Identifier
Mp00284: Standard tableaux —rows⟶ Set partitions
Mp00128: Set partitions —to composition⟶ Integer compositions
Images
=>
Cc0007;cc-rep-0Cc0009;cc-rep-1
[[1]]=>{{1}}=>[1] [[1,2]]=>{{1,2}}=>[2] [[1],[2]]=>{{1},{2}}=>[1,1] [[1,2,3]]=>{{1,2,3}}=>[3] [[1,3],[2]]=>{{1,3},{2}}=>[2,1] [[1,2],[3]]=>{{1,2},{3}}=>[2,1] [[1],[2],[3]]=>{{1},{2},{3}}=>[1,1,1] [[1,2,3,4]]=>{{1,2,3,4}}=>[4] [[1,3,4],[2]]=>{{1,3,4},{2}}=>[3,1] [[1,2,4],[3]]=>{{1,2,4},{3}}=>[3,1] [[1,2,3],[4]]=>{{1,2,3},{4}}=>[3,1] [[1,3],[2,4]]=>{{1,3},{2,4}}=>[2,2] [[1,2],[3,4]]=>{{1,2},{3,4}}=>[2,2] [[1,4],[2],[3]]=>{{1,4},{2},{3}}=>[2,1,1] [[1,3],[2],[4]]=>{{1,3},{2},{4}}=>[2,1,1] [[1,2],[3],[4]]=>{{1,2},{3},{4}}=>[2,1,1] [[1],[2],[3],[4]]=>{{1},{2},{3},{4}}=>[1,1,1,1] [[1,2,3,4,5]]=>{{1,2,3,4,5}}=>[5] [[1,3,4,5],[2]]=>{{1,3,4,5},{2}}=>[4,1] [[1,2,4,5],[3]]=>{{1,2,4,5},{3}}=>[4,1] [[1,2,3,5],[4]]=>{{1,2,3,5},{4}}=>[4,1] [[1,2,3,4],[5]]=>{{1,2,3,4},{5}}=>[4,1] [[1,3,5],[2,4]]=>{{1,3,5},{2,4}}=>[3,2] [[1,2,5],[3,4]]=>{{1,2,5},{3,4}}=>[3,2] [[1,3,4],[2,5]]=>{{1,3,4},{2,5}}=>[3,2] [[1,2,4],[3,5]]=>{{1,2,4},{3,5}}=>[3,2] [[1,2,3],[4,5]]=>{{1,2,3},{4,5}}=>[3,2] [[1,4,5],[2],[3]]=>{{1,4,5},{2},{3}}=>[3,1,1] [[1,3,5],[2],[4]]=>{{1,3,5},{2},{4}}=>[3,1,1] [[1,2,5],[3],[4]]=>{{1,2,5},{3},{4}}=>[3,1,1] [[1,3,4],[2],[5]]=>{{1,3,4},{2},{5}}=>[3,1,1] [[1,2,4],[3],[5]]=>{{1,2,4},{3},{5}}=>[3,1,1] [[1,2,3],[4],[5]]=>{{1,2,3},{4},{5}}=>[3,1,1] [[1,4],[2,5],[3]]=>{{1,4},{2,5},{3}}=>[2,2,1] [[1,3],[2,5],[4]]=>{{1,3},{2,5},{4}}=>[2,2,1] [[1,2],[3,5],[4]]=>{{1,2},{3,5},{4}}=>[2,2,1] [[1,3],[2,4],[5]]=>{{1,3},{2,4},{5}}=>[2,2,1] [[1,2],[3,4],[5]]=>{{1,2},{3,4},{5}}=>[2,2,1] [[1,5],[2],[3],[4]]=>{{1,5},{2},{3},{4}}=>[2,1,1,1] [[1,4],[2],[3],[5]]=>{{1,4},{2},{3},{5}}=>[2,1,1,1] [[1,3],[2],[4],[5]]=>{{1,3},{2},{4},{5}}=>[2,1,1,1] [[1,2],[3],[4],[5]]=>{{1,2},{3},{4},{5}}=>[2,1,1,1] [[1],[2],[3],[4],[5]]=>{{1},{2},{3},{4},{5}}=>[1,1,1,1,1] [[1,2,3,4,5,6]]=>{{1,2,3,4,5,6}}=>[6] [[1,3,4,5,6],[2]]=>{{1,3,4,5,6},{2}}=>[5,1] [[1,2,4,5,6],[3]]=>{{1,2,4,5,6},{3}}=>[5,1] [[1,2,3,5,6],[4]]=>{{1,2,3,5,6},{4}}=>[5,1] [[1,2,3,4,6],[5]]=>{{1,2,3,4,6},{5}}=>[5,1] [[1,2,3,4,5],[6]]=>{{1,2,3,4,5},{6}}=>[5,1] [[1,3,5,6],[2,4]]=>{{1,3,5,6},{2,4}}=>[4,2] [[1,2,5,6],[3,4]]=>{{1,2,5,6},{3,4}}=>[4,2] [[1,3,4,6],[2,5]]=>{{1,3,4,6},{2,5}}=>[4,2] [[1,2,4,6],[3,5]]=>{{1,2,4,6},{3,5}}=>[4,2] [[1,2,3,6],[4,5]]=>{{1,2,3,6},{4,5}}=>[4,2] [[1,3,4,5],[2,6]]=>{{1,3,4,5},{2,6}}=>[4,2] [[1,2,4,5],[3,6]]=>{{1,2,4,5},{3,6}}=>[4,2] [[1,2,3,5],[4,6]]=>{{1,2,3,5},{4,6}}=>[4,2] [[1,2,3,4],[5,6]]=>{{1,2,3,4},{5,6}}=>[4,2] [[1,4,5,6],[2],[3]]=>{{1,4,5,6},{2},{3}}=>[4,1,1] [[1,3,5,6],[2],[4]]=>{{1,3,5,6},{2},{4}}=>[4,1,1] [[1,2,5,6],[3],[4]]=>{{1,2,5,6},{3},{4}}=>[4,1,1] [[1,3,4,6],[2],[5]]=>{{1,3,4,6},{2},{5}}=>[4,1,1] [[1,2,4,6],[3],[5]]=>{{1,2,4,6},{3},{5}}=>[4,1,1] [[1,2,3,6],[4],[5]]=>{{1,2,3,6},{4},{5}}=>[4,1,1] [[1,3,4,5],[2],[6]]=>{{1,3,4,5},{2},{6}}=>[4,1,1] [[1,2,4,5],[3],[6]]=>{{1,2,4,5},{3},{6}}=>[4,1,1] [[1,2,3,5],[4],[6]]=>{{1,2,3,5},{4},{6}}=>[4,1,1] [[1,2,3,4],[5],[6]]=>{{1,2,3,4},{5},{6}}=>[4,1,1] [[1,3,5],[2,4,6]]=>{{1,3,5},{2,4,6}}=>[3,3] [[1,2,5],[3,4,6]]=>{{1,2,5},{3,4,6}}=>[3,3] [[1,3,4],[2,5,6]]=>{{1,3,4},{2,5,6}}=>[3,3] [[1,2,4],[3,5,6]]=>{{1,2,4},{3,5,6}}=>[3,3] [[1,2,3],[4,5,6]]=>{{1,2,3},{4,5,6}}=>[3,3] [[1,4,6],[2,5],[3]]=>{{1,4,6},{2,5},{3}}=>[3,2,1] [[1,3,6],[2,5],[4]]=>{{1,3,6},{2,5},{4}}=>[3,2,1] [[1,2,6],[3,5],[4]]=>{{1,2,6},{3,5},{4}}=>[3,2,1] [[1,3,6],[2,4],[5]]=>{{1,3,6},{2,4},{5}}=>[3,2,1] [[1,2,6],[3,4],[5]]=>{{1,2,6},{3,4},{5}}=>[3,2,1] [[1,4,5],[2,6],[3]]=>{{1,4,5},{2,6},{3}}=>[3,2,1] [[1,3,5],[2,6],[4]]=>{{1,3,5},{2,6},{4}}=>[3,2,1] [[1,2,5],[3,6],[4]]=>{{1,2,5},{3,6},{4}}=>[3,2,1] [[1,3,4],[2,6],[5]]=>{{1,3,4},{2,6},{5}}=>[3,2,1] [[1,2,4],[3,6],[5]]=>{{1,2,4},{3,6},{5}}=>[3,2,1] [[1,2,3],[4,6],[5]]=>{{1,2,3},{4,6},{5}}=>[3,2,1] [[1,3,5],[2,4],[6]]=>{{1,3,5},{2,4},{6}}=>[3,2,1] [[1,2,5],[3,4],[6]]=>{{1,2,5},{3,4},{6}}=>[3,2,1] [[1,3,4],[2,5],[6]]=>{{1,3,4},{2,5},{6}}=>[3,2,1] [[1,2,4],[3,5],[6]]=>{{1,2,4},{3,5},{6}}=>[3,2,1] [[1,2,3],[4,5],[6]]=>{{1,2,3},{4,5},{6}}=>[3,2,1] [[1,5,6],[2],[3],[4]]=>{{1,5,6},{2},{3},{4}}=>[3,1,1,1] [[1,4,6],[2],[3],[5]]=>{{1,4,6},{2},{3},{5}}=>[3,1,1,1] [[1,3,6],[2],[4],[5]]=>{{1,3,6},{2},{4},{5}}=>[3,1,1,1] [[1,2,6],[3],[4],[5]]=>{{1,2,6},{3},{4},{5}}=>[3,1,1,1] [[1,4,5],[2],[3],[6]]=>{{1,4,5},{2},{3},{6}}=>[3,1,1,1] [[1,3,5],[2],[4],[6]]=>{{1,3,5},{2},{4},{6}}=>[3,1,1,1] [[1,2,5],[3],[4],[6]]=>{{1,2,5},{3},{4},{6}}=>[3,1,1,1] [[1,3,4],[2],[5],[6]]=>{{1,3,4},{2},{5},{6}}=>[3,1,1,1] [[1,2,4],[3],[5],[6]]=>{{1,2,4},{3},{5},{6}}=>[3,1,1,1] [[1,2,3],[4],[5],[6]]=>{{1,2,3},{4},{5},{6}}=>[3,1,1,1] [[1,4],[2,5],[3,6]]=>{{1,4},{2,5},{3,6}}=>[2,2,2] [[1,3],[2,5],[4,6]]=>{{1,3},{2,5},{4,6}}=>[2,2,2] [[1,2],[3,5],[4,6]]=>{{1,2},{3,5},{4,6}}=>[2,2,2] [[1,3],[2,4],[5,6]]=>{{1,3},{2,4},{5,6}}=>[2,2,2] [[1,2],[3,4],[5,6]]=>{{1,2},{3,4},{5,6}}=>[2,2,2] [[1,5],[2,6],[3],[4]]=>{{1,5},{2,6},{3},{4}}=>[2,2,1,1] [[1,4],[2,6],[3],[5]]=>{{1,4},{2,6},{3},{5}}=>[2,2,1,1] [[1,3],[2,6],[4],[5]]=>{{1,3},{2,6},{4},{5}}=>[2,2,1,1] [[1,2],[3,6],[4],[5]]=>{{1,2},{3,6},{4},{5}}=>[2,2,1,1] [[1,4],[2,5],[3],[6]]=>{{1,4},{2,5},{3},{6}}=>[2,2,1,1] [[1,3],[2,5],[4],[6]]=>{{1,3},{2,5},{4},{6}}=>[2,2,1,1] [[1,2],[3,5],[4],[6]]=>{{1,2},{3,5},{4},{6}}=>[2,2,1,1] [[1,3],[2,4],[5],[6]]=>{{1,3},{2,4},{5},{6}}=>[2,2,1,1] [[1,2],[3,4],[5],[6]]=>{{1,2},{3,4},{5},{6}}=>[2,2,1,1] [[1,6],[2],[3],[4],[5]]=>{{1,6},{2},{3},{4},{5}}=>[2,1,1,1,1] [[1,5],[2],[3],[4],[6]]=>{{1,5},{2},{3},{4},{6}}=>[2,1,1,1,1] [[1,4],[2],[3],[5],[6]]=>{{1,4},{2},{3},{5},{6}}=>[2,1,1,1,1] [[1,3],[2],[4],[5],[6]]=>{{1,3},{2},{4},{5},{6}}=>[2,1,1,1,1] [[1,2],[3],[4],[5],[6]]=>{{1,2},{3},{4},{5},{6}}=>[2,1,1,1,1] [[1],[2],[3],[4],[5],[6]]=>{{1},{2},{3},{4},{5},{6}}=>[1,1,1,1,1,1] [[1,2,3,4,5,6,7]]=>{{1,2,3,4,5,6,7}}=>[7] [[1,3,4,5,6,7],[2]]=>{{1,3,4,5,6,7},{2}}=>[6,1] [[1,2,4,5,6,7],[3]]=>{{1,2,4,5,6,7},{3}}=>[6,1] [[1,2,3,5,6,7],[4]]=>{{1,2,3,5,6,7},{4}}=>[6,1] [[1,2,3,4,6,7],[5]]=>{{1,2,3,4,6,7},{5}}=>[6,1] [[1,2,3,4,5,7],[6]]=>{{1,2,3,4,5,7},{6}}=>[6,1] [[1,2,3,4,5,6],[7]]=>{{1,2,3,4,5,6},{7}}=>[6,1] [[1,3,5,6,7],[2,4]]=>{{1,3,5,6,7},{2,4}}=>[5,2] [[1,2,5,6,7],[3,4]]=>{{1,2,5,6,7},{3,4}}=>[5,2] [[1,3,4,6,7],[2,5]]=>{{1,3,4,6,7},{2,5}}=>[5,2] [[1,2,4,6,7],[3,5]]=>{{1,2,4,6,7},{3,5}}=>[5,2] [[1,2,3,6,7],[4,5]]=>{{1,2,3,6,7},{4,5}}=>[5,2] [[1,3,4,5,7],[2,6]]=>{{1,3,4,5,7},{2,6}}=>[5,2] [[1,2,4,5,7],[3,6]]=>{{1,2,4,5,7},{3,6}}=>[5,2] [[1,2,3,5,7],[4,6]]=>{{1,2,3,5,7},{4,6}}=>[5,2] [[1,2,3,4,7],[5,6]]=>{{1,2,3,4,7},{5,6}}=>[5,2] [[1,3,4,5,6],[2,7]]=>{{1,3,4,5,6},{2,7}}=>[5,2] [[1,2,4,5,6],[3,7]]=>{{1,2,4,5,6},{3,7}}=>[5,2] [[1,2,3,5,6],[4,7]]=>{{1,2,3,5,6},{4,7}}=>[5,2] [[1,2,3,4,6],[5,7]]=>{{1,2,3,4,6},{5,7}}=>[5,2] [[1,2,3,4,5],[6,7]]=>{{1,2,3,4,5},{6,7}}=>[5,2] [[1,4,5,6,7],[2],[3]]=>{{1,4,5,6,7},{2},{3}}=>[5,1,1] [[1,3,5,6,7],[2],[4]]=>{{1,3,5,6,7},{2},{4}}=>[5,1,1] [[1,2,5,6,7],[3],[4]]=>{{1,2,5,6,7},{3},{4}}=>[5,1,1] [[1,3,4,6,7],[2],[5]]=>{{1,3,4,6,7},{2},{5}}=>[5,1,1] [[1,2,4,6,7],[3],[5]]=>{{1,2,4,6,7},{3},{5}}=>[5,1,1] [[1,2,3,6,7],[4],[5]]=>{{1,2,3,6,7},{4},{5}}=>[5,1,1] [[1,3,4,5,7],[2],[6]]=>{{1,3,4,5,7},{