Identifier
Mp00079:
Set partitions
—shape⟶
Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Images
=>
Cc0009;cc-rep-0Cc0002;cc-rep-1Cc0007;cc-rep-2
{{1}}=>[1]=>[[1]]=>[1]
{{1,2}}=>[2]=>[[1,2]]=>[2]
{{1},{2}}=>[1,1]=>[[1],[2]]=>[1,1]
{{1,2,3}}=>[3]=>[[1,2,3]]=>[3]
{{1,2},{3}}=>[2,1]=>[[1,3],[2]]=>[1,2]
{{1,3},{2}}=>[2,1]=>[[1,3],[2]]=>[1,2]
{{1},{2,3}}=>[2,1]=>[[1,3],[2]]=>[1,2]
{{1},{2},{3}}=>[1,1,1]=>[[1],[2],[3]]=>[1,1,1]
{{1,2,3,4}}=>[4]=>[[1,2,3,4]]=>[4]
{{1,2,3},{4}}=>[3,1]=>[[1,3,4],[2]]=>[1,3]
{{1,2,4},{3}}=>[3,1]=>[[1,3,4],[2]]=>[1,3]
{{1,2},{3,4}}=>[2,2]=>[[1,2],[3,4]]=>[2,2]
{{1,2},{3},{4}}=>[2,1,1]=>[[1,4],[2],[3]]=>[1,1,2]
{{1,3,4},{2}}=>[3,1]=>[[1,3,4],[2]]=>[1,3]
{{1,3},{2,4}}=>[2,2]=>[[1,2],[3,4]]=>[2,2]
{{1,3},{2},{4}}=>[2,1,1]=>[[1,4],[2],[3]]=>[1,1,2]
{{1,4},{2,3}}=>[2,2]=>[[1,2],[3,4]]=>[2,2]
{{1},{2,3,4}}=>[3,1]=>[[1,3,4],[2]]=>[1,3]
{{1},{2,3},{4}}=>[2,1,1]=>[[1,4],[2],[3]]=>[1,1,2]
{{1,4},{2},{3}}=>[2,1,1]=>[[1,4],[2],[3]]=>[1,1,2]
{{1},{2,4},{3}}=>[2,1,1]=>[[1,4],[2],[3]]=>[1,1,2]
{{1},{2},{3,4}}=>[2,1,1]=>[[1,4],[2],[3]]=>[1,1,2]
{{1},{2},{3},{4}}=>[1,1,1,1]=>[[1],[2],[3],[4]]=>[1,1,1,1]
{{1,2,3,4,5}}=>[5]=>[[1,2,3,4,5]]=>[5]
{{1,2,3,4},{5}}=>[4,1]=>[[1,3,4,5],[2]]=>[1,4]
{{1,2,3,5},{4}}=>[4,1]=>[[1,3,4,5],[2]]=>[1,4]
{{1,2,3},{4,5}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,2,3},{4},{5}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1,2,4,5},{3}}=>[4,1]=>[[1,3,4,5],[2]]=>[1,4]
{{1,2,4},{3,5}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,2,4},{3},{5}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1,2,5},{3,4}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,2},{3,4,5}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,2},{3,4},{5}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,2,5},{3},{4}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1,2},{3,5},{4}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,2},{3},{4,5}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,2},{3},{4},{5}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1,3,4,5},{2}}=>[4,1]=>[[1,3,4,5],[2]]=>[1,4]
{{1,3,4},{2,5}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,3,4},{2},{5}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1,3,5},{2,4}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,3},{2,4,5}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,3},{2,4},{5}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,3,5},{2},{4}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1,3},{2,5},{4}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,3},{2},{4,5}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,3},{2},{4},{5}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1,4,5},{2,3}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,4},{2,3,5}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1,4},{2,3},{5}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,5},{2,3,4}}=>[3,2]=>[[1,2,5],[3,4]]=>[2,3]
{{1},{2,3,4,5}}=>[4,1]=>[[1,3,4,5],[2]]=>[1,4]
{{1},{2,3,4},{5}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1,5},{2,3},{4}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1},{2,3,5},{4}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1},{2,3},{4,5}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1},{2,3},{4},{5}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1,4,5},{2},{3}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1,4},{2,5},{3}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,4},{2},{3,5}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1,4},{2},{3},{5}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1,5},{2,4},{3}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1},{2,4,5},{3}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1},{2,4},{3,5}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1},{2,4},{3},{5}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1,5},{2},{3,4}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1},{2,5},{3,4}}=>[2,2,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
{{1},{2},{3,4,5}}=>[3,1,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
{{1},{2},{3,4},{5}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1,5},{2},{3},{4}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1},{2,5},{3},{4}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1},{2},{3,5},{4}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1},{2},{3},{4,5}}=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
{{1},{2},{3},{4},{5}}=>[1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[1,1,1,1,1]
{{1,2,3,4,5,6}}=>[6]=>[[1,2,3,4,5,6]]=>[6]
{{1,2,3,4,5},{6}}=>[5,1]=>[[1,3,4,5,6],[2]]=>[1,5]
{{1,2,3,4,6},{5}}=>[5,1]=>[[1,3,4,5,6],[2]]=>[1,5]
{{1,2,3,4},{5,6}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,2,3,4},{5},{6}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,2,3,5,6},{4}}=>[5,1]=>[[1,3,4,5,6],[2]]=>[1,5]
{{1,2,3,5},{4,6}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,2,3,5},{4},{6}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,2,3,6},{4,5}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,2,3},{4,5,6}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,2,3},{4,5},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,3,6},{4},{5}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,2,3},{4,6},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,3},{4},{5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,3},{4},{5},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,2,4,5,6},{3}}=>[5,1]=>[[1,3,4,5,6],[2]]=>[1,5]
{{1,2,4,5},{3,6}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,2,4,5},{3},{6}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,2,4,6},{3,5}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,2,4},{3,5,6}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,2,4},{3,5},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,4,6},{3},{5}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,2,4},{3,6},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,4},{3},{5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,4},{3},{5},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,2,5,6},{3,4}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,2,5},{3,4,6}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,2,5},{3,4},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,6},{3,4,5}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,2},{3,4,5,6}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,2},{3,4,5},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,6},{3,4},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2},{3,4,6},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2},{3,4},{5,6}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,2},{3,4},{5},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,2,5,6},{3},{4}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,2,5},{3,6},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,5},{3},{4,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2,5},{3},{4},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,2,6},{3,5},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2},{3,5,6},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2},{3,5},{4,6}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,2},{3,5},{4},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,2,6},{3},{4,5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2},{3,6},{4,5}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,2},{3},{4,5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,2},{3},{4,5},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,2,6},{3},{4},{5}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,2},{3,6},{4},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,2},{3},{4,6},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,2},{3},{4},{5,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,2},{3},{4},{5},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,3,4,5,6},{2}}=>[5,1]=>[[1,3,4,5,6],[2]]=>[1,5]
{{1,3,4,5},{2,6}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,3,4,5},{2},{6}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,3,4,6},{2,5}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,3,4},{2,5,6}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,3,4},{2,5},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3,4,6},{2},{5}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,3,4},{2,6},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3,4},{2},{5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3,4},{2},{5},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,3,5,6},{2,4}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,3,5},{2,4,6}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,3,5},{2,4},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3,6},{2,4,5}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,3},{2,4,5,6}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,3},{2,4,5},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3,6},{2,4},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3},{2,4,6},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3},{2,4},{5,6}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,3},{2,4},{5},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,3,5,6},{2},{4}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,3,5},{2,6},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3,5},{2},{4,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3,5},{2},{4},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,3,6},{2,5},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3},{2,5,6},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3},{2,5},{4,6}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,3},{2,5},{4},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,3,6},{2},{4,5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3},{2,6},{4,5}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,3},{2},{4,5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,3},{2},{4,5},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,3,6},{2},{4},{5}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,3},{2,6},{4},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,3},{2},{4,6},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,3},{2},{4},{5,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,3},{2},{4},{5},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,4,5,6},{2,3}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,4,5},{2,3,6}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,4,5},{2,3},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4,6},{2,3,5}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,4},{2,3,5,6}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,4},{2,3,5},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4,6},{2,3},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4},{2,3,6},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4},{2,3},{5,6}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,4},{2,3},{5},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,5,6},{2,3,4}}=>[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]
{{1,5},{2,3,4,6}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1,5},{2,3,4},{6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,6},{2,3,4,5}}=>[4,2]=>[[1,2,5,6],[3,4]]=>[2,4]
{{1},{2,3,4,5,6}}=>[5,1]=>[[1,3,4,5,6],[2]]=>[1,5]
{{1},{2,3,4,5},{6}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,6},{2,3,4},{5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,3,4,6},{5}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1},{2,3,4},{5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,3,4},{5},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,5,6},{2,3},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,5},{2,3,6},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,5},{2,3},{4,6}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,5},{2,3},{4},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,6},{2,3,5},{4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,3,5,6},{4}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1},{2,3,5},{4,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,3,5},{4},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,6},{2,3},{4,5}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1},{2,3,6},{4,5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,3},{4,5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,3},{4,5},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,6},{2,3},{4},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,3,6},{4},{5}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1},{2,3},{4,6},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,3},{4},{5,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,3},{4},{5},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,4,5,6},{2},{3}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1,4,5},{2,6},{3}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4,5},{2},{3,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4,5},{2},{3},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,4,6},{2,5},{3}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4},{2,5,6},{3}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4},{2,5},{3,6}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,4},{2,5},{3},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,4,6},{2},{3,5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4},{2,6},{3,5}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,4},{2},{3,5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,4},{2},{3,5},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,4,6},{2},{3},{5}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,4},{2,6},{3},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,4},{2},{3,6},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,4},{2},{3},{5,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,4},{2},{3},{5},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,5,6},{2,4},{3}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,5},{2,4,6},{3}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,5},{2,4},{3,6}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,5},{2,4},{3},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,6},{2,4,5},{3}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,4,5,6},{3}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1},{2,4,5},{3,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,4,5},{3},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,6},{2,4},{3,5}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1},{2,4,6},{3,5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,4},{3,5,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,4},{3,5},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,6},{2,4},{3},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,4,6},{3},{5}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1},{2,4},{3,6},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,4},{3},{5,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,4},{3},{5},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,5,6},{2},{3,4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,5},{2,6},{3,4}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1,5},{2},{3,4,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1,5},{2},{3,4},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,6},{2,5},{3,4}}=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
{{1},{2,5,6},{3,4}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,5},{3,4,6}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,5},{3,4},{6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,6},{2},{3,4,5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2,6},{3,4,5}}=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
{{1},{2},{3,4,5,6}}=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
{{1},{2},{3,4,5},{6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,6},{2},{3,4},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,6},{3,4},{5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2},{3,4,6},{5}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1},{2},{3,4},{5,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2},{3,4},{5},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,5,6},{2},{3},{4}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1,5},{2,6},{3},{4}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,5},{2},{3,6},{4}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,5},{2},{3},{4,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1,5},{2},{3},{4},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,6},{2,5},{3},{4}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,5,6},{3},{4}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1},{2,5},{3,6},{4}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,5},{3},{4,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,5},{3},{4},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,6},{2},{3,5},{4}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,6},{3,5},{4}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2},{3,5,6},{4}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1},{2},{3,5},{4,6}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2},{3,5},{4},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,6},{2},{3},{4,5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2,6},{3},{4,5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2},{3,6},{4,5}}=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
{{1},{2},{3},{4,5,6}}=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
{{1},{2},{3},{4,5},{6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1,6},{2},{3},{4},{5}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1},{2,6},{3},{4},{5}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1},{2},{3,6},{4},{5}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1},{2},{3},{4,6},{5}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1},{2},{3},{4},{5,6}}=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
{{1},{2},{3},{4},{5},{6}}=>[1,1,1,1,1,1]=>[[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]]=>[7]
{{1,2,3,4,5,6},{7}}=>[6,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
{{1,2,3,4,5,7},{6}}=>[6,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
{{1,2,3,4,5},{6,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,3,4,5},{6},{7}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,3,4,6,7},{5}}=>[6,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
{{1,2,3,4,6},{5,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,3,4,6},{5},{7}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,3,4,7},{5,6}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,3,4},{5,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,3,4},{5,6},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,4,7},{5},{6}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,3,4},{5,7},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,4},{5},{6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,4},{5},{6},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,3,5,6,7},{4}}=>[6,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
{{1,2,3,5,6},{4,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,3,5,6},{4},{7}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,3,5,7},{4,6}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,3,5},{4,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,3,5},{4,6},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,5,7},{4},{6}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,3,5},{4,7},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,5},{4},{6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,5},{4},{6},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,3,6,7},{4,5}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,3,6},{4,5,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,3,6},{4,5},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,7},{4,5,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,3},{4,5,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,3},{4,5,6},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,3,7},{4,5},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3},{4,5,7},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,3},{4,5},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,3},{4,5},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,3,6,7},{4},{5}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,3,6},{4,7},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,6},{4},{5,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3,6},{4},{5},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,3,7},{4,6},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3},{4,6,7},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,3},{4,6},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,3},{4,6},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,3,7},{4},{5,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,3},{4,7},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,3},{4},{5,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,3},{4},{5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,3,7},{4},{5},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,3},{4,7},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,3},{4},{5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,3},{4},{5},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,3},{4},{5},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,2,4,5,6,7},{3}}=>[6,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
{{1,2,4,5,6},{3,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,4,5,6},{3},{7}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,4,5,7},{3,6}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,4,5},{3,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,4,5},{3,6},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4,5,7},{3},{6}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,4,5},{3,7},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4,5},{3},{6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4,5},{3},{6},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,4,6,7},{3,5}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,4,6},{3,5,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,4,6},{3,5},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4,7},{3,5,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,4},{3,5,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,4},{3,5,6},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,4,7},{3,5},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4},{3,5,7},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,4},{3,5},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,4},{3,5},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,4,6,7},{3},{5}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,4,6},{3,7},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4,6},{3},{5,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4,6},{3},{5},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,4,7},{3,6},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4},{3,6,7},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,4},{3,6},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,4},{3,6},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,4,7},{3},{5,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,4},{3,7},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,4},{3},{5,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,4},{3},{5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,4,7},{3},{5},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,4},{3,7},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,4},{3},{5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,4},{3},{5},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,4},{3},{5},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,2,5,6,7},{3,4}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2,5,6},{3,4,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,5,6},{3,4},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,5,7},{3,4,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,5},{3,4,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,5},{3,4,6},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,5,7},{3,4},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,5},{3,4,7},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,5},{3,4},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,5},{3,4},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,6,7},{3,4,5}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,6},{3,4,5,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2,6},{3,4,5},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,7},{3,4,5,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,2},{3,4,5,6,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,2},{3,4,5,6},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,7},{3,4,5},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2},{3,4,5,7},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2},{3,4,5},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,4,5},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,6,7},{3,4},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,6},{3,4,7},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,6},{3,4},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,6},{3,4},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,7},{3,4,6},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2},{3,4,6,7},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2},{3,4,6},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,4,6},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,7},{3,4},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,4,7},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,4},{5,6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,4},{5,6},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2,7},{3,4},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,4,7},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,4},{5,7},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3,4},{5},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3,4},{5},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2,5,6,7},{3},{4}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,2,5,6},{3,7},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,5,6},{3},{4,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,5,6},{3},{4},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,5,7},{3,6},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,5},{3,6,7},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,5},{3,6},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,5},{3,6},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,5,7},{3},{4,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,5},{3,7},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,5},{3},{4,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,5},{3},{4,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,5,7},{3},{4},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,5},{3,7},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,5},{3},{4,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,5},{3},{4},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,5},{3},{4},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,2,6,7},{3,5},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,6},{3,5,7},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,6},{3,5},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,6},{3,5},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,7},{3,5,6},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2},{3,5,6,7},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2},{3,5,6},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,5,6},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,7},{3,5},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,5,7},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,5},{4,6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,5},{4,6},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2,7},{3,5},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,5,7},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,5},{4,7},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3,5},{4},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3,5},{4},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2,6,7},{3},{4,5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2,6},{3,7},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2,6},{3},{4,5,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2,6},{3},{4,5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,7},{3,6},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,6,7},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,6},{4,5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3,6},{4,5},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2,7},{3},{4,5,6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,2},{3,7},{4,5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,2},{3},{4,5,6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,2},{3},{4,5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,7},{3},{4,5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,7},{4,5},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3},{4,5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3},{4,5},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3},{4,5},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2,6,7},{3},{4},{5}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,2,6},{3,7},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,6},{3},{4,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,6},{3},{4},{5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2,6},{3},{4},{5},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,2,7},{3,6},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,6,7},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,6},{4,7},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3,6},{4},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3,6},{4},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2,7},{3},{4,6},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,7},{4,6},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3},{4,6,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3},{4,6},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3},{4,6},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2,7},{3},{4},{5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3,7},{4},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3},{4,7},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,2},{3},{4},{5,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,2},{3},{4},{5,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2,7},{3},{4},{5},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,2},{3,7},{4},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2},{3},{4,7},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2},{3},{4},{5,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2},{3},{4},{5},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,2},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,3,4,5,6,7},{2}}=>[6,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
