Identifier
-
Mp00070:
Permutations
—Robinson-Schensted recording tableau⟶
Standard tableaux
Mp00294: Standard tableaux —peak composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000010: Integer partitions ⟶ ℤ
Values
=>
Cc0007;cc-rep-1
Cc0002;cc-rep
[1]=>[[1]]=>[1]=>[1]=>1
[1,2]=>[[1,2]]=>[2]=>[2]=>1
[2,1]=>[[1],[2]]=>[2]=>[2]=>1
[1,2,3]=>[[1,2,3]]=>[3]=>[3]=>1
[1,3,2]=>[[1,2],[3]]=>[2,1]=>[2,1]=>2
[2,1,3]=>[[1,3],[2]]=>[3]=>[3]=>1
[2,3,1]=>[[1,2],[3]]=>[2,1]=>[2,1]=>2
[3,1,2]=>[[1,3],[2]]=>[3]=>[3]=>1
[3,2,1]=>[[1],[2],[3]]=>[3]=>[3]=>1
[1,2,3,4]=>[[1,2,3,4]]=>[4]=>[4]=>1
[1,2,4,3]=>[[1,2,3],[4]]=>[3,1]=>[3,1]=>2
[1,3,2,4]=>[[1,2,4],[3]]=>[2,2]=>[2,2]=>2
[1,3,4,2]=>[[1,2,3],[4]]=>[3,1]=>[3,1]=>2
[1,4,2,3]=>[[1,2,4],[3]]=>[2,2]=>[2,2]=>2
[1,4,3,2]=>[[1,2],[3],[4]]=>[2,2]=>[2,2]=>2
[2,1,3,4]=>[[1,3,4],[2]]=>[4]=>[4]=>1
[2,1,4,3]=>[[1,3],[2,4]]=>[3,1]=>[3,1]=>2
[2,3,1,4]=>[[1,2,4],[3]]=>[2,2]=>[2,2]=>2
[2,3,4,1]=>[[1,2,3],[4]]=>[3,1]=>[3,1]=>2
[2,4,1,3]=>[[1,2],[3,4]]=>[2,2]=>[2,2]=>2
[2,4,3,1]=>[[1,2],[3],[4]]=>[2,2]=>[2,2]=>2
[3,1,2,4]=>[[1,3,4],[2]]=>[4]=>[4]=>1
[3,1,4,2]=>[[1,3],[2,4]]=>[3,1]=>[3,1]=>2
[3,2,1,4]=>[[1,4],[2],[3]]=>[4]=>[4]=>1
[3,2,4,1]=>[[1,3],[2],[4]]=>[3,1]=>[3,1]=>2
[3,4,1,2]=>[[1,2],[3,4]]=>[2,2]=>[2,2]=>2
[3,4,2,1]=>[[1,2],[3],[4]]=>[2,2]=>[2,2]=>2
[4,1,2,3]=>[[1,3,4],[2]]=>[4]=>[4]=>1
[4,1,3,2]=>[[1,3],[2],[4]]=>[3,1]=>[3,1]=>2
[4,2,1,3]=>[[1,4],[2],[3]]=>[4]=>[4]=>1
[4,2,3,1]=>[[1,3],[2],[4]]=>[3,1]=>[3,1]=>2
[4,3,1,2]=>[[1,4],[2],[3]]=>[4]=>[4]=>1
[4,3,2,1]=>[[1],[2],[3],[4]]=>[4]=>[4]=>1
[1,2,3,4,5]=>[[1,2,3,4,5]]=>[5]=>[5]=>1
[1,2,3,5,4]=>[[1,2,3,4],[5]]=>[4,1]=>[4,1]=>2
[1,2,4,3,5]=>[[1,2,3,5],[4]]=>[3,2]=>[3,2]=>2
[1,2,4,5,3]=>[[1,2,3,4],[5]]=>[4,1]=>[4,1]=>2
[1,2,5,3,4]=>[[1,2,3,5],[4]]=>[3,2]=>[3,2]=>2
[1,2,5,4,3]=>[[1,2,3],[4],[5]]=>[3,2]=>[3,2]=>2
[1,3,2,4,5]=>[[1,2,4,5],[3]]=>[2,3]=>[3,2]=>2
[1,3,2,5,4]=>[[1,2,4],[3,5]]=>[2,2,1]=>[2,2,1]=>3
[1,3,4,2,5]=>[[1,2,3,5],[4]]=>[3,2]=>[3,2]=>2
[1,3,4,5,2]=>[[1,2,3,4],[5]]=>[4,1]=>[4,1]=>2
[1,3,5,2,4]=>[[1,2,3],[4,5]]=>[3,2]=>[3,2]=>2
[1,3,5,4,2]=>[[1,2,3],[4],[5]]=>[3,2]=>[3,2]=>2
[1,4,2,3,5]=>[[1,2,4,5],[3]]=>[2,3]=>[3,2]=>2
[1,4,2,5,3]=>[[1,2,4],[3,5]]=>[2,2,1]=>[2,2,1]=>3
[1,4,3,2,5]=>[[1,2,5],[3],[4]]=>[2,3]=>[3,2]=>2
[1,4,3,5,2]=>[[1,2,4],[3],[5]]=>[2,2,1]=>[2,2,1]=>3
[1,4,5,2,3]=>[[1,2,3],[4,5]]=>[3,2]=>[3,2]=>2
[1,4,5,3,2]=>[[1,2,3],[4],[5]]=>[3,2]=>[3,2]=>2
[1,5,2,3,4]=>[[1,2,4,5],[3]]=>[2,3]=>[3,2]=>2
[1,5,2,4,3]=>[[1,2,4],[3],[5]]=>[2,2,1]=>[2,2,1]=>3
[1,5,3,2,4]=>[[1,2,5],[3],[4]]=>[2,3]=>[3,2]=>2
[1,5,3,4,2]=>[[1,2,4],[3],[5]]=>[2,2,1]=>[2,2,1]=>3
[1,5,4,2,3]=>[[1,2,5],[3],[4]]=>[2,3]=>[3,2]=>2
[1,5,4,3,2]=>[[1,2],[3],[4],[5]]=>[2,3]=>[3,2]=>2
[2,1,3,4,5]=>[[1,3,4,5],[2]]=>[5]=>[5]=>1
[2,1,3,5,4]=>[[1,3,4],[2,5]]=>[4,1]=>[4,1]=>2
[2,1,4,3,5]=>[[1,3,5],[2,4]]=>[3,2]=>[3,2]=>2
[2,1,4,5,3]=>[[1,3,4],[2,5]]=>[4,1]=>[4,1]=>2
[2,1,5,3,4]=>[[1,3,5],[2,4]]=>[3,2]=>[3,2]=>2
[2,1,5,4,3]=>[[1,3],[2,4],[5]]=>[3,2]=>[3,2]=>2
[2,3,1,4,5]=>[[1,2,4,5],[3]]=>[2,3]=>[3,2]=>2
[2,3,1,5,4]=>[[1,2,4],[3,5]]=>[2,2,1]=>[2,2,1]=>3
[2,3,4,1,5]=>[[1,2,3,5],[4]]=>[3,2]=>[3,2]=>2
[2,3,4,5,1]=>[[1,2,3,4],[5]]=>[4,1]=>[4,1]=>2
[2,3,5,1,4]=>[[1,2,3],[4,5]]=>[3,2]=>[3,2]=>2
[2,3,5,4,1]=>[[1,2,3],[4],[5]]=>[3,2]=>[3,2]=>2
[2,4,1,3,5]=>[[1,2,5],[3,4]]=>[2,3]=>[3,2]=>2
[2,4,1,5,3]=>[[1,2,4],[3,5]]=>[2,2,1]=>[2,2,1]=>3
[2,4,3,1,5]=>[[1,2,5],[3],[4]]=>[2,3]=>[3,2]=>2
[2,4,3,5,1]=>[[1,2,4],[3],[5]]=>[2,2,1]=>[2,2,1]=>3
[2,4,5,1,3]=>[[1,2,3],[4,5]]=>[3,2]=>[3,2]=>2
[2,4,5,3,1]=>[[1,2,3],[4],[5]]=>[3,2]=>[3,2]=>2
[2,5,1,3,4]=>[[1,2,5],[3,4]]=>[2,3]=>[3,2]=>2
[2,5,1,4,3]=>[[1,2],[3,4],[5]]=>[2,2,1]=>[2,2,1]=>3
[2,5,3,1,4]=>[[1,2,5],[3],[4]]=>[2,3]=>[3,2]=>2
[2,5,3,4,1]=>[[1,2,4],[3],[5]]=>[2,2,1]=>[2,2,1]=>3
[2,5,4,1,3]=>[[1,2],[3,5],[4]]=>[2,3]=>[3,2]=>2
[2,5,4,3,1]=>[[1,2],[3],[4],[5]]=>[2,3]=>[3,2]=>2
[3,1,2,4,5]=>[[1,3,4,5],[2]]=>[5]=>[5]=>1
[3,1,2,5,4]=>[[1,3,4],[2,5]]=>[4,1]=>[4,1]=>2
[3,1,4,2,5]=>[[1,3,5],[2,4]]=>[3,2]=>[3,2]=>2
[3,1,4,5,2]=>[[1,3,4],[2,5]]=>[4,1]=>[4,1]=>2
[3,1,5,2,4]=>[[1,3,5],[2,4]]=>[3,2]=>[3,2]=>2
[3,1,5,4,2]=>[[1,3],[2,4],[5]]=>[3,2]=>[3,2]=>2
[3,2,1,4,5]=>[[1,4,5],[2],[3]]=>[5]=>[5]=>1
[3,2,1,5,4]=>[[1,4],[2,5],[3]]=>[4,1]=>[4,1]=>2
[3,2,4,1,5]=>[[1,3,5],[2],[4]]=>[3,2]=>[3,2]=>2
[3,2,4,5,1]=>[[1,3,4],[2],[5]]=>[4,1]=>[4,1]=>2
[3,2,5,1,4]=>[[1,3],[2,5],[4]]=>[3,2]=>[3,2]=>2
[3,2,5,4,1]=>[[1,3],[2,4],[5]]=>[3,2]=>[3,2]=>2
[3,4,1,2,5]=>[[1,2,5],[3,4]]=>[2,3]=>[3,2]=>2
[3,4,1,5,2]=>[[1,2,4],[3,5]]=>[2,2,1]=>[2,2,1]=>3
[3,4,2,1,5]=>[[1,2,5],[3],[4]]=>[2,3]=>[3,2]=>2
[3,4,2,5,1]=>[[1,2,4],[3],[5]]=>[2,2,1]=>[2,2,1]=>3
[3,4,5,1,2]=>[[1,2,3],[4,5]]=>[3,2]=>[3,2]=>2
[3,4,5,2,1]=>[[1,2,3],[4],[5]]=>[3,2]=>[3,2]=>2
[3,5,1,2,4]=>[[1,2,5],[3,4]]=>[2,3]=>[3,2]=>2
[3,5,1,4,2]=>[[1,2],[3,4],[5]]=>[2,2,1]=>[2,2,1]=>3
[3,5,2,1,4]=>[[1,2],[3,5],[4]]=>[2,3]=>[3,2]=>2
[3,5,2,4,1]=>[[1,2],[3,4],[5]]=>[2,2,1]=>[2,2,1]=>3
[3,5,4,1,2]=>[[1,2],[3,5],[4]]=>[2,3]=>[3,2]=>2
[3,5,4,2,1]=>[[1,2],[3],[4],[5]]=>[2,3]=>[3,2]=>2
[4,1,2,3,5]=>[[1,3,4,5],[2]]=>[5]=>[5]=>1
[4,1,2,5,3]=>[[1,3,4],[2,5]]=>[4,1]=>[4,1]=>2
[4,1,3,2,5]=>[[1,3,5],[2],[4]]=>[3,2]=>[3,2]=>2
[4,1,3,5,2]=>[[1,3,4],[2],[5]]=>[4,1]=>[4,1]=>2
[4,1,5,2,3]=>[[1,3,5],[2,4]]=>[3,2]=>[3,2]=>2
[4,1,5,3,2]=>[[1,3],[2,4],[5]]=>[3,2]=>[3,2]=>2
[4,2,1,3,5]=>[[1,4,5],[2],[3]]=>[5]=>[5]=>1
[4,2,1,5,3]=>[[1,4],[2,5],[3]]=>[4,1]=>[4,1]=>2
[4,2,3,1,5]=>[[1,3,5],[2],[4]]=>[3,2]=>[3,2]=>2
[4,2,3,5,1]=>[[1,3,4],[2],[5]]=>[4,1]=>[4,1]=>2
[4,2,5,1,3]=>[[1,3],[2,5],[4]]=>[3,2]=>[3,2]=>2
[4,2,5,3,1]=>[[1,3],[2,4],[5]]=>[3,2]=>[3,2]=>2
[4,3,1,2,5]=>[[1,4,5],[2],[3]]=>[5]=>[5]=>1
[4,3,1,5,2]=>[[1,4],[2,5],[3]]=>[4,1]=>[4,1]=>2
[4,3,2,1,5]=>[[1,5],[2],[3],[4]]=>[5]=>[5]=>1
[4,3,2,5,1]=>[[1,4],[2],[3],[5]]=>[4,1]=>[4,1]=>2
[4,3,5,1,2]=>[[1,3],[2,5],[4]]=>[3,2]=>[3,2]=>2
[4,3,5,2,1]=>[[1,3],[2],[4],[5]]=>[3,2]=>[3,2]=>2
[4,5,1,2,3]=>[[1,2,5],[3,4]]=>[2,3]=>[3,2]=>2
[4,5,1,3,2]=>[[1,2],[3,4],[5]]=>[2,2,1]=>[2,2,1]=>3
[4,5,2,1,3]=>[[1,2],[3,5],[4]]=>[2,3]=>[3,2]=>2
[4,5,2,3,1]=>[[1,2],[3,4],[5]]=>[2,2,1]=>[2,2,1]=>3
[4,5,3,1,2]=>[[1,2],[3,5],[4]]=>[2,3]=>[3,2]=>2
[4,5,3,2,1]=>[[1,2],[3],[4],[5]]=>[2,3]=>[3,2]=>2
[5,1,2,3,4]=>[[1,3,4,5],[2]]=>[5]=>[5]=>1
[5,1,2,4,3]=>[[1,3,4],[2],[5]]=>[4,1]=>[4,1]=>2
[5,1,3,2,4]=>[[1,3,5],[2],[4]]=>[3,2]=>[3,2]=>2
[5,1,3,4,2]=>[[1,3,4],[2],[5]]=>[4,1]=>[4,1]=>2
[5,1,4,2,3]=>[[1,3,5],[2],[4]]=>[3,2]=>[3,2]=>2
[5,1,4,3,2]=>[[1,3],[2],[4],[5]]=>[3,2]=>[3,2]=>2
[5,2,1,3,4]=>[[1,4,5],[2],[3]]=>[5]=>[5]=>1
[5,2,1,4,3]=>[[1,4],[2,5],[3]]=>[4,1]=>[4,1]=>2
[5,2,3,1,4]=>[[1,3,5],[2],[4]]=>[3,2]=>[3,2]=>2
[5,2,3,4,1]=>[[1,3,4],[2],[5]]=>[4,1]=>[4,1]=>2
[5,2,4,1,3]=>[[1,3],[2,5],[4]]=>[3,2]=>[3,2]=>2
[5,2,4,3,1]=>[[1,3],[2],[4],[5]]=>[3,2]=>[3,2]=>2
[5,3,1,2,4]=>[[1,4,5],[2],[3]]=>[5]=>[5]=>1
[5,3,1,4,2]=>[[1,4],[2,5],[3]]=>[4,1]=>[4,1]=>2
[5,3,2,1,4]=>[[1,5],[2],[3],[4]]=>[5]=>[5]=>1
[5,3,2,4,1]=>[[1,4],[2],[3],[5]]=>[4,1]=>[4,1]=>2
[5,3,4,1,2]=>[[1,3],[2,5],[4]]=>[3,2]=>[3,2]=>2
[5,3,4,2,1]=>[[1,3],[2],[4],[5]]=>[3,2]=>[3,2]=>2
[5,4,1,2,3]=>[[1,4,5],[2],[3]]=>[5]=>[5]=>1
[5,4,1,3,2]=>[[1,4],[2],[3],[5]]=>[4,1]=>[4,1]=>2
[5,4,2,1,3]=>[[1,5],[2],[3],[4]]=>[5]=>[5]=>1
[5,4,2,3,1]=>[[1,4],[2],[3],[5]]=>[4,1]=>[4,1]=>2
[5,4,3,1,2]=>[[1,5],[2],[3],[4]]=>[5]=>[5]=>1
[5,4,3,2,1]=>[[1],[2],[3],[4],[5]]=>[5]=>[5]=>1
[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]=>[6]=>[6]=>1
[1,2,3,4,6,5]=>[[1,2,3,4,5],[6]]=>[5,1]=>[5,1]=>2
[1,2,3,5,4,6]=>[[1,2,3,4,6],[5]]=>[4,2]=>[4,2]=>2
[1,2,3,5,6,4]=>[[1,2,3,4,5],[6]]=>[5,1]=>[5,1]=>2
[1,2,3,6,4,5]=>[[1,2,3,4,6],[5]]=>[4,2]=>[4,2]=>2
[1,2,3,6,5,4]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[1,2,4,3,5,6]=>[[1,2,3,5,6],[4]]=>[3,3]=>[3,3]=>2
[1,2,4,3,6,5]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[1,2,4,5,3,6]=>[[1,2,3,4,6],[5]]=>[4,2]=>[4,2]=>2
[1,2,4,5,6,3]=>[[1,2,3,4,5],[6]]=>[5,1]=>[5,1]=>2
[1,2,4,6,3,5]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[1,2,4,6,5,3]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[1,2,5,3,4,6]=>[[1,2,3,5,6],[4]]=>[3,3]=>[3,3]=>2
[1,2,5,3,6,4]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[1,2,5,4,3,6]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[1,2,5,4,6,3]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,2,5,6,3,4]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[1,2,5,6,4,3]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[1,2,6,3,4,5]=>[[1,2,3,5,6],[4]]=>[3,3]=>[3,3]=>2
[1,2,6,3,5,4]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,2,6,4,3,5]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[1,2,6,4,5,3]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,2,6,5,3,4]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[1,2,6,5,4,3]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[1,3,2,4,5,6]=>[[1,2,4,5,6],[3]]=>[2,4]=>[4,2]=>2
[1,3,2,4,6,5]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[1,3,2,5,4,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[1,3,2,5,6,4]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[1,3,2,6,4,5]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[1,3,2,6,5,4]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,3,4,2,5,6]=>[[1,2,3,5,6],[4]]=>[3,3]=>[3,3]=>2
[1,3,4,2,6,5]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[1,3,4,5,2,6]=>[[1,2,3,4,6],[5]]=>[4,2]=>[4,2]=>2
[1,3,4,5,6,2]=>[[1,2,3,4,5],[6]]=>[5,1]=>[5,1]=>2
[1,3,4,6,2,5]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[1,3,4,6,5,2]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[1,3,5,2,4,6]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[1,3,5,2,6,4]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[1,3,5,4,2,6]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[1,3,5,4,6,2]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,3,5,6,2,4]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[1,3,5,6,4,2]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[1,3,6,2,4,5]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[1,3,6,2,5,4]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,3,6,4,2,5]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[1,3,6,4,5,2]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,3,6,5,2,4]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[1,3,6,5,4,2]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[1,4,2,3,5,6]=>[[1,2,4,5,6],[3]]=>[2,4]=>[4,2]=>2
[1,4,2,3,6,5]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[1,4,2,5,3,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[1,4,2,5,6,3]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[1,4,2,6,3,5]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[1,4,2,6,5,3]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,4,3,2,5,6]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[1,4,3,2,6,5]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[1,4,3,5,2,6]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,4,3,5,6,2]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,4,3,6,2,5]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,4,3,6,5,2]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,4,5,2,3,6]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[1,4,5,2,6,3]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[1,4,5,3,2,6]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[1,4,5,3,6,2]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,4,5,6,2,3]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[1,4,5,6,3,2]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[1,4,6,2,3,5]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[1,4,6,2,5,3]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,4,6,3,2,5]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[1,4,6,3,5,2]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,4,6,5,2,3]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[1,4,6,5,3,2]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[1,5,2,3,4,6]=>[[1,2,4,5,6],[3]]=>[2,4]=>[4,2]=>2
[1,5,2,3,6,4]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[1,5,2,4,3,6]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,5,2,4,6,3]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,5,2,6,3,4]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[1,5,2,6,4,3]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,5,3,2,4,6]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[1,5,3,2,6,4]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[1,5,3,4,2,6]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,5,3,4,6,2]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,5,3,6,2,4]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,5,3,6,4,2]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,5,4,2,3,6]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[1,5,4,2,6,3]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[1,5,4,3,2,6]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[1,5,4,3,6,2]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,5,4,6,2,3]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,5,4,6,3,2]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,5,6,2,3,4]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[1,5,6,2,4,3]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,5,6,3,2,4]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[1,5,6,3,4,2]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[1,5,6,4,2,3]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[1,5,6,4,3,2]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[1,6,2,3,4,5]=>[[1,2,4,5,6],[3]]=>[2,4]=>[4,2]=>2
[1,6,2,3,5,4]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,6,2,4,3,5]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,6,2,4,5,3]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,6,2,5,3,4]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,6,2,5,4,3]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,6,3,2,4,5]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[1,6,3,2,5,4]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[1,6,3,4,2,5]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,6,3,4,5,2]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,6,3,5,2,4]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,6,3,5,4,2]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,6,4,2,3,5]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[1,6,4,2,5,3]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[1,6,4,3,2,5]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[1,6,4,3,5,2]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,6,4,5,2,3]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[1,6,4,5,3,2]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[1,6,5,2,3,4]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[1,6,5,2,4,3]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,6,5,3,2,4]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[1,6,5,3,4,2]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[1,6,5,4,2,3]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[1,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6]]=>[2,4]=>[4,2]=>2
[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]=>[6]=>[6]=>1
[2,1,3,4,6,5]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[2,1,3,5,4,6]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[2,1,3,5,6,4]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[2,1,3,6,4,5]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[2,1,3,6,5,4]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[2,1,4,3,5,6]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]]=>[3,2,1]=>[3,2,1]=>3
[2,1,4,5,3,6]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[2,1,4,5,6,3]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[2,1,4,6,3,5]=>[[1,3,4],[2,5,6]]=>[4,2]=>[4,2]=>2
[2,1,4,6,5,3]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[2,1,5,3,4,6]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[2,1,5,3,6,4]=>[[1,3,5],[2,4,6]]=>[3,2,1]=>[3,2,1]=>3
[2,1,5,4,3,6]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[2,1,5,4,6,3]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,1,5,6,3,4]=>[[1,3,4],[2,5,6]]=>[4,2]=>[4,2]=>2
[2,1,5,6,4,3]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[2,1,6,3,4,5]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[2,1,6,3,5,4]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,1,6,4,3,5]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[2,1,6,4,5,3]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,1,6,5,3,4]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[2,1,6,5,4,3]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[2,3,1,4,5,6]=>[[1,2,4,5,6],[3]]=>[2,4]=>[4,2]=>2
[2,3,1,4,6,5]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[2,3,1,5,4,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[2,3,1,5,6,4]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[2,3,1,6,4,5]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[2,3,1,6,5,4]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,3,4,1,5,6]=>[[1,2,3,5,6],[4]]=>[3,3]=>[3,3]=>2
[2,3,4,1,6,5]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[2,3,4,5,1,6]=>[[1,2,3,4,6],[5]]=>[4,2]=>[4,2]=>2
[2,3,4,5,6,1]=>[[1,2,3,4,5],[6]]=>[5,1]=>[5,1]=>2
[2,3,4,6,1,5]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[2,3,4,6,5,1]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[2,3,5,1,4,6]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[2,3,5,1,6,4]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[2,3,5,4,1,6]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[2,3,5,4,6,1]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,3,5,6,1,4]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[2,3,5,6,4,1]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[2,3,6,1,4,5]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[2,3,6,1,5,4]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,3,6,4,1,5]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[2,3,6,4,5,1]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,3,6,5,1,4]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[2,3,6,5,4,1]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[2,4,1,3,5,6]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[2,4,1,3,6,5]=>[[1,2,5],[3,4,6]]=>[2,3,1]=>[3,2,1]=>3
[2,4,1,5,3,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[2,4,1,5,6,3]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[2,4,1,6,3,5]=>[[1,2,4],[3,5,6]]=>[2,2,2]=>[2,2,2]=>3
[2,4,1,6,5,3]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,4,3,1,5,6]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[2,4,3,1,6,5]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[2,4,3,5,1,6]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,4,3,5,6,1]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,4,3,6,1,5]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,4,3,6,5,1]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,4,5,1,3,6]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[2,4,5,1,6,3]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[2,4,5,3,1,6]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[2,4,5,3,6,1]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,4,5,6,1,3]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[2,4,5,6,3,1]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[2,4,6,1,3,5]=>[[1,2,3],[4,5,6]]=>[3,3]=>[3,3]=>2
[2,4,6,1,5,3]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,4,6,3,1,5]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[2,4,6,3,5,1]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,4,6,5,1,3]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[2,4,6,5,3,1]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[2,5,1,3,4,6]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[2,5,1,3,6,4]=>[[1,2,5],[3,4,6]]=>[2,3,1]=>[3,2,1]=>3
[2,5,1,4,3,6]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,5,1,4,6,3]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,5,1,6,3,4]=>[[1,2,4],[3,5,6]]=>[2,2,2]=>[2,2,2]=>3
[2,5,1,6,4,3]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,5,3,1,4,6]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[2,5,3,1,6,4]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[2,5,3,4,1,6]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,5,3,4,6,1]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,5,3,6,1,4]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,5,3,6,4,1]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,5,4,1,3,6]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[2,5,4,1,6,3]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[2,5,4,3,1,6]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[2,5,4,3,6,1]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,5,4,6,1,3]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,5,4,6,3,1]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,5,6,1,3,4]=>[[1,2,3],[4,5,6]]=>[3,3]=>[3,3]=>2
[2,5,6,1,4,3]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,5,6,3,1,4]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[2,5,6,3,4,1]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[2,5,6,4,1,3]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[2,5,6,4,3,1]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[2,6,1,3,4,5]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[2,6,1,3,5,4]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,6,1,4,3,5]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,6,1,4,5,3]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,6,1,5,3,4]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,6,1,5,4,3]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,6,3,1,4,5]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[2,6,3,1,5,4]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[2,6,3,4,1,5]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,6,3,4,5,1]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,6,3,5,1,4]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,6,3,5,4,1]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,6,4,1,3,5]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[2,6,4,1,5,3]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[2,6,4,3,1,5]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[2,6,4,3,5,1]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,6,4,5,1,3]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[2,6,4,5,3,1]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[2,6,5,1,3,4]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[2,6,5,1,4,3]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,6,5,3,1,4]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[2,6,5,3,4,1]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[2,6,5,4,1,3]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[2,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6]]=>[2,4]=>[4,2]=>2
[3,1,2,4,5,6]=>[[1,3,4,5,6],[2]]=>[6]=>[6]=>1
[3,1,2,4,6,5]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[3,1,2,5,4,6]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[3,1,2,5,6,4]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[3,1,2,6,4,5]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[3,1,2,6,5,4]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[3,1,4,2,5,6]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[3,1,4,2,6,5]=>[[1,3,5],[2,4,6]]=>[3,2,1]=>[3,2,1]=>3
[3,1,4,5,2,6]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[3,1,4,5,6,2]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[3,1,4,6,2,5]=>[[1,3,4],[2,5,6]]=>[4,2]=>[4,2]=>2
[3,1,4,6,5,2]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[3,1,5,2,4,6]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[3,1,5,2,6,4]=>[[1,3,5],[2,4,6]]=>[3,2,1]=>[3,2,1]=>3
[3,1,5,4,2,6]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[3,1,5,4,6,2]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,1,5,6,2,4]=>[[1,3,4],[2,5,6]]=>[4,2]=>[4,2]=>2
[3,1,5,6,4,2]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[3,1,6,2,4,5]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[3,1,6,2,5,4]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,1,6,4,2,5]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[3,1,6,4,5,2]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,1,6,5,2,4]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[3,1,6,5,4,2]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[3,2,1,4,6,5]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[3,2,1,5,4,6]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[3,2,1,5,6,4]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[3,2,1,6,4,5]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[3,2,1,6,5,4]=>[[1,4],[2,5],[3,6]]=>[4,2]=>[4,2]=>2
[3,2,4,1,5,6]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[3,2,4,1,6,5]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[3,2,4,5,1,6]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[3,2,4,5,6,1]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[3,2,4,6,1,5]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[3,2,4,6,5,1]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[3,2,5,1,4,6]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[3,2,5,1,6,4]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[3,2,5,4,1,6]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[3,2,5,4,6,1]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,2,5,6,1,4]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[3,2,5,6,4,1]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[3,2,6,1,4,5]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[3,2,6,1,5,4]=>[[1,3],[2,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[3,2,6,4,1,5]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[3,2,6,4,5,1]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,2,6,5,1,4]=>[[1,3],[2,4],[5,6]]=>[3,3]=>[3,3]=>2
[3,2,6,5,4,1]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[3,4,1,2,5,6]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[3,4,1,2,6,5]=>[[1,2,5],[3,4,6]]=>[2,3,1]=>[3,2,1]=>3
[3,4,1,5,2,6]=>[[1,2,4,6],[3,5]]=>[2,2,2]=>[2,2,2]=>3
[3,4,1,5,6,2]=>[[1,2,4,5],[3,6]]=>[2,3,1]=>[3,2,1]=>3
[3,4,1,6,2,5]=>[[1,2,4],[3,5,6]]=>[2,2,2]=>[2,2,2]=>3
[3,4,1,6,5,2]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[3,4,2,1,5,6]=>[[1,2,5,6],[3],[4]]=>[2,4]=>[4,2]=>2
[3,4,2,1,6,5]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[3,4,2,5,1,6]=>[[1,2,4,6],[3],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,4,2,5,6,1]=>[[1,2,4,5],[3],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,4,2,6,1,5]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,4,2,6,5,1]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[3,4,5,1,2,6]=>[[1,2,3,6],[4,5]]=>[3,3]=>[3,3]=>2
[3,4,5,1,6,2]=>[[1,2,3,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[3,4,5,2,1,6]=>[[1,2,3,6],[4],[5]]=>[3,3]=>[3,3]=>2
[3,4,5,2,6,1]=>[[1,2,3,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,4,5,6,1,2]=>[[1,2,3,4],[5,6]]=>[4,2]=>[4,2]=>2
[3,4,5,6,2,1]=>[[1,2,3,4],[5],[6]]=>[4,2]=>[4,2]=>2
[3,4,6,1,2,5]=>[[1,2,3],[4,5,6]]=>[3,3]=>[3,3]=>2
[3,4,6,1,5,2]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,4,6,2,1,5]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[3,4,6,2,5,1]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,4,6,5,1,2]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[3,4,6,5,2,1]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[3,5,1,2,4,6]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[3,5,1,2,6,4]=>[[1,2,5],[3,4,6]]=>[2,3,1]=>[3,2,1]=>3
[3,5,1,4,2,6]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,5,1,4,6,2]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,5,1,6,2,4]=>[[1,2,4],[3,5,6]]=>[2,2,2]=>[2,2,2]=>3
[3,5,1,6,4,2]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[3,5,2,1,4,6]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[3,5,2,1,6,4]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[3,5,2,4,1,6]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,5,2,4,6,1]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,5,2,6,1,4]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,5,2,6,4,1]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[3,5,4,1,2,6]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[3,5,4,1,6,2]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[3,5,4,2,1,6]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[3,5,4,2,6,1]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,5,4,6,1,2]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,5,4,6,2,1]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[3,5,6,1,2,4]=>[[1,2,3],[4,5,6]]=>[3,3]=>[3,3]=>2
[3,5,6,1,4,2]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,5,6,2,1,4]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[3,5,6,2,4,1]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[3,5,6,4,1,2]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[3,5,6,4,2,1]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[3,6,1,2,4,5]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[3,6,1,2,5,4]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,6,1,4,2,5]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,6,1,4,5,2]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,6,1,5,2,4]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,6,1,5,4,2]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[3,6,2,1,4,5]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[3,6,2,1,5,4]=>[[1,2],[3,5],[4,6]]=>[2,3,1]=>[3,2,1]=>3
[3,6,2,4,1,5]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,6,2,4,5,1]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,6,2,5,1,4]=>[[1,2],[3,4],[5,6]]=>[2,2,2]=>[2,2,2]=>3
[3,6,2,5,4,1]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[3,6,4,1,2,5]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[3,6,4,1,5,2]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[3,6,4,2,1,5]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[3,6,4,2,5,1]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,6,4,5,1,2]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[3,6,4,5,2,1]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[3,6,5,1,2,4]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[3,6,5,1,4,2]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,6,5,2,1,4]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[3,6,5,2,4,1]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[3,6,5,4,1,2]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[3,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6]]=>[2,4]=>[4,2]=>2
[4,1,2,3,5,6]=>[[1,3,4,5,6],[2]]=>[6]=>[6]=>1
[4,1,2,3,6,5]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[4,1,2,5,3,6]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[4,1,2,5,6,3]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[4,1,2,6,3,5]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[4,1,2,6,5,3]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[4,1,3,2,5,6]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[4,1,3,2,6,5]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[4,1,3,5,2,6]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[4,1,3,5,6,2]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[4,1,3,6,2,5]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[4,1,3,6,5,2]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[4,1,5,2,3,6]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[4,1,5,2,6,3]=>[[1,3,5],[2,4,6]]=>[3,2,1]=>[3,2,1]=>3
[4,1,5,3,2,6]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[4,1,5,3,6,2]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,1,5,6,2,3]=>[[1,3,4],[2,5,6]]=>[4,2]=>[4,2]=>2
[4,1,5,6,3,2]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[4,1,6,2,3,5]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[4,1,6,2,5,3]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,1,6,3,2,5]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[4,1,6,3,5,2]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,1,6,5,2,3]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[4,1,6,5,3,2]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[4,2,1,3,5,6]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[4,2,1,3,6,5]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[4,2,1,5,3,6]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[4,2,1,5,6,3]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[4,2,1,6,3,5]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[4,2,1,6,5,3]=>[[1,4],[2,5],[3,6]]=>[4,2]=>[4,2]=>2
[4,2,3,1,5,6]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[4,2,3,1,6,5]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[4,2,3,5,1,6]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[4,2,3,5,6,1]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[4,2,3,6,1,5]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[4,2,3,6,5,1]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[4,2,5,1,3,6]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[4,2,5,1,6,3]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[4,2,5,3,1,6]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[4,2,5,3,6,1]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,2,5,6,1,3]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[4,2,5,6,3,1]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[4,2,6,1,3,5]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[4,2,6,1,5,3]=>[[1,3],[2,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[4,2,6,3,1,5]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[4,2,6,3,5,1]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,2,6,5,1,3]=>[[1,3],[2,4],[5,6]]=>[3,3]=>[3,3]=>2
[4,2,6,5,3,1]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[4,3,1,2,5,6]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[4,3,1,2,6,5]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[4,3,1,5,2,6]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[4,3,1,5,6,2]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[4,3,1,6,2,5]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[4,3,1,6,5,2]=>[[1,4],[2,5],[3,6]]=>[4,2]=>[4,2]=>2
[4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[4,3,2,1,6,5]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[4,3,2,5,1,6]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[4,3,2,5,6,1]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[4,3,2,6,1,5]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[4,3,2,6,5,1]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[4,3,5,1,2,6]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[4,3,5,1,6,2]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[4,3,5,2,1,6]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[4,3,5,2,6,1]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,3,5,6,1,2]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[4,3,5,6,2,1]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[4,3,6,1,2,5]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[4,3,6,1,5,2]=>[[1,3],[2,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[4,3,6,2,1,5]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[4,3,6,2,5,1]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,3,6,5,1,2]=>[[1,3],[2,4],[5,6]]=>[3,3]=>[3,3]=>2
[4,3,6,5,2,1]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[4,5,1,2,3,6]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[4,5,1,2,6,3]=>[[1,2,5],[3,4,6]]=>[2,3,1]=>[3,2,1]=>3
[4,5,1,3,2,6]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[4,5,1,3,6,2]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,5,1,6,2,3]=>[[1,2,4],[3,5,6]]=>[2,2,2]=>[2,2,2]=>3
[4,5,1,6,3,2]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[4,5,2,1,3,6]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[4,5,2,1,6,3]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[4,5,2,3,1,6]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[4,5,2,3,6,1]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,5,2,6,1,3]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[4,5,2,6,3,1]=>[[1,2,4],[3,5],[6]]=>[2,2,2]=>[2,2,2]=>3
[4,5,3,1,2,6]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[4,5,3,1,6,2]=>[[1,2,5],[3,6],[4]]=>[2,3,1]=>[3,2,1]=>3
[4,5,3,2,1,6]=>[[1,2,6],[3],[4],[5]]=>[2,4]=>[4,2]=>2
[4,5,3,2,6,1]=>[[1,2,5],[3],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,5,3,6,1,2]=>[[1,2,4],[3,6],[5]]=>[2,2,2]=>[2,2,2]=>3
[4,5,3,6,2,1]=>[[1,2,4],[3],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[4,5,6,1,2,3]=>[[1,2,3],[4,5,6]]=>[3,3]=>[3,3]=>2
[4,5,6,1,3,2]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,5,6,2,1,3]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[4,5,6,2,3,1]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[3,2,1]=>3
[4,5,6,3,1,2]=>[[1,2,3],[4,6],[5]]=>[3,3]=>[3,3]=>2
[4,5,6,3,2,1]=>[[1,2,3],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[4,6,1,2,3,5]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[4,6,1,2,5,3]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,6,1,3,2,5]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[4,6,1,3,5,2]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,6,1,5,2,3]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[4,6,1,5,3,2]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[4,6,2,1,3,5]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[4,6,2,1,5,3]=>[[1,2],[3,5],[4,6]]=>[2,3,1]=>[3,2,1]=>3
[4,6,2,3,1,5]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[4,6,2,3,5,1]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,6,2,5,1,3]=>[[1,2],[3,4],[5,6]]=>[2,2,2]=>[2,2,2]=>3
[4,6,2,5,3,1]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[4,6,3,1,2,5]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[4,6,3,1,5,2]=>[[1,2],[3,5],[4,6]]=>[2,3,1]=>[3,2,1]=>3
[4,6,3,2,1,5]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[4,6,3,2,5,1]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,6,3,5,1,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]=>[2,2,2]=>3
[4,6,3,5,2,1]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[4,6,5,1,2,3]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[4,6,5,1,3,2]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,6,5,2,1,3]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[4,6,5,2,3,1]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[4,6,5,3,1,2]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[4,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6]]=>[2,4]=>[4,2]=>2
[5,1,2,3,4,6]=>[[1,3,4,5,6],[2]]=>[6]=>[6]=>1
[5,1,2,3,6,4]=>[[1,3,4,5],[2,6]]=>[5,1]=>[5,1]=>2
[5,1,2,4,3,6]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[5,1,2,4,6,3]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[5,1,2,6,3,4]=>[[1,3,4,6],[2,5]]=>[4,2]=>[4,2]=>2
[5,1,2,6,4,3]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[5,1,3,2,4,6]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[5,1,3,2,6,4]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[5,1,3,4,2,6]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[5,1,3,4,6,2]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[5,1,3,6,2,4]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[5,1,3,6,4,2]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[5,1,4,2,3,6]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[5,1,4,2,6,3]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[5,1,4,3,2,6]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[5,1,4,3,6,2]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,1,4,6,2,3]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[5,1,4,6,3,2]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[5,1,6,2,3,4]=>[[1,3,5,6],[2,4]]=>[3,3]=>[3,3]=>2
[5,1,6,2,4,3]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,1,6,3,2,4]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[5,1,6,3,4,2]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,1,6,4,2,3]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[5,1,6,4,3,2]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[5,2,1,3,4,6]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[5,2,1,3,6,4]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[5,2,1,4,3,6]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[5,2,1,4,6,3]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[5,2,1,6,3,4]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[5,2,1,6,4,3]=>[[1,4],[2,5],[3,6]]=>[4,2]=>[4,2]=>2
[5,2,3,1,4,6]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[5,2,3,1,6,4]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[5,2,3,4,1,6]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[5,2,3,4,6,1]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[5,2,3,6,1,4]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[5,2,3,6,4,1]=>[[1,3,4],[2,5],[6]]=>[4,2]=>[4,2]=>2
[5,2,4,1,3,6]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[5,2,4,1,6,3]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[5,2,4,3,1,6]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[5,2,4,3,6,1]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,2,4,6,1,3]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[5,2,4,6,3,1]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[5,2,6,1,3,4]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[5,2,6,1,4,3]=>[[1,3],[2,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[5,2,6,3,1,4]=>[[1,3,6],[2,4],[5]]=>[3,3]=>[3,3]=>2
[5,2,6,3,4,1]=>[[1,3,5],[2,4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,2,6,4,1,3]=>[[1,3],[2,4],[5,6]]=>[3,3]=>[3,3]=>2
[5,2,6,4,3,1]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[5,3,1,2,4,6]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[5,3,1,2,6,4]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[5,3,1,4,2,6]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[5,3,1,4,6,2]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[5,3,1,6,2,4]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[5,3,1,6,4,2]=>[[1,4],[2,5],[3,6]]=>[4,2]=>[4,2]=>2
[5,3,2,1,4,6]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[5,3,2,1,6,4]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[5,3,2,4,6,1]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[5,3,2,6,1,4]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[5,3,2,6,4,1]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[5,3,4,1,2,6]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[5,3,4,1,6,2]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[5,3,4,2,1,6]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[5,3,4,2,6,1]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,3,4,6,1,2]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[5,3,4,6,2,1]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[5,3,6,1,2,4]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[5,3,6,1,4,2]=>[[1,3],[2,5],[4,6]]=>[3,2,1]=>[3,2,1]=>3
[5,3,6,2,1,4]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[5,3,6,2,4,1]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,3,6,4,1,2]=>[[1,3],[2,4],[5,6]]=>[3,3]=>[3,3]=>2
[5,3,6,4,2,1]=>[[1,3],[2,4],[5],[6]]=>[3,3]=>[3,3]=>2
[5,4,1,2,3,6]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[5,4,1,2,6,3]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[5,4,1,3,2,6]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[5,4,1,3,6,2]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[5,4,1,6,2,3]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[5,4,1,6,3,2]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[5,4,2,1,3,6]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[5,4,2,1,6,3]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[5,4,2,3,1,6]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[5,4,2,3,6,1]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[5,4,2,6,1,3]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[5,4,2,6,3,1]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[5,4,3,1,2,6]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[5,4,3,1,6,2]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]]=>[6]=>[6]=>1
[5,4,3,2,6,1]=>[[1,5],[2],[3],[4],[6]]=>[5,1]=>[5,1]=>2
[5,4,3,6,1,2]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[5,4,3,6,2,1]=>[[1,4],[2],[3],[5],[6]]=>[4,2]=>[4,2]=>2
[5,4,6,1,2,3]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[5,4,6,1,3,2]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,4,6,2,1,3]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[5,4,6,2,3,1]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[5,4,6,3,1,2]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[5,4,6,3,2,1]=>[[1,3],[2],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[5,6,1,2,3,4]=>[[1,2,5,6],[3,4]]=>[2,4]=>[4,2]=>2
[5,6,1,2,4,3]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[5,6,1,3,2,4]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[5,6,1,3,4,2]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[5,6,1,4,2,3]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[5,6,1,4,3,2]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[5,6,2,1,3,4]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[5,6,2,1,4,3]=>[[1,2],[3,5],[4,6]]=>[2,3,1]=>[3,2,1]=>3
[5,6,2,3,1,4]=>[[1,2,6],[3,4],[5]]=>[2,2,2]=>[2,2,2]=>3
[5,6,2,3,4,1]=>[[1,2,5],[3,4],[6]]=>[2,3,1]=>[3,2,1]=>3
[5,6,2,4,1,3]=>[[1,2],[3,4],[5,6]]=>[2,2,2]=>[2,2,2]=>3
[5,6,2,4,3,1]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[5,6,3,1,2,4]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[5,6,3,1,4,2]=>[[1,2],[3,5],[4,6]]=>[2,3,1]=>[3,2,1]=>3
[5,6,3,2,1,4]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[5,6,3,2,4,1]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[5,6,3,4,1,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]=>[2,2,2]=>3
[5,6,3,4,2,1]=>[[1,2],[3,4],[5],[6]]=>[2,2,2]=>[2,2,2]=>3
[5,6,4,1,2,3]=>[[1,2,6],[3,5],[4]]=>[2,4]=>[4,2]=>2
[5,6,4,1,3,2]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[5,6,4,2,1,3]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[5,6,4,2,3,1]=>[[1,2],[3,5],[4],[6]]=>[2,3,1]=>[3,2,1]=>3
[5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5]]=>[2,4]=>[4,2]=>2
[5,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6]]=>[2,4]=>[4,2]=>2
[6,1,2,3,4,5]=>[[1,3,4,5,6],[2]]=>[6]=>[6]=>1
[6,1,2,3,5,4]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[6,1,2,4,3,5]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[6,1,2,4,5,3]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[6,1,2,5,3,4]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[6,1,2,5,4,3]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[6,1,3,2,4,5]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[6,1,3,2,5,4]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[6,1,3,4,2,5]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[6,1,3,4,5,2]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[6,1,3,5,2,4]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[6,1,3,5,4,2]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[6,1,4,2,3,5]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[6,1,4,2,5,3]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[6,1,4,3,2,5]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[6,1,4,3,5,2]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,1,4,5,2,3]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[6,1,4,5,3,2]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[6,1,5,2,3,4]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[6,1,5,2,4,3]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,1,5,3,2,4]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[6,1,5,3,4,2]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,1,5,4,2,3]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[6,1,5,4,3,2]=>[[1,3],[2],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[6,2,1,3,4,5]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[6,2,1,3,5,4]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[6,2,1,4,3,5]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[6,2,1,4,5,3]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[6,2,1,5,3,4]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[6,2,1,5,4,3]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[6,2,3,1,4,5]=>[[1,3,5,6],[2],[4]]=>[3,3]=>[3,3]=>2
[6,2,3,1,5,4]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[6,2,3,4,1,5]=>[[1,3,4,6],[2],[5]]=>[4,2]=>[4,2]=>2
[6,2,3,4,5,1]=>[[1,3,4,5],[2],[6]]=>[5,1]=>[5,1]=>2
[6,2,3,5,1,4]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[6,2,3,5,4,1]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[6,2,4,1,3,5]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[6,2,4,1,5,3]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[6,2,4,3,1,5]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[6,2,4,3,5,1]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,2,4,5,1,3]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[6,2,4,5,3,1]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[6,2,5,1,3,4]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[6,2,5,1,4,3]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,2,5,3,1,4]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[6,2,5,3,4,1]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,2,5,4,1,3]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[6,2,5,4,3,1]=>[[1,3],[2],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[6,3,1,2,4,5]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[6,3,1,2,5,4]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[6,3,1,4,2,5]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[6,3,1,4,5,2]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[6,3,1,5,2,4]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[6,3,1,5,4,2]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[6,3,2,1,4,5]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[6,3,2,1,5,4]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[6,3,2,4,1,5]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[6,3,2,5,1,4]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[6,3,2,5,4,1]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[6,3,4,1,2,5]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[6,3,4,1,5,2]=>[[1,3,5],[2,6],[4]]=>[3,2,1]=>[3,2,1]=>3
[6,3,4,2,1,5]=>[[1,3,6],[2],[4],[5]]=>[3,3]=>[3,3]=>2
[6,3,4,2,5,1]=>[[1,3,5],[2],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,3,4,5,1,2]=>[[1,3,4],[2,6],[5]]=>[4,2]=>[4,2]=>2
[6,3,4,5,2,1]=>[[1,3,4],[2],[5],[6]]=>[4,2]=>[4,2]=>2
[6,3,5,1,2,4]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[6,3,5,1,4,2]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,3,5,2,1,4]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[6,3,5,2,4,1]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,3,5,4,1,2]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[6,3,5,4,2,1]=>[[1,3],[2],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[6,4,1,2,3,5]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[6,4,1,2,5,3]=>[[1,4,5],[2,6],[3]]=>[5,1]=>[5,1]=>2
[6,4,1,3,2,5]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[6,4,1,3,5,2]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[6,4,1,5,2,3]=>[[1,4,6],[2,5],[3]]=>[4,2]=>[4,2]=>2
[6,4,1,5,3,2]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[6,4,2,1,3,5]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[6,4,2,1,5,3]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[6,4,2,3,1,5]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[6,4,2,3,5,1]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[6,4,2,5,1,3]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[6,4,2,5,3,1]=>[[1,4],[2,5],[3],[6]]=>[4,2]=>[4,2]=>2
[6,4,3,1,2,5]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[6,4,3,1,5,2]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[6,4,3,2,1,5]=>[[1,6],[2],[3],[4],[5]]=>[6]=>[6]=>1
[6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6]]=>[5,1]=>[5,1]=>2
[6,4,3,5,1,2]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[6,4,3,5,2,1]=>[[1,4],[2],[3],[5],[6]]=>[4,2]=>[4,2]=>2
[6,4,5,1,2,3]=>[[1,3,6],[2,5],[4]]=>[3,3]=>[3,3]=>2
[6,4,5,1,3,2]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,4,5,2,1,3]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6]]=>[3,2,1]=>[3,2,1]=>3
[6,4,5,3,1,2]=>[[1,3],[2,6],[4],[5]]=>[3,3]=>[3,3]=>2
[6,4,5,3,2,1]=>[[1,3],[2],[4],[5],[6]]=>[3,3]=>[3,3]=>2
[6,5,1,2,3,4]=>[[1,4,5,6],[2],[3]]=>[6]=>[6]=>1
[6,5,1,2,4,3]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[6,5,1,3,2,4]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[6,5,1,3,4,2]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[6,5,1,4,2,3]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[6,5,1,4,3,2]=>[[1,4],[2],[3],[5],[6]]=>[4,2]=>[4,2]=>2
[6,5,2,1,3,4]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[6,5,2,1,4,3]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[6,5,2,3,1,4]=>[[1,4,6],[2],[3],[5]]=>[4,2]=>[4,2]=>2
[6,5,2,3,4,1]=>[[1,4,5],[2],[3],[6]]=>[5,1]=>[5,1]=>2
[6,5,2,4,1,3]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[6,5,2,4,3,1]=>[[1,4],[2],[3],[5],[6]]=>[4,2]=>[4,2]=>2
[6,5,3,1,2,4]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[6,5,3,1,4,2]=>[[1,5],[2,6],[3],[4]]=>[5,1]=>[5,1]=>2
[6,5,3,2,1,4]=>[[1,6],[2],[3],[4],[5]]=>[6]=>[6]=>1
[6,5,3,2,4,1]=>[[1,5],[2],[3],[4],[6]]=>[5,1]=>[5,1]=>2
[6,5,3,4,1,2]=>[[1,4],[2,6],[3],[5]]=>[4,2]=>[4,2]=>2
[6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6]]=>[4,2]=>[4,2]=>2
[6,5,4,1,2,3]=>[[1,5,6],[2],[3],[4]]=>[6]=>[6]=>1
[6,5,4,1,3,2]=>[[1,5],[2],[3],[4],[6]]=>[5,1]=>[5,1]=>2
[6,5,4,2,1,3]=>[[1,6],[2],[3],[4],[5]]=>[6]=>[6]=>1
[6,5,4,2,3,1]=>[[1,5],[2],[3],[4],[6]]=>[5,1]=>[5,1]=>2
[6,5,4,3,1,2]=>[[1,6],[2],[3],[4],[5]]=>[6]=>[6]=>1
[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]]=>[6]=>[6]=>1
[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]=>[7]=>[7]=>1
[1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7]]=>[6,1]=>[6,1]=>2
[1,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]=>[5,2]=>2
[1,2,3,4,6,7,5]=>[[1,2,3,4,5,6],[7]]=>[6,1]=>[6,1]=>2
[1,2,3,4,7,5,6]=>[[1,2,3,4,5,7],[6]]=>[5,2]=>[5,2]=>2
[1,2,3,4,7,6,5]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]=>[4,3]=>2
[1,2,3,5,4,7,6]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,3,5,6,4,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]=>[5,2]=>2
[1,2,3,5,6,7,4]=>[[1,2,3,4,5,6],[7]]=>[6,1]=>[6,1]=>2
[1,2,3,5,7,4,6]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,2,3,5,7,6,4]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,2,3,6,4,5,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]=>[4,3]=>2
[1,2,3,6,4,7,5]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,3,6,5,4,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,2,3,6,5,7,4]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,3,6,7,4,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,2,3,6,7,5,4]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,2,3,7,4,5,6]=>[[1,2,3,4,6,7],[5]]=>[4,3]=>[4,3]=>2
[1,2,3,7,4,6,5]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,3,7,5,4,6]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,2,3,7,5,6,4]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,3,7,6,4,5]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,2,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,2,4,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]=>[4,3]=>2
[1,2,4,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,4,3,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,4,3,7,5,6]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,4,3,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,4,5,3,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]=>[4,3]=>2
[1,2,4,5,3,7,6]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,4,5,6,3,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]=>[5,2]=>2
[1,2,4,5,6,7,3]=>[[1,2,3,4,5,6],[7]]=>[6,1]=>[6,1]=>2
[1,2,4,5,7,3,6]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,2,4,5,7,6,3]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,2,4,6,3,5,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,2,4,6,3,7,5]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,4,6,5,3,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,2,4,6,5,7,3]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,4,6,7,3,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,2,4,6,7,5,3]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,2,4,7,3,5,6]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,2,4,7,3,6,5]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,4,7,5,3,6]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,2,4,7,5,6,3]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,4,7,6,3,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,2,4,7,6,5,3]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,2,5,3,4,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]=>[4,3]=>2
[1,2,5,3,4,7,6]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,5,3,6,4,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,5,3,6,7,4]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,5,3,7,4,6]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,5,3,7,6,4]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,5,4,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,2,5,4,3,7,6]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,2,5,4,6,3,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,5,4,6,7,3]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,5,4,7,3,6]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,5,4,7,6,3]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,5,6,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,2,5,6,3,7,4]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,5,6,4,3,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,2,5,6,4,7,3]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,5,6,7,3,4]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,2,5,6,7,4,3]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,2,5,7,3,4,6]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,2,5,7,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,5,7,4,3,6]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,2,5,7,4,6,3]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,5,7,6,3,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,2,5,7,6,4,3]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,2,6,3,4,5,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]=>[4,3]=>2
[1,2,6,3,4,7,5]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,6,3,5,4,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,6,3,5,7,4]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,6,3,7,4,5]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,6,3,7,5,4]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,6,4,3,5,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,2,6,4,3,7,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,2,6,4,5,3,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,6,4,5,7,3]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,6,4,7,3,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,6,4,7,5,3]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,6,5,3,4,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,2,6,5,3,7,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,2,6,5,4,3,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,2,6,5,4,7,3]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,6,5,7,3,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,6,5,7,4,3]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,6,7,3,4,5]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,2,6,7,3,5,4]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,6,7,4,3,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,2,6,7,4,5,3]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,2,6,7,5,3,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,2,6,7,5,4,3]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,2,7,3,4,5,6]=>[[1,2,3,5,6,7],[4]]=>[3,4]=>[4,3]=>2
[1,2,7,3,4,6,5]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,7,3,5,4,6]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,7,3,5,6,4]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,7,3,6,4,5]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,7,3,6,5,4]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,7,4,3,5,6]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,2,7,4,3,6,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,2,7,4,5,3,6]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,7,4,5,6,3]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,7,4,6,3,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,7,4,6,5,3]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,7,5,3,4,6]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,2,7,5,3,6,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,2,7,5,4,3,6]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,2,7,5,4,6,3]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,7,5,6,3,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,2,7,5,6,4,3]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,2,7,6,3,4,5]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,2,7,6,3,5,4]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,7,6,4,3,5]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,2,7,6,4,5,3]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,2,7,6,5,3,4]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,2,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[1,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]=>[5,2]=>2