2},{6}}=>[5,1,1] [[1,2,4,5,7],[3],[6]]=>{{1,2,4,5,7},{3},{6}}=>[5,1,1] [[1,2,3,5,7],[4],[6]]=>{{1,2,3,5,7},{4},{6}}=>[5,1,1] [[1,2,3,4,7],[5],[6]]=>{{1,2,3,4,7},{5},{6}}=>[5,1,1] [[1,3,4,5,6],[2],[7]]=>{{1,3,4,5,6},{2},{7}}=>[5,1,1] [[1,2,4,5,6],[3],[7]]=>{{1,2,4,5,6},{3},{7}}=>[5,1,1] [[1,2,3,5,6],[4],[7]]=>{{1,2,3,5,6},{4},{7}}=>[5,1,1] [[1,2,3,4,6],[5],[7]]=>{{1,2,3,4,6},{5},{7}}=>[5,1,1] [[1,2,3,4,5],[6],[7]]=>{{1,2,3,4,5},{6},{7}}=>[5,1,1] [[1,3,5,7],[2,4,6]]=>{{1,3,5,7},{2,4,6}}=>[4,3] [[1,2,5,7],[3,4,6]]=>{{1,2,5,7},{3,4,6}}=>[4,3] [[1,3,4,7],[2,5,6]]=>{{1,3,4,7},{2,5,6}}=>[4,3] [[1,2,4,7],[3,5,6]]=>{{1,2,4,7},{3,5,6}}=>[4,3] [[1,2,3,7],[4,5,6]]=>{{1,2,3,7},{4,5,6}}=>[4,3] [[1,3,5,6],[2,4,7]]=>{{1,3,5,6},{2,4,7}}=>[4,3] [[1,2,5,6],[3,4,7]]=>{{1,2,5,6},{3,4,7}}=>[4,3] [[1,3,4,6],[2,5,7]]=>{{1,3,4,6},{2,5,7}}=>[4,3] [[1,2,4,6],[3,5,7]]=>{{1,2,4,6},{3,5,7}}=>[4,3] [[1,2,3,6],[4,5,7]]=>{{1,2,3,6},{4,5,7}}=>[4,3] [[1,3,4,5],[2,6,7]]=>{{1,3,4,5},{2,6,7}}=>[4,3] [[1,2,4,5],[3,6,7]]=>{{1,2,4,5},{3,6,7}}=>[4,3] [[1,2,3,5],[4,6,7]]=>{{1,2,3,5},{4,6,7}}=>[4,3] [[1,2,3,4],[5,6,7]]=>{{1,2,3,4},{5,6,7}}=>[4,3] [[1,4,6,7],[2,5],[3]]=>{{1,4,6,7},{2,5},{3}}=>[4,2,1] [[1,3,6,7],[2,5],[4]]=>{{1,3,6,7},{2,5},{4}}=>[4,2,1] [[1,2,6,7],[3,5],[4]]=>{{1,2,6,7},{3,5},{4}}=>[4,2,1] [[1,3,6,7],[2,4],[5]]=>{{1,3,6,7},{2,4},{5}}=>[4,2,1] [[1,2,6,7],[3,4],[5]]=>{{1,2,6,7},{3,4},{5}}=>[4,2,1] [[1,4,5,7],[2,6],[3]]=>{{1,4,5,7},{2,6},{3}}=>[4,2,1] [[1,3,5,7],[2,6],[4]]=>{{1,3,5,7},{2,6},{4}}=>[4,2,1] [[1,2,5,7],[3,6],[4]]=>{{1,2,5,7},{3,6},{4}}=>[4,2,1] [[1,3,4,7],[2,6],[5]]=>{{1,3,4,7},{2,6},{5}}=>[4,2,1] [[1,2,4,7],[3,6],[5]]=>{{1,2,4,7},{3,6},{5}}=>[4,2,1] [[1,2,3,7],[4,6],[5]]=>{{1,2,3,7},{4,6},{5}}=>[4,2,1] [[1,3,5,7],[2,4],[6]]=>{{1,3,5,7},{2,4},{6}}=>[4,2,1] [[1,2,5,7],[3,4],[6]]=>{{1,2,5,7},{3,4},{6}}=>[4,2,1] [[1,3,4,7],[2,5],[6]]=>{{1,3,4,7},{2,5},{6}}=>[4,2,1] [[1,2,4,7],[3,5],[6]]=>{{1,2,4,7},{3,5},{6}}=>[4,2,1] [[1,2,3,7],[4,5],[6]]=>{{1,2,3,7},{4,5},{6}}=>[4,2,1] [[1,4,5,6],[2,7],[3]]=>{{1,4,5,6},{2,7},{3}}=>[4,2,1] [[1,3,5,6],[2,7],[4]]=>{{1,3,5,6},{2,7},{4}}=>[4,2,1] [[1,2,5,6],[3,7],[4]]=>{{1,2,5,6},{3,7},{4}}=>[4,2,1] [[1,3,4,6],[2,7],[5]]=>{{1,3,4,6},{2,7},{5}}=>[4,2,1] [[1,2,4,6],[3,7],[5]]=>{{1,2,4,6},{3,7},{5}}=>[4,2,1] [[1,2,3,6],[4,7],[5]]=>{{1,2,3,6},{4,7},{5}}=>[4,2,1] [[1,3,4,5],[2,7],[6]]=>{{1,3,4,5},{2,7},{6}}=>[4,2,1] [[1,2,4,5],[3,7],[6]]=>{{1,2,4,5},{3,7},{6}}=>[4,2,1] [[1,2,3,5],[4,7],[6]]=>{{1,2,3,5},{4,7},{6}}=>[4,2,1] [[1,2,3,4],[5,7],[6]]=>{{1,2,3,4},{5,7},{6}}=>[4,2,1] [[1,3,5,6],[2,4],[7]]=>{{1,3,5,6},{2,4},{7}}=>[4,2,1] [[1,2,5,6],[3,4],[7]]=>{{1,2,5,6},{3,4},{7}}=>[4,2,1] [[1,3,4,6],[2,5],[7]]=>{{1,3,4,6},{2,5},{7}}=>[4,2,1] [[1,2,4,6],[3,5],[7]]=>{{1,2,4,6},{3,5},{7}}=>[4,2,1] [[1,2,3,6],[4,5],[7]]=>{{1,2,3,6},{4,5},{7}}=>[4,2,1] [[1,3,4,5],[2,6],[7]]=>{{1,3,4,5},{2,6},{7}}=>[4,2,1] [[1,2,4,5],[3,6],[7]]=>{{1,2,4,5},{3,6},{7}}=>[4,2,1] [[1,2,3,5],[4,6],[7]]=>{{1,2,3,5},{4,6},{7}}=>[4,2,1] [[1,2,3,4],[5,6],[7]]=>{{1,2,3,4},{5,6},{7}}=>[4,2,1] [[1,5,6,7],[2],[3],[4]]=>{{1,5,6,7},{2},{3},{4}}=>[4,1,1,1] [[1,4,6,7],[2],[3],[5]]=>{{1,4,6,7},{2},{3},{5}}=>[4,1,1,1] [[1,3,6,7],[2],[4],[5]]=>{{1,3,6,7},{2},{4},{5}}=>[4,1,1,1] [[1,2,6,7],[3],[4],[5]]=>{{1,2,6,7},{3},{4},{5}}=>[4,1,1,1] [[1,4,5,7],[2],[3],[6]]=>{{1,4,5,7},{2},{3},{6}}=>[4,1,1,1] [[1,3,5,7],[2],[4],[6]]=>{{1,3,5,7},{2},{4},{6}}=>[4,1,1,1] [[1,2,5,7],[3],[4],[6]]=>{{1,2,5,7},{3},{4},{6}}=>[4,1,1,1] [[1,3,4,7],[2],[5],[6]]=>{{1,3,4,7},{2},{5},{6}}=>[4,1,1,1] [[1,2,4,7],[3],[5],[6]]=>{{1,2,4,7},{3},{5},{6}}=>[4,1,1,1] [[1,2,3,7],[4],[5],[6]]=>{{1,2,3,7},{4},{5},{6}}=>[4,1,1,1] [[1,4,5,6],[2],[3],[7]]=>{{1,4,5,6},{2},{3},{7}}=>[4,1,1,1] [[1,3,5,6],[2],[4],[7]]=>{{1,3,5,6},{2},{4},{7}}=>[4,1,1,1] [[1,2,5,6],[3],[4],[7]]=>{{1,2,5,6},{3},{4},{7}}=>[4,1,1,1] [[1,3,4,6],[2],[5],[7]]=>{{1,3,4,6},{2},{5},{7}}=>[4,1,1,1] [[1,2,4,6],[3],[5],[7]]=>{{1,2,4,6},{3},{5},{7}}=>[4,1,1,1] [[1,2,3,6],[4],[5],[7]]=>{{1,2,3,6},{4},{5},{7}}=>[4,1,1,1] [[1,3,4,5],[2],[6],[7]]=>{{1,3,4,5},{2},{6},{7}}=>[4,1,1,1] [[1,2,4,5],[3],[6],[7]]=>{{1,2,4,5},{3},{6},{7}}=>[4,1,1,1] [[1,2,3,5],[4],[6],[7]]=>{{1,2,3,5},{4},{6},{7}}=>[4,1,1,1] [[1,2,3,4],[5],[6],[7]]=>{{1,2,3,4},{5},{6},{7}}=>[4,1,1,1] [[1,4,6],[2,5,7],[3]]=>{{1,4,6},{2,5,7},{3}}=>[3,3,1] [[1,3,6],[2,5,7],[4]]=>{{1,3,6},{2,5,7},{4}}=>[3,3,1] [[1,2,6],[3,5,7],[4]]=>{{1,2,6},{3,5,7},{4}}=>[3,3,1] [[1,3,6],[2,4,7],[5]]=>{{1,3,6},{2,4,7},{5}}=>[3,3,1] [[1,2,6],[3,4,7],[5]]=>{{1,2,6},{3,4,7},{5}}=>[3,3,1] [[1,4,5],[2,6,7],[3]]=>{{1,4,5},{2,6,7},{3}}=>[3,3,1] [[1,3,5],[2,6,7],[4]]=>{{1,3,5},{2,6,7},{4}}=>[3,3,1] [[1,2,5],[3,6,7],[4]]=>{{1,2,5},{3,6,7},{4}}=>[3,3,1] [[1,3,4],[2,6,7],[5]]=>{{1,3,4},{2,6,7},{5}}=>[3,3,1] [[1,2,4],[3,6,7],[5]]=>{{1,2,4},{3,6,7},{5}}=>[3,3,1] [[1,2,3],[4,6,7],[5]]=>{{1,2,3},{4,6,7},{5}}=>[3,3,1] [[1,3,5],[2,4,7],[6]]=>{{1,3,5},{2,4,7},{6}}=>[3,3,1] [[1,2,5],[3,4,7],[6]]=>{{1,2,5},{3,4,7},{6}}=>[3,3,1] [[1,3,4],[2,5,7],[6]]=>{{1,3,4},{2,5,7},{6}}=>[3,3,1] [[1,2,4],[3,5,7],[6]]=>{{1,2,4},{3,5,7},{6}}=>[3,3,1] [[1,2,3],[4,5,7],[6]]=>{{1,2,3},{4,5,7},{6}}=>[3,3,1] [[1,3,5],[2,4,6],[7]]=>{{1,3,5},{2,4,6},{7}}=>[3,3,1] [[1,2,5],[3,4,6],[7]]=>{{1,2,5},{3,4,6},{7}}=>[3,3,1] [[1,3,4],[2,5,6],[7]]=>{{1,3,4},{2,5,6},{7}}=>[3,3,1] [[1,2,4],[3,5,6],[7]]=>{{1,2,4},{3,5,6},{7}}=>[3,3,1] [[1,2,3],[4,5,6],[7]]=>{{1,2,3},{4,5,6},{7}}=>[3,3,1] [[1,4,7],[2,5],[3,6]]=>{{1,4,7},{2,5},{3,6}}=>[3,2,2] [[1,3,7],[2,5],[4,6]]=>{{1,3,7},{2,5},{4,6}}=>[3,2,2] [[1,2,7],[3,5],[4,6]]=>{{1,2,7},{3,5},{4,6}}=>[3,2,2] [[1,3,7],[2,4],[5,6]]=>{{1,3,7},{2,4},{5,6}}=>[3,2,2] [[1,2,7],[3,4],[5,6]]=>{{1,2,7},{3,4},{5,6}}=>[3,2,2] [[1,4,6],[2,5],[3,7]]=>{{1,4,6},{2,5},{3,7}}=>[3,2,2] [[1,3,6],[2,5],[4,7]]=>{{1,3,6},{2,5},{4,7}}=>[3,2,2] [[1,2,6],[3,5],[4,7]]=>{{1,2,6},{3,5},{4,7}}=>[3,2,2] [[1,3,6],[2,4],[5,7]]=>{{1,3,6},{2,4},{5,7}}=>[3,2,2] [[1,2,6],[3,4],[5,7]]=>{{1,2,6},{3,4},{5,7}}=>[3,2,2] [[1,4,5],[2,6],[3,7]]=>{{1,4,5},{2,6},{3,7}}=>[3,2,2] [[1,3,5],[2,6],[4,7]]=>{{1,3,5},{2,6},{4,7}}=>[3,2,2] [[1,2,5],[3,6],[4,7]]=>{{1,2,5},{3,6},{4,7}}=>[3,2,2] [[1,3,4],[2,6],[5,7]]=>{{1,3,4},{2,6},{5,7}}=>[3,2,2] [[1,2,4],[3,6],[5,7]]=>{{1,2,4},{3,6},{5,7}}=>[3,2,2] [[1,2,3],[4,6],[5,7]]=>{{1,2,3},{4,6},{5,7}}=>[3,2,2] [[1,3,5],[2,4],[6,7]]=>{{1,3,5},{2,4},{6,7}}=>[3,2,2] [[1,2,5],[3,4],[6,7]]=>{{1,2,5},{3,4},{6,7}}=>[3,2,2] [[1,3,4],[2,5],[6,7]]=>{{1,3,4},{2,5},{6,7}}=>[3,2,2] [[1,2,4],[3,5],[6,7]]=>{{1,2,4},{3,5},{6,7}}=>[3,2,2] [[1,2,3],[4,5],[6,7]]=>{{1,2,3},{4,5},{6,7}}=>[3,2,2] [[1,5,7],[2,6],[3],[4]]=>{{1,5,7},{2,6},{3},{4}}=>[3,2,1,1] [[1,4,7],[2,6],[3],[5]]=>{{1,4,7},{2,6},{3},{5}}=>[3,2,1,1] [[1,3,7],[2,6],[4],[5]]=>{{1,3,7},{2,6},{4},{5}}=>[3,2,1,1] [[1,2,7],[3,6],[4],[5]]=>{{1,2,7},{3,6},{4},{5}}=>[3,2,1,1] [[1,4,7],[2,5],[3],[6]]=>{{1,4,7},{2,5},{3},{6}}=>[3,2,1,1] [[1,3,7],[2,5],[4],[6]]=>{{1,3,7},{2,5},{4},{6}}=>[3,2,1,1] [[1,2,7],[3,5],[4],[6]]=>{{1,2,7},{3,5},{4},{6}}=>[3,2,1,1] [[1,3,7],[2,4],[5],[6]]=>{{1,3,7},{2,4},{5},{6}}=>[3,2,1,1] [[1,2,7],[3,4],[5],[6]]=>{{1,2,7},{3,4},{5},{6}}=>[3,2,1,1] [[1,5,6],[2,7],[3],[4]]=>{{1,5,6},{2,7},{3},{4}}=>[3,2,1,1] [[1,4,6],[2,7],[3],[5]]=>{{1,4,6},{2,7},{3},{5}}=>[3,2,1,1] [[1,3,6],[2,7],[4],[5]]=>{{1,3,6},{2,7},{4},{5}}=>[3,2,1,1] [[1,2,6],[3,7],[4],[5]]=>{{1,2,6},{3,7},{4},{5}}=>[3,2,1,1] [[1,4,5],[2,7],[3],[6]]=>{{1,4,5},{2,7},{3},{6}}=>[3,2,1,1] [[1,3,5],[2,7],[4],[6]]=>{{1,3,5},{2,7},{4},{6}}=>[3,2,1,1] [[1,2,5],[3,7],[4],[6]]=>{{1,2,5},{3,7},{4},{6}}=>[3,2,1,1] [[1,3,4],[2,7],[5],[6]]=>{{1,3,4},{2,7},{5},{6}}=>[3,2,1,1] [[1,2,4],[3,7],[5],[6]]=>{{1,2,4},{3,7},{5},{6}}=>[3,2,1,1] [[1,2,3],[4,7],[5],[6]]=>{{1,2,3},{4,7},{5},{6}}=>[3,2,1,1] [[1,4,6],[2,5],[3],[7]]=>{{1,4,6},{2,5},{3},{7}}=>[3,2,1,1] [[1,3,6],[2,5],[4],[7]]=>{{1,3,6},{2,5},{4},{7}}=>[3,2,1,1] [[1,2,6],[3,5],[4],[7]]=>{{1,2,6},{3,5},{4},{7}}=>[3,2,1,1] [[1,3,6],[2,4],[5],[7]]=>{{1,3,6},{2,4},{5},{7}}=>[3,2,1,1] [[1,2,6],[3,4],[5],[7]]=>{{1,2,6},{3,4},{5},{7}}=>[3,2,1,1] [[1,4,5],[2,6],[3],[7]]=>{{1,4,5},{2,6},{3},{7}}=>[3,2,1,1] [[1,3,5],[2,6],[4],[7]]=>{{1,3,5},{2,6},{4},{7}}=>[3,2,1,1] [[1,2,5],[3,6],[4],[7]]=>{{1,2,5},{3,6},{4},{7}}=>[3,2,1,1] [[1,3,4],[2,6],[5],[7]]=>{{1,3,4},{2,6},{5},{7}}=>[3,2,1,1] [[1,2,4],[3,6],[5],[7]]=>{{1,2,4},{3,6},{5},{7}}=>[3,2,1,1] [[1,2,3],[4,6],[5],[7]]=>{{1,2,3},{4,6},{5},{7}}=>[3,2,1,1] [[1,3,5],[2,4],[6],[7]]=>{{1,3,5},{2,4},{6},{7}}=>[3,2,1,1] [[1,2,5],[3,4],[6],[7]]=>{{1,2,5},{3,4},{6},{7}}=>[3,2,1,1] [[1,3,4],[2,5],[6],[7]]=>{{1,3,4},{2,5},{6},{7}}=>[3,2,1,1] [[1,2,4],[3,5],[6],[7]]=>{{1,2,4},{3,5},{6},{7}}=>[3,2,1,1] [[1,2,3],[4,5],[6],[7]]=>{{1,2,3},{4,5},{6},{7}}=>[3,2,1,1] [[1,6,7],[2],[3],[4],[5]]=>{{1,6,7},{2},{3},{4},{5}}=>[3,1,1,1,1] [[1,5,7],[2],[3],[4],[6]]=>{{1,5,7},{2},{3},{4},{6}}=>[3,1,1,1,1] [[1,4,7],[2],[3],[5],[6]]=>{{1,4,7},{2},{3},{5},{6}}=>[3,1,1,1,1] [[1,3,7],[2],[4],[5],[6]]=>{{1,3,7},{2},{4},{5},{6}}=>[3,1,1,1,1] [[1,2,7],[3],[4],[5],[6]]=>{{1,2,7},{3},{4},{5},{6}}=>[3,1,1,1,1] [[1,5,6],[2],[3],[4],[7]]=>{{1,5,6},{2},{3},{4},{7}}=>[3,1,1,1,1] [[1,4,6],[2],[3],[5],[7]]=>{{1,4,6},{2},{3},{5},{7}}=>[3,1,1,1,1] [[1,3,6],[2],[4],[5],[7]]=>{{1,3,6},{2},{4},{5},{7}}=>[3,1,1,1,1] [[1,2,6],[3],[4],[5],[7]]=>{{1,2,6},{3},{4},{5},{7}}=>[3,1,1,1,1] [[1,4,5],[2],[3],[6],[7]]=>{{1,4,5},{2},{3},{6},{7}}=>[3,1,1,1,1] [[1,3,5],[2],[4],[6],[7]]=>{{1,3,5},{2},{4},{6},{7}}=>[3,1,1,1,1] [[1,2,5],[3],[4],[6],[7]]=>{{1,2,5},{3},{4},{6},{7}}=>[3,1,1,1,1] [[1,3,4],[2],[5],[6],[7]]=>{{1,3,4},{2},{5},{6},{7}}=>[3,1,1,1,1] [[1,2,4],[3],[5],[6],[7]]=>{{1,2,4},{3},{5},{6},{7}}=>[3,1,1,1,1] [[1,2,3],[4],[5],[6],[7]]=>{{1,2,3},{4},{5},{6},{7}}=>[3,1,1,1,1] [[1,5],[2,6],[3,7],[4]]=>{{1,5},{2,6},{3,7},{4}}=>[2,2,2,1] [[1,4],[2,6],[3,7],[5]]=>{{1,4},{2,6},{3,7},{5}}=>[2,2,2,1] [[1,3],[2,6],[4,7],[5]]=>{{1,3},{2,6},{4,7},{5}}=>[2,2,2,1] [[1,2],[3,6],[4,7],[5]]=>{{1,2},{3,6},{4,7},{5}}=>[2,2,2,1] [[1,4],[2,5],[3,7],[6]]=>{{1,4},{2,5},{3,7},{6}}=>[2,2,2,1] [[1,3],[2,5],[4,7],[6]]=>{{1,3},{2,5},{4,7},{6}}=>[2,2,2,1] [[1,2],[3,5],[4,7],[6]]=>{{1,2},{3,5},{4,7},{6}}=>[2,2,2,1] [[1,3],[2,4],[5,7],[6]]=>{{1,3},{2,4},{5,7},{6}}=>[2,2,2,1] [[1,2],[3,4],[5,7],[6]]=>{{1,2},{3,4},{5,7},{6}}=>[2,2,2,1] [[1,4],[2,5],[3,6],[7]]=>{{1,4},{2,5},{3,6},{7}}=>[2,2,2,1] [[1,3],[2,5],[4,6],[7]]=>{{1,3},{2,5},{4,6},{7}}=>[2,2,2,1] [[1,2],[3,5],[4,6],[7]]=>{{1,2},{3,5},{4,6},{7}}=>[2,2,2,1] [[1,3],[2,4],[5,6],[7]]=>{{1,3},{2,4},{5,6},{7}}=>[2,2,2,1] [[1,2],[3,4],[5,6],[7]]=>{{1,2},{3,4},{5,6},{7}}=>[2,2,2,1] [[1,6],[2,7],[3],[4],[5]]=>{{1,6},{2,7},{3},{4},{5}}=>[2,2,1,1,1] [[1,5],[2,7],[3],[4],[6]]=>{{1,5},{2,7},{3},{4},{6}}=>[2,2,1,1,1] [[1,4],[2,7],[3],[5],[6]]=>{{1,4},{2,7},{3},{5},{6}}=>[2,2,1,1,1] [[1,3],[2,7],[4],[5],[6]]=>{{1,3},{2,7},{4},{5},{6}}=>[2,2,1,1,1] [[1,2],[3,7],[4],[5],[6]]=>{{1,2},{3,7},{4},{5},{6}}=>[2,2,1,1,1] [[1,5],[2,6],[3],[4],[7]]=>{{1,5},{2,6},{3},{4},{7}}=>[2,2,1,1,1] [[1,4],[2,6],[3],[5],[7]]=>{{1,4},{2,6},{3},{5},{7}}=>[2,2,1,1,1] [[1,3],[2,6],[4],[5],[7]]=>{{1,3},{2,6},{4},{5},{7}}=>[2,2,1,1,1] [[1,2],[3,6],[4],[5],[7]]=>{{1,2},{3,6},{4},{5},{7}}=>[2,2,1,1,1] [[1,4],[2,5],[3],[6],[7]]=>{{1,4},{2,5},{3},{6},{7}}=>[2,2,1,1,1] [[1,3],[2,5],[4],[6],[7]]=>{{1,3},{2,5},{4},{6},{7}}=>[2,2,1,1,1] [[1,2],[3,5],[4],[6],[7]]=>{{1,2},{3,5},{4},{6},{7}}=>[2,2,1,1,1] [[1,3],[2,4],[5],[6],[7]]=>{{1,3},{2,4},{5},{6},{7}}=>[2,2,1,1,1] [[1,2],[3,4],[5],[6],[7]]=>{{1,2},{3,4},{5},{6},{7}}=>[2,2,1,1,1] [[1,7],[2],[3],[4],[5],[6]]=>{{1,7},{2},{3},{4},{5},{6}}=>[2,1,1,1,1,1] [[1,6],[2],[3],[4],[5],[7]]=>{{1,6},{2},{3},{4},{5},{7}}=>[2,1,1,1,1,1] [[1,5],[2],[3],[4],[6],[7]]=>{{1,5},{2},{3},{4},{6},{7}}=>[2,1,1,1,1,1] [[1,4],[2],[3],[5],[6],[7]]=>{{1,4},{2},{3},{5},{6},{7}}=>[2,1,1,1,1,1] [[1,3],[2],[4],[5],[6],[7]]=>{{1,3},{2},{4},{5},{6},{7}}=>[2,1,1,1,1,1] [[1,2],[3],[4],[5],[6],[7]]=>{{1,2},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1] [[1],[2],[3],[4],[5],[6],[7]]=>{{1},{2},{3},{4},{5},{6},{7}}=>[1,1,1,1,1,1,1] [[1,2,3,4,5,6,7,8]]=>{{1,2,3,4,5,6,7,8}}=>[8] [[1,3,4,5,6,7,8],[2]]=>{{1,3,4,5,6,7,8},{2}}=>[7,1] [[1,2,4,5,6,7,8],[3]]=>{{1,2,4,5,6,7,8},{3}}=>[7,1] [[1,2,3,5,6,7,8],[4]]=>{{1,2,3,5,6,7,8},{4}}=>[7,1] [[1,2,3,4,6,7,8],[5]]=>{{1,2,3,4,6,7,8},{5}}=>[7,1] [[1,2,3,4,5,7,8],[6]]=>{{1,2,3,4,5,7,8},{6}}=>[7,1] [[1,2,3,4,5,6,8],[7]]=>{{1,2,3,4,5,6,8},{7}}=>[7,1] [[1,2,3,4,5,6,7],[8]]=>{{1,2,3,4,5,6,7},{8}}=>[7,1] [[1,3,5,6,7,8],[2,4]]=>{{1,3,5,6,7,8},{2,4}}=>[6,2] [[1,2,5,6,7,8],[3,4]]=>{{1,2,5,6,7,8},{3,4}}=>[6,2] [[1,3,4,6,7,8],[2,5]]=>{{1,3,4,6,7,8},{2,5}}=>[6,2] [[1,2,4,6,7,8],[3,5]]=>{{1,2,4,6,7,8},{3,5}}=>[6,2] [[1,2,3,6,7,8],[4,5]]=>{{1,2,3,6,7,8},{4,5}}=>[6,2] [[1,3,4,5,7,8],[2,6]]=>{{1,3,4,5,7,8},{2,6}}=>[6,2] [[1,2,4,5,7,8],[3,6]]=>{{1,2,4,5,7,8},{3,6}}=>[6,2] [[1,2,3,5,7,8],[4,6]]=>{{1,2,3,5,7,8},{4,6}}=>[6,2] [[1,2,3,4,7,8],[5,6]]=>{{1,2,3,4,7,8},{5,6}}=>[6,2] [[1,3,4,5,6,8],[2,7]]=>{{1,3,4,5,6,8},{2,7}}=>[6,2] [[1,2,4,5,6,8],[3,7]]=>{{1,2,4,5,6,8},{3,7}}=>[6,2] [[1,2,3,5,6,8],[4,7]]=>{{1,2,3,5,6,8},{4,7}}=>[6,2] [[1,2,3,4,6,8],[5,7]]=>{{1,2,3,4,6,8},{5,7}}=>[6,2] [[1,2,3,4,5,8],[6,7]]=>{{1,2,3,4,5,8},{6,7}}=>[6,2] [[1,3,4,5,6,7],[2,8]]=>{{1,3,4,5,6,7},{2,8}}=>[6,2] [[1,2,4,5,6,7],[3,8]]=>{{1,2,4,5,6,7},{3,8}}=>[6,2] [[1,2,3,5,6,7],[4,8]]=>{{1,2,3,5,6,7},{4,8}}=>[6,2] [[1,2,3,4,6,7],[5,8]]=>{{1,2,3,4,6,7},{5,8}}=>[6,2] [[1,2,3,4,5,7],[6,8]]=>{{1,2,3,4,5,7},{6,8}}=>[6,2] [[1,2,3,4,5,6],[7,8]]=>{{1,2,3,4,5,6},{7,8}}=>[6,2] [[1,4,5,6,7,8],[2],[3]]=>{{1,4,5,6,7,8},{2},{3}}=>[6,1,1] [[1,3,5,6,7,8],[2],[4]]=>{{1,3,5,6,7,8},{2},{4}}=>[6,1,1] [[1,2,5,6,7,8],[3],[4]]=>{{1,2,5,6,7,8},{3},{4}}=>[6,1,1] [[1,3,4,6,7,8],[2],[5]]=>{{1,3,4,6,7,8},{2},{5}}=>[6,1,1] [[1,2,4,6,7,8],[3],[5]]=>{{1,2,4,6,7,8},{3},{5}}=>[6,1,1] [[1,2,3,6,7,8],[4],[5]]=>{{1,2,3,6,7,8},{4},{5}}=>[6,1,1] [[1,3,4,5,7,8],[2],[6]]=>{{1,3,4,5,7,8},{2},{6}}=>[6,1,1] [[1,2,4,5,7,8],[3],[6]]=>{{1,2,4,5,7,8},{3},{6}}=>[6,1,1] [[1,2,3,5,7,8],[4],[6]]=>{{1,2,3,5,7,8},{4},{6}}=>[6,1,1] [[1,2,3,4,7,8],[5],[6]]=>{{1,2,3,4,7,8},{5},{6}}=>[6,1,1] [[1,3,4,5,6,8],[2],[7]]=>{{1,3,4,5,6,8},{2},{7}}=>[6,1,1] [[1,2,4,5,6,8],[3],[7]]=>{{1,2,4,5,6,8},{3},{7}}=>[6,1,1] [[1,2,3,5,6,8],[4],[7]]=>{{1,2,3,5,6,8},{4},{7}}=>[6,1,1] [[1,2,3,4,6,8],[5],[7]]=>{{1,2,3,4,6,8},{5},{7}}=>[6,1,1] [[1,2,3,4,5,8],[6],[7]]=>{{1,2,3,4,5,8},{6},{7}}=>[6,1,1] [[1,3,4,5,6,7],[2],[8]]=>{{1,3,4,5,6,7},{2},{8}}=>[6,1,1] [[1,2,4,5,6,7],[3],[8]]=>{{1,2,4,5,6