{{1,3,4,5,6},{2,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,3,4,5,6},{2},{7}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,3,4,5,7},{2,6}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,3,4,5},{2,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,4,5},{2,6},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4,5,7},{2},{6}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,3,4,5},{2,7},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4,5},{2},{6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4,5},{2},{6},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,3,4,6,7},{2,5}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,3,4,6},{2,5,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,4,6},{2,5},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4,7},{2,5,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,4},{2,5,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,4},{2,5,6},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,4,7},{2,5},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4},{2,5,7},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,4},{2,5},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,4},{2,5},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,4,6,7},{2},{5}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,3,4,6},{2,7},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4,6},{2},{5,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4,6},{2},{5},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,3,4,7},{2,6},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4},{2,6,7},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,4},{2,6},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,4},{2,6},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,4,7},{2},{5,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,4},{2,7},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,4},{2},{5,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,4},{2},{5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,4,7},{2},{5},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,3,4},{2,7},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,4},{2},{5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,4},{2},{5},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,4},{2},{5},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,3,5,6,7},{2,4}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,3,5,6},{2,4,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,5,6},{2,4},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,5,7},{2,4,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,5},{2,4,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,5},{2,4,6},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,5,7},{2,4},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,5},{2,4,7},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,5},{2,4},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,5},{2,4},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,6,7},{2,4,5}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,6},{2,4,5,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3,6},{2,4,5},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,7},{2,4,5,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,3},{2,4,5,6,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,3},{2,4,5,6},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,7},{2,4,5},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3},{2,4,5,7},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3},{2,4,5},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,4,5},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,6,7},{2,4},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,6},{2,4,7},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,6},{2,4},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,6},{2,4},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,7},{2,4,6},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3},{2,4,6,7},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3},{2,4,6},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,4,6},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,7},{2,4},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,4,7},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,4},{5,6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,4},{5,6},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3,7},{2,4},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,4,7},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,4},{5,7},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2,4},{5},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2,4},{5},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3,5,6,7},{2},{4}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,3,5,6},{2,7},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,5,6},{2},{4,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,5,6},{2},{4},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,3,5,7},{2,6},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,5},{2,6,7},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,5},{2,6},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,5},{2,6},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,5,7},{2},{4,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,5},{2,7},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,5},{2},{4,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,5},{2},{4,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,5,7},{2},{4},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,3,5},{2,7},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,5},{2},{4,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,5},{2},{4},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,5},{2},{4},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,3,6,7},{2,5},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,6},{2,5,7},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,6},{2,5},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,6},{2,5},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,7},{2,5,6},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3},{2,5,6,7},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3},{2,5,6},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,5,6},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,7},{2,5},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,5,7},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,5},{4,6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,5},{4,6},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3,7},{2,5},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,5,7},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,5},{4,7},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2,5},{4},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2,5},{4},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3,6,7},{2},{4,5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3,6},{2,7},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3,6},{2},{4,5,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3,6},{2},{4,5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,7},{2,6},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,6,7},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,6},{4,5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2,6},{4,5},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3,7},{2},{4,5,6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,3},{2,7},{4,5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,3},{2},{4,5,6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,3},{2},{4,5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,7},{2},{4,5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,7},{4,5},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2},{4,5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2},{4,5},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2},{4,5},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3,6,7},{2},{4},{5}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,3,6},{2,7},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,6},{2},{4,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,6},{2},{4},{5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3,6},{2},{4},{5},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,3,7},{2,6},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,6,7},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,6},{4,7},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2,6},{4},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2,6},{4},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3,7},{2},{4,6},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,7},{4,6},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2},{4,6,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2},{4,6},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2},{4,6},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3,7},{2},{4},{5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2,7},{4},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2},{4,7},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,3},{2},{4},{5,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,3},{2},{4},{5,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3,7},{2},{4},{5},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,3},{2,7},{4},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3},{2},{4,7},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3},{2},{4},{5,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3},{2},{4},{5},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,3},{2},{4},{5},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,4,5,6,7},{2,3}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,4,5,6},{2,3,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,4,5,6},{2,3},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,5,7},{2,3,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,4,5},{2,3,6,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,4,5},{2,3,6},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4,5,7},{2,3},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,5},{2,3,7},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4,5},{2,3},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4,5},{2,3},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,6,7},{2,3,5}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,4,6},{2,3,5,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,4,6},{2,3,5},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4,7},{2,3,5,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,4},{2,3,5,6,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,4},{2,3,5,6},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,7},{2,3,5},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4},{2,3,5,7},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4},{2,3,5},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,3,5},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,6,7},{2,3},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,6},{2,3,7},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4,6},{2,3},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4,6},{2,3},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,7},{2,3,6},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4},{2,3,6,7},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4},{2,3,6},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,3,6},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,7},{2,3},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,3,7},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,3},{5,6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,3},{5,6},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4,7},{2,3},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,3,7},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,3},{5,7},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2,3},{5},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2,3},{5},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,5,6,7},{2,3,4}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,5,6},{2,3,4,7}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,5,6},{2,3,4},{7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,5,7},{2,3,4,6}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,5},{2,3,4,6,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,5},{2,3,4,6},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,5,7},{2,3,4},{6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,5},{2,3,4,7},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,5},{2,3,4},{6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,3,4},{6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6,7},{2,3,4,5}}=>[4,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
{{1,6},{2,3,4,5,7}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1,6},{2,3,4,5},{7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,7},{2,3,4,5,6}}=>[5,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
{{1},{2,3,4,5,6,7}}=>[6,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
{{1},{2,3,4,5,6},{7}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,7},{2,3,4,5},{6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,4,5,7},{6}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1},{2,3,4,5},{6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,4,5},{6},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,6,7},{2,3,4},{5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,6},{2,3,4,7},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,6},{2,3,4},{5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,3,4},{5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,3,4,6},{5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,4,6,7},{5}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1},{2,3,4,6},{5,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,4,6},{5},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,7},{2,3,4},{5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,3,4,7},{5,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,4},{5,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,3,4},{5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,3,4},{5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,4,7},{5},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2,3,4},{5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,4},{5},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,4},{5},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,5,6,7},{2,3},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,5,6},{2,3,7},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,5,6},{2,3},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5,6},{2,3},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,7},{2,3,6},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,5},{2,3,6,7},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,5},{2,3,6},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,3,6},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,7},{2,3},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,3,7},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,3},{4,6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,3},{4,6},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5,7},{2,3},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,3,7},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,3},{4,7},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2,3},{4},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2,3},{4},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6,7},{2,3,5},{4}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,6},{2,3,5,7},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,6},{2,3,5},{4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,3,5},{4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,3,5,6},{4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,5,6,7},{4}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1},{2,3,5,6},{4,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,5,6},{4},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,7},{2,3,5},{4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,3,5,7},{4,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,5},{4,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,3,5},{4,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,3,5},{4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,5,7},{4},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2,3,5},{4,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,5},{4},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,5},{4},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,6,7},{2,3},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,3,7},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,3},{4,5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,3},{4,5},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,7},{2,3,6},{4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,3,6,7},{4,5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3,6},{4,5,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,3,6},{4,5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,3},{4,5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,3,7},{4,5,6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,3},{4,5,6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,3},{4,5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,3},{4,5},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,3,7},{4,5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3},{4,5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3},{4,5},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,3},{4,5},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6,7},{2,3},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,3,7},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,3},{4,7},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2,3},{4},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2,3},{4},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,3,6},{4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,6,7},{4},{5}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2,3,6},{4,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,6},{4},{5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3,6},{4},{5},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,7},{2,3},{4,6},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,3,7},{4,6},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3},{4,6,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3},{4,6},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,3},{4,6},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,3},{4},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,3,7},{4},{5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3},{4,7},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,3},{4},{5,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,3},{4},{5,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,3},{4},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,3,7},{4},{5},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2,3},{4,7},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,3},{4},{5,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,3},{4},{5},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,3},{4},{5},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,4,5,6,7},{2},{3}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1,4,5,6},{2,7},{3}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,5,6},{2},{3,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,5,6},{2},{3},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,4,5,7},{2,6},{3}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,5},{2,6,7},{3}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4,5},{2,6},{3,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4,5},{2,6},{3},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,5,7},{2},{3,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,5},{2,7},{3,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4,5},{2},{3,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4,5},{2},{3,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,5,7},{2},{3},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,4,5},{2,7},{3},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,5},{2},{3,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,5},{2},{3},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,5},{2},{3},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,4,6,7},{2,5},{3}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,6},{2,5,7},{3}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4,6},{2,5},{3,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4,6},{2,5},{3},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,7},{2,5,6},{3}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4},{2,5,6,7},{3}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4},{2,5,6},{3,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,5,6},{3},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,7},{2,5},{3,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,5,7},{3,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,5},{3,6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,5},{3,6},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4,7},{2,5},{3},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,5,7},{3},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,5},{3,7},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2,5},{3},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2,5},{3},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4,6,7},{2},{3,5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4,6},{2,7},{3,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4,6},{2},{3,5,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4,6},{2},{3,5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,7},{2,6},{3,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,6,7},{3,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,6},{3,5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2,6},{3,5},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4,7},{2},{3,5,6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,4},{2,7},{3,5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,4},{2},{3,5,6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,4},{2},{3,5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,7},{2},{3,5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,7},{3,5},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2},{3,5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2},{3,5},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2},{3,5},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4,6,7},{2},{3},{5}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,4,6},{2,7},{3},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,6},{2},{3,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,6},{2},{3},{5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4,6},{2},{3},{5},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,4,7},{2,6},{3},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,6,7},{3},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,6},{3,7},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2,6},{3},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2,6},{3},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4,7},{2},{3,6},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,7},{3,6},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2},{3,6,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2},{3,6},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2},{3,6},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4,7},{2},{3},{5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2,7},{3},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2},{3,7},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,4},{2},{3},{5,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,4},{2},{3},{5,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4,7},{2},{3},{5},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,4},{2,7},{3},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4},{2},{3,7},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4},{2},{3},{5,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4},{2},{3},{5},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,4},{2},{3},{5},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,5,6,7},{2,4},{3}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,5,6},{2,4,7},{3}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,5,6},{2,4},{3,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5,6},{2,4},{3},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,7},{2,4,6},{3}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,5},{2,4,6,7},{3}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,5},{2,4,6},{3,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,4,6},{3},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,7},{2,4},{3,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,4,7},{3,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,4},{3,6,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,4},{3,6},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5,7},{2,4},{3},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,4,7},{3},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,4},{3,7},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2,4},{3},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2,4},{3},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6,7},{2,4,5},{3}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,6},{2,4,5,7},{3}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,6},{2,4,5},{3,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,4,5},{3},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,4,5,6},{3}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,4,5,6,7},{3}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1},{2,4,5,6},{3,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,4,5,6},{3},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,7},{2,4,5},{3,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,4,5,7},{3,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,4,5},{3,6,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,4,5},{3,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,4,5},{3},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4,5,7},{3},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2,4,5},{3,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4,5},{3},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4,5},{3},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,6,7},{2,4},{3,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,4,7},{3,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,4},{3,5,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,4},{3,5},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,7},{2,4,6},{3,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,4,6,7},{3,5}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,4,6},{3,5,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,4,6},{3,5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,4},{3,5,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,4,7},{3,5,6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,4},{3,5,6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,4},{3,5,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,4},{3,5},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,4,7},{3,5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4},{3,5,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4},{3,5},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,4},{3,5},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6,7},{2,4},{3},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,4,7},{3},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,4},{3,7},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2,4},{3},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2,4},{3},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,4,6},{3},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4,6,7},{3},{5}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2,4,6},{3,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4,6},{3},{5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4,6},{3},{5},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,7},{2,4},{3,6},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,4,7},{3,6},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4},{3,6,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4},{3,6},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,4},{3,6},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,4},{3},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,4,7},{3},{5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4},{3,7},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,4},{3},{5,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,4},{3},{5,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,4},{3},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,4,7},{3},{5},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2,4},{3,7},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,4},{3},{5,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,4},{3},{5},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,4},{3},{5},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,5,6,7},{2},{3,4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,5,6},{2,7},{3,4}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5,6},{2},{3,4,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,5,6},{2},{3,4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,7},{2,6},{3,4}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,6,7},{3,4}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,6},{3,4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2,6},{3,4},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5,7},{2},{3,4,6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,5},{2,7},{3,4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,5},{2},{3,4,6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,5},{2},{3,4,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,7},{2},{3,4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,7},{3,4},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2},{3,4,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2},{3,4},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2},{3,4},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6,7},{2,5},{3,4}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,5,7},{3,4}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,5},{3,4,7}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2,5},{3,4},{7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,7},{2,5,6},{3,4}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,5,6,7},{3,4}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,5,6},{3,4,7}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,5,6},{3,4},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,5},{3,4,6}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,5,7},{3,4,6}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,5},{3,4,6,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,5},{3,4,6},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,5},{3,4},{6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,5,7},{3,4},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5},{3,4,7},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5},{3,4},{6,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,5},{3,4},{6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6,7},{2},{3,4,5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1,6},{2,7},{3,4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1,6},{2},{3,4,5,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1,6},{2},{3,4,5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2,6},{3,4,5}}=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
{{1},{2,6,7},{3,4,5}}=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
{{1},{2,6},{3,4,5,7}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,6},{3,4,5},{7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,7},{2},{3,4,5,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2,7},{3,4,5,6}}=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