[1,3,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,3,2,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,3,2,4,6,7,5]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,3,2,4,7,5,6]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,3,2,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,3,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,3,2,5,6,4,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,3,2,5,6,7,4]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,3,2,5,7,4,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[1,3,2,5,7,6,4]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,3,2,6,4,5,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,3,2,6,4,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,3,2,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,3,2,6,5,7,4]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,3,2,6,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[1,3,2,6,7,5,4]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,3,2,7,4,5,6]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,3,2,7,4,6,5]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,3,2,7,5,4,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,3,2,7,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,3,2,7,6,4,5]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,3,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,3,4,2,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]=>[4,3]=>2
[1,3,4,2,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,4,2,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,4,2,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,4,2,7,5,6]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,4,2,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,4,5,2,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]=>[4,3]=>2
[1,3,4,5,2,7,6]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,4,5,6,2,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]=>[5,2]=>2
[1,3,4,5,6,7,2]=>[[1,2,3,4,5,6],[7]]=>[6,1]=>[6,1]=>2
[1,3,4,5,7,2,6]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,3,4,5,7,6,2]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,3,4,6,2,5,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,3,4,6,2,7,5]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,4,6,5,2,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,3,4,6,5,7,2]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,4,6,7,2,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,3,4,6,7,5,2]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,3,4,7,2,5,6]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,3,4,7,2,6,5]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,4,7,5,2,6]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,3,4,7,5,6,2]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,4,7,6,2,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,3,4,7,6,5,2]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,3,5,2,4,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,3,5,2,4,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,5,2,6,4,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,5,2,6,7,4]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,5,2,7,4,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,5,2,7,6,4]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,5,4,2,6,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,3,5,4,2,7,6]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,3,5,4,6,2,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,5,4,6,7,2]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,5,4,7,2,6]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,5,4,7,6,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,5,6,2,4,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,3,5,6,2,7,4]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,5,6,4,2,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,3,5,6,4,7,2]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,5,6,7,2,4]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,3,5,6,7,4,2]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,3,5,7,2,4,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[1,3,5,7,2,6,4]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,5,7,4,2,6]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,3,5,7,4,6,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,5,7,6,2,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,3,5,7,6,4,2]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,3,6,2,4,5,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,3,6,2,4,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,6,2,5,4,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,6,2,5,7,4]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,6,2,7,4,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,6,2,7,5,4]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,6,4,2,5,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,3,6,4,2,7,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,3,6,4,5,2,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,6,4,5,7,2]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,6,4,7,2,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,6,4,7,5,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,6,5,2,4,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,3,6,5,2,7,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,3,6,5,4,2,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,3,6,5,4,7,2]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,6,5,7,2,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,6,5,7,4,2]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,6,7,2,4,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[1,3,6,7,2,5,4]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,6,7,4,2,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,3,6,7,4,5,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,3,6,7,5,2,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,3,6,7,5,4,2]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,3,7,2,4,5,6]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,3,7,2,4,6,5]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,7,2,5,4,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,7,2,5,6,4]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,7,2,6,4,5]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,7,2,6,5,4]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,7,4,2,5,6]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,3,7,4,2,6,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,3,7,4,5,2,6]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,7,4,5,6,2]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,7,4,6,2,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,7,4,6,5,2]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,7,5,2,4,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,3,7,5,2,6,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,3,7,5,4,2,6]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,3,7,5,4,6,2]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,7,5,6,2,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,3,7,5,6,4,2]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,3,7,6,2,4,5]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,3,7,6,2,5,4]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,7,6,4,2,5]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,3,7,6,4,5,2]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,3,7,6,5,2,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,3,7,6,5,4,2]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[1,4,2,3,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]=>[5,2]=>2
[1,4,2,3,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,4,2,3,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,4,2,3,6,7,5]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,4,2,3,7,5,6]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,4,2,3,7,6,5]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,4,2,5,3,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,4,2,5,3,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,2,5,6,3,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,4,2,5,6,7,3]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,4,2,5,7,3,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[1,4,2,5,7,6,3]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,4,2,6,3,5,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,4,2,6,3,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,2,6,5,3,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,4,2,6,5,7,3]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,2,6,7,3,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[1,4,2,6,7,5,3]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,4,2,7,3,5,6]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,4,2,7,3,6,5]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,2,7,5,3,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,4,2,7,5,6,3]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,2,7,6,3,5]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,4,2,7,6,5,3]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,4,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,4,3,2,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,4,3,2,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,4,3,2,6,7,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,4,3,2,7,5,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,4,3,2,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[1,4,3,5,2,6,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,4,3,5,2,7,6]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,3,5,6,2,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,4,3,5,6,7,2]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,4,3,5,7,2,6]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,4,3,5,7,6,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,4,3,6,2,5,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,4,3,6,2,7,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,3,6,5,2,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,4,3,6,5,7,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,3,6,7,2,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,4,3,6,7,5,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,4,3,7,2,5,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,4,3,7,2,6,5]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,3,7,5,2,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,4,3,7,5,6,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,4,3,7,6,2,5]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[1,4,3,7,6,5,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,4,5,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,4,5,2,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,5,2,6,3,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,5,2,6,7,3]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,5,2,7,3,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,5,2,7,6,3]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,5,3,2,6,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[1,4,5,3,2,7,6]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,4,5,3,6,2,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,5,3,6,7,2]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,5,3,7,2,6]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,5,3,7,6,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,5,6,2,3,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[1,4,5,6,2,7,3]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[1,4,5,6,3,2,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[1,4,5,6,3,7,2]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,4,5,6,7,2,3]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[1,4,5,6,7,3,2]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[1,4,5,7,2,3,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[1,4,5,7,2,6,3]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,4,5,7,3,2,6]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,4,5,7,3,6,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,4,5,7,6,2,3]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,4,5,7,6,3,2]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,4,6,2,3,5,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,4,6,2,3,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,6,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,6,2,5,7,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,6,2,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,6,2,7,5,3]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,6,3,2,5,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,4,6,3,2,7,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,4,6,3,5,2,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,6,3,5,7,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,6,3,7,2,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,6,3,7,5,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,6,5,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,4,6,5,2,7,3]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,4,6,5,3,2,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,4,6,5,3,7,2]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,6,5,7,2,3]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,6,5,7,3,2]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,6,7,2,3,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[1,4,6,7,2,5,3]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,4,6,7,3,2,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,4,6,7,3,5,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,4,6,7,5,2,3]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,4,6,7,5,3,2]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,4,7,2,3,5,6]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,4,7,2,3,6,5]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,7,2,5,3,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,7,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,7,2,6,3,5]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,7,3,2,5,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,4,7,3,2,6,5]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,7,3,5,2,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,7,3,5,6,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,7,3,6,2,5]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,7,3,6,5,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,7,5,2,3,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,4,7,5,2,6,3]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,4,7,5,3,2,6]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,4,7,5,3,6,2]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,7,5,6,2,3]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,4,7,5,6,3,2]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,4,7,6,2,3,5]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,4,7,6,2,5,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,7,6,3,2,5]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,4,7,6,3,5,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,4,7,6,5,2,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,4,7,6,5,3,2]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[1,5,2,3,4,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]=>[5,2]=>2
[1,5,2,3,4,7,6]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,5,2,3,6,4,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,2,3,6,7,4]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,5,2,3,7,4,6]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,2,3,7,6,4]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,2,4,3,6,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,5,2,4,3,7,6]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,2,4,6,3,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,2,4,6,7,3]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,5,2,4,7,3,6]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,2,4,7,6,3]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,2,6,3,4,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,5,2,6,3,7,4]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,2,6,4,3,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,5,2,6,4,7,3]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,2,6,7,3,4]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,2,6,7,4,3]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,2,7,3,4,6]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,5,2,7,3,6,4]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,2,7,4,3,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,5,2,7,4,6,3]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,2,7,6,3,4]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,5,2,7,6,4,3]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,5,3,2,4,6,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,5,3,2,4,7,6]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,5,3,2,6,4,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,5,3,2,6,7,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,5,3,2,7,4,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,5,3,2,7,6,4]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,3,4,2,6,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,5,3,4,2,7,6]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,3,4,6,2,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,3,4,6,7,2]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,5,3,4,7,2,6]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,3,4,7,6,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,3,6,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,5,3,6,2,7,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,3,6,4,2,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,5,3,6,4,7,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,3,6,7,2,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,3,6,7,4,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,3,7,2,4,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,5,3,7,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,3,7,4,2,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,5,3,7,4,6,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,3,7,6,2,4]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[1,5,3,7,6,4,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,5,4,2,3,6,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,5,4,2,3,7,6]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,5,4,2,6,3,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,5,4,2,6,7,3]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,5,4,2,7,3,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,5,4,2,7,6,3]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,4,3,2,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,5,4,3,2,7,6]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,5,4,3,6,2,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,4,3,6,7,2]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,5,4,3,7,2,6]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,4,3,7,6,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,4,6,2,3,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,5,4,6,2,7,3]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,4,6,3,2,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,5,4,6,3,7,2]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,4,6,7,2,3]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,5,4,6,7,3,2]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,5,4,7,2,3,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,5,4,7,2,6,3]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,4,7,3,2,6]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,5,4,7,3,6,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,5,4,7,6,2,3]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[1,5,4,7,6,3,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,5,6,2,3,4,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,5,6,2,3,7,4]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,6,2,4,3,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,5,6,2,4,7,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,6,2,7,3,4]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,6,2,7,4,3]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,6,3,2,4,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,5,6,3,2,7,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,5,6,3,4,2,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,5,6,3,4,7,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,6,3,7,2,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,5,6,3,7,4,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,6,4,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,5,6,4,2,7,3]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[1,5,6,4,3,2,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[1,5,6,4,3,7,2]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,6,4,7,2,3]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,5,6,4,7,3,2]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[1,5,6,7,2,4,3]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,5,6,7,3,2,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,5,6,7,3,4,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[1,5,6,7,4,2,3]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[1,5,6,7,4,3,2]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[1,5,7,2,3,4,6]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,5,7,2,3,6,4]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,7,2,4,3,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,5,7,2,4,6,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,7,2,6,3,4]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,5,7,2,6,4,3]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,7,3,2,4,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,5,7,3,2,6,4]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,7,3,4,2,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,5,7,3,4,6,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,7,3,6,2,4]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,7,3,6,4,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,7,4,2,3,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,5,7,4,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,7,4,3,2,6]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,5,7,4,3,6,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,7,4,6,2,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,7,4,6,3,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,5,7,6,2,3,4]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,5,7,6,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,7,6,3,2,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,5,7,6,3,4,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,5,7,6,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,5,7,6,4,3,2]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[1,6,2,3,4,5,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]=>[5,2]=>2
[1,6,2,3,4,7,5]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[1,6,2,3,5,4,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,2,3,5,7,4]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,6,2,3,7,4,5]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,2,3,7,5,4]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,2,4,3,5,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,2,4,3,7,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,2,4,5,3,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,2,4,5,7,3]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,6,2,4,7,3,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,2,4,7,5,3]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,2,5,3,4,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,2,5,3,7,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,2,5,4,3,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,2,5,4,7,3]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,2,5,7,3,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,2,5,7,4,3]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,2,7,3,4,5]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,2,7,3,5,4]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,2,7,4,3,5]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,2,7,4,5,3]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,2,7,5,3,4]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,2,7,5,4,3]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,6,3,2,4,5,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,6,3,2,4,7,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,6,3,2,5,4,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,6,3,2,5,7,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,6,3,2,7,4,5]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,6,3,2,7,5,4]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,3,4,2,5,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,3,4,2,7,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,3,4,5,2,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,3,4,5,7,2]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,6,3,4,7,2,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,3,4,7,5,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,3,5,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,3,5,2,7,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,3,5,4,2,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,3,5,4,7,2]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,3,5,7,2,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,3,5,7,4,2]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,3,7,2,4,5]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,3,7,2,5,4]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,3,7,4,2,5]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,3,7,4,5,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,3,7,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[1,6,3,7,5,4,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,6,4,2,3,5,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,6,4,2,3,7,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,6,4,2,5,3,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,6,4,2,5,7,3]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,6,4,2,7,3,5]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,6,4,2,7,5,3]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,4,3,2,5,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,6,4,3,2,7,5]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,6,4,3,5,2,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,4,3,5,7,2]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,6,4,3,7,2,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,4,3,7,5,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,4,5,2,3,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,4,5,2,7,3]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,4,5,3,2,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,4,5,3,7,2]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,4,5,7,2,3]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,4,5,7,3,2]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,4,7,2,3,5]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,4,7,2,5,3]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,4,7,3,2,5]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,4,7,3,5,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,4,7,5,2,3]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[1,6,4,7,5,3,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,6,5,2,3,4,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,6,5,2,3,7,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,6,5,2,4,3,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,5,2,4,7,3]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,6,5,2,7,3,4]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,6,5,2,7,4,3]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,5,3,2,4,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,6,5,3,2,7,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,6,5,3,4,2,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,5,3,4,7,2]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,6,5,3,7,2,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,5,3,7,4,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,5,4,2,3,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,6,5,4,2,7,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,6,5,4,3,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[1,6,5,4,3,7,2]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,6,5,4,7,2,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,6,5,4,7,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,6,5,7,2,3,4]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,6,5,7,2,4,3]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,5,7,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,5,7,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,6,5,7,4,2,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,6,5,7,4,3,2]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,6,7,2,3,4,5]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[1,6,7,2,3,5,4]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,6,7,2,4,3,5]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,6,7,2,4,5,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,6,7,2,5,3,4]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,6,7,2,5,4,3]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,6,7,3,2,4,5]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,6,7,3,2,5,4]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,6,7,3,4,2,5]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[1,6,7,3,4,5,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,6,7,3,5,2,4]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,6,7,3,5,4,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,6,7,4,2,3,5]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,6,7,4,2,5,3]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[1,6,7,4,3,2,5]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,6,7,4,3,5,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,6,7,4,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[1,6,7,4,5,3,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[1,6,7,5,2,3,4]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[1,6,7,5,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,6,7,5,3,2,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,6,7,5,3,4,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[1,6,7,5,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[1,6,7,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[1,7,2,3,4,5,6]=>[[1,2,4,5,6,7],[3]]=>[2,5]=>[5,2]=>2
[1,7,2,3,4,6,5]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,2,3,5,4,6]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,2,3,5,6,4]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,2,3,6,4,5]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,2,3,6,5,4]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,2,4,3,5,6]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,2,4,3,6,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,2,4,5,3,6]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,2,4,5,6,3]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,2,4,6,3,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,2,4,6,5,3]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,2,5,3,4,6]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,2,5,3,6,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,2,5,4,3,6]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,2,5,4,6,3]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,2,5,6,3,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,2,5,6,4,3]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,2,6,3,4,5]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,2,6,3,5,4]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,2,6,4,3,5]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,2,6,4,5,3]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,2,6,5,3,4]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,2,6,5,4,3]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,7,3,2,4,5,6]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,7,3,2,4,6,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,7,3,2,5,4,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,7,3,2,5,6,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,7,3,2,6,4,5]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,7,3,2,6,5,4]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,3,4,2,5,6]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,3,4,2,6,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,3,4,5,2,6]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,3,4,6,2,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,3,4,6,5,2]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,3,5,2,4,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,3,5,2,6,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,3,5,4,2,6]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,3,5,4,6,2]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,3,5,6,2,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,3,5,6,4,2]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,3,6,2,4,5]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,3,6,2,5,4]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,3,6,4,2,5]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,3,6,4,5,2]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,3,6,5,2,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,3,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,7,4,2,3,5,6]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,7,4,2,3,6,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,7,4,2,5,3,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,7,4,2,5,6,3]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,7,4,2,6,3,5]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,7,4,2,6,5,3]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,4,3,2,5,6]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,7,4,3,2,6,5]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,7,4,3,5,2,6]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,4,3,5,6,2]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,4,3,6,2,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,4,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,4,5,2,3,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,4,5,2,6,3]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,4,5,3,2,6]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,4,5,3,6,2]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,4,5,6,2,3]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,4,5,6,3,2]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,4,6,2,3,5]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,4,6,2,5,3]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,4,6,3,2,5]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,4,6,3,5,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,4,6,5,2,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,4,6,5,3,2]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,7,5,2,3,4,6]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,7,5,2,3,6,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[1,7,5,2,4,3,6]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,5,2,4,6,3]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,5,2,6,3,4]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[1,7,5,2,6,4,3]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,5,3,2,4,6]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,7,5,3,2,6,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,7,5,3,4,2,6]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,5,3,4,6,2]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,5,3,6,2,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,5,3,6,4,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,5,4,2,3,6]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,7,5,4,2,6,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,7,5,4,3,2,6]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[1,7,5,4,3,6,2]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,5,4,6,2,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,5,4,6,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,5,6,2,3,4]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[1,7,5,6,2,4,3]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,5,6,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,5,6,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[1,7,5,6,4,2,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[1,7,5,6,4,3,2]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[1,7,6,2,3,4,5]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[1,7,6,2,3,5,4]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,6,2,4,3,5]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,6,2,4,5,3]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,6,2,5,3,4]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,6,2,5,4,3]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,6,3,2,4,5]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,7,6,3,2,5,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,7,6,3,4,2,5]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,6,3,4,5,2]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,6,3,5,2,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,6,3,5,4,2]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,6,4,2,3,5]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,7,6,4,2,5,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[1,7,6,4,3,2,5]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[1,7,6,4,3,5,2]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,6,4,5,2,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[1,7,6,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[1,7,6,5,2,3,4]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[1,7,6,5,2,4,3]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,6,5,3,2,4]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[1,7,6,5,3,4,2]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[1,7,6,5,4,2,3]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[1,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,5]=>[5,2]=>2
[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[7]=>[7]=>1
[2,1,3,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[2,1,3,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[2,1,3,4,6,7,5]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[2,1,3,4,7,5,6]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[2,1,3,4,7,6,5]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[2,1,3,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[2,1,3,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,3,5,6,4,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[2,1,3,5,6,7,4]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[2,1,3,5,7,4,6]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[2,1,3,5,7,6,4]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[2,1,3,6,4,5,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[2,1,3,6,4,7,5]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,3,6,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[2,1,3,6,5,7,4]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,3,6,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[2,1,3,6,7,5,4]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[2,1,3,7,4,5,6]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[2,1,3,7,4,6,5]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,3,7,5,4,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[2,1,3,7,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,3,7,6,4,5]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[2,1,3,7,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,1,4,3,5,6,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[2,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,4,3,6,7,5]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,4,3,7,5,6]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,4,3,7,6,5]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,4,5,3,6,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[2,1,4,5,3,7,6]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,4,5,6,3,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[2,1,4,5,6,7,3]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[2,1,4,5,7,3,6]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[2,1,4,5,7,6,3]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[2,1,4,6,3,5,7]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[2,1,4,6,3,7,5]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,4,6,5,3,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[2,1,4,6,5,7,3]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,4,6,7,3,5]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[2,1,4,6,7,5,3]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[2,1,4,7,3,5,6]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[2,1,4,7,3,6,5]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,4,7,5,3,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[2,1,4,7,5,6,3]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,4,7,6,3,5]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[2,1,4,7,6,5,3]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,1,5,3,4,6,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[2,1,5,3,4,7,6]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,5,3,6,4,7]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,5,3,6,7,4]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,5,3,7,4,6]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,5,3,7,6,4]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,5,4,3,6,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[2,1,5,4,3,7,6]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,1,5,4,6,3,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,5,4,6,7,3]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,5,4,7,3,6]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,5,4,7,6,3]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,5,6,3,4,7]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[2,1,5,6,3,7,4]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,5,6,4,3,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[2,1,5,6,4,7,3]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,5,6,7,3,4]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[2,1,5,6,7,4,3]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[2,1,5,7,3,4,6]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[2,1,5,7,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,5,7,4,3,6]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[2,1,5,7,4,6,3]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,5,7,6,3,4]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[2,1,5,7,6,4,3]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,1,6,3,4,5,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[2,1,6,3,4,7,5]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,6,3,5,4,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,6,3,5,7,4]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,6,3,7,4,5]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,6,3,7,5,4]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,6,4,3,5,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[2,1,6,4,3,7,5]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,1,6,4,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,6,4,5,7,3]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,6,4,7,3,5]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,6,4,7,5,3]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,6,5,3,4,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[2,1,6,5,3,7,4]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,1,6,5,4,3,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,1,6,5,4,7,3]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,6,5,7,3,4]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,6,5,7,4,3]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,6,7,3,4,5]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[2,1,6,7,3,5,4]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,6,7,4,3,5]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[2,1,6,7,4,5,3]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,1,6,7,5,3,4]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[2,1,6,7,5,4,3]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,1,7,3,4,5,6]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[2,1,7,3,4,6,5]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,7,3,5,4,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,7,3,5,6,4]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,7,3,6,4,5]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,7,3,6,5,4]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,7,4,3,5,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[2,1,7,4,3,6,5]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,1,7,4,5,3,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,7,4,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,7,4,6,3,5]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,7,4,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,7,5,3,4,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[2,1,7,5,3,6,4]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,1,7,5,4,3,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,1,7,5,4,6,3]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,7,5,6,3,4]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,1,7,5,6,4,3]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,1,7,6,3,4,5]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[2,1,7,6,3,5,4]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,7,6,4,3,5]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,1,7,6,4,5,3]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,1,7,6,5,3,4]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,1,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[2,3,1,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]=>[5,2]=>2
[2,3,1,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[2,3,1,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[2,3,1,4,6,7,5]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[2,3,1,4,7,5,6]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[2,3,1,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,3,1,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[2,3,1,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,3,1,5,6,4,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[2,3,1,5,6,7,4]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[2,3,1,5,7,4,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[2,3,1,5,7,6,4]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,3,1,6,4,5,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[2,3,1,6,4,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,3,1,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,3,1,6,5,7,4]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,3,1,6,7,4,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[2,3,1,6,7,5,4]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,3,1,7,4,5,6]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[2,3,1,7,4,6,5]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,3,1,7,5,4,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,3,1,7,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,3,1,7,6,4,5]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,3,1,7,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,3,4,1,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]=>[4,3]=>2
[2,3,4,1,5,7,6]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,4,1,6,5,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,4,1,6,7,5]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,4,1,7,5,6]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,4,1,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,4,5,1,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]=>[4,3]=>2
[2,3,4,5,1,7,6]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,4,5,6,1,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]=>[5,2]=>2
[2,3,4,5,6,7,1]=>[[1,2,3,4,5,6],[7]]=>[6,1]=>[6,1]=>2
[2,3,4,5,7,1,6]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[2,3,4,5,7,6,1]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[2,3,4,6,1,5,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[2,3,4,6,1,7,5]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,4,6,5,1,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[2,3,4,6,5,7,1]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,4,6,7,1,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[2,3,4,6,7,5,1]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[2,3,4,7,1,5,6]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[2,3,4,7,1,6,5]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,4,7,5,1,6]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[2,3,4,7,5,6,1]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,4,7,6,1,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,3,4,7,6,5,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,3,5,1,4,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[2,3,5,1,4,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,5,1,6,4,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,5,1,6,7,4]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,5,1,7,4,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,5,1,7,6,4]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,5,4,1,6,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[2,3,5,4,1,7,6]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,3,5,4,6,1,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,5,4,6,7,1]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,5,4,7,1,6]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,5,4,7,6,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,5,6,1,4,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[2,3,5,6,1,7,4]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,5,6,4,1,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[2,3,5,6,4,7,1]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,5,6,7,1,4]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[2,3,5,6,7,4,1]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[2,3,5,7,1,4,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[2,3,5,7,1,6,4]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,5,7,4,1,6]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,3,5,7,4,6,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,5,7,6,1,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,3,5,7,6,4,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,3,6,1,4,5,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[2,3,6,1,4,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,6,1,5,4,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,6,1,5,7,4]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,6,1,7,4,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,6,1,7,5,4]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,6,4,1,5,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[2,3,6,4,1,7,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,3,6,4,5,1,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,6,4,5,7,1]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,6,4,7,1,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,6,4,7,5,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,6,5,1,4,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,3,6,5,1,7,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,3,6,5,4,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,3,6,5,4,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,6,5,7,1,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,6,5,7,4,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,6,7,1,4,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[2,3,6,7,1,5,4]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,6,7,4,1,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,3,6,7,4,5,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,3,6,7,5,1,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,3,6,7,5,4,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,3,7,1,4,5,6]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[2,3,7,1,4,6,5]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,7,1,5,4,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,7,1,5,6,4]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,7,1,6,4,5]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,7,1,6,5,4]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,7,4,1,5,6]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[2,3,7,4,1,6,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,3,7,4,5,1,6]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,7,4,5,6,1]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,7,4,6,1,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,7,4,6,5,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,7,5,1,4,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,3,7,5,1,6,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,3,7,5,4,1,6]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,3,7,5,4,6,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,7,5,6,1,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,3,7,5,6,4,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,3,7,6,1,4,5]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,3,7,6,1,5,4]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,7,6,4,1,5]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,3,7,6,4,5,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,3,7,6,5,1,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,3,7,6,5,4,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[2,4,1,3,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[2,4,1,3,5,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[2,4,1,3,6,5,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[2,4,1,3,6,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[2,4,1,3,7,5,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[2,4,1,3,7,6,5]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,4,1,5,3,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[2,4,1,5,3,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,1,5,6,3,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[2,4,1,5,6,7,3]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[2,4,1,5,7,3,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[2,4,1,5,7,6,3]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,4,1,6,3,5,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[2,4,1,6,3,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,1,6,5,3,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,4,1,6,5,7,3]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,1,6,7,3,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[2,4,1,6,7,5,3]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,4,1,7,3,5,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[2,4,1,7,3,6,5]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,1,7,5,3,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,4,1,7,5,6,3]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,1,7,6,3,5]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,4,1,7,6,5,3]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,4,3,1,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[2,4,3,1,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,4,3,1,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,4,3,1,6,7,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,4,3,1,7,5,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,4,3,1,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[2,4,3,5,1,6,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,4,3,5,1,7,6]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,3,5,6,1,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,4,3,5,6,7,1]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,4,3,5,7,1,6]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,4,3,5,7,6,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,4,3,6,1,5,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,4,3,6,1,7,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,3,6,5,1,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,4,3,6,5,7,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,3,6,7,1,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,4,3,6,7,5,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,4,3,7,1,5,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,4,3,7,1,6,5]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,3,7,5,1,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,4,3,7,5,6,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,4,3,7,6,1,5]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[2,4,3,7,6,5,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,4,5,1,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[2,4,5,1,3,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,5,1,6,3,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,5,1,6,7,3]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,5,1,7,3,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,5,1,7,6,3]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,5,3,1,6,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[2,4,5,3,1,7,6]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,4,5,3,6,1,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,5,3,6,7,1]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,5,3,7,1,6]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,5,3,7,6,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,5,6,1,3,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[2,4,5,6,1,7,3]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[2,4,5,6,3,1,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[2,4,5,6,3,7,1]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,4,5,6,7,1,3]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[2,4,5,6,7,3,1]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[2,4,5,7,1,3,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[2,4,5,7,1,6,3]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,4,5,7,3,1,6]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,4,5,7,3,6,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,4,5,7,6,1,3]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,4,5,7,6,3,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,4,6,1,3,5,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[2,4,6,1,3,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,6,1,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,6,1,5,7,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,6,1,7,3,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,6,1,7,5,3]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,6,3,1,5,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,4,6,3,1,7,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,4,6,3,5,1,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,6,3,5,7,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,6,3,7,1,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,6,3,7,5,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,6,5,1,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,4,6,5,1,7,3]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,4,6,5,3,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,4,6,5,3,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,6,5,7,1,3]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,6,5,7,3,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,6,7,1,3