1,1] {{1},{2,4,6},{3},{5},{7}}=>[3,1,1,1,1] {{1,7},{2,4},{3,6},{5}}=>[2,2,2,1] {{1},{2,4,7},{3,6},{5}}=>[3,2,1,1] {{1},{2,4},{3,6,7},{5}}=>[3,2,1,1] {{1},{2,4},{3,6},{5,7}}=>[2,2,2,1] {{1},{2,4},{3,6},{5},{7}}=>[2,2,1,1,1] {{1,7},{2,4},{3},{5,6}}=>[2,2,2,1] {{1},{2,4,7},{3},{5,6}}=>[3,2,1,1] {{1},{2,4},{3,7},{5,6}}=>[2,2,2,1] {{1},{2,4},{3},{5,6,7}}=>[3,2,1,1] {{1},{2,4},{3},{5,6},{7}}=>[2,2,1,1,1] {{1,7},{2,4},{3},{5},{6}}=>[2,2,1,1,1] {{1},{2,4,7},{3},{5},{6}}=>[3,1,1,1,1] {{1},{2,4},{3,7},{5},{6}}=>[2,2,1,1,1] {{1},{2,4},{3},{5,7},{6}}=>[2,2,1,1,1] {{1},{2,4},{3},{5},{6,7}}=>[2,2,1,1,1] {{1},{2,4},{3},{5},{6},{7}}=>[2,1,1,1,1,1] {{1,5,6,7},{2},{3,4}}=>[4,2,1] {{1,5,6},{2,7},{3,4}}=>[3,2,2] {{1,5,6},{2},{3,4,7}}=>[3,3,1] {{1,5,6},{2},{3,4},{7}}=>[3,2,1,1] {{1,5,7},{2,6},{3,4}}=>[3,2,2] {{1,5},{2,6,7},{3,4}}=>[3,2,2] {{1,5},{2,6},{3,4,7}}=>[3,2,2] {{1,5},{2,6},{3,4},{7}}=>[2,2,2,1] {{1,5,7},{2},{3,4,6}}=>[3,3,1] {{1,5},{2,7},{3,4,6}}=>[3,2,2] {{1,5},{2},{3,4,6,7}}=>[4,2,1] {{1,5},{2},{3,4,6},{7}}=>[3,2,1,1] {{1,5,7},{2},{3,4},{6}}=>[3,2,1,1] {{1,5},{2,7},{3,4},{6}}=>[2,2,2,1] {{1,5},{2},{3,4,7},{6}}=>[3,2,1,1] {{1,5},{2},{3,4},{6,7}}=>[2,2,2,1] {{1,5},{2},{3,4},{6},{7}}=>[2,2,1,1,1] {{1,6,7},{2,5},{3,4}}=>[3,2,2] {{1,6},{2,5,7},{3,4}}=>[3,2,2] {{1,6},{2,5},{3,4,7}}=>[3,2,2] {{1,6},{2,5},{3,4},{7}}=>[2,2,2,1] {{1,7},{2,5,6},{3,4}}=>[3,2,2] {{1},{2,5,6,7},{3,4}}=>[4,2,1] {{1},{2,5,6},{3,4,7}}=>[3,3,1] {{1},{2,5,6},{3,4},{7}}=>[3,2,1,1] {{1,7},{2,5},{3,4,6}}=>[3,2,2] {{1},{2,5,7},{3,4,6}}=>[3,3,1] {{1},{2,5},{3,4,6,7}}=>[4,2,1] {{1},{2,5},{3,4,6},{7}}=>[3,2,1,1] {{1,7},{2,5},{3,4},{6}}=>[2,2,2,1] {{1},{2,5,7},{3,4},{6}}=>[3,2,1,1] {{1},{2,5},{3,4,7},{6}}=>[3,2,1,1] {{1},{2,5},{3,4},{6,7}}=>[2,2,2,1] {{1},{2,5},{3,4},{6},{7}}=>[2,2,1,1,1] {{1,6,7},{2},{3,4,5}}=>[3,3,1] {{1,6},{2,7},{3,4,5}}=>[3,2,2] {{1,6},{2},{3,4,5,7}}=>[4,2,1] {{1,6},{2},{3,4,5},{7}}=>[3,2,1,1] {{1,7},{2,6},{3,4,5}}=>[3,2,2] {{1},{2,6,7},{3,4,5}}=>[3,3,1] {{1},{2,6},{3,4,5,7}}=>[4,2,1] {{1},{2,6},{3,4,5},{7}}=>[3,2,1,1] {{1,7},{2},{3,4,5,6}}=>[4,2,1] {{1},{2,7},{3,4,5,6}}=>[4,2,1] {{1},{2},{3,4,5,6,7}}=>[5,1,1] {{1},{2},{3,4,5,6},{7}}=>[4,1,1,1] {{1,7},{2},{3,4,5},{6}}=>[3,2,1,1] {{1},{2,7},{3,4,5},{6}}=>[3,2,1,1] {{1},{2},{3,4,5,7},{6}}=>[4,1,1,1] {{1},{2},{3,4,5},{6,7}}=>[3,2,1,1] {{1},{2},{3,4,5},{6},{7}}=>[3,1,1,1,1] {{1,6,7},{2},{3,4},{5}}=>[3,2,1,1] {{1,6},{2,7},{3,4},{5}}=>[2,2,2,1] {{1,6},{2},{3,4,7},{5}}=>[3,2,1,1] {{1,6},{2},{3,4},{5,7}}=>[2,2,2,1] {{1,6},{2},{3,4},{5},{7}}=>[2,2,1,1,1] {{1,7},{2,6},{3,4},{5}}=>[2,2,2,1] {{1},{2,6,7},{3,4},{5}}=>[3,2,1,1] {{1},{2,6},{3,4,7},{5}}=>[3,2,1,1] {{1},{2,6},{3,4},{5,7}}=>[2,2,2,1] {{1},{2,6},{3,4},{5},{7}}=>[2,2,1,1,1] {{1,7},{2},{3,4,6},{5}}=>[3,2,1,1] {{1},{2,7},{3,4,6},{5}}=>[3,2,1,1] {{1},{2},{3,4,6,7},{5}}=>[4,1,1,1] {{1},{2},{3,4,6},{5,7}}=>[3,2,1,1] {{1},{2},{3,4,6},{5},{7}}=>[3,1,1,1,1] {{1,7},{2},{3,4},{5,6}}=>[2,2,2,1] {{1},{2,7},{3,4},{5,6}}=>[2,2,2,1] {{1},{2},{3,4,7},{5,6}}=>[3,2,1,1] {{1},{2},{3,4},{5,6,7}}=>[3,2,1,1] {{1},{2},{3,4},{5,6},{7}}=>[2,2,1,1,1] {{1,7},{2},{3,4},{5},{6}}=>[2,2,1,1,1] {{1},{2,7},{3,4},{5},{6}}=>[2,2,1,1,1] {{1},{2},{3,4,7},{5},{6}}=>[3,1,1,1,1] {{1},{2},{3,4},{5,7},{6}}=>[2,2,1,1,1] {{1},{2},