Identifier
-
Mp00258:
Set partitions
—Standard tableau associated to a set partition⟶
Standard tableaux
St000738: Standard tableaux ⟶ ℤ
Values
=>
Cc0009;cc-rep-0
Cc0007;cc-rep
{{1}}=>[[1]]=>1
{{1,2}}=>[[1,2]]=>1
{{1},{2}}=>[[1],[2]]=>2
{{1,2,3}}=>[[1,2,3]]=>1
{{1,2},{3}}=>[[1,2],[3]]=>3
{{1,3},{2}}=>[[1,3],[2]]=>2
{{1},{2,3}}=>[[1,3],[2]]=>2
{{1},{2},{3}}=>[[1],[2],[3]]=>3
{{1,2,3,4}}=>[[1,2,3,4]]=>1
{{1,2,3},{4}}=>[[1,2,3],[4]]=>4
{{1,2,4},{3}}=>[[1,2,4],[3]]=>3
{{1,2},{3,4}}=>[[1,2],[3,4]]=>3
{{1,2},{3},{4}}=>[[1,2],[3],[4]]=>4
{{1,3,4},{2}}=>[[1,3,4],[2]]=>2
{{1,3},{2,4}}=>[[1,3],[2,4]]=>2
{{1,3},{2},{4}}=>[[1,3],[2],[4]]=>4
{{1,4},{2,3}}=>[[1,3],[2,4]]=>2
{{1},{2,3,4}}=>[[1,3,4],[2]]=>2
{{1},{2,3},{4}}=>[[1,3],[2],[4]]=>4
{{1,4},{2},{3}}=>[[1,4],[2],[3]]=>3
{{1},{2,4},{3}}=>[[1,4],[2],[3]]=>3
{{1},{2},{3,4}}=>[[1,4],[2],[3]]=>3
{{1},{2},{3},{4}}=>[[1],[2],[3],[4]]=>4
{{1,2,3,4,5}}=>[[1,2,3,4,5]]=>1
{{1,2,3,4},{5}}=>[[1,2,3,4],[5]]=>5
{{1,2,3,5},{4}}=>[[1,2,3,5],[4]]=>4
{{1,2,3},{4,5}}=>[[1,2,3],[4,5]]=>4
{{1,2,3},{4},{5}}=>[[1,2,3],[4],[5]]=>5
{{1,2,4,5},{3}}=>[[1,2,4,5],[3]]=>3
{{1,2,4},{3,5}}=>[[1,2,4],[3,5]]=>3
{{1,2,4},{3},{5}}=>[[1,2,4],[3],[5]]=>5
{{1,2,5},{3,4}}=>[[1,2,5],[3,4]]=>3
{{1,2},{3,4,5}}=>[[1,2,5],[3,4]]=>3
{{1,2},{3,4},{5}}=>[[1,2],[3,4],[5]]=>5
{{1,2,5},{3},{4}}=>[[1,2,5],[3],[4]]=>4
{{1,2},{3,5},{4}}=>[[1,2],[3,5],[4]]=>4
{{1,2},{3},{4,5}}=>[[1,2],[3,5],[4]]=>4
{{1,2},{3},{4},{5}}=>[[1,2],[3],[4],[5]]=>5
{{1,3,4,5},{2}}=>[[1,3,4,5],[2]]=>2
{{1,3,4},{2,5}}=>[[1,3,4],[2,5]]=>2
{{1,3,4},{2},{5}}=>[[1,3,4],[2],[5]]=>5
{{1,3,5},{2,4}}=>[[1,3,5],[2,4]]=>2
{{1,3},{2,4,5}}=>[[1,3,5],[2,4]]=>2
{{1,3},{2,4},{5}}=>[[1,3],[2,4],[5]]=>5
{{1,3,5},{2},{4}}=>[[1,3,5],[2],[4]]=>4
{{1,3},{2,5},{4}}=>[[1,3],[2,5],[4]]=>4
{{1,3},{2},{4,5}}=>[[1,3],[2,5],[4]]=>4
{{1,3},{2},{4},{5}}=>[[1,3],[2],[4],[5]]=>5
{{1,4,5},{2,3}}=>[[1,3,5],[2,4]]=>2
{{1,4},{2,3,5}}=>[[1,3,5],[2,4]]=>2
{{1,4},{2,3},{5}}=>[[1,3],[2,4],[5]]=>5
{{1,5},{2,3,4}}=>[[1,3,4],[2,5]]=>2
{{1},{2,3,4,5}}=>[[1,3,4,5],[2]]=>2
{{1},{2,3,4},{5}}=>[[1,3,4],[2],[5]]=>5
{{1,5},{2,3},{4}}=>[[1,3],[2,5],[4]]=>4
{{1},{2,3,5},{4}}=>[[1,3,5],[2],[4]]=>4
{{1},{2,3},{4,5}}=>[[1,3],[2,5],[4]]=>4
{{1},{2,3},{4},{5}}=>[[1,3],[2],[4],[5]]=>5
{{1,4,5},{2},{3}}=>[[1,4,5],[2],[3]]=>3
{{1,4},{2,5},{3}}=>[[1,4],[2,5],[3]]=>3
{{1,4},{2},{3,5}}=>[[1,4],[2,5],[3]]=>3
{{1,4},{2},{3},{5}}=>[[1,4],[2],[3],[5]]=>5
{{1,5},{2,4},{3}}=>[[1,4],[2,5],[3]]=>3
{{1},{2,4,5},{3}}=>[[1,4,5],[2],[3]]=>3
{{1},{2,4},{3,5}}=>[[1,4],[2,5],[3]]=>3
{{1},{2,4},{3},{5}}=>[[1,4],[2],[3],[5]]=>5
{{1,5},{2},{3,4}}=>[[1,4],[2,5],[3]]=>3
{{1},{2,5},{3,4}}=>[[1,4],[2,5],[3]]=>3
{{1},{2},{3,4,5}}=>[[1,4,5],[2],[3]]=>3
{{1},{2},{3,4},{5}}=>[[1,4],[2],[3],[5]]=>5
{{1,5},{2},{3},{4}}=>[[1,5],[2],[3],[4]]=>4
{{1},{2,5},{3},{4}}=>[[1,5],[2],[3],[4]]=>4
{{1},{2},{3,5},{4}}=>[[1,5],[2],[3],[4]]=>4
{{1},{2},{3},{4,5}}=>[[1,5],[2],[3],[4]]=>4
{{1},{2},{3},{4},{5}}=>[[1],[2],[3],[4],[5]]=>5
{{1,2,3,4,5,6}}=>[[1,2,3,4,5,6]]=>1
{{1,2,3,4,5},{6}}=>[[1,2,3,4,5],[6]]=>6
{{1,2,3,4,6},{5}}=>[[1,2,3,4,6],[5]]=>5
{{1,2,3,4},{5,6}}=>[[1,2,3,4],[5,6]]=>5
{{1,2,3,4},{5},{6}}=>[[1,2,3,4],[5],[6]]=>6
{{1,2,3,5,6},{4}}=>[[1,2,3,5,6],[4]]=>4
{{1,2,3,5},{4,6}}=>[[1,2,3,5],[4,6]]=>4
{{1,2,3,5},{4},{6}}=>[[1,2,3,5],[4],[6]]=>6
{{1,2,3,6},{4,5}}=>[[1,2,3,6],[4,5]]=>4
{{1,2,3},{4,5,6}}=>[[1,2,3],[4,5,6]]=>4
{{1,2,3},{4,5},{6}}=>[[1,2,3],[4,5],[6]]=>6
{{1,2,3,6},{4},{5}}=>[[1,2,3,6],[4],[5]]=>5
{{1,2,3},{4,6},{5}}=>[[1,2,3],[4,6],[5]]=>5
{{1,2,3},{4},{5,6}}=>[[1,2,3],[4,6],[5]]=>5
{{1,2,3},{4},{5},{6}}=>[[1,2,3],[4],[5],[6]]=>6
{{1,2,4,5,6},{3}}=>[[1,2,4,5,6],[3]]=>3
{{1,2,4,5},{3,6}}=>[[1,2,4,5],[3,6]]=>3
{{1,2,4,5},{3},{6}}=>[[1,2,4,5],[3],[6]]=>6
{{1,2,4,6},{3,5}}=>[[1,2,4,6],[3,5]]=>3
{{1,2,4},{3,5,6}}=>[[1,2,4],[3,5,6]]=>3
{{1,2,4},{3,5},{6}}=>[[1,2,4],[3,5],[6]]=>6
{{1,2,4,6},{3},{5}}=>[[1,2,4,6],[3],[5]]=>5
{{1,2,4},{3,6},{5}}=>[[1,2,4],[3,6],[5]]=>5
{{1,2,4},{3},{5,6}}=>[[1,2,4],[3,6],[5]]=>5
{{1,2,4},{3},{5},{6}}=>[[1,2,4],[3],[5],[6]]=>6
{{1,2,5,6},{3,4}}=>[[1,2,5,6],[3,4]]=>3
{{1,2,5},{3,4,6}}=>[[1,2,5],[3,4,6]]=>3
{{1,2,5},{3,4},{6}}=>[[1,2,5],[3,4],[6]]=>6
{{1,2,6},{3,4,5}}=>[[1,2,5],[3,4,6]]=>3
{{1,2},{3,4,5,6}}=>[[1,2,5,6],[3,4]]=>3
{{1,2},{3,4,5},{6}}=>[[1,2,5],[3,4],[6]]=>6
{{1,2,6},{3,4},{5}}=>[[1,2,6],[3,4],[5]]=>5
{{1,2},{3,4,6},{5}}=>[[1,2,6],[3,4],[5]]=>5
{{1,2},{3,4},{5,6}}=>[[1,2],[3,4],[5,6]]=>5
{{1,2},{3,4},{5},{6}}=>[[1,2],[3,4],[5],[6]]=>6
{{1,2,5,6},{3},{4}}=>[[1,2,5,6],[3],[4]]=>4
{{1,2,5},{3,6},{4}}=>[[1,2,5],[3,6],[4]]=>4
{{1,2,5},{3},{4,6}}=>[[1,2,5],[3,6],[4]]=>4
{{1,2,5},{3},{4},{6}}=>[[1,2,5],[3],[4],[6]]=>6
{{1,2,6},{3,5},{4}}=>[[1,2,6],[3,5],[4]]=>4
{{1,2},{3,5,6},{4}}=>[[1,2,6],[3,5],[4]]=>4
{{1,2},{3,5},{4,6}}=>[[1,2],[3,5],[4,6]]=>4
{{1,2},{3,5},{4},{6}}=>[[1,2],[3,5],[4],[6]]=>6
{{1,2,6},{3},{4,5}}=>[[1,2,6],[3,5],[4]]=>4
{{1,2},{3,6},{4,5}}=>[[1,2],[3,5],[4,6]]=>4
{{1,2},{3},{4,5,6}}=>[[1,2,6],[3,5],[4]]=>4
{{1,2},{3},{4,5},{6}}=>[[1,2],[3,5],[4],[6]]=>6
{{1,2,6},{3},{4},{5}}=>[[1,2,6],[3],[4],[5]]=>5
{{1,2},{3,6},{4},{5}}=>[[1,2],[3,6],[4],[5]]=>5
{{1,2},{3},{4,6},{5}}=>[[1,2],[3,6],[4],[5]]=>5
{{1,2},{3},{4},{5,6}}=>[[1,2],[3,6],[4],[5]]=>5
{{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]]=>2
{{1,3,4,5},{2,6}}=>[[1,3,4,5],[2,6]]=>2
{{1,3,4,5},{2},{6}}=>[[1,3,4,5],[2],[6]]=>6
{{1,3,4,6},{2,5}}=>[[1,3,4,6],[2,5]]=>2
{{1,3,4},{2,5,6}}=>[[1,3,4],[2,5,6]]=>2
{{1,3,4},{2,5},{6}}=>[[1,3,4],[2,5],[6]]=>6
{{1,3,4,6},{2},{5}}=>[[1,3,4,6],[2],[5]]=>5
{{1,3,4},{2,6},{5}}=>[[1,3,4],[2,6],[5]]=>5
{{1,3,4},{2},{5,6}}=>[[1,3,4],[2,6],[5]]=>5
{{1,3,4},{2},{5},{6}}=>[[1,3,4],[2],[5],[6]]=>6
{{1,3,5,6},{2,4}}=>[[1,3,5,6],[2,4]]=>2
{{1,3,5},{2,4,6}}=>[[1,3,5],[2,4,6]]=>2
{{1,3,5},{2,4},{6}}=>[[1,3,5],[2,4],[6]]=>6
{{1,3,6},{2,4,5}}=>[[1,3,5],[2,4,6]]=>2
{{1,3},{2,4,5,6}}=>[[1,3,5,6],[2,4]]=>2
{{1,3},{2,4,5},{6}}=>[[1,3,5],[2,4],[6]]=>6
{{1,3,6},{2,4},{5}}=>[[1,3,6],[2,4],[5]]=>5
{{1,3},{2,4,6},{5}}=>[[1,3,6],[2,4],[5]]=>5
{{1,3},{2,4},{5,6}}=>[[1,3],[2,4],[5,6]]=>5
{{1,3},{2,4},{5},{6}}=>[[1,3],[2,4],[5],[6]]=>6
{{1,3,5,6},{2},{4}}=>[[1,3,5,6],[2],[4]]=>4
{{1,3,5},{2,6},{4}}=>[[1,3,5],[2,6],[4]]=>4
{{1,3,5},{2},{4,6}}=>[[1,3,5],[2,6],[4]]=>4
{{1,3,5},{2},{4},{6}}=>[[1,3,5],[2],[4],[6]]=>6
{{1,3,6},{2,5},{4}}=>[[1,3,6],[2,5],[4]]=>4
{{1,3},{2,5,6},{4}}=>[[1,3,6],[2,5],[4]]=>4
{{1,3},{2,5},{4,6}}=>[[1,3],[2,5],[4,6]]=>4
{{1,3},{2,5},{4},{6}}=>[[1,3],[2,5],[4],[6]]=>6
{{1,3,6},{2},{4,5}}=>[[1,3,6],[2,5],[4]]=>4
{{1,3},{2,6},{4,5}}=>[[1,3],[2,5],[4,6]]=>4
{{1,3},{2},{4,5,6}}=>[[1,3,6],[2,5],[4]]=>4
{{1,3},{2},{4,5},{6}}=>[[1,3],[2,5],[4],[6]]=>6
{{1,3,6},{2},{4},{5}}=>[[1,3,6],[2],[4],[5]]=>5
{{1,3},{2,6},{4},{5}}=>[[1,3],[2,6],[4],[5]]=>5
{{1,3},{2},{4,6},{5}}=>[[1,3],[2,6],[4],[5]]=>5
{{1,3},{2},{4},{5,6}}=>[[1,3],[2,6],[4],[5]]=>5
{{1,3},{2},{4},{5},{6}}=>[[1,3],[2],[4],[5],[6]]=>6
{{1,4,5,6},{2,3}}=>[[1,3,5,6],[2,4]]=>2
{{1,4,5},{2,3,6}}=>[[1,3,5],[2,4,6]]=>2
{{1,4,5},{2,3},{6}}=>[[1,3,5],[2,4],[6]]=>6
{{1,4,6},{2,3,5}}=>[[1,3,5],[2,4,6]]=>2
{{1,4},{2,3,5,6}}=>[[1,3,5,6],[2,4]]=>2
{{1,4},{2,3,5},{6}}=>[[1,3,5],[2,4],[6]]=>6
{{1,4,6},{2,3},{5}}=>[[1,3,6],[2,4],[5]]=>5
{{1,4},{2,3,6},{5}}=>[[1,3,6],[2,4],[5]]=>5
{{1,4},{2,3},{5,6}}=>[[1,3],[2,4],[5,6]]=>5
{{1,4},{2,3},{5},{6}}=>[[1,3],[2,4],[5],[6]]=>6
{{1,5,6},{2,3,4}}=>[[1,3,4],[2,5,6]]=>2
{{1,5},{2,3,4,6}}=>[[1,3,4,6],[2,5]]=>2
{{1,5},{2,3,4},{6}}=>[[1,3,4],[2,5],[6]]=>6
{{1,6},{2,3,4,5}}=>[[1,3,4,5],[2,6]]=>2
{{1},{2,3,4,5,6}}=>[[1,3,4,5,6],[2]]=>2
{{1},{2,3,4,5},{6}}=>[[1,3,4,5],[2],[6]]=>6
{{1,6},{2,3,4},{5}}=>[[1,3,4],[2,6],[5]]=>5
{{1},{2,3,4,6},{5}}=>[[1,3,4,6],[2],[5]]=>5
{{1},{2,3,4},{5,6}}=>[[1,3,4],[2,6],[5]]=>5
{{1},{2,3,4},{5},{6}}=>[[1,3,4],[2],[5],[6]]=>6
{{1,5,6},{2,3},{4}}=>[[1,3,6],[2,5],[4]]=>4
{{1,5},{2,3,6},{4}}=>[[1,3,6],[2,5],[4]]=>4
{{1,5},{2,3},{4,6}}=>[[1,3],[2,5],[4,6]]=>4
{{1,5},{2,3},{4},{6}}=>[[1,3],[2,5],[4],[6]]=>6
{{1,6},{2,3,5},{4}}=>[[1,3,5],[2,6],[4]]=>4
{{1},{2,3,5,6},{4}}=>[[1,3,5,6],[2],[4]]=>4
{{1},{2,3,5},{4,6}}=>[[1,3,5],[2,6],[4]]=>4
{{1},{2,3,5},{4},{6}}=>[[1,3,5],[2],[4],[6]]=>6
{{1,6},{2,3},{4,5}}=>[[1,3],[2,5],[4,6]]=>4
{{1},{2,3,6},{4,5}}=>[[1,3,6],[2,5],[4]]=>4
{{1},{2,3},{4,5,6}}=>[[1,3,6],[2,5],[4]]=>4
{{1},{2,3},{4,5},{6}}=>[[1,3],[2,5],[4],[6]]=>6
{{1,6},{2,3},{4},{5}}=>[[1,3],[2,6],[4],[5]]=>5
{{1},{2,3,6},{4},{5}}=>[[1,3,6],[2],[4],[5]]=>5
{{1},{2,3},{4,6},{5}}=>[[1,3],[2,6],[4],[5]]=>5
{{1},{2,3},{4},{5,6}}=>[[1,3],[2,6],[4],[5]]=>5
{{1},{2,3},{4},{5},{6}}=>[[1,3],[2],[4],[5],[6]]=>6
{{1,4,5,6},{2},{3}}=>[[1,4,5,6],[2],[3]]=>3
{{1,4,5},{2,6},{3}}=>[[1,4,5],[2,6],[3]]=>3
{{1,4,5},{2},{3,6}}=>[[1,4,5],[2,6],[3]]=>3
{{1,4,5},{2},{3},{6}}=>[[1,4,5],[2],[3],[6]]=>6
{{1,4,6},{2,5},{3}}=>[[1,4,6],[2,5],[3]]=>3
{{1,4},{2,5,6},{3}}=>[[1,4,6],[2,5],[3]]=>3
{{1,4},{2,5},{3,6}}=>[[1,4],[2,5],[3,6]]=>3
{{1,4},{2,5},{3},{6}}=>[[1,4],[2,5],[3],[6]]=>6
{{1,4,6},{2},{3,5}}=>[[1,4,6],[2,5],[3]]=>3
{{1,4},{2,6},{3,5}}=>[[1,4],[2,5],[3,6]]=>3
{{1,4},{2},{3,5,6}}=>[[1,4,6],[2,5],[3]]=>3
{{1,4},{2},{3,5},{6}}=>[[1,4],[2,5],[3],[6]]=>6
{{1,4,6},{2},{3},{5}}=>[[1,4,6],[2],[3],[5]]=>5
{{1,4},{2,6},{3},{5}}=>[[1,4],[2,6],[3],[5]]=>5
{{1,4},{2},{3,6},{5}}=>[[1,4],[2,6],[3],[5]]=>5
{{1,4},{2},{3},{5,6}}=>[[1,4],[2,6],[3],[5]]=>5
{{1,4},{2},{3},{5},{6}}=>[[1,4],[2],[3],[5],[6]]=>6
{{1,5,6},{2,4},{3}}=>[[1,4,6],[2,5],[3]]=>3
{{1,5},{2,4,6},{3}}=>[[1,4,6],[2,5],[3]]=>3
{{1,5},{2,4},{3,6}}=>[[1,4],[2,5],[3,6]]=>3
{{1,5},{2,4},{3},{6}}=>[[1,4],[2,5],[3],[6]]=>6
{{1,6},{2,4,5},{3}}=>[[1,4,5],[2,6],[3]]=>3
{{1},{2,4,5,6},{3}}=>[[1,4,5,6],[2],[3]]=>3
{{1},{2,4,5},{3,6}}=>[[1,4,5],[2,6],[3]]=>3
{{1},{2,4,5},{3},{6}}=>[[1,4,5],[2],[3],[6]]=>6
{{1,6},{2,4},{3,5}}=>[[1,4],[2,5],[3,6]]=>3
{{1},{2,4,6},{3,5}}=>[[1,4,6],[2,5],[3]]=>3
{{1},{2,4},{3,5,6}}=>[[1,4,6],[2,5],[3]]=>3
{{1},{2,4},{3,5},{6}}=>[[1,4],[2,5],[3],[6]]=>6
{{1,6},{2,4},{3},{5}}=>[[1,4],[2,6],[3],[5]]=>5
{{1},{2,4,6},{3},{5}}=>[[1,4,6],[2],[3],[5]]=>5
{{1},{2,4},{3,6},{5}}=>[[1,4],[2,6],[3],[5]]=>5
{{1},{2,4},{3},{5,6}}=>[[1,4],[2,6],[3],[5]]=>5
{{1},{2,4},{3},{5},{6}}=>[[1,4],[2],[3],[5],[6]]=>6
{{1,5,6},{2},{3,4}}=>[[1,4,6],[2,5],[3]]=>3
{{1,5},{2,6},{3,4}}=>[[1,4],[2,5],[3,6]]=>3
{{1,5},{2},{3,4,6}}=>[[1,4,6],[2,5],[3]]=>3
{{1,5},{2},{3,4},{6}}=>[[1,4],[2,5],[3],[6]]=>6
{{1,6},{2,5},{3,4}}=>[[1,4],[2,5],[3,6]]=>3
{{1},{2,5,6},{3,4}}=>[[1,4,6],[2,5],[3]]=>3
{{1},{2,5},{3,4,6}}=>[[1,4,6],[2,5],[3]]=>3
{{1},{2,5},{3,4},{6}}=>[[1,4],[2,5],[3],[6]]=>6
{{1,6},{2},{3,4,5}}=>[[1,4,5],[2,6],[3]]=>3
{{1},{2,6},{3,4,5}}=>[[1,4,5],[2,6],[3]]=>3
{{1},{2},{3,4,5,6}}=>[[1,4,5,6],[2],[3]]=>3
{{1},{2},{3,4,5},{6}}=>[[1,4,5],[2],[3],[6]]=>6
{{1,6},{2},{3,4},{5}}=>[[1,4],[2,6],[3],[5]]=>5
{{1},{2,6},{3,4},{5}}=>[[1,4],[2,6],[3],[5]]=>5
{{1},{2},{3,4,6},{5}}=>[[1,4,6],[2],[3],[5]]=>5
{{1},{2},{3,4},{5,6}}=>[[1,4],[2,6],[3],[5]]=>5
{{1},{2},{3,4},{5},{6}}=>[[1,4],[2],[3],[5],[6]]=>6
{{1,5,6},{2},{3},{4}}=>[[1,5,6],[2],[3],[4]]=>4
{{1,5},{2,6},{3},{4}}=>[[1,5],[2,6],[3],[4]]=>4
{{1,5},{2},{3,6},{4}}=>[[1,5],[2,6],[3],[4]]=>4
{{1,5},{2},{3},{4,6}}=>[[1,5],[2,6],[3],[4]]=>4
{{1,5},{2},{3},{4},{6}}=>[[1,5],[2],[3],[4],[6]]=>6
{{1,6},{2,5},{3},{4}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2,5,6},{3},{4}}=>[[1,5,6],[2],[3],[4]]=>4
{{1},{2,5},{3,6},{4}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2,5},{3},{4,6}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2,5},{3},{4},{6}}=>[[1,5],[2],[3],[4],[6]]=>6
{{1,6},{2},{3,5},{4}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2,6},{3,5},{4}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2},{3,5,6},{4}}=>[[1,5,6],[2],[3],[4]]=>4
{{1},{2},{3,5},{4,6}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2},{3,5},{4},{6}}=>[[1,5],[2],[3],[4],[6]]=>6