,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[2,4,6,7,1,5,3]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,4,6,7,3,1,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,4,6,7,3,5,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,4,6,7,5,1,3]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,4,6,7,5,3,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,4,7,1,3,5,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[2,4,7,1,3,6,5]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,7,1,5,3,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,7,1,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,7,1,6,3,5]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,7,1,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,7,3,1,5,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,4,7,3,1,6,5]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,7,3,5,1,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,7,3,5,6,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,7,3,6,1,5]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,7,3,6,5,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,7,5,1,3,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,4,7,5,1,6,3]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,4,7,5,3,1,6]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,4,7,5,3,6,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,7,5,6,1,3]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,4,7,5,6,3,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,4,7,6,1,3,5]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[2,4,7,6,1,5,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,7,6,3,1,5]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,4,7,6,3,5,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,4,7,6,5,1,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,4,7,6,5,3,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[2,5,1,3,4,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[2,5,1,3,4,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[2,5,1,3,6,4,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,1,3,6,7,4]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[2,5,1,3,7,4,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,1,3,7,6,4]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,1,4,3,6,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,5,1,4,3,7,6]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,1,4,6,3,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,1,4,6,7,3]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,5,1,4,7,3,6]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,1,4,7,6,3]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,1,6,3,4,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,1,6,3,7,4]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,1,6,4,3,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,1,6,4,7,3]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,1,6,7,3,4]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,1,6,7,4,3]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,1,7,3,4,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,1,7,3,6,4]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,1,7,4,3,6]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,1,7,4,6,3]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,1,7,6,3,4]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,1,7,6,4,3]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,5,3,1,4,6,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[2,5,3,1,4,7,6]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,5,3,1,6,4,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,5,3,1,6,7,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,5,3,1,7,4,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,5,3,1,7,6,4]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,3,4,1,6,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,5,3,4,1,7,6]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,3,4,6,1,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,3,4,6,7,1]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,5,3,4,7,1,6]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,3,4,7,6,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,3,6,1,4,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,5,3,6,1,7,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,3,6,4,1,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,3,6,4,7,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,3,6,7,1,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,3,6,7,4,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,3,7,1,4,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,5,3,7,1,6,4]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,3,7,4,1,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,3,7,4,6,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,3,7,6,1,4]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[2,5,3,7,6,4,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,5,4,1,3,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[2,5,4,1,3,7,6]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,5,4,1,6,3,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,5,4,1,6,7,3]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,5,4,1,7,3,6]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,5,4,1,7,6,3]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,4,3,1,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[2,5,4,3,1,7,6]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,5,4,3,6,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,4,3,6,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,5,4,3,7,1,6]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,4,3,7,6,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,4,6,1,3,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,5,4,6,1,7,3]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,4,6,3,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,4,6,3,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,4,6,7,1,3]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,5,4,6,7,3,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,5,4,7,1,3,6]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,5,4,7,1,6,3]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,4,7,3,1,6]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,5,4,7,3,6,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,5,4,7,6,1,3]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[2,5,4,7,6,3,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,5,6,1,3,4,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[2,5,6,1,3,7,4]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,6,1,4,3,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,5,6,1,4,7,3]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,6,1,7,3,4]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,6,1,7,4,3]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,6,3,1,4,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,5,6,3,1,7,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,5,6,3,4,1,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,5,6,3,4,7,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,6,3,7,1,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,5,6,3,7,4,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,6,4,1,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,5,6,4,1,7,3]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[2,5,6,4,3,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[2,5,6,4,3,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,6,4,7,1,3]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,5,6,4,7,3,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,6,7,1,3,4]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[2,5,6,7,1,4,3]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,5,6,7,3,1,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,5,6,7,3,4,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[2,5,6,7,4,1,3]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[2,5,6,7,4,3,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[2,5,7,1,3,4,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[2,5,7,1,3,6,4]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,7,1,4,3,6]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,5,7,1,4,6,3]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,7,1,6,3,4]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,5,7,1,6,4,3]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,7,3,1,4,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,5,7,3,1,6,4]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,7,3,4,1,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,5,7,3,4,6,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,7,3,6,1,4]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,7,3,6,4,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,7,4,1,3,6]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[2,5,7,4,1,6,3]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,7,4,3,1,6]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,5,7,4,3,6,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,7,4,6,1,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,7,4,6,3,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,5,7,6,1,3,4]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[2,5,7,6,1,4,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,7,6,3,1,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,5,7,6,3,4,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,5,7,6,4,1,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,5,7,6,4,3,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[2,6,1,3,4,5,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[2,6,1,3,4,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[2,6,1,3,5,4,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,1,3,5,7,4]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,6,1,3,7,4,5]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,1,3,7,5,4]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,1,4,3,5,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,6,1,4,3,7,5]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,1,4,5,3,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,1,4,5,7,3]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,6,1,4,7,3,5]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,1,4,7,5,3]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,1,5,3,4,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,6,1,5,3,7,4]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,1,5,4,3,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,1,5,4,7,3]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,1,5,7,3,4]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,1,5,7,4,3]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,1,7,3,4,5]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,1,7,3,5,4]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,1,7,4,3,5]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,1,7,4,5,3]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,1,7,5,3,4]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,1,7,5,4,3]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,6,3,1,4,5,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[2,6,3,1,4,7,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,6,3,1,5,4,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,6,3,1,5,7,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,6,3,1,7,4,5]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,6,3,1,7,5,4]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,3,4,1,5,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,6,3,4,1,7,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,3,4,5,1,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,3,4,5,7,1]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,6,3,4,7,1,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,3,4,7,5,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,3,5,1,4,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,6,3,5,1,7,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,3,5,4,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,3,5,4,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,3,5,7,1,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,3,5,7,4,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,3,7,1,4,5]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,6,3,7,1,5,4]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,3,7,4,1,5]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,3,7,4,5,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,3,7,5,1,4]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[2,6,3,7,5,4,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,6,4,1,3,5,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[2,6,4,1,3,7,5]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,6,4,1,5,3,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,6,4,1,5,7,3]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,6,4,1,7,3,5]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,6,4,1,7,5,3]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,4,3,1,5,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[2,6,4,3,1,7,5]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,6,4,3,5,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,4,3,5,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,6,4,3,7,1,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,4,3,7,5,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,4,5,1,3,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,6,4,5,1,7,3]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,4,5,3,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,4,5,3,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,4,5,7,1,3]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,4,5,7,3,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,4,7,1,3,5]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,6,4,7,1,5,3]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,4,7,3,1,5]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,4,7,3,5,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,4,7,5,1,3]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[2,6,4,7,5,3,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,6,5,1,3,4,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[2,6,5,1,3,7,4]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,6,5,1,4,3,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,5,1,4,7,3]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,6,5,1,7,3,4]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,6,5,1,7,4,3]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,5,3,1,4,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[2,6,5,3,1,7,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,6,5,3,4,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,5,3,4,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,6,5,3,7,1,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,5,3,7,4,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,5,4,1,3,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[2,6,5,4,1,7,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,6,5,4,3,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[2,6,5,4,3,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,6,5,4,7,1,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,6,5,4,7,3,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,6,5,7,1,3,4]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,6,5,7,1,4,3]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,5,7,3,1,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,5,7,3,4,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,6,5,7,4,1,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,6,5,7,4,3,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,6,7,1,3,4,5]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[2,6,7,1,3,5,4]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,6,7,1,4,3,5]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,6,7,1,4,5,3]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,6,7,1,5,3,4]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,6,7,1,5,4,3]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,6,7,3,1,4,5]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[2,6,7,3,1,5,4]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,6,7,3,4,1,5]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[2,6,7,3,4,5,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,6,7,3,5,1,4]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,6,7,3,5,4,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,6,7,4,1,3,5]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[2,6,7,4,1,5,3]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[2,6,7,4,3,1,5]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,6,7,4,3,5,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,6,7,4,5,1,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[2,6,7,4,5,3,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[2,6,7,5,1,3,4]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[2,6,7,5,1,4,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,6,7,5,3,1,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,6,7,5,3,4,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[2,6,7,5,4,1,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[2,6,7,5,4,3,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[2,7,1,3,4,5,6]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[2,7,1,3,4,6,5]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,1,3,5,4,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,1,3,5,6,4]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,1,3,6,4,5]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,1,3,6,5,4]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,1,4,3,5,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,1,4,3,6,5]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,1,4,5,3,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,1,4,5,6,3]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,1,4,6,3,5]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,1,4,6,5,3]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,1,5,3,4,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,1,5,3,6,4]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,1,5,4,3,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,1,5,4,6,3]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,1,5,6,3,4]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,1,5,6,4,3]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,1,6,3,4,5]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,1,6,3,5,4]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,1,6,4,3,5]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,1,6,4,5,3]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,1,6,5,3,4]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,1,6,5,4,3]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,7,3,1,4,5,6]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[2,7,3,1,4,6,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,7,3,1,5,4,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,7,3,1,5,6,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,7,3,1,6,4,5]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,7,3,1,6,5,4]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,3,4,1,5,6]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,3,4,1,6,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,3,4,5,1,6]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,3,4,5,6,1]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,3,4,6,1,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,3,4,6,5,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,3,5,1,4,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,3,5,1,6,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,3,5,4,1,6]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,3,5,4,6,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,3,5,6,1,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,3,5,6,4,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,3,6,1,4,5]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,3,6,1,5,4]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,3,6,4,1,5]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,3,6,4,5,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,3,6,5,1,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,3,6,5,4,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,7,4,1,3,5,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[2,7,4,1,3,6,5]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,7,4,1,5,3,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,7,4,1,5,6,3]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,7,4,1,6,3,5]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,7,4,1,6,5,3]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,4,3,1,5,6]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[2,7,4,3,1,6,5]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,7,4,3,5,1,6]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,4,3,5,6,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,4,3,6,1,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,4,3,6,5,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,4,5,1,3,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,4,5,1,6,3]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,4,5,3,1,6]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,4,5,3,6,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,4,5,6,1,3]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,4,5,6,3,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,4,6,1,3,5]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,4,6,1,5,3]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,4,6,3,1,5]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,4,6,3,5,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,4,6,5,1,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,4,6,5,3,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,7,5,1,3,4,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[2,7,5,1,3,6,4]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[2,7,5,1,4,3,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,5,1,4,6,3]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,5,1,6,3,4]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[2,7,5,1,6,4,3]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,5,3,1,4,6]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[2,7,5,3,1,6,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,7,5,3,4,1,6]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,5,3,4,6,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,5,3,6,1,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,5,3,6,4,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,5,4,1,3,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[2,7,5,4,1,6,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,7,5,4,3,1,6]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[2,7,5,4,3,6,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,5,4,6,1,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,5,4,6,3,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,5,6,1,3,4]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[2,7,5,6,1,4,3]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,5,6,3,1,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,5,6,3,4,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[2,7,5,6,4,1,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[2,7,5,6,4,3,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[2,7,6,1,3,4,5]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[2,7,6,1,3,5,4]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,6,1,4,3,5]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,6,1,4,5,3]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,6,1,5,3,4]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,6,1,5,4,3]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,6,3,1,4,5]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[2,7,6,3,1,5,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,7,6,3,4,1,5]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,6,3,4,5,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,6,3,5,1,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,6,3,5,4,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,6,4,1,3,5]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[2,7,6,4,1,5,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[2,7,6,4,3,1,5]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[2,7,6,4,3,5,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,6,4,5,1,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[2,7,6,4,5,3,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[2,7,6,5,1,3,4]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[2,7,6,5,1,4,3]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,6,5,3,1,4]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[2,7,6,5,3,4,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[2,7,6,5,4,1,3]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[2,7,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,5]=>[5,2]=>2
[3,1,2,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[7]=>[7]=>1
[3,1,2,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[3,1,2,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[3,1,2,4,6,7,5]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[3,1,2,4,7,5,6]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[3,1,2,4,7,6,5]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,1,2,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[3,1,2,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,2,5,6,4,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[3,1,2,5,6,7,4]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[3,1,2,5,7,4,6]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[3,1,2,5,7,6,4]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,1,2,6,4,5,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[3,1,2,6,4,7,5]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,2,6,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,1,2,6,5,7,4]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,2,6,7,4,5]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[3,1,2,6,7,5,4]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,1,2,7,4,5,6]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[3,1,2,7,4,6,5]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,2,7,5,4,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,1,2,7,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,2,7,6,4,5]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,1,2,7,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,1,4,2,5,6,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[3,1,4,2,5,7,6]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,4,2,6,5,7]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,4,2,6,7,5]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,4,2,7,5,6]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,4,2,7,6,5]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,4,5,2,6,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[3,1,4,5,2,7,6]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,4,5,6,2,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[3,1,4,5,6,7,2]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[3,1,4,5,7,2,6]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[3,1,4,5,7,6,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,1,4,6,2,5,7]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[3,1,4,6,2,7,5]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,4,6,5,2,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,1,4,6,5,7,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,4,6,7,2,5]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[3,1,4,6,7,5,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,1,4,7,2,5,6]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[3,1,4,7,2,6,5]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,4,7,5,2,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,1,4,7,5,6,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,4,7,6,2,5]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[3,1,4,7,6,5,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,1,5,2,4,6,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[3,1,5,2,4,7,6]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,5,2,6,4,7]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,5,2,6,7,4]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,5,2,7,4,6]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,5,2,7,6,4]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,5,4,2,6,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,1,5,4,2,7,6]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,1,5,4,6,2,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,5,4,6,7,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,5,4,7,2,6]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,5,4,7,6,2]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,5,6,2,4,7]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[3,1,5,6,2,7,4]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,5,6,4,2,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,1,5,6,4,7,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,5,6,7,2,4]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[3,1,5,6,7,4,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,1,5,7,2,4,6]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[3,1,5,7,2,6,4]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,5,7,4,2,6]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[3,1,5,7,4,6,2]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,5,7,6,2,4]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[3,1,5,7,6,4,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,1,6,2,4,5,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[3,1,6,2,4,7,5]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,6,2,5,4,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,6,2,5,7,4]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,6,2,7,4,5]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,6,2,7,5,4]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,6,4,2,5,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,1,6,4,2,7,5]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,1,6,4,5,2,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,6,4,5,7,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,6,4,7,2,5]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,6,4,7,5,2]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,6,5,2,4,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,1,6,5,2,7,4]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,1,6,5,4,2,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,1,6,5,4,7,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,6,5,7,2,4]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,6,5,7,4,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,6,7,2,4,5]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[3,1,6,7,2,5,4]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,6,7,4,2,5]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[3,1,6,7,4,5,2]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,1,6,7,5,2,4]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[3,1,6,7,5,4,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,1,7,2,4,5,6]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[3,1,7,2,4,6,5]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,7,2,5,4,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,7,2,5,6,4]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,7,2,6,4,5]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,7,2,6,5,4]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,7,4,2,5,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,1,7,4,2,6,5]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,1,7,4,5,2,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,7,4,5,6,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,7,4,6,2,5]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,7,4,6,5,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,7,5,2,4,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,1,7,5,2,6,4]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,1,7,5,4,2,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,1,7,5,4,6,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,7,5,6,2,4]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,1,7,5,6,4,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,1,7,6,2,4,5]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,1,7,6,2,5,4]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,7,6,4,2,5]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,1,7,6,4,5,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,1,7,6,5,2,4]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,1,7,6,5,4,2]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[3,2,1,4,5,7,6]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[3,2,1,4,6,5,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[3,2,1,4,6,7,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[3,2,1,4,7,5,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[3,2,1,4,7,6,5]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[3,2,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[3,2,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[3,2,1,5,6,4,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[3,2,1,5,6,7,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[3,2,1,5,7,4,6]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[3,2,1,5,7,6,4]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[3,2,1,6,4,5,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[3,2,1,6,4,7,5]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[3,2,1,6,5,4,7]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[3,2,1,6,5,7,4]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,1,6,7,4,5]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[3,2,1,6,7,5,4]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[3,2,1,7,4,5,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[3,2,1,7,4,6,5]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,1,7,5,4,6]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[3,2,1,7,5,6,4]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,1,7,6,4,5]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[3,2,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[3,2,4,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[3,2,4,1,5,7,6]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[3,2,4,1,6,5,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[3,2,4,1,6,7,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[3,2,4,1,7,5,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[3,2,4,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,4,5,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[3,2,4,5,1,7,6]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[3,2,4,5,6,1,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[3,2,4,5,6,7,1]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[3,2,4,5,7,1,6]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[3,2,4,5,7,6,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,2,4,6,1,5,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[3,2,4,6,1,7,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[3,2,4,6,5,1,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,2,4,6,5,7,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,4,6,7,1,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[3,2,4,6,7,5,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,2,4,7,1,5,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[3,2,4,7,1,6,5]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,4,7,5,1,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,2,4,7,5,6,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,4,7,6,1,5]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[3,2,4,7,6,5,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,2,5,1,4,6,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[3,2,5,1,4,7,6]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[3,2,5,1,6,4,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[3,2,5,1,6,7,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[3,2,5,1,7,4,6]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[3,2,5,1,7,6,4]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,5,4,1,6,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,2,5,4,1,7,6]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,2,5,4,6,1,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,2,5,4,6,7,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,5,4,7,1,6]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,2,5,4,7,6,1]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,5,6,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[3,2,5,6,1,7,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[3,2,5,6,4,1,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[3,2,5,6,4,7,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,5,6,7,1,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[3,2,5,6,7,4,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[3,2,5,7,1,4,6]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[3,2,5,7,1,6,4]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,5,7,4,1,6]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[3,2,5,7,4,6,1]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,5,7,6,1,4]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[3,2,5,7,6,4,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,2,6,1,4,5,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[3,2,6,1,4,7,5]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[3,2,6,1,5,4,7]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,2,6,1,5,7,4]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,6,1,7,4,5]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[3,2,6,1,7,5,4]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,6,4,1,5,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,2,6,4,1,7,5]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,2,6,4,5,1,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,2,6,4,5,7,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,6,4,7,1,5]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,2,6,4,7,5,1]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,6,5,1,4,7]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[3,2,6,5,1,7,4]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,6,5,4,1,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,2,6,5,4,7,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,6,5,7,1,4]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,6,5,7,4,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,6,7,1,4,5]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[3,2,6,7,1,5,4]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,6,7,4,1,5]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[3,2,6,7,4,5,1]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,2,6,7,5,1,4]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[3,2,6,7,5,4,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,2,7,1,4,5,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[3,2,7,1,4,6,5]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,7,1,5,4,6]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,2,7,1,5,6,4]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,7,1,6,4,5]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,2,7,1,6,5,4]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,7,4,1,5,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[3,2,7,4,1,6,5]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,7,4,5,1,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,2,7,4,5,6,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,7,4,6,1,5]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,7,4,6,5,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,7,5,1,4,6]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[3,2,7,5,1,6,4]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,7,5,4,1,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,2,7,5,4,6,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,7,5,6,1,4]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,7,5,6,4,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,2,7,6,1,4,5]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[3,2,7,6,1,5,4]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,7,6,4,1,5]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,2,7,6,4,5,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,2,7,6,5,1,4]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[3,2,7,6,5,4,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[3,4,1,2,5,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[3,4,1,2,6,5,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[3,4,1,2,6,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[3,4,1,2,7,5,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[3,4,1,2,7,6,5]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,4,1,5,2,6,7]=>[[1,2,4,6,7],[3,5]]=>[2,2,3]=>[3,2,2]=>3
[3,4,1,5,2,7,6]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,1,5,6,2,7]=>[[1,2,4,5,7],[3,6]]=>[2,3,2]=>[3,2,2]=>3
[3,4,1,5,6,7,2]=>[[1,2,4,5,6],[3,7]]=>[2,4,1]=>[4,2,1]=>3
[3,4,1,5,7,2,6]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[3,4,1,5,7,6,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,4,1,6,2,5,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[3,4,1,6,2,7,5]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,1,6,5,2,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,4,1,6,5,7,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,1,6,7,2,5]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[3,4,1,6,7,5,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,4,1,7,2,5,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[3,4,1,7,2,6,5]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,1,7,5,2,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,4,1,7,5,6,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,1,7,6,2,5]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,4,1,7,6,5,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,4,2,1,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[2,5]=>[5,2]=>2
[3,4,2,1,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,4,2,1,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,4,2,1,6,7,5]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,4,2,1,7,5,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,4,2,1,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[3,4,2,5,1,6,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,4,2,5,1,7,6]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,2,5,6,1,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,4,2,5,6,7,1]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,4,2,5,7,1,6]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,4,2,5,7,6,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,4,2,6,1,5,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,4,2,6,1,7,5]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,2,6,5,1,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,4,2,6,5,7,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,2,6,7,1,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,4,2,6,7,5,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,4,2,7,1,5,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,4,2,7,1,6,5]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,2,7,5,1,6]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,4,2,7,5,6,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,4,2,7,6,1,5]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[3,4,2,7,6,5,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,4,5,1,2,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]=>[4,3]=>2
[3,4,5,1,2,7,6]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,5,1,6,2,7]=>[[1,2,3,5,7],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,5,1,6,7,2]=>[[1,2,3,5,6],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,5,1,7,2,6]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,5,1,7,6,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,5,2,1,6,7]=>[[1,2,3,6,7],[4],[5]]=>[3,4]=>[4,3]=>2
[3,4,5,2,1,7,6]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,4,5,2,6,1,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,5,2,6,7,1]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,5,2,7,1,6]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,5,2,7,6,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,5,6,1,2,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]=>[4,3]=>2
[3,4,5,6,1,7,2]=>[[1,2,3,4,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[3,4,5,6,2,1,7]=>[[1,2,3,4,7],[5],[6]]=>[4,3]=>[4,3]=>2
[3,4,5,6,2,7,1]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,4,5,6,7,1,2]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[5,2]=>2
[3,4,5,6,7,2,1]=>[[1,2,3,4,5],[6],[7]]=>[5,2]=>[5,2]=>2
[3,4,5,7,1,2,6]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[3,4,5,7,1,6,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,4,5,7,2,1,6]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[3,4,5,7,2,6,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,4,5,7,6,1,2]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[3,4,5,7,6,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,4,6,1,2,5,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[3,4,6,1,2,7,5]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,6,1,5,2,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,6,1,5,7,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,6,1,7,2,5]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,6,1,7,5,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,6,2,1,5,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[3,4,6,2,1,7,5]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,4,6,2,5,1,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,6,2,5,7,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,6,2,7,1,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,6,2,7,5,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,6,5,1,2,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[3,4,6,5,1,7,2]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,4,6,5,2,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,4,6,5,2,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,6,5,7,1,2]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,6,5,7,2,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,6,7,1,2,5]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[3,4,6,7,1,5,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,4,6,7,2,1,5]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[3,4,6,7,2,5,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,4,6,7,5,1,2]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[3,4,6,7,5,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,4,7,1,2,5,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[3,4,7,1,2,6,5]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,7,1,5,2,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,7,1,5,6,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,7,1,6,2,5]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,7,1,6,5,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,7,2,1,5,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[3,4,7,2,1,6,5]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,7,2,5,1,6]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,7,2,5,6,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,7,2,6,1,5]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,7,2,6,5,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,7,5,1,2,6]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[3,4,7,5,1,6,2]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,4,7,5,2,1,6]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,4,7,5,2,6,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,7,5,6,1,2]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,4,7,5,6,2,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,4,7,6,1,2,5]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[3,4,7,6,1,5,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,7,6,2,1,5]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[3,4,7,6,2,5,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,4,7,6,5,1,2]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[3,4,7,6,5,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[3,5,1,2,4,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[3,5,1,2,4,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[3,5,1,2,6,4,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,1,2,6,7,4]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[3,5,1,2,7,4,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,1,2,7,6,4]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,1,4,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,5,1,4,2,7,6]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,1,4,6,2,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,1,4,6,7,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,5,1,4,7,2,6]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,1,4,7,6,2]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,1,6,2,4,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,1,6,2,7,4]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,1,6,4,2,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,1,6,4,7,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,1,6,7,2,4]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,1,6,7,4,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,1,7,2,4,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,1,7,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,1,7,4,2,6]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,1,7,4,6,2]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,1,7,6,2,4]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,1,7,6,4,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,5,2,1,4,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,5,2,1,4,7,6]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,5,2,1,6,4,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,5,2,1,6,7,4]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,5,2,1,7,4,6]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,5,2,1,7,6,4]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,2,4,1,6,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,5,2,4,1,7,6]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,2,4,6,1,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,2,4,6,7,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,5,2,4,7,1,6]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,2,4,7,6,1]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,2,6,1,4,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,5,2,6,1,7,4]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,2,6,4,1,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,2,6,4,7,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,2,6,7,1,4]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,2,6,7,4,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,2,7,1,4,6]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,5,2,7,1,6,4]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,2,7,4,1,6]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,2,7,4,6,1]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,2,7,6,1,4]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[3,5,2,7,6,4,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,5,4,1,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,5,4,1,2,7,6]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,5,4,1,6,2,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,5,4,1,6,7,2]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,5,4,1,7,2,6]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,5,4,1,7,6,2]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,4,2,1,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[3,5,4,2,1,7,6]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,5,4,2,6,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,4,2,6,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,5,4,2,7,1,6]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,4,2,7,6,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,4,6,1,2,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,5,4,6,1,7,2]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,4,6,2,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,4,6,2,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,4,6,7,1,2]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,5,4,6,7,2,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,5,4,7,1,2,6]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,5,4,7,1,6,2]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,4,7,2,1,6]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,5,4,7,2,6,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,5,4,7,6,1,2]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[3,5,4,7,6,2,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,5,6,1,2,4,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[3,5,6,1,2,7,4]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,6,1,4,2,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,5,6,1,4,7,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,6,1,7,2,4]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,6,1,7,4,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,6,2,1,4,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[3,5,6,2,1,7,4]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,5,6,2,4,1,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,5,6,2,4,7,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,6,2,7,1,4]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,5,6,2,7,4,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,6,4,1,2,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[3,5,6,4,1,7,2]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[3,5,6,4,2,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[3,5,6,4,2,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,6,4,7,1,2]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,5,6,4,7,2,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,6,7,1,2,4]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[3,5,6,7,1,4,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,5,6,7,2,1,4]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[3,5,6,7,2,4,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[3,5,6,7,4,1,2]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[3,5,6,7,4,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[3,5,7,1,2,4,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[3,5,7,1,2,6,4]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,7,1,4,2,6]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,5,7,1,4,6,2]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,7,1,6,2,4]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,5,7,1,6,4,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,7,2,1,4,6]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[3,5,7,2,1,6,4]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,7,2,4,1,6]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,5,7,2,4,6,1]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,7,2,6,1,4]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,7,2,6,4,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,7,4,1,2,6]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[3,5,7,4,1,6,2]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,7,4,2,1,6]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[3,5,7,4,2,6,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,7,4,6,1,2]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,7,4,6,2,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,5,7,6,1,2,4]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[3,5,7,6,1,4,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,7,6,2,1,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[3,5,7,6,2,4,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,5,7,6,4,1,2]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[3,5,7,6,4,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[3,6,1,2,4,5,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[3,6,1,2,4,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,1,2,5,4,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,1,2,5,7,4]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,1,2,7,4,5]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,1,2,7,5,4]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,1,4,2,5,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,6,1,4,2,7,5]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,1,4,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,1,4,5,7,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,1,4,7,2,5]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,1,4,7,5,2]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,1,5,2,4,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,6,1,5,2,7,4]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,1,5,4,2,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,1,5,4,7,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,1,5,7,2,4]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,1,5,7,4,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,1,7,2,4,5]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,1,7,2,5,4]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,1,7,4,2,5]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,1,7,4,5,2]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,1,7,5,2,4]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,1,7,5,4,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,6,2,1,4,5,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,6,2,1,4,7,5]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,6,2,1,5,4,7]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,2,1,5,7,4]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,2,1,7,4,5]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,6,2,1,7,5,4]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,2,4,1,5,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,6,2,4,1,7,5]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,2,4,5,1,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,2,4,5,7,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,2,4,7,1,5]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,2,4,7,5,1]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,2,5,1,4,7]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,2,5,1,7,4]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,2,5,4,1,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,2,5,4,7,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,2,5,7,1,4]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,2,5,7,4,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,2,7,1,4,5]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,6,2,7,1,5,4]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,2,7,4,1,5]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,2,7,4,5,1]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,2,7,5,1,4]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[3,6,2,7,5,4,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,6,4,1,2,5,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,6,4,1,2,7,5]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,6,4,1,5,2,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,6,4,1,5,7,2]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,6,4,1,7,2,5]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,6,4,1,7,5,2]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,4,2,1,5,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[3,6,4,2,1,7,5]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,6,4,2,5,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,4,2,5,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,4,2,7,1,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,4,2,7,5,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,4,5,1,2,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,6,4,5,1,7,2]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,4,5,2,