{3,4},{5},{6,7}}=>[2,2,1,1,1] {{1},{2},{3,4},{5},{6},{7}}=>[2,1,1,1,1,1] {{1,5,6,7},{2},{3},{4}}=>[4,1,1,1] {{1,5,6},{2,7},{3},{4}}=>[3,2,1,1] {{1,5,6},{2},{3,7},{4}}=>[3,2,1,1] {{1,5,6},{2},{3},{4,7}}=>[3,2,1,1] {{1,5,6},{2},{3},{4},{7}}=>[3,1,1,1,1] {{1,5,7},{2,6},{3},{4}}=>[3,2,1,1] {{1,5},{2,6,7},{3},{4}}=>[3,2,1,1] {{1,5},{2,6},{3,7},{4}}=>[2,2,2,1] {{1,5},{2,6},{3},{4,7}}=>[2,2,2,1] {{1,5},{2,6},{3},{4},{7}}=>[2,2,1,1,1] {{1,5,7},{2},{3,6},{4}}=>[3,2,1,1] {{1,5},{2,7},{3,6},{4}}=>[2,2,2,1] {{1,5},{2},{3,6,7},{4}}=>[3,2,1,1] {{1,5},{2},{3,6},{4,7}}=>[2,2,2,1] {{1,5},{2},{3,6},{4},{7}}=>[2,2,1,1,1] {{1,5,7},{2},{3},{4,6}}=>[3,2,1,1] {{1,5},{2,7},{3},{4,6}}=>[2,2,2,1] {{1,5},{2},{3,7},{4,6}}=>[2,2,2,1] {{1,5},{2},{3},{4,6,7}}=>[3,2,1,1] {{1,5},{2},{3},{4,6},{7}}=>[2,2,1,1,1] {{1,5,7},{2},{3},{4},{6}}=>[3,1,1,1,1] {{1,5},{2,7},{3},{4},{6}}=>[2,2,1,1,1] {{1,5},{2},{3,7},{4},{6}}=>[2,2,1,1,1] {{1,5},{2},{3},{4,7},{6}}=>[2,2,1,1,1] {{1,5},{2},{3},{4},{6,7}}=>[2,2,1,1,1] {{1,5},{2},{3},{4},{6},{7}}=>[2,1,1,1,1,1] {{1,6,7},{2,5},{3},{4}}=>[3,2,1,1] {{1,6},{2,5,7},{3},{4}}=>[3,2,1,1] {{1,6},{2,5},{3,7},{4}}=>[2,2,2,1] {{1,6},{2,5},{3},{4,7}}=>[2,2,2,1] {{1,6},{2,5},{3},{4},{7}}=>[2,2,1,1,1] {{1,7},{2,5,6},{3},{4}}=>[3,2,1,1] {{1},{2,5,6,7},{3},{4}}=>[4,1,1,1] {{1},{2,5,6},{3,7},{4}}=>[3,2,1,1] {{1},{2,5,6},{3},{4,7}}=>[3,2,1,1] {{1},{2,5,6},{3},{4},{7}}=>[3,1,1,1,1] {{1,7},{2,5},{3,6},{4}}=>[2,2,2,1] {{1},{2,5,7},{3,6},{4}}=>[3,2,1,1] {{1},{2,5},{3,6,7},{4}}=>[3,2,1,1] {{1},{2,5},{3,6},{4,7}}=>[2,2,2,1] {{1},{2,5},{3,6},{4},{7}}=>[2,2,1,1,1] {{1,7},{2,5},{3},{4,6}}=>[2,2,2,1] {{1},{2,5,7},{3},{4,6}}=>[3,2,1,1] {{1},{2,5},{3,7},{4,6}}=>[2,2,2,1] {{1},{2,5},{3},{4,6,7}}=>[3,2,1,1] {{1},{2,5},{3},{4,6},{7}}=>[2,2,1,1,1] {{1,7},{2,5},{3},{4},{6}}=>[2,2,1,1,1] {{1},{2,5,7},{3},{4},{6}}=>[3,1,1,1,1] {{1},{2,5},{3,7},{4},{6}}=>[2,2,1,1,1] {{1},{2,5},{3},{4,7},{6}}=>[2,2,1,1,1] {{1},{2,5},{3},{4},{6,7}}=>[2,2,1,1,1] {{1},{2,5},{3},{4},{6},{7}}=>[2,1,1,1,1,1] {{1,6,7},{2},{3,5},{4}}=>[3,2,1,1] {{1,6},{2,7},{3,5},{4}}=>[2,2,2,1] {{1,6},{2},{3,5,7},{4}}=>[3,2,1,1] {{1,6},{2},{3,5},{4,7}}=>[2,2,2,1] {{1,6},{2},{3,5},{4},{7}}=>[2,2,1,1,1] {{1,7},{2,6},{3,5},{4}}=>[2,2,2,1] {{1},{2,6,7},{3,5},{4}}=>[3,2,1,1] {{1},{2,6},{3,5,7},{4}}=>[3,2,1,1] {{1},{2,6},{3,5},{4,7}}=>[2,2,2,1] {{1},{2,6},{3,5},{4},{7}}=>[2,2,1,1,1] {{1,7},{2},{3,5,6},{4}}=>[3,2,1,1] {{1},{2,7},{3,5,6},{4}}=>[3,2,1,1] {{1},{2},{3,5,6,7},{4}}=>[4,1,1,1] {{1},{2},{3,5,6},{4,7}}=>[3,2,1,1] {{1},{2},{3,5,6},{4},{7}}=>[3,1,1,1,1] {{1,7},{2},{3,5},{4,6}}=>[2,2,2,1] {{1},{2,7},{3,5},{4,6}}=>[2,2,2,1] {{1},{2},{3,5,7},{4,6}}=>[3,2,1,1] {{1},{2},{3,5},{4,6,7}}=>[3,2,1,1] {{1},{2},{3,5},{4,6},{7}}=>[2,2,1,1,1] {{1,7},{2},{3,5},{4},{6}}=>[2,2,1,1,1] {{1},{2,7},{3,5},{4},{6}}=>[2,2,1,1,1] {{1},{2},{3,5,7},{4},{6}}=>[3,1,1,1,1] {{1},{2},{3,5},{4,7},{6}}=>[2,2,1,1,1] {{1},{2},{3,5},{4},{6,7}}=>[2,2,1,1,1] {{1},{2},{3,5},{4},{6},{7}}=>[2,1,1,1,1,1] {{1,6,7},{2},{3},{4,5}}=>[3,2,1,1] {{1,6},{2,7},{3},{4,5}}=>[2,2,2,1] {{1,6},{2},{3,7},{4,5}}=>[2,2,2,1] {{1,6},{2},{3},{4,5,7}}=>[3,2,1,1] {{1,6},{2},{3},{4,5},{7}}=>[2,2,1,1,1] {{1,7},{2,6},{3},{4,5}}=>[2,2,2,1] {{1},{2,6,7},{3},{4,5}}=>[3,2,1,1] {{1},{2,6},{3,7},{4,5}}=>