{{1,6},{2},{3},{4,5}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2,6},{3},{4,5}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2},{3,6},{4,5}}=>[[1,5],[2,6],[3],[4]]=>4
{{1},{2},{3},{4,5,6}}=>[[1,5,6],[2],[3],[4]]=>4
{{1},{2},{3},{4,5},{6}}=>[[1,5],[2],[3],[4],[6]]=>6
{{1,6},{2},{3},{4},{5}}=>[[1,6],[2],[3],[4],[5]]=>5
{{1},{2,6},{3},{4},{5}}=>[[1,6],[2],[3],[4],[5]]=>5
{{1},{2},{3,6},{4},{5}}=>[[1,6],[2],[3],[4],[5]]=>5
{{1},{2},{3},{4,6},{5}}=>[[1,6],[2],[3],[4],[5]]=>5
{{1},{2},{3},{4},{5,6}}=>[[1,6],[2],[3],[4],[5]]=>5
{{1},{2},{3},{4},{5},{6}}=>[[1],[2],[3],[4],[5],[6]]=>6
{{1,2,3,4,5,6,7}}=>[[1,2,3,4,5,6,7]]=>1
{{1,2,3,4,5,6},{7}}=>[[1,2,3,4,5,6],[7]]=>7
{{1,2,3,4,5,7},{6}}=>[[1,2,3,4,5,7],[6]]=>6
{{1,2,3,4,5},{6,7}}=>[[1,2,3,4,5],[6,7]]=>6
{{1,2,3,4,5},{6},{7}}=>[[1,2,3,4,5],[6],[7]]=>7
{{1,2,3,4,6,7},{5}}=>[[1,2,3,4,6,7],[5]]=>5
{{1,2,3,4,6},{5,7}}=>[[1,2,3,4,6],[5,7]]=>5
{{1,2,3,4,6},{5},{7}}=>[[1,2,3,4,6],[5],[7]]=>7
{{1,2,3,4,7},{5,6}}=>[[1,2,3,4,7],[5,6]]=>5
{{1,2,3,4},{5,6,7}}=>[[1,2,3,4],[5,6,7]]=>5
{{1,2,3,4},{5,6},{7}}=>[[1,2,3,4],[5,6],[7]]=>7
{{1,2,3,4,7},{5},{6}}=>[[1,2,3,4,7],[5],[6]]=>6
{{1,2,3,4},{5,7},{6}}=>[[1,2,3,4],[5,7],[6]]=>6
{{1,2,3,4},{5},{6,7}}=>[[1,2,3,4],[5,7],[6]]=>6
{{1,2,3,4},{5},{6},{7}}=>[[1,2,3,4],[5],[6],[7]]=>7
{{1,2,3,5,6,7},{4}}=>[[1,2,3,5,6,7],[4]]=>4
{{1,2,3,5,6},{4,7}}=>[[1,2,3,5,6],[4,7]]=>4
{{1,2,3,5,6},{4},{7}}=>[[1,2,3,5,6],[4],[7]]=>7
{{1,2,3,5,7},{4,6}}=>[[1,2,3,5,7],[4,6]]=>4
{{1,2,3,5},{4,6,7}}=>[[1,2,3,5],[4,6,7]]=>4
{{1,2,3,5},{4,6},{7}}=>[[1,2,3,5],[4,6],[7]]=>7
{{1,2,3,5,7},{4},{6}}=>[[1,2,3,5,7],[4],[6]]=>6
{{1,2,3,5},{4,7},{6}}=>[[1,2,3,5],[4,7],[6]]=>6
{{1,2,3,5},{4},{6,7}}=>[[1,2,3,5],[4,7],[6]]=>6
{{1,2,3,5},{4},{6},{7}}=>[[1,2,3,5],[4],[6],[7]]=>7
{{1,2,3,6,7},{4,5}}=>[[1,2,3,6,7],[4,5]]=>4
{{1,2,3,6},{4,5,7}}=>[[1,2,3,6],[4,5,7]]=>4
{{1,2,3,6},{4,5},{7}}=>[[1,2,3,6],[4,5],[7]]=>7
{{1,2,3,7},{4,5,6}}=>[[1,2,3,7],[4,5,6]]=>4
{{1,2,3},{4,5,6,7}}=>[[1,2,3,7],[4,5,6]]=>4
{{1,2,3},{4,5,6},{7}}=>[[1,2,3],[4,5,6],[7]]=>7
{{1,2,3,7},{4,5},{6}}=>[[1,2,3,7],[4,5],[6]]=>6
{{1,2,3},{4,5,7},{6}}=>[[1,2,3],[4,5,7],[6]]=>6
{{1,2,3},{4,5},{6,7}}=>[[1,2,3],[4,5],[6,7]]=>6
{{1,2,3},{4,5},{6},{7}}=>[[1,2,3],[4,5],[6],[7]]=>7
{{1,2,3,6,7},{4},{5}}=>[[1,2,3,6,7],[4],[5]]=>5
{{1,2,3,6},{4,7},{5}}=>[[1,2,3,6],[4,7],[5]]=>5
{{1,2,3,6},{4},{5,7}}=>[[1,2,3,6],[4,7],[5]]=>5
{{1,2,3,6},{4},{5},{7}}=>[[1,2,3,6],[4],[5],[7]]=>7
{{1,2,3,7},{4,6},{5}}=>[[1,2,3,7],[4,6],[5]]=>5
{{1,2,3},{4,6,7},{5}}=>[[1,2,3],[4,6,7],[5]]=>5
{{1,2,3},{4,6},{5,7}}=>[[1,2,3],[4,6],[5,7]]=>5
{{1,2,3},{4,6},{5},{7}}=>[[1,2,3],[4,6],[5],[7]]=>7
{{1,2,3,7},{4},{5,6}}=>[[1,2,3,7],[4,6],[5]]=>5
{{1,2,3},{4,7},{5,6}}=>[[1,2,3],[4,6],[5,7]]=>5
{{1,2,3},{4},{5,6,7}}=>[[1,2,3],[4,6,7],[5]]=>5
{{1,2,3},{4},{5,6},{7}}=>[[1,2,3],[4,6],[5],[7]]=>7
{{1,2,3,7},{4},{5},{6}}=>[[1,2,3,7],[4],[5],[6]]=>6
{{1,2,3},{4,7},{5},{6}}=>[[1,2,3],[4,7],[5],[6]]=>6
{{1,2,3},{4},{5,7},{6}}=>[[1,2,3],[4,7],[5],[6]]=>6
{{1,2,3},{4},{5},{6,7}}=>[[1,2,3],[4,7],[5],[6]]=>6
{{1,2,3},{4},{5},{6},{7}}=>[[1,2,3],[4],[5],[6],[7]]=>7
{{1,2,4,5,6,7},{3}}=>[[1,2,4,5,6,7],[3]]=>3
{{1,2,4,5,6},{3,7}}=>[[1,2,4,5,6],[3,7]]=>3
{{1,2,4,5,6},{3},{7}}=>[[1,2,4,5,6],[3],[7]]=>7
{{1,2,4,5,7},{3,6}}=>[[1,2,4,5,7],[3,6]]=>3
{{1,2,4,5},{3,6,7}}=>[[1,2,4,5],[3,6,7]]=>3
{{1,2,4,5},{3,6},{7}}=>[[1,2,4,5],[3,6],[7]]=>7
{{1,2,4,5,7},{3},{6}}=>[[1,2,4,5,7],[3],[6]]=>6
{{1,2,4,5},{3,7},{6}}=>[[1,2,4,5],[3,7],[6]]=>6
{{1,2,4,5},{3},{6,7}}=>[[1,2,4,5],[3,7],[6]]=>6
{{1,2,4,5},{3},{6},{7}}=>[[1,2,4,5],[3],[6],[7]]=>7
{{1,2,4,6,7},{3,5}}=>[[1,2,4,6,7],[3,5]]=>3
{{1,2,4,6},{3,5,7}}=>[[1,2,4,6],[3,5,7]]=>3
{{1,2,4,6},{3,5},{7}}=>[[1,2,4,6],[3,5],[7]]=>7
{{1,2,4,7},{3,5,6}}=>[[1,2,4,7],[3,5,6]]=>3
{{1,2,4},{3,5,6,7}}=>[[1,2,4,7],[3,5,6]]=>3
{{1,2,4},{3,5,6},{7}}=>[[1,2,4],[3,5,6],[7]]=>7
{{1,2,4,7},{3,5},{6}}=>[[1,2,4,7],[3,5],[6]]=>6
{{1,2,4},{3,5,7},{6}}=>[[1,2,4],[3,5,7],[6]]=>6
{{1,2,4},{3,5},{6,7}}=>[[1,2,4],[3,5],[6,7]]=>6
{{1,2,4},{3,5},{6},{7}}=>[[1,2,4],[3,5],[6],[7]]=>7
{{1,2,4,6,7},{3},{5}}=>[[1,2,4,6,7],[3],[5]]=>5
{{1,2,4,6},{3,7},{5}}=>[[1,2,4,6],[3,7],[5]]=>5
{{1,2,4,6},{3},{5,7}}=>[[1,2,4,6],[3,7],[5]]=>5
{{1,2,4,6},{3},{5},{7}}=>[[1,2,4,6],[3],[5],[7]]=>7
{{1,2,4,7},{3,6},{5}}=>[[1,2,4,7],[3,6],[5]]=>5
{{1,2,4},{3,6,7},{5}}=>[[1,2,4],[3,6,7],[5]]=>5
{{1,2,4},{3,6},{5,7}}=>[[1,2,4],[3,6],[5,7]]=>5
{{1,2,4},{3,6},{5},{7}}=>[[1,2,4],[3,6],[5],[7]]=>7
{{1,2,4,7},{3},{5,6}}=>[[1,2,4,7],[3,6],[5]]=>5
{{1,2,4},{3,7},{5,6}}=>[[1,2,4],[3,6],[5,7]]=>5
{{1,2,4},{3},{5,6,7}}=>[[1,2,4],[3,6,7],[5]]=>5
{{1,2,4},{3},{5,6},{7}}=>[[1,2,4],[3,6],[5],[7]]=>7
{{1,2,4,7},{3},{5},{6}}=>[[1,2,4,7],[3],[5],[6]]=>6
{{1,2,4},{3,7},{5},{6}}=>[[1,2,4],[3,7],[5],[6]]=>6
{{1,2,4},{3},{5,7},{6}}=>[[1,2,4],[3,7],[5],[6]]=>6
{{1,2,4},{3},{5},{6,7}}=>[[1,2,4],[3,7],[5],[6]]=>6
{{1,2,4},{3},{5},{6},{7}}=>[[1,2,4],[3],[5],[6],[7]]=>7
{{1,2,5,6,7},{3,4}}=>[[1,2,5,6,7],[3,4]]=>3
{{1,2,5,6},{3,4,7}}=>[[1,2,5,6],[3,4,7]]=>3
{{1,2,5,6},{3,4},{7}}=>[[1,2,5,6],[3,4],[7]]=>7
{{1,2,5,7},{3,4,6}}=>[[1,2,5,7],[3,4,6]]=>3
{{1,2,5},{3,4,6,7}}=>[[1,2,5,7],[3,4,6]]=>3
{{1,2,5},{3,4,6},{7}}=>[[1,2,5],[3,4,6],[7]]=>7
{{1,2,5,7},{3,4},{6}}=>[[1,2,5,7],[3,4],[6]]=>6
{{1,2,5},{3,4,7},{6}}=>[[1,2,5],[3,4,7],[6]]=>6
{{1,2,5},{3,4},{6,7}}=>[[1,2,5],[3,4],[6,7]]=>6
{{1,2,5},{3,4},{6},{7}}=>[[1,2,5],[3,4],[6],[7]]=>7
{{1,2,6,7},{3,4,5}}=>[[1,2,5,7],[3,4,6]]=>3
{{1,2,6},{3,4,5,7}}=>[[1,2,5,7],[3,4,6]]=>3
{{1,2,6},{3,4,5},{7}}=>[[1,2,5],[3,4,6],[7]]=>7
{{1,2,7},{3,4,5,6}}=>[[1,2,5,6],[3,4,7]]=>3
{{1,2},{3,4,5,6,7}}=>[[1,2,5,6,7],[3,4]]=>3
{{1,2},{3,4,5,6},{7}}=>[[1,2,5,6],[3,4],[7]]=>7
{{1,2,7},{3,4,5},{6}}=>[[1,2,5],[3,4,7],[6]]=>6
{{1,2},{3,4,5,7},{6}}=>[[1,2,5,7],[3,4],[6]]=>6
{{1,2},{3,4,5},{6,7}}=>[[1,2,5],[3,4],[6,7]]=>6
{{1,2},{3,4,5},{6},{7}}=>[[1,2,5],[3,4],[6],[7]]=>7
{{1,2,6,7},{3,4},{5}}=>[[1,2,6,7],[3,4],[5]]=>5
{{1,2,6},{3,4,7},{5}}=>[[1,2,6],[3,4,7],[5]]=>5
{{1,2,6},{3,4},{5,7}}=>[[1,2,6],[3,4],[5,7]]=>5
{{1,2,6},{3,4},{5},{7}}=>[[1,2,6],[3,4],[5],[7]]=>7
{{1,2,7},{3,4,6},{5}}=>[[1,2,6],[3,4,7],[5]]=>5
{{1,2},{3,4,6,7},{5}}=>[[1,2,6,7],[3,4],[5]]=>5
{{1,2},{3,4,6},{5,7}}=>[[1,2,6],[3,4],[5,7]]=>5
{{1,2},{3,4,6},{5},{7}}=>[[1,2,6],[3,4],[5],[7]]=>7
{{1,2,7},{3,4},{5,6}}=>[[1,2,7],[3,4],[5,6]]=>5
{{1,2},{3,4,7},{5,6}}=>[[1,2,7],[3,4],[5,6]]=>5
{{1,2},{3,4},{5,6,7}}=>[[1,2,7],[3,4],[5,6]]=>5
{{1,2},{3,4},{5,6},{7}}=>[[1,2],[3,4],[5,6],[7]]=>7
{{1,2,7},{3,4},{5},{6}}=>[[1,2,7],[3,4],[5],[6]]=>6
{{1,2},{3,4,7},{5},{6}}=>[[1,2,7],[3,4],[5],[6]]=>6
{{1,2},{3,4},{5,7},{6}}=>[[1,2],[3,4],[5,7],[6]]=>6
{{1,2},{3,4},{5},{6,7}}=>[[1,2],[3,4],[5,7],[6]]=>6
{{1,2},{3,4},{5},{6},{7}}=>[[1,2],[3,4],[5],[6],[7]]=>7
{{1,2,5,6,7},{3},{4}}=>[[1,2,5,6,7],[3],[4]]=>4
{{1,2,5,6},{3,7},{4}}=>[[1,2,5,6],[3,7],[4]]=>4
{{1,2,5,6},{3},{4,7}}=>[[1,2,5,6],[3,7],[4]]=>4
{{1,2,5,6},{3},{4},{7}}=>[[1,2,5,6],[3],[4],[7]]=>7
{{1,2,5,7},{3,6},{4}}=>[[1,2,5,7],[3,6],[4]]=>4
{{1,2,5},{3,6,7},{4}}=>[[1,2,5],[3,6,7],[4]]=>4
{{1,2,5},{3,6},{4,7}}=>[[1,2,5],[3,6],[4,7]]=>4
{{1,2,5},{3,6},{4},{7}}=>[[1,2,5],[3,6],[4],[7]]=>7
{{1,2,5,7},{3},{4,6}}=>[[1,2,5,7],[3,6],[4]]=>4
{{1,2,5},{3,7},{4,6}}=>[[1,2,5],[3,6],[4,7]]=>4
{{1,2,5},{3},{4,6,7}}=>[[1,2,5],[3,6,7],[4]]=>4
{{1,2,5},{3},{4,6},{7}}=>[[1,2,5],[3,6],[4],[7]]=>7
{{1,2,5,7},{3},{4},{6}}=>[[1,2,5,7],[3],[4],[6]]=>6
{{1,2,5},{3,7},{4},{6}}=>[[1,2,5],[3,7],[4],[6]]=>6
{{1,2,5},{3},{4,7},{6}}=>[[1,2,5],[3,7],[4],[6]]=>6
{{1,2,5},{3},{4},{6,7}}=>[[1,2,5],[3,7],[4],[6]]=>6
{{1,2,5},{3},{4},{6},{7}}=>[[1,2,5],[3],[4],[6],[7]]=>7
{{1,2,6,7},{3,5},{4}}=>[[1,2,6,7],[3,5],[4]]=>4
{{1,2,6},{3,5,7},{4}}=>[[1,2,6],[3,5,7],[4]]=>4
{{1,2,6},{3,5},{4,7}}=>[[1,2,6],[3,5],[4,7]]=>4
{{1,2,6},{3,5},{4},{7}}=>[[1,2,6],[3,5],[4],[7]]=>7
{{1,2,7},{3,5,6},{4}}=>[[1,2,6],[3,5,7],[4]]=>4
{{1,2},{3,5,6,7},{4}}=>[[1,2,6,7],[3,5],[4]]=>4
{{1,2},{3,5,6},{4,7}}=>[[1,2,6],[3,5],[4,7]]=>4
{{1,2},{3,5,6},{4},{7}}=>[[1,2,6],[3,5],[4],[7]]=>7
{{1,2,7},{3,5},{4,6}}=>[[1,2,7],[3,5],[4,6]]=>4
{{1,2},{3,5,7},{4,6}}=>[[1,2,7],[3,5],[4,6]]=>4
{{1,2},{3,5},{4,6,7}}=>[[1,2,7],[3,5],[4,6]]=>4
{{1,2},{3,5},{4,6},{7}}=>[[1,2],[3,5],[4,6],[7]]=>7
{{1,2,7},{3,5},{4},{6}}=>[[1,2,7],[3,5],[4],[6]]=>6
{{1,2},{3,5,7},{4},{6}}=>[[1,2,7],[3,5],[4],[6]]=>6
{{1,2},{3,5},{4,7},{6}}=>[[1,2],[3,5],[4,7],[6]]=>6
{{1,2},{3,5},{4},{6,7}}=>[[1,2],[3,5],[4,7],[6]]=>6
{{1,2},{3,5},{4},{6},{7}}=>[[1,2],[3,5],[4],[6],[7]]=>7
{{1,2,6,7},{3},{4,5}}=>[[1,2,6,7],[3,5],[4]]=>4
{{1,2,6},{3,7},{4,5}}=>[[1,2,6],[3,5],[4,7]]=>4
{{1,2,6},{3},{4,5,7}}=>[[1,2,6],[3,5,7],[4]]=>4
{{1,2,6},{3},{4,5},{7}}=>[[1,2,6],[3,5],[4],[7]]=>7
{{1,2,7},{3,6},{4,5}}=>[[1,2,7],[3,5],[4,6]]=>4
{{1,2},{3,6,7},{4,5}}=>[[1,2,7],[3,5],[4,6]]=>4
{{1,2},{3,6},{4,5,7}}=>[[1,2,7],[3,5],[4,6]]=>4
{{1,2},{3,6},{4,5},{7}}=>[[1,2],[3,5],[4,6],[7]]=>7
{{1,2,7},{3},{4,5,6}}=>[[1,2,6],[3,5,7],[4]]=>4
{{1,2},{3,7},{4,5,6}}=>[[1,2,6],[3,5],[4,7]]=>4
{{1,2},{3},{4,5,6,7}}=>[[1,2,6,7],[3,5],[4]]=>4
{{1,2},{3},{4,5,6},{7}}=>[[1,2,6],[3,5],[4],[7]]=>7
{{1,2,7},{3},{4,5},{6}}=>[[1,2,7],[3,5],[4],[6]]=>6
{{1,2},{3,7},{4,5},{6}}=>[[1,2],[3,5],[4,7],[6]]=>6
{{1,2},{3},{4,5,7},{6}}=>[[1,2,7],[3,5],[4],[6]]=>6
{{1,2},{3},{4,5},{6,7}}=>[[1,2],[3,5],[4,7],[6]]=>6
{{1,2},{3},{4,5},{6},{7}}=>[[1,2],[3,5],[4],[6],[7]]=>7
{{1,2,6,7},{3},{4},{5}}=>[[1,2,6,7],[3],[4],[5]]=>5
{{1,2,6},{3,7},{4},{5}}=>[[1,2,6],[3,7],[4],[5]]=>5
{{1,2,6},{3},{4,7},{5}}=>[[1,2,6],[3,7],[4],[5]]=>5
{{1,2,6},{3},{4},{5,7}}=>[[1,2,6],[3,7],[4],[5]]=>5
{{1,2,6},{3},{4},{5},{7}}=>[[1,2,6],[3],[4],[5],[7]]=>7
{{1,2,7},{3,6},{4},{5}}=>[[1,2,7],[3,6],[4],[5]]=>5
{{1,2},{3,6,7},{4},{5}}=>[[1,2,7],[3,6],[4],[5]]=>5
{{1,2},{3,6},{4,7},{5}}=>[[1,2],[3,6],[4,7],[5]]=>5
{{1,2},{3,6},{4},{5,7}}=>[[1,2],[3,6],[4,7],[5]]=>5
{{1,2},{3,6},{4},{5},{7}}=>[[1,2],[3,6],[4],[5],[7]]=>7
{{1,2,7},{3},{4,6},{5}}=>[[1,2,7],[3,6],[4],[5]]=>5
{{1,2},{3,7},{4,6},{5}}=>[[1,2],[3,6],[4,7],[5]]=>5
{{1,2},{3},{4,6,7},{5}}=>[[1,2,7],[3,6],[4],[5]]=>5
{{1,2},{3},{4,6},{5,7}}=>[[1,2],[3,6],[4,7],[5]]=>5
{{1,2},{3},{4,6},{5},{7}}=>[[1,2],[3,6],[4],[5],[7]]=>7
{{1,2,7},{3},{4},{5,6}}=>[[1,2,7],[3,6],[4],[5]]=>5
{{1,2},{3,7},{4},{5,6}}=>[[1,2],[3,6],[4,7],[5]]=>5
{{1,2},{3},{4,7},{5,6}}=>[[1,2],[3,6],[4,7],[5]]=>5
{{1,2},{3},{4},{5,6,7}}=>[[1,2,7],[3,6],[4],[5]]=>5
{{1,2},{3},{4},{5,6},{7}}=>[[1,2],[3,6],[4],[5],[7]]=>7
{{1,2,7},{3},{4},{5},{6}}=>[[1,2,7],[3],[4],[5],[6]]=>6
{{1,2},{3,7},{4},{5},{6}}=>[[1,2],[3,7],[4],[5],[6]]=>6
{{1,2},{3},{4,7},{5},{6}}=>[[1,2],[3,7],[4],[5],[6]]=>6
{{1,2},{3},{4},{5,7},{6}}=>[[1,2],[3,7],[4],[5],[6]]=>6
{{1,2},{3},{4},{5},{6,7}}=>[[1,2],[3,7],[4],[5],[6]]=>6
{{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]]=>2
{{1,3,4,5,6},{2,7}}=>[[1,3,4,5,6],[2,7]]=>2
{{1,3,4,5,6},{2},{7}}=>[[1,3,4,5,6],[2],[7]]=>7
{{1,3,4,5,7},{2,6}}=>[[1,3,4,5,7],[2,6]]=>2
{{1,3,4,5},{2,6,7}}=>[[1,3,4,5],[2,6,7]]=>2
{{1,3,4,5},{2,6},{7}}=>[[1,3,4,5],[2,6],[7]]=>7
{{1,3,4,5,7},{2},{6}}=>[[1,3,4,5,7],[2],[6]]=>6
{{1,3,4,5},{2,7},{6}}=>[[1,3,4,5],[2,7],[6]]=>6
{{1,3,4,5},{2},{6,7}}=>[[1,3,4,5],[2,7],[6]]=>6
{{1,3,4,5},{2},{6},{7}}=>[[1,3,4,5],[2],[6],[7]]=>7
{{1,3,4,6,7},{2,5}}=>[[1,3,4,6,7],[2,5]]=>2
{{1,3,4,6},{2,5,7}}=>[[1,3,4,6],[2,5,7]]=>2
{{1,3,4,6},{2,5},{7}}=>[[1,3,4,6],[2,5],[7]]=>7
{{1,3,4,7},{2,5,6}}=>[[1,3,4,7],[2,5,6]]=>2
{{1,3,4},{2,5,6,7}}=>[[1,3,4,7],[2,5,6]]=>2
{{1,3,4},{2,5,6},{7}}=>[[1,3,4],[2,5,6],[7]]=>7
{{1,3,4,7},{2,5},{6}}=>[[1,3,4,7],[2,5],[6]]=>6
{{1,3,4},{2,5,7},{6}}=>[[1,3,4],[2,5,7],[6]]=>6
{{1,3,4},{2,5},{6,7}}=>[[1,3,4],[2,5],[6,7]]=>6
{{1,3,4},{2,5},{6},{7}}=>[[1,3,4],[2,5],[6],[7]]=>7
{{1,3,4,6,7},{2},{5}}=>[[1,3,4,6,7],[2],[5]]=>5
{{1,3,4,6},{2,7},{5}}=>[[1,3,4,6],[2,7],[5]]=>5
{{1,3,4,6},{2},{5,7}}=>[[1,3,4,6],[2,7],[5]]=>5