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,4,5,2,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,4,5,7,1,2]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,4,5,7,2,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,4,7,1,2,5]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,6,4,7,1,5,2]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,4,7,2,1,5]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,4,7,2,5,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,4,7,5,1,2]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[3,6,4,7,5,2,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,6,5,1,2,4,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,6,5,1,2,7,4]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,6,5,1,4,2,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,5,1,4,7,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,5,1,7,2,4]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,6,5,1,7,4,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,5,2,1,4,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[3,6,5,2,1,7,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,6,5,2,4,1,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,5,2,4,7,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,5,2,7,1,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,5,2,7,4,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,5,4,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[3,6,5,4,1,7,2]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,6,5,4,2,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[3,6,5,4,2,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,6,5,4,7,1,2]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,6,5,4,7,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,6,5,7,1,2,4]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,6,5,7,1,4,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,5,7,2,1,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,5,7,2,4,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,6,5,7,4,1,2]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,6,5,7,4,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,6,7,1,2,4,5]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[3,6,7,1,2,5,4]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,6,7,1,4,2,5]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,6,7,1,4,5,2]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,6,7,1,5,2,4]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,6,7,1,5,4,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,6,7,2,1,4,5]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[3,6,7,2,1,5,4]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,6,7,2,4,1,5]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[3,6,7,2,4,5,1]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,6,7,2,5,1,4]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,6,7,2,5,4,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,6,7,4,1,2,5]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[3,6,7,4,1,5,2]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[3,6,7,4,2,1,5]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[3,6,7,4,2,5,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,6,7,4,5,1,2]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[3,6,7,4,5,2,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[3,6,7,5,1,2,4]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[3,6,7,5,1,4,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,6,7,5,2,1,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[3,6,7,5,2,4,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[3,6,7,5,4,1,2]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[3,6,7,5,4,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[3,7,1,2,4,5,6]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[3,7,1,2,4,6,5]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,1,2,5,4,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,1,2,5,6,4]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,1,2,6,4,5]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,1,2,6,5,4]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,1,4,2,5,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,7,1,4,2,6,5]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,1,4,5,2,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,1,4,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,1,4,6,2,5]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,1,4,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,1,5,2,4,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,7,1,5,2,6,4]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,1,5,4,2,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,1,5,4,6,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,1,5,6,2,4]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,1,5,6,4,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,1,6,2,4,5]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,7,1,6,2,5,4]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,1,6,4,2,5]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,1,6,4,5,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,1,6,5,2,4]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,1,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,7,2,1,4,5,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,7,2,1,4,6,5]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,2,1,5,4,6]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,2,1,5,6,4]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,2,1,6,4,5]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,2,1,6,5,4]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,2,4,1,5,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,7,2,4,1,6,5]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,2,4,5,1,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,2,4,5,6,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,2,4,6,1,5]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,2,4,6,5,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,2,5,1,4,6]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,2,5,1,6,4]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,2,5,4,1,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,2,5,4,6,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,2,5,6,1,4]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,2,5,6,4,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,2,6,1,4,5]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,2,6,1,5,4]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,2,6,4,1,5]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,2,6,4,5,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,2,6,5,1,4]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,2,6,5,4,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,7,4,1,2,5,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,7,4,1,2,6,5]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,7,4,1,5,2,6]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,7,4,1,5,6,2]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,7,4,1,6,2,5]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,7,4,1,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,4,2,1,5,6]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[3,7,4,2,1,6,5]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,7,4,2,5,1,6]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,4,2,5,6,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,4,2,6,1,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,4,2,6,5,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,4,5,1,2,6]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,7,4,5,1,6,2]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,4,5,2,1,6]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,4,5,2,6,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,4,5,6,1,2]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,4,5,6,2,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,4,6,1,2,5]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,7,4,6,1,5,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,4,6,2,1,5]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,4,6,2,5,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,4,6,5,1,2]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,4,6,5,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,7,5,1,2,4,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,7,5,1,2,6,4]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[3,7,5,1,4,2,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,5,1,4,6,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,5,1,6,2,4]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[3,7,5,1,6,4,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,5,2,1,4,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[3,7,5,2,1,6,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,7,5,2,4,1,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,5,2,4,6,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,5,2,6,1,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,5,2,6,4,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,5,4,1,2,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[3,7,5,4,1,6,2]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,7,5,4,2,1,6]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[3,7,5,4,2,6,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,5,4,6,1,2]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,5,4,6,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,5,6,1,2,4]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[3,7,5,6,1,4,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,5,6,2,1,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,5,6,2,4,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[3,7,5,6,4,1,2]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[3,7,5,6,4,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[3,7,6,1,2,4,5]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[3,7,6,1,2,5,4]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,6,1,4,2,5]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,6,1,4,5,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,6,1,5,2,4]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,6,1,5,4,2]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,6,2,1,4,5]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[3,7,6,2,1,5,4]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,7,6,2,4,1,5]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,6,2,4,5,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,6,2,5,1,4]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,6,2,5,4,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,6,4,1,2,5]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[3,7,6,4,1,5,2]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[3,7,6,4,2,1,5]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[3,7,6,4,2,5,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,6,4,5,1,2]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[3,7,6,4,5,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[3,7,6,5,1,2,4]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[3,7,6,5,1,4,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,6,5,2,1,4]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[3,7,6,5,2,4,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[3,7,6,5,4,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[3,7,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,5]=>[5,2]=>2
[4,1,2,3,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[7]=>[7]=>1
[4,1,2,3,5,7,6]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[4,1,2,3,6,5,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[4,1,2,3,6,7,5]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[4,1,2,3,7,5,6]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[4,1,2,3,7,6,5]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,1,2,5,3,6,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[4,1,2,5,3,7,6]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,2,5,6,3,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[4,1,2,5,6,7,3]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[4,1,2,5,7,3,6]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[4,1,2,5,7,6,3]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,1,2,6,3,5,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[4,1,2,6,3,7,5]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,2,6,5,3,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,1,2,6,5,7,3]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,2,6,7,3,5]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[4,1,2,6,7,5,3]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,1,2,7,3,5,6]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[4,1,2,7,3,6,5]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,2,7,5,3,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,1,2,7,5,6,3]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,2,7,6,3,5]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,1,2,7,6,5,3]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,1,3,2,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[4,1,3,2,5,7,6]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,1,3,2,6,5,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,1,3,2,6,7,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,1,3,2,7,5,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,1,3,2,7,6,5]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,3,5,2,6,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[4,1,3,5,2,7,6]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,1,3,5,6,2,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[4,1,3,5,6,7,2]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[4,1,3,5,7,2,6]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[4,1,3,5,7,6,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,1,3,6,2,5,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[4,1,3,6,2,7,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,1,3,6,5,2,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,1,3,6,5,7,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,3,6,7,2,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[4,1,3,6,7,5,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,1,3,7,2,5,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[4,1,3,7,2,6,5]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,3,7,5,2,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,1,3,7,5,6,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,3,7,6,2,5]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[4,1,3,7,6,5,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,1,5,2,3,6,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[4,1,5,2,3,7,6]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,5,2,6,3,7]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,5,2,6,7,3]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,5,2,7,3,6]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,5,2,7,6,3]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,5,3,2,6,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,1,5,3,2,7,6]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,1,5,3,6,2,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,5,3,6,7,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,5,3,7,2,6]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,5,3,7,6,2]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,5,6,2,3,7]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[4,1,5,6,2,7,3]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,5,6,3,2,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,1,5,6,3,7,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,5,6,7,2,3]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[4,1,5,6,7,3,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,1,5,7,2,3,6]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[4,1,5,7,2,6,3]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,5,7,3,2,6]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[4,1,5,7,3,6,2]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,5,7,6,2,3]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[4,1,5,7,6,3,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,1,6,2,3,5,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[4,1,6,2,3,7,5]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,6,2,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,6,2,5,7,3]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,6,2,7,3,5]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,6,2,7,5,3]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,6,3,2,5,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,1,6,3,2,7,5]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,1,6,3,5,2,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,6,3,5,7,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,6,3,7,2,5]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,6,3,7,5,2]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,6,5,2,3,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,1,6,5,2,7,3]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,1,6,5,3,2,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,1,6,5,3,7,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,6,5,7,2,3]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,6,5,7,3,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,6,7,2,3,5]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[4,1,6,7,2,5,3]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,6,7,3,2,5]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[4,1,6,7,3,5,2]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,1,6,7,5,2,3]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[4,1,6,7,5,3,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,1,7,2,3,5,6]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[4,1,7,2,3,6,5]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,7,2,5,3,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,7,2,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,7,2,6,3,5]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,7,2,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,7,3,2,5,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,1,7,3,2,6,5]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,7,3,5,2,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,7,3,5,6,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,7,3,6,2,5]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,7,3,6,5,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,7,5,2,3,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,1,7,5,2,6,3]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,1,7,5,3,2,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,1,7,5,3,6,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,7,5,6,2,3]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,1,7,5,6,3,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,1,7,6,2,3,5]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,1,7,6,2,5,3]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,7,6,3,2,5]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,1,7,6,3,5,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,1,7,6,5,2,3]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,1,7,6,5,3,2]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[4,2,1,3,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[4,2,1,3,5,7,6]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[4,2,1,3,6,5,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[4,2,1,3,6,7,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[4,2,1,3,7,5,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[4,2,1,3,7,6,5]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[4,2,1,5,3,6,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[4,2,1,5,3,7,6]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[4,2,1,5,6,3,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[4,2,1,5,6,7,3]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[4,2,1,5,7,3,6]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[4,2,1,5,7,6,3]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[4,2,1,6,3,5,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[4,2,1,6,3,7,5]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[4,2,1,6,5,3,7]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[4,2,1,6,5,7,3]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,1,6,7,3,5]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[4,2,1,6,7,5,3]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[4,2,1,7,3,5,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[4,2,1,7,3,6,5]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,1,7,5,3,6]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[4,2,1,7,5,6,3]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,1,7,6,3,5]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[4,2,1,7,6,5,3]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[4,2,3,1,5,7,6]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,2,3,1,6,5,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,2,3,1,6,7,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,2,3,1,7,5,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,2,3,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,3,5,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[4,2,3,5,1,7,6]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,2,3,5,6,1,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[4,2,3,5,6,7,1]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[4,2,3,5,7,1,6]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[4,2,3,5,7,6,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,2,3,6,1,5,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[4,2,3,6,1,7,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,2,3,6,5,1,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,2,3,6,5,7,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,3,6,7,1,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[4,2,3,6,7,5,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,2,3,7,1,5,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[4,2,3,7,1,6,5]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,3,7,5,1,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,2,3,7,5,6,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,3,7,6,1,5]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[4,2,3,7,6,5,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,2,5,1,3,6,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[4,2,5,1,3,7,6]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,2,5,1,6,3,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,2,5,1,6,7,3]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,2,5,1,7,3,6]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,2,5,1,7,6,3]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,5,3,1,6,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,2,5,3,1,7,6]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,2,5,3,6,1,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,2,5,3,6,7,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,5,3,7,1,6]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,2,5,3,7,6,1]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,5,6,1,3,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[4,2,5,6,1,7,3]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,2,5,6,3,1,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[4,2,5,6,3,7,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,5,6,7,1,3]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[4,2,5,6,7,3,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[4,2,5,7,1,3,6]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[4,2,5,7,1,6,3]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,5,7,3,1,6]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[4,2,5,7,3,6,1]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,5,7,6,1,3]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[4,2,5,7,6,3,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,2,6,1,3,5,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[4,2,6,1,3,7,5]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,2,6,1,5,3,7]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,2,6,1,5,7,3]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,6,1,7,3,5]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,2,6,1,7,5,3]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,6,3,1,5,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,2,6,3,1,7,5]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,2,6,3,5,1,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,2,6,3,5,7,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,6,3,7,1,5]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,2,6,3,7,5,1]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,6,5,1,3,7]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[4,2,6,5,1,7,3]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,6,5,3,1,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,2,6,5,3,7,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,6,5,7,1,3]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,6,5,7,3,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,6,7,1,3,5]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[4,2,6,7,1,5,3]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,6,7,3,1,5]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[4,2,6,7,3,5,1]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,2,6,7,5,1,3]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[4,2,6,7,5,3,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,2,7,1,3,5,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[4,2,7,1,3,6,5]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,7,1,5,3,6]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,2,7,1,5,6,3]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,7,1,6,3,5]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,2,7,1,6,5,3]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,7,3,1,5,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[4,2,7,3,1,6,5]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,7,3,5,1,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,2,7,3,5,6,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,7,3,6,1,5]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,7,3,6,5,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,7,5,1,3,6]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[4,2,7,5,1,6,3]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,7,5,3,1,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,2,7,5,3,6,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,7,5,6,1,3]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,7,5,6,3,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,2,7,6,1,3,5]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[4,2,7,6,1,5,3]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,7,6,3,1,5]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,2,7,6,3,5,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,2,7,6,5,1,3]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[4,2,7,6,5,3,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[4,3,1,2,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[4,3,1,2,5,7,6]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[4,3,1,2,6,5,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[4,3,1,2,6,7,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[4,3,1,2,7,5,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[4,3,1,2,7,6,5]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[4,3,1,5,2,6,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[4,3,1,5,2,7,6]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[4,3,1,5,6,2,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[4,3,1,5,6,7,2]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[4,3,1,5,7,2,6]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[4,3,1,5,7,6,2]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[4,3,1,6,2,5,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[4,3,1,6,2,7,5]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[4,3,1,6,5,2,7]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[4,3,1,6,5,7,2]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,1,6,7,2,5]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[4,3,1,6,7,5,2]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[4,3,1,7,2,5,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[4,3,1,7,2,6,5]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,1,7,5,2,6]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[4,3,1,7,5,6,2]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,1,7,6,2,5]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[4,3,1,7,6,5,2]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[4,3,2,1,5,7,6]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[4,3,2,1,6,5,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[4,3,2,1,6,7,5]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[4,3,2,1,7,5,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[4,3,2,1,7,6,5]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[4,3,2,5,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[4,3,2,5,1,7,6]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,3,2,5,6,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[4,3,2,5,6,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[4,3,2,5,7,1,6]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[4,3,2,5,7,6,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[4,3,2,6,1,5,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[4,3,2,6,1,7,5]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,3,2,6,5,1,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[4,3,2,6,5,7,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,2,6,7,1,5]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[4,3,2,6,7,5,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[4,3,2,7,1,5,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[4,3,2,7,1,6,5]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,3,2,7,5,1,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[4,3,2,7,5,6,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,2,7,6,1,5]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[4,3,2,7,6,5,1]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[4,3,5,1,2,6,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[4,3,5,1,2,7,6]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,3,5,1,6,2,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,3,5,1,6,7,2]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,3,5,1,7,2,6]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,3,5,1,7,6,2]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,5,2,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[4,3,5,2,1,7,6]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,3,5,2,6,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,5,2,6,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,5,2,7,1,6]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,5,2,7,6,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,5,6,1,2,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[4,3,5,6,1,7,2]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[4,3,5,6,2,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[4,3,5,6,2,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,5,6,7,1,2]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[4,3,5,6,7,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[4,3,5,7,1,2,6]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[4,3,5,7,1,6,2]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,5,7,2,1,6]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[4,3,5,7,2,6,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,5,7,6,1,2]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[4,3,5,7,6,2,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,3,6,1,2,5,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[4,3,6,1,2,7,5]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[4,3,6,1,5,2,7]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,6,1,5,7,2]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,6,1,7,2,5]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[4,3,6,1,7,5,2]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,6,2,1,5,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[4,3,6,2,1,7,5]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,3,6,2,5,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,6,2,5,7,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,6,2,7,1,5]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,6,2,7,5,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,6,5,1,2,7]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[4,3,6,5,1,7,2]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,6,5,2,1,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,3,6,5,2,7,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,6,5,7,1,2]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,6,5,7,2,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,6,7,1,2,5]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[4,3,6,7,1,5,2]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,6,7,2,1,5]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[4,3,6,7,2,5,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,3,6,7,5,1,2]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[4,3,6,7,5,2,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,3,7,1,2,5,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[4,3,7,1,2,6,5]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,7,1,5,2,6]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,7,1,5,6,2]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,7,1,6,2,5]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,7,1,6,5,2]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,7,2,1,5,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[4,3,7,2,1,6,5]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,3,7,2,5,1,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,7,2,5,6,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,7,2,6,1,5]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,3,7,2,6,5,1]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,7,5,1,2,6]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[4,3,7,5,1,6,2]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,7,5,2,1,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,3,7,5,2,6,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,7,5,6,1,2]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,7,5,6,2,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,3,7,6,1,2,5]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[4,3,7,6,1,5,2]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,7,6,2,1,5]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[4,3,7,6,2,5,1]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,3,7,6,5,1,2]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[4,3,7,6,5,2,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[4,5,1,2,3,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[4,5,1,2,3,7,6]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,5,1,2,6,3,7]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,1,2,6,7,3]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,5,1,2,7,3,6]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,1,2,7,6,3]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,1,3,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,5,1,3,2,7,6]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,1,3,6,2,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,1,3,6,7,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,5,1,3,7,2,6]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,1,3,7,6,2]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,1,6,2,3,7]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,1,6,2,7,3]=>[[1,2,4,6],[3,5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,1,6,3,2,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,1,6,3,7,2]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,1,6,7,2,3]=>[[1,2,4,5],[3,6,7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,1,6,7,3,2]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,1,7,2,3,6]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,1,7,2,6,3]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,1,7,3,2,6]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,1,7,3,6,2]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,1,7,6,2,3]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,1,7,6,3,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,5,2,1,3,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,5,2,1,3,7,6]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[4,5,2,1,6,3,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[4,5,2,1,6,7,3]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[4,5,2,1,7,3,6]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[4,5,2,1,7,6,3]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,2,3,1,6,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,5,2,3,1,7,6]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,2,3,6,1,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,2,3,6,7,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,5,2,3,7,1,6]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,2,3,7,6,1]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,2,6,1,3,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,5,2,6,1,7,3]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,2,6,3,1,7]=>[[1,2,4,7],[3,5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,2,6,3,7,1]=>[[1,2,4,6],[3,5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,2,6,7,1,3]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,2,6,7,3,1]=>[[1,2,4,5],[3,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,2,7,1,3,6]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,5,2,7,1,6,3]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,2,7,3,1,6]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,2,7,3,6,1]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,2,7,6,1,3]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[4,5,2,7,6,3,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,5,3,1,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,5,3,1,2,7,6]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[4,5,3,1,6,2,7]=>[[1,2,5,7],[3,6],[4]]=>[2,3,2]=>[3,2,2]=>3
[4,5,3,1,6,7,2]=>[[1,2,5,6],[3,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[4,5,3,1,7,2,6]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[4,5,3,1,7,6,2]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,3,2,1,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,5]=>[5,2]=>2
[4,5,3,2,1,7,6]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,5,3,2,6,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,3,2,6,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,5,3,2,7,1,6]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,3,2,7,6,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,3,6,1,2,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,5,3,6,1,7,2]=>[[1,2,4,6],[3,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,3,6,2,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,3,6,2,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,3,6,7,1,2]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,5,3,6,7,2,1]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,5,3,7,1,2,6]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,5,3,7,1,6,2]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,3,7,2,1,6]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,5,3,7,2,6,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,5,3,7,6,1,2]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[4,5,3,7,6,2,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[4,5,6,1,2,7,3]=>[[1,2,3,6],[4,5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,6,1,3,2,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,5,6,1,3,7,2]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,6,1,7,2,3]=>[[1,2,3,5],[4,6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,6,1,7,3,2]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,6,2,1,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[4,5,6,2,1,7,3]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,5,6,2,3,1,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,5,6,2,3,7,1]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,6,2,7,1,3]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,5,6,2,7,3,1]=>[[1,2,3,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,6,3,1,2,7]=>[[1,2,3,7],[4,6],[5]]=>[3,4]=>[4,3]=>2
[4,5,6,3,1,7,2]=>[[1,2,3,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[4,5,6,3,2,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[4,5,6,3,2,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,6,3,7,1,2]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,5,6,3,7,2,1]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,6,7,1,2,3]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[4,3]=>2
[4,5,6,7,1,3,2]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,5,6,7,2,1,3]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[4,5,6,7,2,3,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[4,5,6,7,3,1,2]=>[[1,2,3,4],[5,7],[6]]=>[4,3]=>[4,3]=>2
[4,5,6,7,3,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[4,5,7,1,2,3,6]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[4,5,7,1,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,7,1,3,2,6]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,5,7,1,3,6,2]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,7,1,6,2,3]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,5,7,1,6,3,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,7,2,1,3,6]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[4,5,7,2,1,6,3]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,7,2,3,1,6]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,5,7,2,3,6,1]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,7,2,6,1,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,7,2,6,3,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,7,3,1,2,6]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[4,5,7,3,1,6,2]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,7,3,2,1,6]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[4,5,7,3,2,6,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,7,3,6,1,2]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,7,3,6,2,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,5,7,6,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[4,5,7,6,1,3,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,7,6,2,1,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[4,5,7,6,2,3,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,5,7,6,3,1,2]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[4,5,7,6,3,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[4,6,1,2,3,5,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[4,6,1,2,3,7,5]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,1,2,5,3,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,1,2,5,7,3]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,1,2,7,3,5]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,1,2,7,5,3]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,1,3,2,5,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,6,1,3,2,7,5]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,1,3,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,1,3,5,7,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,1,3,7,2,5]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,1,3,7,5,2]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,1,5,2,3,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,6,1,5,2,7,3]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,1,5,3,2,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,1,5,3,7,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,1,5,7,2,3]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,1,5,7,3,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,1,7,2,3,5]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,1,7,2,5,3]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,1,7,3,2,5]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,1,7,3,5,2]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,1,7,5,2,3]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,1,7,5,3,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,6,2,1,3,5,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,6,2,1,3,7,5]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[4,6,2,1,5,3,7]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,2,1,5,7,3]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,2,1,7,3,5]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[4,6,2,1,7,5,3]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,2,3,1,5,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,6,2,3,1,7,5]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,2,3,5,1,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,2,3,5,7,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,2,3,7,1,5]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,2,3,7,5,1]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,2,5,1,3,7]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,2,5,1,7,3]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,2,5,3,1,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,2,5,3,7,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,2,5,7,1,3]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,2,5,7,3,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,2,7,1,3,5]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,6,2,7,1,5,3]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,2,7,3,1,5]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,2,7,3,5,1]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,2,7,5,1,3]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[4,6,2,7,5,3,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,6,3,1,2,5,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,6,3,1,2,7,5]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[4,6,3,1,5,2,7]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,3,1,5,7,2]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,3,1,7,2,5]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[4,6,3,1,7,5,2]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,3,2,1,5,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,6,3,2,1,7,5]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,6,3,2,5,1,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,3,2,5,7,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,3,2,7,1,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,3,2,7,5,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,3,5,1,2,7]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,3,5,1,7,2]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,3,5,2,1,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,3,5,2,7,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,3,5,7,1,2]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,3,5,7,2,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,3,7,1,2,5]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,6,3,7,1,5,2]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,3,7,2,1,5]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,3,7,2,5,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,3,7,5,1,2]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[4,6,3,7,5,2,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,6,5,1,2,3,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,6,5,1,2,7,3]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[4,6,5,1,3,2,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,5,1,3,7,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,5,1,7,2,3]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[4,6,5,1,7,3,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,5,2,1,3,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,6,5,2,1,7,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,6,5,2,3,1,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,5,2,3,7,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,5,2,7,1,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,5,2,7,3,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,5,3,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,6,5,3,1,7,2]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,6,5,3,2,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[4,6,5,3,2,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,6,5,3,7,1,2]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,6,5,3,7,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,6,5,7,1,2,3]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,6,5,7,1,3,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,5,7,2,1,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,5,7,2,3,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,6,5,7,3,1,2]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,6,5,7,3,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,6,7,1,2,3,5]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[4,6,7,1,2,5,3]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,6,7,1,3,2,5]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,6,7,1,3,5,2]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,6,7,1,5,2,3]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,6,7,1,5,3,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,6,7,2,1,3,5]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[4,6,7,2,1,5,3]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,6,7,2,3,1,5]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[4,6,7,2,3,5,1]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,6,7,2,5,1,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,6,7,2,5,3,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,6,7,3,1,2,5]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[4,6,7,3,1,5,2]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[4,6,7,3,2,1,5]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[4,6,7,3,2,5,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,6,7,3,5,1,2]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[4,6,7,3,5,2,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[4,6,7,5,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[4,6,7,5,1,3,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,6,7,5,2,1,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[4,6,7,5,2,3,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[4,6,7,5,3,1,2]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[4,6,7,5,3,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[4,7,1,2,3,5,6]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[4,7,1,2,3,6,5]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,1,2,5,3,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,1,2,5,6,3]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,1,2,6,3,5]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,1,2,6,5,3]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,1,3,2,5,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,7,1,3,2,6,5]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,1,3,5,2,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,1,3,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,1,3,6,2,5]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,1,3,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,1,5,2,3,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,7,1,5,2,6,3]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,1,5,3,2,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,1,5,3,6,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,1,5,6,2,3]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,1,5,6,3,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,1,6,2,3,5]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,7,1,6,2,5,3]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,1,6,3,2,5]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,1,6,3,5,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,1,6,5,2,3]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,1,6,5,3,2]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,7,2,1,3,5,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,7,2,1,3,6,5]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,2,1,5,3,6]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,2,1,5,6,3]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,2,1,6,3,5]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,2,1,6,5,3]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,2,3,1,5,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,7,2,3,1,6,5]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,2,3,5,1,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,2,3,5,6,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,2,3,6,1,5]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,2,3,6,5,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,2,5,1,3,6]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,2,5,1,6,3]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,2,5,3,1,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,2,5,3,6,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,2,5,6,1,3]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,2,5,6,3,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,2,6,1,3,5]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,2,6,1,5,3]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,2,6,3,1,5]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,2,6,3,5,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,2,6,5,1,3]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,2,6,5,3,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,7,3,1,2,5,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,7,3,1,2,6,5]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,3,1,5,2,6]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,3,1,5,6,2]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,3,1,6,2,5]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,3,1,6,5,2]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,3,2,1,5,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,7,3,2,1,6,5]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,7,3,2,5,1,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,3,2,5,6,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,3,2,6,1,5]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,3,2,6,5,1]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,3,5,1,2,6]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,3,5,1,6,2]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,3,5,2,1,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,3,5,2,6,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,3,5,6,1,2]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,3,5,6,2,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,3,6,1,2,5]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,3,6,1,5,2]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,3,6,2,1,5]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,3,6,2,5,1]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,3,6,5,1,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,3,6,5,2,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,7,5,1,2,3,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,7,5,1,2,6,3]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[4,7,5,1,3,2,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,5,1,3,6,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,5,1,6,2,3]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[4,7,5,1,6,3,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,5,2,1,3,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,7,5,2,1,6,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,7,5,2,3,1,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,5,2,3,6,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,5,2,6,1,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,5,2,6,3,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,5,3,1,2,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,7,5,3,1,6,2]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,7,5,3,2,1,6]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[4,7,5,3,2,6,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,5,3,6,1,2]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,5,3,6,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,5,6,1,2,3]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[4,7,5,6,1,3,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,5,6,2,1,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,5,6,2,3,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[4,7,5,6,3,1,2]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[4,7,5,6,3,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[4,7,6,1,2,3,5]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[4,7,6,1,2,5,3]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,6,1,3,2,5]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,6,1,3,5,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,6,1,5,2,3]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,6,1,5,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,6,2,1,3,5]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,7,6,2,1,5,3]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,7,6,2,3,1,5]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,6,2,3,5,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,6,2,5,1,3]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,6,2,5,3,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,6,3,1,2,5]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,7,6,3,1,5,2]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[4,7,6,3,2,1,5]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[4,7,6,3,2,5,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,6,3,5,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[4,7,6,3,5,2,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[4,7,6,5,1,2,3]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[4,7,6,5,1,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,6,5,2,1,3]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[4,7,6,5,2,3,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[4,7,6,5,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[4,7,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,5]=>[5,2]=>2
[5,1,2,3,4,6,7]=>[[1,3,4,5,6,7],[2]]=>[7]=>[7]=>1
[5,1,2,3,4,7,6]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[5,1,2,3,6,4,7]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[5,1,2,3,6,7,4]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[5,1,2,3,7,4,6]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[5,1,2,3,7,6,4]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[5,1,2,4,3,6,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[5,1,2,4,3,7,6]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,1,2,4,6,3,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[5,1,2,4,6,7,3]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[5,1,2,4,7,3,6]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[5,1,2,4,7,6,3]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[5,1,2,6,3,4,7]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[5,1,2,6,3,7,4]=>[[1,3,4,6],[2,5,7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,2,6,4,3,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[5,1,2,6,4,7,3]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,2,6,7,3,4]=>[[1,3,4,5],[2,6,7]]=>[5,2]=>[5,2]=>2