[2,2,2,1] {{1},{2,6},{3},{4,5,7}}=>[3,2,1,1] {{1},{2,6},{3},{4,5},{7}}=>[2,2,1,1,1] {{1,7},{2},{3,6},{4,5}}=>[2,2,2,1] {{1},{2,7},{3,6},{4,5}}=>[2,2,2,1] {{1},{2},{3,6,7},{4,5}}=>[3,2,1,1] {{1},{2},{3,6},{4,5,7}}=>[3,2,1,1] {{1},{2},{3,6},{4,5},{7}}=>[2,2,1,1,1] {{1,7},{2},{3},{4,5,6}}=>[3,2,1,1] {{1},{2,7},{3},{4,5,6}}=>[3,2,1,1] {{1},{2},{3,7},{4,5,6}}=>[3,2,1,1] {{1},{2},{3},{4,5,6,7}}=>[4,1,1,1] {{1},{2},{3},{4,5,6},{7}}=>[3,1,1,1,1] {{1,7},{2},{3},{4,5},{6}}=>[2,2,1,1,1] {{1},{2,7},{3},{4,5},{6}}=>[2,2,1,1,1] {{1},{2},{3,7},{4,5},{6}}=>[2,2,1,1,1] {{1},{2},{3},{4,5,7},{6}}=>[3,1,1,1,1] {{1},{2},{3},{4,5},{6,7}}=>[2,2,1,1,1] {{1},{2},{3},{4,5},{6},{7}}=>[2,1,1,1,1,1] {{1,6,7},{2},{3},{4},{5}}=>[3,1,1,1,1] {{1,6},{2,7},{3},{4},{5}}=>[2,2,1,1,1] {{1,6},{2},{3,7},{4},{5}}=>[2,2,1,1,1] {{1,6},{2},{3},{4,7},{5}}=>[2,2,1,1,1] {{1,6},{2},{3},{4},{5,7}}=>[2,2,1,1,1] {{1,6},{2},{3},{4},{5},{7}}=>[2,1,1,1,1,1] {{1,7},{2,6},{3},{4},{5}}=>[2,2,1,1,1] {{1},{2,6,7},{3},{4},{5}}=>[3,1,1,1,1] {{1},{2,6},{3,7},{4},{5}}=>[2,2,1,1,1] {{1},{2,6},{3},{4,7},{5}}=>[2,2,1,1,1] {{1},{2,6},{3},{4},{5,7}}=>[2,2,1,1,1] {{1},{2,6},{3},{4},{5},{7}}=>[2,1,1,1,1,1] {{1,7},{2},{3,6},{4},{5}}=>[2,2,1,1,1] {{1},{2,7},{3,6},{4},{5}}=>[2,2,1,1,1] {{1},{2},{3,6,7},{4},{5}}=>[3,1,1,1,1] {{1},{2},{3,6},{4,7},{5}}=>[2,2,1,1,1] {{1},{2},{3,6},{4},{5,7}}=>[2,2,1,1,1] {{1},{2},{3,6},{4},{5},{7}}=>[2,1,1,1,1,1] {{1,7},{2},{3},{4,6},{5}}=>[2,2,1,1,1] {{1},{2,7},{3},{4,6},{5}}=>[2,2,1,1,1] {{1},{2},{3,7},{4,6},{5}}=>[2,2,1,1,1] {{1},{2},{3},{4,6,7},{5}}=>[3,1,1,1,1] {{1},{2},{3},{4,6},{5,7}}=>[2,2,1,1,1] {{1},{2},{3},{4,6},{5},{7}}=>[2,1,1,1,1,1] {{1,7},{2},{3},{4},{5,6}}=>[2,2,1,1,1] {{1},{2,7},{3},{4},{5,6}}=>[2,2,1,1,1] {{1},{2},{3,7},{4},{5,6}}=>[2,2,1,1,1] {{1},{2},{3},{4,7},{5,6}}=>[2,2,1,1,1] {{1},{2},{3},{4},{5,6,7}}=>[3,1,1,1,1] {{1},{2},{3},{4},{5,6},{7}}=>[2,1,1,1,1,1] {{1,7},{2},{3},{4},{5},{6}}=>[2,1,1,1,1,1] {{1},{2,7},{3},{4},{5},{6}}=>[2,1,1,1,1,1] {{1},{2},{3,7},{4},{5},{6}}=>[2,1,1,1,1,1] {{1},{2},{3},{4,7},{5},{6}}=>[2,1,1,1,1,1] {{1},{2},{3},{4},{5,7},{6}}=>[2,1,1,1,1,1] {{1},{2},{3},{4},{5},{6,7}}=>[2,1,1,1,1,1] {{1},{2},{3},{4},{5},{6},{7}}=>[1,1,1,1,1,1,1] {{1,2},{3,4},{5,6},{7,8}}=>[2,2,2,2] {{1,3},{2,4},{5,6},{7,8}}=>[2,2,2,2] {{1,4},{2,3},{5,6},{7,8}}=>[2,2,2,2] {{1,5},{2,3},{4,6},{7,8}}=>[2,2,2,2] {{1,6},{2,3},{4,5},{7,8}}=>[2,2,2,2] {{1,7},{2,3},{4,5},{6,8}}=>[2,2,2,2] {{1,8},{2,3},{4,5},{6,7}}=>[2,2,2,2] {{1,8},{2,4},{3,5},{6,7}}=>[2,2,2,2] {{1,7},{2,4},{3,5},{6,8}}=>[2,2,2,2] {{1,6},{2,4},{3,5},{7,8}}=>[2,2,2,2] {{1,5},{2,4},{3,6},{7,8}}=>[2,2,2,2] {{1,4},{2,5},{3,6},{7,8}}=>[2,2,2,2] {{1,3},{2,5},{4,6},{7,8}}=>[2,2,2,2] {{1,2},{3,5},{4,6},{7,8}}=>[2,2,2,2] {{1,2},{3,6},{4,5},{7,8}}=>[2,2,2,2] {{1,3},{2,6},{4,5},{7,8}}=>[2,2,2,2] {{1,4},{2,6},{3,5},{7,8}}=>[2,2,2,2] {{1,5},{2,6},{3,4},{7,8}}=>[2,2,2,2] {{1,6},{2,5},{3,4},{7,8}}=>[2,2,2,2] {{1,7},{2,5},{3,4},{6,8}}=>[2,2,2,2] {{1,8},{2,5},{3,4},{6,7}}=>[2,2,2,2] {{1,8},{2,6},{3,4},{5,7}}=>[2,2,2,2] {{1,7},{2,6},{3,4},{5,8}}=>[2,2,2,2] {{1,6},{2,7},{3,4},{5,8}}=>[2,2,2,2] {{1,5},{2,7},{3,4},{6,8}}=>[2,2,2,2] {{1,4},{2,7},{3,5},{6,8}}=>[2,2,2,2] {{1,3},{2,7},{4,5},{6,8}}=>[2,2,2,2] {{1,2},{3,7},{4,5},{6,8}}=>[2,2,2,2] {{1,2},{3,8},{4,5},{6,7}}=>[2,2,2,2] {{1,3},{2,8},{4,5},{6,7}}=>[2,2,2,2] {{1,4},{2,8},{3,5},{6,7}}=>[2,2,2,2] {{1,5},{2,8},{3,4},{6,7}}=>[2,2,2,2] {{1,6},{2,8},{3,4},{5,7}}=>[2,2,2,2] {{1,7},{2,8},{3,4},{5,6}}=>[2,2,2,2] {{1,8},{2,7},{3,4},{5,6}}=>[2,2,2,2] {{1,8},{2,7},{3,5},{4,6}}=>[2,2,2,2] {{1,7},{2,8},{3,5},{4,6}}=>[2,2,2,2] {{1,6},{2,8},{3,5},{4,7}}=>[2,2,2,2] {{1,5},{2,8},{3,6},{4,7}}=>[2,2,2,2] {{1,4},{2,8},{3,6},{5,7}}=>[2,2,2,2] {{1,3},{2,8},{4,6},{5,7}}=>[2,2,2,2] {{1,2},{3,8},{4,6},{5,7}}=>[2,2,2,2] {{1,2},{3,7},{4,6},{5,8}}=>[2,2,2,2] {{1,3},{2,7},{4,6},{5,8}}=>[2,2,2,2] {{1,4},{2,7},{3,6},{5,8}}=>[2,2,2,2] {{1,5},{2,7},{3,6},{4,8}}=>[2,2,2,2] {{1,6},{2,7},{3,5},{4,8}}=>[2,2,2,2] {{1,7},{2,6},{3,5},{4,8}}=>[2,2,2,2] {{1,8},{2,6},{3,5},{4,7}}=>[2,2,2,2] {{1,8},{2,5},{3,6},{4,7}}=>[2,2,2,2] {{1,7},{2,5},{3,6},{4,8}}=>[2,2,2,2] {{1,6},{2,5},{3,7},{4,8}}=>[2,2,2,2] {{1,5},{2,6},{3,7},{4,8}}=>[2,2,2,2] {{1,4},{2,6},{3,7},{5,8}}=>[2,2,2,2] {{1,3},{2,6},{4,7},{5,8}}=>[2,2,2,2] {{1,2},{3,6},{4,7},{5,8}}=>[2,2,2,2] {{1,2},{3,5},{4,7},{6,8}}=>[2,2,2,2] {{1,3},{2,5},{4,7},{6,8}}=>[2,2,2,2] {{1,4},{2,5},{3,7},{6,8}}=>[2,2,2,2] {{1,5},{2,4},{3,7},{6,8}}=>[2,2,2,2] {{1,6},{2,4},{3,7},{5,8}}=>[2,2,2,2] {{1,7},{2,4},{3,6},{5,8}}=>[2,2,2,2] {{1,8},{2,4},{3,6},{5,7}}=>[2,2,2,2] {{1,8},{2,3},{4,6},{5,7}}=>[2,2,2,2] {{1,7},{2,3},{4,6},{5,8}}=>[2,2,2,2] {{1,6},{2,3},{4,7},{5,8}}=>[2,2,2,2] {{1,5},{2,3},{4,7},{6,8}}=>[2,2,2,2] {{1,4},{2,3},{5,7},{6,8}}=>[2,2,2,2] {{1,3},{2,4},{5,7},{6,8}}=>[2,2,2,2] {{1,2},{3,4},{5,7},{6,8}}=>[2,2,2,2] {{1,2},{3,4},{5,8},{6,7}}=>[2,2,2,2] {{1,3},{2,4},{5,8},{6,7}}=>[2,2,2,2] {{1,4},{2,3},{5,8},{6,7}}=>[2,2,2,2] {{1,5},{2,3},{4,8},{6,7}}=>[2,2,2,2] {{1,6},{2,3},{4,8},{5,7}}=>[2,2,2,2] {{1,7},{2,3},{4,8},{5,6}}=>[2,2,2,2] {{1,8},{2,3},{4,7},{5,6}}=>[2,2,2,2] {{1,8},{2,4},{3,7},{5,6}}=>[2,2,2,2] {{1,7},{2,4},{3,8},{5,6}}=>[2,2,2,2] {{1,6},{2,4},{3,8},{5,7}}=>[2,2,2,2] {{1,5},{2,4},{3,8},{6,7}}=>[2,2,2,2] {{1,4},{2,5},{3,8},{6,7}}=>[2,2,2,2] {{1,3},{2,5},{4,8},{6,7}}=>[2,2,2,2] {{1,2},{3,5},{4,8},{6,7}}=>[2,2,2,2] {{1,2},{3,6},{4,8},{5,7}}=>[2,2,2,2] {{1,3},{2,6},{4,8},{5,7}}=>[2,2,2,2] {{1,4},{2,6},{3,8},{5,7}}=>[2,2,2,2] {{1,5},{2,6},{3,8},{4,7}}=>[2,2,2,2] {{1,6},{2,5},{3,8},{4,7}}=>[2,2,2,2] {{1,7},{2,5},{3,8},{4,6}}=>[2,2,2,2] {{1,8},{2,5},{3,7},{4,6}}=>[2,2,2,2] {{1,8},{2,6},{3,7},{4,5}}=>[2,2,2,2] {{1,7},{2,6},{3,8},{4,5}}=>[2,2,2,2] {{1,6},{2,7},{3,8},{4,5}}=>[2,2,2,2] {{1,5},{2,7},{3,8},{4,6}}=>[2,2,2,2] {{1,4},{2,7},{3,8},{5,6}}=>[2,2,2,2] {{1,3},{2,7},{4,8},{5,6}}=>[2,2,2,2] {{1,2},{3,7},{4,8},{5,6}}=>[2,2,2,2] {{1,2},{3,8},{4,7},{5,6}}=>[2,2,2,2] {{1,3},{2,8},{4,7},{5,6}}=>[2,2,2,2] {{1,4},{2,8},{3,7},{5,6}}=>[2,2,2,2] {{1,5},{2,8},{3,7},{4,6}}=>[2,2,2,2] {{1,6},{2,8},{3,7},{4,5}}=>[2,2,2,2] {{1,7},{2,8},{3,6},{4,5}}=>[2,2,2,2] {{1,8},{2,7},{3,6},{4,5}}=>[2,2,2,2] {{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,1,1,1,1,1,1,1] {{1},{2,3},{4,5,6,8},{7}}=>[4,2,1,1] {{1},{2,3},{4,5,6,7,8}}=>[5,2,1] {{1,2},{3,4},{5,7,8},{6}}=>[3,2,2,1] {{1,2},{3,4},{5,6,8},{7}}=>[3,2,2,1] {{1,2},{3,4},{5,6,7,8}}=>[4,2,2] {{1,2},{3,6,7,8},{4},{5}}=>[4,2,1,1] {{1,2},{3,5,6},{4},{7,8}}=>[3,2,2,1] {{1,2},{3,5,6,8},{4},{7}}=>[4,2,1,1] {{1,2},{3,5,6,7,8},{4}}=>[5,2,1] {{1,2},{3,6,7,8},{4,5}}=>[4,2,2] {{1,2},{3,4,6},{5},{7,8}}=>[3,2,2,1] {{1,2},{3,4,6,8},{5},{7}}=>[4,2,1,1] {{1,2},{3,4,6,7,8},{5}}=>[5,2,1] {{1,2},{3,4,5,6},{7,8}}=>[4,2,2] {{1,2},{3,4,5,7,8},{6}}=>[5,2,1] {{1,2},{3,4,8},{5,6,7}}=>[3,3,2] {{1,2},{3,4,5,8},{6,7}}=>[4,2,2] {{1,2},{3,4,5,6,8},{7}}=>[5,2,1] {{1,2},{3,4,5,6,7,8}}=>[6,2] {{1,3},{2},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1] {{1,5},{2},{3},{4},{6},{7},{8}}=>[2,1,1,1,1,1,1] {{1,7},{2},{3},{4},{5},{6},{8}}=>[2,1,1,1,1,1,1] {{1,5,7},{2},{3},{4},{6},{8}}=>[3,1,1,1,1,1] {{1,5,6,7,8},{2},{3},{4}}=>[5,1,1,1] {{1,4,5,6},{2},{3},{7,8}}=>[4,2,1,1] {{1,3,4},{2},{5,6},{7,8}}=>[3,2,2,1] {{1,3,4},{2},{5,7,8},{6}}=>[3,3,1,1] {{1,3,4},{2},{5,6,7,8}}=>[4,3,1] {{1,3,5},{2},{4},{6},{7},{8}}=>[3,1,1,1,1,1] {{1,3,7},{2},{4},{5},{6},{8}}=>[3,1,1,1,1,1] {{1,3,5,7},{2},{4},{6},{8}}=>[4,1,1,1,1] {{1,3,4,5,6,7,8},{2}}=>[7,1] {{1,2,3},{4,5,8},{6,7}}=>[3,3,2] {{1,4},{2,3},{5,6,7,8}}=>[4,2,2] {{1,6,7,8},{2,3},{4,5}}=>[4,2,2] {{1,4,6,8},{2,3},{5},{7}}=>[4,2,1,1] {{1,4,6,7,8},{2,3},{5}}=>[5,2,1] {{1,4,5,6},{2,3},{7,8}}=>[4,2,2] {{1,4,8},{2,3},{5,6,7}}=>[3,3,2] {{1,4,5,8},{2,3},{6,7}}=>[4,2,2] {{1,4,5,6,8},{2,3},{7}}=>[5,2,1] {{1,4,5,6,7,8},{2,3}}=>[6,2] {{1,2,4},{3},{5,6},{7,8}}=>[3,2,2,1] {{1,2,4},{3},{5,6,8},{7}}=>[3,3,1,1] {{1,2,4},{3},{5,6,7,8}}=>[4,3,1] {{1,2,4,6},{3},{5},{7,8}}=>[4,2,1,1] {{1,2,4,6,8},{3},{5},{7}}=>[5,1,1,1] {{1,2,4,6,7,8},{3},{5}}=>[6,1,1] {{1,2,4,5,6},{3},{7,8}}=>[5,2,1] {{1,2,4,5,8},{3},{6,7}}=>[5,2,1] {{1,2,4,5,6,8},{3},{7}}=>[6,1,1] {{1,2,4,5,6,7,8},{3}}=>[7,1] {{1,2,3,4},{5,6},{7,8}}=>[4,2,2] {{1,2,3,4},{5,7,8},{6}}=>[4,3,1] {{1,2,3,4},{5,8},{6,7}}=>[4,2,2] {{1,2,3,4},{5,6,8},{7}}=>[4,3,1] {{1,2,3,4},{5,6,7,8}}=>[4,4] {{1,5,8},{2,3,4},{6,7}}=>[3,3,2] {{1,5,6,8},{2,3,4},{7}}=>[4,3,1] {{1,5,6,7,8},{2,3,4}}=>[5,3] {{1,6,8},{2,5},{3,4},{7}}=>[3,2,2,1] {{1,6,7,8},{2,5},{3,4}}=>[4,2,2] {{1,7,8},{2,5,6},{3,4}}=>[3,3,2] {{1,2,3,6,7,8},{4},{5}}=>[6,1,1] {{1,2,3,5,6},{4},{7,8}}=>[5,2,1] {{1,2,3,4,5},{6,7,8}}=>[5,3] {{1,6,7,8},{2,3,4,5}}=>[4,4] {{1,2,6},{3,4,5},{7,8}}=>[3,3,2] {{1,7,8},{2,6},{3,4,5}}=>[3,3,2] {{1,2,8},{3,4,5},{6,7}}=>[3,3,2] {{1,2,6,7,8},{3,4,5}}=>[5,3] {{1,2,3,6},{4,5},{7,8}}=>[4,2,2] {{1,8},{2,3,6,7},{4,5}}=>[4,2,2] {{1,2,3,8},{4,5},{6,7}}=>[4,2,2] {{1,2,3,6,8},{4,5},{7}}=>[5,2,1] {{1,2,3,6,7,8},{4,5}}=>[6,2] {{1,2,3,4,6},{5},{7,8}}=>[5,2,1] {{1,8},{2,7},{3,4,6},{5}}=>[3,2,2,1] {{1,8},{2,3,7},{4,6},{5}}=>[3,2,2,1] {{1,2,8},{3,7},{4,6},{5}}=>[3,2,2,1] {{1,8},{2,3,4,6,7},{5}}=>[5,2,1] {{1,2,3,4,6,8},{5},{7}}=>[6,1,1] {{1,2,3,4,6,7,8},{5}}=>[7,1] {{1,2,3,4,5,6},{7,8}}=>[6,2] {{1,2,7,8},{3,4,5,6}}=>[4,4] {{1,2,8},{3,7},{4,5,6}}=>[3,3,2] {{1,2,3,8},{4,5,6},{7}}=>[4,3,1] {{1,2,3,7,8},{4,5,6}}=>[5,3] {{1,2,8},{3,4,7},{5,6}}=>[3,3,2] {{1,2,3,8},{4,7},{5,6}}=>[4,2,2] {{1,2,8},{3,4,5,7},{6}}=>[4,3,1] {{1,2,3,8},{4,5,7},{6}}=>[4,3,1] {{1,2,3,4,8},{5,7},{6}}=>[5,2,1] {{1,2,3,4,5,7,8},{6}}=>[7,1] {{1,8},{2,3,4,5,6,7}}=>[6,2] {{1,2,3,8},{4,5,6,7}}=>[4,4] {{1,2,3,4,8},{5,6,7}}=>[5,3] {{1,2,3,4,5,8},{6,7}}=>[6,2] {{1,2,3,4,5,6,8},{7}}=>[7,1] {{1,2,3,4,5,6,7,8}}=>[8] {{1,3,5,7},{2},{4},{6,8}}=>[4,2,1,1] {{1,4,6},{2},{3,7},{5,8}}=>[3,2,2,1] {{1},{2,7},{3,4},{