{{1},{2},{3,4,5,6,7}}=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
{{1},{2},{3,4,5,6},{7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,7},{2},{3,4,5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,7},{3,4,5},{6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,4,5,7},{6}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2},{3,4,5},{6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,4,5},{6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,6,7},{2},{3,4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,7},{3,4},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2},{3,4,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2},{3,4},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2},{3,4},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,6},{3,4},{5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,6,7},{3,4},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,6},{3,4,7},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,6},{3,4},{5,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,6},{3,4},{5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2},{3,4,6},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,7},{3,4,6},{5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,4,6,7},{5}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2},{3,4,6},{5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,4,6},{5},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,7},{2},{3,4},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,7},{3,4},{5,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2},{3,4,7},{5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,4},{5,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,4},{5,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2},{3,4},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,7},{3,4},{5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,4,7},{5},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2},{3,4},{5,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,4},{5},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,4},{5},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,5,6,7},{2},{3},{4}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1,5,6},{2,7},{3},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,6},{2},{3,7},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,6},{2},{3},{4,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5,6},{2},{3},{4},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,5,7},{2,6},{3},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,6,7},{3},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,6},{3,7},{4}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2,6},{3},{4,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2,6},{3},{4},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,5,7},{2},{3,6},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,7},{3,6},{4}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2},{3,6,7},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2},{3,6},{4,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2},{3,6},{4},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,5,7},{2},{3},{4,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2,7},{3},{4,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2},{3,7},{4,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,5},{2},{3},{4,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,5},{2},{3},{4,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,5,7},{2},{3},{4},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,5},{2,7},{3},{4},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,5},{2},{3,7},{4},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,5},{2},{3},{4,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,5},{2},{3},{4},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,5},{2},{3},{4},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,6,7},{2,5},{3},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,5,7},{3},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,5},{3,7},{4}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2,5},{3},{4,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2,5},{3},{4},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,5,6},{3},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5,6,7},{3},{4}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2,5,6},{3,7},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5,6},{3},{4,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5,6},{3},{4},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,7},{2,5},{3,6},{4}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,5,7},{3,6},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5},{3,6,7},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5},{3,6},{4,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,5},{3,6},{4},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,5},{3},{4,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,5,7},{3},{4,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5},{3,7},{4,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,5},{3},{4,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,5},{3},{4,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,5},{3},{4},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,5,7},{3},{4},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2,5},{3,7},{4},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,5},{3},{4,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,5},{3},{4},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,5},{3},{4},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,6,7},{2},{3,5},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,7},{3,5},{4}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2},{3,5,7},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2},{3,5},{4,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2},{3,5},{4},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,6},{3,5},{4}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,6,7},{3,5},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,6},{3,5,7},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,6},{3,5},{4,7}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,6},{3,5},{4},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2},{3,5,6},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,7},{3,5,6},{4}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,5,6,7},{4}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2},{3,5,6},{4,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,5,6},{4},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,7},{2},{3,5},{4,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,7},{3,5},{4,6}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2},{3,5,7},{4,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,5},{4,6,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,5},{4,6},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2},{3,5},{4},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,7},{3,5},{4},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,5,7},{4},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2},{3,5},{4,7},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,5},{4},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,5},{4},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,6,7},{2},{3},{4,5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2,7},{3},{4,5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2},{3,7},{4,5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1,6},{2},{3},{4,5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1,6},{2},{3},{4,5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2,6},{3},{4,5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,6,7},{3},{4,5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,6},{3,7},{4,5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,6},{3},{4,5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,6},{3},{4,5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2},{3,6},{4,5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2,7},{3,6},{4,5}}=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
{{1},{2},{3,6,7},{4,5}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,6},{4,5,7}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,6},{4,5},{7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,7},{2},{3},{4,5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2,7},{3},{4,5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3,7},{4,5,6}}=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
{{1},{2},{3},{4,5,6,7}}=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
{{1},{2},{3},{4,5,6},{7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,7},{2},{3},{4,5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,7},{3},{4,5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,7},{4,5},{6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3},{4,5,7},{6}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2},{3},{4,5},{6,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3},{4,5},{6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,6,7},{2},{3},{4},{5}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1,6},{2,7},{3},{4},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6},{2},{3,7},{4},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6},{2},{3},{4,7},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6},{2},{3},{4},{5,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1,6},{2},{3},{4},{5},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,7},{2,6},{3},{4},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,6,7},{3},{4},{5}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2,6},{3,7},{4},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,6},{3},{4,7},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,6},{3},{4},{5,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,6},{3},{4},{5},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,7},{2},{3,6},{4},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,7},{3,6},{4},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,6,7},{4},{5}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2},{3,6},{4,7},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,6},{4},{5,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,6},{4},{5},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,7},{2},{3},{4,6},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,7},{3},{4,6},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,7},{4,6},{5}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3},{4,6,7},{5}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2},{3},{4,6},{5,7}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3},{4,6},{5},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,7},{2},{3},{4},{5,6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2,7},{3},{4},{5,6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3,7},{4},{5,6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3},{4,7},{5,6}}=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
{{1},{2},{3},{4},{5,6,7}}=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
{{1},{2},{3},{4},{5,6},{7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1,7},{2},{3},{4},{5},{6}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1},{2,7},{3},{4},{5},{6}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1},{2},{3,7},{4},{5},{6}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1},{2},{3},{4,7},{5},{6}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1},{2},{3},{4},{5,7},{6}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6,7}}=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6},{7}}=>[1,1,1,1,1,1,1]=>[[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]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,4},{5,6},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,3},{5,6},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,3},{4,6},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,3},{4,5},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,3},{4,5},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,3},{4,5},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,4},{3,5},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,4},{3,5},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,4},{3,5},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,4},{3,6},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,5},{3,6},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,5},{4,6},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,5},{4,6},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,6},{4,5},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,6},{4,5},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,6},{3,5},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,6},{3,4},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,5},{3,4},{7,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,5},{3,4},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,5},{3,4},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,6},{3,4},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,6},{3,4},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,7},{3,4},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,7},{3,4},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,7},{3,5},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,7},{4,5},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,7},{4,5},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,8},{4,5},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,8},{4,5},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,8},{3,5},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,8},{3,4},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,8},{3,4},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,8},{3,4},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,7},{3,4},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,7},{3,5},{4,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,8},{3,5},{4,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,8},{3,5},{4,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,8},{3,6},{4,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,8},{3,6},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,8},{4,6},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,8},{4,6},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,7},{4,6},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,7},{4,6},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,7},{3,6},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,7},{3,6},{4,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,7},{3,5},{4,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,6},{3,5},{4,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,6},{3,5},{4,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,5},{3,6},{4,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,5},{3,6},{4,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,5},{3,7},{4,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,6},{3,7},{4,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,6},{3,7},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,6},{4,7},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,6},{4,7},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,5},{4,7},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,5},{4,7},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,5},{3,7},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,4},{3,7},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,4},{3,7},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,4},{3,6},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,4},{3,6},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,3},{4,6},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,3},{4,6},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,3},{4,7},{5,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,3},{4,7},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,3},{5,7},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,4},{5,7},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,4},{5,7},{6,8}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,4},{5,8},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,4},{5,8},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,3},{5,8},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,3},{4,8},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,3},{4,8},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,3},{4,8},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,3},{4,7},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,4},{3,7},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,4},{3,8},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,4},{3,8},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,4},{3,8},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,5},{3,8},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,5},{4,8},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,5},{4,8},{6,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,6},{4,8},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,6},{4,8},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,6},{3,8},{5,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,6},{3,8},{4,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,5},{3,8},{4,7}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,5},{3,8},{4,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,5},{3,7},{4,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,6},{3,7},{4,5}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,6},{3,8},{4,5}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,7},{3,8},{4,5}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,7},{3,8},{4,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,7},{3,8},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,7},{4,8},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,7},{4,8},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,2},{3,8},{4,7},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,3},{2,8},{4,7},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,4},{2,8},{3,7},{5,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,5},{2,8},{3,7},{4,6}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,8},{3,7},{4,5}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,7},{2,8},{3,6},{4,5}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,8},{2,7},{3,6},{4,5}}=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
{{1,6},{2,7},{3,8},{4,9},{5,10}}=>[2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[2,2,2,2,2]
{{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,1]
{{1},{2},{3},{4},{5},{6},{7,8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6,8},{7}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6,7,8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2},{3},{4},{5,6},{7},{8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5,6},{7,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4},{5,7},{6},{8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5,8},{6},{7}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5,7,8},{6}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2},{3},{4},{5,6,7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2},{3},{4},{5,8},{6,7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4},{5,6,8},{7}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2},{3},{4},{5,6,7,8}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2},{3},{4,5},{6},{7,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4,8},{5},{6},{7}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1},{2},{3},{4,6,7,8},{5}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2},{3},{4,8},{5,6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4,7,8},{5,6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3},{4,8},{5,7},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4,8},{5,6,7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3},{4,5,6,7,8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2},{3,4},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3,4},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3,4},{5,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,5},{4},{6,7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,8},{4},{5},{6},{7}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1},{2},{3,7,8},{4},{5,6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,5,7,8},{4},{6}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2},{3,8},{4},{5,6,7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,5,8},{4},{6,7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,5,6,7,8},{4}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2},{3,4,5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2},{3,4,5},{6,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2},{3,8},{4,5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3,6,7,8},{4,5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,8},{4,6},{5},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3,7,8},{4,6},{5}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,8},{4,7},{5},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3,8},{4,6,7},{5}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,4,5,6},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,8},{4,5,6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,7,8},{4,5,6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2},{3,8},{4,7},{5,6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2},{3,4,5,8},{6},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2},{3,4,5,6,7},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2},{3,8},{4,5,6,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,4,8},{5,6,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2},{3,4,5,8},{6,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,4,5,6,8},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2},{3,4,5,6,7,8}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1},{2,3},{4},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,3},{4},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,3},{4},{5,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3},{4,5},{6,7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,3},{4,5},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,3},{4,5},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3},{4,6,7},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,3},{4,6,8},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,3},{4,6,7,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3},{4,5,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3},{4,7},{5,6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,3},{4,8},{5,6},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,3},{4,7,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3},{4,8},{5,7},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,3},{4,5,8},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,3},{4,8},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3},{4,5,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3},{4,5,6,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3},{4,5,6,7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,4},{3},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,4},{3},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,4},{3},{5},{6,7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4},{3},{5,6},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,4},{3},{5,7,8},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4},{3},{5,8},{6,7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,4},{3},{5,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5},{3},{4},{6,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,8},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1},{2,5,8},{3},{4},{6},{7}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2,8},{3},{4},{5,6,7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,5,6,8},{3},{4},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,5,6,7,8},{3},{4}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,4,5},{3},{6,7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,5},{3},{6,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,5},{3},{6,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,6},{3},{4,5},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,6,8},{3},{4,5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,6,7,8},{3},{4,5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,6},{3},{5},{7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,6,7},{3},{5},{8}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,8},{3},{4,6,7},{5}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,8},{3},{5},{6,7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,6,8},{3},{5},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,4,6,7,8},{3},{5}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,7,8},{3},{4,5,6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,4,7},{3},{5,6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,8},{3},{4,7},{5,6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,4,8},{3},{5,6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,7,8},{3},{5,6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,8},{3},{5,7},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,5,7,8},{3},{6}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,4,8},{3},{5,6,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,4,5,8},{3},{6,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,5,6,8},{3},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,4,5,6,7,8},{3}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1},{2,3,4},{5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2,3,4},{5},{6,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,4},{5,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,4},{5,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,4},{5,6,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5},{3,4},{6,7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,5},{3,4},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,5},{3,4},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,8},{3,4},{5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,6,7},{3,4},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,6,8},{3,4},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,7},{3,4},{5,6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,8},{3,4},{5,6},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,7,8},{3,4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,8},{3,4},{5,7},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,8},{3,4},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,8},{3,4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,6,7,8},{3,4}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,3,5},{4},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2,3,5},{4},{6,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,6},{3,5},{4},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,7},{3,5},{4},{6},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,8},{3,5},{4},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,6,7},{3,5},{4},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,8},{3,5},{4},{6,7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,6,8},{3,5},{4},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,6,7,8},{3,5},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,6},{4},{5},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2,3,7},{4},{5},{6},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2,8},{3,7},{4},{5},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,3,8},{4},{5},{6},{7}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1},{2,3,7,8},{4},{5},{6}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,3,6,7},{4},{5},{8}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,3,6,8},{4},{5},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,3,6,7,8},{4},{5}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,7},{3,5,6},{4},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,8},{3,5,6},{4},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,3,7},{4},{5,6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,8},{3,7},{4},{5,6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,3,5,7},{4},{6},{8}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,8},{3,5,7},{4},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,3,5,8},{4},{6},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,3,5,7,8},{4},{6}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,3,5,6,7},{4},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,8},{3,5,6,7},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,8},{4},{5,6,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,5,8},{4},{6,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,5,6,8},{4},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,8},{3,4,5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,8},{3,4,5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,8},{3,4,5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,6,7,8},{3,4,5}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1},{2,3,6},{4,5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,7},{3,6},{4,5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,8},{3,6},{4,5},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,7,8},{3,6},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,8},{3,7},{4,5},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,3,8},{4,5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,3,6,7},{4,5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,8},{3,6,7},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,8},{4,5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,6,8},{4,5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,4,6},{5},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,8},{3,4,6},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,7,8},{3,4,6},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,8},{3,7},{4,6},{5}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,3,8},{4,6},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,3,7,8},{4,6},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,4,8},{5},{6},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1},{2,3,4,7,8},{5},{6}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,8},{3,4,6,7},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,8},{4,6,7},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,4,6,8},{5},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,3,4,6,7,8},{5}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1},{2,3,4,5,6},{7},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,3,4,5,6},{7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,8},{3,4,5,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,8},{3,7},{4,5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,8},{4,5,6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,8},{3,4,7},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,8},{4,7},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,4,8},{5,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,4,5,7},{6},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,8},{3,4,5,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,8},{4,5,7},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,4,8},{5,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,4,5,8},{6},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1},{2,3,4,5,7,8},{6}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1},{2,3,4,8},{5,6,7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1},{2,3,4,5,8},{6,7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,3,4,5,6,8},{7}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1},{2,3,4,5,6,7,8}}=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