{{1,3,4,6},{2},{5},{7}}=>[[1,3,4,6],[2],[5],[7]]=>7
{{1,3,4,7},{2,6},{5}}=>[[1,3,4,7],[2,6],[5]]=>5
{{1,3,4},{2,6,7},{5}}=>[[1,3,4],[2,6,7],[5]]=>5
{{1,3,4},{2,6},{5,7}}=>[[1,3,4],[2,6],[5,7]]=>5
{{1,3,4},{2,6},{5},{7}}=>[[1,3,4],[2,6],[5],[7]]=>7
{{1,3,4,7},{2},{5,6}}=>[[1,3,4,7],[2,6],[5]]=>5
{{1,3,4},{2,7},{5,6}}=>[[1,3,4],[2,6],[5,7]]=>5
{{1,3,4},{2},{5,6,7}}=>[[1,3,4],[2,6,7],[5]]=>5
{{1,3,4},{2},{5,6},{7}}=>[[1,3,4],[2,6],[5],[7]]=>7
{{1,3,4,7},{2},{5},{6}}=>[[1,3,4,7],[2],[5],[6]]=>6
{{1,3,4},{2,7},{5},{6}}=>[[1,3,4],[2,7],[5],[6]]=>6
{{1,3,4},{2},{5,7},{6}}=>[[1,3,4],[2,7],[5],[6]]=>6
{{1,3,4},{2},{5},{6,7}}=>[[1,3,4],[2,7],[5],[6]]=>6
{{1,3,4},{2},{5},{6},{7}}=>[[1,3,4],[2],[5],[6],[7]]=>7
{{1,3,5,6,7},{2,4}}=>[[1,3,5,6,7],[2,4]]=>2
{{1,3,5,6},{2,4,7}}=>[[1,3,5,6],[2,4,7]]=>2
{{1,3,5,6},{2,4},{7}}=>[[1,3,5,6],[2,4],[7]]=>7
{{1,3,5,7},{2,4,6}}=>[[1,3,5,7],[2,4,6]]=>2
{{1,3,5},{2,4,6,7}}=>[[1,3,5,7],[2,4,6]]=>2
{{1,3,5},{2,4,6},{7}}=>[[1,3,5],[2,4,6],[7]]=>7
{{1,3,5,7},{2,4},{6}}=>[[1,3,5,7],[2,4],[6]]=>6
{{1,3,5},{2,4,7},{6}}=>[[1,3,5],[2,4,7],[6]]=>6
{{1,3,5},{2,4},{6,7}}=>[[1,3,5],[2,4],[6,7]]=>6
{{1,3,5},{2,4},{6},{7}}=>[[1,3,5],[2,4],[6],[7]]=>7
{{1,3,6,7},{2,4,5}}=>[[1,3,5,7],[2,4,6]]=>2
{{1,3,6},{2,4,5,7}}=>[[1,3,5,7],[2,4,6]]=>2
{{1,3,6},{2,4,5},{7}}=>[[1,3,5],[2,4,6],[7]]=>7
{{1,3,7},{2,4,5,6}}=>[[1,3,5,6],[2,4,7]]=>2
{{1,3},{2,4,5,6,7}}=>[[1,3,5,6,7],[2,4]]=>2
{{1,3},{2,4,5,6},{7}}=>[[1,3,5,6],[2,4],[7]]=>7
{{1,3,7},{2,4,5},{6}}=>[[1,3,5],[2,4,7],[6]]=>6
{{1,3},{2,4,5,7},{6}}=>[[1,3,5,7],[2,4],[6]]=>6
{{1,3},{2,4,5},{6,7}}=>[[1,3,5],[2,4],[6,7]]=>6
{{1,3},{2,4,5},{6},{7}}=>[[1,3,5],[2,4],[6],[7]]=>7
{{1,3,6,7},{2,4},{5}}=>[[1,3,6,7],[2,4],[5]]=>5
{{1,3,6},{2,4,7},{5}}=>[[1,3,6],[2,4,7],[5]]=>5
{{1,3,6},{2,4},{5,7}}=>[[1,3,6],[2,4],[5,7]]=>5
{{1,3,6},{2,4},{5},{7}}=>[[1,3,6],[2,4],[5],[7]]=>7
{{1,3,7},{2,4,6},{5}}=>[[1,3,6],[2,4,7],[5]]=>5
{{1,3},{2,4,6,7},{5}}=>[[1,3,6,7],[2,4],[5]]=>5
{{1,3},{2,4,6},{5,7}}=>[[1,3,6],[2,4],[5,7]]=>5
{{1,3},{2,4,6},{5},{7}}=>[[1,3,6],[2,4],[5],[7]]=>7
{{1,3,7},{2,4},{5,6}}=>[[1,3,7],[2,4],[5,6]]=>5
{{1,3},{2,4,7},{5,6}}=>[[1,3,7],[2,4],[5,6]]=>5
{{1,3},{2,4},{5,6,7}}=>[[1,3,7],[2,4],[5,6]]=>5
{{1,3},{2,4},{5,6},{7}}=>[[1,3],[2,4],[5,6],[7]]=>7
{{1,3,7},{2,4},{5},{6}}=>[[1,3,7],[2,4],[5],[6]]=>6
{{1,3},{2,4,7},{5},{6}}=>[[1,3,7],[2,4],[5],[6]]=>6
{{1,3},{2,4},{5,7},{6}}=>[[1,3],[2,4],[5,7],[6]]=>6
{{1,3},{2,4},{5},{6,7}}=>[[1,3],[2,4],[5,7],[6]]=>6
{{1,3},{2,4},{5},{6},{7}}=>[[1,3],[2,4],[5],[6],[7]]=>7
{{1,3,5,6,7},{2},{4}}=>[[1,3,5,6,7],[2],[4]]=>4
{{1,3,5,6},{2,7},{4}}=>[[1,3,5,6],[2,7],[4]]=>4
{{1,3,5,6},{2},{4,7}}=>[[1,3,5,6],[2,7],[4]]=>4
{{1,3,5,6},{2},{4},{7}}=>[[1,3,5,6],[2],[4],[7]]=>7
{{1,3,5,7},{2,6},{4}}=>[[1,3,5,7],[2,6],[4]]=>4
{{1,3,5},{2,6,7},{4}}=>[[1,3,5],[2,6,7],[4]]=>4
{{1,3,5},{2,6},{4,7}}=>[[1,3,5],[2,6],[4,7]]=>4
{{1,3,5},{2,6},{4},{7}}=>[[1,3,5],[2,6],[4],[7]]=>7
{{1,3,5,7},{2},{4,6}}=>[[1,3,5,7],[2,6],[4]]=>4
{{1,3,5},{2,7},{4,6}}=>[[1,3,5],[2,6],[4,7]]=>4
{{1,3,5},{2},{4,6,7}}=>[[1,3,5],[2,6,7],[4]]=>4
{{1,3,5},{2},{4,6},{7}}=>[[1,3,5],[2,6],[4],[7]]=>7
{{1,3,5,7},{2},{4},{6}}=>[[1,3,5,7],[2],[4],[6]]=>6
{{1,3,5},{2,7},{4},{6}}=>[[1,3,5],[2,7],[4],[6]]=>6
{{1,3,5},{2},{4,7},{6}}=>[[1,3,5],[2,7],[4],[6]]=>6
{{1,3,5},{2},{4},{6,7}}=>[[1,3,5],[2,7],[4],[6]]=>6
{{1,3,5},{2},{4},{6},{7}}=>[[1,3,5],[2],[4],[6],[7]]=>7
{{1,3,6,7},{2,5},{4}}=>[[1,3,6,7],[2,5],[4]]=>4
{{1,3,6},{2,5,7},{4}}=>[[1,3,6],[2,5,7],[4]]=>4
{{1,3,6},{2,5},{4,7}}=>[[1,3,6],[2,5],[4,7]]=>4
{{1,3,6},{2,5},{4},{7}}=>[[1,3,6],[2,5],[4],[7]]=>7
{{1,3,7},{2,5,6},{4}}=>[[1,3,6],[2,5,7],[4]]=>4
{{1,3},{2,5,6,7},{4}}=>[[1,3,6,7],[2,5],[4]]=>4
{{1,3},{2,5,6},{4,7}}=>[[1,3,6],[2,5],[4,7]]=>4
{{1,3},{2,5,6},{4},{7}}=>[[1,3,6],[2,5],[4],[7]]=>7
{{1,3,7},{2,5},{4,6}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,3},{2,5,7},{4,6}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,3},{2,5},{4,6,7}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,3},{2,5},{4,6},{7}}=>[[1,3],[2,5],[4,6],[7]]=>7
{{1,3,7},{2,5},{4},{6}}=>[[1,3,7],[2,5],[4],[6]]=>6
{{1,3},{2,5,7},{4},{6}}=>[[1,3,7],[2,5],[4],[6]]=>6
{{1,3},{2,5},{4,7},{6}}=>[[1,3],[2,5],[4,7],[6]]=>6
{{1,3},{2,5},{4},{6,7}}=>[[1,3],[2,5],[4,7],[6]]=>6
{{1,3},{2,5},{4},{6},{7}}=>[[1,3],[2,5],[4],[6],[7]]=>7
{{1,3,6,7},{2},{4,5}}=>[[1,3,6,7],[2,5],[4]]=>4
{{1,3,6},{2,7},{4,5}}=>[[1,3,6],[2,5],[4,7]]=>4
{{1,3,6},{2},{4,5,7}}=>[[1,3,6],[2,5,7],[4]]=>4
{{1,3,6},{2},{4,5},{7}}=>[[1,3,6],[2,5],[4],[7]]=>7
{{1,3,7},{2,6},{4,5}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,3},{2,6,7},{4,5}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,3},{2,6},{4,5,7}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,3},{2,6},{4,5},{7}}=>[[1,3],[2,5],[4,6],[7]]=>7
{{1,3,7},{2},{4,5,6}}=>[[1,3,6],[2,5,7],[4]]=>4
{{1,3},{2,7},{4,5,6}}=>[[1,3,6],[2,5],[4,7]]=>4
{{1,3},{2},{4,5,6,7}}=>[[1,3,6,7],[2,5],[4]]=>4
{{1,3},{2},{4,5,6},{7}}=>[[1,3,6],[2,5],[4],[7]]=>7
{{1,3,7},{2},{4,5},{6}}=>[[1,3,7],[2,5],[4],[6]]=>6
{{1,3},{2,7},{4,5},{6}}=>[[1,3],[2,5],[4,7],[6]]=>6
{{1,3},{2},{4,5,7},{6}}=>[[1,3,7],[2,5],[4],[6]]=>6
{{1,3},{2},{4,5},{6,7}}=>[[1,3],[2,5],[4,7],[6]]=>6
{{1,3},{2},{4,5},{6},{7}}=>[[1,3],[2,5],[4],[6],[7]]=>7
{{1,3,6,7},{2},{4},{5}}=>[[1,3,6,7],[2],[4],[5]]=>5
{{1,3,6},{2,7},{4},{5}}=>[[1,3,6],[2,7],[4],[5]]=>5
{{1,3,6},{2},{4,7},{5}}=>[[1,3,6],[2,7],[4],[5]]=>5
{{1,3,6},{2},{4},{5,7}}=>[[1,3,6],[2,7],[4],[5]]=>5
{{1,3,6},{2},{4},{5},{7}}=>[[1,3,6],[2],[4],[5],[7]]=>7
{{1,3,7},{2,6},{4},{5}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1,3},{2,6,7},{4},{5}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1,3},{2,6},{4,7},{5}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1,3},{2,6},{4},{5,7}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1,3},{2,6},{4},{5},{7}}=>[[1,3],[2,6],[4],[5],[7]]=>7
{{1,3,7},{2},{4,6},{5}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1,3},{2,7},{4,6},{5}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1,3},{2},{4,6,7},{5}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1,3},{2},{4,6},{5,7}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1,3},{2},{4,6},{5},{7}}=>[[1,3],[2,6],[4],[5],[7]]=>7
{{1,3,7},{2},{4},{5,6}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1,3},{2,7},{4},{5,6}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1,3},{2},{4,7},{5,6}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1,3},{2},{4},{5,6,7}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1,3},{2},{4},{5,6},{7}}=>[[1,3],[2,6],[4],[5],[7]]=>7
{{1,3,7},{2},{4},{5},{6}}=>[[1,3,7],[2],[4],[5],[6]]=>6
{{1,3},{2,7},{4},{5},{6}}=>[[1,3],[2,7],[4],[5],[6]]=>6
{{1,3},{2},{4,7},{5},{6}}=>[[1,3],[2,7],[4],[5],[6]]=>6
{{1,3},{2},{4},{5,7},{6}}=>[[1,3],[2,7],[4],[5],[6]]=>6
{{1,3},{2},{4},{5},{6,7}}=>[[1,3],[2,7],[4],[5],[6]]=>6
{{1,3},{2},{4},{5},{6},{7}}=>[[1,3],[2],[4],[5],[6],[7]]=>7
{{1,4,5,6,7},{2,3}}=>[[1,3,5,6,7],[2,4]]=>2
{{1,4,5,6},{2,3,7}}=>[[1,3,5,6],[2,4,7]]=>2
{{1,4,5,6},{2,3},{7}}=>[[1,3,5,6],[2,4],[7]]=>7
{{1,4,5,7},{2,3,6}}=>[[1,3,5,7],[2,4,6]]=>2
{{1,4,5},{2,3,6,7}}=>[[1,3,5,7],[2,4,6]]=>2
{{1,4,5},{2,3,6},{7}}=>[[1,3,5],[2,4,6],[7]]=>7
{{1,4,5,7},{2,3},{6}}=>[[1,3,5,7],[2,4],[6]]=>6
{{1,4,5},{2,3,7},{6}}=>[[1,3,5],[2,4,7],[6]]=>6
{{1,4,5},{2,3},{6,7}}=>[[1,3,5],[2,4],[6,7]]=>6
{{1,4,5},{2,3},{6},{7}}=>[[1,3,5],[2,4],[6],[7]]=>7
{{1,4,6,7},{2,3,5}}=>[[1,3,5,7],[2,4,6]]=>2
{{1,4,6},{2,3,5,7}}=>[[1,3,5,7],[2,4,6]]=>2
{{1,4,6},{2,3,5},{7}}=>[[1,3,5],[2,4,6],[7]]=>7
{{1,4,7},{2,3,5,6}}=>[[1,3,5,6],[2,4,7]]=>2
{{1,4},{2,3,5,6,7}}=>[[1,3,5,6,7],[2,4]]=>2
{{1,4},{2,3,5,6},{7}}=>[[1,3,5,6],[2,4],[7]]=>7
{{1,4,7},{2,3,5},{6}}=>[[1,3,5],[2,4,7],[6]]=>6
{{1,4},{2,3,5,7},{6}}=>[[1,3,5,7],[2,4],[6]]=>6
{{1,4},{2,3,5},{6,7}}=>[[1,3,5],[2,4],[6,7]]=>6
{{1,4},{2,3,5},{6},{7}}=>[[1,3,5],[2,4],[6],[7]]=>7
{{1,4,6,7},{2,3},{5}}=>[[1,3,6,7],[2,4],[5]]=>5
{{1,4,6},{2,3,7},{5}}=>[[1,3,6],[2,4,7],[5]]=>5
{{1,4,6},{2,3},{5,7}}=>[[1,3,6],[2,4],[5,7]]=>5
{{1,4,6},{2,3},{5},{7}}=>[[1,3,6],[2,4],[5],[7]]=>7
{{1,4,7},{2,3,6},{5}}=>[[1,3,6],[2,4,7],[5]]=>5
{{1,4},{2,3,6,7},{5}}=>[[1,3,6,7],[2,4],[5]]=>5
{{1,4},{2,3,6},{5,7}}=>[[1,3,6],[2,4],[5,7]]=>5
{{1,4},{2,3,6},{5},{7}}=>[[1,3,6],[2,4],[5],[7]]=>7
{{1,4,7},{2,3},{5,6}}=>[[1,3,7],[2,4],[5,6]]=>5
{{1,4},{2,3,7},{5,6}}=>[[1,3,7],[2,4],[5,6]]=>5
{{1,4},{2,3},{5,6,7}}=>[[1,3,7],[2,4],[5,6]]=>5
{{1,4},{2,3},{5,6},{7}}=>[[1,3],[2,4],[5,6],[7]]=>7
{{1,4,7},{2,3},{5},{6}}=>[[1,3,7],[2,4],[5],[6]]=>6
{{1,4},{2,3,7},{5},{6}}=>[[1,3,7],[2,4],[5],[6]]=>6
{{1,4},{2,3},{5,7},{6}}=>[[1,3],[2,4],[5,7],[6]]=>6
{{1,4},{2,3},{5},{6,7}}=>[[1,3],[2,4],[5,7],[6]]=>6
{{1,4},{2,3},{5},{6},{7}}=>[[1,3],[2,4],[5],[6],[7]]=>7
{{1,5,6,7},{2,3,4}}=>[[1,3,4,7],[2,5,6]]=>2
{{1,5,6},{2,3,4,7}}=>[[1,3,4,7],[2,5,6]]=>2
{{1,5,6},{2,3,4},{7}}=>[[1,3,4],[2,5,6],[7]]=>7
{{1,5,7},{2,3,4,6}}=>[[1,3,4,6],[2,5,7]]=>2
{{1,5},{2,3,4,6,7}}=>[[1,3,4,6,7],[2,5]]=>2
{{1,5},{2,3,4,6},{7}}=>[[1,3,4,6],[2,5],[7]]=>7
{{1,5,7},{2,3,4},{6}}=>[[1,3,4],[2,5,7],[6]]=>6
{{1,5},{2,3,4,7},{6}}=>[[1,3,4,7],[2,5],[6]]=>6
{{1,5},{2,3,4},{6,7}}=>[[1,3,4],[2,5],[6,7]]=>6
{{1,5},{2,3,4},{6},{7}}=>[[1,3,4],[2,5],[6],[7]]=>7
{{1,6,7},{2,3,4,5}}=>[[1,3,4,5],[2,6,7]]=>2
{{1,6},{2,3,4,5,7}}=>[[1,3,4,5,7],[2,6]]=>2
{{1,6},{2,3,4,5},{7}}=>[[1,3,4,5],[2,6],[7]]=>7
{{1,7},{2,3,4,5,6}}=>[[1,3,4,5,6],[2,7]]=>2
{{1},{2,3,4,5,6,7}}=>[[1,3,4,5,6,7],[2]]=>2
{{1},{2,3,4,5,6},{7}}=>[[1,3,4,5,6],[2],[7]]=>7
{{1,7},{2,3,4,5},{6}}=>[[1,3,4,5],[2,7],[6]]=>6
{{1},{2,3,4,5,7},{6}}=>[[1,3,4,5,7],[2],[6]]=>6
{{1},{2,3,4,5},{6,7}}=>[[1,3,4,5],[2,7],[6]]=>6
{{1},{2,3,4,5},{6},{7}}=>[[1,3,4,5],[2],[6],[7]]=>7
{{1,6,7},{2,3,4},{5}}=>[[1,3,4],[2,6,7],[5]]=>5
{{1,6},{2,3,4,7},{5}}=>[[1,3,4,7],[2,6],[5]]=>5
{{1,6},{2,3,4},{5,7}}=>[[1,3,4],[2,6],[5,7]]=>5
{{1,6},{2,3,4},{5},{7}}=>[[1,3,4],[2,6],[5],[7]]=>7
{{1,7},{2,3,4,6},{5}}=>[[1,3,4,6],[2,7],[5]]=>5
{{1},{2,3,4,6,7},{5}}=>[[1,3,4,6,7],[2],[5]]=>5
{{1},{2,3,4,6},{5,7}}=>[[1,3,4,6],[2,7],[5]]=>5
{{1},{2,3,4,6},{5},{7}}=>[[1,3,4,6],[2],[5],[7]]=>7
{{1,7},{2,3,4},{5,6}}=>[[1,3,4],[2,6],[5,7]]=>5
{{1},{2,3,4,7},{5,6}}=>[[1,3,4,7],[2,6],[5]]=>5
{{1},{2,3,4},{5,6,7}}=>[[1,3,4],[2,6,7],[5]]=>5
{{1},{2,3,4},{5,6},{7}}=>[[1,3,4],[2,6],[5],[7]]=>7
{{1,7},{2,3,4},{5},{6}}=>[[1,3,4],[2,7],[5],[6]]=>6
{{1},{2,3,4,7},{5},{6}}=>[[1,3,4,7],[2],[5],[6]]=>6
{{1},{2,3,4},{5,7},{6}}=>[[1,3,4],[2,7],[5],[6]]=>6
{{1},{2,3,4},{5},{6,7}}=>[[1,3,4],[2,7],[5],[6]]=>6
{{1},{2,3,4},{5},{6},{7}}=>[[1,3,4],[2],[5],[6],[7]]=>7
{{1,5,6,7},{2,3},{4}}=>[[1,3,6,7],[2,5],[4]]=>4
{{1,5,6},{2,3,7},{4}}=>[[1,3,6],[2,5,7],[4]]=>4
{{1,5,6},{2,3},{4,7}}=>[[1,3,6],[2,5],[4,7]]=>4
{{1,5,6},{2,3},{4},{7}}=>[[1,3,6],[2,5],[4],[7]]=>7
{{1,5,7},{2,3,6},{4}}=>[[1,3,6],[2,5,7],[4]]=>4
{{1,5},{2,3,6,7},{4}}=>[[1,3,6,7],[2,5],[4]]=>4
{{1,5},{2,3,6},{4,7}}=>[[1,3,6],[2,5],[4,7]]=>4
{{1,5},{2,3,6},{4},{7}}=>[[1,3,6],[2,5],[4],[7]]=>7
{{1,5,7},{2,3},{4,6}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,5},{2,3,7},{4,6}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,5},{2,3},{4,6,7}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,5},{2,3},{4,6},{7}}=>[[1,3],[2,5],[4,6],[7]]=>7
{{1,5,7},{2,3},{4},{6}}=>[[1,3,7],[2,5],[4],[6]]=>6
{{1,5},{2,3,7},{4},{6}}=>[[1,3,7],[2,5],[4],[6]]=>6
{{1,5},{2,3},{4,7},{6}}=>[[1,3],[2,5],[4,7],[6]]=>6
{{1,5},{2,3},{4},{6,7}}=>[[1,3],[2,5],[4,7],[6]]=>6
{{1,5},{2,3},{4},{6},{7}}=>[[1,3],[2,5],[4],[6],[7]]=>7
{{1,6,7},{2,3,5},{4}}=>[[1,3,5],[2,6,7],[4]]=>4
{{1,6},{2,3,5,7},{4}}=>[[1,3,5,7],[2,6],[4]]=>4
{{1,6},{2,3,5},{4,7}}=>[[1,3,5],[2,6],[4,7]]=>4
{{1,6},{2,3,5},{4},{7}}=>[[1,3,5],[2,6],[4],[7]]=>7
{{1,7},{2,3,5,6},{4}}=>[[1,3,5,6],[2,7],[4]]=>4
{{1},{2,3,5,6,7},{4}}=>[[1,3,5,6,7],[2],[4]]=>4
{{1},{2,3,5,6},{4,7}}=>[[1,3,5,6],[2,7],[4]]=>4