[5,1,2,6,7,4,3]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[5,1,2,7,3,4,6]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[5,1,2,7,3,6,4]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,2,7,4,3,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[5,1,2,7,4,6,3]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,2,7,6,3,4]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[5,1,2,7,6,4,3]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,1,3,2,4,6,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[5,1,3,2,4,7,6]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,1,3,2,6,4,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,1,3,2,6,7,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,1,3,2,7,4,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,1,3,2,7,6,4]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,3,4,2,6,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[5,1,3,4,2,7,6]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,1,3,4,6,2,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[5,1,3,4,6,7,2]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[5,1,3,4,7,2,6]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[5,1,3,4,7,6,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[5,1,3,6,2,4,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[5,1,3,6,2,7,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,1,3,6,4,2,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[5,1,3,6,4,7,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,3,6,7,2,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[5,1,3,6,7,4,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[5,1,3,7,2,4,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[5,1,3,7,2,6,4]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,3,7,4,2,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[5,1,3,7,4,6,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,3,7,6,2,4]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[5,1,3,7,6,4,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,1,4,2,3,6,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[5,1,4,2,3,7,6]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,1,4,2,6,3,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,1,4,2,6,7,3]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,1,4,2,7,3,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,1,4,2,7,6,3]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,4,3,2,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[5,1,4,3,2,7,6]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,1,4,3,6,2,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,4,3,6,7,2]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,4,3,7,2,6]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,4,3,7,6,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,4,6,2,3,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[5,1,4,6,2,7,3]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,1,4,6,3,2,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[5,1,4,6,3,7,2]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,4,6,7,2,3]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[5,1,4,6,7,3,2]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[5,1,4,7,2,3,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[5,1,4,7,2,6,3]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,4,7,3,2,6]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[5,1,4,7,3,6,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,4,7,6,2,3]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[5,1,4,7,6,3,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,1,6,2,3,4,7]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[5,1,6,2,3,7,4]=>[[1,3,5,6],[2,4,7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,6,2,4,3,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,6,2,4,7,3]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,6,2,7,3,4]=>[[1,3,5,7],[2,4,6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,6,2,7,4,3]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,6,3,2,4,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[5,1,6,3,2,7,4]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,1,6,3,4,2,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,6,3,4,7,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,6,3,7,2,4]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,6,3,7,4,2]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,6,4,2,3,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[5,1,6,4,2,7,3]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,1,6,4,3,2,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,1,6,4,3,7,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,6,4,7,2,3]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,6,4,7,3,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,6,7,2,3,4]=>[[1,3,4,7],[2,5,6]]=>[4,3]=>[4,3]=>2
[5,1,6,7,2,4,3]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,6,7,3,2,4]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[5,1,6,7,3,4,2]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,1,6,7,4,2,3]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[5,1,6,7,4,3,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,1,7,2,3,4,6]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[5,1,7,2,3,6,4]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,7,2,4,3,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,7,2,4,6,3]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,7,2,6,3,4]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,7,2,6,4,3]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,7,3,2,4,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[5,1,7,3,2,6,4]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,7,3,4,2,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,1,7,3,4,6,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,7,3,6,2,4]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,7,3,6,4,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,7,4,2,3,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[5,1,7,4,2,6,3]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,7,4,3,2,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,1,7,4,3,6,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,7,4,6,2,3]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,7,4,6,3,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,1,7,6,2,3,4]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[5,1,7,6,2,4,3]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,7,6,3,2,4]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,1,7,6,3,4,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,1,7,6,4,2,3]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,1,7,6,4,3,2]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[5,2,1,3,4,6,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[5,2,1,3,4,7,6]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[5,2,1,3,6,4,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[5,2,1,3,6,7,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[5,2,1,3,7,4,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[5,2,1,3,7,6,4]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[5,2,1,4,3,6,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[5,2,1,4,3,7,6]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[5,2,1,4,6,3,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[5,2,1,4,6,7,3]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[5,2,1,4,7,3,6]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[5,2,1,4,7,6,3]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[5,2,1,6,3,4,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[5,2,1,6,3,7,4]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[5,2,1,6,4,3,7]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[5,2,1,6,4,7,3]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,1,6,7,3,4]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[5,2,1,6,7,4,3]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[5,2,1,7,3,4,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[5,2,1,7,3,6,4]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,1,7,4,3,6]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[5,2,1,7,4,6,3]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,1,7,6,3,4]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[5,2,1,7,6,4,3]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[5,2,3,1,4,6,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[5,2,3,1,4,7,6]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,2,3,1,6,4,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,2,3,1,6,7,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,2,3,1,7,4,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,2,3,1,7,6,4]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[5,2,3,4,1,7,6]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,2,3,4,6,1,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[5,2,3,4,6,7,1]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[5,2,3,4,7,1,6]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[5,2,3,4,7,6,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[5,2,3,6,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[5,2,3,6,1,7,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,2,3,6,4,1,7]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[5,2,3,6,4,7,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,3,6,7,1,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[5,2,3,6,7,4,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[5,2,3,7,1,4,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[5,2,3,7,1,6,4]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,3,7,4,1,6]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[5,2,3,7,4,6,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,3,7,6,1,4]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[5,2,3,7,6,4,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,2,4,1,3,6,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[5,2,4,1,3,7,6]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,2,4,1,6,3,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,2,4,1,6,7,3]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,2,4,1,7,3,6]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,2,4,1,7,6,3]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,4,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[5,2,4,3,1,7,6]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,2,4,3,6,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,2,4,3,6,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,4,3,7,1,6]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,2,4,3,7,6,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,4,6,1,3,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[5,2,4,6,1,7,3]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,2,4,6,3,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[5,2,4,6,3,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,4,6,7,1,3]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[5,2,4,6,7,3,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[5,2,4,7,1,3,6]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[5,2,4,7,1,6,3]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,4,7,3,1,6]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[5,2,4,7,3,6,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,4,7,6,1,3]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[5,2,4,7,6,3,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,2,6,1,3,4,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[5,2,6,1,3,7,4]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,2,6,1,4,3,7]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[5,2,6,1,4,7,3]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,6,1,7,3,4]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,2,6,1,7,4,3]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,6,3,1,4,7]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[5,2,6,3,1,7,4]=>[[1,3,6],[2,4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,2,6,3,4,1,7]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,2,6,3,4,7,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,6,3,7,1,4]=>[[1,3,5],[2,4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,2,6,3,7,4,1]=>[[1,3,5],[2,4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,6,4,1,3,7]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[5,2,6,4,1,7,3]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,6,4,3,1,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,2,6,4,3,7,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,6,4,7,1,3]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,6,4,7,3,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,6,7,1,3,4]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[5,2,6,7,1,4,3]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,6,7,3,1,4]=>[[1,3,4],[2,5,7],[6]]=>[4,3]=>[4,3]=>2
[5,2,6,7,3,4,1]=>[[1,3,4],[2,5,6],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,2,6,7,4,1,3]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[5,2,6,7,4,3,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,2,7,1,3,4,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[5,2,7,1,3,6,4]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,7,1,4,3,6]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[5,2,7,1,4,6,3]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,7,1,6,3,4]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[5,2,7,1,6,4,3]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,7,3,1,4,6]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[5,2,7,3,1,6,4]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,7,3,4,1,6]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,2,7,3,4,6,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,7,3,6,1,4]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,7,3,6,4,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,7,4,1,3,6]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[5,2,7,4,1,6,3]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,7,4,3,1,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,2,7,4,3,6,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,7,4,6,1,3]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,7,4,6,3,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,2,7,6,1,3,4]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[5,2,7,6,1,4,3]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,7,6,3,1,4]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,2,7,6,3,4,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,2,7,6,4,1,3]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[5,2,7,6,4,3,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[5,3,1,2,4,6,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[5,3,1,2,4,7,6]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[5,3,1,2,6,4,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[5,3,1,2,6,7,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[5,3,1,2,7,4,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[5,3,1,2,7,6,4]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[5,3,1,4,2,6,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[5,3,1,4,2,7,6]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[5,3,1,4,6,2,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[5,3,1,4,6,7,2]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[5,3,1,4,7,2,6]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[5,3,1,4,7,6,2]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[5,3,1,6,2,4,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[5,3,1,6,2,7,4]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[5,3,1,6,4,2,7]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[5,3,1,6,4,7,2]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,1,6,7,2,4]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[5,3,1,6,7,4,2]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[5,3,1,7,2,4,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[5,3,1,7,2,6,4]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,1,7,4,2,6]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[5,3,1,7,4,6,2]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,1,7,6,2,4]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[5,3,1,7,6,4,2]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[5,3,2,1,4,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[5,3,2,1,4,7,6]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[5,3,2,1,6,4,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[5,3,2,1,6,7,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[5,3,2,1,7,4,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[5,3,2,1,7,6,4]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[5,3,2,4,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[5,3,2,4,1,7,6]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,3,2,4,6,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[5,3,2,4,6,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[5,3,2,4,7,1,6]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[5,3,2,4,7,6,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[5,3,2,6,1,4,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[5,3,2,6,1,7,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,3,2,6,4,1,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[5,3,2,6,4,7,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,2,6,7,1,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[5,3,2,6,7,4,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[5,3,2,7,1,4,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[5,3,2,7,1,6,4]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,3,2,7,4,1,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[5,3,2,7,4,6,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,2,7,6,1,4]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[5,3,2,7,6,4,1]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[5,3,4,1,2,6,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[5,3,4,1,2,7,6]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,3,4,1,6,2,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,3,4,1,6,7,2]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,3,4,1,7,2,6]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,3,4,1,7,6,2]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,4,2,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[5,3,4,2,1,7,6]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,3,4,2,6,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,4,2,6,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,4,2,7,1,6]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,4,2,7,6,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,4,6,1,2,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[5,3,4,6,1,7,2]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,3,4,6,2,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[5,3,4,6,2,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,4,6,7,1,2]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[5,3,4,6,7,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[5,3,4,7,1,2,6]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[5,3,4,7,1,6,2]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,4,7,2,1,6]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[5,3,4,7,2,6,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,4,7,6,1,2]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[5,3,4,7,6,2,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,3,6,1,2,4,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[5,3,6,1,2,7,4]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,3,6,1,4,2,7]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,6,1,4,7,2]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,6,1,7,2,4]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,3,6,1,7,4,2]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,6,2,1,4,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[5,3,6,2,1,7,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,3,6,2,4,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,6,2,4,7,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,6,2,7,1,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,6,2,7,4,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,6,4,1,2,7]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[5,3,6,4,1,7,2]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,6,4,2,1,7]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,3,6,4,2,7,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,6,4,7,1,2]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,6,4,7,2,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,6,7,1,2,4]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[5,3,6,7,1,4,2]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,6,7,2,1,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[5,3,6,7,2,4,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,3,6,7,4,1,2]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[5,3,6,7,4,2,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,3,7,1,2,4,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[5,3,7,1,2,6,4]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,7,1,4,2,6]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,7,1,4,6,2]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,7,1,6,2,4]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,7,1,6,4,2]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,7,2,1,4,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[5,3,7,2,1,6,4]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,3,7,2,4,1,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,7,2,4,6,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,7,2,6,1,4]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,3,7,2,6,4,1]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,7,4,1,2,6]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[5,3,7,4,1,6,2]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,7,4,2,1,6]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,3,7,4,2,6,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,7,4,6,1,2]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,7,4,6,2,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,3,7,6,1,2,4]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[5,3,7,6,1,4,2]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,7,6,2,1,4]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[5,3,7,6,2,4,1]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,3,7,6,4,1,2]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[5,3,7,6,4,2,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[5,4,1,2,3,6,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[5,4,1,2,3,7,6]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[5,4,1,2,6,3,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[5,4,1,2,6,7,3]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[5,4,1,2,7,3,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[5,4,1,2,7,6,3]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[5,4,1,3,2,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[5,4,1,3,2,7,6]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,4,1,3,6,2,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[5,4,1,3,6,7,2]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[5,4,1,3,7,2,6]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[5,4,1,3,7,6,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[5,4,1,6,2,3,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[5,4,1,6,2,7,3]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[5,4,1,6,3,2,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[5,4,1,6,3,7,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,1,6,7,2,3]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[5,4,1,6,7,3,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[5,4,1,7,2,3,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[5,4,1,7,2,6,3]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,1,7,3,2,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[5,4,1,7,3,6,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,1,7,6,2,3]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[5,4,1,7,6,3,2]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[5,4,2,1,3,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[5,4,2,1,3,7,6]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[5,4,2,1,6,3,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[5,4,2,1,6,7,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[5,4,2,1,7,3,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[5,4,2,1,7,6,3]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[5,4,2,3,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[5,4,2,3,1,7,6]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,4,2,3,6,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[5,4,2,3,6,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[5,4,2,3,7,1,6]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[5,4,2,3,7,6,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[5,4,2,6,1,3,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[5,4,2,6,1,7,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,4,2,6,3,1,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[5,4,2,6,3,7,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,2,6,7,1,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[5,4,2,6,7,3,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[5,4,2,7,1,3,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[5,4,2,7,1,6,3]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,4,2,7,3,1,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[5,4,2,7,3,6,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,2,7,6,1,3]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[5,4,2,7,6,3,1]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[5,4,3,1,2,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[5,4,3,1,2,7,6]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[5,4,3,1,6,2,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[5,4,3,1,6,7,2]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[5,4,3,1,7,2,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[5,4,3,1,7,6,2]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[5,4,3,2,1,7,6]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[5,4,3,2,6,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[5,4,3,2,6,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[5,4,3,2,7,1,6]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[5,4,3,2,7,6,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[5,4,3,6,1,2,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[5,4,3,6,1,7,2]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,4,3,6,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[5,4,3,6,2,7,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,3,6,7,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[5,4,3,6,7,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[5,4,3,7,1,2,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[5,4,3,7,1,6,2]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[5,4,3,7,2,1,6]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[5,4,3,7,2,6,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,3,7,6,1,2]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[5,4,3,7,6,2,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[5,4,6,1,2,3,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[5,4,6,1,2,7,3]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[5,4,6,1,3,2,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,6,1,3,7,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,6,1,7,2,3]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[5,4,6,1,7,3,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,4,6,2,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[5,4,6,2,1,7,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,4,6,2,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,6,2,3,7,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,6,2,7,1,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,6,2,7,3,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,4,6,3,1,2,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[5,4,6,3,1,7,2]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,4,6,3,2,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,4,6,3,2,7,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,6,3,7,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,6,3,7,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,4,6,7,1,2,3]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[5,4,6,7,1,3,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,6,7,2,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[5,4,6,7,2,3,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[5,4,6,7,3,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[5,4,6,7,3,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[5,4,7,1,2,3,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[5,4,7,1,2,6,3]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,7,1,3,2,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,7,1,3,6,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,7,1,6,2,3]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,7,1,6,3,2]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,4,7,2,1,3,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[5,4,7,2,1,6,3]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,4,7,2,3,1,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,7,2,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,7,2,6,1,3]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,7,2,6,3,1]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,4,7,3,1,2,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[5,4,7,3,1,6,2]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[5,4,7,3,2,1,6]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[5,4,7,3,2,6,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,7,3,6,1,2]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,4,7,3,6,2,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,4,7,6,1,2,3]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[5,4,7,6,1,3,2]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,7,6,2,1,3]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[5,4,7,6,2,3,1]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,4,7,6,3,1,2]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[5,4,7,6,3,2,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[5,6,1,2,3,4,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[5,6,1,2,3,7,4]=>[[1,2,5,6],[3,4,7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,1,2,4,3,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,1,2,4,7,3]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,1,2,7,3,4]=>[[1,2,5,7],[3,4,6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,1,2,7,4,3]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,1,3,2,4,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,6,1,3,2,7,4]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,1,3,4,2,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,1,3,4,7,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,1,3,7,2,4]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,1,3,7,4,2]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,1,4,2,3,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,6,1,4,2,7,3]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,1,4,3,2,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,1,4,3,7,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,1,4,7,2,3]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,1,4,7,3,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,1,7,2,3,4]=>[[1,2,4,7],[3,5,6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,1,7,2,4,3]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,1,7,3,2,4]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,1,7,3,4,2]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,1,7,4,2,3]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,1,7,4,3,2]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[5,6,2,1,3,4,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[5,6,2,1,3,7,4]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[5,6,2,1,4,3,7]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,2,1,4,7,3]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,2,1,7,3,4]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[5,6,2,1,7,4,3]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,2,3,1,4,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,6,2,3,1,7,4]=>[[1,2,6],[3,4,7],[5]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,2,3,4,1,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,2,3,4,7,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,2,3,7,1,4]=>[[1,2,5],[3,4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,2,3,7,4,1]=>[[1,2,5],[3,4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,2,4,1,3,7]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,2,4,1,7,3]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,2,4,3,1,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,2,4,3,7,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,2,4,7,1,3]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,2,4,7,3,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,2,7,1,3,4]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,6,2,7,1,4,3]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,2,7,3,1,4]=>[[1,2,4],[3,5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,2,7,3,4,1]=>[[1,2,4],[3,5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,2,7,4,1,3]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[5,6,2,7,4,3,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[5,6,3,1,2,4,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[5,6,3,1,2,7,4]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[5,6,3,1,4,2,7]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,3,1,4,7,2]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,3,1,7,2,4]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[5,6,3,1,7,4,2]=>[[1,2,5],[3,6],[4,7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,3,2,1,4,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,6,3,2,1,7,4]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[5,6,3,2,4,1,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,3,2,4,7,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,3,2,7,1,4]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,3,2,7,4,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,3,4,1,2,7]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,3,4,1,7,2]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,3,4,2,1,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,3,4,2,7,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,3,4,7,1,2]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,3,4,7,2,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,3,7,1,2,4]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,6,3,7,1,4,2]=>[[1,2,4],[3,6],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,3,7,2,1,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,3,7,2,4,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,3,7,4,1,2]=>[[1,2,4],[3,5],[6,7]]=>[2,2,3]=>[3,2,2]=>3
[5,6,3,7,4,2,1]=>[[1,2,4],[3,5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[5,6,4,1,2,3,7]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[5,6,4,1,2,7,3]=>[[1,2,6],[3,5,7],[4]]=>[2,4,1]=>[4,2,1]=>3
[5,6,4,1,3,2,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,4,1,3,7,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,4,1,7,2,3]=>[[1,2,5],[3,6,7],[4]]=>[2,3,2]=>[3,2,2]=>3
[5,6,4,1,7,3,2]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,4,2,1,3,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,6,4,2,1,7,3]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[5,6,4,2,3,1,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,4,2,3,7,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,4,2,7,1,3]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,4,2,7,3,1]=>[[1,2,5],[3,6],[4],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,4,3,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,6,4,3,1,7,2]=>[[1,2,6],[3,7],[4],[5]]=>[2,4,1]=>[4,2,1]=>3
[5,6,4,3,2,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[5,6,4,3,2,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,6,4,3,7,1,2]=>[[1,2,5],[3,7],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,6,4,3,7,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,6,4,7,1,2,3]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,6,4,7,1,3,2]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,4,7,2,1,3]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,4,7,2,3,1]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,6,4,7,3,1,2]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,6,4,7,3,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[5,6,7,1,2,3,4]=>[[1,2,3,7],[4,5,6]]=>[3,4]=>[4,3]=>2
[5,6,7,1,2,4,3]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,6,7,1,3,2,4]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,6,7,1,3,4,2]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,6,7,1,4,2,3]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,6,7,1,4,3,2]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,6,7,2,1,3,4]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[5,6,7,2,1,4,3]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,6,7,2,3,1,4]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[5,6,7,2,3,4,1]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,6,7,2,4,1,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,6,7,2,4,3,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,6,7,3,1,2,4]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[5,6,7,3,1,4,2]=>[[1,2,3],[4,6],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[5,6,7,3,2,1,4]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[5,6,7,3,2,4,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,6,7,3,4,1,2]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[5,6,7,3,4,2,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[5,6,7,4,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>[3,4]=>[4,3]=>2
[5,6,7,4,1,3,2]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,6,7,4,2,1,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[5,6,7,4,2,3,1]=>[[1,2,3],[4,6],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[5,6,7,4,3,1,2]=>[[1,2,3],[4,7],[5],[6]]=>[3,4]=>[4,3]=>2
[5,6,7,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[5,7,1,2,3,4,6]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[5,7,1,2,3,6,4]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,1,2,4,3,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,1,2,4,6,3]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,1,2,6,3,4]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,1,2,6,4,3]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,1,3,2,4,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,7,1,3,2,6,4]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,1,3,4,2,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,1,3,4,6,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,1,3,6,2,4]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,1,3,6,4,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,1,4,2,3,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,7,1,4,2,6,3]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,1,4,3,2,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,1,4,3,6,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,1,4,6,2,3]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,1,4,6,3,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,1,6,2,3,4]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,7,1,6,2,4,3]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,1,6,3,2,4]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,1,6,3,4,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,1,6,4,2,3]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,1,6,4,3,2]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[5,7,2,1,3,4,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[5,7,2,1,3,6,4]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,2,1,4,3,6]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,2,1,4,6,3]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,2,1,6,3,4]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,2,1,6,4,3]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,2,3,1,4,6]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[5,7,2,3,1,6,4]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,2,3,4,1,6]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,2,3,4,6,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,2,3,6,1,4]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,2,3,6,4,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,2,4,1,3,6]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,2,4,1,6,3]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,2,4,3,1,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,2,4,3,6,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,2,4,6,1,3]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,2,4,6,3,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,2,6,1,3,4]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,2,6,1,4,3]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,2,6,3,1,4]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,2,6,3,4,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,2,6,4,1,3]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,2,6,4,3,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[5,7,3,1,2,4,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[5,7,3,1,2,6,4]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,3,1,4,2,6]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,3,1,4,6,2]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,3,1,6,2,4]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,3,1,6,4,2]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,3,2,1,4,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,7,3,2,1,6,4]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[5,7,3,2,4,1,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,3,2,4,6,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,3,2,6,1,4]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,3,2,6,4,1]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,3,4,1,2,6]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,3,4,1,6,2]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,3,4,2,1,6]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,3,4,2,6,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,3,4,6,1,2]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,3,4,6,2,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,3,6,1,2,4]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,3,6,2,1,4]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,3,6,2,4,1]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,3,6,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,3,6,4,2,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[5,7,4,1,2,3,6]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[5,7,4,1,2,6,3]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,4,1,3,2,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,4,1,3,6,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,4,1,6,2,3]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,4,1,6,3,2]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,4,2,1,3,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,7,4,2,1,6,3]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[5,7,4,2,3,1,6]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,4,2,3,6,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,4,2,6,1,3]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,4,2,6,3,1]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,4,3,1,2,6]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,7,4,3,1,6,2]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[5,7,4,3,2,1,6]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[5,7,4,3,2,6,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,4,3,6,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,4,3,6,2,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,4,6,1,2,3]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,4,6,1,3,2]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,4,6,2,1,3]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,4,6,2,3,1]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[5,7,4,6,3,1,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[5,7,4,6,3,2,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[5,7,6,1,2,3,4]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[5,7,6,1,2,4,3]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,6,1,3,2,4]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,6,1,3,4,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,6,1,4,2,3]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,6,1,4,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,6,2,1,3,4]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,7,6,2,1,4,3]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[5,7,6,2,3,1,4]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,6,2,3,4,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,6,2,4,1,3]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,6,2,4,3,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,6,3,1,2,4]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,7,6,3,1,4,2]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[5,7,6,3,2,1,4]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[5,7,6,3,2,4,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,6,3,4,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[5,7,6,3,4,2,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[5,7,6,4,1,2,3]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[5,7,6,4,1,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,6,4,2,1,3]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[5,7,6,4,2,3,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[5,7,6,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[5,7,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,5]=>[5,2]=>2
[6,1,2,3,4,5,7]=>[[1,3,4,5,6,7],[2]]=>[7]=>[7]=>1
[6,1,2,3,4,7,5]=>[[1,3,4,5,6],[2,7]]=>[6,1]=>[6,1]=>2
[6,1,2,3,5,4,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[6,1,2,3,5,7,4]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[6,1,2,3,7,4,5]=>[[1,3,4,5,7],[2,6]]=>[5,2]=>[5,2]=>2
[6,1,2,3,7,5,4]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[6,1,2,4,3,5,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[6,1,2,4,3,7,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,1,2,4,5,3,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[6,1,2,4,5,7,3]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[6,1,2,4,7,3,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,1,2,4,7,5,3]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[6,1,2,5,3,4,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[6,1,2,5,3,7,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,1,2,5,4,3,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[6,1,2,5,4,7,3]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,2,5,7,3,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,1,2,5,7,4,3]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[6,1,2,7,3,4,5]=>[[1,3,4,6,7],[2,5]]=>[4,3]=>[4,3]=>2
[6,1,2,7,3,5,4]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,2,7,4,3,5]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[6,1,2,7,4,5,3]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,2,7,5,3,4]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[6,1,2,7,5,4,3]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,1,3,2,4,5,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[6,1,3,2,4,7,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,1,3,2,5,4,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,1,3,2,5,7,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,1,3,2,7,4,5]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,1,3,2,7,5,4]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,3,4,2,5,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[6,1,3,4,2,7,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,1,3,4,5,2,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[6,1,3,4,5,7,2]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[6,1,3,4,7,2,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,1,3,4,7,5,2]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[6,1,3,5,2,4,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,1,3,5,2,7,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,1,3,5,4,2,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[6,1,3,5,4,7,2]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,3,5,7,2,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,1,3,5,7,4,2]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[6,1,3,7,2,4,5]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,1,3,7,2,5,4]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,3,7,4,2,5]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[6,1,3,7,4,5,2]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,3,7,5,2,4]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[6,1,3,7,5,4,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,1,4,2,3,5,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[6,1,4,2,3,7,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,1,4,2,5,3,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,1,4,2,5,7,3]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,1,4,2,7,3,5]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,1,4,2,7,5,3]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,4,3,2,5,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[6,1,4,3,2,7,5]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,1,4,3,5,2,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,4,3,5,7,2]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,4,3,7,2,5]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,4,3,7,5,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,4,5,2,3,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,1,4,5,2,7,3]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,1,4,5,3,2,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[6,1,4,5,3,7,2]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,4,5,7,2,3]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,1,4,5,7,3,2]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[6,1,4,7,2,3,5]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,1,4,7,2,5,3]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,4,7,3,2,5]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,1,4,7,3,5,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,4,7,5,2,3]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[6,1,4,7,5,3,2]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,1,5,2,3,4,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[6,1,5,2,3,7,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,1,5,2,4,3,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,5,2,4,7,3]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,5,2,7,3,4]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,1,5,2,7,4,3]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,5,3,2,4,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[6,1,5,3,2,7,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,1,5,3,4,2,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,5,3,4,7,2]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,5,3,7,2,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,5,3,7,4,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,5,4,2,3,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[6,1,5,4,2,7,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,1,5,4,3,2,7]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,1,5,4,3,7,2]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,5,4,7,2,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,5,4,7,3,2]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,5,7,2,3,4]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,1,5,7,2,4,3]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,5,7,3,2,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,1,5,7,3,4,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,1,5,7,4,2,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,1,5,7,4,3,2]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,1,7,2,3,4,5]=>[[1,3,5,6,7],[2,4]]=>[3,4]=>[4,3]=>2
[6,1,7,2,3,5,4]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,7,2,4,3,5]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,7,2,4,5,3]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,7,2,5,3,4]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,7,2,5,4,3]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,7,3,2,4,5]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[6,1,7,3,2,5,4]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,7,3,4,2,5]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,1,7,3,4,5,2]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,7,3,5,2,4]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,7,3,5,4,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,7,4,2,3,5]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[6,1,7,4,2,5,3]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,7,4,3,2,5]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,1,7,4,3,5,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,7,4,5,2,3]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,7,4,5,3,2]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,1,7,5,2,3,4]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[6,1,7,5,2,4,3]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,7,5,3,2,4]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,1,7,5,3,4,2]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,1,7,5,4,2,3]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,1,7,5,4,3,2]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[6,2,1,3,4,5,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[6,2,1,3,4,7,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,2,1,3,5,4,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,2,1,3,5,7,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,2,1,3,7,4,5]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,2,1,3,7,5,4]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[6,2,1,4,3,5,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,2,1,4,3,7,5]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[6,2,1,4,5,3,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,2,1,4,5,7,3]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,2,1,4,7,3,5]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[6,2,1,4,7,5,3]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[6,2,1,5,3,4,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,2,1,5,3,7,4]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[6,2,1,5,4,3,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,2,1,5,4,7,3]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,1,5,7,3,4]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[6,2,1,5,7,4,3]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,2,1,7,3,4,5]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,2,1,7,3,5,4]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,1,7,4,3,5]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[6,2,1,7,4,5,3]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,1,7,5,3,4]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[6,2,1,7,5,4,3]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[6,2,3,1,4,5,7]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[6,2,3,1,4,7,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,2,3,1,5,4,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,2,3,1,5,7,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,2,3,1,7,4,5]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,2,3,1,7,5,4]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,3,4,1,5,7]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[6,2,3,4,1,7,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,2,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[6,2,3,4,5,7,1]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[6,2,3,4,7,1,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,2,3,4,7,5,1]=>[[1,3,4,5],[2,6],[7]]=>[5,2]=>[5,2]=>2
[6,2,3,5,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,2,3,5,1,7,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,2,3,5,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[6,2,3,5,4,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,3,5,7,1,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,2,3,5,7,4,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[6,2,3,7,1,4,5]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,2,3,7,1,5,4]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,3,7,4,1,5]=>[[1,3,4,7],[2,5],[6]]=>[4,3]=>[4,3]=>2
[6,2,3,7,4,5,1]=>[[1,3,4,6],[2,5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,3,7,5,1,4]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[6,2,3,7,5,4,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,2,4,1,3,5,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,2,4,1,3,7,5]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,2,4,1,5,3,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,2,4,1,5,7,3]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,2,4,1,7,3,5]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,2,4,1,7,5,3]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,4,3,1,5,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[6,2,4,3,1,7,5]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,2,4,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,4,3,5,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,4,3,7,1,5]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,4,3,7,5,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,4,5,1,3,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,2,4,5,1,7,3]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,2,4,5,3,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[6,2,4,5,3,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,4,5,7,1,3]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,2,4,5,7,3,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[6,2,4,7,1,3,5]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[6,2,4,7,1,5,3]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,4,7,3,1,5]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,2,4,7,3,5,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,4,7,5,1,3]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[6,2,4,7,5,3,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,2,5,1,3,4,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,2,5,1,3,7,4]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,2,5,1,4,3,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,5,1,4,7,3]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,5,1,7,3,4]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,2,5,1,7,4,3]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,5,3,1,4,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[6,2,5,3,1,7,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,2,5,3,4,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,5,3,4,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,5,3,7,1,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,5,3,7,4,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,5,4,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,2,5,4,1,7,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,2,5,4,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,2,5,4,3,7,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,5,4,7,1,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,5,4,7,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,5,7,1,3,4]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[6,2,5,7,1,4,3]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,5,7,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,2,5,7,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,2,5,7,4,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,2,5,7,4,3,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,2,7,1,3,4,5]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,2,7,1,3,5,4]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,7,1,4,3,5]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,7,1,4,5,3]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,7,1,5,3,4]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,7,1,5,4,3]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,7,3,1,4,5]=>[[1,3,6,7],[2,4],[5]]=>[3,4]=>[4,3]=>2