,7},{3},{8}}=>[6,1,1] [[1,2,3,5,6,7],[4],[8]]=>{{1,2,3,5,6,7},{4},{8}}=>[6,1,1] [[1,2,3,4,6,7],[5],[8]]=>{{1,2,3,4,6,7},{5},{8}}=>[6,1,1] [[1,2,3,4,5,7],[6],[8]]=>{{1,2,3,4,5,7},{6},{8}}=>[6,1,1] [[1,2,3,4,5,6],[7],[8]]=>{{1,2,3,4,5,6},{7},{8}}=>[6,1,1] [[1,3,5,7,8],[2,4,6]]=>{{1,3,5,7,8},{2,4,6}}=>[5,3] [[1,2,5,7,8],[3,4,6]]=>{{1,2,5,7,8},{3,4,6}}=>[5,3] [[1,3,4,7,8],[2,5,6]]=>{{1,3,4,7,8},{2,5,6}}=>[5,3] [[1,2,4,7,8],[3,5,6]]=>{{1,2,4,7,8},{3,5,6}}=>[5,3] [[1,2,3,7,8],[4,5,6]]=>{{1,2,3,7,8},{4,5,6}}=>[5,3] [[1,3,5,6,8],[2,4,7]]=>{{1,3,5,6,8},{2,4,7}}=>[5,3] [[1,2,5,6,8],[3,4,7]]=>{{1,2,5,6,8},{3,4,7}}=>[5,3] [[1,3,4,6,8],[2,5,7]]=>{{1,3,4,6,8},{2,5,7}}=>[5,3] [[1,2,4,6,8],[3,5,7]]=>{{1,2,4,6,8},{3,5,7}}=>[5,3] [[1,2,3,6,8],[4,5,7]]=>{{1,2,3,6,8},{4,5,7}}=>[5,3] [[1,2,4,5,8],[3,6,7]]=>{{1,2,4,5,8},{3,6,7}}=>[5,3] [[1,2,3,5,8],[4,6,7]]=>{{1,2,3,5,8},{4,6,7}}=>[5,3] [[1,2,3,4,8],[5,6,7]]=>{{1,2,3,4,8},{5,6,7}}=>[5,3] [[1,3,5,6,7],[2,4,8]]=>{{1,3,5,6,7},{2,4,8}}=>[5,3] [[1,2,5,6,7],[3,4,8]]=>{{1,2,5,6,7},{3,4,8}}=>[5,3] [[1,3,4,6,7],[2,5,8]]=>{{1,3,4,6,7},{2,5,8}}=>[5,3] [[1,2,4,6,7],[3,5,8]]=>{{1,2,4,6,7},{3,5,8}}=>[5,3] [[1,2,3,6,7],[4,5,8]]=>{{1,2,3,6,7},{4,5,8}}=>[5,3] [[1,3,4,5,7],[2,6,8]]=>{{1,3,4,5,7},{2,6,8}}=>[5,3] [[1,2,4,5,7],[3,6,8]]=>{{1,2,4,5,7},{3,6,8}}=>[5,3] [[1,2,3,5,7],[4,6,8]]=>{{1,2,3,5,7},{4,6,8}}=>[5,3] [[1,2,3,4,7],[5,6,8]]=>{{1,2,3,4,7},{5,6,8}}=>[5,3] [[1,2,4,5,6],[3,7,8]]=>{{1,2,4,5,6},{3,7,8}}=>[5,3] [[1,2,3,5,6],[4,7,8]]=>{{1,2,3,5,6},{4,7,8}}=>[5,3] [[1,2,3,4,6],[5,7,8]]=>{{1,2,3,4,6},{5,7,8}}=>[5,3] [[1,2,3,4,5],[6,7,8]]=>{{1,2,3,4,5},{6,7,8}}=>[5,3] [[1,4,6,7,8],[2,5],[3]]=>{{1,4,6,7,8},{2,5},{3}}=>[5,2,1] [[1,3,6,7,8],[2,5],[4]]=>{{1,3,6,7,8},{2,5},{4}}=>[5,2,1] [[1,2,6,7,8],[3,5],[4]]=>{{1,2,6,7,8},{3,5},{4}}=>[5,2,1] [[1,3,6,7,8],[2,4],[5]]=>{{1,3,6,7,8},{2,4},{5}}=>[5,2,1] [[1,2,5,7,8],[3,6],[4]]=>{{1,2,5,7,8},{3,6},{4}}=>[5,2,1] [[1,3,4,7,8],[2,6],[5]]=>{{1,3,4,7,8},{2,6},{5}}=>[5,2,1] [[1,2,4,7,8],[3,6],[5]]=>{{1,2,4,7,8},{3,6},{5}}=>[5,2,1] [[1,2,3,7,8],[4,6],[5]]=>{{1,2,3,7,8},{4,6},{5}}=>[5,2,1] [[1,3,4,7,8],[2,5],[6]]=>{{1,3,4,7,8},{2,5},{6}}=>[5,2,1] [[1,3,5,6,8],[2,7],[4]]=>{{1,3,5,6,8},{2,7},{4}}=>[5,2,1] [[1,2,5,6,8],[3,7],[4]]=>{{1,2,5,6,8},{3,7},{4}}=>[5,2,1] [[1,3,4,6,8],[2,7],[5]]=>{{1,3,4,6,8},{2,7},{5}}=>[5,2,1] [[1,2,4,6,8],[3,7],[5]]=>{{1,2,4,6,8},{3,7},{5}}=>[5,2,1] [[1,3,4,5,8],[2,7],[6]]=>{{1,3,4,5,8},{2,7},{6}}=>[5,2,1] [[1,2,3,4,8],[5,7],[6]]=>{{1,2,3,4,8},{5,7},{6}}=>[5,2,1] [[1,3,5,6,8],[2,4],[7]]=>{{1,3,5,6,8},{2,4},{7}}=>[5,2,1] [[1,2,5,6,8],[3,4],[7]]=>{{1,2,5,6,8},{3,4},{7}}=>[5,2,1] [[1,3,4,6,8],[2,5],[7]]=>{{1,3,4,6,8},{2,5},{7}}=>[5,2,1] [[1,2,3,6,8],[4,5],[7]]=>{{1,2,3,6,8},{4,5},{7}}=>[5,2,1] [[1,2,4,5,8],[3,6],[7]]=>{{1,2,4,5,8},{3,6},{7}}=>[5,2,1] [[1,2,3,4,8],[5,6],[7]]=>{{1,2,3,4,8},{5,6},{7}}=>[5,2,1] [[1,3,4,6,7],[2,8],[5]]=>{{1,3,4,6,7},{2,8},{5}}=>[5,2,1] [[1,2,4,6,7],[3,8],[5]]=>{{1,2,4,6,7},{3,8},{5}}=>[5,2,1] [[1,3,4,5,7],[2,8],[6]]=>{{1,3,4,5,7},{2,8},{6}}=>[5,2,1] [[1,2,4,5,7],[3,8],[6]]=>{{1,2,4,5,7},{3,8},{6}}=>[5,2,1] [[1,2,3,5,7],[4,8],[6]]=>{{1,2,3,5,7},{4,8},{6}}=>[5,2,1] [[1,3,4,5,6],[2,8],[7]]=>{{1,3,4,5,6},{2,8},{7}}=>[5,2,1] [[1,2,3,5,6],[4,8],[7]]=>{{1,2,3,5,6},{4,8},{7}}=>[5,2,1] [[1,2,3,4,6],[5,8],[7]]=>{{1,2,3,4,6},{5,8},{7}}=>[5,2,1] [[1,2,3,4,5],[6,8],[7]]=>{{1,2,3,4,5},{6,8},{7}}=>[5,2,1] [[1,3,5,6,7],[2,4],[8]]=>{{1,3,5,6,7},{2,4},{8}}=>[5,2,1] [[1,3,4,6,7],[2,5],[8]]=>{{1,3,4,6,7},{2,5},{8}}=>[5,2,1] [[1,2,4,6,7],[3,5],[8]]=>{{1,2,4,6,7},{3,5},{8}}=>[5,2,1] [[1,2,3,6,7],[4,5],[8]]=>{{1,2,3,6,7},{4,5},{8}}=>[5,2,1] [[1,2,4,5,7],[3,6],[8]]=>{{1,2,4,5,7},{3,6},{8}}=>[5,2,1] [[1,2,3,5,7],[4,6],[8]]=>{{1,2,3,5,7},{4,6},{8}}=>[5,2,1] [[1,2,3,4,7],[5,6],[8]]=>{{1,2,3,4,7},{5,6},{8}}=>[5,2,1] [[1,2,3,5,6],[4,7],[8]]=>{{1,2,3,5,6},{4,7},{8}}=>[5,2,1] [[1,2,3,4,6],[5,7],[8]]=>{{1,2,3,4,6},{5,7},{8}}=>[5,2,1] [[1,2,3,4,5],[6,7],[8]]=>{{1,2,3,4,5},{6,7},{8}}=>[5,2,1] [[1,5,6,7,8],[2],[3],[4]]=>{{1,5,6,7,8},{2},{3},{4}}=>[5,1,1,1] [[1,2,6,7,8],[3],[4],[5]]=>{{1,2,6,7,8},{3},{4},{5}}=>[5,1,1,1] [[1,3,5,7,8],[2],[4],[6]]=>{{1,3,5,7,8},{2},{4},{6}}=>[5,1,1,1] [[1,2,5,7,8],[3],[4],[6]]=>{{1,2,5,7,8},{3},{4},{6}}=>[5,1,1,1] [[1,3,4,7,8],[2],[5],[6]]=>{{1,3,4,7,8},{2},{5},{6}}=>[5,1,1,1] [[1,2,4,7,8],[3],[5],[6]]=>{{1,2,4,7,8},{3},{5},{6}}=>[5,1,1,1] [[1,2,3,7,8],[4],[5],[6]]=>{{1,2,3,7,8},{4},{5},{6}}=>[5,1,1,1] [[1,4,5,6,8],[2],[3],[7]]=>{{1,4,5,6,8},{2},{3},{7}}=>[5,1,1,1] [[1,3,5,6,8],[2],[4],[7]]=>{{1,3,5,6,8},{2},{4},{7}}=>[5,1,1,1] [[1,2,5,6,8],[3],[4],[7]]=>{{1,2,5,6,8},{3},{4},{7}}=>[5,1,1,1] [[1,3,4,6,8],[2],[5],[7]]=>{{1,3,4,6,8},{2},{5},{7}}=>[5,1,1,1] [[1,2,4,6,8],[3],[5],[7]]=>{{1,2,4,6,8},{3},{5},{7}}=>[5,1,1,1] [[1,2,3,6,8],[4],[5],[7]]=>{{1,2,3,6,8},{4},{5},{7}}=>[5,1,1,1] [[1,3,4,5,8],[2],[6],[7]]=>{{1,3,4,5,8},{2},{6},{7}}=>[5,1,1,1] [[1,2,3,5,8],[4],[6],[7]]=>{{1,2,3,5,8},{4},{6},{7}}=>[5,1,1,1] [[1,2,3,4,8],[5],[6],[7]]=>{{1,2,3,4,8},{5},{6},{7}}=>[5,1,1,1] [[1,4,5,6,7],[2],[3],[8]]=>{{1,4,5,6,7},{2},{3},{8}}=>[5,1,1,1] [[1,2,5,6,7],[3],[4],[8]]=>{{1,2,5,6,7},{3},{4},{8}}=>[5,1,1,1] [[1,2,3,5,7],[4],[6],[8]]=>{{1,2,3,5,7},{4},{6},{8}}=>[5,1,1,1] [[1,2,3,4,7],[5],[6],[8]]=>{{1,2,3,4,7},{5},{6},{8}}=>[5,1,1,1] [[1,3,4,5,6],[2],[7],[8]]=>{{1,3,4,5,6},{2},{7},{8}}=>[5,1,1,1] [[1,2,3,5,6],[4],[7],[8]]=>{{1,2,3,5,6},{4},{7},{8}}=>[5,1,1,1] [[1,2,3,4,6],[5],[7],[8]]=>{{1,2,3,4,6},{5},{7},{8}}=>[5,1,1,1] [[1,2,3,4,5],[6],[7],[8]]=>{{1,2,3,4,5},{6},{7},{8}}=>[5,1,1,1] [[1,3,5,7],[2,4,6,8]]=>{{1,3,5,7},{2,4,6,8}}=>[4,4] [[1,2,5,7],[3,4,6,8]]=>{{1,2,5,7},{3,4,6,8}}=>[4,4] [[1,3,4,7],[2,5,6,8]]=>{{1,3,4,7},{2,5,6,8}}=>[4,4] [[1,2,4,7],[3,5,6,8]]=>{{1,2,4,7},{3,5,6,8}}=>[4,4] [[1,2,3,7],[4,5,6,8]]=>{{1,2,3,7},{4,5,6,8}}=>[4,4] [[1,3,5,6],[2,4,7,8]]=>{{1,3,5,6},{2,4,7,8}}=>[4,4] [[1,2,5,6],[3,4,7,8]]=>{{1,2,5,6},{3,4,7,8}}=>[4,4] [[1,3,4,6],[2,5,7,8]]=>{{1,3,4,6},{2,5,7,8}}=>[4,4] [[1,2,4,6],[3,5,7,8]]=>{{1,2,4,6},{3,5,7,8}}=>[4,4] [[1,2,3,6],[4,5,7,8]]=>{{1,2,3,6},{4,5,7,8}}=>[4,4] [[1,3,4,5],[2,6,7,8]]=>{{1,3,4,5},{2,6,7,8}}=>[4,4] [[1,2,4,5],[3,6,7,8]]=>{{1,2,4,5},{3,6,7,8}}=>[4,4] [[1,2,3,5],[4,6,7,8]]=>{{1,2,3,5},{4,6,7,8}}=>[4,4] [[1,2,3,4],[5,6,7,8]]=>{{1,2,3,4},{5,6,7,8}}=>[4,4] [[1,3,6,8],[2,5,7],[4]]=>{{1,3,6,8},{2,5,7},{4}}=>[4,3,1] [[1,2,6,8],[3,5,7],[4]]=>{{1,2,6,8},{3,5,7},{4}}=>[4,3,1] [[1,2,5,8],[3,6,7],[4]]=>{{1,2,5,8},{3,6,7},{4}}=>[4,3,1] [[1,2,5,8],[3,4,7],[6]]=>{{1,2,5,8},{3,4,7},{6}}=>[4,3,1] [[1,3,4,8],[2,5,7],[6]]=>{{1,3,4,8},{2,5,7},{6}}=>[4,3,1] [[1,2,3,8],[4,5,7],[6]]=>{{1,2,3,8},{4,5,7},{6}}=>[4,3,1] [[1,2,5,8],[3,4,6],[7]]=>{{1,2,5,8},{3,4,6},{7}}=>[4,3,1] [[1,2,4,8],[3,5,6],[7]]=>{{1,2,4,8},{3,5,6},{7}}=>[4,3,1] [[1,2,3,8],[4,5,6],[7]]=>{{1,2,3,8},{4,5,6},{7}}=>[4,3,1] [[1,2,6,7],[3,5,8],[4]]=>{{1,2,6,7},{3,5,8},{4}}=>[4,3,1] [[1,3,6,7],[2,4,8],[5]]=>{{1,3,6,7},{2,4,8},{5}}=>[4,3,1] [[1,4,5,7],[2,6,8],[3]]=>{{1,4,5,7},{2,6,8},{3}}=>[4,3,1] [[1,3,5,7],[2,6,8],[4]]=>{{1,3,5,7},{2,6,8},{4}}=>[4,3,1] [[1,3,4,7],[2,6,8],[5]]=>{{1,3,4,7},{2,6,8},{5}}=>[4,3,1] [[1,2,4,7],[3,6,8],[5]]=>{{1,2,4,7},{3,6,8},{5}}=>[4,3,1] [[1,3,5,7],[2,4,8],[6]]=>{{1,3,5,7},{2,4,8},{6}}=>[4,3,1] [[1,2,5,7],[3,4,8],[6