{{1},{2,3,5,6},{4},{7}}=>[[1,3,5,6],[2],[4],[7]]=>7
{{1,7},{2,3,5},{4,6}}=>[[1,3,5],[2,6],[4,7]]=>4
{{1},{2,3,5,7},{4,6}}=>[[1,3,5,7],[2,6],[4]]=>4
{{1},{2,3,5},{4,6,7}}=>[[1,3,5],[2,6,7],[4]]=>4
{{1},{2,3,5},{4,6},{7}}=>[[1,3,5],[2,6],[4],[7]]=>7
{{1,7},{2,3,5},{4},{6}}=>[[1,3,5],[2,7],[4],[6]]=>6
{{1},{2,3,5,7},{4},{6}}=>[[1,3,5,7],[2],[4],[6]]=>6
{{1},{2,3,5},{4,7},{6}}=>[[1,3,5],[2,7],[4],[6]]=>6
{{1},{2,3,5},{4},{6,7}}=>[[1,3,5],[2,7],[4],[6]]=>6
{{1},{2,3,5},{4},{6},{7}}=>[[1,3,5],[2],[4],[6],[7]]=>7
{{1,6,7},{2,3},{4,5}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,6},{2,3,7},{4,5}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,6},{2,3},{4,5,7}}=>[[1,3,7],[2,5],[4,6]]=>4
{{1,6},{2,3},{4,5},{7}}=>[[1,3],[2,5],[4,6],[7]]=>7
{{1,7},{2,3,6},{4,5}}=>[[1,3,6],[2,5],[4,7]]=>4
{{1},{2,3,6,7},{4,5}}=>[[1,3,6,7],[2,5],[4]]=>4
{{1},{2,3,6},{4,5,7}}=>[[1,3,6],[2,5,7],[4]]=>4
{{1},{2,3,6},{4,5},{7}}=>[[1,3,6],[2,5],[4],[7]]=>7
{{1,7},{2,3},{4,5,6}}=>[[1,3,6],[2,5],[4,7]]=>4
{{1},{2,3,7},{4,5,6}}=>[[1,3,6],[2,5,7],[4]]=>4
{{1},{2,3},{4,5,6,7}}=>[[1,3,6,7],[2,5],[4]]=>4
{{1},{2,3},{4,5,6},{7}}=>[[1,3,6],[2,5],[4],[7]]=>7
{{1,7},{2,3},{4,5},{6}}=>[[1,3],[2,5],[4,7],[6]]=>6
{{1},{2,3,7},{4,5},{6}}=>[[1,3,7],[2,5],[4],[6]]=>6
{{1},{2,3},{4,5,7},{6}}=>[[1,3,7],[2,5],[4],[6]]=>6
{{1},{2,3},{4,5},{6,7}}=>[[1,3],[2,5],[4,7],[6]]=>6
{{1},{2,3},{4,5},{6},{7}}=>[[1,3],[2,5],[4],[6],[7]]=>7
{{1,6,7},{2,3},{4},{5}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1,6},{2,3,7},{4},{5}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1,6},{2,3},{4,7},{5}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1,6},{2,3},{4},{5,7}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1,6},{2,3},{4},{5},{7}}=>[[1,3],[2,6],[4],[5],[7]]=>7
{{1,7},{2,3,6},{4},{5}}=>[[1,3,6],[2,7],[4],[5]]=>5
{{1},{2,3,6,7},{4},{5}}=>[[1,3,6,7],[2],[4],[5]]=>5
{{1},{2,3,6},{4,7},{5}}=>[[1,3,6],[2,7],[4],[5]]=>5
{{1},{2,3,6},{4},{5,7}}=>[[1,3,6],[2,7],[4],[5]]=>5
{{1},{2,3,6},{4},{5},{7}}=>[[1,3,6],[2],[4],[5],[7]]=>7
{{1,7},{2,3},{4,6},{5}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1},{2,3,7},{4,6},{5}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1},{2,3},{4,6,7},{5}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1},{2,3},{4,6},{5,7}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1},{2,3},{4,6},{5},{7}}=>[[1,3],[2,6],[4],[5],[7]]=>7
{{1,7},{2,3},{4},{5,6}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1},{2,3,7},{4},{5,6}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1},{2,3},{4,7},{5,6}}=>[[1,3],[2,6],[4,7],[5]]=>5
{{1},{2,3},{4},{5,6,7}}=>[[1,3,7],[2,6],[4],[5]]=>5
{{1},{2,3},{4},{5,6},{7}}=>[[1,3],[2,6],[4],[5],[7]]=>7
{{1,7},{2,3},{4},{5},{6}}=>[[1,3],[2,7],[4],[5],[6]]=>6
{{1},{2,3,7},{4},{5},{6}}=>[[1,3,7],[2],[4],[5],[6]]=>6
{{1},{2,3},{4,7},{5},{6}}=>[[1,3],[2,7],[4],[5],[6]]=>6
{{1},{2,3},{4},{5,7},{6}}=>[[1,3],[2,7],[4],[5],[6]]=>6
{{1},{2,3},{4},{5},{6,7}}=>[[1,3],[2,7],[4],[5],[6]]=>6
{{1},{2,3},{4},{5},{6},{7}}=>[[1,3],[2],[4],[5],[6],[7]]=>7
{{1,4,5,6,7},{2},{3}}=>[[1,4,5,6,7],[2],[3]]=>3
{{1,4,5,6},{2,7},{3}}=>[[1,4,5,6],[2,7],[3]]=>3
{{1,4,5,6},{2},{3,7}}=>[[1,4,5,6],[2,7],[3]]=>3
{{1,4,5,6},{2},{3},{7}}=>[[1,4,5,6],[2],[3],[7]]=>7
{{1,4,5,7},{2,6},{3}}=>[[1,4,5,7],[2,6],[3]]=>3
{{1,4,5},{2,6,7},{3}}=>[[1,4,5],[2,6,7],[3]]=>3
{{1,4,5},{2,6},{3,7}}=>[[1,4,5],[2,6],[3,7]]=>3
{{1,4,5},{2,6},{3},{7}}=>[[1,4,5],[2,6],[3],[7]]=>7
{{1,4,5,7},{2},{3,6}}=>[[1,4,5,7],[2,6],[3]]=>3
{{1,4,5},{2,7},{3,6}}=>[[1,4,5],[2,6],[3,7]]=>3
{{1,4,5},{2},{3,6,7}}=>[[1,4,5],[2,6,7],[3]]=>3
{{1,4,5},{2},{3,6},{7}}=>[[1,4,5],[2,6],[3],[7]]=>7
{{1,4,5,7},{2},{3},{6}}=>[[1,4,5,7],[2],[3],[6]]=>6
{{1,4,5},{2,7},{3},{6}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1,4,5},{2},{3,7},{6}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1,4,5},{2},{3},{6,7}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1,4,5},{2},{3},{6},{7}}=>[[1,4,5],[2],[3],[6],[7]]=>7
{{1,4,6,7},{2,5},{3}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1,4,6},{2,5,7},{3}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1,4,6},{2,5},{3,7}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1,4,6},{2,5},{3},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,4,7},{2,5,6},{3}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1,4},{2,5,6,7},{3}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1,4},{2,5,6},{3,7}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1,4},{2,5,6},{3},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,4,7},{2,5},{3,6}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,4},{2,5,7},{3,6}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,4},{2,5},{3,6,7}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,4},{2,5},{3,6},{7}}=>[[1,4],[2,5],[3,6],[7]]=>7
{{1,4,7},{2,5},{3},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1,4},{2,5,7},{3},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1,4},{2,5},{3,7},{6}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1,4},{2,5},{3},{6,7}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1,4},{2,5},{3},{6},{7}}=>[[1,4],[2,5],[3],[6],[7]]=>7
{{1,4,6,7},{2},{3,5}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1,4,6},{2,7},{3,5}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1,4,6},{2},{3,5,7}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1,4,6},{2},{3,5},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,4,7},{2,6},{3,5}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,4},{2,6,7},{3,5}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,4},{2,6},{3,5,7}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,4},{2,6},{3,5},{7}}=>[[1,4],[2,5],[3,6],[7]]=>7
{{1,4,7},{2},{3,5,6}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1,4},{2,7},{3,5,6}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1,4},{2},{3,5,6,7}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1,4},{2},{3,5,6},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,4,7},{2},{3,5},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1,4},{2,7},{3,5},{6}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1,4},{2},{3,5,7},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1,4},{2},{3,5},{6,7}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1,4},{2},{3,5},{6},{7}}=>[[1,4],[2,5],[3],[6],[7]]=>7
{{1,4,6,7},{2},{3},{5}}=>[[1,4,6,7],[2],[3],[5]]=>5
{{1,4,6},{2,7},{3},{5}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1,4,6},{2},{3,7},{5}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1,4,6},{2},{3},{5,7}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1,4,6},{2},{3},{5},{7}}=>[[1,4,6],[2],[3],[5],[7]]=>7
{{1,4,7},{2,6},{3},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,4},{2,6,7},{3},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,4},{2,6},{3,7},{5}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,4},{2,6},{3},{5,7}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,4},{2,6},{3},{5},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,4,7},{2},{3,6},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,4},{2,7},{3,6},{5}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,4},{2},{3,6,7},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,4},{2},{3,6},{5,7}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,4},{2},{3,6},{5},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,4,7},{2},{3},{5,6}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,4},{2,7},{3},{5,6}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,4},{2},{3,7},{5,6}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,4},{2},{3},{5,6,7}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,4},{2},{3},{5,6},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,4,7},{2},{3},{5},{6}}=>[[1,4,7],[2],[3],[5],[6]]=>6
{{1,4},{2,7},{3},{5},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1,4},{2},{3,7},{5},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1,4},{2},{3},{5,7},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1,4},{2},{3},{5},{6,7}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1,4},{2},{3},{5},{6},{7}}=>[[1,4],[2],[3],[5],[6],[7]]=>7
{{1,5,6,7},{2,4},{3}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1,5,6},{2,4,7},{3}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1,5,6},{2,4},{3,7}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1,5,6},{2,4},{3},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,5,7},{2,4,6},{3}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1,5},{2,4,6,7},{3}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1,5},{2,4,6},{3,7}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1,5},{2,4,6},{3},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,5,7},{2,4},{3,6}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,5},{2,4,7},{3,6}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,5},{2,4},{3,6,7}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,5},{2,4},{3,6},{7}}=>[[1,4],[2,5],[3,6],[7]]=>7
{{1,5,7},{2,4},{3},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1,5},{2,4,7},{3},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1,5},{2,4},{3,7},{6}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1,5},{2,4},{3},{6,7}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1,5},{2,4},{3},{6},{7}}=>[[1,4],[2,5],[3],[6],[7]]=>7
{{1,6,7},{2,4,5},{3}}=>[[1,4,5],[2,6,7],[3]]=>3
{{1,6},{2,4,5,7},{3}}=>[[1,4,5,7],[2,6],[3]]=>3
{{1,6},{2,4,5},{3,7}}=>[[1,4,5],[2,6],[3,7]]=>3
{{1,6},{2,4,5},{3},{7}}=>[[1,4,5],[2,6],[3],[7]]=>7
{{1,7},{2,4,5,6},{3}}=>[[1,4,5,6],[2,7],[3]]=>3
{{1},{2,4,5,6,7},{3}}=>[[1,4,5,6,7],[2],[3]]=>3
{{1},{2,4,5,6},{3,7}}=>[[1,4,5,6],[2,7],[3]]=>3
{{1},{2,4,5,6},{3},{7}}=>[[1,4,5,6],[2],[3],[7]]=>7
{{1,7},{2,4,5},{3,6}}=>[[1,4,5],[2,6],[3,7]]=>3
{{1},{2,4,5,7},{3,6}}=>[[1,4,5,7],[2,6],[3]]=>3
{{1},{2,4,5},{3,6,7}}=>[[1,4,5],[2,6,7],[3]]=>3
{{1},{2,4,5},{3,6},{7}}=>[[1,4,5],[2,6],[3],[7]]=>7
{{1,7},{2,4,5},{3},{6}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1},{2,4,5,7},{3},{6}}=>[[1,4,5,7],[2],[3],[6]]=>6
{{1},{2,4,5},{3,7},{6}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1},{2,4,5},{3},{6,7}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1},{2,4,5},{3},{6},{7}}=>[[1,4,5],[2],[3],[6],[7]]=>7
{{1,6,7},{2,4},{3,5}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,6},{2,4,7},{3,5}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,6},{2,4},{3,5,7}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,6},{2,4},{3,5},{7}}=>[[1,4],[2,5],[3,6],[7]]=>7
{{1,7},{2,4,6},{3,5}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1},{2,4,6,7},{3,5}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1},{2,4,6},{3,5,7}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1},{2,4,6},{3,5},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,7},{2,4},{3,5,6}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1},{2,4,7},{3,5,6}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1},{2,4},{3,5,6,7}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1},{2,4},{3,5,6},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,7},{2,4},{3,5},{6}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1},{2,4,7},{3,5},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1},{2,4},{3,5,7},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1},{2,4},{3,5},{6,7}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1},{2,4},{3,5},{6},{7}}=>[[1,4],[2,5],[3],[6],[7]]=>7
{{1,6,7},{2,4},{3},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,6},{2,4,7},{3},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,6},{2,4},{3,7},{5}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,6},{2,4},{3},{5,7}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,6},{2,4},{3},{5},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,7},{2,4,6},{3},{5}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1},{2,4,6,7},{3},{5}}=>[[1,4,6,7],[2],[3],[5]]=>5