[6,2,7,3,1,5,4]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,7,3,4,1,5]=>[[1,3,5,7],[2,4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,2,7,3,4,5,1]=>[[1,3,5,6],[2,4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,7,3,5,1,4]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,7,3,5,4,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,7,4,1,3,5]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[6,2,7,4,1,5,3]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,7,4,3,1,5]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,2,7,4,3,5,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,7,4,5,1,3]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,7,4,5,3,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,2,7,5,1,3,4]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[6,2,7,5,1,4,3]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,7,5,3,1,4]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,2,7,5,3,4,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,2,7,5,4,1,3]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[6,2,7,5,4,3,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[6,3,1,2,4,5,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[6,3,1,2,4,7,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,3,1,2,5,4,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,3,1,2,5,7,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,3,1,2,7,4,5]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,3,1,2,7,5,4]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[6,3,1,4,2,5,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,3,1,4,2,7,5]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[6,3,1,4,5,2,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,3,1,4,5,7,2]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,3,1,4,7,2,5]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[6,3,1,4,7,5,2]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[6,3,1,5,2,4,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,3,1,5,2,7,4]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[6,3,1,5,4,2,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,3,1,5,4,7,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,1,5,7,2,4]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[6,3,1,5,7,4,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,3,1,7,2,4,5]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,3,1,7,2,5,4]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,1,7,4,2,5]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[6,3,1,7,4,5,2]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,1,7,5,2,4]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[6,3,1,7,5,4,2]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[6,3,2,1,4,5,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[6,3,2,1,4,7,5]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,3,2,1,5,4,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,3,2,1,5,7,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,3,2,1,7,4,5]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,3,2,1,7,5,4]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[6,3,2,4,1,5,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[6,3,2,4,1,7,5]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[6,3,2,4,5,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[6,3,2,4,7,1,5]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,3,2,4,7,5,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,3,2,5,1,4,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,3,2,5,1,7,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,3,2,5,4,1,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,3,2,5,4,7,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,2,5,7,1,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,3,2,5,7,4,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,3,2,7,1,4,5]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,3,2,7,1,5,4]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,3,2,7,4,1,5]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,3,2,7,4,5,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,2,7,5,1,4]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[6,3,2,7,5,4,1]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[6,3,4,1,2,5,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,3,4,1,2,7,5]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,3,4,1,5,2,7]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,3,4,1,5,7,2]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,3,4,1,7,2,5]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,3,4,1,7,5,2]=>[[1,3,5],[2,6],[4,7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,4,2,1,5,7]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[6,3,4,2,1,7,5]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,3,4,2,5,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,4,2,5,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,4,2,7,1,5]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,4,2,7,5,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,4,5,1,2,7]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[6,3,4,5,1,7,2]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,3,4,5,2,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[6,3,4,5,2,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,4,5,7,1,2]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[6,3,4,5,7,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[6,3,4,7,1,2,5]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[6,3,4,7,1,5,2]=>[[1,3,4],[2,6],[5,7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,4,7,2,1,5]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,3,4,7,2,5,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,4,7,5,1,2]=>[[1,3,4],[2,5],[6,7]]=>[4,3]=>[4,3]=>2
[6,3,4,7,5,2,1]=>[[1,3,4],[2,5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,3,5,1,2,4,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,3,5,1,2,7,4]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,3,5,1,4,2,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,5,1,4,7,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,5,1,7,2,4]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,3,5,1,7,4,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,5,2,1,4,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,3,5,2,1,7,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,3,5,2,4,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,5,2,4,7,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,5,2,7,1,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,5,2,7,4,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,5,4,1,2,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,3,5,4,1,7,2]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,3,5,4,2,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,3,5,4,2,7,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,5,4,7,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,5,4,7,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,5,7,1,2,4]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[6,3,5,7,1,4,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,5,7,2,1,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,3,5,7,2,4,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,3,5,7,4,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,3,5,7,4,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,3,7,1,2,4,5]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,3,7,1,2,5,4]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,7,1,4,2,5]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,7,1,4,5,2]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,7,1,5,2,4]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,7,1,5,4,2]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,7,2,1,4,5]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,3,7,2,1,5,4]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,3,7,2,4,1,5]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,7,2,4,5,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,7,2,5,1,4]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,3,7,2,5,4,1]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,7,4,1,2,5]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[6,3,7,4,1,5,2]=>[[1,3,6],[2,4],[5,7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,7,4,2,1,5]=>[[1,3,7],[2,4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,3,7,4,2,5,1]=>[[1,3,6],[2,4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,7,4,5,1,2]=>[[1,3,5],[2,4],[6,7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,7,4,5,2,1]=>[[1,3,5],[2,4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,3,7,5,1,2,4]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[6,3,7,5,1,4,2]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,7,5,2,1,4]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[6,3,7,5,2,4,1]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,3,7,5,4,1,2]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[6,3,7,5,4,2,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[6,4,1,2,3,5,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[6,4,1,2,3,7,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,4,1,2,5,3,7]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,4,1,2,5,7,3]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,4,1,2,7,3,5]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,4,1,2,7,5,3]=>[[1,4,5],[2,6],[3,7]]=>[5,2]=>[5,2]=>2
[6,4,1,3,2,5,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[6,4,1,3,2,7,5]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,4,1,3,5,2,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[6,4,1,3,5,7,2]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[6,4,1,3,7,2,5]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,4,1,3,7,5,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,4,1,5,2,3,7]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,4,1,5,2,7,3]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[6,4,1,5,3,2,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,4,1,5,3,7,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,1,5,7,2,3]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[6,4,1,5,7,3,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,4,1,7,2,3,5]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,4,1,7,2,5,3]=>[[1,4,6],[2,5],[3,7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,1,7,3,2,5]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,4,1,7,3,5,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,1,7,5,2,3]=>[[1,4,7],[2,5],[3,6]]=>[4,3]=>[4,3]=>2
[6,4,1,7,5,3,2]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[6,4,2,1,3,5,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[6,4,2,1,3,7,5]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,4,2,1,5,3,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,4,2,1,5,7,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,4,2,1,7,3,5]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,4,2,1,7,5,3]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[6,4,2,3,1,5,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[6,4,2,3,1,7,5]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,4,2,3,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[6,4,2,3,5,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[6,4,2,3,7,1,5]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,4,2,3,7,5,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,4,2,5,1,3,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,4,2,5,1,7,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,4,2,5,3,1,7]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,4,2,5,3,7,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,2,5,7,1,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,4,2,5,7,3,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,4,2,7,1,3,5]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,4,2,7,1,5,3]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,4,2,7,3,1,5]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,4,2,7,3,5,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,2,7,5,1,3]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[6,4,2,7,5,3,1]=>[[1,4],[2,5],[3,6],[7]]=>[4,3]=>[4,3]=>2
[6,4,3,1,2,5,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[6,4,3,1,2,7,5]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,4,3,1,5,2,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,4,3,1,5,7,2]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,4,3,1,7,2,5]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,4,3,1,7,5,2]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[6,4,3,2,1,5,7]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[6,4,3,2,1,7,5]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[6,4,3,2,5,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[6,4,3,2,5,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[6,4,3,2,7,1,5]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[6,4,3,2,7,5,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[6,4,3,5,1,2,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,4,3,5,1,7,2]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,4,3,5,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[6,4,3,5,2,7,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,3,5,7,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,4,3,5,7,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[6,4,3,7,1,2,5]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,4,3,7,1,5,2]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,4,3,7,2,1,5]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[6,4,3,7,2,5,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,3,7,5,1,2]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[6,4,3,7,5,2,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[6,4,5,1,2,3,7]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,4,5,1,2,7,3]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[6,4,5,1,3,2,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,5,1,3,7,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,5,1,7,2,3]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[6,4,5,1,7,3,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,4,5,2,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,4,5,2,1,7,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,4,5,2,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,5,2,3,7,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,5,2,7,1,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,5,2,7,3,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,4,5,3,1,2,7]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,4,5,3,1,7,2]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,4,5,3,2,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,4,5,3,2,7,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,5,3,7,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,5,3,7,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,4,5,7,1,2,3]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[6,4,5,7,1,3,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,5,7,2,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,4,5,7,2,3,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,4,5,7,3,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[6,4,5,7,3,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,4,7,1,2,3,5]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,4,7,1,2,5,3]=>[[1,3,6],[2,5],[4,7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,7,1,3,2,5]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,7,1,3,5,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,7,1,5,2,3]=>[[1,3,7],[2,5],[4,6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,7,1,5,3,2]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,4,7,2,1,3,5]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,4,7,2,1,5,3]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,4,7,2,3,1,5]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,7,2,3,5,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,7,2,5,1,3]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,7,2,5,3,1]=>[[1,3],[2,5],[4,6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,4,7,3,1,2,5]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,4,7,3,1,5,2]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,4,7,3,2,1,5]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,4,7,3,2,5,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,7,3,5,1,2]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,4,7,3,5,2,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,4,7,5,1,2,3]=>[[1,3,7],[2,4],[5,6]]=>[3,4]=>[4,3]=>2
[6,4,7,5,1,3,2]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,7,5,2,1,3]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[6,4,7,5,2,3,1]=>[[1,3],[2,4],[5,6],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,4,7,5,3,1,2]=>[[1,3],[2,4],[5,7],[6]]=>[3,4]=>[4,3]=>2
[6,4,7,5,3,2,1]=>[[1,3],[2,4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[6,5,1,2,3,4,7]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[6,5,1,2,3,7,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[6,5,1,2,4,3,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[6,5,1,2,4,7,3]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[6,5,1,2,7,3,4]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[6,5,1,2,7,4,3]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,5,1,3,2,4,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[6,5,1,3,2,7,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,5,1,3,4,2,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[6,5,1,3,4,7,2]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[6,5,1,3,7,2,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,5,1,3,7,4,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,5,1,4,2,3,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[6,5,1,4,2,7,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,5,1,4,3,2,7]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[6,5,1,4,3,7,2]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,1,4,7,2,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,5,1,4,7,3,2]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[6,5,1,7,2,3,4]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[6,5,1,7,2,4,3]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,1,7,3,2,4]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,5,1,7,3,4,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,1,7,4,2,3]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,5,1,7,4,3,2]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[6,5,2,1,3,4,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[6,5,2,1,3,7,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,5,2,1,4,3,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,5,2,1,4,7,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,5,2,1,7,3,4]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,5,2,1,7,4,3]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[6,5,2,3,1,4,7]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[6,5,2,3,1,7,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,5,2,3,4,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[6,5,2,3,4,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[6,5,2,3,7,1,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,5,2,3,7,4,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[6,5,2,4,1,3,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,5,2,4,1,7,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,5,2,4,3,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[6,5,2,4,3,7,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,2,4,7,1,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,5,2,4,7,3,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[6,5,2,7,1,3,4]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,5,2,7,1,4,3]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,5,2,7,3,1,4]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[6,5,2,7,3,4,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,2,7,4,1,3]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[6,5,2,7,4,3,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[6,5,3,1,2,4,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[6,5,3,1,2,7,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,5,3,1,4,2,7]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,5,3,1,4,7,2]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,5,3,1,7,2,4]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,5,3,1,7,4,2]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[6,5,3,2,1,4,7]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[6,5,3,2,1,7,4]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[6,5,3,2,4,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[6,5,3,2,4,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[6,5,3,2,7,1,4]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[6,5,3,2,7,4,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[6,5,3,4,1,2,7]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,5,3,4,1,7,2]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[6,5,3,4,2,7,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,3,4,7,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[6,5,3,4,7,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[6,5,3,7,1,2,4]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,5,3,7,1,4,2]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[6,5,3,7,2,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[6,5,3,7,2,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,3,7,4,1,2]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[6,5,3,7,4,2,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[6,5,4,1,2,3,7]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[6,5,4,1,2,7,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[6,5,4,1,3,2,7]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[6,5,4,1,3,7,2]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[6,5,4,1,7,2,3]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[6,5,4,1,7,3,2]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[6,5,4,2,1,3,7]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[6,5,4,2,1,7,3]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[6,5,4,2,3,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[6,5,4,2,3,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[6,5,4,2,7,1,3]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[6,5,4,2,7,3,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[6,5,4,3,1,2,7]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[6,5,4,3,1,7,2]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]]=>[7]=>[7]=>1
[6,5,4,3,2,7,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[6,1]=>[6,1]=>2
[6,5,4,3,7,1,2]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[6,5,4,3,7,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[5,2]=>[5,2]=>2
[6,5,4,7,1,2,3]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[6,5,4,7,1,3,2]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,4,7,2,1,3]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[6,5,4,7,2,3,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[6,5,4,7,3,1,2]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[6,5,4,7,3,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[6,5,7,1,2,3,4]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[6,5,7,1,2,4,3]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,5,7,1,3,2,4]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,5,7,1,3,4,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,5,7,1,4,2,3]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,5,7,1,4,3,2]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,5,7,2,1,3,4]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,5,7,2,1,4,3]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,5,7,2,3,1,4]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,5,7,2,3,4,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,5,7,2,4,1,3]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,5,7,2,4,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,5,7,3,1,2,4]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,5,7,3,1,4,2]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[6,5,7,3,2,1,4]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,5,7,3,2,4,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,5,7,3,4,1,2]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[6,5,7,3,4,2,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[6,5,7,4,1,2,3]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[6,5,7,4,1,3,2]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,5,7,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,5,7,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[6,5,7,4,3,1,2]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[6,5,7,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[6,7,1,2,3,4,5]=>[[1,2,5,6,7],[3,4]]=>[2,5]=>[5,2]=>2
[6,7,1,2,3,5,4]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,1,2,4,3,5]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,1,2,4,5,3]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,1,2,5,3,4]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,1,2,5,4,3]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,1,3,2,4,5]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[6,7,1,3,2,5,4]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,1,3,4,2,5]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,1,3,4,5,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,1,3,5,2,4]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,1,3,5,4,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,1,4,2,3,5]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[6,7,1,4,2,5,3]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,1,4,3,2,5]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,1,4,3,5,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,1,4,5,2,3]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,1,4,5,3,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,1,5,2,3,4]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[6,7,1,5,2,4,3]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,1,5,3,2,4]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,1,5,3,4,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,1,5,4,2,3]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,1,5,4,3,2]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[6,7,2,1,3,4,5]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[6,7,2,1,3,5,4]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,2,1,4,3,5]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,2,1,4,5,3]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,2,1,5,3,4]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,2,1,5,4,3]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,2,3,1,4,5]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]=>[3,2,2]=>3
[6,7,2,3,1,5,4]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,2,3,4,1,5]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,2,3,4,5,1]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,2,3,5,1,4]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,2,3,5,4,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,2,4,1,3,5]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,2,4,1,5,3]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,2,4,3,1,5]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,2,4,3,5,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,2,4,5,1,3]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,2,4,5,3,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,2,5,1,3,4]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,2,5,1,4,3]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,2,5,3,1,4]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,2,5,3,4,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,2,5,4,1,3]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,2,5,4,3,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[6,7,3,1,2,4,5]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[6,7,3,1,2,5,4]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,3,1,4,2,5]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,3,1,4,5,2]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,3,1,5,2,4]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,3,1,5,4,2]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,3,2,1,4,5]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[6,7,3,2,1,5,4]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[6,7,3,2,4,1,5]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,3,2,4,5,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,3,2,5,1,4]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,3,2,5,4,1]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,3,4,1,2,5]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,3,4,1,5,2]=>[[1,2,6],[3,4],[5,7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,3,4,2,1,5]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,3,4,2,5,1]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,3,4,5,1,2]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,3,4,5,2,1]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,3,5,1,2,4]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,3,5,1,4,2]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,3,5,2,1,4]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,3,5,2,4,1]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,3,5,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,3,5,4,2,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[6,7,4,1,2,3,5]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[6,7,4,1,2,5,3]=>[[1,2,6],[3,5],[4,7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,4,1,3,2,5]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,4,1,3,5,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,4,1,5,2,3]=>[[1,2,7],[3,5],[4,6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,4,1,5,3,2]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,4,2,1,3,5]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[6,7,4,2,1,5,3]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[6,7,4,2,3,1,5]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,4,2,3,5,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,4,2,5,1,3]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,4,2,5,3,1]=>[[1,2],[3,5],[4,6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,4,3,1,2,5]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[6,7,4,3,1,5,2]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[6,7,4,3,2,1,5]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[6,7,4,3,2,5,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,4,3,5,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,4,3,5,2,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,4,5,1,2,3]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,4,5,1,3,2]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,4,5,2,1,3]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,4,5,2,3,1]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]=>4
[6,7,4,5,3,1,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,3]=>[3,2,2]=>3
[6,7,4,5,3,2,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,3]=>[3,2,2]=>3
[6,7,5,1,2,3,4]=>[[1,2,6,7],[3,5],[4]]=>[2,5]=>[5,2]=>2
[6,7,5,1,2,4,3]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,5,1,3,2,4]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,5,1,3,4,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,5,1,4,2,3]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,5,1,4,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,5,2,1,3,4]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[6,7,5,2,1,4,3]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[6,7,5,2,3,1,4]=>[[1,2,7],[3,5],[4],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,5,2,3,4,1]=>[[1,2,6],[3,5],[4],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,5,2,4,1,3]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,5,2,4,3,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,5,3,1,2,4]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[6,7,5,3,1,4,2]=>[[1,2],[3,6],[4,7],[5]]=>[2,4,1]=>[4,2,1]=>3
[6,7,5,3,2,1,4]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[6,7,5,3,2,4,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,5,3,4,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,3,2]=>[3,2,2]=>3
[6,7,5,3,4,2,1]=>[[1,2],[3,5],[4],[6],[7]]=>[2,3,2]=>[3,2,2]=>3
[6,7,5,4,1,2,3]=>[[1,2,7],[3,6],[4],[5]]=>[2,5]=>[5,2]=>2
[6,7,5,4,1,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,5,4,2,1,3]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[6,7,5,4,2,3,1]=>[[1,2],[3,6],[4],[5],[7]]=>[2,4,1]=>[4,2,1]=>3
[6,7,5,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,5]=>[5,2]=>2
[6,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,5]=>[5,2]=>2
[7,1,2,3,4,5,6]=>[[1,3,4,5,6,7],[2]]=>[7]=>[7]=>1
[7,1,2,3,4,6,5]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[7,1,2,3,5,4,6]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[7,1,2,3,5,6,4]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[7,1,2,3,6,4,5]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[7,1,2,3,6,5,4]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,1,2,4,3,5,6]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[7,1,2,4,3,6,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,1,2,4,5,3,6]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[7,1,2,4,5,6,3]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[7,1,2,4,6,3,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,1,2,4,6,5,3]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,1,2,5,3,4,6]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[7,1,2,5,3,6,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,1,2,5,4,3,6]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,2,5,4,6,3]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,2,5,6,3,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,1,2,5,6,4,3]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,1,2,6,3,4,5]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[7,1,2,6,3,5,4]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,2,6,4,3,5]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,2,6,4,5,3]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,2,6,5,3,4]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,2,6,5,4,3]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,1,3,2,4,5,6]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[7,1,3,2,4,6,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,1,3,2,5,4,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,1,3,2,5,6,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,1,3,2,6,4,5]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,1,3,2,6,5,4]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,3,4,2,5,6]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[7,1,3,4,2,6,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,1,3,4,5,2,6]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[7,1,3,4,5,6,2]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[7,1,3,4,6,2,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,1,3,4,6,5,2]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,1,3,5,2,4,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,1,3,5,2,6,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,1,3,5,4,2,6]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,3,5,4,6,2]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,3,5,6,2,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,1,3,5,6,4,2]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,1,3,6,2,4,5]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,1,3,6,2,5,4]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,3,6,4,2,5]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,3,6,4,5,2]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,3,6,5,2,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,3,6,5,4,2]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,1,4,2,3,5,6]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[7,1,4,2,3,6,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,1,4,2,5,3,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,1,4,2,5,6,3]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,1,4,2,6,3,5]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,1,4,2,6,5,3]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,4,3,2,5,6]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,1,4,3,2,6,5]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,1,4,3,5,2,6]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,4,3,5,6,2]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,4,3,6,2,5]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,4,3,6,5,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,4,5,2,3,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,1,4,5,2,6,3]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,1,4,5,3,2,6]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,4,5,3,6,2]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,4,5,6,2,3]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,1,4,5,6,3,2]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,1,4,6,2,3,5]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,1,4,6,2,5,3]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,4,6,3,2,5]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,4,6,3,5,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,4,6,5,2,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,4,6,5,3,2]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,1,5,2,3,4,6]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[7,1,5,2,3,6,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,1,5,2,4,3,6]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,5,2,4,6,3]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,5,2,6,3,4]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,1,5,2,6,4,3]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,5,3,2,4,6]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,1,5,3,2,6,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,1,5,3,4,2,6]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,5,3,4,6,2]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,5,3,6,2,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,5,3,6,4,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,5,4,2,3,6]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,1,5,4,2,6,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,1,5,4,3,2,6]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,1,5,4,3,6,2]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,5,4,6,2,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,5,4,6,3,2]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,5,6,2,3,4]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,1,5,6,2,4,3]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,5,6,3,2,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,5,6,3,4,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,1,5,6,4,2,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,1,5,6,4,3,2]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,1,6,2,3,4,5]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[7,1,6,2,3,5,4]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,6,2,4,3,5]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,6,2,4,5,3]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,6,2,5,3,4]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,6,2,5,4,3]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,6,3,2,4,5]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,1,6,3,2,5,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,1,6,3,4,2,5]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,6,3,4,5,2]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,6,3,5,2,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,6,3,5,4,2]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,6,4,2,3,5]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,1,6,4,2,5,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,1,6,4,3,2,5]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,1,6,4,3,5,2]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,6,4,5,2,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,1,6,4,5,3,2]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,1,6,5,2,3,4]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,1,6,5,2,4,3]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,6,5,3,2,4]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,1,6,5,3,4,2]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,1,6,5,4,2,3]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,1,6,5,4,3,2]=>[[1,3],[2],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[7,2,1,3,4,5,6]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[7,2,1,3,4,6,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,2,1,3,5,4,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,2,1,3,5,6,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,2,1,3,6,4,5]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,2,1,3,6,5,4]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,2,1,4,3,5,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,2,1,4,3,6,5]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[7,2,1,4,5,3,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,2,1,4,5,6,3]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,2,1,4,6,3,5]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[7,2,1,4,6,5,3]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,2,1,5,3,4,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,2,1,5,3,6,4]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[7,2,1,5,4,3,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,2,1,5,4,6,3]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,1,5,6,3,4]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[7,2,1,5,6,4,3]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,2,1,6,3,4,5]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,2,1,6,3,5,4]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,1,6,4,3,5]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,2,1,6,4,5,3]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,1,6,5,3,4]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,2,1,6,5,4,3]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,2,3,1,4,5,6]=>[[1,3,5,6,7],[2],[4]]=>[3,4]=>[4,3]=>2
[7,2,3,1,4,6,5]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,2,3,1,5,4,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,2,3,1,5,6,4]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,2,3,1,6,4,5]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,2,3,1,6,5,4]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,3,4,1,5,6]=>[[1,3,4,6,7],[2],[5]]=>[4,3]=>[4,3]=>2
[7,2,3,4,1,6,5]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,2,3,4,5,1,6]=>[[1,3,4,5,7],[2],[6]]=>[5,2]=>[5,2]=>2
[7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]=>[6,1]=>[6,1]=>2
[7,2,3,4,6,1,5]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,2,3,4,6,5,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,2,3,5,1,4,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,2,3,5,1,6,4]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,2,3,5,4,1,6]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,2,3,5,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,3,5,6,1,4]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,2,3,5,6,4,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,2,3,6,1,4,5]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,2,3,6,1,5,4]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,3,6,4,1,5]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,2,3,6,4,5,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,3,6,5,1,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,2,3,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,2,4,1,3,5,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,2,4,1,3,6,5]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,2,4,1,5,3,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,2,4,1,5,6,3]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,2,4,1,6,3,5]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,2,4,1,6,5,3]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,4,3,1,5,6]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,2,4,3,1,6,5]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,2,4,3,5,1,6]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,4,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,4,3,6,1,5]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,4,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,4,5,1,3,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,2,4,5,1,6,3]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,2,4,5,3,1,6]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,2,4,5,3,6,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,4,5,6,1,3]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,2,4,5,6,3,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,2,4,6,1,3,5]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[7,2,4,6,1,5,3]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,4,6,3,1,5]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,2,4,6,3,5,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,4,6,5,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,2,4,6,5,3,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,2,5,1,3,4,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,2,5,1,3,6,4]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,2,5,1,4,3,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,5,1,4,6,3]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,5,1,6,3,4]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,2,5,1,6,4,3]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,5,3,1,4,6]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,2,5,3,1,6,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,2,5,3,4,1,6]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,5,3,4,6,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,5,3,6,1,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,5,3,6,4,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,5,4,1,3,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,2,5,4,1,6,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,2,5,4,3,1,6]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,2,5,4,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,5,4,6,1,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,5,4,6,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,5,6,1,3,4]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[7,2,5,6,1,4,3]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,5,6,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,2,5,6,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,2,5,6,4,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,2,5,6,4,3,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,2,6,1,3,4,5]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,2,6,1,3,5,4]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,6,1,4,3,5]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,6,1,4,5,3]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,6,1,5,3,4]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,6,1,5,4,3]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,6,3,1,4,5]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,2,6,3,1,5,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,2,6,3,4,1,5]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,6,3,4,5,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,6,3,5,1,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,6,3,5,4,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,6,4,1,3,5]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,2,6,4,1,5,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,2,6,4,3,1,5]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,2,6,4,3,5,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,6,4,5,1,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,2,6,4,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,2,6,5,1,3,4]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,2,6,5,1,4,3]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,6,5,3,1,4]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,2,6,5,3,4,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,2,6,5,4,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,2,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[7,3,1,2,4,5,6]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[7,3,1,2,4,6,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,3,1,2,5,4,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,3,1,2,5,6,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,3,1,2,6,4,5]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,3,1,2,6,5,4]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,3,1,4,2,5,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,3,1,4,2,6,5]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[7,3,1,4,5,2,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,3,1,4,5,6,2]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,3,1,4,6,2,5]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[7,3,1,4,6,5,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,3,1,5,2,4,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,3,1,5,2,6,4]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[7,3,1,5,4,2,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,3,1,5,4,6,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,1,5,6,2,4]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[7,3,1,5,6,4,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,3,1,6,2,4,5]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,3,1,6,2,5,4]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,1,6,4,2,5]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,3,1,6,4,5,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,1,6,5,2,4]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,3,1,6,5,4,2]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,3,2,1,4,5,6]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,3,2,1,4,6,5]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,3,2,1,5,4,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,3,2,1,5,6,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,3,2,1,6,4,5]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,3,2,1,6,5,4]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[7,3,2,4,1,5,6]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,3,2,4,1,6,5]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,3,2,4,5,1,6]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,3,2,4,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,3,2,4,6,1,5]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,3,2,4,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,3,2,5,1,4,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,3,2,5,1,6,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,3,2,5,4,1,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,3,2,5,4,6,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,2,5,6,1,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,3,2,5,6,4,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,3,2,6,1,4,5]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,3,2,6,1,5,4]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,3,2,6,4,1,5]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,3,2,6,4,5,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,2,6,5,1,4]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[7,3,2,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,3,4,1,2,5,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,3,4,1,2,6,5]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,3,4,1,5,2,6]=>[[1,3,5,7],[2,6],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,3,4,1,5,6,2]=>[[1,3,5,6],[2,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,3,4,1,6,2,5]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,3,4,1,6,5,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,3,4,2,1,5,6]=>[[1,3,6,7],[2],[4],[5]]=>[3,4]=>[4,3]=>2
[7,3,4,2,1,6,5]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,3,4,2,5,1,6]=>[[1,3,5,7],[2],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,4,2,5,6,1]=>[[1,3,5,6],[2],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,4,2,6,1,5]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,4,2,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,3,4,5,1,2,6]=>[[1,3,4,7],[2,6],[5]]=>[4,3]=>[4,3]=>2
[7,3,4,5,1,6,2]=>[[1,3,4,6],[2,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,3,4,5,2,1,6]=>[[1,3,4,7],[2],[5],[6]]=>[4,3]=>[4,3]=>2
[7,3,4,5,2,6,1]=>[[1,3,4,6],[2],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,4,5,6,1,2]=>[[1,3,4,5],[2,7],[6]]=>[5,2]=>[5,2]=>2
[7,3,4,5,6,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[5,2]=>[5,2]=>2
[7,3,4,6,1,2,5]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[7,3,4,6,1,5,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,4,6,2,1,5]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,3,4,6,2,5,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,4,6,5,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,3,4,6,5,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,3,5,1,2,4,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,3,5,1,2,6,4]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,3,5,1,4,2,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,5,1,4,6,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,5,1,6,2,4]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,3,5,1,6,4,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,3,5,2,1,4,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,3,5,2,1,6,4]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,3,5,2,4,1,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,5,2,4,6,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,5,2,6,1,4]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,5,2,6,4,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,3,5,4,1,2,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,3,5,4,1,6,2]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,3,5,4,2,1,6]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,3,5,4,2,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,5,4,6,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,5,4,6,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,3,5,6,1,2,4]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[7,3,5,6,1,4,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,5,6,2,1,4]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,3,5,6,2,4,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,3,5,6,4,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,3,5,6,4,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,3,6,1,2,4,5]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,3,6,1,2,5,4]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,6,1,4,2,5]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,6,1,4,5,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,6,1,5,2,4]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,6,1,5,4,2]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,3,6,2,1,4,5]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,3,6,2,1,5,4]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,3,6,2,4,1,5]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,6,2,4,5,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,6,2,5,1,4]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,6,2,5,4,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,3,6,4,1,2,5]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,3,6,4,1,5,2]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,3,6,4,2,1,5]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,3,6,4,2,5,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,6,4,5,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,3,6,4,5,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,3,6,5,1,2,4]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,3,6,5,1,4,2]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,6,5,2,1,4]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,3,6,5,2,4,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,3,6,5,4,1,2]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,3,6,5,4,2,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[7,4,1,2,3,5,6]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[7,4,1,2,3,6,5]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,4,1,2,5,3,6]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,4,1,2,5,6,3]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,4,1,2,6,3,5]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,4,1,2,6,5,3]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,4,1,3,2,5,6]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,4,1,3,2,6,5]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,4,1,3,5,2,6]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,4,1,3,5,6,2]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,4,1,3,6,2,5]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,4,1,3,6,5,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,4,1,5,2,3,6]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,4,1,5,2,6,3]=>[[1,4,6],[2,5,7],[3]]=>[4,2,1]=>[4,2,1]=>3
[7,4,1,5,3,2,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,4,1,5,3,6,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,1,5,6,2,3]=>[[1,4,5],[2,6,7],[3]]=>[5,2]=>[5,2]=>2
[7,4,1,5,6,3,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,4,1,6,2,3,5]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,4,1,6,2,5,3]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,1,6,3,2,5]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,4,1,6,3,5,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,1,6,5,2,3]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,4,1,6,5,3,2]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,4,2,1,3,5,6]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,4,2,1,3,6,5]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,4,2,1,5,3,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,4,2,1,5,6,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,4,2,1,6,3,5]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,4,2,1,6,5,3]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[7,4,2,3,1,5,6]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,4,2,3,1,6,5]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,4,2,3,5,1,6]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,4,2,3,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,4,2,3,6,1,5]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,4,2,3,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,4,2,5,1,3,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,4,2,5,1,6,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,4,2,5,3,1,6]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,4,2,5,3,6,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,2,5,6,1,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,4,2,5,6,3,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,4,2,6,1,3,5]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,4,2,6,1,5,3]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,4,2,6,3,1,5]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,4,2,6,3,5,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,2,6,5,1,3]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[7,4,2,6,5,3,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,4,3,1,2,5,6]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,4,3,1,2,6,5]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,4,3,1,5,2,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,4,3,1,5,6,2]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,4,3,1,6,2,5]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,4,3,1,6,5,2]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[7,4,3,2,1,5,6]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,4,3,2,1,6,5]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,4,3,2,5,1,6]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,4,3,2,6,1,5]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,4,3,2,6,5,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,4,3,5,1,2,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,4,3,5,1,6,2]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,4,3,5,2,1,6]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,4,3,5,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,3,5,6,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,4,3,5,6,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,4,3,6,1,2,5]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,4,3,6,1,5,2]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,4,3,6,2,1,5]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,4,3,6,2,5,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,3,6,5,1,2]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[7,4,3,6,5,2,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,4,5,1,2,3,6]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,4,5,1,2,6,3]=>[[1,3,6],[2,5,7],[4]]=>[3,3,1]=>[3,3,1]=>3