]]=>{{1,2,5,7},{3,4,8},{6}}=>[4,3,1] [[1,2,4,7],[3,5,8],[6]]=>{{1,2,4,7},{3,5,8},{6}}=>[4,3,1] [[1,3,4,5],[2,7,8],[6]]=>{{1,3,4,5},{2,7,8},{6}}=>[4,3,1] [[1,2,4,5],[3,7,8],[6]]=>{{1,2,4,5},{3,7,8},{6}}=>[4,3,1] [[1,2,3,4],[5,7,8],[6]]=>{{1,2,3,4},{5,7,8},{6}}=>[4,3,1] [[1,3,5,6],[2,4,8],[7]]=>{{1,3,5,6},{2,4,8},{7}}=>[4,3,1] [[1,2,3,6],[4,5,8],[7]]=>{{1,2,3,6},{4,5,8},{7}}=>[4,3,1] [[1,2,4,5],[3,6,8],[7]]=>{{1,2,4,5},{3,6,8},{7}}=>[4,3,1] [[1,2,3,4],[5,6,8],[7]]=>{{1,2,3,4},{5,6,8},{7}}=>[4,3,1] [[1,3,5,7],[2,4,6],[8]]=>{{1,3,5,7},{2,4,6},{8}}=>[4,3,1] [[1,2,3,7],[4,5,6],[8]]=>{{1,2,3,7},{4,5,6},{8}}=>[4,3,1] [[1,3,4,6],[2,5,7],[8]]=>{{1,3,4,6},{2,5,7},{8}}=>[4,3,1] [[1,2,3,5],[4,6,7],[8]]=>{{1,2,3,5},{4,6,7},{8}}=>[4,3,1] [[1,2,3,4],[5,6,7],[8]]=>{{1,2,3,4},{5,6,7},{8}}=>[4,3,1] [[1,4,7,8],[2,5],[3,6]]=>{{1,4,7,8},{2,5},{3,6}}=>[4,2,2] [[1,2,7,8],[3,5],[4,6]]=>{{1,2,7,8},{3,5},{4,6}}=>[4,2,2] [[1,2,6,8],[3,5],[4,7]]=>{{1,2,6,8},{3,5},{4,7}}=>[4,2,2] [[1,3,6,8],[2,4],[5,7]]=>{{1,3,6,8},{2,4},{5,7}}=>[4,2,2] [[1,4,5,8],[2,6],[3,7]]=>{{1,4,5,8},{2,6},{3,7}}=>[4,2,2] [[1,3,5,8],[2,6],[4,7]]=>{{1,3,5,8},{2,6},{4,7}}=>[4,2,2] [[1,2,5,8],[3,6],[4,7]]=>{{1,2,5,8},{3,6},{4,7}}=>[4,2,2] [[1,3,4,8],[2,6],[5,7]]=>{{1,3,4,8},{2,6},{5,7}}=>[4,2,2] [[1,3,5,8],[2,4],[6,7]]=>{{1,3,5,8},{2,4},{6,7}}=>[4,2,2] [[1,2,4,8],[3,5],[6,7]]=>{{1,2,4,8},{3,5},{6,7}}=>[4,2,2] [[1,2,3,8],[4,5],[6,7]]=>{{1,2,3,8},{4,5},{6,7}}=>[4,2,2] [[1,3,6,7],[2,4],[5,8]]=>{{1,3,6,7},{2,4},{5,8}}=>[4,2,2] [[1,2,6,7],[3,4],[5,8]]=>{{1,2,6,7},{3,4},{5,8}}=>[4,2,2] [[1,4,5,7],[2,6],[3,8]]=>{{1,4,5,7},{2,6},{3,8}}=>[4,2,2] [[1,3,5,7],[2,6],[4,8]]=>{{1,3,5,7},{2,6},{4,8}}=>[4,2,2] [[1,3,4,7],[2,6],[5,8]]=>{{1,3,4,7},{2,6},{5,8}}=>[4,2,2] [[1,2,3,7],[4,6],[5,8]]=>{{1,2,3,7},{4,6},{5,8}}=>[4,2,2] [[1,2,5,7],[3,4],[6,8]]=>{{1,2,5,7},{3,4},{6,8}}=>[4,2,2] [[1,3,4,7],[2,5],[6,8]]=>{{1,3,4,7},{2,5},{6,8}}=>[4,2,2] [[1,2,5,6],[3,7],[4,8]]=>{{1,2,5,6},{3,7},{4,8}}=>[4,2,2] [[1,3,4,6],[2,7],[5,8]]=>{{1,3,4,6},{2,7},{5,8}}=>[4,2,2] [[1,2,4,6],[3,7],[5,8]]=>{{1,2,4,6},{3,7},{5,8}}=>[4,2,2] [[1,2,3,6],[4,7],[5,8]]=>{{1,2,3,6},{4,7},{5,8}}=>[4,2,2] [[1,2,4,5],[3,7],[6,8]]=>{{1,2,4,5},{3,7},{6,8}}=>[4,2,2] [[1,2,3,5],[4,7],[6,8]]=>{{1,2,3,5},{4,7},{6,8}}=>[4,2,2] [[1,2,3,4],[5,7],[6,8]]=>{{1,2,3,4},{5,7},{6,8}}=>[4,2,2] [[1,3,5,6],[2,4],[7,8]]=>{{1,3,5,6},{2,4},{7,8}}=>[4,2,2] [[1,3,4,6],[2,5],[7,8]]=>{{1,3,4,6},{2,5},{7,8}}=>[4,2,2] [[1,2,4,6],[3,5],[7,8]]=>{{1,2,4,6},{3,5},{7,8}}=>[4,2,2] [[1,2,3,6],[4,5],[7,8]]=>{{1,2,3,6},{4,5},{7,8}}=>[4,2,2] [[1,2,4,5],[3,6],[7,8]]=>{{1,2,4,5},{3,6},{7,8}}=>[4,2,2] [[1,2,3,5],[4,6],[7,8]]=>{{1,2,3,5},{4,6},{7,8}}=>[4,2,2] [[1,2,3,4],[5,6],[7,8]]=>{{1,2,3,4},{5,6},{7,8}}=>[4,2,2] [[1,5,7,8],[2,6],[3],[4]]=>{{1,5,7,8},{2,6},{3},{4}}=>[4,2,1,1] [[1,4,7,8],[2,6],[3],[5]]=>{{1,4,7,8},{2,6},{3},{5}}=>[4,2,1,1] [[1,3,7,8],[2,6],[4],[5]]=>{{1,3,7,8},{2,6},{4},{5}}=>[4,2,1,1] [[1,2,7,8],[3,6],[4],[5]]=>{{1,2,7,8},{3,6},{4},{5}}=>[4,2,1,1] [[1,4,7,8],[2,5],[3],[6]]=>{{1,4,7,8},{2,5},{3},{6}}=>[4,2,1,1] [[1,3,7,8],[2,5],[4],[6]]=>{{1,3,7,8},{2,5},{4},{6}}=>[4,2,1,1] [[1,2,7,8],[3,5],[4],[6]]=>{{1,2,7,8},{3,5},{4},{6}}=>[4,2,1,1] [[1,3,7,8],[2,4],[5],[6]]=>{{1,3,7,8},{2,4},{5},{6}}=>[4,2,1,1] [[1,2,7,8],[3,4],[5],[6]]=>{{1,2,7,8},{3,4},{5},{6}}=>[4,2,1,1] [[1,5,6,8],[2,7],[3],[4]]=>{{1,5,6,8},{2,7},{3},{4}}=>[4,2,1,1] [[1,4,6,8],[2,7],[3],[5]]=>{{1,4,6,8},{2,7},{3},{5}}=>[4,2,1,1] [[1,3,6,8],[2,7],[4],[5]]=>{{1,3,6,8},{2,7},{4},{5}}=>[4,2,1,1] [[1,2,6,8],[3,7],[4],[5]]=>{{1,2,6,8},{3,7},{4},{5}}=>[4,2,1,1] [[1,4,5,8],[2,7],[3],[6]]=>{{1,4,5,8},{2,7},{3},{6}}=>[4,2,1,1] [[1,3,5,8],[2,7],[4],[6]]=>{{1,3,5,8},{2,7},{4},{6}}=>[4,2,1,1] [[1,2,5,8],[3,7],[4],[6]]=>{{1,2,5,8},{3,7},{4},{6}}=>[4,2,1,1] [[1,3,4,8],[2,7],[5],[6]]=>{{1,3,4,8},{2,7},{5},{6}}=>[4,2,1,1] [[1,2,4,8],[3,7],[5],[6]]=>{{1,2,4,8},{3,7},{5},{6}}=>[4,2,1,1] [[1,2,3,8],[4,7],[5],[6]]=>{{1,2,3,8},{4,7},{5},{6}}=>[4,2,1,1] [[1,4,6,8],[2,5],[3],[7]]=>{{1,4,6,8},{2,5},{3},{7}}=>[4,2,1,1] [[1,3,6,8],[2,5],[4],[7]]=>{{1,3,6,8},{2,5},{4},{7}}=>[4,2,1,1] [[1,2,6,8],[3,5],[4],[7]]=>{{1,2,6,8},{3,5},{4},{7}}=>[4,2,1,1] [[1,3,6,8],[2,4],[5],[7]]=>{{1,3,6,8},{2,4},{5},{7}}=>[4,2,1,1] [[1,2,6,8],[3,4],[5],[7]]=>{{1,2,6,8},{3,4},{5},{7}}=>[4,2,1,1] [[1,4,5,8],[2,6],[3],[7]]=>{{1,4,5,8},{2,6},{3},{7}}=>[4,2,1,1] [[1,3,5,8],[2,6],[4],[7]]=>{{1,3,5,8},{2,6},{4},{7}}=>[4,2,1,1] [[1,2,5,8],[3,6],[4],[7]]=>{{1,2,5,8},{3,6},{4},{7}}=>[4,2,1,1] [[1,3,4,8],[2,6],[5],[7]]=>{{1,3,4,8},{2,6},{5},{7}}=>[4,2,1,1] [[1,2,4,8],[3,6],[5],[7]]=>{{1,2,4,8},{3,6},{5},{7}}=>[4,2,1,1] [[1,2,3,8],[4,6],[5],[7]]=>{{1,2,3,8},{4,6},{5},{7}}=>[4,2,1,1] [[1,2,5,8],[3,4],[6],[7]]=>{{1,2,5,8},{3,4},{6},{7}}=>[4,2,1,1] [[1,3,4,8],[2,5],[6],[7]]=>{{1,3,4,8},{2,5},{6},{7}}=>[4,2,1,1] [[1,2,4,8],[3,5],[6],[7]]=>{{1,2,4,8},{3,5},{6},{7}}=>[4,2,1,1] [[1,2,3,8],[4,5],[6],[7]]=>{{1,2,3,8},{4,5},{6},{7}}=>[4,2,1,1] [[1,5,6,7],[2,8],[3],[4]]=>{{1,5,6,7},{2,8},{3},{4}}=>[4,2,1,1] [[1,4,6,7],[2,8],[3],[5]]=>{{1,4,6,7},{2,8},{3},{5}}=>[4,2,1,1] [[1,3,6,7],[2,8],[4],[5]]=>{{1,3,6,7},{2,8},{4},{5}}=>[4,2,1,1] [[1,2,6,7],[3,8],[4],[5]]=>{{1,2,6,7},{3,8},{4},{5}}=>[4,2,1,1] [[1,4,5,7],[2,8],[3],[6]]=>{{1,4,5,7},{2,8},{3},{6}}=>[4,2,1,1] [[1,3,5,7],[2,8],[4],[6]]=>{{1,3,5,7},{2,8},{4},{6}}=>[4,2,1,1] [[1,2,5,7],[3,8],[4],[6]]=>{{1,2,5,7},{3,8},{4},{6}}=>[4,2,1,1] [[1,3,4,7],[2,8],[5],[6]]=>{{1,3,4,7},{2,8},{5},{6}}=>[4,2,1,1] [[1,2,4,7],[3,8],[5],[6]]=>{{1,2,4,7},{3,8},{5},{6}}=>[4,2,1,1] [[1,4,5,6],[2,8],[3],[7]]=>{{1,4,5,6},{2,8},{3},{7}}=>[4,2,1,1] [[1,3,5,6],[2,8],[4],[7]]=>{{1,3,5,6},{2,8},{4},{7}}=>[4,2,1,1] [[1,2,5,6],[3,8],[4],[7]]=>{{1,2,5,6},{3,8},{4},{7}}=>[4,2,1,1] [[1,3,4,6],[2,8],[5],[7]]=>{{1,3,4,6},{2,8},{5},{7}}=>[4,2,1,1] [[1,2,4,6],[3,8],[5],[7]]=>{{1,2,4,6},{3,8},{5},{7}}=>[4,2,1,1] [[1,2,3,6],[4,8],[5],[7]]=>{{1,2,3,6},{4,8},{5},{7}}=>[4,2,1,1] [[1,3,4,5],[2,8],[6],[7]]=>{{1,3,4,5},{2,8},{6},{7}}=>[4,2,1,1] [[1,2,4,5],[3,8],[6],[7]]=>{{1,2,4,5},{3,8},{6},{7}}=>[4,2,1,1] [[1,2,3,5],[4,8],[6],[7]]=>{{1,2,3,5},{4,8},{6},{7}}=>[4,2,1,1] [[1,4,6,7],[2,5],[3],[8]]=>{{1,4,6,7},{2,5},{3},{8}}=>[4,2,1,1] [[1,3,6,7],[2,5],[4],[8]]=>{{1,3,6,7},{2,5},{4},{8}}=>[4,2,1,1] [[1,4,5,7],[2,6],[3],[8]]=>{{1,4,5,7},{2,6},{3},{8}}=>[4,2,1,1] [[1,3,5,7],[2,6],[4],[8]]=>{{1,3,5,7},{2,6},{4},{8}}=>[4,2,1,1] [[1,2,5,7],[3,6],[4],[8]]=>{{1,2,5,7},{3,6},{4},{8}}=>[4,2,1,1] [[1,3,4,7],[2,6],[5],[8]]=>{{1,3,4,7},{2,6},{5},{8}}=>[4,2,1,1] [[1,2,4,7],[3,6],[5],[8]]=>{{1,2,4,7},{3,6},{5},{8}}=>[4,2,1,1] [[1,2,3,7],[4,6],[5],[8]]=>{{1,2,3,7},{4,6},{5},{8}}=>[4,2,1,1] [[1,3,5,7],[2,4],[6],[8]]=>{{1,3,5,7},{2,4},{6},{8}}=>[4,2,1,1] [[1,2,5,7],[3,4],[6],[8]]=>{{1,2,5,7},{3,4},{6},{8}}=>[4,2,1,1] [[1,3,4,7],[2,5],[6],[8]]=>{{1,3,4,7},{2,5},{6},{8}}=>[4,2,1,1] [[1,2,4,7],[3,5],[6],[8]]=>{{1,2,4,7},{3,5},{6},{8}}=>[4,2,1,1] [[1,2,3,7],[4,5],[6],[8]]=>{{1,2,3,7},{4,5},{6},{8}}=>[4,2,1,1] [[1,4,5,6],[2,7],[3],[8]]=>{{1,4,5,6},{2,7},{3},{8}}=>[4,2,1,1] [[1,3,4,6],[2,7],[5],[8]]=>{{1,3,4,6},{2,7},{5},{8}}=>[4,2,1,1] [[1,2,4,6],[3,7],[5],[8]]=>{{1,2,4,6},{3,7},{5},{8}}=>[4,2,1,1] [[1,2,3,6],[4,7],[5],[8]]=>{{1,2,3,6},{4,7},{5},{8}}=>[4,2,1,1] [[1,3,4,5],[2,7],