{{1},{2,4,6},{3,7},{5}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1},{2,4,6},{3},{5,7}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1},{2,4,6},{3},{5},{7}}=>[[1,4,6],[2],[3],[5],[7]]=>7
{{1,7},{2,4},{3,6},{5}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1},{2,4,7},{3,6},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1},{2,4},{3,6,7},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1},{2,4},{3,6},{5,7}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1},{2,4},{3,6},{5},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,7},{2,4},{3},{5,6}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1},{2,4,7},{3},{5,6}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1},{2,4},{3,7},{5,6}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1},{2,4},{3},{5,6,7}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1},{2,4},{3},{5,6},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,7},{2,4},{3},{5},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1},{2,4,7},{3},{5},{6}}=>[[1,4,7],[2],[3],[5],[6]]=>6
{{1},{2,4},{3,7},{5},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1},{2,4},{3},{5,7},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1},{2,4},{3},{5},{6,7}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1},{2,4},{3},{5},{6},{7}}=>[[1,4],[2],[3],[5],[6],[7]]=>7
{{1,5,6,7},{2},{3,4}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1,5,6},{2,7},{3,4}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1,5,6},{2},{3,4,7}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1,5,6},{2},{3,4},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,5,7},{2,6},{3,4}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,5},{2,6,7},{3,4}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,5},{2,6},{3,4,7}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,5},{2,6},{3,4},{7}}=>[[1,4],[2,5],[3,6],[7]]=>7
{{1,5,7},{2},{3,4,6}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1,5},{2,7},{3,4,6}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1,5},{2},{3,4,6,7}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1,5},{2},{3,4,6},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,5,7},{2},{3,4},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1,5},{2,7},{3,4},{6}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1,5},{2},{3,4,7},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1,5},{2},{3,4},{6,7}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1,5},{2},{3,4},{6},{7}}=>[[1,4],[2,5],[3],[6],[7]]=>7
{{1,6,7},{2,5},{3,4}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,6},{2,5,7},{3,4}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,6},{2,5},{3,4,7}}=>[[1,4,7],[2,5],[3,6]]=>3
{{1,6},{2,5},{3,4},{7}}=>[[1,4],[2,5],[3,6],[7]]=>7
{{1,7},{2,5,6},{3,4}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1},{2,5,6,7},{3,4}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1},{2,5,6},{3,4,7}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1},{2,5,6},{3,4},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,7},{2,5},{3,4,6}}=>[[1,4,6],[2,5],[3,7]]=>3
{{1},{2,5,7},{3,4,6}}=>[[1,4,6],[2,5,7],[3]]=>3
{{1},{2,5},{3,4,6,7}}=>[[1,4,6,7],[2,5],[3]]=>3
{{1},{2,5},{3,4,6},{7}}=>[[1,4,6],[2,5],[3],[7]]=>7
{{1,7},{2,5},{3,4},{6}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1},{2,5,7},{3,4},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1},{2,5},{3,4,7},{6}}=>[[1,4,7],[2,5],[3],[6]]=>6
{{1},{2,5},{3,4},{6,7}}=>[[1,4],[2,5],[3,7],[6]]=>6
{{1},{2,5},{3,4},{6},{7}}=>[[1,4],[2,5],[3],[6],[7]]=>7
{{1,6,7},{2},{3,4,5}}=>[[1,4,5],[2,6,7],[3]]=>3
{{1,6},{2,7},{3,4,5}}=>[[1,4,5],[2,6],[3,7]]=>3
{{1,6},{2},{3,4,5,7}}=>[[1,4,5,7],[2,6],[3]]=>3
{{1,6},{2},{3,4,5},{7}}=>[[1,4,5],[2,6],[3],[7]]=>7
{{1,7},{2,6},{3,4,5}}=>[[1,4,5],[2,6],[3,7]]=>3
{{1},{2,6,7},{3,4,5}}=>[[1,4,5],[2,6,7],[3]]=>3
{{1},{2,6},{3,4,5,7}}=>[[1,4,5,7],[2,6],[3]]=>3
{{1},{2,6},{3,4,5},{7}}=>[[1,4,5],[2,6],[3],[7]]=>7
{{1,7},{2},{3,4,5,6}}=>[[1,4,5,6],[2,7],[3]]=>3
{{1},{2,7},{3,4,5,6}}=>[[1,4,5,6],[2,7],[3]]=>3
{{1},{2},{3,4,5,6,7}}=>[[1,4,5,6,7],[2],[3]]=>3
{{1},{2},{3,4,5,6},{7}}=>[[1,4,5,6],[2],[3],[7]]=>7
{{1,7},{2},{3,4,5},{6}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1},{2,7},{3,4,5},{6}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1},{2},{3,4,5,7},{6}}=>[[1,4,5,7],[2],[3],[6]]=>6
{{1},{2},{3,4,5},{6,7}}=>[[1,4,5],[2,7],[3],[6]]=>6
{{1},{2},{3,4,5},{6},{7}}=>[[1,4,5],[2],[3],[6],[7]]=>7
{{1,6,7},{2},{3,4},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,6},{2,7},{3,4},{5}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,6},{2},{3,4,7},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1,6},{2},{3,4},{5,7}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1,6},{2},{3,4},{5},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,7},{2,6},{3,4},{5}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1},{2,6,7},{3,4},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1},{2,6},{3,4,7},{5}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1},{2,6},{3,4},{5,7}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1},{2,6},{3,4},{5},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,7},{2},{3,4,6},{5}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1},{2,7},{3,4,6},{5}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1},{2},{3,4,6,7},{5}}=>[[1,4,6,7],[2],[3],[5]]=>5
{{1},{2},{3,4,6},{5,7}}=>[[1,4,6],[2,7],[3],[5]]=>5
{{1},{2},{3,4,6},{5},{7}}=>[[1,4,6],[2],[3],[5],[7]]=>7
{{1,7},{2},{3,4},{5,6}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1},{2,7},{3,4},{5,6}}=>[[1,4],[2,6],[3,7],[5]]=>5
{{1},{2},{3,4,7},{5,6}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1},{2},{3,4},{5,6,7}}=>[[1,4,7],[2,6],[3],[5]]=>5
{{1},{2},{3,4},{5,6},{7}}=>[[1,4],[2,6],[3],[5],[7]]=>7
{{1,7},{2},{3,4},{5},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1},{2,7},{3,4},{5},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1},{2},{3,4,7},{5},{6}}=>[[1,4,7],[2],[3],[5],[6]]=>6
{{1},{2},{3,4},{5,7},{6}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1},{2},{3,4},{5},{6,7}}=>[[1,4],[2,7],[3],[5],[6]]=>6
{{1},{2},{3,4},{5},{6},{7}}=>[[1,4],[2],[3],[5],[6],[7]]=>7
{{1,5,6,7},{2},{3},{4}}=>[[1,5,6,7],[2],[3],[4]]=>4
{{1,5,6},{2,7},{3},{4}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1,5,6},{2},{3,7},{4}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1,5,6},{2},{3},{4,7}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1,5,6},{2},{3},{4},{7}}=>[[1,5,6],[2],[3],[4],[7]]=>7
{{1,5,7},{2,6},{3},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,5},{2,6,7},{3},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,5},{2,6},{3,7},{4}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,5},{2,6},{3},{4,7}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,5},{2,6},{3},{4},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,5,7},{2},{3,6},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,5},{2,7},{3,6},{4}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,5},{2},{3,6,7},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,5},{2},{3,6},{4,7}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,5},{2},{3,6},{4},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,5,7},{2},{3},{4,6}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,5},{2,7},{3},{4,6}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,5},{2},{3,7},{4,6}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,5},{2},{3},{4,6,7}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,5},{2},{3},{4,6},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,5,7},{2},{3},{4},{6}}=>[[1,5,7],[2],[3],[4],[6]]=>6
{{1,5},{2,7},{3},{4},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1,5},{2},{3,7},{4},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1,5},{2},{3},{4,7},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1,5},{2},{3},{4},{6,7}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1,5},{2},{3},{4},{6},{7}}=>[[1,5],[2],[3],[4],[6],[7]]=>7
{{1,6,7},{2,5},{3},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,6},{2,5,7},{3},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,6},{2,5},{3,7},{4}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,6},{2,5},{3},{4,7}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,6},{2,5},{3},{4},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2,5,6},{3},{4}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2,5,6,7},{3},{4}}=>[[1,5,6,7],[2],[3],[4]]=>4
{{1},{2,5,6},{3,7},{4}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2,5,6},{3},{4,7}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2,5,6},{3},{4},{7}}=>[[1,5,6],[2],[3],[4],[7]]=>7
{{1,7},{2,5},{3,6},{4}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,5,7},{3,6},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2,5},{3,6,7},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2,5},{3,6},{4,7}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,5},{3,6},{4},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2,5},{3},{4,6}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,5,7},{3},{4,6}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2,5},{3,7},{4,6}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,5},{3},{4,6,7}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2,5},{3},{4,6},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2,5},{3},{4},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2,5,7},{3},{4},{6}}=>[[1,5,7],[2],[3],[4],[6]]=>6
{{1},{2,5},{3,7},{4},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2,5},{3},{4,7},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2,5},{3},{4},{6,7}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2,5},{3},{4},{6},{7}}=>[[1,5],[2],[3],[4],[6],[7]]=>7
{{1,6,7},{2},{3,5},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,6},{2,7},{3,5},{4}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,6},{2},{3,5,7},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,6},{2},{3,5},{4,7}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,6},{2},{3,5},{4},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2,6},{3,5},{4}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,6,7},{3,5},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2,6},{3,5,7},{4}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2,6},{3,5},{4,7}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,6},{3,5},{4},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2},{3,5,6},{4}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2,7},{3,5,6},{4}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2},{3,5,6,7},{4}}=>[[1,5,6,7],[2],[3],[4]]=>4
{{1},{2},{3,5,6},{4,7}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2},{3,5,6},{4},{7}}=>[[1,5,6],[2],[3],[4],[7]]=>7
{{1,7},{2},{3,5},{4,6}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,7},{3,5},{4,6}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2},{3,5,7},{4,6}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2},{3,5},{4,6,7}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2},{3,5},{4,6},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2},{3,5},{4},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2,7},{3,5},{4},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2},{3,5,7},{4},{6}}=>[[1,5,7],[2],[3],[4],[6]]=>6
{{1},{2},{3,5},{4,7},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2},{3,5},{4},{6,7}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2},{3,5},{4},{6},{7}}=>[[1,5],[2],[3],[4],[6],[7]]=>7