{{1,2},{3},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1,2},{3},{4},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,2},{3},{4},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,2},{3},{4},{5,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3},{4,5},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3},{4,6,7,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3},{4,5,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3},{4,5,8},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2},{3},{4,5,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3},{4,5,6,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3},{4,5,6,7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2},{3,4},{5},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4},{5,7,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4},{5,6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4},{5,6,7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2},{3,5},{4},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,6,7,8},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3,5,6},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,7,8},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5,7,8},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3,8},{4},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5,8},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5,6,8},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3,5,6,7,8},{4}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2},{3,4,5},{6},{7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2},{3,8},{4,5},{6},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,2},{3,7,8},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,6,8},{4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,6,7,8},{4,5}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2},{3,4,6},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,7,8},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4,8},{5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2},{3,4,7,8},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3,8},{4,6,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4,8},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4,6,8},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3,4,6,7,8},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2},{3,4,5,6},{7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2},{3,8},{4,5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4,8},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,8},{4,5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4,8},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4,5,8},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3,4,5,7,8},{6}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2},{3,4,5,6,7},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2},{3,8},{4,5,6,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2},{3,4,8},{5,6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2},{3,4,5,8},{6,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2},{3,4,5,6,8},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2},{3,4,5,6,7,8}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,3},{2},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1,3},{2},{4},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,3},{2},{4},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,3},{2},{4},{5},{6,7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3},{2},{4},{5,7,8},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3},{2},{4},{5,8},{6,7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4},{5,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2},{4,5},{6,7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4,5},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4,5},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2},{4,6},{5},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4,6,7},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3},{2},{4,8},{5},{6,7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4,6,8},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3},{2},{4,6,7,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2},{4,5,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2},{4,7},{5,6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4,8},{5,6},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4,7,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2},{4,8},{5,7},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4,5,7,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2},{4,8},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2},{4,5,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2},{4,5,6,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2},{4,5,6,7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,4},{2},{3},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1,4},{2},{3},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4},{2},{3},{5},{6,7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4},{2},{3},{5,6},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,4},{2},{3},{5,8},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4},{2},{3},{5,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2},{3},{4},{6},{7},{8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1,5},{2},{3},{4},{6,7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6},{2},{3},{4},{5},{7},{8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1,6},{2},{3},{4},{5},{7,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,7},{2},{3},{4},{5},{6},{8}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1,8},{2},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
{{1,7,8},{2},{3},{4},{5},{6}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,8},{2},{3},{4},{5},{6,7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6,8},{2},{3},{4},{5},{7}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,6,7,8},{2},{3},{4},{5}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,7},{2},{3},{4},{5,6},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,5,7},{2},{3},{4},{6},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,8},{2},{3},{4},{5,7},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,5,7,8},{2},{3},{4},{6}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,8},{2},{3},{4},{5,6,7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5,6,8},{2},{3},{4},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,5,6,7,8},{2},{3},{4}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,4,5},{2},{3},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,4,5},{2},{3},{6,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,5},{2},{3},{6,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2},{3},{4,5},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,8},{2},{3},{4,5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6,7},{2},{3},{4,5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6,7,8},{2},{3},{4,5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2},{3},{4,6},{5},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4,6,8},{2},{3},{5},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,4,5,6},{2},{3},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2},{3},{4,5,6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,8},{2},{3},{5,6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,7,8},{2},{3},{5,6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,8},{2},{3},{6},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,4,5,6,7},{2},{3},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,4,8},{2},{3},{5,6,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,5,8},{2},{3},{6,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,6,8},{2},{3},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,3,4},{2},{5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,3,4},{2},{5},{6},{7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,4},{2},{5},{6,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,4},{2},{5},{6,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,4},{2},{5,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2},{5,7,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,4},{2},{5,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2},{5,6,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,4},{2},{5,6,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5},{2},{3,4},{6},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,5},{2},{3,4},{6},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2},{3,4},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,8},{2},{3,4},{5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6,7,8},{2},{3,4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6},{2},{3,4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7,8},{2},{3,4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2},{3,4},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5,7,8},{2},{3,4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6,7},{2},{3,4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2},{3,4},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2},{3,4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6,8},{2},{3,4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5},{2},{4},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,3,5},{2},{4},{6},{7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,5},{2},{4},{6,7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,5},{2},{4},{6,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,5},{2},{4},{6,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2},{3,5},{4},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6},{2},{3,5},{4},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,8},{2},{3,5},{4},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6,8},{2},{3,5},{4},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6,7,8},{2},{3,5},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6},{2},{4},{5},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,3,7},{2},{4},{5},{6},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,3,8},{2},{4},{5},{6},{7}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,3,7,8},{2},{4},{5},{6}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,3,5,6},{2},{4},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2},{3,5,6},{4},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,7,8},{2},{3,5,6},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,7},{2},{4},{5,6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,5,7},{2},{4},{6},{8}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,3,5,8},{2},{4},{6},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,3,5,7,8},{2},{4},{6}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,3,8},{2},{4},{5,6,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,5,8},{2},{4},{6,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,6,8},{2},{4},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,3,4,5},{2},{6},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5},{2},{6,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5},{2},{6,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5},{2},{6,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,6},{2},{3,4,5},{7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6},{2},{3,4,5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2},{3,4,5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,7,8},{2},{3,4,5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2},{3,4,5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2},{3,4,5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,6},{2},{4,5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2},{3,6},{4,5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2},{3,6},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2},{4,5},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,7,8},{2},{4,5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2},{3,6,7},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2},{4,5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6,8},{2},{4,5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,6},{2},{5},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7},{2},{4,6},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,7,8},{2},{4,6},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,8},{2},{5},{6},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,3,4,7,8},{2},{5},{6}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,8},{2},{3,4,6,7},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,8},{2},{4,6,7},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,4,6,8},{2},{5},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,3,4,5,6},{2},{7},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,3,4,5,6},{2},{7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,8},{2},{3,4,5,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7},{2},{4,5,6},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,8},{2},{4,5,6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2},{3,4,7},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2},{4,7},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4,8},{2},{5,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2},{3,4,5,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,8},{2},{4,5,7},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,4,8},{2},{5,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5,8},{2},{6},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,3,4,5,6,7},{2},{8}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,3,4,5,8},{2},{6,7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,3,4,5,6,8},{2},{7}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,3,4,5,6,7,8},{2}}=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
{{1,2,3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,2,3},{4},{5},{6},{7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,3},{4},{5},{6,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,3},{4,6,7},{5},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,3},{4,5,8},{6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,3},{4,5,7,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3},{4,5,6,7},{8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3},{4,5,8},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,3},{4,5,6,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,4},{2,3},{5},{6},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4},{2,3},{5,7,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3},{5,6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3},{5,6,7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5},{2,3},{4},{6},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,5},{2,3},{4},{6,7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2,3},{4},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,6},{2,3},{4},{5},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7},{2,3},{4},{5},{6},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,8},{2,3},{4},{5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6,8},{2,3},{4},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5,6},{2,3},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3},{4},{5,6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2,3},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,3},{4},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5,7,8},{2,3},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6,7},{2,3},{4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3},{4},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,3},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6,8},{2,3},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5},{2,3},{6,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3},{4,5},{6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,8},{2,3},{4,5},{6},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2,3},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,3},{4,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,3},{4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7,8},{2,3},{4,5}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,6},{2,3},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3},{4,6},{5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2,3},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,3},{5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,7,8},{2,3},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6,7},{2,3},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3},{4,6,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,3},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6,8},{2,3},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6,7,8},{2,3},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,4,5,6},{2,3},{7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,7},{2,3},{4,5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,3},{5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,3},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5,7},{2,3},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3},{4,5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,3},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5,8},{2,3},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,6,7},{2,3},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,4,8},{2,3},{5,6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,5,8},{2,3},{6,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,5,6,8},{2,3},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,4,5,6,7,8},{2,3}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,4},{3},{5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,2,4},{3},{5,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3},{5,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3},{5,6,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4},{3},{5,6,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5},{2,4},{3},{6},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,5},{2,4},{3},{6},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2,4},{3},{6,7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2,4},{3},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2,4},{3},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4},{3},{5},{6},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,8},{2,4},{3},{5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,8},{2,4},{3},{5},{6,7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,6,7,8},{2,4},{3},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6},{2,4},{3},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4},{3},{5,6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2,4},{3},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,4},{3},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,8},{2,4},{3},{5,7},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5,7,8},{2,4},{3},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,4},{3},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,4},{3},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6,8},{2,4},{3},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5},{3},{4},{6},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,2,5},{3},{4},{6},{7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6},{2,5},{3},{4},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6},{2,5},{3},{4},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7},{2,5},{3},{4},{6},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,8},{2,5},{3},{4},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,7,8},{2,5},{3},{4},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6,7,8},{2,5},{3},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,6},{3},{4},{5},{7},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,2,6},{3},{4},{5},{7,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,7,8},{2,6},{3},{4},{5}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,7},{3},{4},{5},{6},{8}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,8},{2,7},{3},{4},{5},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,2,8},{3},{4},{5},{6},{7}}=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
{{1,2,7,8},{3},{4},{5},{6}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,2,5,6},{3},{4},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7,8},{2,5,6},{3},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2,5,7},{3},{4},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,5,7,8},{3},{4},{6}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,2,5,6,7},{3},{4},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,8},{2,5,6,7},{3},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,6,8},{3},{4},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,6},{2,4,5},{3},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,5},{3},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,7,8},{2,4,5},{3},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6,7},{2,4,5},{3},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2,4,5},{3},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,4,5},{3},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,6},{3},{4,5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,6},{3},{4,5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2,6},{3},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7,8},{3},{4,5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,6,7},{3},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3},{4,5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6,8},{3},{4,5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,6},{3},{5},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2,4,6},{3},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,7,8},{2,4,6},{3},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,7,8},{3},{4,6},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,4,7},{3},{5},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,4,8},{3},{5},{6},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,2,4,7,8},{3},{5},{6}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,8},{2,4,6,7},{3},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,8},{3},{4,6,7},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4,8},{3},{5},{6,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,6,8},{3},{5},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,2,4,6,7,8},{3},{5}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,2,4,5,6},{3},{7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,7},{2,4,5,6},{3},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,4,5,6},{3},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,7},{3},{4,5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3},{4,5,6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4,7},{3},{5,6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,4,7},{3},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3},{4,7},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4,8},{3},{5,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,4,5,7},{3},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,8},{3},{4,5,7},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4,8},{3},{5,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,5,7,8},{3},{6}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,2,4,5,8},{3},{6,7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,4,5,6,8},{3},{7}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,2,4,5,6,7,8},{3}}=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
{{1,2,3,4},{5},{6},{7},{8}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,2,3,4},{5},{6,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,4},{5,6},{7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,3,4},{5,7,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,4},{5,6,7},{8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,4},{5,8},{6,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,3,4},{5,6,8},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,4},{5,6,7,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,5},{2,3,4},{6},{7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5},{2,3,4},{6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,4},{5},{7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6},{2,3,4},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,4},{5},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,8},{2,3,4},{5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,8},{2,3,4},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,3,4},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6},{2,3,4},{7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2,3,4},{5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,3,4},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,3,4},{6},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2,3,4},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,3,4},{6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6,7},{2,3,4},{8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5,8},{2,3,4},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5,6,8},{2,3,4},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5,6,7,8},{2,3,4}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,5},{3,4},{6},{7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,5},{3,4},{6,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3,4},{6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3,4},{6,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,7},{2,5},{3,4},{6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2,5},{3,4},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,5},{3,4},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,5},{3,4},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7,8},{2,5},{3,4}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,6},{3,4},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,6},{3,4},{5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,8},{2,6},{3,4},{5},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2,6},{3,4},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,7},{3,4},{5},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,2,8},{3,4},{5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,7,8},{3,4},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,6,7},{3,4},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,4},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6,8},{3,4},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,6},{3,4},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,5,6},{3,4},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7,8},{2,5,6},{3,4}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,7},{3,4},{5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,4},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5,7},{3,4},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,5,7},{3,4},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,4},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5,8},{3,4},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,6,8},{3,4},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,5},{4},{6},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,5},{4},{6,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,6},{2,3,5},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,3,5},{4},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,7,8},{2,3,5},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6,7},{2,3,5},{4},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2,3,5},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,3,5},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,6},{3,5},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,6},{3,5},{4},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7,8},{2,6},{3,5},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7,8},{3,5},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,6,7},{3,5},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,5},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6,8},{3,5},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,6},{4},{5},{7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3,6},{4},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,7,8},{2,3,6},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,7,8},{3,6},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3,7},{4},{5},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,3,8},{4},{5},{6},{7}}=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
{{1,2,3,7,8},{4},{5},{6}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,8},{2,3,6,7},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,8},{3,6,7},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,3,8},{4},{5},{6,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,6,8},{4},{5},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,2,3,6,7,8},{4},{5}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,2,3,5,6},{4},{7},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,2,3,5,6},{4},{7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,7},{2,3,5,6},{4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3,5,6},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,7},{3,5,6},{4},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2,7},{3,5,6},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,5,6},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,3,7},{4},{5,6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3,7},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,7},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3,8},{4},{5,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,5,7},{4},{6},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,8},{2,3,5,7},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,8},{3,5,7},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,3,8},{4},{5,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,5,8},{4},{6},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,2,3,5,7,8},{4},{6}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,2,3,5,6,7},{4},{8}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,8},{2,3,5,6,7},{4}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,5,6,7,8},{4}}=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
{{1,2,3,4,5},{6},{7},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,2,3,4,5},{6,7},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,5},{6,8},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,5},{6,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,6},{2,3,4,5},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2,3,4,5},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6,7,8},{2,3,4,5}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,6},{3,4,5},{7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,6},{3,4,5},{7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,7},{2,6},{3,4,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,6},{3,4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7,8},{2,6},{3,4,5}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,8},{2,7},{3,4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,4,5},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,6,7,8},{3,4,5}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,6},{4,5},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,6},{4,5},{7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,8},{2,3,6},{4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,6},{4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3,7},{4,5},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3,7},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,7},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3,8},{4,5},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,6,7},{4,5},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,8},{2,3,6,7},{4,5}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,3,8},{4,5},{6,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,3,6,8},{4,5},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,6,7,8},{4,5}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,3,4,6},{5},{7},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,2,3,4,6},{5},{7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,8},{2,3,4,6},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,7},{3,4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,4,6},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,7,8},{3,4,6},{5}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,7},{4,6},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,3,7},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,7},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3,8},{4,6},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,7,8},{4,6},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,7},{5},{6},{8}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,8},{2,3,4,7},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,8},{3,4,7},{5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,3,8},{4,7},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,4,8},{5},{6},{7}}=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