5,6,8}}=>[3,2,2,1] {{1,7},{2,3},{4},{5,6,8}}=>[3,2,2,1] {{1,2},{3,7},{4,6,8},{5}}=>[3,2,2,1] {{1,2},{3,5,8},{4,7},{6}}=>[3,2,2,1] {{1,7},{2,3,8},{4,5},{6}}=>[3,2,2,1] {{1},{2,5},{3,4,8},{6,7}}=>[3,2,2,1] {{1,4,8},{2,3,7},{5},{6}}=>[3,3,1,1] {{1,2,4},{3,7,8},{5},{6}}=>[3,3,1,1] {{1,2,4,7},{3,8},{5},{6}}=>[4,2,1,1] {{1,4,7},{2,3,8},{5},{6}}=>[3,3,1,1] {{1,2},{3,5,7},{4,8},{6}}=>[3,2,2,1] {{1,4,6,7},{2,8},{3},{5}}=>[4,2,1,1] {{1,4,5,7},{2},{3,8},{6}}=>[4,2,1,1] {{1,3,5},{2,6},{4},{7,8}}=>[3,2,2,1] {{1,3,5},{2,7},{4,8},{6}}=>[3,2,2,1] {{1,3,6},{2,7,8},{4},{5}}=>[3,3,1,1] {{1,2,4,8},{3,6},{5},{7}}=>[4,2,1,1] {{1,4,8},{2,3,6},{5},{7}}=>[3,3,1,1] {{1,6},{2,5},{3,4,8},{7}}=>[3,2,2,1] {{1,6},{2,3,5},{4,8},{7}}=>[3,2,2,1] {{1,2,6},{3,5},{4,8},{7}}=>[3,2,2,1] {{1,2,8},{3,5},{4,7},{6}}=>[3,2,2,1] {{1,8},{2,3,5},{4,7},{6}}=>[3,2,2,1] {{1,8},{2,5},{3,4,7},{6}}=>[3,2,2,1] {{1,3,6},{2},{4,7},{5,8}}=>[3,2,2,1] {{1,3,5},{2},{4,7},{6,8}}=>[3,2,2,1] {{1,3,5,7},{2},{4,6},{8}}=>[4,2,1,1] {{1,4,7},{2,5},{3,6},{8}}=>[3,2,2,1] {{1,3,7},{2,5},{4,6},{8}}=>[3,2,2,1] {{1,3,5,7},{2,4},{6},{8}}=>[4,2,1,1] {{1,2},{3,4,6},{5,8},{7}}=>[3,2,2,1] {{1,2,4},{3,6},{5,8},{7}}=>[3,2,2,1] {{1,2,4},{3,6,8},{5},{7}}=>[3,3,1,1] {{1,2,4},{3,6},{5},{7,8}}=>[3,2,2,1] {{1,2,4,6},{3},{5,8},{7}}=>[4,2,1,1] {{1,3},{2,5,8},{4,7},{6}}=>[3,2,2,1] {{1,4},{2,6},{3,5,7},{8}}=>[3,2,2,1] {{1,3,7},{2,5,8},{4},{6}}=>[3,3,1,1] {{1,3,7},{2,6},{4},{5,8}}=>[3,2,2,1] {{1,3,7},{2,5},{4},{6,8}}=>[3,2,2,1] {{1,3},{2,4,7},{5},{6,8}}=>[3,2,2,1] {{1,4},{2,5,8},{3,7},{6}}=>[3,2,2,1] {{1,4},{2,5,7},{3},{6,8}}=>[3,2,2,1] {{1,3},{2,4,6},{5,8},{7}}=>[3,2,2,1] {{1,3,6},{2},{4,7},{5},{8}}=>[3,2,1,1,1] {{1,3},{2},{4,7},{5,8},{6}}=>[2,2,2,1,1] {{1,5},{2,6},{3,7},{4},{8}}=>[2,2,2,1,1] {{1},{2,6},{3,7},{4,8},{5}}=>[2,2,2,1,1] {{1,3,5,7},{2,4,6,8}}=>[4,4] {{1,3,4,7},{2,5,6,8}}=>[4,4] {{1},{2,6},{3,7},{4},{5},{8}}=>[2,2,1,1,1,1] {{1,2,5,6},{3,4,7,8}}=>[4,4] {{1,2,4,6},{3,5,7,8}}=>[4,4] {{1,5},{2},{3},{4,8},{6},{7}}=>[2,2,1,1,1,1] {{1,4},{2,6},{3,5,7,8}}=>[4,2,2] {{1,3,4,5,7},{2,6,8}}=>[5,3] {{1,3,6,7},{2,4,5,8}}=>[4,4] {{1,7},{2,4,5},{3,6,8}}=>[3,3,2] {{1,5},{2,3,7},{4,6,8}}=>[3,3,2] {{1,4,5,7},{2,8},{3,6}}=>[4,2,2] {{1,3},{2,4,5,6,7,8}}=>[6,2] {{1,4},{2,3,5,6,7,8}}=>[6,2] {{1,2,4},{3,5,6,7,8}}=>[5,3] {{1,2,4},{3,5,6},{7,8}}=>[3,3,2] {{1,5},{2,3,4,6,7,8}}=>[6,2] {{1,5},{2,3,4,6},{7,8}}=>[4,2,2] {{1,2,4,6,7},{3,8},{5}}=>[5,2,1] {{1,2,4,7,8},{3,6},{5}}=>[5,2,1] {{1,2,3,4,6,8},{5,7}}=>[6,2] {{1,2},{3,4,6,8},{5,7}}=>[4,2,2] {{1,3,5,6,7,8},{2,4}}=>[6,2] {{1,3,5,6},{2,4},{7,8}}=>[4,2,2] {{1,2,3,4,6},{5,7,8}}=>[5,3] {{1,3,4,6,7,8},{2,5}}=>[6,2] {{1,3,5,7},{2,6},{4,8}}=>[4,2,2] {{1,2,3,6},{4,5,7,8}}=>[4,4] {{1,2,3,5,6,8},{4,7}}=>[6,2] {{1,2,4,5,6,8},{3,7}}=>[6,2] {{1,5},{2,6},{3,4,7,8}}=>[4,2,2] {{1,5},{2,4,6,8},{3,7}}=>[4,2,2] {{1,4,5,8},{2,3,6,7}}=>[4,4] {{1,5,6},{2,3,4,7,8}}=>[5,3] {{1,5,7},{2,4,6,8},{3}}=>[4,3,1] {{1,5,6},{2,3,4,8},{7}}=>[4,3,1] {{1,6},{2,5},{3,4,7,8}}=>[4,2,2] {{1,3,5,7},{2,4,8},{6}}=>[4,3,1] {{1,5,6,7},{2},{3,4,8}}=>[4,3,1] {{1,2,4,5,7,8},{3,6}}=>[6,2] {{1,2,3,6},{4,5,8},{7}}=>[4,3,1] {{1,2,3,6,7},{4,5,8}}=>[5,3] {{1,2,3,7},{4,5,6,8}}=>[4,4] {{1,2,3,4,6},{5,8},{7}}=>[5,2,1] {{1,2,6},{3,4,5,8},{7}}=>[4,3,1] {{1,2,4,8},{3,5