{{1,6,7},{2},{3},{4,5}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,6},{2,7},{3},{4,5}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,6},{2},{3,7},{4,5}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1,6},{2},{3},{4,5,7}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1,6},{2},{3},{4,5},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2,6},{3},{4,5}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,6,7},{3},{4,5}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2,6},{3,7},{4,5}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,6},{3},{4,5,7}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2,6},{3},{4,5},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2},{3,6},{4,5}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2,7},{3,6},{4,5}}=>[[1,5],[2,6],[3,7],[4]]=>4
{{1},{2},{3,6,7},{4,5}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2},{3,6},{4,5,7}}=>[[1,5,7],[2,6],[3],[4]]=>4
{{1},{2},{3,6},{4,5},{7}}=>[[1,5],[2,6],[3],[4],[7]]=>7
{{1,7},{2},{3},{4,5,6}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2,7},{3},{4,5,6}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2},{3,7},{4,5,6}}=>[[1,5,6],[2,7],[3],[4]]=>4
{{1},{2},{3},{4,5,6,7}}=>[[1,5,6,7],[2],[3],[4]]=>4
{{1},{2},{3},{4,5,6},{7}}=>[[1,5,6],[2],[3],[4],[7]]=>7
{{1,7},{2},{3},{4,5},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2,7},{3},{4,5},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2},{3,7},{4,5},{6}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2},{3},{4,5,7},{6}}=>[[1,5,7],[2],[3],[4],[6]]=>6
{{1},{2},{3},{4,5},{6,7}}=>[[1,5],[2,7],[3],[4],[6]]=>6
{{1},{2},{3},{4,5},{6},{7}}=>[[1,5],[2],[3],[4],[6],[7]]=>7
{{1,6,7},{2},{3},{4},{5}}=>[[1,6,7],[2],[3],[4],[5]]=>5
{{1,6},{2,7},{3},{4},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1,6},{2},{3,7},{4},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1,6},{2},{3},{4,7},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1,6},{2},{3},{4},{5,7}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1,6},{2},{3},{4},{5},{7}}=>[[1,6],[2],[3],[4],[5],[7]]=>7
{{1,7},{2,6},{3},{4},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2,6,7},{3},{4},{5}}=>[[1,6,7],[2],[3],[4],[5]]=>5
{{1},{2,6},{3,7},{4},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2,6},{3},{4,7},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2,6},{3},{4},{5,7}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2,6},{3},{4},{5},{7}}=>[[1,6],[2],[3],[4],[5],[7]]=>7
{{1,7},{2},{3,6},{4},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2,7},{3,6},{4},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3,6,7},{4},{5}}=>[[1,6,7],[2],[3],[4],[5]]=>5
{{1},{2},{3,6},{4,7},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3,6},{4},{5,7}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3,6},{4},{5},{7}}=>[[1,6],[2],[3],[4],[5],[7]]=>7
{{1,7},{2},{3},{4,6},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2,7},{3},{4,6},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3,7},{4,6},{5}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3},{4,6,7},{5}}=>[[1,6,7],[2],[3],[4],[5]]=>5
{{1},{2},{3},{4,6},{5,7}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3},{4,6},{5},{7}}=>[[1,6],[2],[3],[4],[5],[7]]=>7
{{1,7},{2},{3},{4},{5,6}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2,7},{3},{4},{5,6}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3,7},{4},{5,6}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3},{4,7},{5,6}}=>[[1,6],[2,7],[3],[4],[5]]=>5
{{1},{2},{3},{4},{5,6,7}}=>[[1,6,7],[2],[3],[4],[5]]=>5
{{1},{2},{3},{4},{5,6},{7}}=>[[1,6],[2],[3],[4],[5],[7]]=>7
{{1,7},{2},{3},{4},{5},{6}}=>[[1,7],[2],[3],[4],[5],[6]]=>6
{{1},{2,7},{3},{4},{5},{6}}=>[[1,7],[2],[3],[4],[5],[6]]=>6
{{1},{2},{3,7},{4},{5},{6}}=>[[1,7],[2],[3],[4],[5],[6]]=>6
{{1},{2},{3},{4,7},{5},{6}}=>[[1,7],[2],[3],[4],[5],[6]]=>6
{{1},{2},{3},{4},{5,7},{6}}=>[[1,7],[2],[3],[4],[5],[6]]=>6
{{1},{2},{3},{4},{5},{6,7}}=>[[1,7],[2],[3],[4],[5],[6]]=>6
{{1},{2},{3},{4},{5},{6},{7}}=>[[1],[2],[3],[4],[5],[6],[7]]=>7
{{1,2},{3,4},{5,6},{7,8}}=>[[1,2],[3,4],[5,6],[7,8]]=>7
{{1,3},{2,4},{5,6},{7,8}}=>[[1,3],[2,4],[5,6],[7,8]]=>7
{{1,4},{2,3},{5,6},{7,8}}=>[[1,3],[2,4],[5,6],[7,8]]=>7
{{1,5},{2,3},{4,6},{7,8}}=>[[1,3],[2,5],[4,6],[7,8]]=>7
{{1,6},{2,3},{4,5},{7,8}}=>[[1,3],[2,5],[4,6],[7,8]]=>7
{{1,7},{2,3},{4,5},{6,8}}=>[[1,3],[2,5],[4,7],[6,8]]=>6
{{1,8},{2,3},{4,5},{6,7}}=>[[1,3],[2,5],[4,7],[6,8]]=>6
{{1,8},{2,4},{3,5},{6,7}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,7},{2,4},{3,5},{6,8}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,6},{2,4},{3,5},{7,8}}=>[[1,4],[2,5],[3,6],[7,8]]=>7
{{1,5},{2,4},{3,6},{7,8}}=>[[1,4],[2,5],[3,6],[7,8]]=>7
{{1,4},{2,5},{3,6},{7,8}}=>[[1,4],[2,5],[3,6],[7,8]]=>7
{{1,3},{2,5},{4,6},{7,8}}=>[[1,3],[2,5],[4,6],[7,8]]=>7
{{1,2},{3,5},{4,6},{7,8}}=>[[1,2],[3,5],[4,6],[7,8]]=>7
{{1,2},{3,6},{4,5},{7,8}}=>[[1,2],[3,5],[4,6],[7,8]]=>7
{{1,3},{2,6},{4,5},{7,8}}=>[[1,3],[2,5],[4,6],[7,8]]=>7
{{1,4},{2,6},{3,5},{7,8}}=>[[1,4],[2,5],[3,6],[7,8]]=>7
{{1,5},{2,6},{3,4},{7,8}}=>[[1,4],[2,5],[3,6],[7,8]]=>7
{{1,6},{2,5},{3,4},{7,8}}=>[[1,4],[2,5],[3,6],[7,8]]=>7
{{1,7},{2,5},{3,4},{6,8}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,8},{2,5},{3,4},{6,7}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,8},{2,6},{3,4},{5,7}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,7},{2,6},{3,4},{5,8}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,6},{2,7},{3,4},{5,8}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,5},{2,7},{3,4},{6,8}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,4},{2,7},{3,5},{6,8}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,3},{2,7},{4,5},{6,8}}=>[[1,3],[2,5],[4,7],[6,8]]=>6
{{1,2},{3,7},{4,5},{6,8}}=>[[1,2],[3,5],[4,7],[6,8]]=>6
{{1,2},{3,8},{4,5},{6,7}}=>[[1,2],[3,5],[4,7],[6,8]]=>6
{{1,3},{2,8},{4,5},{6,7}}=>[[1,3],[2,5],[4,7],[6,8]]=>6
{{1,4},{2,8},{3,5},{6,7}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,5},{2,8},{3,4},{6,7}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,6},{2,8},{3,4},{5,7}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,7},{2,8},{3,4},{5,6}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,8},{2,7},{3,4},{5,6}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,8},{2,7},{3,5},{4,6}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,7},{2,8},{3,5},{4,6}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,6},{2,8},{3,5},{4,7}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,5},{2,8},{3,6},{4,7}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,4},{2,8},{3,6},{5,7}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,3},{2,8},{4,6},{5,7}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,2},{3,8},{4,6},{5,7}}=>[[1,2],[3,6],[4,7],[5,8]]=>5
{{1,2},{3,7},{4,6},{5,8}}=>[[1,2],[3,6],[4,7],[5,8]]=>5
{{1,3},{2,7},{4,6},{5,8}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,4},{2,7},{3,6},{5,8}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,5},{2,7},{3,6},{4,8}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,6},{2,7},{3,5},{4,8}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,7},{2,6},{3,5},{4,8}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,8},{2,6},{3,5},{4,7}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,8},{2,5},{3,6},{4,7}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,7},{2,5},{3,6},{4,8}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,6},{2,5},{3,7},{4,8}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,5},{2,6},{3,7},{4,8}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,4},{2,6},{3,7},{5,8}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,3},{2,6},{4,7},{5,8}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,2},{3,6},{4,7},{5,8}}=>[[1,2],[3,6],[4,7],[5,8]]=>5
{{1,2},{3,5},{4,7},{6,8}}=>[[1,2],[3,5],[4,7],[6,8]]=>6
{{1,3},{2,5},{4,7},{6,8}}=>[[1,3],[2,5],[4,7],[6,8]]=>6
{{1,4},{2,5},{3,7},{6,8}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,5},{2,4},{3,7},{6,8}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,6},{2,4},{3,7},{5,8}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,7},{2,4},{3,6},{5,8}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,8},{2,4},{3,6},{5,7}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,8},{2,3},{4,6},{5,7}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,7},{2,3},{4,6},{5,8}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,6},{2,3},{4,7},{5,8}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,5},{2,3},{4,7},{6,8}}=>[[1,3],[2,5],[4,7],[6,8]]=>6
{{1,4},{2,3},{5,7},{6,8}}=>[[1,3],[2,4],[5,7],[6,8]]=>6
{{1,3},{2,4},{5,7},{6,8}}=>[[1,3],[2,4],[5,7],[6,8]]=>6
{{1,2},{3,4},{5,7},{6,8}}=>[[1,2],[3,4],[5,7],[6,8]]=>6
{{1,2},{3,4},{5,8},{6,7}}=>[[1,2],[3,4],[5,7],[6,8]]=>6
{{1,3},{2,4},{5,8},{6,7}}=>[[1,3],[2,4],[5,7],[6,8]]=>6
{{1,4},{2,3},{5,8},{6,7}}=>[[1,3],[2,4],[5,7],[6,8]]=>6
{{1,5},{2,3},{4,8},{6,7}}=>[[1,3],[2,5],[4,7],[6,8]]=>6
{{1,6},{2,3},{4,8},{5,7}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,7},{2,3},{4,8},{5,6}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,8},{2,3},{4,7},{5,6}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,8},{2,4},{3,7},{5,6}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,7},{2,4},{3,8},{5,6}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,6},{2,4},{3,8},{5,7}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,5},{2,4},{3,8},{6,7}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,4},{2,5},{3,8},{6,7}}=>[[1,4],[2,5],[3,7],[6,8]]=>6
{{1,3},{2,5},{4,8},{6,7}}=>[[1,3],[2,5],[4,7],[6,8]]=>6
{{1,2},{3,5},{4,8},{6,7}}=>[[1,2],[3,5],[4,7],[6,8]]=>6
{{1,2},{3,6},{4,8},{5,7}}=>[[1,2],[3,6],[4,7],[5,8]]=>5
{{1,3},{2,6},{4,8},{5,7}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,4},{2,6},{3,8},{5,7}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,5},{2,6},{3,8},{4,7}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,6},{2,5},{3,8},{4,7}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,7},{2,5},{3,8},{4,6}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,8},{2,5},{3,7},{4,6}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,8},{2,6},{3,7},{4,5}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,7},{2,6},{3,8},{4,5}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,6},{2,7},{3,8},{4,5}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,5},{2,7},{3,8},{4,6}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,4},{2,7},{3,8},{5,6}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,3},{2,7},{4,8},{5,6}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,2},{3,7},{4,8},{5,6}}=>[[1,2],[3,6],[4,7],[5,8]]=>5
{{1,2},{3,8},{4,7},{5,6}}=>[[1,2],[3,6],[4,7],[5,8]]=>5
{{1,3},{2,8},{4,7},{5,6}}=>[[1,3],[2,6],[4,7],[5,8]]=>5
{{1,4},{2,8},{3,7},{5,6}}=>[[1,4],[2,6],[3,7],[5,8]]=>5
{{1,5},{2,8},{3,7},{4,6}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,6},{2,8},{3,7},{4,5}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,7},{2,8},{3,6},{4,5}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1,8},{2,7},{3,6},{4,5}}=>[[1,5],[2,6],[3,7],[4,8]]=>4
{{1},{2,3},{4,5,6,8},{7}}=>[[1,3,6,8],[2,5],[4],[7]]=>7
{{1},{2,4,6,8},{3},{5},{7}}=>[[1,4,6,8],[2],[3],[5],[7]]=>7
{{1},{2,4,8},{3},{5,7},{6}}=>[[1,4,8],[2,7],[3],[5],[6]]=>6
{{1},{2,8},{3,4},{5,6,7}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1},{2,3,5},{4},{6,7,8}}=>[[1,3,5],[2,7,8],[4],[6]]=>6
{{1},{2,6,8},{3,5},{4},{7}}=>[[1,5,8],[2,6],[3],[4],[7]]=>7
{{1},{2,8},{3,5,7},{4},{6}}=>[[1,5,7],[2,8],[3],[4],[6]]=>6
{{1},{2,8},{3,7},{4,6},{5}}=>[[1,6],[2,7],[3,8],[4],[5]]=>5
{{1,2},{3,4},{5,7,8},{6}}=>[[1,2,8],[3,4],[5,7],[6]]=>6
{{1,2},{3,4},{5,6,8},{7}}=>[[1,2,8],[3,4],[5,6],[7]]=>7
{{1,2},{3,6,7,8},{4},{5}}=>[[1,2,7,8],[3,6],[4],[5]]=>5
{{1,2},{3,5,6},{4},{7,8}}=>[[1,2,6],[3,5],[4,8],[7]]=>7