{{1,2,3,4,7,8},{5},{6}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,2,3,4,6,7},{5},{8}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,8},{2,3,4,6,7},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,6,8},{5},{7}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,2,3,4,6,7,8},{5}}=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
{{1,2,3,4,5,6},{7},{8}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,2,3,4,5,6},{7,8}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,7},{2,3,4,5,6},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,8},{2,3,4,5,6},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,7},{3,4,5,6},{8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,7,8},{3,4,5,6}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,3,7},{4,5,6},{8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,8},{2,3,7},{4,5,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,8},{3,7},{4,5,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,3,8},{4,5,6},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,7,8},{4,5,6}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,4,7},{5,6},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,8},{2,3,4,7},{5,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,8},{3,4,7},{5,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,3,8},{4,7},{5,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,3,4,8},{5,6},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,5,7},{6},{8}}=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
{{1,8},{2,3,4,5,7},{6}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,8},{3,4,5,7},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,8},{4,5,7},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,4,8},{5,7},{6}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,5,7,8},{6}}=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
{{1,2,3,4,5,6,7},{8}}=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
{{1,8},{2,3,4,5,6,7}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,8},{3,4,5,6,7}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,8},{4,5,6,7}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,3,4,8},{5,6,7}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,4,5,8},{6,7}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,3,4,5,6,8},{7}}=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
{{1,2,3,4,5,6,7,8}}=>[8]=>[[1,2,3,4,5,6,7,8]]=>[8]
{{1,3,5,6,7,8},{2,4}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,3,4,6,7,8},{2,5}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,4,6,7,8},{3,5}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,4,5,7,8},{3,6}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,3,5,7,8},{4,6}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,4,5,6,8},{3,7}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,3,5,6,8},{4,7}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,3,4,6,8},{5,7}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,4,5,6,7},{3,8}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,3,5,7,8},{2,4,6}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,5,7,8},{3,4,6}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,3,4,7,8},{2,5,6}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,4,7,8},{3,5,6}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,5,6,8},{3,4,7}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,3,4,6,8},{2,5,7}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,4,6,8},{3,5,7}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,6,8},{4,5,7}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,5,8},{4,6,7}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,6,7},{4,5,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,3,4,5,7},{2,6,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,4,7},{5,6,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,4,5,6},{3,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,5,6},{4,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,3,4,6},{5,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,3,6,7,8},{2,4},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,3,4,7,8},{2,6},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,4,7,8},{3,6},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,3,4,5,8},{2,7},{6}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,3,4,6,7},{2,8},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,4,6,7},{3,8},{5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,3,4,5,7},{2,8},{6}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,5,7},{4,8},{6}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,3,4,5,6},{2,8},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,5,6},{4,8},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,6},{5,8},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,3,5,6,7},{2,4},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,5,7},{4,6},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,5,6},{4,7},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,6},{5,7},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,3,5,7},{2,4,6,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,5,7},{3,4,6,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,3,4,7},{2,5,6,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,3,7},{4,5,6,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,3,5,6},{2,4,7,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,5,6},{3,4,7,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,4,6},{3,5,7,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,3,6},{4,5,7,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,3,6,8},{2,5,7},{4}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,6,8},{3,5,7},{4}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,5,8},{3,6,7},{4}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,5,8},{3,4,6},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,4,8},{3,5,6},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,4,7},{3,6,8},{5}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,3,5,7},{2,4,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,4,7},{3,5,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,3,4,5},{2,7,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,4,5},{3,7,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,3,5,6},{2,4,8},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,6},{4,5,8},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,5},{4,6,7},{8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,7,8},{3,5},{4,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,6,8},{3,5},{4,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,3,6,8},{2,4},{5,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,3,5,8},{2,6},{4,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,3,5,8},{2,4},{6,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,4,8},{3,5},{6,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,5,7},{2,6},{3,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,3,5,7},{2,6},{4,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,3,5,6},{2,4},{7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,4,6},{3,5},{7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5,7,8},{2,6},{3},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,7,8},{2,6},{3},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7,8},{2,6},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7,8},{2,5},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7,8},{2,4},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6,8},{2,7},{3},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6,8},{2,7},{3},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6,8},{2,7},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,6,8},{3,7},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,8},{2,7},{3},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,8},{2,7},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,8},{3,7},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,8},{2,7},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,8},{3,7},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6,8},{2,5},{3},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6,8},{2,5},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6,8},{2,4},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,8},{2,6},{3},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,8},{2,6},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,8},{3,6},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,8},{2,6},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,8},{3,6},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,8},{2,5},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,8},{3,5},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6,7},{2,8},{3},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6,7},{2,8},{3},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6,7},{2,8},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,6,7},{3,8},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,7},{2,8},{3},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,7},{2,8},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,7},{3,8},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,7},{2,8},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,7},{3,8},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,6},{2,8},{3},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,6},{2,8},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,6},{3,8},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,6},{2,8},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,6},{3,8},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,6},{4,8},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5},{2,8},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,5},{3,8},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,5},{4,8},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6,7},{2,5},{3},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6,7},{2,5},{4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,7},{2,6},{3},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,7},{2,6},{4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,7},{3,6},{4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,7},{2,6},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,7},{3,6},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,7},{2,4},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,7},{3,5},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,6},{2,7},{3},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,6},{2,7},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,6},{3,7},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,6},{4,7},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5},{2,7},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,5},{3,7},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,5},{4,7},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,6},{3,5},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5},{2,6},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,5},{3,6},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,5},{4,6},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7},{2,4,8},{5,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,5},{2,6,8},{3,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,4},{2,6,8},{5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,5},{2,4,8},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,5},{3,4,8},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,4},{2,5,8},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,4},{3,5,8},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,6},{2,5,7},{3,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,5},{3,4,6},{7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,4},{2,5,6},{7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,4},{3,5,6},{7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5,7},{2,6,8},{3},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,7},{2,6,8},{3},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,7},{2,6,8},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,7},{3,6,8},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,7},{2,5,8},{3},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,7},{2,5,8},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,7},{3,5,8},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,7},{2,4,8},{5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,7},{3,4,8},{5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6},{2,7,8},{3},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,6},{2,7,8},{3},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,6},{2,7,8},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,6},{3,7,8},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,5},{2,7,8},{3},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,5},{2,7,8},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5},{3,7,8},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,4},{2,7,8},{5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4},{3,7,8},{5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,6},{2,5,8},{3},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,6},{2,5,8},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,6},{3,5,8},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,6},{2,4,8},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,6},{3,4,8},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,5},{2,6,8},{3},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,5},{2,6,8},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5},{3,6,8},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,4},{2,6,8},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4},{3,6,8},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5},{3,4,8},{6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4},{3,5,8},{6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,6},{2,5,7},{3},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,6},{2,5,7},{4},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,6},{3,5,7},{4},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,6},{2,4,7},{5},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,5},{2,6,7},{4},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5},{3,6,7},{4},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,4},{2,6,7},{5},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,5},{2,4,7},{6},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5},{3,4,7},{6},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4},{3,5,7},{6},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5},{3,4,6},{7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,8},{2,6},{3,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,6},{3,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,6},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,6},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,5},{3,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,5},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,5},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,4},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,5},{3,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,5},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3,5},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,4},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,6},{3,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,6},{3,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,6},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7},{3,6},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,5},{3,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,5},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7},{3,5},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,4},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7},{3,4},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,7},{3,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,7},{3,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2,7},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3,7},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2,7},{3,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2,7},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3,7},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,7},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3,7},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,5},{3,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2,5},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3,5},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2,4},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3,4},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2,6},{3,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2,6},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3,6},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,6},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3,6},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3},{4,6},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2,4},{6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,5},{6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,5},{3,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,5},{4,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,4},{5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3,4},{5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2,6},{3,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,6},{5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3,6},{5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3},{4,6},{5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,5},{6,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,4},{5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6,7},{2,8},{3},{4},{5}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,4},{2,8},{5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,7},{2,6},{3},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,7},{2,5},{3},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,7},{2,4},{5},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,6},{2,7},{3},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,5},{2,4},{6},{7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5},{2,6},{3,7},{4},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2,6},{4,7},{5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2,5},{4,7},{6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,4},{2,5},{3,6},{7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2,5},{4,6},{7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7},{2,8},{3},{4},{5},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6},{2,8},{3},{4},{5},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4},{2,8},{3},{5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,3},{2,8},{4},{5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,5},{2,6},{3},{4},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4},{2,5},{3},{6},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,3},{2,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,3,5,8},{2},{4,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,7},{2},{4},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,7},{2,4},{3},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,8},{3},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,4},{3,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,4},{3,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,5,8},{4,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,8},{2,6},{3,4},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,6},{3,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,8},{3},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,5},{3},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3,6,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3,6},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3,7},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3,5,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2},{3,4,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3},{4,7,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5,7},{3},{4,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,5,7},{4},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,7},{2},{3,4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2},{3,5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3,8},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2},{3,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2},{3,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6},{3,4,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,7},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,6,7},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,6},{4,7,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3},{4},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6},{3,4},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,7},{3,4},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3},{4},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,7},{4,6,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5,8},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,8},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5},{3,4,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,5,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,7},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,6},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,6,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,6,7},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,6},{4},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,7},{4},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,7,8},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,4,7},{5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,8},{2,3,7},{5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,7},{2,3,8},{5},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,7},{2,8},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,8},{4},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2,8},{4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2,7},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,6},{3,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,6},{3,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,8},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,7},{3,5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,7},{3,4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,8},{3,4,6},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,3,6},{4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3,8},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,6},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,7},{3,4,6},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,6,8},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5,7},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,7},{4,5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,7},{3},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,8},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,8},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2},{4,5,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2,3},{4,5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,8},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,8},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7,8},{2,5},{3,6},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,6,8},{3},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2,4,5},{3,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,5},{3},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7,8},{2},{3,6},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,8},{2,7},{3,6},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,5,7},{3,6},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,6,7},{3},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,5,7},{2},{3,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5},{2,6},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2,8},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6,8},{2},{3,7},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,8},{2,4,6},{3,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,5},{3},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2,8},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,8},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,6},{3,4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2},{3,4,7},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6,8},{2,4},{3,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,8},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,7,8},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2,3,7},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,6},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,4},{3,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,4,8},{3},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6,8},{2,5,7},{3},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6,8},{2,7},{3,5},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,7},{3},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,8},{3,4},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2},{3,4,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2,5},{3,4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,6,8},{3,4},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,3,6},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5},{2,4,8},{3,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,7},{3,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,8},{3,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,8},{3,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5},{3,4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,5},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,6},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6},{3,4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,7},{3,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,8},{3,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,8},{3,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,8},{3,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,8},{3,4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,8},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3,8},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,7},{3,4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,7},{3,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,6},{3,4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,6},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,3,6},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,3,5},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,5},{3,4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4,7},{3,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4,7},{3,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,8},{3,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2,8},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,7},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,8},{3,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,7},{3,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,6},{3,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,8},{3,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,5},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7},{3,8},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,8},{3,4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,8},{3,4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,7},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,7},{3,4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2},{4,6,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2,4,6,8},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,6,8},{3},{5,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2},{4,6,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2},{4,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2},{4,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2},{4,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5,7},{2},{4,6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7},{2},{4,6,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,7},{2},{4,6},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5,7},{2},{4,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2,4,8},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,8},{3,5,7},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4},{2,8},{3,5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,7},{3,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5,7},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,7},{4,6,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,4,6},{5},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2,4,6},{3},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,4,8},{3},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,8},{3,5,7},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,6},{3,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,6},{3,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,8},{3,7},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,8},{3,6},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,8},{3,6},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,6,8},{3,5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2,6,8},{3,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5},{3,6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5},{4,6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,6,8},{3},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2,4},{3,6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,8},{3,5,7},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2,8},{3,5,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,8},{3},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,7},{3},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,7},{3},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,4,6},{3},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,7},{2,4},{3,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,8},{3,5},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,6,8},{3,7},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2,7},{3,5,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2,7},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,6,8},{3,5},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,6},{3,5,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,4,6},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,6},{4,5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5,6},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