[6],[8]]=>{{1,3,4,5},{2,7},{6},{8}}=>[4,2,1,1] [[1,2,4,5],[3,7],[6],[8]]=>{{1,2,4,5},{3,7},{6},{8}}=>[4,2,1,1] [[1,2,3,5],[4,7],[6],[8]]=>{{1,2,3,5},{4,7},{6},{8}}=>[4,2,1,1] [[1,3,5,6],[2,4],[7],[8]]=>{{1,3,5,6},{2,4},{7},{8}}=>[4,2,1,1] [[1,2,5,6],[3,4],[7],[8]]=>{{1,2,5,6},{3,4},{7},{8}}=>[4,2,1,1] [[1,2,4,6],[3,5],[7],[8]]=>{{1,2,4,6},{3,5},{7},{8}}=>[4,2,1,1] [[1,2,3,6],[4,5],[7],[8]]=>{{1,2,3,6},{4,5},{7},{8}}=>[4,2,1,1] [[1,3,4,5],[2,6],[7],[8]]=>{{1,3,4,5},{2,6},{7},{8}}=>[4,2,1,1] [[1,2,4,5],[3,6],[7],[8]]=>{{1,2,4,5},{3,6},{7},{8}}=>[4,2,1,1] [[1,2,3,5],[4,6],[7],[8]]=>{{1,2,3,5},{4,6},{7},{8}}=>[4,2,1,1] [[1,6,7,8],[2],[3],[4],[5]]=>{{1,6,7,8},{2},{3},{4},{5}}=>[4,1,1,1,1] [[1,5,7,8],[2],[3],[4],[6]]=>{{1,5,7,8},{2},{3},{4},{6}}=>[4,1,1,1,1] [[1,3,7,8],[2],[4],[5],[6]]=>{{1,3,7,8},{2},{4},{5},{6}}=>[4,1,1,1,1] [[1,2,7,8],[3],[4],[5],[6]]=>{{1,2,7,8},{3},{4},{5},{6}}=>[4,1,1,1,1] [[1,5,6,8],[2],[3],[4],[7]]=>{{1,5,6,8},{2},{3},{4},{7}}=>[4,1,1,1,1] [[1,4,6,8],[2],[3],[5],[7]]=>{{1,4,6,8},{2},{3},{5},{7}}=>[4,1,1,1,1] [[1,4,5,8],[2],[3],[6],[7]]=>{{1,4,5,8},{2},{3},{6},{7}}=>[4,1,1,1,1] [[1,3,5,8],[2],[4],[6],[7]]=>{{1,3,5,8},{2},{4},{6},{7}}=>[4,1,1,1,1] [[1,3,4,8],[2],[5],[6],[7]]=>{{1,3,4,8},{2},{5},{6},{7}}=>[4,1,1,1,1] [[1,2,4,8],[3],[5],[6],[7]]=>{{1,2,4,8},{3},{5},{6},{7}}=>[4,1,1,1,1] [[1,2,3,8],[4],[5],[6],[7]]=>{{1,2,3,8},{4},{5},{6},{7}}=>[4,1,1,1,1] [[1,5,6,7],[2],[3],[4],[8]]=>{{1,5,6,7},{2},{3},{4},{8}}=>[4,1,1,1,1] [[1,3,5,7],[2],[4],[6],[8]]=>{{1,3,5,7},{2},{4},{6},{8}}=>[4,1,1,1,1] [[1,4,5,6],[2],[3],[7],[8]]=>{{1,4,5,6},{2},{3},{7},{8}}=>[4,1,1,1,1] [[1,3,4,5],[2],[6],[7],[8]]=>{{1,3,4,5},{2},{6},{7},{8}}=>[4,1,1,1,1] [[1,2,3,4],[5],[6],[7],[8]]=>{{1,2,3,4},{5},{6},{7},{8}}=>[4,1,1,1,1] [[1,4,7],[2,5,8],[3,6]]=>{{1,4,7},{2,5,8},{3,6}}=>[3,3,2] [[1,3,7],[2,4,8],[5,6]]=>{{1,3,7},{2,4,8},{5,6}}=>[3,3,2] [[1,4,6],[2,5,8],[3,7]]=>{{1,4,6},{2,5,8},{3,7}}=>[3,3,2] [[1,3,6],[2,5,8],[4,7]]=>{{1,3,6},{2,5,8},{4,7}}=>[3,3,2] [[1,2,6],[3,4,8],[5,7]]=>{{1,2,6},{3,4,8},{5,7}}=>[3,3,2] [[1,4,5],[2,6,8],[3,7]]=>{{1,4,5},{2,6,8},{3,7}}=>[3,3,2] [[1,3,5],[2,6,8],[4,7]]=>{{1,3,5},{2,6,8},{4,7}}=>[3,3,2] [[1,2,5],[3,6,8],[4,7]]=>{{1,2,5},{3,6,8},{4,7}}=>[3,3,2] [[1,3,4],[2,6,8],[5,7]]=>{{1,3,4},{2,6,8},{5,7}}=>[3,3,2] [[1,3,5],[2,4,8],[6,7]]=>{{1,3,5},{2,4,8},{6,7}}=>[3,3,2] [[1,2,5],[3,4,8],[6,7]]=>{{1,2,5},{3,4,8},{6,7}}=>[3,3,2] [[1,3,4],[2,5,8],[6,7]]=>{{1,3,4},{2,5,8},{6,7}}=>[3,3,2] [[1,2,4],[3,5,8],[6,7]]=>{{1,2,4},{3,5,8},{6,7}}=>[3,3,2] [[1,2,3],[4,5,8],[6,7]]=>{{1,2,3},{4,5,8},{6,7}}=>[3,3,2] [[1,4,6],[2,5,7],[3,8]]=>{{1,4,6},{2,5,7},{3,8}}=>[3,3,2] [[1,3,6],[2,5,7],[4,8]]=>{{1,3,6},{2,5,7},{4,8}}=>[3,3,2] [[1,2,4],[3,5,7],[6,8]]=>{{1,2,4},{3,5,7},{6,8}}=>[3,3,2] [[1,2,5],[3,4,6],[7,8]]=>{{1,2,5},{3,4,6},{7,8}}=>[3,3,2] [[1,3,4],[2,5,6],[7,8]]=>{{1,3,4},{2,5,6},{7,8}}=>[3,3,2] [[1,2,4],[3,5,6],[7,8]]=>{{1,2,4},{3,5,6},{7,8}}=>[3,3,2] [[1,5,7],[2,6,8],[3],[4]]=>{{1,5,7},{2,6,8},{3},{4}}=>[3,3,1,1] [[1,4,7],[2,6,8],[3],[5]]=>{{1,4,7},{2,6,8},{3},{5}}=>[3,3,1,1] [[1,3,7],[2,6,8],[4],[5]]=>{{1,3,7},{2,6,8},{4},{5}}=>[3,3,1,1] [[1,2,7],[3,6,8],[4],[5]]=>{{1,2,7},{3,6,8},{4},{5}}=>[3,3,1,1] [[1,4,7],[2,5,8],[3],[6]]=>{{1,4,7},{2,5,8},{3},{6}}=>[3,3,1,1] [[1,3,7],[2,5,8],[4],[6]]=>{{1,3,7},{2,5,8},{4},{6}}=>[3,3,1,1] [[1,2,7],[3,5,8],[4],[6]]=>{{1,2,7},{3,5,8},{4},{6}}=>[3,3,1,1] [[1,3,7],[2,4,8],[5],[6]]=>{{1,3,7},{2,4,8},{5},{6}}=>[3,3,1,1] [[1,2,7],[3,4,8],[5],[6]]=>{{1,2,7},{3,4,8},{5},{6}}=>[3,3,1,1] [[1,5,6],[2,7,8],[3],[4]]=>{{1,5,6},{2,7,8},{3},{4}}=>[3,3,1,1] [[1,4,6],[2,7,8],[3],[5]]=>{{1,4,6},{2,7,8},{3},{5}}=>[3,3,1,1] [[1,3,6],[2,7,8],[4],[5]]=>{{1,3,6},{2,7,8},{4},{5}}=>[3,3,1,1] [[1,2,6],[3,7,8],[4],[5]]=>{{1,2,6},{3,7,8},{4},{5}}=>[3,3,1,1] [[1,4,5],[2,7,8],[3],[6]]=>{{1,4,5},{2,7,8},{3},{6}}=>[3,3,1,1] [[1,3,5],[2,7,8],[4],[6]]=>{{1,3,5},{2,7,8},{4},{6}}=>[3,3,1,1] [[1,2,5],[3,7,8],[4],[6]]=>{{1,2,5},{3,7,8},{4},{6}}=>[3,3,1,1] [[1,3,4],[2,7,8],[5],[6]]=>{{1,3,4},{2,7,8},{5},{6}}=>[3,3,1,1] [[1,2,4],[3,7,8],[5],[6]]=>{{1,2,4},{3,7,8},{5},{6}}=>[3,3,1,1] [[1,4,6],[2,5,8],[3],[7]]=>{{1,4,6},{2,5,8},{3},{7}}=>[3,3,1,1] [[1,3,6],[2,5,8],[4],[7]]=>{{1,3,6},{2,5,8},{4},{7}}=>[3,3,1,1] [[1,2,6],[3,5,8],[4],[7]]=>{{1,2,6},{3,5,8},{4},{7}}=>[3,3,1,1] [[1,3,6],[2,4,8],[5],[7]]=>{{1,3,6},{2,4,8},{5},{7}}=>[3,3,1,1] [[1,2,6],[3,4,8],[5],[7]]=>{{1,2,6},{3,4,8},{5},{7}}=>[3,3,1,1] [[1,4,5],[2,6,8],[3],[7]]=>{{1,4,5},{2,6,8},{3},{7}}=>[3,3,1,1] [[1,3,5],[2,6,8],[4],[7]]=>{{1,3,5},{2,6,8},{4},{7}}=>[3,3,1,1] [[1,2,5],[3,6,8],[4],[7]]=>{{1,2,5},{3,6,8},{4},{7}}=>[3,3,1,1] [[1,3,4],[2,6,8],[5],[7]]=>{{1,3,4},{2,6,8},{5},{7}}=>[3,3,1,1] [[1,2,4],[3,6,8],[5],[7]]=>{{1,2,4},{3,6,8},{5},{7}}=>[3,3,1,1] [[1,2,3],[4,6,8],[5],[7]]=>{{1,2,3},{4,6,8},{5},{7}}=>[3,3,1,1] [[1,3,5],[2,4,8],[6],[7]]=>{{1,3,5},{2,4,8},{6},{7}}=>[3,3,1,1] [[1,2,5],[3,4,8],[6],[7]]=>{{1,2,5},{3,4,8},{6},{7}}=>[3,3,1,1] [[1,3,4],[2,5,8],[6],[7]]=>{{1,3,4},{2,5,8},{6},{7}}=>[3,3,1,1] [[1,2,4],[3,5,8],[6],[7]]=>{{1,2,4},{3,5,8},{6},{7}}=>[3,3,1,1] [[1,2,3],[4,5,8],[6],[7]]=>{{1,2,3},{4,5,8},{6},{7}}=>[3,3,1,1] [[1,4,6],[2,5,7],[3],[8]]=>{{1,4,6},{2,5,7},{3},{8}}=>[3,3,1,1] [[1,3,6],[2,5,7],[4],[8]]=>{{1,3,6},{2,5,7},{4},{8}}=>[3,3,1,1] [[1,2,6],[3,5,7],[4],[8]]=>{{1,2,6},{3,5,7},{4},{8}}=>[3,3,1,1] [[1,3,6],[2,4,7],[5],[8]]=>{{1,3,6},{2,4,7},{5},{8}}=>[3,3,1,1] [[1,3,5],[2,6,7],[4],[8]]=>{{1,3,5},{2,6,7},{4},{8}}=>[3,3,1,1] [[1,2,5],[3,6,7],[4],[8]]=>{{1,2,5},{3,6,7},{4},{8}}=>[3,3,1,1] [[1,3,4],[2,6,7],[5],[8]]=>{{1,3,4},{2,6,7},{5},{8}}=>[3,3,1,1] [[1,2,3],[4,6,7],[5],[8]]=>{{1,2,3},{4,6,7},{5},{8}}=>[3,3,1,1] [[1,3,5],[2,4,7],[6],[8]]=>{{1,3,5},{2,4,7},{6},{8}}=>[3,3,1,1] [[1,2,5],[3,4,7],[6],[8]]=>{{1,2,5},{3,4,7},{6},{8}}=>[3,3,1,1] [[1,3,4],[2,5,7],[6],[8]]=>{{1,3,4},{2,5,7},{6},{8}}=>[3,3,1,1] [[1,2,4],[3,5,7],[6],[8]]=>{{1,2,4},{3,5,7},{6},{8}}=>[3,3,1,1] [[1,3,5],[2,4,6],[7],[8]]=>{{1,3,5},{2,4,6},{7},{8}}=>[3,3,1,1] [[1,2,5],[3,4,6],[7],[8]]=>{{1,2,5},{3,4,6},{7},{8}}=>[3,3,1,1] [[1,5,8],[2,6],[3,7],[4]]=>{{1,5,8},{2,6},{3,7},{4}}=>[3,2,2,1] [[1,4,8],[2,6],[3,7],[5]]=>{{1,4,8},{2,6},{3,7},{5}}=>[3,2,2,1] [[1,3,8],[2,6],[4,7],[5]]=>{{1,3,8},{2,6},{4,7},{5}}=>[3,2,2,1] [[1,2,8],[3,6],[4,7],[5]]=>{{1,2,8},{3,6},{4,7},{5}}=>[3,2,2,1] [[1,4,8],[2,5],[3,7],[6]]=>{{1,4,8},{2,5},{3,7},{6}}=>[3,2,2,1] [[1,3,8],[2,5],[4,7],[6]]=>{{1,3,8},{2,5},{4,7},{6}}=>[3,2,2,1] [[1,2,8],[3,5],[4,7],[6]]=>{{1,2,8},{3,5},{4,7},{6}}=>[3,2,2,1] [[1,3,8],[2,4],[5,7],[6]]=>{{1,3,8},{2,4},{5,7},{6}}=>[3,2,2,1] [[1,2,8],[3,4],[5,7],[6]]=>{{1,2,8},{3,4},{5,7},{6}}=>[3,2,2,1] [[1,4,8],[2,5],[3,6],[7]]=>{{1,4,8},{2,5},{3,6},{7}}=>[3,2,2,1] [[1,3,8],[2,5],[4,6],[7]]=>{{1,3,8},{2,5},{4,6},{7}}=>[3,2,2,1] [[1,2,8],[3,5],[4,6],[7]]=>{{1,2,8},{3,5},{4,6},{7}}=>[3,2,2,1] [[1,3,8],[2,4],[5,6],[7]]=>{{1,3,8},{2,4},{5,6},{7}}=>[3,2,2,1] [[1,2,8],[3,4],[5,6],[7]]=>{{1,2,8},{3,4},{5,6},{7}}=>[3,2,2,1] [[1,5,7],[2,6],[3,8],[4]]=>{{1,5,7},{2,6},{3,8},{4}}=>[3,2,2,1] [[1,4,7],[2,6],[3,8],[5]]=>{{1,4,7},{2,6},{3,8},{5}}=>[3,2,2,1] [[1,3,7],[2,6],[4,8],[5]]=>{{1,3,7},{2,6},{4,8},{5}}=>[3,2,2,1] [[1,2,7],[3,6],[4,8],[5]]=>{{1,2,7},{3,6},{4,8},{5}}=>[3,2,2,1] [[1,4,7],[2