{{1,2},{3,7,8},{4},{5,6}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,2},{3,5,8},{4},{6,7}}=>[[1,2,8],[3,5],[4,7],[6]]=>6
{{1,2},{3,5,6,8},{4},{7}}=>[[1,2,6,8],[3,5],[4],[7]]=>7
{{1,2},{3,6,8},{4,5},{7}}=>[[1,2,8],[3,5],[4,6],[7]]=>7
{{1,2},{3,4,6},{5},{7,8}}=>[[1,2,6],[3,4],[5,8],[7]]=>7
{{1,2},{3,7,8},{4,6},{5}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,2},{3,8},{4,6,7},{5}}=>[[1,2,7],[3,6],[4,8],[5]]=>5
{{1,2},{3,4,8},{5},{6,7}}=>[[1,2,8],[3,4],[5,7],[6]]=>6
{{1,2},{3,4,6,8},{5},{7}}=>[[1,2,6,8],[3,4],[5],[7]]=>7
{{1,2},{3,8},{4,5,7},{6}}=>[[1,2,7],[3,5],[4,8],[6]]=>6
{{1,2},{3,4,8},{5,7},{6}}=>[[1,2,8],[3,4],[5,7],[6]]=>6
{{1,3},{2},{4,6,8},{5},{7}}=>[[1,3,8],[2,6],[4],[5],[7]]=>7
{{1,3},{2},{4,8},{5,7},{6}}=>[[1,3],[2,7],[4,8],[5],[6]]=>6
{{1,3},{2},{4,5,6,8},{7}}=>[[1,3,6,8],[2,5],[4],[7]]=>7
{{1,5,6,7,8},{2},{3},{4}}=>[[1,5,6,7,8],[2],[3],[4]]=>4
{{1,6,7,8},{2},{3},{4,5}}=>[[1,5,7,8],[2,6],[3],[4]]=>4
{{1,4,5,6},{2},{3},{7,8}}=>[[1,4,5,6],[2,8],[3],[7]]=>7
{{1,4,7,8},{2},{3},{5,6}}=>[[1,4,7,8],[2,6],[3],[5]]=>5
{{1,4,5,8},{2},{3},{6,7}}=>[[1,4,5,8],[2,7],[3],[6]]=>6
{{1,3,4},{2},{5,6},{7,8}}=>[[1,3,4],[2,6],[5,8],[7]]=>7
{{1,3,4},{2},{5,7,8},{6}}=>[[1,3,4],[2,7,8],[5],[6]]=>6
{{1,3,4},{2},{5,8},{6,7}}=>[[1,3,4],[2,7],[5,8],[6]]=>6
{{1,5,6},{2},{3,4},{7,8}}=>[[1,4,6],[2,5],[3,8],[7]]=>7
{{1,7,8},{2},{3,4},{5,6}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,5,8},{2},{3,4},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,3,5},{2},{4},{6,8},{7}}=>[[1,3,5],[2,8],[4],[6],[7]]=>7
{{1,3,5},{2},{4},{6,7,8}}=>[[1,3,5],[2,7,8],[4],[6]]=>6
{{1,6,7,8},{2},{3,5},{4}}=>[[1,5,7,8],[2,6],[3],[4]]=>4
{{1,7,8},{2},{3,5,6},{4}}=>[[1,5,6],[2,7,8],[3],[4]]=>4
{{1,3,5,7},{2},{4},{6},{8}}=>[[1,3,5,7],[2],[4],[6],[8]]=>8
{{1,3,6},{2},{4,5},{7,8}}=>[[1,3,6],[2,5],[4,8],[7]]=>7
{{1,7,8},{2},{3,6},{4,5}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,3,8},{2},{4,5},{6,7}}=>[[1,3,8],[2,5],[4,7],[6]]=>6
{{1,3,7},{2},{4,6},{5},{8}}=>[[1,3,7],[2,6],[4],[5],[8]]=>8
{{1,3,8},{2},{4,6,7},{5}}=>[[1,3,7],[2,6,8],[4],[5]]=>5
{{1,3,8},{2},{4,7},{5,6}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,4},{2,3},{5,7,8},{6}}=>[[1,3,8],[2,4],[5,7],[6]]=>6
{{1,4},{2,3},{5,6,8},{7}}=>[[1,3,8],[2,4],[5,6],[7]]=>7
{{1,8},{2,3},{4},{5,6,7}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,6,8},{2,3},{4,5},{7}}=>[[1,3,8],[2,5],[4,6],[7]]=>7
{{1,4,6},{2,3},{5},{7,8}}=>[[1,3,6],[2,4],[5,8],[7]]=>7
{{1,8},{2,3},{4,6,7},{5}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,4,8},{2,3},{5},{6,7}}=>[[1,3,8],[2,4],[5,7],[6]]=>6
{{1,4,6,8},{2,3},{5},{7}}=>[[1,3,6,8],[2,4],[5],[7]]=>7
{{1,8},{2,3},{4,5,7},{6}}=>[[1,3,7],[2,5],[4,8],[6]]=>6
{{1,4,8},{2,3},{5,7},{6}}=>[[1,3,8],[2,4],[5,7],[6]]=>6
{{1,2,4},{3},{5,6},{7,8}}=>[[1,2,4],[3,6],[5,8],[7]]=>7
{{1,2,4},{3},{5,8},{6,7}}=>[[1,2,4],[3,7],[5,8],[6]]=>6
{{1,2,4},{3},{5,6,8},{7}}=>[[1,2,4],[3,6,8],[5],[7]]=>7
{{1,5},{2,4},{3},{6,8},{7}}=>[[1,4],[2,5],[3,8],[6],[7]]=>7
{{1,5,6},{2,4},{3},{7,8}}=>[[1,4,6],[2,5],[3,8],[7]]=>7
{{1,7,8},{2,4},{3},{5,6}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,5,7},{2,4},{3},{6},{8}}=>[[1,4,7],[2,5],[3],[6],[8]]=>8
{{1,5,8},{2,4},{3},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,6,7,8},{2,5},{3},{4}}=>[[1,5,7,8],[2,6],[3],[4]]=>4
{{1,7,8},{2,5,6},{3},{4}}=>[[1,5,6],[2,7,8],[3],[4]]=>4
{{1,8},{2,5,6,7},{3},{4}}=>[[1,5,6,7],[2,8],[3],[4]]=>4
{{1,6},{2,4,5},{3},{7,8}}=>[[1,4,5],[2,6],[3,8],[7]]=>7
{{1,8},{2,4,5},{3},{6,7}}=>[[1,4,5],[2,7],[3,8],[6]]=>6
{{1,2,6},{3},{4,5},{7,8}}=>[[1,2,6],[3,5],[4,8],[7]]=>7
{{1,7,8},{2,6},{3},{4,5}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,8},{2,6,7},{3},{4,5}}=>[[1,5,7],[2,6],[3,8],[4]]=>4
{{1,2,8},{3},{4,5},{6,7}}=>[[1,2,8],[3,5],[4,7],[6]]=>6
{{1,2,6,8},{3},{4,5},{7}}=>[[1,2,6,8],[3,5],[4],[7]]=>7
{{1,2,4,6},{3},{5},{7,8}}=>[[1,2,4,6],[3,8],[5],[7]]=>7
{{1,7},{2,4,6},{3},{5},{8}}=>[[1,4,6],[2,7],[3],[5],[8]]=>8
{{1,2,4,8},{3},{5},{6,7}}=>[[1,2,4,8],[3,7],[5],[6]]=>6
{{1,2,4,6,8},{3},{5},{7}}=>[[1,2,4,6,8],[3],[5],[7]]=>7
{{1,8},{2,4,7},{3},{5,6}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,2,8},{3},{4,7},{5,6}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,2,8},{3},{4,5,7},{6}}=>[[1,2,7],[3,5,8],[4],[6]]=>6
{{1,2,4,8},{3},{5,7},{6}}=>[[1,2,4,8],[3,7],[5],[6]]=>6
{{1,6,8},{2,5},{3,4},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,8},{2,5,7},{3,4},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,6},{2,3,5},{4},{7,8}}=>[[1,3,5],[2,6],[4,8],[7]]=>7
{{1,8},{2,3,5},{4},{6,7}}=>[[1,3,5],[2,7],[4,8],[6]]=>6
{{1,6,8},{2,3,5},{4},{7}}=>[[1,3,5],[2,6,8],[4],[7]]=>7
{{1,2,6},{3,5},{4},{7,8}}=>[[1,2,6],[3,5],[4,8],[7]]=>7
{{1,7},{2,6},{3,5},{4},{8}}=>[[1,5],[2,6],[3,7],[4],[8]]=>8
{{1,7,8},{2,6},{3,5},{4}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,8},{2,6,7},{3,5},{4}}=>[[1,5,7],[2,6],[3,8],[4]]=>4
{{1,2,8},{3,5},{4},{6,7}}=>[[1,2,8],[3,5],[4,7],[6]]=>6
{{1,2,6,8},{3,5},{4},{7}}=>[[1,2,6,8],[3,5],[4],[7]]=>7
{{1,8},{2,7},{3,5,6},{4}}=>[[1,5,6],[2,7],[3,8],[4]]=>4
{{1,8},{2,3,7},{4},{5,6}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,2,8},{3,7},{4},{5,6}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,8},{2,3,5,7},{4},{6}}=>[[1,3,5,7],[2,8],[4],[6]]=>6
{{1,2,8},{3,5,7},{4},{6}}=>[[1,2,7],[3,5,8],[4],[6]]=>6
{{1,8},{2,3,7},{4,5},{6}}=>[[1,3,7],[2,5],[4,8],[6]]=>6
{{1,8},{2,7},{3,4,6},{5}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,8},{2,3,7},{4,6},{5}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,2,8},{3,7},{4,6},{5}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,5,7,8},{2,6},{3},{4}}=>[[1,5,7,8],[2,6],[3],[4]]=>4
{{1,5,6,8},{2,7},{3},{4}}=>[[1,5,6,8],[2,7],[3],[4]]=>4
{{1,2,4,8},{3,7},{5},{6}}=>[[1,2,4,8],[3,7],[5],[6]]=>6
{{1,3,6,8},{2,4},{5},{7}}=>[[1,3,6,8],[2,4],[5],[7]]=>7
{{1,2,5,8},{3,6},{4},{7}}=>[[1,2,5,8],[3,6],[4],[7]]=>7
{{1,3,4,8},{2,6},{5},{7}}=>[[1,3,4,8],[2,6],[5],[7]]=>7
{{1,2,4,8},{3,6},{5},{7}}=>[[1,2,4,8],[3,6],[5],[7]]=>7
{{1,4,6,7},{2,8},{3},{5}}=>[[1,4,6,7],[2,8],[3],[5]]=>5
{{1,3,5,7},{2,8},{4},{6}}=>[[1,3,5,7],[2,8],[4],[6]]=>6
{{1,3,4,7},{2,8},{5},{6}}=>[[1,3,4,7],[2,8],[5],[6]]=>6
{{1,2,4,7},{3,8},{5},{6}}=>[[1,2,4,7],[3,8],[5],[6]]=>6
{{1,2,5,6},{3,8},{4},{7}}=>[[1,2,5,6],[3,8],[4],[7]]=>7
{{1,3,5,7},{2,6},{4},{8}}=>[[1,3,5,7],[2,6],[4],[8]]=>8
{{1,3,5,7},{2,4},{6},{8}}=>[[1,3,5,7],[2,4],[6],[8]]=>8
{{1,4,7},{2,6,8},{3},{5}}=>[[1,4,7],[2,6,8],[3],[5]]=>5
{{1,3,7},{2,4,8},{5},{6}}=>[[1,3,7],[2,4,8],[5],[6]]=>6
{{1,3,6},{2,7,8},{4},{5}}=>[[1,3,6],[2,7,8],[4],[5]]=>5
{{1,2,4},{3,7,8},{5},{6}}=>[[1,2,4],[3,7,8],[5],[6]]=>6
{{1,2,6},{3,5,8},{4},{7}}=>[[1,2,6],[3,5,8],[4],[7]]=>7
{{1,3,6},{2,4,8},{5},{7}}=>[[1,3,6],[2,4,8],[5],[7]]=>7
{{1,3,5},{2,6,8},{4},{7}}=>[[1,3,5],[2,6,8],[4],[7]]=>7
{{1,3,4},{2,6,8},{5},{7}}=>[[1,3,4],[2,6,8],[5],[7]]=>7
{{1,2,4},{3,6,8},{5},{7}}=>[[1,2,4],[3,6,8],[5],[7]]=>7
{{1,4,8},{2,6},{3,7},{5}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,3,8},{2,6},{4,7},{5}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,2,8},{3,6},{4,7},{5}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,4,8},{2,5},{3,7},{6}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,3,8},{2,5},{4,7},{6}}=>[[1,3,8],[2,5],[4,7],[6]]=>6
{{1,2,8},{3,5},{4,7},{6}}=>[[1,2,8],[3,5],[4,7],[6]]=>6
{{1,4,8},{2,5},{3,6},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,4,7},{2,6},{3,8},{5}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,3,7},{2,6},{4,8},{5}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,2,7},{3,6},{4,8},{5}}=>[[1,2,7],[3,6],[4,8],[5]]=>5
{{1,4,7},{2,5},{3,8},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,3,7},{2,5},{4,8},{6}}=>[[1,3,7],[2,5],[4,8],[6]]=>6
{{1,2,7},{3,5},{4,8},{6}}=>[[1,2,7],[3,5],[4,8],[6]]=>6
{{1,4,6},{2,7},{3,8},{5}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,3,6},{2,7},{4,8},{5}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1,2,6},{3,7},{4,8},{5}}=>[[1,2,6],[3,7],[4,8],[5]]=>5
{{1,3,5},{2,7},{4,8},{6}}=>[[1,3,5],[2,7],[4,8],[6]]=>6
{{1,2,5},{3,7},{4,8},{6}}=>[[1,2,5],[3,7],[4,8],[6]]=>6
{{1,3,6},{2,5},{4,8},{7}}=>[[1,3,6],[2,5],[4,8],[7]]=>7
{{1,2,6},{3,5},{4,8},{7}}=>[[1,2,6],[3,5],[4,8],[7]]=>7
{{1,3,5},{2,6},{4,8},{7}}=>[[1,3,5],[2,6],[4,8],[7]]=>7
{{1,2,5},{3,6},{4,8},{7}}=>[[1,2,5],[3,6],[4,8],[7]]=>7
{{1,3,4},{2,6},{5,8},{7}}=>[[1,3,4],[2,6],[5,8],[7]]=>7
{{1,2,4},{3,6},{5,8},{7}}=>[[1,2,4],[3,6],[5,8],[7]]=>7
{{1,3,5},{2,4},{6,8},{7}}=>[[1,3,5],[2,4],[6,8],[7]]=>7
{{1,4,7},{2,5},{3,6},{8}}=>[[1,4,7],[2,5],[3,6],[8]]=>8
{{1,3,7},{2,5},{4,6},{8}}=>[[1,3,7],[2,5],[4,6],[8]]=>8
{{1,3,5,8},{2},{4,6},{7}}=>[[1,3,5,8],[2,6],[4],[7]]=>7
{{1,3,5,7},{2},{4},{6,8}}=>[[1,3,5,7],[2,8],[4],[6]]=>6
{{1,5,7},{2,4},{3},{6,8}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,5},{2,4,8},{3},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,5,8},{2,4},{3,6},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,6,8},{2,4},{3,5},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1},{2,3,5,8},{4,6},{7}}=>[[1,3,5,8],[2,6],[4],[7]]=>7
{{1,5,8},{2,6},{3,4},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,4,8},{2,6},{3,5},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,4},{2,5,8},{3},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,4,7},{2,5},{3},{6,8}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,4},{2},{3,6,7},{5,8}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,4},{2},{3,6},{5,7,8}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,4},{2},{3,7},{5,6,8}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,4},{2},{3,5,8},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,5},{2},{3,4,8},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,2,5},{3},{4,7,8},{6}}=>[[1,2,5],[3,7,8],[4],[6]]=>6
{{1,2,5,7},{3},{4,8},{6}}=>[[1,2,5,7],[3,8],[4],[6]]=>6
{{1},{2,3,5,7},{4},{6,8}}=>[[1,3,5,7],[2,8],[4],[6]]=>6
{{1,5,7},{2},{3,4},{6,8}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,4,7},{2},{3,5},{6,8}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,4},{2},{3,8},{5,6,7}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,4,6},{2},{3,8},{5,7}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,4,6},{2},{3,7},{5,8}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1},{2,6},{3,4,7},{5,8}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,6},{2,3,7},{4},{5,8}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,2},{3,6,7},{4,8},{5}}=>[[1,2,7],[3,6],[4,8],[5]]=>5
{{1,2},{3,6},{4,7,8},{5}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,6},{2,3},{4},{5,7,8}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1},{2,6},{3,4},{5,7,8}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1},{2,7},{3,4},{5,6,8}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,7},{2,3},{4},{5,6,8}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,2},{3,7},{4,6,8},{5}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,2},{3,5,8},{4,7},{6}}=>[[1,2,8],[3,5],[4,7],[6]]=>6
{{1,7},{2,3,8},{4,5},{6}}=>[[1,3,8],[2,5],[4,7],[6]]=>6
{{1},{2,5},{3,4,8},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1},{2,4},{3,5,8},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1},{2,4},{3,7},{5,6,8}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1},{2,4},{3,6},{5,7,8}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1},{2,4},{3,6,7},{5,8}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,3},{2,6,7},{4},{5,8}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,3},{2,6},{4},{5,7,8}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,3},{2,7},{4},{5,6,8}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,3},{2,7,8},{4,5},{6}}=>[[1,3,8],[2,5],[4,7],[6]]=>6
{{1,3,8},{2,4,7},{5},{6}}=>[[1,3,7],[2,4,8],[5],[6]]=>6
{{1,4,8},{2,3,7},{5},{6}}=>[[1,3,7],[2,4,8],[5],[6]]=>6