5,6},{3},{4,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,6},{3},{4,5,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2,3},{4,5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,3},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,3,8},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6},{2,8},{3,4},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,8},{3,4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,8},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,5,8},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5},{3,8},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3,6},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4,6},{3},{5,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4},{3,8},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3,8},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,8},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,8},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,8},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,8},{5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,3},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,6},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,6,8},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2,3,6},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4,5},{3,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,6},{4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,6},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5,8},{3,4},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,5},{3,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2,8},{3,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,5,6},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,8},{2,5},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4},{3,7,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,4},{3,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,8},{3,5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,7,8},{3,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,8},{3},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,8},{3,4},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,3,8},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5},{3,7},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,7},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2,7},{3},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,7},{3},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,6,7},{3},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,6},{3},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5,7,8},{3},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6,7},{2,5,8},{3},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2,5,6,8},{3},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2,6,8},{3},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,6,8},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,8},{3,6},{4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,6},{3},{4,5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,5,6},{3},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,5},{3},{4,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7,8},{2,5},{3},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4},{3,6,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7,8},{2,4},{3,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,7},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,7},{4,5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,6,7},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,6},{4,7,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,7,8},{3},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2,4,8},{3},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,5,8},{3},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2,5,8},{3,4},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,5,8},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,7},{3},{4,6},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2},{3,4,6},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2},{3,6},{4,5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2},{3,5,6},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2},{3,5},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2},{3,5},{4,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2},{3,7,8},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2},{3,8},{4,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2},{3,8},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2},{3,8},{4,5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2},{3,4,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3},{4,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6,8},{3},{4,7},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6,8},{2,3},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2},{3,7},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6,8},{2},{3,7},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,8},{2},{3,6,7},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2},{3},{4},{5},{6},{7},{8},{9}}=>[1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,1]
{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6},{7,9},{8}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6,9},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5,9},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3},{4,9},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3,9},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2,9},{3},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[1,1,1,1,1,1,1,1,1,1]
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6},{7,8,9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6,9},{7,8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5,9},{6,7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1},{2},{3},{4,9},{5,6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1},{2},{3,9},{4,5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1},{2,9},{3,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,9},{2,3},{4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,2,3,4,5,6,7,8},{9}}=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
{{1},{2,3,4,5,6,7,8,9}}=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
{{1,2,3,4,5,6,7,8,9},{10}}=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
{{1,2,3,4,5,6,8},{7},{9}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1},{2,3,4,5,6,7,9},{8}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1},{2,3,4,5,6,7,8,9,10}}=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
{{1,2,3,4,5,6,7,9},{8},{10}}=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
{{1,2,3,4,5,8},{6,7},{9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,3,4,5,7,8},{6},{9}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1},{2,3,4,5,6,9},{7,8}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1},{2,3,4,5,6,8,9},{7}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1},{2,3,4,5,6,7,8,10},{9}}=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
{{1,4,6,8},{2},{3,5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,7},{2,3},{4,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2},{3,6},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2},{4,6},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7,8},{2},{3,6},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6,7},{2},{3,5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,8},{2},{3,7},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2},{3,7},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2},{3,6},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2,3},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5,8},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,7,8},{3},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2,4,8},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5,8},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4},{3,5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,6},{3,5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,6},{3,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,6,7},{3,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3,6},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3,7},{5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,7},{5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,8},{3},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,3},{4,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,3},{5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,6},{5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,7},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3,7},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,7},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3},{4},{5,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2,3,4},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4},{3,6,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,7},{3,6,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,6},{3,5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4},{3,5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,7,8},{3},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4},{3,5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5},{3,7,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6},{3,7,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,8},{3,6,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4,5,6,7,8}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,4},{2,3,5,6,7,8}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,5},{2,3,4,6,7,8}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,4},{2,6},{3,5,7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5},{2,6},{3,4,7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5},{2,4,6,8},{3,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,5,8},{2,3,6,7}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,4},{2},{3,5,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2},{3,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2},{3,4,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2},{3,4,7,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2},{3,4,7,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5},{2},{3,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2},{3,4,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2},{3,4,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6,7},{2},{3,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6},{2},{3,7,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,6},{2},{4},{5,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2},{3,6},{4},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3,5,7,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2,4},{3},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,3},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4},{3},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,4},{3},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,6,7},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6,7},{2},{4},{5,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7},{2},{4},{5,6,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2},{3,7},{4},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2},{3,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,5},{3},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4,5},{3,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4},{3,5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,3},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,5},{3,4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2},{3,5,6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4},{2},{3,6,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,3},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2},{3},{5,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5,6},{3,7},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,6},{3},{4,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5},{3,7},{4,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2},{3,6,7},{4,5,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,6,7},{4},{5,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,6},{4,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2},{3,4,6,8},{5,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,6},{4,5,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5},{3},{4,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5},{3,6},{4,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5},{3,6,7},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2},{3,5,6,7},{4,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,5,6},{4,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2},{3,5},{4,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,8},{3,5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,6,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,7},{3,6},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,8},{4,5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4,7,8},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2,3,4,8},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,7},{3},{5,6,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2},{3,4,5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,7},{4,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2},{3,7},{4,5,6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,5,7},{4,6,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,6},{3,5},{4,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6},{3,5,7},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2},{3,6,7},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2},{3,6},{4,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2},{3},{4,6,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,6},{3},{4,5,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2},{3,4},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3},{4,7,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2},{3,4,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6},{3,7},{4,5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2},{3,7},{4,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6},{3},{4,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2,5},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,6},{3},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2,6},{3},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,7},{3,4},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2,8},{3},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,8},{3,5},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,8},{3},{4,5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5,8},{3},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,5,8},{3},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2,7},{3},{4,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,5},{3,6,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,6},{3,5,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,3},{4,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3},{4,6,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,3},{4,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,5,6},{3,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,6},{4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,5},{3,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6,7},{3},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,7},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,4,8},{3},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6},{2,8},{3},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2},{3,6,8},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5},{2},{3,6,8},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,5},{3},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6,8},{3},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,6},{3},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5,7},{3},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2},{3,6},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2},{3,8},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2},{3,7},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,6},{3},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,5,8},{3,6},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,5,8},{3},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,5,6},{3},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,5},{3},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5},{3},{4,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,7},{3},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,7},{3},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5,8},{3,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,8},{3,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,8},{3,6,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,7,8},{3,6},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,5},{3,6,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,5,7},{3},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,8},{3,6},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,7},{3,6,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,5},{3},{4,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,5},{3,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6,8},{3,7},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5,7},{3,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7},{2,8},{3},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,8},{3},{4,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,7,8},{3,5},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,8},{3,5,6},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,5,6},{3,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6,7},{3,8},{4}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,4,6},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2,3,5},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4,6},{3,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,8},{3,4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7},{3,8},{4,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2},{4,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2},{4,7,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2},{3,7,8},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2},{3,8},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6,7},{2},{4,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,8},{2},{3,6,7},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6},{2},{3,4,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2},{3,5,7,8},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6,7},{2},{3,5,8},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4},{2,6,8},{3},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4,6},{3},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2},{3,6,8},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2},{3,5,7},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4},{2},{3,5,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5,7},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2},{3,4,7},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2},{3,4,7},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3},{4,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5,8},{3},{4,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3,4,7},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5},{4,6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3},{4,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,6},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3,7},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3},{4,6,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5},{3},{4,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5,6},{4,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,8},{4,5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2,8},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6},{3,8},{4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4,7},{3},{5,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7},{2,5},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7},{3,4},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4,7},{3},{5},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4},{3},{5,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4},{5,6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4,7},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,8},{3,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3,4},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4,7},{5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4,6},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,4},{2,8},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,4,8},{5},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2,5,6},{3,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,8},{3,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,8},{3,4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5,7},{3},{4},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,5,8},{3},{4,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6},{2,8},{4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2},{3,5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3,5,8},{4,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5,7},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7},{3,5},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,7},{2,4},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,4,7},{5},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2,5,7},{3},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4,6},{5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,4},{5,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,5},{3,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,5},{4,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,5},{4,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,8},{3,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,5},{3,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3,4,5},{6,7,8,9,10}}=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]
{{1,6},{2,4},{3,7,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,3,4,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,5,7},{2,4,6,8},{3}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5,6},{2,3,4,8},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5},{2,3},{4,7,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4},{3,5,7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,6},{2,5},{3,4,7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,3,7},{2},{4,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2},{4,7},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3},{2},{4,7},{5,8},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,4,7},{3},{5,8},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,7},{3,4,5,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2,3,4,7},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,8},{2,6,7},{3},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,6},{2,8},{3},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4},{3,5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,3,7},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5,8},{3,7},{4},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,7},{3,5,8},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,7},{3,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,5},{3,4,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,8},{3,6},{4,5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,7},{4,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,7},{3,4,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6,8},{3,4},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,7},{3},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4},{2,5},{3},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2,3,6,8},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5},{3,6,8},{4},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,5,6,7},{3,8},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,8},{3,5},{4,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,7},{3,4,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6},{2,3,7},{4},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,6},{3,7},{4,8},{5}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,6},{3,7},{4},{5},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6,7},{2,3,8},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,4,6},{3,5,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,6},{2},{3,5,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2},{3,8},{4},{5},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,5},{2},{3},{4,8},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,7},{2},{3,4},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2},{3,4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,7},{3},{4,5,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6,7},{2},{3,4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2},{3,4,6},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,8},{3,7},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,8},{2,7},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,7,8},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,7,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,6,8},{4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,8},{3,4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,3},{4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,7},{3,4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,6,8},{4,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6,8},{2},{4,7},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,7},{2,6},{3},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2,4,7},{3},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,5,7},{2},{3},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4},{2},{5,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4},{5,7,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,6},{3},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6,7,8},{3},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2},{3,6,7,8},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,8},{2},{3,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2,4,6},{3,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2},{3,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,7},{3,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,8},{4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6},{3,4,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3},{4,5,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3},{4,6,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,5,6},{4,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,5,7},{4,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,7},{4,6},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,6},{4,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5,8},{4,6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5},{2},{3,4,6,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2,6,7},{3,4},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5,7,8},{4,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,5,7},{2},{3,6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2},{3,5,6,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,8},{2},{3,5,7},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,8},{2,5,7},{4},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2,5,6,8},{4},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7},{2,6},{4,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2,4,7},{3},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6,8},{2,4},{3},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,8},{2,6},{3},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2},{3,4,6,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,7},{3,4,5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6},{3,4,5,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2},{3,4,5,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2,7},{3,4,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4},{3,5,6,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4},{2,7},{3,5,6,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,8},{2,6},{3,5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6,8},{2,4},{3,5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,8},{2,5,7},{4,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5},{2,7},{3,4,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,8},{3,5,6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2,4,5},{3,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,7},{3,8},{4},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,7},{3,5,6},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,8},{3,6,7},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,7},{2,5,6},{3},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,6,8},{3,4,7},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,7},{2,3,6},{4},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2,6},{4,5,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,3,8},{5},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4},{2,3,8},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,5},{4,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2},{4,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6,7},{2},{3,4,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,5},{3},{4,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5},{3},{4,8},{6,7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5,8},{2,4},{3,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,7},{3,5,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,6},{3,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,3,5},{4,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,7},{3},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5},{3,8},{4,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,7},{4,8},{5},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,7},{2,3},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,7,8},{5},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,5,7},{3,4,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6},{2,4},{3,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,5},{6,7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,4,8},{3,5},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,6},{3,5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5},{3,6},{4},{7,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,5,7},{3,6,8},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5,7},{3,8},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2,4},{3,5,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,4},{3,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5},{3,6},{4,7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,5},{3,6,8},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,6,7},{4,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,8},{2},{4,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6},{2},{3,7,8},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,7},{2},{3,5,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4},{2,6,8},{3,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,7,8},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,6,8},{4},{5,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3},{4,6},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,6,8},{3},{4,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,5,6,8},{4,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,5,7},{3,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,4,6,7},{5,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,6},{3,7,8},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,7},{3,5},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2},{3,6,8},{4,5,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3},