,5],[3,8],[6]]=>{{1,4,7},{2,5},{3,8},{6}}=>[3,2,2,1] [[1,3,7],[2,5],[4,8],[6]]=>{{1,3,7},{2,5},{4,8},{6}}=>[3,2,2,1] [[1,2,7],[3,5],[4,8],[6]]=>{{1,2,7},{3,5},{4,8},{6}}=>[3,2,2,1] [[1,3,7],[2,4],[5,8],[6]]=>{{1,3,7},{2,4},{5,8},{6}}=>[3,2,2,1] [[1,2,7],[3,4],[5,8],[6]]=>{{1,2,7},{3,4},{5,8},{6}}=>[3,2,2,1] [[1,5,6],[2,7],[3,8],[4]]=>{{1,5,6},{2,7},{3,8},{4}}=>[3,2,2,1] [[1,4,6],[2,7],[3,8],[5]]=>{{1,4,6},{2,7},{3,8},{5}}=>[3,2,2,1] [[1,3,6],[2,7],[4,8],[5]]=>{{1,3,6},{2,7},{4,8},{5}}=>[3,2,2,1] [[1,2,6],[3,7],[4,8],[5]]=>{{1,2,6},{3,7},{4,8},{5}}=>[3,2,2,1] [[1,4,5],[2,7],[3,8],[6]]=>{{1,4,5},{2,7},{3,8},{6}}=>[3,2,2,1] [[1,3,5],[2,7],[4,8],[6]]=>{{1,3,5},{2,7},{4,8},{6}}=>[3,2,2,1] [[1,2,5],[3,7],[4,8],[6]]=>{{1,2,5},{3,7},{4,8},{6}}=>[3,2,2,1] [[1,3,4],[2,7],[5,8],[6]]=>{{1,3,4},{2,7},{5,8},{6}}=>[3,2,2,1] [[1,2,4],[3,7],[5,8],[6]]=>{{1,2,4},{3,7},{5,8},{6}}=>[3,2,2,1] [[1,2,3],[4,7],[5,8],[6]]=>{{1,2,3},{4,7},{5,8},{6}}=>[3,2,2,1] [[1,4,6],[2,5],[3,8],[7]]=>{{1,4,6},{2,5},{3,8},{7}}=>[3,2,2,1] [[1,3,6],[2,5],[4,8],[7]]=>{{1,3,6},{2,5},{4,8},{7}}=>[3,2,2,1] [[1,2,6],[3,5],[4,8],[7]]=>{{1,2,6},{3,5},{4,8},{7}}=>[3,2,2,1] [[1,3,6],[2,4],[5,8],[7]]=>{{1,3,6},{2,4},{5,8},{7}}=>[3,2,2,1] [[1,2,6],[3,4],[5,8],[7]]=>{{1,2,6},{3,4},{5,8},{7}}=>[3,2,2,1] [[1,4,5],[2,6],[3,8],[7]]=>{{1,4,5},{2,6},{3,8},{7}}=>[3,2,2,1] [[1,3,5],[2,6],[4,8],[7]]=>{{1,3,5},{2,6},{4,8},{7}}=>[3,2,2,1] [[1,2,5],[3,6],[4,8],[7]]=>{{1,2,5},{3,6},{4,8},{7}}=>[3,2,2,1] [[1,3,4],[2,6],[5,8],[7]]=>{{1,3,4},{2,6},{5,8},{7}}=>[3,2,2,1] [[1,2,4],[3,6],[5,8],[7]]=>{{1,2,4},{3,6},{5,8},{7}}=>[3,2,2,1] [[1,2,3],[4,6],[5,8],[7]]=>{{1,2,3},{4,6},{5,8},{7}}=>[3,2,2,1] [[1,3,5],[2,4],[6,8],[7]]=>{{1,3,5},{2,4},{6,8},{7}}=>[3,2,2,1] [[1,2,5],[3,4],[6,8],[7]]=>{{1,2,5},{3,4},{6,8},{7}}=>[3,2,2,1] [[1,3,4],[2,5],[6,8],[7]]=>{{1,3,4},{2,5},{6,8},{7}}=>[3,2,2,1] [[1,4,7],[2,5],[3,6],[8]]=>{{1,4,7},{2,5},{3,6},{8}}=>[3,2,2,1] [[1,3,7],[2,5],[4,6],[8]]=>{{1,3,7},{2,5},{4,6},{8}}=>[3,2,2,1] [[1,2,7],[3,5],[4,6],[8]]=>{{1,2,7},{3,5},{4,6},{8}}=>[3,2,2,1] [[1,3,7],[2,4],[5,6],[8]]=>{{1,3,7},{2,4},{5,6},{8}}=>[3,2,2,1] [[1,2,7],[3,4],[5,6],[8]]=>{{1,2,7},{3,4},{5,6},{8}}=>[3,2,2,1] [[1,2,6],[3,5],[4,7],[8]]=>{{1,2,6},{3,5},{4,7},{8}}=>[3,2,2,1] [[1,3,6],[2,4],[5,7],[8]]=>{{1,3,6},{2,4},{5,7},{8}}=>[3,2,2,1] [[1,2,6],[3,4],[5,7],[8]]=>{{1,2,6},{3,4},{5,7},{8}}=>[3,2,2,1] [[1,4,5],[2,6],[3,7],[8]]=>{{1,4,5},{2,6},{3,7},{8}}=>[3,2,2,1] [[1,3,5],[2,6],[4,7],[8]]=>{{1,3,5},{2,6},{4,7},{8}}=>[3,2,2,1] [[1,2,5],[3,6],[4,7],[8]]=>{{1,2,5},{3,6},{4,7},{8}}=>[3,2,2,1] [[1,3,4],[2,6],[5,7],[8]]=>{{1,3,4},{2,6},{5,7},{8}}=>[3,2,2,1] [[1,2,4],[3,6],[5,7],[8]]=>{{1,2,4},{3,6},{5,7},{8}}=>[3,2,2,1] [[1,2,3],[4,6],[5,7],[8]]=>{{1,2,3},{4,6},{5,7},{8}}=>[3,2,2,1] [[1,2,5],[3,4],[6,7],[8]]=>{{1,2,5},{3,4},{6,7},{8}}=>[3,2,2,1] [[1,3,4],[2,5],[6,7],[8]]=>{{1,3,4},{2,5},{6,7},{8}}=>[3,2,2,1] [[1,3,8],[2,4],[5],[6],[7]]=>{{1,3,8},{2,4},{5},{6},{7}}=>[3,2,1,1,1] [[1,2,8],[3,4],[5],[6],[7]]=>{{1,2,8},{3,4},{5},{6},{7}}=>[3,2,1,1,1] [[1,6,7],[2,8],[3],[4],[5]]=>{{1,6,7},{2,8},{3},{4},{5}}=>[3,2,1,1,1] [[1,3,4],[2,8],[5],[6],[7]]=>{{1,3,4},{2,8},{5},{6},{7}}=>[3,2,1,1,1] [[1,4,7],[2,6],[3],[5],[8]]=>{{1,4,7},{2,6},{3},{5},{8}}=>[3,2,1,1,1] [[1,4,7],[2,5],[3],[6],[8]]=>{{1,4,7},{2,5},{3},{6},{8}}=>[3,2,1,1,1] [[1,3,7],[2,4],[5],[6],[8]]=>{{1,3,7},{2,4},{5},{6},{8}}=>[3,2,1,1,1] [[1,4,6],[2,7],[3],[5],[8]]=>{{1,4,6},{2,7},{3},{5},{8}}=>[3,2,1,1,1] [[1,3,5],[2,4],[6],[7],[8]]=>{{1,3,5},{2,4},{6},{7},{8}}=>[3,2,1,1,1] [[1,2,5],[3,4],[6],[7],[8]]=>{{1,2,5},{3,4},{6},{7},{8}}=>[3,2,1,1,1] [[1,7,8],[2],[3],[4],[5],[6]]=>{{1,7,8},{2},{3},{4},{5},{6}}=>[3,1,1,1,1,1] [[1,6,8],[2],[3],[4],[5],[7]]=>{{1,6,8},{2},{3},{4},{5},{7}}=>[3,1,1,1,1,1] [[1,5,8],[2],[3],[4],[6],[7]]=>{{1,5,8},{2},{3},{4},{6},{7}}=>[3,1,1,1,1,1] [[1,3,8],[2],[4],[5],[6],[7]]=>{{1,3,8},{2},{4},{5},{6},{7}}=>[3,1,1,1,1,1] [[1,2,8],[3],[4],[5],[6],[7]]=>{{1,2,8},{3},{4},{5},{6},{7}}=>[3,1,1,1,1,1] [[1,6,7],[2],[3],[4],[5],[8]]=>{{1,6,7},{2},{3},{4},{5},{8}}=>[3,1,1,1,1,1] [[1,5,7],[2],[3],[4],[6],[8]]=>{{1,5,7},{2},{3},{4},{6},{8}}=>[3,1,1,1,1,1] [[1,3,7],[2],[4],[5],[6],[8]]=>{{1,3,7},{2},{4},{5},{6},{8}}=>[3,1,1,1,1,1] [[1,2,7],[3],[4],[5],[6],[8]]=>{{1,2,7},{3},{4},{5},{6},{8}}=>[3,1,1,1,1,1] [[1,5,6],[2],[3],[4],[7],[8]]=>{{1,5,6},{2},{3},{4},{7},{8}}=>[3,1,1,1,1,1] [[1,4,6],[2],[3],[5],[7],[8]]=>{{1,4,6},{2},{3},{5},{7},{8}}=>[3,1,1,1,1,1] [[1,3,6],[2],[4],[5],[7],[8]]=>{{1,3,6},{2},{4},{5},{7},{8}}=>[3,1,1,1,1,1] [[1,2,6],[3],[4],[5],[7],[8]]=>{{1,2,6},{3},{4},{5},{7},{8}}=>[3,1,1,1,1,1] [[1,4,5],[2],[3],[6],[7],[8]]=>{{1,4,5},{2},{3},{6},{7},{8}}=>[3,1,1,1,1,1] [[1,3,5],[2],[4],[6],[7],[8]]=>{{1,3,5},{2},{4},{6},{7},{8}}=>[3,1,1,1,1,1] [[1,2,5],[3],[4],[6],[7],[8]]=>{{1,2,5},{3},{4},{6},{7},{8}}=>[3,1,1,1,1,1] [[1,3,4],[2],[5],[6],[7],[8]]=>{{1,3,4},{2},{5},{6},{7},{8}}=>[3,1,1,1,1,1] [[1,2,4],[3],[5],[6],[7],[8]]=>{{1,2,4},{3},{5},{6},{7},{8}}=>[3,1,1,1,1,1] [[1,2,3],[4],[5],[6],[7],[8]]=>{{1,2,3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1] [[1,5],[2,6],[3,7],[4,8]]=>{{1,5},{2,6},{3,7},{4,8}}=>[2,2,2,2] [[1,4],[2,6],[3,7],[5,8]]=>{{1,4},{2,6},{3,7},{5,8}}=>[2,2,2,2] [[1,3],[2,6],[4,7],[5,8]]=>{{1,3},{2,6},{4,7},{5,8}}=>[2,2,2,2] [[1,2],[3,6],[4,7],[5,8]]=>{{1,2},{3,6},{4,7},{5,8}}=>[2,2,2,2] [[1,4],[2,5],[3,7],[6,8]]=>{{1,4},{2,5},{3,7},{6,8}}=>[2,2,2,2] [[1,3],[2,5],[4,7],[6,8]]=>{{1,3},{2,5},{4,7},{6,8}}=>[2,2,2,2] [[1,2],[3,5],[4,7],[6,8]]=>{{1,2},{3,5},{4,7},{6,8}}=>[2,2,2,2] [[1,3],[2,4],[5,7],[6,8]]=>{{1,3},{2,4},{5,7},{6,8}}=>[2,2,2,2] [[1,2],[3,4],[5,7],[6,8]]=>{{1,2},{3,4},{5,7},{6,8}}=>[2,2,2,2] [[1,4],[2,5],[3,6],[7,8]]=>{{1,4},{2,5},{3,6},{7,8}}=>[2,2,2,2] [[1,3],[2,5],[4,6],[7,8]]=>{{1,3},{2,5},{4,6},{7,8}}=>[2,2,2,2] [[1,2],[3,5],[4,6],[7,8]]=>{{1,2},{3,5},{4,6},{7,8}}=>[2,2,2,2] [[1,3],[2,4],[5,6],[7,8]]=>{{1,3},{2,4},{5,6},{7,8}}=>[2,2,2,2] [[1,2],[3,4],[5,6],[7,8]]=>{{1,2},{3,4},{5,6},{7,8}}=>[2,2,2,2] [[1,5],[2,6],[3,7],[4],[8]]=>{{1,5},{2,6},{3,7},{4},{8}}=>[2,2,2,1,1] [[1,3],[2,6],[4,7],[5],[8]]=>{{1,3},{2,6},{4,7},{5},{8}}=>[2,2,2,1,1] [[1,3],[2,5],[4,7],[6],[8]]=>{{1,3},{2,5},{4,7},{6},{8}}=>[2,2,2,1,1] [[1,4],[2,5],[3,6],[7],[8]]=>{{1,4},{2,5},{3,6},{7},{8}}=>[2,2,2,1,1] [[1,3],[2,5],[4,6],[7],[8]]=>{{1,3},{2,5},{4,6},{7},{8}}=>[2,2,2,1,1] [[1,7],[2,8],[3],[4],[5],[6]]=>{{1,7},{2,8},{3},{4},{5},{6}}=>[2,2,1,1,1,1] [[1,6],[2,8],[3],[4],[5],[7]]=>{{1,6},{2,8},{3},{4},{5},{7}}=>[2,2,1,1,1,1] [[1,4],[2,8],[3],[5],[6],[7]]=>{{1,4},{2,8},{3},{5},{6},{7}}=>[2,2,1,1,1,1] [[1,3],[2,8],[4],[5],[6],[7]]=>{{1,3},{2,8},{4},{5},{6},{7}}=>[2,2,1,1,1,1] [[1,2],[3,8],[4],[5],[6],[7]]=>{{1,2},{3,8},{4},{5},{6},{7}}=>[2,2,1,1,1,1] [[1,5],[2,6],[3],[4],[7],[8]]=>{{1,5},{2,6},{3},{4},{7},{8}}=>[2,2,1,1,1,1] [[1,2],[3,6],[4],[5],[7],[8]]=>{{1,2},{3,6},{4},{5},{7},{8}}=>[2,2,1,1,1,1] [[1,4],[2,5],[3],[6],[7],[8]]=>{{1,4},{2,5},{3},{6},{7},{8}}=>[2,2,1,1,1,1] [[1,2],[3,5],[4],[6],[7],[8]]=>{{1,2},{3,5},{4},{6},{7},{8}}=>[2,2,1,1,1,1] [[1,3],[2,4],[5],[6],[7],[8]]=>{{1,3},{2,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1] [[1,2],[3,4],[5],[6],[7],[8]]=>{{1,2},{3,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