[7,4,5,1,3,2,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,5,1,3,6,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,5,1,6,2,3]=>[[1,3,5],[2,6,7],[4]]=>[3,2,2]=>[3,2,2]=>3
[7,4,5,1,6,3,2]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,4,5,2,1,3,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,4,5,2,1,6,3]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,4,5,2,3,1,6]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,5,2,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,5,2,6,1,3]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,5,2,6,3,1]=>[[1,3,5],[2,6],[4],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,4,5,3,1,2,6]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,4,5,3,1,6,2]=>[[1,3,6],[2,7],[4],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,4,5,3,2,1,6]=>[[1,3,7],[2],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,4,5,3,2,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,5,3,6,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,5,3,6,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,4,5,6,1,2,3]=>[[1,3,4],[2,6,7],[5]]=>[4,3]=>[4,3]=>2
[7,4,5,6,1,3,2]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,5,6,2,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,4,5,6,2,3,1]=>[[1,3,4],[2,6],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,4,5,6,3,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[4,3]=>[4,3]=>2
[7,4,5,6,3,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,4,6,1,2,3,5]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,4,6,1,2,5,3]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,6,1,3,2,5]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,6,1,3,5,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,6,1,5,2,3]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,6,1,5,3,2]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,4,6,2,1,3,5]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,4,6,2,1,5,3]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,4,6,2,3,1,5]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,6,2,3,5,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,6,2,5,1,3]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,6,2,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,4,6,3,1,2,5]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,4,6,3,1,5,2]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,4,6,3,2,1,5]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,4,6,3,2,5,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,6,3,5,1,2]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,4,6,3,5,2,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,4,6,5,1,2,3]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,4,6,5,1,3,2]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,6,5,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,4,6,5,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,4,6,5,3,1,2]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,4,6,5,3,2,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[7,5,1,2,3,4,6]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[7,5,1,2,3,6,4]=>[[1,4,5,6],[2,7],[3]]=>[6,1]=>[6,1]=>2
[7,5,1,2,4,3,6]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,5,1,2,4,6,3]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,5,1,2,6,3,4]=>[[1,4,5,7],[2,6],[3]]=>[5,2]=>[5,2]=>2
[7,5,1,2,6,4,3]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,5,1,3,2,4,6]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,5,1,3,2,6,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,5,1,3,4,2,6]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,5,1,3,4,6,2]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,5,1,3,6,2,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,5,1,3,6,4,2]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,5,1,4,2,3,6]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,5,1,4,2,6,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,5,1,4,3,2,6]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,5,1,4,3,6,2]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,1,4,6,2,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,5,1,4,6,3,2]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,5,1,6,2,3,4]=>[[1,4,6,7],[2,5],[3]]=>[4,3]=>[4,3]=>2
[7,5,1,6,2,4,3]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,1,6,3,2,4]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,5,1,6,3,4,2]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,1,6,4,2,3]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,5,1,6,4,3,2]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,5,2,1,3,4,6]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,5,2,1,3,6,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,5,2,1,4,3,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,5,2,1,4,6,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,5,2,1,6,3,4]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,5,2,1,6,4,3]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[7,5,2,3,1,4,6]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,5,2,3,1,6,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,5,2,3,4,1,6]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,5,2,3,4,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,5,2,3,6,1,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,5,2,3,6,4,1]=>[[1,4,5],[2,6],[3],[7]]=>[5,2]=>[5,2]=>2
[7,5,2,4,1,3,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,5,2,4,1,6,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,5,2,4,3,1,6]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,5,2,4,3,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,2,4,6,1,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,5,2,4,6,3,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,5,2,6,1,3,4]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,5,2,6,1,4,3]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,5,2,6,3,1,4]=>[[1,4,7],[2,5],[3],[6]]=>[4,3]=>[4,3]=>2
[7,5,2,6,3,4,1]=>[[1,4,6],[2,5],[3],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,2,6,4,1,3]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[7,5,2,6,4,3,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,5,3,1,2,4,6]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,5,3,1,2,6,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,5,3,1,4,2,6]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,5,3,1,4,6,2]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,5,3,1,6,2,4]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,5,3,1,6,4,2]=>[[1,5],[2,6],[3,7],[4]]=>[5,2]=>[5,2]=>2
[7,5,3,2,1,4,6]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,5,3,2,1,6,4]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,5,3,2,4,1,6]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,5,3,2,4,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,5,3,2,6,1,4]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,5,3,2,6,4,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,5,3,4,1,2,6]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,5,3,4,1,6,2]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,5,3,4,2,1,6]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,3,4,6,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,5,3,4,6,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,5,3,6,1,2,4]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,5,3,6,1,4,2]=>[[1,4],[2,6],[3,7],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,5,3,6,2,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,5,3,6,2,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,3,6,4,1,2]=>[[1,4],[2,5],[3,7],[6]]=>[4,3]=>[4,3]=>2
[7,5,3,6,4,2,1]=>[[1,4],[2,5],[3],[6],[7]]=>[4,3]=>[4,3]=>2
[7,5,4,1,2,3,6]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,5,4,1,2,6,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,5,4,1,3,2,6]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,5,4,1,3,6,2]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,5,4,1,6,2,3]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,5,4,1,6,3,2]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,5,4,2,1,3,6]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,5,4,2,1,6,3]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,5,4,2,3,1,6]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,5,4,2,3,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,5,4,2,6,1,3]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,5,4,2,6,3,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,5,4,3,1,2,6]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,5,4,3,1,6,2]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,5,4,3,2,1,6]=>[[1,7],[2],[3],[4],[5],[6]]=>[7]=>[7]=>1
[7,5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[6,1]=>[6,1]=>2
[7,5,4,3,6,1,2]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,5,4,3,6,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[5,2]=>[5,2]=>2
[7,5,4,6,1,2,3]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,5,4,6,1,3,2]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,4,6,2,1,3]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,5,4,6,2,3,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,5,4,6,3,1,2]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,5,4,6,3,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,5,6,1,2,3,4]=>[[1,3,6,7],[2,5],[4]]=>[3,4]=>[4,3]=>2
[7,5,6,1,2,4,3]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,5,6,1,3,2,4]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,5,6,1,3,4,2]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,5,6,1,4,2,3]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,5,6,1,4,3,2]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,5,6,2,1,3,4]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,5,6,2,1,4,3]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,5,6,2,3,1,4]=>[[1,3,7],[2,5],[4],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,5,6,2,3,4,1]=>[[1,3,6],[2,5],[4],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,5,6,2,4,1,3]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,5,6,2,4,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,5,6,3,1,2,4]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,5,6,3,1,4,2]=>[[1,3],[2,6],[4,7],[5]]=>[3,3,1]=>[3,3,1]=>3
[7,5,6,3,2,1,4]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,5,6,3,2,4,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,5,6,3,4,1,2]=>[[1,3],[2,5],[4,7],[6]]=>[3,2,2]=>[3,2,2]=>3
[7,5,6,3,4,2,1]=>[[1,3],[2,5],[4],[6],[7]]=>[3,2,2]=>[3,2,2]=>3
[7,5,6,4,1,2,3]=>[[1,3,7],[2,6],[4],[5]]=>[3,4]=>[4,3]=>2
[7,5,6,4,1,3,2]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,5,6,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,5,6,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>[3,3,1]=>[3,3,1]=>3
[7,5,6,4,3,1,2]=>[[1,3],[2,7],[4],[5],[6]]=>[3,4]=>[4,3]=>2
[7,5,6,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[3,4]=>[4,3]=>2
[7,6,1,2,3,4,5]=>[[1,4,5,6,7],[2],[3]]=>[7]=>[7]=>1
[7,6,1,2,3,5,4]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,6,1,2,4,3,5]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,1,2,4,5,3]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,6,1,2,5,3,4]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,1,2,5,4,3]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,1,3,2,4,5]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,1,3,2,5,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,6,1,3,4,2,5]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,1,3,4,5,2]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,6,1,3,5,2,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,1,3,5,4,2]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,1,4,2,3,5]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,1,4,2,5,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,6,1,4,3,2,5]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,1,4,3,5,2]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,1,4,5,2,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,1,4,5,3,2]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,1,5,2,3,4]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,1,5,2,4,3]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,1,5,3,2,4]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,1,5,3,4,2]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,1,5,4,2,3]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,1,5,4,3,2]=>[[1,4],[2],[3],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,6,2,1,3,4,5]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,6,2,1,3,5,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,6,2,1,4,3,5]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,6,2,1,4,5,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,6,2,1,5,3,4]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,6,2,1,5,4,3]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,6,2,3,1,4,5]=>[[1,4,6,7],[2],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,2,3,1,5,4]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,6,2,3,4,1,5]=>[[1,4,5,7],[2],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,2,3,4,5,1]=>[[1,4,5,6],[2],[3],[7]]=>[6,1]=>[6,1]=>2
[7,6,2,3,5,1,4]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,2,3,5,4,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,2,4,1,3,5]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,2,4,1,5,3]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,6,2,4,3,1,5]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,2,4,3,5,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,2,4,5,1,3]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,2,4,5,3,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,2,5,1,3,4]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,2,5,1,4,3]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,2,5,3,1,4]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,2,5,3,4,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,2,5,4,1,3]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,2,5,4,3,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,6,3,1,2,4,5]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,6,3,1,2,5,4]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,6,3,1,4,2,5]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,6,3,1,4,5,2]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,6,3,1,5,2,4]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,6,3,1,5,4,2]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,6,3,2,1,4,5]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,6,3,2,1,5,4]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,6,3,2,4,1,5]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,3,2,4,5,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,6,3,2,5,1,4]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,3,2,5,4,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,6,3,4,1,2,5]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,3,4,1,5,2]=>[[1,4,6],[2,7],[3],[5]]=>[4,2,1]=>[4,2,1]=>3
[7,6,3,4,2,1,5]=>[[1,4,7],[2],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,3,4,2,5,1]=>[[1,4,6],[2],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,3,4,5,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[5,2]=>[5,2]=>2
[7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,3,5,1,2,4]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,3,5,1,4,2]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,3,5,2,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,3,5,2,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,3,5,4,1,2]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,3,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,6,4,1,2,3,5]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,6,4,1,2,5,3]=>[[1,5,6],[2,7],[3],[4]]=>[6,1]=>[6,1]=>2
[7,6,4,1,3,2,5]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,4,1,3,5,2]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,6,4,1,5,2,3]=>[[1,5,7],[2,6],[3],[4]]=>[5,2]=>[5,2]=>2
[7,6,4,1,5,3,2]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,6,4,2,1,3,5]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,6,4,2,1,5,3]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,6,4,2,3,1,5]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,4,2,3,5,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,6,4,2,5,1,3]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,4,2,5,3,1]=>[[1,5],[2,6],[3],[4],[7]]=>[5,2]=>[5,2]=>2
[7,6,4,3,1,2,5]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,6,4,3,1,5,2]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,6,4,3,2,1,5]=>[[1,7],[2],[3],[4],[5],[6]]=>[7]=>[7]=>1
[7,6,4,3,2,5,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[6,1]=>[6,1]=>2
[7,6,4,3,5,1,2]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,4,5,1,2,3]=>[[1,4,7],[2,6],[3],[5]]=>[4,3]=>[4,3]=>2
[7,6,4,5,1,3,2]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,4,5,2,1,3]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,4,5,2,3,1]=>[[1,4],[2,6],[3],[5],[7]]=>[4,2,1]=>[4,2,1]=>3
[7,6,4,5,3,1,2]=>[[1,4],[2,7],[3],[5],[6]]=>[4,3]=>[4,3]=>2
[7,6,4,5,3,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[4,3]=>[4,3]=>2
[7,6,5,1,2,3,4]=>[[1,5,6,7],[2],[3],[4]]=>[7]=>[7]=>1
[7,6,5,1,2,4,3]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,6,5,1,3,2,4]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,5,1,3,4,2]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,6,5,1,4,2,3]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,5,1,4,3,2]=>[[1,5],[2],[3],[4],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,5,2,1,3,4]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,6,5,2,1,4,3]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,6,5,2,3,1,4]=>[[1,5,7],[2],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,5,2,3,4,1]=>[[1,5,6],[2],[3],[4],[7]]=>[6,1]=>[6,1]=>2
[7,6,5,2,4,1,3]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,5,2,4,3,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,5,3,1,2,4]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,6,5,3,1,4,2]=>[[1,6],[2,7],[3],[4],[5]]=>[6,1]=>[6,1]=>2
[7,6,5,3,2,1,4]=>[[1,7],[2],[3],[4],[5],[6]]=>[7]=>[7]=>1
[7,6,5,3,2,4,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[6,1]=>[6,1]=>2
[7,6,5,3,4,1,2]=>[[1,5],[2,7],[3],[4],[6]]=>[5,2]=>[5,2]=>2
[7,6,5,3,4,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[5,2]=>[5,2]=>2
[7,6,5,4,1,2,3]=>[[1,6,7],[2],[3],[4],[5]]=>[7]=>[7]=>1
[7,6,5,4,1,3,2]=>[[1,6],[2],[3],[4],[5],[7]]=>[6,1]=>[6,1]=>2
[7,6,5,4,2,1,3]=>[[1,7],[2],[3],[4],[5],[6]]=>[7]=>[7]=>1
[7,6,5,4,2,3,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[6,1]=>[6,1]=>2
[7,6,5,4,3,1,2]=>[[1,7],[2],[3],[4],[5],[6]]=>[7]=>[7]=>1
[7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[7]=>[7]=>1
[8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8]=>[8]=>1
[7,8,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,6]=>[6,2]=>2
[8,6,7,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[7,6,8,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[6,7,8,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[8,7,5,6,4,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,8,5,6,4,3,2,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[8,6,5,7,4,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,5,6,7,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,6,5,8,4,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,7,5,8,4,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,5,6,8,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,5,7,8,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,6,7,8,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,8,6,4,5,3,2,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,6,7,4,5,3,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,6,8,4,5,3,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,7,5,4,6,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,4,5,6,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,6,5,4,7,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,5,6,4,7,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,6,4,5,7,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,4,5,6,7,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,6,5,4,8,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,7,5,4,8,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,5,6,4,8,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,5,7,4,8,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,4,8,3,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,6,4,5,8,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,7,4,5,8,3,2,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,5,4,6,8,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,4,5,6,8,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,5,4,7,8,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,6,4,7,8,3,2,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,4,5,7,8,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,4,6,7,8,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[4,5,6,7,8,3,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,6,5,3,4,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[6,2]=>[6,2]=>2
[7,8,6,5,3,4,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,6,7,5,3,4,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,5,3,4,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,8,5,6,3,4,2,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,6,7,3,4,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,8,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,7,5,8,3,4,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,5,7,8,3,4,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,7,8,3,4,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,6,4,3,5,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[6,2]=>[6,2]=>2
[7,8,6,4,3,5,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,6,7,4,3,5,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,4,3,5,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,4,3,5,2,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,3,4,5,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[7,8,6,3,4,5,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,6,7,3,4,5,2,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,3,4,5,2,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,3,4,5,2,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[6,2]=>[6,2]=>2
[7,8,5,4,3,6,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,4,5,3,6,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,5,3,4,6,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[7,8,5,3,4,6,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[8,7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[7,8,3,4,5,6,2,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,6,5,4,3,7,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[6,2]=>[6,2]=>2
[8,6,4,3,5,7,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[8,5,4,3,6,7,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[8,5,3,4,6,7,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[8,4,3,5,6,7,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[8,3,4,5,6,7,2,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[7,6,5,4,3,8,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[6,2]=>[6,2]=>2
[6,7,5,4,3,8,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,6,4,3,8,2,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,4,3,8,2,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,4,3,8,2,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,4,5,3,8,2,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,4,6,3,8,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,5,6,3,8,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,4,7,3,8,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,5,7,3,8,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,6,7,3,8,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,6,7,3,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,3,4,8,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[7,6,4,3,5,8,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[7,6,3,4,5,8,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[7,5,4,3,6,8,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[7,5,3,4,6,8,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[7,3,4,5,6,8,2,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[6,5,4,3,7,8,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[6,5,3,4,7,8,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[6,3,4,5,7,8,2,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[5,4,3,6,7,8,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[5,3,4,6,7,8,2,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[4,3,5,6,7,8,2,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[3,4,5,6,7,8,2,1]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[8,7,6,5,4,2,3,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[7,1]=>[7,1]=>2
[7,8,6,5,4,2,3,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,6,7,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,8,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,5,6,4,2,3,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,5,7,4,2,3,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,6,7,4,2,3,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,5,8,4,2,3,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,5,8,4,2,3,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,6,8,4,2,3,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,7,8,4,2,3,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,6,4,5,2,3,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,5,4,6,2,3,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,4,5,6,2,3,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,8,4,5,6,2,3,1]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,5,4,7,2,3,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,6,4,7,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,4,5,7,2,3,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,5,6,7,2,3,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,5,4,8,2,3,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,6,4,8,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,7,4,8,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,4,5,8,2,3,1]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,6,7,8,2,3,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,6,5,3,2,4,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[7,1]=>[7,1]=>2
[7,8,6,5,3,2,4,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,6,7,5,3,2,4,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,8,5,3,2,4,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,8,5,3,2,4,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,5,6,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,5,7,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,6,7,3,2,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,5,8,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,5,8,3,2,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,7,8,3,2,4,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,6,5,2,3,4,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[8,6,7,5,2,3,4,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,8,5,2,3,4,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,8,5,2,3,4,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,5,6,2,3,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,8,5,6,2,3,4,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,6,5,7,2,3,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,6,7,2,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,5,8,2,3,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,5,8,2,3,4,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,7,8,2,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,7,8,2,3,4,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,6,4,3,2,5,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[7,1]=>[7,1]=>2
[7,8,6,4,3,2,5,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,6,7,4,3,2,5,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,8,4,3,2,5,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,8,4,3,2,5,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,3,4,2,5,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,8,6,3,4,2,5,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,7,3,4,2,5,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,3,4,2,5,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,8,3,4,2,5,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,4,2,3,5,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,8,4,2,3,5,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,3,2,4,5,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[7,8,6,3,2,4,5,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,6,7,3,2,4,5,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,8,3,2,4,5,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,2,3,4,5,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,8,6,2,3,4,5,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,6,7,2,3,4,5,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,8,2,3,4,5,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,8,2,3,4,5,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,5,4,3,2,6,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[7,1]=>[7,1]=>2
[7,8,5,4,3,2,6,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,7,5,3,4,2,6,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,8,5,3,4,2,6,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,4,3,5,2,6,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,5,3,2,4,6,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[8,7,4,3,2,5,6,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[7,8,4,3,2,5,6,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,3,4,2,5,6,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,4,2,3,5,6,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,3,2,4,5,6,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,7,2,3,4,5,6,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[7,8,2,3,4,5,6,1]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,6,5,4,3,2,7,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[7,1]=>[7,1]=>2
[8,5,6,4,3,2,7,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,4,5,3,2,7,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,4,6,3,2,7,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,5,3,4,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,6,3,4,2,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,4,3,5,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,3,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,4,3,6,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,5,3,6,2,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,3,5,6,2,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,3,4,5,6,2,7,1]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,5,4,2,3,7,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[8,6,5,3,2,4,7,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[8,6,4,3,2,5,7,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[8,6,4,2,3,5,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[8,6,2,3,4,5,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[8,5,4,3,2,6,7,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[8,4,5,3,2,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,4,5,2,6,7,1]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,4,2,3,6,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[8,4,5,2,3,6,7,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,3,2,5,6,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[8,3,4,2,5,6,7,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,2,3,5,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[8,3,2,4,5,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[8,2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[7,6,5,4,3,2,8,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[7,1]=>[7,1]=>2
[6,7,5,4,3,2,8,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,5,6,4,3,2,8,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,7,4,3,2,8,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,7,4,3,2,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,4,5,3,2,8,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,4,5,3,2,8,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,5,6,3,2,8,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,7,3,2,8,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,5,7,3,2,8,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,6,7,3,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,5,3,4,2,8,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,6,3,4,2,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,7,3,4,2,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,4,3,5,2,8,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,3,4,5,2,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,4,3,6,2,8,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,5,3,6,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,3,4,6,2,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,3,4,5,6,2,8,1]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,4,3,7,2,8,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,5,3,7,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,3,7,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,6,3,7,2,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,3,4,7,2,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,6,3,4,7,2,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,3,5,7,2,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,4,5,7,2,8,1]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,3,6,7,2,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,5,3,6,7,2,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,5,6,7,2,8,1]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,5,6,7,2,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,5,4,2,3,8,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[6,7,5,4,2,3,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,5,6,4,2,3,8,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,7,4,2,3,8,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,7,4,2,3,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,4,5,2,3,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,4,5,2,3,8,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,4,6,2,3,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,5,6,2,3,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,7,2,3,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,4,7,2,3,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,6,7,2,3,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,6,7,2,3,8,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,5,3,2,4,8,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[6,7,5,3,2,4,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,5,7,3,2,4,8,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,5,2,3,4,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,5,6,2,3,4,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,7,2,3,4,8,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,4,3,2,5,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,6,4,2,3,5,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,6,3,2,4,5,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[6,7,3,2,4,5,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,6,2,3,4,5,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[6,7,2,3,4,5,8,1]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,5,4,3,2,6,8,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[7,4,3,5,2,6,8,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,4,2,3,6,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,4,5,2,3,6,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,3,2,4,6,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,5,2,3,4,6,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[7,4,3,2,5,6,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,3,2,4,5,6,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[7,2,3,4,5,6,8,1]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[6,5,4,3,2,7,8,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[5,4,6,3,2,7,8,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,6,3,2,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,3,4,2,7,8,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,4,5,2,7,8,1]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,3,6,2,7,8,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,5,6,2,7,8,1]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,6,2,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,2,3,7,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[5,6,4,2,3,7,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,4,5,2,3,7,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,6,2,3,7,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,6,2,3,7,8,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,3,2,4,7,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[6,5,2,3,4,7,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[6,2,3,4,5,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[5,4,3,2,6,7,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[4,5,3,2,6,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,3,4,2,6,7,8,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,5,2,6,7,8,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,5,2,6,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,2,3,6,7,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[4,5,2,3,6,7,8,1]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,3,2,4,6,7,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[5,2,3,4,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[4,3,2,5,6,7,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[3,4,2,5,6,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,2,3,5,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[3,2,4,5,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[2,3,4,5,6,7,8,1]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]=>[7,1]=>2
[8,7,6,5,4,3,1,2]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[8]=>[8]=>1
[7,8,6,5,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[8,6,7,5,4,3,1,2]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,6,8,5,4,3,1,2]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,7,8,5,4,3,1,2]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,7,5,6,4,3,1,2]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,8,5,6,4,3,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,6,5,7,4,3,1,2]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,6,5,8,4,3,1,2]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,7,5,8,4,3,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,5,6,8,4,3,1,2]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,7,8,4,3,1,2]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,6,7,8,4,3,1,2]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,6,4,5,3,1,2]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[7,8,6,4,5,3,1,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,6,7,4,5,3,1,2]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,4,5,3,1,2]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,5,4,6,3,1,2]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,5,6,4,7,3,1,2]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,4,5,7,3,1,2]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,5,4,6,7,3,1,2]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,6,5,4,8,3,1,2]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[7,5,6,4,8,3,1,2]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,7,4,8,3,1,2]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,4,5,8,3,1,2]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[6,7,4,5,8,3,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,4,7,8,3,1,2]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[5,6,4,7,8,3,1,2]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,6,7,8,3,1,2]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,5,6,7,8,3,1,2]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[8,7,6,5,3,4,1,2]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,8,6,5,3,4,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,8,5,3,4,1,2]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,5,3,4,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,5,6,3,4,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,5,7,3,4,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,6,7,3,4,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,8,3,4,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,5,8,3,4,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,6,8,3,4,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,7,8,3,4,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,7,8,3,4,1,2]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,7,8,4,3,5,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,3,4,5,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,6,7,3,4,5,1,2]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,5,4,3,6,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,4,5,3,6,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,8,4,5,3,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,5,3,4,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,4,3,5,6,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,8,4,3,5,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,3,4,5,6,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,8,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[8,6,5,4,3,7,1,2]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,5,4,6,3,7,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,3,6,7,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,3,4,6,7,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,4,3,5,6,7,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,3,4,5,6,7,1,2]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[7,6,5,4,3,8,1,2]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,5,6,4,3,8,1,2]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,4,3,8,1,2]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,4,5,3,8,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,4,6,3,8,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,4,7,3,8,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,4,7,3,8,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,6,7,3,8,1,2]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,3,4,8,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,4,3,5,8,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,3,4,5,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,5,4,3,6,8,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,4,5,3,6,8,1,2]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,3,4,6,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,3,4,5,6,8,1,2]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[6,5,4,3,7,8,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[5,6,4,3,7,8,1,2]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,3,7,8,1,2]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,3,7,8,1,2]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,4,7,8,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[6,4,3,5,7,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[6,3,4,5,7,8,1,2]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[5,4,3,6,7,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[4,5,3,6,7,8,1,2]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,4,6,7,8,1,2]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[4,3,5,6,7,8,1,2]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[3,4,5,6,7,8,1,2]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[8,7,6,5,4,2,1,3]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[8]=>[8]=>1
[7,8,6,5,4,2,1,3]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[8,6,7,5,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,6,8,5,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,7,8,5,4,2,1,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,7,5,6,4,2,1,3]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,8,5,6,4,2,1,3]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,6,5,8,4,2,1,3]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,7,5,8,4,2,1,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,5,6,8,4,2,1,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,7,8,4,2,1,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,6,7,8,4,2,1,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,6,4,5,2,1,3]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,4,5,6,7,2,1,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,6,5,4,8,2,1,3]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[6,7,5,4,8,2,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,7,4,8,2,1,3]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,4,8,2,1,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,4,5,8,2,1,3]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,4,5,6,8,2,1,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[5,4,6,7,8,2,1,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,5,6,7,8,2,1,3]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[8,7,6,5,4,1,2,3]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,8,6,5,4,1,2,3]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,6,8,5,4,1,2,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,7,8,5,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[7,8,5,6,4,1,2,3]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,6,5,7,4,1,2,3]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,5,6,7,4,1,2,3]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[7,6,5,8,4,1,2,3]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,7,5,8,4,1,2,3]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,5,6,8,4,1,2,3]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[6,5,7,8,4,1,2,3]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[5,6,7,8,4,1,2,3]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[8,7,6,4,5,1,2,3]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,6,7,4,5,1,2,3]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,4,5,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,5,4,6,1,2,3]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,8,5,4,6,1,2,3]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,4,5,6,1,2,3]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[7,8,4,5,6,1,2,3]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[8,6,5,4,7,1,2,3]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,5,6,4,7,1,2,3]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,4,5,7,1,2,3]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,5,4,6,7,1,2,3]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,4,5,6,7,1,2,3]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[7,6,5,4,8,1,2,3]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,7,5,4,8,1,2,3]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,5,7,4,8,1,2,3]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,4,8,1,2,3]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,4,5,8,1,2,3]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[7,5,4,6,8,1,2,3]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[6,5,4,7,8,1,2,3]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[5,6,4,7,8,1,2,3]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,4,6,7,8,1,2,3]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[4,5,6,7,8,1,2,3]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[8,7,6,5,3,2,1,4]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[8]=>[8]=>1
[7,8,6,5,3,2,1,4]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[8,6,7,5,3,2,1,4]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,6,8,5,3,2,1,4]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,7,8,5,3,2,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,7,5,6,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,8,5,6,3,2,1,4]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,6,5,7,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,5,6,7,3,2,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,6,5,8,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,7,5,8,3,2,1,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,5,6,8,3,2,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,7,8,3,2,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,6,7,8,3,2,1,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,6,5,2,3,1,4]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,8,6,5,2,3,1,4]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,7,5,2,3,1,4]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,5,2,3,1,4]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,5,2,3,1,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,5,6,2,3,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,8,5,6,2,3,1,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,5,7,2,3,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,6,7,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,8,2,3,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,5,8,2,3,1,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,6,8,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,7,8,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,7,8,2,3,1,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,6,5,3,1,2,4]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,8,6,5,3,1,2,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,6,7,5,3,1,2,4]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,6,8,5,3,1,2,4]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,7,5,6,3,1,2,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,8,5,6,3,1,2,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,5,8,3,1,2,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,7,5,8,3,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,5,6,8,3,1,2,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[6,5,7,8,3,1,2,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[5,6,7,8,3,1,2,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[8,7,6,5,2,1,3,4]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,8,6,5,2,1,3,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,6,8,5,2,1,3,4]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,7,8,5,2,1,3,4]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[8,7,5,6,2,1,3,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,8,5,6,2,1,3,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,6,5,7,2,1,3,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,5,6,7,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[7,6,5,8,2,1,3,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,7,5,8,2,1,3,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,5,6,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[6,5,7,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[5,6,7,8,2,1,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[8,7,6,5,1,2,3,4]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,6,5,1,2,3,4]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,6,7,5,1,2,3,4]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[7,6,8,5,1,2,3,4]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[6,7,8,5,1,2,3,4]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[8,7,5,6,1,2,3,4]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,8,5,6,1,2,3,4]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[8,6,5,7,1,2,3,4]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,5,6,7,1,2,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[7,6,5,8,1,2,3,4]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,7,5,8,1,2,3,4]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,5,6,8,1,2,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,5,7,8,1,2,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[8,7,6,4,3,2,1,5]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[8]=>[8]=>1
[7,8,6,4,3,2,1,5]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[8,6,7,4,3,2,1,5]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,6,8,4,3,2,1,5]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,7,8,4,3,2,1,5]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,7,6,3,4,2,1,5]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[7,8,6,3,4,2,1,5]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,8,3,4,2,1,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,6,4,2,3,1,5]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,6,8,4,2,3,1,5]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,4,2,3,1,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,3,2,4,1,5]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,6,7,3,2,4,1,5]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,3,2,4,1,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,2,3,4,1,5]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,6,7,2,3,4,1,5]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,2,3,4,1,5]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,2,3,4,1,5]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,4,3,1,2,5]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[6,7,8,4,3,1,2,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[8,7,6,3,4,1,2,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,8,6,3,4,1,2,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,6,7,3,4,1,2,5]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,3,4,1,2,5]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,6,4,2,1,3,5]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,8,6,4,2,1,3,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,6,7,4,2,1,3,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,7,8,4,2,1,3,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[8,7,6,4,1,2,3,5]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,6,4,1,2,3,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[7,6,8,4,1,2,3,5]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[6,7,8,4,1,2,3,5]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[8,7,6,3,2,1,4,5]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,8,6,3,2,1,4,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,6,7,3,2,1,4,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,6,8,3,2,1,4,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,7,8,3,2,1,4,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[8,7,6,2,3,1,4,5]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,8,6,2,3,1,4,5]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,6,7,2,3,1,4,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,8,2,3,1,4,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,2,3,1,4,5]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,7,6,3,1,2,4,5]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,6,3,1,2,4,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,6,7,3,1,2,4,5]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[7,6,8,3,1,2,4,5]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[6,7,8,3,1,2,4,5]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[8,7,6,2,1,3,4,5]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,6,2,1,3,4,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,6,7,2,1,3,4,5]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[6,7,8,2,1,3,4,5]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[8,7,6,1,2,3,4,5]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[7,8,6,1,2,3,4,5]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[8,6,7,1,2,3,4,5]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,6,8,1,2,3,4,5]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,7,8,1,2,3,4,5]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[8,7,5,4,3,2,1,6]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[8]=>[8]=>1
[7,8,5,4,3,2,1,6]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[8,7,4,5,3,2,1,6]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,8,4,5,3,2,1,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,7,5,3,4,2,1,6]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,3,4,5,2,1,6]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,8,3,4,5,2,1,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,4,5,2,3,1,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,8,4,5,2,3,1,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,5,3,2,4,1,6]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,8,5,2,3,4,1,6]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,4,3,2,5,1,6]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,8,4,3,2,5,1,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,3,4,2,5,1,6]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,8,3,4,2,5,1,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,2,3,4,5,1,6]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[7,8,2,3,4,5,1,6]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,5,4,3,1,2,6]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,8,5,4,3,1,2,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,7,5,3,4,1,2,6]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,3,4,5,1,2,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,8,3,4,5,1,2,6]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,5,4,2,1,3,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,7,5,4,1,2,3,6]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,5,4,1,2,3,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,7,4,5,1,2,3,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,8,4,5,1,2,3,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[8,7,5,3,2,1,4,6]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,8,5,3,2,1,4,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,7,5,3,1,2,4,6]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,5,3,1,2,4,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,7,5,2,1,3,4,6]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,5,2,1,3,4,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,7,5,1,2,3,4,6]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[7,8,5,1,2,3,4,6]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[8,7,4,3,2,1,5,6]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,8,4,3,2,1,5,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,7,3,4,2,1,5,6]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,8,3,4,2,1,5,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,4,2,3,1,5,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,3,2,4,1,5,6]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,8,3,2,4,1,5,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,2,3,4,1,5,6]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[7,8,2,3,4,1,5,6]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,4,3,1,2,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,7,3,4,1,2,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,8,3,4,1,2,5,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[8,7,4,2,1,3,5,6]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,4,2,1,3,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,7,4,1,2,3,5,6]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[7,8,4,1,2,3,5,6]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[8,7,3,2,1,4,5,6]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,8,3,2,1,4,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,7,2,3,1,4,5,6]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[7,8,2,3,1,4,5,6]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,8,3,1,2,4,5,6]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[8,7,2,1,3,4,5,6]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[7,8,2,1,3,4,5,6]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[8,7,1,2,3,4,5,6]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[7,8,1,2,3,4,5,6]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[8,6,5,4,3,2,1,7]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[8]=>[8]=>1