,6},{7}}=>[4,3,1] {{1,4,8},{2,3,5,6},{7}}=>[4,3,1] {{1,3,5,6},{2,4,8},{7}}=>[4,3,1] {{1,5},{2,3,4,8},{6,7}}=>[4,2,2] {{1,3,5},{2,4,8},{6,7}}=>[3,3,2] {{1,4,8},{2,3,5},{6,7}}=>[3,3,2] {{1,2,4,8},{3,5},{6,7}}=>[4,2,2] {{1,5,8},{2,3,4,6,7}}=>[5,3] {{1,3,4},{2,5,6,7,8}}=>[5,3] {{1,4,6,7},{2,3,8},{5}}=>[4,3,1] {{1,3,8},{2,4,6,7},{5}}=>[4,3,1] {{1,3,5},{2,8},{4,6,7}}=>[3,3,2] {{1,4,7,8},{2,3,6},{5}}=>[4,3,1] {{1,2,3,6,8},{4,5,7}}=>[5,3] {{1,2,5,6,8},{3,4,7}}=>[5,3] {{1,2,6,8},{3,4,5,7}}=>[4,4] {{1,6},{2,3,5},{4,7,8}}=>[3,3,2] {{1,2,6},{3,5},{4,7,8}}=>[3,3,2] {{1,2,5},{3,6},{4,7,8}}=>[3,3,2] {{1,5},{2,3,6},{4,7,8}}=>[3,3,2] {{1,4,7,8},{2,6},{3,5}}=>[4,2,2] {{1,2,7,8},{3,5},{4,6}}=>[4,2,2] {{1,7,8},{2,3,5},{4,6}}=>[3,3,2] {{1,7,8},{2,5},{3,4,6}}=>[3,3,2] {{1,7,8},{2,4,6},{3,5}}=>[3,3,2] {{1,3,6,8},{2,4,5,7}}=>[4,4] {{1,4,8},{2,3,5,7},{6}}=>[4,3,1] {{1,4,6,7,8},{2,3,5}}=>[5,3] {{1,2,4,6,7,8},{3,5}}=>[6,2] {{1,3,6,7,8},{2,4,5}}=>[5,3] {{1,6},{2,3,4,5,7,8}}=>[6,2] {{1,2,3,5,6},{4,7,8}}=>[5,3] {{1,3,5},{2,6},{4,7,8}}=>[3,3,2] {{1,4,5,7,8},{2,3,6}}=>[5,3] {{1,3,5,7,8},{2,4,6}}=>[5,3] {{1,3,7},{2,4,5,8},{6}}=>[4,3,1] {{1,2,4,5,6,7},{3,8}}=>[6,2] {{1,2,5,8},{3,4,6,7}}=>[4,4] {{1,2,5,8},{3,4,6},{7}}=>[4,3,1] {{1,3},{2,4,5,6,8},{7}}=>[5,2,1] {{1,6,7},{2,3,4,5,8}}=>[5,3] {{1,7},{2,3,4},{5,6,8}}=>[3,3,2] {{1,2,3,4,7},{5,6,8}}=>[5,3] {{1,4,5},{2,3,7,8},{6}}=>[4,3,1] {{1,2,4,5},{3,7,8},{6}}=>[4,3,1] {{1,5,7,8},{2,3,4,6}}=>[4,4] {{1,4,6,8},{2,3,5,7}}=>[4,4] {{1,3,4,7,8},{2,5,6}}=>[5,3] {{1,2,4,7},{3,6,8},{5}}=>[4,3,1] {{1,4,8},{2,3,6,7},{5}}=>[4,3,1] {{1,3,7},{2,4,8},{5,6}}=>[3,3,2] {{1,3,7},{2,6},{4,5,8}}=>[3,3,2] {{1,2,6},{3,7},{4,5,8}}=>[3,3,2] {{1,2,5},{3,4,8},{6,7}}=>[3,3,2] {{1,2},{3,4,6},{5,7,8}}=>[3,3,2] {{1,2,3},{4,7},{5,6,8}}=>[3,3,2] {{1,2,3,5,8},{4,6,7}}=>[5,3] {{1,2,6},{3,4,5,7,8}}=>[5,3] {{1,2,5,7,8},{3,4,6}}=>[5,3] {{1,2,5,8},{3,6,7},{4}}=>[4,3,1] {{1},{2,3,5,8},{4,6,7}}=>[4,3,1] {{1,5},{2,6,7,8},{3,4}}=>[4,2,2] {{1,2,4,6,8},{3,5,7}}=>[5,3] {{1,7},{2,6,8},{3,4,5}}=>[3,3,2] {{1,2,6},{3,5,7,8},{4}}=>[4,3,1] {{1},{2,3,6},{4,5,7,8}}=>[4,3,1] {{1,7,8},{2,4},{3,5,6}}=>[3,3,2] {{1,3,5},{2},{4,6},{7},{8}}=>[3,2,1,1,1] {{1,3},{2,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1] {{1,3,7},{2},{4},{5},{6,8}}=>[3,2,1,1,1] {{1,3,6},{2},{4},{5,8},{7}}=>[3,2,1,1,1] {{1},{2},{3},{4,7},{5,8},{6}}=>[2,2,1,1,1,1] {{1},{2},{3,7},{4,8},{5},{6}}=>[2,2,1,1,1,1] {{1,4},{2,5},{3},{6},{7},{8}}=>[2,2,1,1,1,1] {{1,3,7},{2,4},{5},{6},{8}}=>[3,2,1,1,1] {{1,7},{2},{3},{4},{5},{6,8}}=>[2,2,1,1,1,1] {{1,6},{2},{3},{4},{5,8},{7}}=>[2,2,1,1,1,1] {{1,4,7},{2,5},{3},{6},{8}}=>[3,2,1,1,1] {{1,4},{2,6},{3},{5,8},{7}}=>[2,2,2,1,1] {{1,5},{2,6},{3},{4,8},{7}}=>[2,2,2,1,1] {{1,5},{2,6},{3},{4},{7},{8}}=>[2,2,1,1,1,1] {{1,3},{2,6},{4,7},{5},{8}}=>[2,2,2,1,1] {{1,4},{2,5},{3,6},{7},{8}}=>[2,2,2,1,1] {{1,3},{2,5},{4,6},{7},{8}}=>[2,2,2,1,1] {{1,3,5},{2,4},{6},{7},{8}}=>[3,2,1,1,1] {{1,5,7},{2},{3},{4},{6,8}}=>[3,2,1,1,1] {{1,5},{2},{3},{4,6},{7},{8}}=>[2,2,1,1,1,1] {{1,4},{2},{3,6},{5},{7},{8}}=>[2,2,1,1,1,1] {{1},{2,5},{3,6},{4},{7},{8}}=>[2,2,1,1,1,1] {{1,4,6},{2},{3,5,7},{8}}=>[3,3,1,1] {{1,6},{2},{3},{4,7},{5},{8}}=>[2,2,1,1,1,1] {{1,6},{2},{3},{4,7},{5,8}}=>[2,2,2,1,1] {{1,5},{2},{3},{4,7},{6