1] [[1,8],[2],[3],[4],[5],[6],[7]]=>{{1,8},{2},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1,1] [[1,7],[2],[3],[4],[5],[6],[8]]=>{{1,7},{2},{3},{4},{5},{6},{8}}=>[2,1,1,1,1,1,1] [[1,6],[2],[3],[4],[5],[7],[8]]=>{{1,6},{2},{3},{4},{5},{7},{8}}=>[2,1,1,1,1,1,1] [[1,5],[2],[3],[4],[6],[7],[8]]=>{{1,5},{2},{3},{4},{6},{7},{8}}=>[2,1,1,1,1,1,1] [[1,4],[2],[3],[5],[6],[7],[8]]=>{{1,4},{2},{3},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1] [[1,3],[2],[4],[5],[6],[7],[8]]=>{{1,3},{2},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1] [[1,2],[3],[4],[5],[6],[7],[8]]=>{{1,2},{3},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1] [[1],[2],[3],[4],[5],[6],[7],[8]]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,1,1,1,1,1,1,1] [[1,2,3,4,5],[6,7,8,9,10]]=>{{1,2,3,4,5},{6,7,8,9,10}}=>[5,5] [[1,2,3,4,5,6,7,8,9]]=>{{1,2,3,4,5,6,7,8,9}}=>[9] [[1,2,3,4,5,6,7,8],[9]]=>{{1,2,3,4,5,6,7,8},{9}}=>[8,1] [[1,2,3,4,5,6,7],[8,9]]=>{{1,2,3,4,5,6,7},{8,9}}=>[7,2] [[1,2,3,4,5,6,7],[8],[9]]=>{{1,2,3,4,5,6,7},{8},{9}}=>[7,1,1] [[1,2,3,4,5,6],[7,8,9]]=>{{1,2,3,4,5,6},{7,8,9}}=>[6,3] [[1,2,3,4,5,6],[7,8],[9]]=>{{1,2,3,4,5,6},{7,8},{9}}=>[6,2,1] [[1,2,3,4,5,6],[7],[8],[9]]=>{{1,2,3,4,5,6},{7},{8},{9}}=>[6,1,1,1] [[1,2,3,4,5],[6,7,8,9]]=>{{1,2,3,4,5},{6,7,8,9}}=>[5,4] [[1,2,3,4,5],[6,7,8],[9]]=>{{1,2,3,4,5},{6,7,8},{9}}=>[5,3,1] [[1,2,3,4,5],[6],[7],[8],[9]]=>{{1,2,3,4,5},{6},{7},{8},{9}}=>[5,1,1,1,1] [[1,2,3,4],[5],[6],[7],[8],[9]]=>{{1,2,3,4},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1] [[1,2,3],[4],[5],[6],[7],[8],[9]]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1] [[1,2],[3,4],[5],[6],[7],[8],[9]]=>{{1,2},{3,4},{5},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1] [[1,2],[3],[4],[5],[6],[7],[8],[9]]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1] [[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}=>[1,1,1,1,1,1,1,1,1] [[1,2,3,4,5,6,7,8,9,10]]=>{{1,2,3,4,5,6,7,8,9,10}}=>[10] [[1,2,3,4,5,6,7,8,9],[10]]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[9,1] [[1,2,3,4,5,6,7,8],[9,10]]=>{{1,2,3,4,5,6,7,8},{9,10}}=>[8,2] [[1,2,3,4,5,6,7,8],[9],[10]]=>{{1,2,3,4,5,6,7,8},{9},{10}}=>[8,1,1] [[1,2,3,4,5,6,7],[8,9,10]]=>{{1,2,3,4,5,6,7},{8,9,10}}=>[7,3] [[1,2,3,4,5,6,7],[8,9],[10]]=>{{1,2,3,4,5,6,7},{8,9},{10}}=>[7,2,1] [[1,2,3,4,5,6,7],[8],[9],[10]]=>{{1,2,3,4,5,6,7},{8},{9},{10}}=>[7,1,1,1] [[1,2,3,4,5,6],[7,8,9,10]]=>{{1,2,3,4,5,6},{7,8,9,10}}=>[6,4] [[1,2,3,4,5,6],[7],[8],[9],[10]]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}=>[6,1,1,1,1] [[1,2,3,4,5],[6],[7],[8],[9],[10]]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}=>[5,1,1,1,1,1] [[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}=>[4,1,1,1,1,1,1] [[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}=>[3,1,1,1,1,1,1,1] [[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>{{1,2},{3,4},{5},{6},{7},{8},{9},{10}}=>[2,2,1,1,1,1,1,1] [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1] [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[1,1,1,1,1,1,1,1,1,1] [[1,3,4,5,6,7,8,9],[2]]=>{{1,3,4,5,6,7,8,9},{2}}=>[8,1] [[1,4,5,6,7,8,9],[2],[3]]=>{{1,4,5,6,7,8,9},{2},{3}}=>[7,1,1] [[1,2,3,4,9],[5,6,7,8]]=>{{1,2,3,4,9},{5,6,7,8}}=>[5,4] [[1,7,8,9],[2],[3],[4],[5],[6]]=>{{1,7,8,9},{2},{3},{4},{5},{6}}=>[4,1,1,1,1,1] [[1,8,9],[2],[3],[4],[5],[6],[7]]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>[3,1,1,1,1,1,1] [[1,9],[2],[3],[4],[5],[6],[7],[8]]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1] [[1,3,4,5,6,7,8,9,10],[2]]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[9,1] [[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>[4,1,1,1,1,1,1] [[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1,1] [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1] [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>{{1,4,9},{2,6,12},{3,8},{5,11},{7},{10}}=>[3,3,2,2,1,1] [[1,8],[2,9],[3],[4],[5],[6],[7]]=>{{1,8},{2,9},{3},{4},{5},{6},{7}}=>[2,2,1,1,1,1,1] [[1,6],[2,7],[3,8],[4,9],[5,10]]=>{{1,6},{2,7},{3,8},{4,9},{5,10}}=>[2,2,2,2,2] [[1,2,3,4,5,7],[6,8],[9]]=>{{1,2,3,4,5,7},{6,8},{9}}=>[6,2,1] [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}=>[2,2,2,2,2,2] [[1,2,3,4,5,6,7,9],[8]]=>{{1,2,3,4,5,6,7,9},{8}}=>[8,1] [[1,2,3,4,5,6,9],[7,8]]=>{{1,2,3,4,5,6,9},{7,8}}=>[7,2] [[1,2,3,4,5,6,9],[7],[8]]=>{{1,2,3,4,5,6,9},{7},{8}}=>[7,1,1] [[1,2,3,4,5,9],[6,7,8]]=>{{1,2,3,4,5,9},{6,7,8}}=>[6,3] [[1,2,3,4,5,9],[6,7],[8]]=>{{1,2,3,4,5,9},{6,7},{8}}=>[6,2,1] [[1,2,3,4,9],[5,6],[7],[8]]=>{{1,2,3,4,9},{5,6},{7},{8}}=>[5,2,1,1] [[1,2,3,9],[4,5],[6],[7],[8]]=>{{1,2,3,9},{4,5},{6},{7},{8}}=>[4,2,1,1,1] [[1,2,3,9],[4],[5],[6],[7],[8]]=>{{1,2,3,9},{4},{5},{6},{7},{8}}=>[4,1,1,1,1,1] [[1,2,9],[3],[4],[5],[6],[7],[8]]=>{{1,2,9},{3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1] [[1,3],[2,9],[4],[5],[6],[7],[8]]=>{{1,3},{2,9},{4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1] [[1,2,3,4,5,6,7,8,10],[9]]=>{{1,2,3,4,5,6,7,8,10},{9}}=>[9,1] [[1,2,3,4,5,6,7,10],[8,9]]=>{{1,2,3,4,5,6,7,10},{8,9}}=>[8,2] [[1,2,3,4,5,6,10],[7,8,9]]=>{{1,2,3,4,5,6,10},{7,8,9}}=>[7,3] [[1,2,3,4,5,6,10],[7,8],[9]]=>{{1,2,3,4,5,6,10},{7,8},{9}}=>[7,2,1] [[1,2,3,4,5,10],[6,7,8,9]]=>{{1,2,3,4,5,10},{6,7,8,9}}=>[6,4] [[1,2,3,4,10],[5,6],[7],[8],[9]]=>{{1,2,3,4,10},{5,6},{7},{8},{9}}=>[5,2,1,1,1] [[1,2,3,10],[4,5],[6],[7],[8],[9]]=>{{1,2,3,10},{4,5},{6},{7},{8},{9}}=>[4,2,1,1,1,1] [[1,2,3,10],[4],[5],[6],[7],[8],[9]]=>{{1,2,3,10},{4},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1] [[1,2,4,5,6,7,8,9],[3]]=>{{1,2,4,5,6,7,8,9},{3}}=>[8,1] [[1,6,8,9],[2],[3],[4],[5],[7]]=>{{1,6,8,9},{2},{3},{4},{5},{7}}=>[4,1,1,1,1,1] [[1,7,9],[2],[3],[4],[5],[6],[8]]=>{{1,7,9},{2},{3},{4},{5},{6},{8}}=>[3,1,1,1,1,1,1] [[1,8],[2],[3],[4],[5],[6],[7],[9]]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>[2,1,1,1,1,1,1,1] [[1,2,4,5,6,7,8,9,10],[3]]=>{{1,2,4,5,6,7,8,9,10},{3}}=>[9,1] [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}=>[2,1,1,1,1,1,1,1,1] [[1,3,4,5,6,7,8],[2],[9]]=>{{1,3,4,5,6,7,8},{2},{9}}=>[7,1,1] [[1,3,4,5,6,7],[2,9],[8]]=>{{1,3,4,5,6,7},{2,9},{8}}=>[6,2,1] [[1,3,4,5,6],[2,8,9],[7]]=>{{1,3,4,5,6},{2,8,9},{7}}=>[5,3,1] [[1,3,4],[2],[5],[6],[7],[8],[9]]=>{{1,3,4},{2},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1] [[1,3],[2],[4],[5],[6],[7],[8],[9]]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1] [[1,3,4,5,6,7,8,9],[2],[10]]=>{{1,3,4,5,6,7,8,9},{2},{10}}=>[8,1,1] [[1,3,4,5,6,7,8],[2,10],[9]]=>{{1,3,4,5,6,7,8},{2,10},{9}}=>[7,2,1] [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1] [[1,2,3,5,6,7,8,9,10],[4]]=>{{1,2,3,5,6,7,8,9,10},{4}}=>[9,1] [[1,2,3,4,6,7,8,9,10],[5]]=>{{1,2,3,4,6,7,8,9,10},{5}}=>[9,1] [[1,2,3,4,5,6,7,9,10],[8]]=>{{1,2,3,4,5,6,7,9,10},{8}}=>[9,1] [[1,2,3,4,5,6,8,9,10],[7]]=>{{1,2,3,4,5,6,8,9,10},{7}}=>[9,1] [[1,2,3,4,5,7,8,9,10],[6]]=>{{1,2,3,4,5,7,8,9,10},{6}}=>[9,1] [[1,7,8],[2],[3],[4],[5],[6],[9]]=>{{1,7,8},{2},{3},{4},{5},{6},{9}}=>[3,1,1,1,1,1,1] [[1,2,5,10],[3,7],[4,9],[6],[8]]=>{{1,2,5,10},{3,7},{4,9},{6},{8}}=>[4,2,2,1,1]
Map
rows
Description
The set partition whose blocks are the rows of the tableau.
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.