{{1,4,7},{2,3,8},{5},{6}}=>[[1,3,7],[2,4,8],[5],[6]]=>6
{{1,3,7},{2,8},{4,5},{6}}=>[[1,3,7],[2,5],[4,8],[6]]=>6
{{1,3},{2,8},{4},{5,6,7}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,3,6},{2,8},{4},{5,7}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1,3,6},{2,7},{4},{5,8}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1},{2,4,6},{3,7},{5,8}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1},{2,4,6},{3,8},{5,7}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1},{2,4},{3,8},{5,6,7}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1},{2,4,7},{3,5},{6,8}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1},{2,5,7},{3,4},{6,8}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1},{2,8},{3,4,6},{5,7}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,8},{2,3,6},{4},{5,7}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1,2,6},{3,8},{4,7},{5}}=>[[1,2,6],[3,7],[4,8],[5]]=>5
{{1,7},{2,3,6},{4},{5,8}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1},{2,7},{3,4,6},{5,8}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,2},{3,6,8},{4,7},{5}}=>[[1,2,8],[3,6],[4,7],[5]]=>5
{{1,2},{3,5,7},{4,8},{6}}=>[[1,2,7],[3,5],[4,8],[6]]=>6
{{1,2},{3,7},{4,5,8},{6}}=>[[1,2,8],[3,5],[4,7],[6]]=>6
{{1,4,8},{2,7},{3},{5,6}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,3,7},{2,8},{4},{5,6}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,3,7},{2,8},{4,6},{5}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,3,7},{2},{4,5,8},{6}}=>[[1,3,7],[2,5,8],[4],[6]]=>6
{{1,7},{2,3},{4,5,8},{6}}=>[[1,3,8],[2,5],[4,7],[6]]=>6
{{1,7},{2,3,8},{4,6},{5}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,7},{2,3,8},{4},{5,6}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,7,8},{2,5},{3,6},{4}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,7},{2,4,6,8},{3},{5}}=>[[1,4,6,8],[2,7],[3],[5]]=>5
{{1,7},{2,4,5},{3,8},{6}}=>[[1,4,5],[2,7],[3,8],[6]]=>6
{{1,4,6},{2,5},{3},{7,8}}=>[[1,4,6],[2,5],[3,8],[7]]=>7
{{1,5,7,8},{2},{3,6},{4}}=>[[1,5,7,8],[2,6],[3],[4]]=>4
{{1,5,8},{2,7},{3,6},{4}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,8},{2,5,7},{3,6},{4}}=>[[1,5,7],[2,6],[3,8],[4]]=>4
{{1,5,8},{2,6,7},{3},{4}}=>[[1,5,7],[2,6,8],[3],[4]]=>4
{{1,4,5,7},{2},{3,8},{6}}=>[[1,4,5,7],[2,8],[3],[6]]=>6
{{1,3,5},{2,6},{4},{7,8}}=>[[1,3,5],[2,6],[4,8],[7]]=>7
{{1,3,6},{2,8},{4,7},{5}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1,4,6,8},{2},{3,7},{5}}=>[[1,4,6,8],[2,7],[3],[5]]=>5
{{1,8},{2,4,6},{3,7},{5}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,4,8},{2,5},{3},{6,7}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,3,5},{2,8},{4},{6,7}}=>[[1,3,5],[2,7],[4,8],[6]]=>6
{{1,5},{2,3,8},{4},{6,7}}=>[[1,3,8],[2,5],[4,7],[6]]=>6
{{1,8},{2,6},{3,4,7},{5}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,6,8},{2},{3,4,7},{5}}=>[[1,4,7],[2,6,8],[3],[5]]=>5
{{1,6,8},{2,4},{3,7},{5}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,6},{2,3,8},{4,7},{5}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,6},{2,3,7,8},{4},{5}}=>[[1,3,7,8],[2,6],[4],[5]]=>5
{{1,5},{2,3,7},{4,8},{6}}=>[[1,3,7],[2,5],[4,8],[6]]=>6
{{1,5},{2,3,6},{4},{7,8}}=>[[1,3,6],[2,5],[4,8],[7]]=>7
{{1,5,7},{2,4},{3,8},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,6,7},{2,4,8},{3},{5}}=>[[1,4,7],[2,6,8],[3],[5]]=>5
{{1,6,8},{2,5,7},{3},{4}}=>[[1,5,7],[2,6,8],[3],[4]]=>4
{{1,6,8},{2,7},{3,5},{4}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,6,8},{2,7},{3},{4,5}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,6,7},{2,8},{3,4},{5}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,5,7},{2},{3,4,8},{6}}=>[[1,4,7],[2,5,8],[3],[6]]=>6
{{1,7},{2,5},{3,4,8},{6}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,7},{2,6,8},{3,4},{5}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,4,8},{2,3,6},{5},{7}}=>[[1,3,6],[2,4,8],[5],[7]]=>7
{{1,5},{2,4,8},{3,7},{6}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,5},{2,4,7},{3,8},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,5},{2,4,8},{3,6},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,6},{2,4,8},{3,5},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,6},{2,5},{3,4,8},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,6},{2,3,5},{4,8},{7}}=>[[1,3,5],[2,6],[4,8],[7]]=>7
{{1,5},{2,3,6},{4,8},{7}}=>[[1,3,6],[2,5],[4,8],[7]]=>7
{{1,5},{2,6},{3,4,8},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,4,8},{2,7},{3,6},{5}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,4,7},{2,8},{3,6},{5}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,4,6},{2,8},{3,7},{5}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,4,7},{2,8},{3,5},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,5},{2,8},{3,4,7},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,5},{2,3,8},{4,7},{6}}=>[[1,3,8],[2,5],[4,7],[6]]=>6
{{1,2,5},{3,8},{4,7},{6}}=>[[1,2,5],[3,7],[4,8],[6]]=>6
{{1,5},{2,7},{3,4,8},{6}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,4,8},{2,7},{3,5},{6}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,7},{2,6},{3,4,8},{5}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,7},{2,3,6},{4,8},{5}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1,8},{2,3,6},{4,7},{5}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1,8},{2,3,5},{4,7},{6}}=>[[1,3,5],[2,7],[4,8],[6]]=>6
{{1,8},{2,5},{3,4,7},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,8},{2,4,7},{3,5},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,8},{2,4,7},{3,6},{5}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,7},{2,4,8},{3,6},{5}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,3,5},{2,8},{4,7},{6}}=>[[1,3,5],[2,7],[4,8],[6]]=>6
{{1,3,8},{2,7},{4,6},{5}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,6},{2,4,8},{3,7},{5}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,6},{2,4,7},{3,8},{5}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,7},{2,4,6},{3,8},{5}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,7},{2,4,8},{3,5},{6}}=>[[1,4,8],[2,5],[3,7],[6]]=>6
{{1,7},{2,3,5},{4,8},{6}}=>[[1,3,5],[2,7],[4,8],[6]]=>6
{{1,2,7},{3,8},{4,6},{5}}=>[[1,2,7],[3,6],[4,8],[5]]=>5
{{1,7},{2,8},{3,4,6},{5}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,6},{2,8},{3,4,7},{5}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,6},{2,3,7},{4,8},{5}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,6},{2,7},{3,4,8},{5}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,3,5},{2},{4,6,8},{7}}=>[[1,3,5],[2,6,8],[4],[7]]=>7
{{1,3},{2,4,6,8},{5},{7}}=>[[1,3,6,8],[2,4],[5],[7]]=>7
{{1},{2,4,6,8},{3},{5,7}}=>[[1,4,6,8],[2,7],[3],[5]]=>5
{{1,3},{2},{4,6,8},{5,7}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,3,6},{2},{4,8},{5,7}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1,3,6},{2},{4,7},{5,8}}=>[[1,3,6],[2,7],[4,8],[5]]=>5
{{1,3,5},{2},{4,7},{6,8}}=>[[1,3,5],[2,7],[4,8],[6]]=>6
{{1,3,5,7},{2},{4,6},{8}}=>[[1,3,5,7],[2,6],[4],[8]]=>8
{{1,3,7},{2},{4,6,8},{5}}=>[[1,3,7],[2,6,8],[4],[5]]=>5
{{1,3,7},{2},{4,6},{5,8}}=>[[1,3,7],[2,6],[4,8],[5]]=>5
{{1,3,5,7},{2},{4,8},{6}}=>[[1,3,5,7],[2,8],[4],[6]]=>6
{{1,3},{2,4,8},{5,7},{6}}=>[[1,3,8],[2,4],[5,7],[6]]=>6
{{1},{2,4,8},{3,5,7},{6}}=>[[1,4,7],[2,5,8],[3],[6]]=>6
{{1,4},{2,8},{3,5,7},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,4},{2,5,7},{3,8},{6}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,3},{2,5,7},{4,8},{6}}=>[[1,3,7],[2,5],[4,8],[6]]=>6
{{1,3},{2,7},{4,6,8},{5}}=>[[1,3,8],[2,6],[4,7],[5]]=>5
{{1,3,7},{2,4,6},{5},{8}}=>[[1,3,6],[2,4,7],[5],[8]]=>8
{{1,7},{2,4,6},{3},{5,8}}=>[[1,4,6],[2,7],[3,8],[5]]=>5
{{1,5,7},{2,4,8},{3},{6}}=>[[1,4,7],[2,5,8],[3],[6]]=>6
{{1},{2,8},{3,5,7},{4,6}}=>[[1,5,7],[2,6],[3,8],[4]]=>4
{{1,7},{2,4,6},{3,5},{8}}=>[[1,4,6],[2,5],[3,7],[8]]=>8
{{1,4,7},{2,6},{3,5},{8}}=>[[1,4,7],[2,5],[3,6],[8]]=>8
{{1},{2,5,8},{3,7},{4,6}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1},{2,5,8},{3,6},{4,7}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1},{2,4,8},{3,6},{5,7}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1},{2,4,6,8},{3,5},{7}}=>[[1,4,6,8],[2,5],[3],[7]]=>7
{{1,4},{2,6,8},{3,5},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,4},{2,5},{3,6,8},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,3},{2,5},{4,6,8},{7}}=>[[1,3,8],[2,5],[4,6],[7]]=>7
{{1,5},{2,4,6,8},{3},{7}}=>[[1,4,6,8],[2,5],[3],[7]]=>7
{{1,5},{2,4},{3,6,8},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1},{2,6,8},{3,5,7},{4}}=>[[1,5,7],[2,6,8],[3],[4]]=>4
{{1,6},{2,8},{3,5,7},{4}}=>[[1,5,7],[2,6],[3,8],[4]]=>4
{{1,6},{2,4,8},{3},{5,7}}=>[[1,4,8],[2,6],[3,7],[5]]=>5
{{1,6},{2,4,7},{3},{5,8}}=>[[1,4,7],[2,6],[3,8],[5]]=>5
{{1,5},{2,4,7},{3},{6,8}}=>[[1,4,7],[2,5],[3,8],[6]]=>6
{{1,5,7},{2,4,6},{3},{8}}=>[[1,4,6],[2,5,7],[3],[8]]=>8
{{1,5,7},{2,4},{3,6},{8}}=>[[1,4,7],[2,5],[3,6],[8]]=>8
{{1},{2,6,8},{3,5},{4,7}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1},{2,4,6,8},{3,7},{5}}=>[[1,4,6,8],[2,7],[3],[5]]=>5
{{1,6},{2,7},{3,5,8},{4}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,3,5},{2,7},{4},{6,8}}=>[[1,3,5],[2,7],[4,8],[6]]=>6
{{1,7},{2,6,8},{3,5},{4}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,7},{2,6},{3,5,8},{4}}=>[[1,5,8],[2,6],[3,7],[4]]=>4
{{1,2},{3,4,6},{5,8},{7}}=>[[1,2,6],[3,4],[5,8],[7]]=>7
{{1,2},{3,6},{4,5,8},{7}}=>[[1,2,8],[3,5],[4,6],[7]]=>7
{{1,2},{3,5,6},{4,8},{7}}=>[[1,2,6],[3,5],[4,8],[7]]=>7
{{1,2,5,6},{3},{4,8},{7}}=>[[1,2,5,6],[3,8],[4],[7]]=>7
{{1,2,6},{3},{4,5,8},{7}}=>[[1,2,6],[3,5,8],[4],[7]]=>7
{{1,6},{2,3},{4,5,8},{7}}=>[[1,3,8],[2,5],[4,6],[7]]=>7
{{1,5,6},{2,3},{4,8},{7}}=>[[1,3,6],[2,5],[4,8],[7]]=>7
{{1,5,6},{2,3,8},{4},{7}}=>[[1,3,6],[2,5,8],[4],[7]]=>7
{{1,5,6},{2,8},{3,4},{7}}=>[[1,4,6],[2,5],[3,8],[7]]=>7
{{1,5},{2,8},{3,4,6},{7}}=>[[1,4,6],[2,5],[3,8],[7]]=>7
{{1,5},{2,3,8},{4,6},{7}}=>[[1,3,8],[2,5],[4,6],[7]]=>7
{{1,6},{2,3,5,8},{4},{7}}=>[[1,3,5,8],[2,6],[4],[7]]=>7
{{1,2,5},{3,8},{4,6},{7}}=>[[1,2,5],[3,6],[4,8],[7]]=>7
{{1,2,4},{3,6},{5},{7,8}}=>[[1,2,4],[3,6],[5,8],[7]]=>7
{{1,2,4,6},{3},{5,8},{7}}=>[[1,2,4,6],[3,8],[5],[7]]=>7
{{1,2,4},{3,8},{5,7},{6}}=>[[1,2,4],[3,7],[5,8],[6]]=>6
{{1,2,4},{3,8},{5},{6,7}}=>[[1,2,4],[3,7],[5,8],[6]]=>6
{{1,4},{2,3,8},{5},{6,7}}=>[[1,3,8],[2,4],[5,7],[6]]=>6
{{1,3,4},{2,8},{5},{6,7}}=>[[1,3,4],[2,7],[5,8],[6]]=>6
{{1,3,4},{2,8},{5,7},{6}}=>[[1,3,4],[2,7],[5,8],[6]]=>6
{{1,4},{2,3,8},{5,7},{6}}=>[[1,3,8],[2,4],[5,7],[6]]=>6
{{1,4,6},{2,3},{5,8},{7}}=>[[1,3,6],[2,4],[5,8],[7]]=>7
{{1,4},{2,3,6},{5},{7,8}}=>[[1,3,6],[2,4],[5,8],[7]]=>7
{{1,4},{2,3,6,8},{5},{7}}=>[[1,3,6,8],[2,4],[5],[7]]=>7
{{1,4},{2,3,6},{5,8},{7}}=>[[1,3,6],[2,4],[5,8],[7]]=>7
{{1,8},{2,4,5},{3,7},{6}}=>[[1,4,5],[2,7],[3,8],[6]]=>6
{{1,3,8},{2,6},{4,5},{7}}=>[[1,3,8],[2,5],[4,6],[7]]=>7
{{1,3,4},{2,6},{5},{7,8}}=>[[1,3,4],[2,6],[5,8],[7]]=>7
{{1,6},{2,5,8},{3,4},{7}}=>[[1,4,8],[2,5],[3,6],[7]]=>7
{{1,6},{2,4,5},{3,8},{7}}=>[[1,4,5],[2,6],[3,8],[7]]=>7
{{1,4,5},{2,8},{3,6},{7}}=>[[1,4,5],[2,6],[3,8],[7]]=>7
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Description
The first entry in the last row of a standard tableau.
For the last entry in the first row, see St000734The last entry in the first row of a standard tableau..
For the last entry in the first row, see St000734The last entry in the first row of a standard tableau..
Map
Standard tableau associated to a set partition
Description
Sends a set partition to the associated standard tableau.
The $j$th column of the standard tableau associated to a set partition is the set of $j$th smallest elements of its blocks arranged in increassing order.
The $j$th column of the standard tableau associated to a set partition is the set of $j$th smallest elements of its blocks arranged in increassing order.
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