,8}}=>[2,2,2,1,1] {{1,5,7},{2},{3},{4,6},{8}}=>[3,2,1,1,1] {{1,4,7},{2},{3,6},{5},{8}}=>[3,2,1,1,1] {{1,4},{2},{3,7},{5},{6,8}}=>[2,2,2,1,1] {{1,5},{2},{3,7},{4,8},{6}}=>[2,2,2,1,1] {{1,5},{2},{3,7},{4},{6},{8}}=>[2,2,1,1,1,1] {{1,7},{2,5},{3,6},{4},{8}}=>[2,2,2,1,1] {{1},{2,6},{3},{4,8},{5},{7}}=>[2,2,1,1,1,1] {{1,2,4,5,6},{3,7,8}}=>[5,3] {{1,4,6},{2,3,5,7,8}}=>[5,3] {{1,4,6},{2,5,7},{3,8}}=>[3,3,2] {{1,3,4,6,8},{2,5,7}}=>[5,3] {{1,8},{2,3,4,6},{5,7}}=>[4,2,2] {{1,7},{2,3},{4,5,6,8}}=>[4,2,2] {{1,7},{2,3,5,6},{4,8}}=>[4,2,2] {{1,4,7,8},{2,3,5,6}}=>[4,4] {{1,5,7,8},{2,3},{4,6}}=>[4,2,2] {{1,5,6,8},{2,3},{4,7}}=>[4,2,2] {{1,2,3,5,7,8},{4,6}}=>[6,2] {{1,2,5},{3,4,6},{7,8}}=>[3,3,2] {{1,4,6},{2,3,5},{7,8}}=>[3,3,2] {{1,4,8},{2,3,7},{5,6}}=>[3,3,2] {{1,3,5,8},{2,4},{6,7}}=>[4,2,2] {{1,2},{3,4,7},{5,6,8}}=>[3,3,2] {{1,4,7},{2,3},{5,6,8}}=>[3,3,2] {{1,3,7},{2,4},{5,6,8}}=>[3,3,2] {{1,3,7},{2,6,8},{4,5}}=>[3,3,2] {{1,7},{2,3,5,8},{4,6}}=>[4,2,2] {{1,2,6},{3,8},{4,5,7}}=>[3,3,2] {{1,2,8},{3,4,6},{5,7}}=>[3,3,2] {{1,2,5},{3,4,6,7,8}}=>[5,3] {{1,2},{3,5,7,8},{4,6}}=>[4,2,2] {{1,5,7,8},{2,6},{3,4}}=>[4,2,2] {{1,5,8},{2,7},{3,4,6}}=>[3,3,2] {{1,2},{3,6,8},{4,5,7}}=>[3,3,2] {{1,6,8},{2,3},{4,5,7}}=>[3,3,2] {{1,6,8},{2,5,7},{3,4}}=>[3,3,2] {{1,6,8},{2,4,7},{3,5}}=>[3,3,2] {{1,3,4},{2,5,6},{7,8}}=>[3,3,2] {{1,3,4},{2,5,8},{6,7}}=>[3,3,2] {{1,3,4},{2,8},{5,6,7}}=>[3,3,2] {{1,3,6,7},{2,8},{4,5}}=>[4,2,2] {{1,8},{2,3,6},{4,5,7}}=>[3,3,2] {{1,2,7},{3,4,5,6,8}}=>[5,3] {{1,2},{3,5,6},{4,7,8}}=>[3,3,2] {{1,5,6},{2,3},{4,7,8}}=>[3,3,2] {{1,5,6},{2,7,8},{3,4}}=>[3,3,2] {{1,4,5},{2,7,8},{3,6}}=>[3,3,2] {{1,7},{2,6},{3,4,5,8}}=>[4,2,2] {{1,2},{3,7},{4,5,6,8}}=>[4,2,2] {{1,7},{2,5,6,8},{3,4}}=>[4,2,2] {{1,2,4,6},{3,5},{7,8}}=>[4,2,2] {{1,4,6,7,8},{2},{3,5}}=>[5,2,1] {{1,4,5},{2,3,6,7,8}}=>[5,3] {{1,4,5},{2,3,6},{7,8}}=>[3,3,2] {{1,4,5},{2,3,8},{6,7}}=>[3,3,2] {{1,4,7},{2,3,8},{5,6}}=>[3,3,2] {{1,3,4},{2,7},{5,6,8}}=>[3,3,2] {{1,3,6,8},{2,7},{4,5}}=>[4,2,2] {{1,2},{3,6,7},{4,5,8}}=>[3,3,2] {{1,6,7},{2,3},{4,5,8}}=>[3,3,2] {{1,6,7},{2,5,8},{3,4}}=>[3,3,2] {{1,5,6},{2,8},{3,4,7}}=>[3,3,2] {{1,6,7},{2,4,5},{3,8}}=>[3,3,2] {{1,2,4},{3,6,7,8},{5}}=>[4,3,1] {{1,2,4},{3,5,6,8},{7}}=>[4,3,1] {{1,2,4,7,8},{3,5,6}}=>[5,3] {{1,2,4},{3,6},{5,7,8}}=>[3,3,2] {{1,2,4,6},{3},{5,7,8}}=>[4,3,1] {{1,4,6},{2,3,5,8},{7}}=>[4,3,1] {{1,4,6},{2,3,8},{5,7}}=>[3,3,2] {{1,6},{2,3,5,8},{4,7}}=>[4,2,2] {{1,3,5},{2,7,8},{4,6}}=>[3,3,2] {{1,3,4},{2,6,8},{5,7}}=>[3,3,2] {{1,3,4},{2,5,7,8},{6}}=>[4,3,1] {{1,3,6},{2,7},{4,5,8}}=>[3,3,2] {{1,4,5,6},{2},{3,7,8}}=>[4,3,1] {{1,3,5,6},{2,4,7,8}}=>[4,4] {{1,2,3,5,7},{4,8},{6}}=>[5,2,1] {{1,2,4,7},{3,5,8},{6}}=>[4,3,1] {{1,2,5,7,8},{3},{4,6}}=>[5,2,1] {{1,2,5,7},{3,4,6,8}}=>[4,4] {{1,3,6,7,8},{2,4},{5}}=>[5,2,1] {{1,3,6,8},{2,5,7},{4}}=>[4,3,1] {{1,2,6,8},{3},{4,5,7}}=>[4,3,1] {{1,2,6,8},{3,5,7},{4}}=>[4,3,1] {{1,2,4},{3,5,8},{6,7}}=>[3,3,2] {{1,2,6,8},{3,5},{4,7}}=>[4,2,2] {{1,2,3,5,6},{4,8},{7}}=>[5,2,1] {{1,4,6,8},{2,3,5},{7}}=>[4,3,1]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
Properties
surjective, graded
Sage code
def mapping(elt):
    return elt.shape()
Weight
26
Created
Jan 26, 2020 at 12:32 by FindStatCrew
Updated
Jan 26, 2020 at 12:32 by Martin Rubey