{4,7},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7,8},{2,4},{3,5},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6,8},{2},{3},{5,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,6},{3,7,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2},{4,6},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,6,7},{3},{5,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5},{3,7,8},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,7},{2},{3,6,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2,4,5},{6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,8},{4,6,7},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4,5},{6,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,7,8},{3},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,7,8},{5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,8},{2,4},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2},{3},{4,5,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5},{2,3,7},{4,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,6,7},{5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,6},{2,3,7},{5},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2,4,5,7},{3},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2,4,5},{3,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6,7},{2},{3},{4,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,7},{2,6},{3,4},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,7},{3,5,8},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2},{4,6,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5,8},{3,4,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,6,7},{2,4,5,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1},{2,8},{3,5,6},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,6,7},{3},{4,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2,7,8},{3,4},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,7},{3,4,6,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,7},{2},{3,8},{4,5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,5},{3,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1},{2,6,8},{3,7},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,5,8},{3,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,5},{3,7,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,6},{3,8},{4,5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5,6},{2},{3,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5,6},{2},{4,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,6,7},{3,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5},{2,7,8},{3,4},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,5},{2},{4,7,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2,5},{4,7,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,6},{3},{4,5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,7,8},{4,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,5},{2,8},{3,7},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2,4},{5},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2},{4,5,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2},{3,5},{4,7,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,4,7},{5,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,8},{2,5,7},{3},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,4,6},{5,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,5,8},{3,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2},{3,4,5,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4},{3,6},{5,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2},{4,6},{5,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2,5},{4},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,4,5,6},{3,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,6},{3,5},{4,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2,4},{3,7},{6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2,4,6,7},{3},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,6},{3,5,7,8},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,8},{3,5},{4,7},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7},{2,4},{3,6},{5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,5,7,8},{3,6},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6},{2,4,7},{3},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2,5,6,7},{4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2,6,7,8},{4},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4},{3,6,7,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4},{3,8},{5,7},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3},{2,7},{4,6},{5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,4,7},{3,6,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,7},{2,3,5},{6},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,7},{2,3,6},{5},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5},{2,3,6,7},{4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2,3,7},{5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,8},{3,4,6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5,7},{3,4,6},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,6},{4,5,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2,3},{4,5,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3,6},{2},{4,5,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4},{2,3,5},{6,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,5,7},{3,4},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,5},{6,8},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,6},{4,5,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5,8},{3,4,7},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,7},{4,6,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,7},{4,5,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,8},{2},{3,5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,8},{2},{3,5},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,3,5,8},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,6,8},{3},{4},{5,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3,6,8},{4},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,4},{2},{3},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,5},{2},{3},{4},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,6},{2},{3},{4},{5},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,7},{2},{3},{4},{5},{6},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,2,3},{4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,3,4},{2},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,8,9},{2},{3},{4},{5},{6},{7}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,8},{2},{3,6},{4,5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2},{3,5,6},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,8},{2},{3,4,6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3},{2,4,8},{5},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6},{3,4,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4},{3,6,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,6},{4,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,4,6},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,7},{2,3},{4,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4},{3,8},{5,6},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3,4,5,6,7,8,9}}=>[9]=>[[1,2,3,4,5,6,7,8,9]]=>[9]
{{1,2,3,4,5,6,7},{8,9}}=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
{{1,2,3,4,5,6,7},{8},{9}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1,2,3,4,5,6},{7,8,9}}=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
{{1,2,3,4,5,6},{7,8},{9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,3,4,5,6},{7},{8},{9}}=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[1,1,1,6]
{{1,2,3,4,5},{6,7,8,9}}=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
{{1,2,3,4,5},{6,7,8},{9}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
{{1,2,3,4,5},{6},{7},{8},{9}}=>[5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[1,1,1,1,5]
{{1,2,3,4},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1,2,3,4,5,6,7,8,9,10}}=>[10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[10]
{{1,2,3,4,5,6,7,8},{9,10}}=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
{{1,2,3,4,5,6,7,8},{9},{10}}=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
{{1,2,3,4,5,6,7},{8,9,10}}=>[7,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]
{{1,2,3,4,5,6,7},{8,9},{10}}=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
{{1,2,3,4,5,6,7},{8},{9},{10}}=>[7,1,1,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[1,1,1,7]
{{1,2,3,4,5,6},{7,8,9,10}}=>[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]
{{1,2,3,4,5,6},{7},{8},{9},{10}}=>[6,1,1,1,1]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[1,1,1,1,6]
{{1,2,3,4,5},{6},{7},{8},{9},{10}}=>[5,1,1,1,1,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
{{1,2,3,4},{5},{6},{7},{8},{9},{10}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}=>[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,3]
{{1,4},{2,3},{5},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,5},{2},{3,4},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,6},{2},{3},{4,5},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,7},{2},{3},{4},{5,6},{8},{9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,8},{2},{3},{4},{5},{6,7},{9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,9},{2},{3},{4},{5},{6},{7,8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,2,3},{4,7},{5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3},{4,6,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,7},{3},{4,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,5},{3,8},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,7,8},{3},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,6},{3},{4,5,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,5,6},{3},{4,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,6},{3,4,7,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2},{4,7},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3,6,7,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,7},{4},{5,6,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,6},{4},{5,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3},{4,6,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3},{4,6},{5,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,6},{3,7,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,5,6},{4,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,5},{4,7,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5},{3,4,7,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,7},{2},{3,6},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,8},{3,6,7},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,3,6},{4,7,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,5,7},{2,3,6,8}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,5},{2,3,7},{4,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5},{2,3,6,8},{4,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1},{2,5},{3,4,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,6,8},{3,4,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5,7},{2,6},{3,4,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6},{2,5,7},{3,4,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5,7},{2,3,6},{4,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5,7},{2,3,8},{4,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1},{2,7},{3,6},{4,5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,4,5,8},{3,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,7},{2,5,8},{3,4,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6},{2,5},{3,4,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,5,8},{3,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,5},{2,7},{3,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,5,7},{3,6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,7},{2,8},{3,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,5},{2,7},{3,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,7},{2,5},{3,4,6,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1},{2,6},{3,4,5,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,7},{3,6,8},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,4,5,7},{3,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5,7},{2,8},{3,4,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,6},{2,7},{4,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,8},{3},{4,7},{5}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3},{2},{4,7},{5},{6,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,3,4,7},{2},{5},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2},{3,5},{6,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5,7},{2},{3,6},{4},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,7},{3,5},{4},{6,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,6},{2,4},{3},{5,7},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,7},{3,5,6,8},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,8},{3,6},{4},{5,7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7},{2,5},{3},{4,6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,7},{3,4,6,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2,3,5,7},{4},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5,8},{2},{3,6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,6},{2},{5,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,6},{3},{4,8},{5,7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2},{3,7},{4,6},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,6},{3,5,8},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,4,7},{3,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5},{3,4,6,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2,3,5,7},{6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5,6,8},{3,7},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,7},{3,5},{4,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5},{2,3,7},{4},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5},{2,3,8},{4},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5,8},{2,3,6},{4},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2,3,8},{4},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6},{2,4,8},{3},{5},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,6,8},{2,3,7},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2,3},{4,7},{5},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,6},{2,3},{4,7,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,3},{4,8},{5},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,7},{2,4},{3,8},{5},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2},{3,4,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4},{3,5,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,5},{3},{4,8},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5,8},{2,4,6},{3},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,8},{2,3,5},{6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,4},{3,5,7},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4},{3,5,8},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,7},{3,5,6},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,7},{2,3,5},{4},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,5},{3,8},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,8},{4,6},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,5,7},{3},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,7},{2},{4,5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,7},{3,5,8},{6}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2},{3,5,7,8},{4,6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2},{3,5,8},{4,6,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5,7},{3,6},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,7,8},{2},{3},{4,6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5,7,8},{3},{4,6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5,6,7,8,9},{2}}=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
{{1,7,8,9},{2},{3},{4},{5},{6}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1,3,4,5,6,7,8,9,10},{2}}=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,3]
{{1,5,6,7},{2},{3,8},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7,8},{2},{3,5},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6,8},{2},{3},{4,7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,5,6,7,8,9},{3}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1,3,4,5,6,7,8},{2},{9}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1},{2,4,5,6,7,8,9,10},{3}}=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
{{1},{2,5,6,7,8,9},{3,4}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,4,5,6,7,8},{2,3},{9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,3,4,5,6,7,8,9},{2},{10}}=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
{{1},{2,3,5},{4,6,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1},{2,3,5},{4,6,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2},{3,4,5,6,7,8,9,10}}=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
{{1,2,3,4},{5,6,7,8,9,10}}=>[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]
{{1,3},{2,5,6},{4},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5},{3,7,8},{6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2},{3,7},{4,5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2},{3,5},{4,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5,7,8},{4},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,7},{2},{3,5,6,8},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2},{3,5,7},{4,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2},{3,5,7},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,3,5},{7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,8},{2},{3},{4,6,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,5,6},{2},{3,4,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,6},{2,4,5},{7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2},{3},{4},{5},{6,7},{8,9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2,3,7},{4,5},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2},{4,5,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3},{4,5,7},{6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2},{3,4,6},{5,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2},{3,4,7},{5,6,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2},{3},{4,6,8},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3},{4,6,7},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,4},{5},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5},{3},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,5},{4},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,7},{2,8},{3},{4,5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,8},{3},{5,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,6,7},{3},{4,5,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,8},{2,5,6},{3},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6,8},{2,7},{3,4},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6,7},{2,4},{3,8},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3,5},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,4,8},{3,6},{5,10},{7},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,6},{2,7},{3},{4,5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,4,6},{5,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,7,8},{3,5},{4,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,5,6},{2,7},{3,4},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2,7,8},{3},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,8},{2},{3,5},{4,6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,6},{2},{3,5,8},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,3,8,9},{4},{5},{6},{7}}=>[5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[1,1,1,1,5]
{{1,2,3,9},{4,5},{6},{7},{8}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1,2,3,4,9,10},{5},{6},{7},{8}}=>[6,1,1,1,1]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[1,1,1,1,6]
{{1,2,3,4,8,9},{5},{6},{7}}=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[1,1,1,6]
{{1,2,3,4,9},{5,6},{7},{8}}=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[1,1,2,5]
{{1,2,3,4,10},{5,6},{7},{8},{9}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,2,3,9,10},{4},{5},{6},{7},{8}}=>[5,1,1,1,1,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
{{1,2,8,9},{3,7},{4},{5},{6}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1,2,4,8,9},{3},{5},{6},{7}}=>[5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[1,1,1,1,5]
{{1,2,9},{3,8},{4,5},{6},{7}}=>[3,2,2,1,1]=>[[1,4,9],[2,6],[3,8],[5],[7]]=>[1,1,2,2,3]
{{1,2,5,9},{3,4},{6},{7},{8}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1,2,3,10},{4,5},{6},{7},{8},{9}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1},{2,6,8},{3},{4,5,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,6,7},{3,8},{4,5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,6},{3,8},{4,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,9},{2,3,4,5,6,7,8}}=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
{{1,8},{2,3,4,5,6,7},{9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,7},{2,3,4,5,6},{8},{9}}=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[1,1,2,5]
{{1,6},{2,3,4,5},{7},{8},{9}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1,5},{2,3,4},{6},{7},{8},{9}}=>[3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,3]
{{1,3,8},{2,6,7},{4},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,7},{3,6},{4},{5,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,8},{3},{4,6},{5,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,10},{2,3,4,5,6,7,8,9}}=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
{{1,9},{2,3,4,5,6,8},{7}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,10},{2,3,4,5,6,7,9},{8}}=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
{{1,9},{2,3,4,5,8},{6,7}}=>[5,2,2]=>[[1,2,7,8,9],[3,4],[5,6]]=>[2,2,5]
{{1,9},{2,3,4,5,7,8},{6}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,3},{2,5,6},{4,7},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,3},{2,7},{4,5,6},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,5,8},{3},{4,6,7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4},{2,6,7},{3,5},{8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,7,8},{3,6},{5}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,4,5},{3,6,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,4,5},{3,6,8},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5,6},{3,7,8},{4}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,4},{3,5,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6},{2,3,8},{5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4},{2},{3,5,6,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6},{2,7},{4,5,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,9},{2,8},{3,7},{4,6},{5},{10}}=>[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[1,1,2,2,2,2]
{{1},{2,10},{3,9},{4,8},{5,7},{6}}=>[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[1,1,2,2,2,2]
{{1,4,6},{2,3,5,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2,4,6},{3},{5,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1},{2,4,6,7,8},{3,5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,6},{3,4,5,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1},{2,3,5,8},{4,7},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,3,4,5,6,7,9},{8}}=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
{{1,2,3,4,5,6,7,8,10},{9}}=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
{{1,2},{3,4,5,6,7,8},{9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,3,4,5,6,7,9},{2},{8}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1,5,7,8},{2,3,4,6}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,3,6,8},{2,4,5,7}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,2,6,8},{3,4,5,7}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,6},{2,3,4,5,7,8}}=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
{{1,2,6},{3,4,5,8},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,4,8},{2,3,5,6},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5},{2,3,4,8},{6,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,8},{2,3,5},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,4},{3,5,6,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,5,8},{2,3,4,6,7}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,3,4},{2,5,6,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,4,6,7},{2,3,8},{5}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,3,8},{2,4,6,7},{5}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,3,5},{2,8},{4,6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,7,8},{2,3,6},{5}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,6},{2,3,5},{4,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,6},{3,5},{4,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,5},{3,6},{4,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5},{2,3,6},{4,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,7,8},{2,6},{3,5}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,7,8},{2,3,5},{4,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,7,8},{2,5},{3,4,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,7,8},{2,4,6},{3,5}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,8},{2,3,5,7},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,5},{3,4,6,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}=>[2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[2,2,2,2,2,2]
{{1},{2},{3},{4},{5},{6,9},{7},{8},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,8},{2,3},{4},{5},{6},{7},{9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,2},{3},{4},{5},{6},{7},{8,9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,3,4,5,6,7},{2,9},{8}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,3,4,5,7},{6,8},{9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,3,4,5,6,8},{2,9},{7}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,3,4,5,6,9},{2,8},{7}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,3,4,5,6,7,8},{2,10},{9}}=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
{{1,2},{3,4,5,6,7,8,9}}=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
{{1,2,3},{4,5,6,7,8,9}}=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
{{1,2,3,4},{5,6,7,8,9}}=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
{{1},{2},{3,4,5,6,7,8,9}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1,2},{3,5,6,7,8,9},{4}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,4,5,6,7},{3},{8,9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,3},{4,5,6,7,8,9,10}}=>[7,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]
{{1,2,3},{4,5,7,8,9},{6}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
{{1,2,3,5,6},{4},{7,8,9}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
{{1,2,3,4},{5,6,7,9},{8}}=>[4,4,1]=>[[1,3,4,5],[2,7,8,9],[6]]=>[1,4,4]
{{1},{2},{3},{4},{5,7},{6,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4,6},{5,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3,5},{4,8},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,4},{3,8},{5},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4},{5},{6,8},{7,9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2},{3},{4,7},{5,8},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4},{5,7},{6,9},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2},{3,6},{4,8},{5},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3},{4,6,7},{5,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3},{4,6},{5,9},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2,5},{3,8},{4},{6},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2},{3,5,6},{4,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,5},{4,9},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2,4,5},{3,8},{6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4},{3,9},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,3},{2,9},{4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,4,6,7,8},{2,3,5}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,3,6,7,8},{2,4,5}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,3,5},{2,6},{4,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,5,7,8},{2,3,6}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,3,7},{2,4,5,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5,8},{2,4,6},{3,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,5,8},{3,4,6,7}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1},{2,3,5,7},{4,6},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,3,4,5,7},{6,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,3,5,8},{4,6,7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,3},{2,6,8},{4,5},{7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4,6,7},{2},{3},{5,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,7,8},{2},{3,5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,7,8},{3,5},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,7,8},{3,6},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2},{3,7,8},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1},{2,3,4,6,8},{5,7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,3,4,5,6,8},{7,9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,5,6},{2,3},{4,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,3,9},{4},{5},{6},{7},{8}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1,2,9},{3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,2,3,10},{4},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1,3},{2,4,5,6,8},{7}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,6,7},{2,3,4,5,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,7},{2,3,4},{5,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,5},{2,3,7,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,4,6,8},{2,3,5,7}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,4,8},{2,3,6,7},{5}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,3,7},{2,6},{4,5,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,6},{3,7},{4,5,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2},{3,4,6},{5,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,3},{4,7},{5,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5},{2,6,7,8},{3,4}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,7},{2,6,8},{3,4,5}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,6},{3,5,7,8},{4}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1},{2,3,6},{4,5,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,7,8},{2,4},{3,5,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1},{2,3,9},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,2,3,4,5,6,8,9},{7}}=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
{{1,2,4,5,6,7,8,9},{3}}=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
{{1,2,3,4,5,6,7,9,10},{8}}=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
{{1,2},{3,5},{4},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,9},{2,4},{3},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,9},{2},{3,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,10},{2,3},{4},{5},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
{{1,3},{2,5,8},{4},{6,7}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,9},{2,8},{3},{4},{5},{6},{7}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,3,9},{2},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,10},{2,9},{3},{4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
{{1},{2,9},{3,8},{4},{5},{6},{7}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,2,7},{3},{4},{5},{6},{8,9}}=>[3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,3]
{{1,2},{3,4,9},{5},{6},{7},{8}}=>[3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,3]
{{1,3,8},{2},{4},{5},{6},{7},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,3,10},{2},{4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,3]
{{1},{2,4},{3,5,6,7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,5,6},{2},{3},{4,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,3,5},{2},{4,6},{7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,7},{2},{4},{5},{6,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,3,6},{2},{4},{5,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,7},{4,8},{5},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,7},{2},{3},{4},{5},{6,8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6},{2},{3},{4},{5,8},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4},{2,6},{3},{5,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2,6},{3},{4,8},{7}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5,7},{2},{3},{4},{6,8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5},{2},{3},{4,6},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4},{2},{3,6},{5},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1},{2,5},{3,6},{4},{7},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,4,6},{2},{3,5,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,6},{2},{3},{4,7},{5},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,6},{2},{3},{4,7},{5,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2},{3},{4,7},{6,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5,7},{2},{3},{4,6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,7},{2},{3,6},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4},{2},{3,7},{5},{6,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2},{3,7},{4,8},{6}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,5},{2},{3,7},{4},{6},{8}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,7},{2,5},{3,6},{4},{8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,6},{3},{4,8},{5},{7}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,5},{2,3,4,8},{6},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,5},{2,3,8},{6},{7}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2,3,4,6},{5,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,7},{2,3},{4,5,6,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,7},{2,3,5,6},{4,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,4,7,8},{2,3,5,6}}=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
{{1,5,7,8},{2,3},{4,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5,6,8},{2,3},{4,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5},{2},{3,4,6,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,6},{2},{3},{4,5,7,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2,6,7,8},{3},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5},{3,6,7,8},{4}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,7},{2},{5,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4,9},{3,6},{5,10},{7},{8}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,4,8},{3,7},{5,10},{6},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,4,9},{3,7},{5,10},{6},{8}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,4,9},{3,8},{5,10},{6},{7}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,5,10},{3,6},{4,8},{7},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,5,10},{3,6},{4,9},{7},{8}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,5,10},{3,7},{4,8},{6},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,5,10},{3,7},{4,9},{6},{8}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,5,10},{3,8},{4,9},{6},{7}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,6},{3,7},{4,8},{5,10},{9}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,2,6},{3,7},{4,9},{5,10},{8}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,2,6},{3,8},{4,9},{5,10},{7}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,2,7},{3,8},{4,9},{5,10},{6}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,3,6},{2,4,8},{5,10},{7},{9}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,6},{2,4,9},{5,10},{7},{8}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,7},{2,4,8},{5,10},{6},{9}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,7},{2,4,9},{5,10},{6},{8}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,8},{2,4,9},{5,10},{6},{7}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,6},{2,5,10},{4,8},{7},{9}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,6},{2,5,10},{4,9},{7},{8}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,7},{2,5,10},{4,8},{6},{9}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,7},{2,5,10},{4,9},{6},{8}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,8},{2,5,10},{4,9},{6},{7}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,3,7},{2,6},{4,8},{5,10},{9}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,3,7},{2,6},{4,9},{5,10},{8}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,3,8},{2,6},{4,9},{5,10},{7}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,3,8},{2,7},{4,9},{5,10},{6}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,4,8},{2,5,10},{3,6},{7},{9}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,4,9},{2,5,10},{3,6},{7},{8}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,4,8},{2,5,10},{3,7},{6},{9}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,4,9},{2,5,10},{3,7},{6},{8}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,4,9},{2,5,10},{3,8},{6},{7}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,4,8},{2,6},{3,7},{5,10},{9}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,4,9},{2,6},{3,7},{5,10},{8}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,4,9},{2,6},{3,8},{5,10},{7}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,4,9},{2,7},{3,8},{5,10},{6}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,5,10},{2,6},{3,7},{4,8},{9}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,5,10},{2,6},{3,7},{4,9},{8}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,5,10},{2,6},{3,8},{4,9},{7}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,5,10},{2,7},{3,8},{4,9},{6}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,3,7},{2,4,8},{5,10},{6,12},{9},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,4,8},{5,11},{6,12},{9},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,4,9},{5,10},{6,12},{8},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,4,9},{5,11},{6,12},{8},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,4,10},{5,11},{6,12},{8},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,4,9},{5,10},{6,12},{7},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,4,9},{5,11},{6,12},{7},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,4,10},{5,11},{6,12},{7},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,9},{2,4,10},{5,11},{6,12},{7},{8}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,5,10},{4,8},{6,12},{9},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,5,11},{4,8},{6,12},{9},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,5,10},{4,9},{6,12},{8},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,5,11},{4,9},{6,12},{8},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,5,11},{4,10},{6,12},{8},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,5,10},{4,9},{6,12},{7},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,5,11},{4,9},{6,12},{7},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,5,11},{4,10},{6,12},{7},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,9},{2,5,11},{4,10},{6,12},{7},{8}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,6,12},{4,8},{5,10},{9},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,6,12},{4,8},{5,11},{9},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,6,12},{4,9},{5,10},{8},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,6,12},{4,9},{5,11},{8},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,7},{2,6,12},{4,10},{5,11},{8},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,6,12},{4,9},{5,10},{7},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,6,12},{4,9},{5,11},{7},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,8},{2,6,12},{4,10},{5,11},{7},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,3,9},{2,6,12},{4,10},{5,11},{7},{8}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,8},{2,5,10},{3,7},{6,12},{9},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,8},{2,5,11},{3,7},{6,12},{9},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,9},{2,5,10},{3,7},{6,12},{8},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,9},{2,5,11},{3,7},{6,12},{8},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,10},{2,5,11},{3,7},{6,12},{8},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,9},{2,5,10},{3,8},{6,12},{7},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,9},{2,5,11},{3,8},{6,12},{7},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,10},{2,5,11},{3,8},{6,12},{7},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,10},{2,5,11},{3,9},{6,12},{7},{8}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,8},{2,6,12},{3,7},{5,10},{9},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,8},{2,6,12},{3,7},{5,11},{9},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,9},{2,6,12},{3,7},{5,10},{8},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,9},{2,6,12},{3,7},{5,11},{8},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,10},{2,6,12},{3,7},{5,11},{8},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,9},{2,6,12},{3,8},{5,10},{7},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,9},{2,6,12},{3,8},{5,11},{7},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,10},{2,6,12},{3,8},{5,11},{7},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,10},{2,6,12},{3,9},{5,11},{7},{8}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,10},{2,6,12},{3,7},{4,8},{9},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,11},{2,6,12},{3,7},{4,8},{9},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,10},{2,6,12},{3,7},{4,9},{8},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,11},{2,6,12},{3,7},{4,9},{8},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,11},{2,6,12},{3,7},{4,10},{8},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,10},{2,6,12},{3,8},{4,9},{7},{11}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,11},{2,6,12},{3,8},{4,9},{7},{10}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,11},{2,6,12},{3,8},{4,10},{7},{9}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,11},{2,6,12},{3,9},{4,10},{7},{8}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,4,6},{2,3,5},{7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2},{3,6,8},{4,5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1},{2,3,4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,6,9},{2},{3},{4},{5},{7},{8}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,5,9},{2},{3},{4},{6},{7},{8}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,6,7,9},{2},{3},{4},{5},{8}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1,3},{2,4,5,6,7},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,4},{3,5,6,7,8,9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1},{2,5},{3,4,6,7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,4},{2,3,5,6,7},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,4},{3,5,6,7},{8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,3},{2,4,5,6,7,8},{9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1},{2,4},{3,5,6,7,8,9,10}}=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
{{1},{2,5},{3,4,6,7,8,9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1},{2,3,5},{4,6,7,8,9}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
{{1},{2,6},{3,4,5,7,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,3,4,6},{5,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,5},{2,3,4,6,7},{8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,4},{2,3,5,6,7,8},{9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,4},{3,5,6,7,8},{9}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
{{1,3},{2,4,5,6,7,8,9},{10}}=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
{{1,2,7},{3},{4,6,8},{5}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,2,4,6,8,10},{3},{5},{7},{9}}=>[6,1,1,1,1]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[1,1,1,1,6]
{{1,2,4,6,9},{3,10},{5},{7},{8}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,2,4,7,10},{3,8},{5},{6},{9}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,2,4,7,9},{3},{5,10},{6},{8}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,2,4,8},{3,9},{5,10},{6},{7}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,5,8,10},{3,6},{4},{7},{9}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,2,5,9},{3,6,10},{4},{7},{8}}=>[4,3,1,1,1]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[1,1,1,3,4]
{{1,2,5,7,10},{3},{4,8},{6},{9}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,2,5,7,9},{3},{4},{6,10},{8}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,2,5,8},{3,9},{4},{6,10},{7}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,6,10},{3,7},{4,8},{5},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,6,9},{3,7},{4},{5,10},{8}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,2,6,8},{3},{4,9},{5,10},{7}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,3,6,8,10},{2,4},{5},{7},{9}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,3,6,9},{2,4,10},{5},{7},{8}}=>[4,3,1,1,1]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[1,1,1,3,4]
{{1,3,7,10},{2,4,8},{5},{6},{9}}=>[4,3,1,1,1]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[1,1,1,3,4]
{{1,3,7,9},{2,4},{5,10},{6},{8}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,3,5,8,10},{2},{4,6},{7},{9}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,3,5,9},{2},{4,6,10},{7},{8}}=>[4,3,1,1,1]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[1,1,1,3,4]
{{1,3,5,7,10},{2},{4},{6,8},{9}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,3,5,7,9},{2},{4},{6},{8,10}}=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
{{1,3,5,8},{2,9},{4},{6},{7,10}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,3,6,10},{2,7},{4},{5,8},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,3,6,9},{2,7},{4},{5},{8,10}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,3,6,8},{2},{4,9},{5},{7,10}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,3,7},{2,8},{4,9},{5},{6,10}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,4,8,10},{2,5},{3,6},{7},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,4,7,10},{2,5},{3},{6,8},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,4,7,9},{2,5},{3},{6},{8,10}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,4,8},{2,5,9},{3},{6},{7,10}}=>[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[1,1,2,3,3]
{{1,4,6,10},{2},{3,7},{5,8},{9}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,4,6,9},{2},{3,7},{5},{8,10}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,4,6,8},{2},{3},{5,9},{7,10}}=>[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[1,1,2,2,4]
{{1,4,7},{2,8},{3},{5,9},{6,10}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,5,9},{2,6},{3,7},{4},{8,10}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,5,8},{2,6},{3},{4,9},{7,10}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,5,7},{2},{3,8},{4,9},{6,10}}=>[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
{{1,4,9},{2,5,10},{3,11},{6},{7},{8,12}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,10},{2,6,11},{3,7},{4},{8},{9,12}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1,5,9},{2,6,10},{3},{4},{7,11},{8,12}}=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[1,1,2,2,3,3]
{{1},{2,4,6},{3},{5,7,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5,7},{3},{4,6,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,8},{2,9},{3},{4},{5},{6},{7}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2,7},{3,8},{4},{5},{6}}=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
{{1,7},{2},{3,9},{4},{5},{6},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,6},{2},{3},{4,9},{5},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,5,6},{2},{3,8},{4},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,5},{2},{3},{4},{6,9},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,4},{2},{3},{5},{6},{7,9},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,3},{2},{4},{5},{6},{7},{8,9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,2,3,4,5,6,9},{7,8}}=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
{{1,2,3,4,5,6,7,10},{8,9}}=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
{{1},{2,3,4,5,6,7,10},{8,9}}=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
{{1,3,4,5,6,9},{2},{7,8}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1},{2},{3},{4,6,8},{5,7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2},{3,5,8},{4,6},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2,8},{3},{4},{5},{6},{7},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,2,7},{3},{4},{5},{6},{8},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,2,9},{3,4,5,6,7,8}}=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
{{1},{2,3,4,5,6,7},{8,9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1},{2,3,4,5,6,9},{7},{8}}=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[1,1,1,6]
{{1},{2,3,4,5,9},{6},{7},{8}}=>[5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[1,1,1,1,5]
{{1},{2,3,4,9},{5},{6},{7},{8}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1},{2,3,4,5,6,7,10},{8},{9}}=>[7,1,1,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[1,1,1,7]
{{1},{2,3,4,5,9},{6,7},{8}}=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[1,1,2,5]
{{1},{2,3,4,5,6,10},{7},{8},{9}}=>[6,1,1,1,1]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[1,1,1,1,6]
{{1},{2,3,4,9},{5,6},{7},{8}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1},{2,3,4,5,10},{6},{7},{8},{9}}=>[5,1,1,1,1,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
{{1},{2,3,9},{4,5},{6},{7},{8}}=>[3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,3]
{{1},{2,3,4,10},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1},{2,3,10},{4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,3]
{{1},{2,3},{4},{5},{6},{7,9},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,2,7},{3,8},{4},{5,6}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2,6,7},{3},{4,8},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,4},{3,6},{5,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1},{2,5},{3},{4,7},{6,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1,4,8},{2,3,7},{5,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2},{3,4,7},{5,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,7},{2,3},{5,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,7},{2,4},{5,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,7},{2,6,8},{4,5}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,7},{2,3,5,8},{4,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,6},{3,8},{4,5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,8},{3,4,6},{5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2},{3,5,7,8},{4,6}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5,7,8},{2,6},{3,4}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,5,8},{2,7},{3,4,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6,8},{2,3},{4,5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6,8},{2,5,7},{3,4}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6,8},{2,4,7},{3,5}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1},{2,4},{3,5},{6,7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,6,8},{3},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,5,6,9},{2},{3},{4},{7},{8}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1,4,5,9},{2},{3},{6},{7},{8}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1,3,4,9},{2},{5},{6},{7},{8}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1,6},{2},{3},{4},{5},{7,8,9}}=>[3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,3]
{{1,5},{2},{3},{4},{6,7,8,9}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1,7,8,10},{2},{3},{4},{5},{6},{9}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1,4},{2},{3},{5,6,7,9},{8}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1,6,7,10},{2},{3},{4},{5},{8},{9}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1,3},{2},{4,5,6,9},{7},{8}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1,5,6,10},{2},{3},{4},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1,2},{3,4,5,9},{6},{7},{8}}=>[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[1,1,1,2,4]
{{1,4,5,10},{2},{3},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1,3,4,10},{2},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
{{1,5},{2,3,4,6},{7,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,3,4},{2,8},{5,6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,6,7},{2,8},{4,5}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,8},{2,3,6},{4,5,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,7},{3,4,5,6,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,2},{3,5,6},{4,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5,6},{2,7,8},{3,4}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,5},{2,7,8},{3,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,7},{2,6},{3,4,5,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2},{3,7},{4,5,6,8}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,7},{2,5,6,8},{3,4}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,3,7},{4},{5,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,4,5,6,7},{2},{8,9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,3,4},{2,6},{5,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,4,5,6},{2,8,9},{7}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
{{1,3,4,5,6},{2},{7,8,9}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
{{1,3,4,5,6,7,8},{2},{9,10}}=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
{{1,7},{2},{3,4,5,8},{6}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4},{2,3,5,6},{7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,5},{2,4},{6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2,5,6,7},{3},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2,6},{3},{4},{5},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,2,5},{3},{4},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1,2,4},{3},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
{{1},{2},{3,4,5,7},{6,8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,4,7},{2},{3},{5,6,8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1,4,5},{2},{3,6,7},{8}}=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
{{1},{2,5},{3,4,6,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4,5,6},{3,7},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,2},{3},{4},{5},{6},{7,9},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,2},{3},{4},{5},{6},{7},{8,10},{9}}=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
{{1,3},{2},{4},{5},{6},{7,9},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2,3},{4},{5},{6},{7},{8,9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,2},{3},{4},{5},{6},{7},{8},{9,10}}=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
{{1},{2,3,6},{4},{5,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,3,7},{4},{5,8},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4},{3,7},{5},{6,8}}=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
{{1},{2,5},{3},{4,6,8},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,5},{3},{4,6,7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,2},{3,4,6,8},{5,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2,3,4,5,8,9},{6},{7}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1,2,3,4,5,9},{6,7},{8}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,3,4,5,6,9,10},{7},{8}}=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
{{1,2,3,4,8,9},{5,7},{6}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,3,4,6,8,9},{5},{7}}=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
{{1,2,3,4,9},{5,8},{6,7}}=>[5,2,2]=>[[1,2,7,8,9],[3,4],[5,6]]=>[2,2,5]
{{1,2,3,4,7,9},{5,6},{8}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,3,4,5,6,10},{7,8},{9}}=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
{{1,4,6,7,8},{2},{3,5}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,4,5},{2,3,6,7,8}}=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
{{1,4,5},{2,3,6},{7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,5},{2,3,8},{6,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,7},{2,3,8},{5,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,4},{2,7},{5,6,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,6,8},{2,7},{4,5}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,2},{3,6,7},{4,5,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6,7},{2,3},{4,5,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6,7},{2,5,8},{3,4}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,5,6},{2,8},{3,4,7}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,6,7},{2,4,5},{3,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1},{2,4,6,8,10},{3},{5},{7},{9}}=>[5,1,1,1,1,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
{{1},{2,4,6,10},{3},{5},{7,9},{8}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1},{2,4,8,10},{3},{5,7},{6},{9}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1},{2,4,10},{3},{5,7,9},{6},{8}}=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[1,1,1,1,3,3]
{{1},{2,4,10},{3},{5,9},{6,8},{7}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1},{2,6,8,10},{3,5},{4},{7},{9}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1},{2,6,10},{3,5},{4},{7,9},{8}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1},{2,8,10},{3,5,7},{4},{6},{9}}=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[1,1,1,1,3,3]
{{1},{2,8,10},{3,7},{4,6},{5},{9}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1},{2,10},{3,5,7,9},{4},{6},{8}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1},{2,10},{3,5,9},{4},{6,8},{7}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1},{2,10},{3,7,9},{4,6},{5},{8}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1},{2,10},{3,9},{4,6,8},{5},{7}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,3},{2},{4,6,8,10},{5},{7},{9}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1,3},{2},{4,6,10},{5},{7,9},{8}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,3},{2},{4,8,10},{5,7},{6},{9}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,3},{2},{4,10},{5,7,9},{6},{8}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,3},{2},{4,10},{5,9},{6,8},{7}}=>[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[1,1,2,2,2,2]
{{1,3,5},{2},{4},{6,8,10},{7},{9}}=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[1,1,1,1,3,3]
{{1,3,5},{2},{4},{6,10},{7,9},{8}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,5},{2,4},{3},{6,8,10},{7},{9}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,5},{2,4},{3},{6,10},{7,9},{8}}=>[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[1,1,2,2,2,2]
{{1,3,5,7},{2},{4},{6},{8,10},{9}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1,3,7},{2},{4,6},{5},{8,10},{9}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,5,7},{2,4},{3},{6},{8,10},{9}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,7},{2,4,6},{3},{5},{8,10},{9}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,7},{2,6},{3,5},{4},{8,10},{9}}=>[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[1,1,2,2,2,2]
{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>[5,1,1,1,1,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
{{1,3,5,9},{2},{4},{6,8},{7},{10}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1,3,7,9},{2},{4,6},{5},{8},{10}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1,3,9},{2},{4,6,8},{5},{7},{10}}=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[1,1,1,1,3,3]
{{1,3,9},{2},{4,8},{5,7},{6},{10}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,5,7,9},{2,4},{3},{6},{8},{10}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1,5,9},{2,4},{3},{6,8},{7},{10}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,7,9},{2,4,6},{3},{5},{8},{10}}=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[1,1,1,1,3,3]
{{1,7,9},{2,6},{3,5},{4},{8},{10}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,9},{2,4,6,8},{3},{5},{7},{10}}=>[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,4]
{{1,9},{2,4,8},{3},{5,7},{6},{10}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,9},{2,6,8},{3,5},{4},{7},{10}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,9},{2,8},{3,5,7},{4},{6},{10}}=>[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[1,1,1,2,2,3]
{{1,9},{2},{3},{4},{5},{6,7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,9},{2},{3},{4},{5},{6,8},{7}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2,5},{3},{4},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3,5},{4},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3},{4,5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,9},{2},{3},{4},{5},{6,7,8}}=>[3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,3]
{{1},{2},{3},{4},{5},{6,8},{7},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
{{1,6,8,9},{2},{3},{4},{5},{7}}=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
{{1,5},{2},{3},{4},{6},{7},{8,9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,2,9},{3,6},{4},{5},{7},{8}}=>[3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,3]
{{1,10},{2,6},{3},{4},{5},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
{{1,10},{2},{3,6},{4},{5},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
{{1},{2,3},{4,5},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1,10},{2},{3},{4,6},{5},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
{{1},{2},{3,4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
{{1,10},{2},{3},{4},{5,6},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
{{1,2,4},{3,6,7,8},{5}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,4},{3,5,6,8},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,3,6},{4},{5,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,4},{3,5,6,8},{7}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1},{2,5},{3,4,6},{7,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,2},{3},{4,7},{5,6,8}}=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
{{1,4},{2},{3},{5},{6,9},{7},{8}}=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
{{1},{2,4,6},{3},{5,7},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1,4,6},{2,3,5,8},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,6},{2,3,5,8},{4,7}}=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
{{1,3,5},{2,7,8},{4,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,3,4},{2,5,7,8},{6}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,4,5,6},{2},{3,7,8}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,2,5,7,8},{3},{4,6}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1},{2,3,6,8},{4,7},{5}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3,6},{2,4},{5,7,8}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,4,8},{2,5,7},{3,6}}=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
{{1,2,6,8},{3},{4,5,7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1,4,6,8},{2,3,5},{7}}=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
{{1},{2,3,4,6,7},{5,8}}=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
{{1,2,3,4,5,7},{6},{8,9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1},{2,3,6},{4,7},{5},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,7},{3,8},{5},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,5,7},{3},{4,8},{6}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,7},{3,5},{6},{8}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,5,8},{3,6},{4},{7}}=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
{{1},{2,4,6,7},{3,5},{8}}=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
{{1,3},{2},{4,5,6,7,8,9}}=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
{{1,2,4},{3},{5,6,7,8,9}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
{{1,2,3,5},{4},{6,7,8,9}}=>[4,4,1]=>[[1,3,4,5],[2,7,8,9],[6]]=>[1,4,4]
{{1,2,3,4,6},{5},{7,8,9}}=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[1,3,5]
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
searching the database
Sorry, this map was not found in the database.