[8,5,6,4,3,2,1,7]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,6,4,5,3,2,1,7]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,4,5,6,3,2,1,7]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,6,5,3,4,2,1,7]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,5,6,3,4,2,1,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,5,3,6,2,1,7]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,3,5,6,2,1,7]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,3,4,5,6,2,1,7]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[8,6,5,4,2,3,1,7]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,5,6,4,2,3,1,7]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,5,6,2,3,1,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,5,3,2,4,1,7]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,6,5,2,3,4,1,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,6,2,3,4,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,4,2,3,5,1,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,6,3,2,4,5,1,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,4,3,2,6,1,7]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,4,3,5,2,6,1,7]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,2,3,6,1,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,4,5,2,3,6,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,5,3,2,4,6,1,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,2,3,4,6,1,7]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[8,3,4,2,5,6,1,7]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,4,5,6,1,7]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[8,2,3,4,5,6,1,7]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[8,6,5,4,3,1,2,7]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[8,6,4,5,3,1,2,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,6,5,3,4,1,2,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,5,6,3,4,1,2,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,3,4,5,1,2,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,5,4,3,6,1,2,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,4,5,3,6,1,2,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,3,4,6,1,2,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,4,3,5,6,1,2,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,3,4,5,6,1,2,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[8,6,5,4,2,1,3,7]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[8,5,6,4,2,1,3,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,4,5,6,2,1,3,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,6,5,4,1,2,3,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[8,5,6,4,1,2,3,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,6,4,5,1,2,3,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,4,5,6,1,2,3,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[8,6,5,3,2,1,4,7]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[8,5,6,3,2,1,4,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,6,5,2,3,1,4,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,5,6,2,3,1,4,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,6,3,1,2,4,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,6,5,2,1,3,4,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[8,5,6,2,1,3,4,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,6,5,1,2,3,4,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[8,5,6,1,2,3,4,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,6,4,3,2,1,5,7]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[8,6,3,4,2,1,5,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,6,4,2,3,1,5,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,6,3,2,4,1,5,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,6,2,3,4,1,5,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[8,6,4,3,1,2,5,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[8,6,3,4,1,2,5,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,6,4,2,1,3,5,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[8,6,4,1,2,3,5,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[8,6,3,2,1,4,5,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[8,6,1,2,3,4,5,7]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[8,5,4,3,2,1,6,7]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[8,4,5,3,2,1,6,7]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,4,3,5,2,1,6,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,3,4,5,2,1,6,7]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[8,4,5,2,3,1,6,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,2,3,4,1,6,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[8,4,2,3,5,1,6,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[8,2,3,4,5,1,6,7]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[8,5,3,4,1,2,6,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,3,4,5,1,2,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[8,5,4,2,1,3,6,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[8,5,4,1,2,3,6,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[8,4,5,1,2,3,6,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,5,3,2,1,4,6,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[8,5,3,1,2,4,6,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[8,5,2,1,3,4,6,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[8,5,1,2,3,4,6,7]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[8,4,3,2,1,5,6,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[8,3,4,2,1,5,6,7]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[8,4,2,3,1,5,6,7]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[8,2,3,4,1,5,6,7]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[8,3,4,1,2,5,6,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,4,2,1,3,5,6,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[8,4,1,2,3,5,6,7]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[8,3,2,1,4,5,6,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[8,2,3,1,4,5,6,7]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[8,3,1,2,4,5,6,7]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[8,2,1,3,4,5,6,7]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[8,1,2,3,4,5,6,7]=>[[1,3,4,5,6,7,8],[2]]=>[8]=>[8]=>1
[7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[8]=>[8]=>1
[6,7,5,4,3,2,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[7,5,6,4,3,2,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,5,7,4,3,2,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,6,7,4,3,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,6,4,5,3,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,7,4,5,3,2,1,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,5,4,6,3,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,5,6,3,2,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,4,7,3,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,6,4,7,3,2,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,4,6,7,3,2,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,5,6,7,3,2,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,6,5,3,4,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[6,7,5,3,4,2,1,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,5,6,3,4,2,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,7,3,4,2,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,3,4,2,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,4,3,5,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[6,7,4,3,5,2,1,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,3,4,5,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,5,4,3,6,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[7,3,4,5,6,2,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[6,5,4,3,7,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[5,6,4,3,7,2,1,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,6,3,7,2,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,3,6,7,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[3,4,5,6,7,2,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,6,5,4,2,3,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[6,7,5,4,2,3,1,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,5,6,4,2,3,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,4,2,3,1,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,5,2,3,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,4,5,2,3,1,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,4,6,2,3,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,4,7,2,3,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,4,7,2,3,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,6,7,2,3,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,6,7,2,3,1,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,3,2,4,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[6,5,7,3,2,4,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,3,2,4,1,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,5,2,3,4,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,7,5,2,3,4,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,5,6,2,3,4,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,2,3,4,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,2,3,4,1,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,3,2,5,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[6,7,4,3,2,5,1,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,7,3,4,2,5,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,4,2,3,5,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,7,4,2,3,5,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,3,2,4,5,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,7,3,2,4,5,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,2,3,4,5,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[6,7,2,3,4,5,1,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,5,4,3,2,6,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,4,5,3,2,6,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,3,4,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,3,5,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,5,2,3,6,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,3,2,4,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,4,2,3,5,6,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[7,2,3,4,5,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[6,5,4,3,2,7,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[5,6,4,3,2,7,1,8]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,3,2,7,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,4,2,7,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,4,5,2,7,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,6,2,7,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,3,6,2,7,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,4,6,2,7,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,5,6,2,7,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,6,2,7,1,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,6,2,3,7,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,3,2,4,7,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,4,2,3,5,7,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[6,3,2,4,5,7,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[6,2,3,4,5,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[5,4,3,2,6,7,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[3,4,5,2,6,7,1,8]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,3,6,7,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[4,5,2,3,6,7,1,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,3,4,6,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[4,3,2,5,6,7,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[3,4,2,5,6,7,1,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,2,3,5,6,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[3,2,4,5,6,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[2,3,4,5,6,7,1,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]=>[6,2]=>2
[7,6,5,4,3,1,2,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[6,7,5,4,3,1,2,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,5,6,4,3,1,2,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,6,4,5,3,1,2,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,4,6,7,3,1,2,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[4,5,6,7,3,1,2,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[7,6,5,3,4,1,2,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,7,3,4,5,1,2,8]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,4,3,7,1,2,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,4,5,3,7,1,2,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,3,4,7,1,2,8]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,4,5,7,1,2,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[4,3,5,6,7,1,2,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[3,4,5,6,7,1,2,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[7,6,5,4,2,1,3,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[6,5,7,4,2,1,3,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,6,4,5,2,1,3,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,5,4,6,2,1,3,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,4,6,7,2,1,3,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[4,5,6,7,2,1,3,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[7,6,5,4,1,2,3,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[5,6,7,4,1,2,3,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[7,4,5,6,1,2,3,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[5,4,6,7,1,2,3,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[4,5,6,7,1,2,3,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[7,6,5,3,2,1,4,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,6,5,2,3,1,4,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,7,5,2,3,1,4,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,5,6,2,3,1,4,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,5,7,2,3,1,4,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,2,3,1,4,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,5,2,1,3,4,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[6,7,5,2,1,3,4,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[7,5,6,2,1,3,4,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,6,7,2,1,3,4,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[7,6,5,1,2,3,4,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[6,7,5,1,2,3,4,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[7,5,6,1,2,3,4,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,5,7,1,2,3,4,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[5,6,7,1,2,3,4,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[7,6,4,3,2,1,5,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[6,7,4,3,2,1,5,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,6,3,4,2,1,5,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,7,3,4,2,1,5,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,4,2,3,1,5,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,6,3,2,4,1,5,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,7,3,2,4,1,5,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,6,2,3,4,1,5,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[6,7,2,3,4,1,5,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,6,4,3,1,2,5,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[6,7,3,4,1,2,5,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,4,2,1,3,5,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,6,3,2,1,4,5,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[6,7,3,2,1,4,5,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[7,6,2,3,1,4,5,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[6,7,2,3,1,4,5,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,7,3,1,2,4,5,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[7,6,1,2,3,4,5,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[6,7,1,2,3,4,5,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[7,5,4,3,2,1,6,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[7,4,5,3,2,1,6,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,4,3,5,2,1,6,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,3,4,5,2,1,6,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[7,5,4,2,3,1,6,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,5,3,2,4,1,6,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,5,2,3,4,1,6,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[7,4,2,3,5,1,6,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[7,2,3,4,5,1,6,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[7,5,4,3,1,2,6,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,4,5,2,1,3,6,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[7,4,5,1,2,3,6,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,5,3,2,1,4,6,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,5,2,3,1,4,6,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[7,5,3,1,2,4,6,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[7,5,1,2,3,4,6,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[7,4,3,2,1,5,6,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[7,2,3,4,1,5,6,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[7,4,3,1,2,5,6,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[7,3,4,1,2,5,6,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,4,1,2,3,5,6,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[7,3,2,1,4,5,6,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[7,2,3,1,4,5,6,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[7,3,1,2,4,5,6,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[7,2,1,3,4,5,6,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[7,1,2,3,4,5,6,8]=>[[1,3,4,5,6,7,8],[2]]=>[8]=>[8]=>1
[6,5,4,3,2,1,7,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[8]=>[8]=>1
[5,6,4,3,2,1,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[5,4,6,3,2,1,7,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,5,6,3,2,1,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,5,3,4,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,6,3,4,2,1,7,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,4,3,6,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[3,4,5,6,2,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[5,4,6,2,3,1,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,3,2,4,1,7,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,5,2,3,4,1,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[5,6,2,3,4,1,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,4,3,2,5,1,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,2,3,4,5,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[5,4,3,2,6,1,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[4,5,3,2,6,1,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,3,5,2,6,1,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,5,2,6,1,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,2,4,6,1,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[5,2,3,4,6,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[4,3,2,5,6,1,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[3,4,2,5,6,1,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,3,5,6,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[3,2,4,5,6,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[2,3,4,5,6,1,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]=>[5,3]=>2
[6,5,4,3,1,2,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[6,4,5,3,1,2,7,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,4,6,3,1,2,7,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,6,3,4,1,2,7,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,4,3,6,1,2,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[4,3,5,6,1,2,7,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[3,4,5,6,1,2,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[6,5,4,2,1,3,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[5,6,4,2,1,3,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[6,4,5,2,1,3,7,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[4,5,6,2,1,3,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[6,5,4,1,2,3,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[4,5,6,1,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[6,5,3,2,1,4,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[5,6,3,2,1,4,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,6,2,1,3,4,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[6,4,3,2,1,5,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[6,3,4,2,1,5,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[6,4,3,1,2,5,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[6,4,2,1,3,5,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[6,4,1,2,3,5,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[6,2,3,1,4,5,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[6,3,1,2,4,5,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[6,1,2,3,4,5,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[8]=>[8]=>1
[5,4,3,2,1,6,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[8]=>[8]=>1
[4,5,3,2,1,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[5,3,4,2,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[4,3,5,2,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[3,4,5,2,1,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[5,4,2,3,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[4,5,2,3,1,6,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,3,2,4,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[5,2,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[4,3,2,5,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[3,4,2,5,1,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,2,3,5,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[3,2,4,5,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[2,3,4,5,1,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]=>[4,4]=>2
[5,4,3,1,2,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[5,3,4,1,2,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[4,3,5,1,2,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[3,4,5,1,2,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[5,4,2,1,3,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[4,5,2,1,3,6,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[5,4,1,2,3,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[4,5,1,2,3,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[5,3,2,1,4,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[5,2,3,1,4,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[5,3,1,2,4,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[5,2,1,3,4,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[5,1,2,3,4,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[8]=>[8]=>1
[4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[8]=>[8]=>1
[3,4,2,1,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[4,2,3,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[3,2,4,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[2,3,4,1,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]=>[5,3]=>2
[4,3,1,2,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[3,4,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[4,2,1,3,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[4,1,2,3,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[8]=>[8]=>1
[3,2,1,4,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[8]=>[8]=>1
[2,3,1,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]=>[6,2]=>2
[3,1,2,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[8]=>[8]=>1
[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[8]=>[8]=>1
[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]=>[8]=>[8]=>1
[6,8,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,6]=>[6,2]=>2
[5,8,7,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,6]=>[6,2]=>2
[5,7,8,6,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[6,5,8,7,4,3,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[5,6,8,7,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[5,7,6,8,4,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,8,7,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,6]=>[6,2]=>2
[4,7,8,6,5,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[4,6,8,7,5,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[4,7,6,8,5,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,6,7,8,5,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,4,7,8,6,3,2,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,5,8,7,6,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[4,5,7,8,6,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,6,4,8,7,3,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,6,5,8,7,3,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,5,6,8,7,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,7,6,4,8,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,7,6,5,8,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,7,5,8,3,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,4,7,6,8,3,2,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,5,7,6,8,3,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,5,7,8,3,2,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,6]=>[6,2]=>2
[3,7,8,6,5,4,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[3,6,8,7,5,4,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[3,7,6,8,5,4,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,5,8,7,6,4,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[3,5,7,8,6,4,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,5,6,8,7,4,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,7,6,5,8,4,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,7,6,8,4,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,7,8,4,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[4,3,8,7,6,5,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[4,3,7,8,6,5,2,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,3,6,7,8,5,2,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,4,8,7,6,5,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[3,4,6,7,8,5,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,4,3,8,7,6,2,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,4,3,7,8,6,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[3,5,4,7,8,6,2,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,5,8,7,6,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,4,5,7,8,6,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,5,4,3,8,7,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[5,6,4,3,8,7,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,5,6,3,8,7,2,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,6,5,4,8,7,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,3,6,5,8,7,2,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,4,3,6,8,7,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[4,5,3,6,8,7,2,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,5,6,8,7,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,7,6,4,3,8,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,6,5,3,8,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,7,6,3,8,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,6,5,4,8,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,7,6,4,8,2,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,7,4,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,7,6,5,8,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,6,5,8,2,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,7,5,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,3,7,6,8,2,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,4,7,6,8,2,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,5,7,6,8,2,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,7,6,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,5,4,7,8,2,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,4,7,8,2,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,5,7,8,2,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,5,7,8,2,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,4,6,7,8,2,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,6]=>[6,2]=>2
[2,7,8,6,5,4,3,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[2,6,8,7,5,4,3,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[2,7,6,8,5,4,3,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[2,6,7,8,5,4,3,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,5,8,7,6,4,3,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[2,6,7,5,8,4,3,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,6,7,8,4,3,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,4,8,7,6,5,3,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[2,4,7,8,6,5,3,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,4,6,8,7,5,3,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,4,6,7,8,5,3,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,5,4,8,7,6,3,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[2,5,4,7,8,6,3,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,5,7,8,6,3,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,6,5,4,8,7,3,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,6,4,8,7,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,5,8,7,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,5,6,8,7,3,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,7,6,5,4,8,3,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,6,7,4,8,3,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,7,6,5,8,3,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,7,5,8,3,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,4,7,6,8,3,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,4,7,8,3,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,6,4,7,8,3,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,5,7,8,3,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,6,7,8,3,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,6,7,8,3,1]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[3,2,8,7,6,5,4,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[3,2,7,8,6,5,4,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,2,6,8,7,5,4,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,2,5,7,8,6,4,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,2,5,7,6,8,4,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,5,6,7,8,4,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,3,8,7,6,5,4,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[2,3,6,7,8,5,4,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,3,5,7,8,6,4,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,3,6,5,8,7,4,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,3,5,6,8,7,4,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,3,7,6,5,8,4,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,7,6,8,4,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,5,6,7,8,4,1]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[4,3,2,8,7,6,5,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,3,2,7,8,6,5,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,4,2,8,7,6,5,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,4,2,7,8,6,5,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,8,7,6,5,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[2,4,3,6,8,7,5,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,6,7,8,5,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,2,4,8,7,6,5,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,3,4,8,7,6,5,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,3,4,7,8,6,5,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,3,4,6,8,7,5,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,3,4,7,6,8,5,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,6,7,8,5,1]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[5,4,3,2,8,7,6,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[5,4,3,2,7,8,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[3,5,4,2,7,8,6,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,5,2,7,8,6,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,3,8,7,6,1]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,4,3,7,8,6,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,3,7,8,6,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,4,7,8,6,1]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,4,8,7,6,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,3,5,4,7,8,6,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,2,5,8,7,6,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,3,2,5,7,8,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[3,4,2,5,8,7,6,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,2,5,7,8,6,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,2,4,5,7,8,6,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,3,4,5,8,7,6,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,3,4,5,7,8,6,1]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[6,5,4,3,2,8,7,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[4,6,5,3,2,8,7,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,3,2,8,7,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,3,2,8,7,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,5,4,2,8,7,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,4,2,8,7,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,5,2,8,7,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,3,6,2,8,7,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,3,6,2,8,7,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,5,6,2,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,5,4,3,8,7,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,6,5,3,8,7,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,6,3,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,6,5,4,8,7,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,6,4,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,6,5,8,7,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,3,6,5,8,7,1]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,4,6,5,8,7,1]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,6,5,8,7,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,2,6,8,7,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[2,5,4,3,6,8,7,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,3,6,8,7,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,4,6,8,7,1]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,2,5,6,8,7,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[3,4,2,5,6,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,3,5,6,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,2,4,5,6,8,7,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,3,4,5,6,8,7,1]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[5,7,6,4,3,2,8,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,7,6,5,3,2,8,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,6,7,5,3,2,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,5,7,3,2,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,7,6,4,2,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,6,7,4,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,7,6,5,2,8,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,6,7,5,2,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,7,6,5,2,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,6,7,5,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,3,7,6,2,8,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,4,7,6,2,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,5,7,6,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,5,3,7,2,8,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,5,4,7,2,8,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,6,4,7,2,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,5,7,2,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,6,5,7,2,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,4,6,7,2,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,6,5,4,3,8,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,6,5,7,4,3,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,6,7,4,3,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,7,5,3,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,4,7,6,3,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,6,5,7,3,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,4,6,7,3,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,5,6,7,3,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,7,6,5,4,8,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,6,7,5,4,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,7,6,4,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,5,7,4,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,5,6,7,4,8,1]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,7,6,5,4,8,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,5,7,6,4,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,5,6,7,4,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,3,2,7,6,5,8,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,6,7,5,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,2,7,6,5,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,2,6,7,5,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,7,6,5,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,6,7,5,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,4,7,6,5,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,7,6,5,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,6,7,5,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,3,2,7,6,8,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,5,4,2,7,6,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,5,2,7,6,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,5,2,7,6,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,4,3,7,6,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,5,4,7,6,8,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,5,4,7,6,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,2,5,7,6,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,2,5,7,6,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,5,7,6,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,4,5,7,6,8,1]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,4,5,7,6,8,1]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,5,4,2,7,8,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,5,6,4,2,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,6,5,2,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,4,6,2,7,8,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,5,4,3,7,8,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,5,6,4,3,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,6,5,3,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,5,6,3,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,6,4,7,8,1]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,6,5,4,7,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,5,6,4,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,6,5,7,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,2,6,5,7,8,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,6,5,7,8,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,4,6,5,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,4,2,6,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,5,4,3,6,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,4,5,3,6,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,5,4,6,7,8,1]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,5,4,6,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,3,5,6,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,6]=>[6,2]=>2
[1,7,8,6,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[1,6,8,7,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[1,7,6,8,5,4,3,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,6,7,8,5,4,3,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,5,8,7,6,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[1,6,5,8,7,4,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,7,6,5,8,4,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,5,8,4,3,2]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,5,7,6,8,4,3,2]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,6,5,7,8,4,3,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,5,6,7,8,4,3,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,4,8,7,6,5,3,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[1,4,7,8,6,5,3,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,4,6,8,7,5,3,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,4,6,7,8,5,3,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,5,4,7,8,6,3,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,4,5,8,7,6,3,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,4,6,5,8,7,3,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,7,6,5,4,8,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,7,6,5,8,3,2]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,6,7,5,8,3,2]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,5,4,7,8,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,5,6,4,7,8,3,2]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,4,6,7,8,3,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,6,7,8,3,2]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,3,8,7,6,5,4,2]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[1,3,7,8,6,5,4,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,3,6,8,7,5,4,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,3,6,7,8,5,4,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,3,5,8,7,6,4,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,3,5,7,8,6,4,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,3,5,6,8,7,4,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,3,6,7,5,8,4,2]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,5,7,8,4,2]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,6,7,8,4,2]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,4,3,8,7,6,5,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,4,3,7,8,6,5,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,4,3,6,8,7,5,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,4,3,7,6,8,5,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,3,6,7,8,5,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,8,7,6,5,2]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,3,4,7,6,8,5,2]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,4,6,7,8,5,2]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,5,4,3,8,7,6,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,4,5,3,8,7,6,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,4,5,3,7,8,6,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,4,8,7,6,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,4,3,5,8,7,6,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,4,3,5,7,8,6,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,5,8,7,6,2]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,3,4,5,7,8,6,2]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,6,5,4,3,8,7,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,5,6,4,3,8,7,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,6,5,3,8,7,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,6,3,8,7,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,5,4,8,7,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,6,5,8,7,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,3,6,8,7,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,3,6,8,7,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,4,5,6,8,7,2]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,7,6,5,4,3,8,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,6,7,5,4,3,8,2]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,5,7,4,3,8,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,6,7,4,3,8,2]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,6,7,5,3,8,2]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,6,4,7,3,8,2]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,6,5,7,3,8,2]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,4,6,7,3,8,2]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,5,6,7,3,8,2]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,6,5,7,4,8,2]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,5,6,7,4,8,2]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,4,7,6,5,8,2]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,4,6,7,5,8,2]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,5,4,7,6,8,2]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,4,5,7,6,8,2]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,4,6,3,7,8,2]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,3,6,5,7,8,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,4,6,5,7,8,2]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,4,3,6,7,8,2]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,4,5,3,6,7,8,2]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,3,5,6,7,8,2]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,3,4,5,6,7,8,2]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]=>[7,1]=>2
[2,1,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[2,1,7,8,6,5,4,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,1,6,8,7,5,4,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,1,7,6,8,5,4,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,6,7,8,5,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,5,8,7,6,4,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,1,5,7,8,6,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,6,5,8,7,4,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,5,6,8,7,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,7,6,5,8,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,7,5,8,4,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,7,6,8,4,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,5,7,8,4,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,6,7,8,4,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,1,4,8,7,6,5,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,1,4,7,8,6,5,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,4,6,8,7,5,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,4,6,7,8,5,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,1,5,4,8,7,6,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,5,4,7,8,6,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,5,8,7,6,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,4,5,7,8,6,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,1,6,5,4,8,7,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,6,4,8,7,3]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,4,6,5,8,7,3]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,4,6,8,7,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,5,6,8,7,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,1,7,6,5,4,8,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,6,7,5,4,8,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,5,7,6,4,8,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,6,5,7,4,8,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,5,6,7,4,8,3]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,4,7,6,5,8,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,6,7,5,8,3]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,5,4,7,6,8,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,5,6,4,7,8,3]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,5,4,6,7,8,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,5,6,7,8,3]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,2,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[1,2,7,8,6,5,4,3]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,2,7,6,8,5,4,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,6,7,8,5,4,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,5,8,7,6,4,3]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,2,6,5,8,7,4,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,5,6,8,7,4,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,7,6,5,8,4,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,7,6,8,4,3]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,6,5,7,8,4,3]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,6,7,8,4,3]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,4,8,7,6,5,3]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,2,4,7,8,6,5,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,4,6,8,7,5,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,4,6,7,8,5,3]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,5,4,8,7,6,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,4,5,8,7,6,3]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,4,5,7,8,6,3]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,6,5,4,8,7,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,4,6,8,7,3]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,5,6,8,7,3]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,7,6,5,4,8,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,5,7,6,4,8,3]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,5,6,7,4,8,3]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,4,7,6,5,8,3]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,5,4,7,6,8,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,6,5,4,7,8,3]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,5,6,4,7,8,3]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,5,4,6,7,8,3]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,4,5,6,7,8,3]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]=>[7,1]=>2
[3,2,1,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,2,1,7,8,6,5,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,2,1,6,8,7,5,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,2,1,7,6,8,5,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,6,7,8,5,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[3,2,1,5,8,7,6,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,2,1,5,7,8,6,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[3,2,1,6,5,8,7,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,5,6,8,7,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[3,2,1,7,6,5,8,4]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,6,7,5,8,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,1,5,7,6,8,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,1,6,5,7,8,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,5,6,7,8,4]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[2,3,1,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[2,3,1,7,8,6,5,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,6,8,7,5,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,7,6,8,5,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,6,7,8,5,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,1,5,7,8,6,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,1,6,5,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,7,6,5,8,4]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,1,6,7,5,8,4]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,1,5,7,6,8,4]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,1,5,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,3,2,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,3,2,6,8,7,5,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,3,2,7,6,8,5,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,6,7,8,5,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,5,8,7,6,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,3,2,5,7,8,6,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,6,5,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,5,6,8,7,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,7,6,5,8,4]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,2,6,7,5,8,4]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,2,6,5,7,8,4]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,2,5,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,3,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,1,3,7,8,6,5,4]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,3,6,8,7,5,4]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,3,6,7,8,5,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,1,3,6,5,8,7,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,3,5,6,7,8,4]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,2,3,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,2,3,7,8,6,5,4]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,3,6,8,7,5,4]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,3,7,6,8,5,4]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,6,7,8,5,4]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,3,5,8,7,6,4]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,3,5,7,8,6,4]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,3,6,5,8,7,4]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,5,6,8,7,4]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,3,7,6,5,8,4]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,6,7,5,8,4]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,5,7,6,8,4]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,6,5,7,8,4]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,5,6,7,8,4]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]=>[7,1]=>2
[4,3,2,1,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[4,3,2,1,7,8,6,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[4,3,2,1,6,8,7,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[4,3,2,1,7,6,8,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[4,3,2,1,6,7,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[3,4,2,1,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,2,1,7,8,6,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,2,1,6,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,2,1,7,6,8,5]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,2,1,6,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,4,3,1,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,1,7,8,6,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,3,1,6,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,3,1,7,6,8,5]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,1,6,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,2,4,1,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,2,4,1,7,8,6,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,1,6,8,7,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,1,7,6,8,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,4,1,6,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,3,4,1,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,1,7,8,6,5]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,1,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,1,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,4,1,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,3,2,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,4,3,2,6,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,3,2,7,6,8,5]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,3,2,6,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,3,4,2,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,3,4,2,7,8,6,5]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,4,2,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,4,2,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,4,2,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,3,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,4,3,7,8,6,5]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,3,6,8,7,5]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,3,7,6,8,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,4,3,6,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,4,3,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,4,3,7,8,6,5]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,3,6,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,3,7,6,8,5]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,4,3,6,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,1,4,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,2,1,4,7,8,6,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[3,2,1,4,6,8,7,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[3,2,1,4,7,6,8,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,1,4,6,7,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[2,3,1,4,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,4,7,8,6,5]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,1,4,7,6,8,5]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,1,4,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,3,2,4,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,3,2,4,6,8,7,5]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,4,7,6,8,5]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,2,4,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,3,4,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,3,4,7,8,6,5]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,1,3,4,7,6,8,5]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,3,4,6,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,2,3,4,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,3,4,7,8,6,5]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,3,4,6,8,7,5]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,3,4,7,6,8,5]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,4,6,7,8,5]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]=>[7,1]=>2
[5,4,3,2,1,8,7,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[5,4,3,2,1,7,8,6]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[4,5,3,2,1,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,5,4,2,1,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,5,4,2,1,7,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,3,5,2,1,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,2,1,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,3,1,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,5,4,3,1,7,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,4,5,3,1,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,3,1,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,2,5,4,1,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,4,1,7,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,5,4,1,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,2,5,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,5,1,7,8,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,4,2,5,1,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,5,1,7,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,5,1,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,5,1,7,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,4,5,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,5,1,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,5,1,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,4,3,2,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,5,4,3,2,7,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,4,5,3,2,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,3,2,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,3,5,4,2,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,3,4,5,2,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,4,5,2,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,5,4,3,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,5,3,8,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,4,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,4,3,7,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,4,5,3,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,4,5,3,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,2,5,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,5,4,7,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,3,5,4,8,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,3,5,4,7,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,5,4,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,5,4,7,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,1,5,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[4,3,2,1,5,7,8,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[2,4,3,1,5,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,2,4,1,5,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,1,5,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,3,4,1,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,1,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,3,2,5,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,3,2,5,7,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,3,4,2,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,3,5,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,3,5,7,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,4,3,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,3,5,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,1,4,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[3,2,1,4,5,7,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[2,3,1,4,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,3,2,4,5,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,4,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,3,4,5,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,1,3,4,5,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,2,3,4,5,8,7,6]=>[[1,2,3,4,5,6],[7],[8]]=>[6,2]=>[6,2]=>2
[1,2,3,4,5,7,8,6]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]=>[7,1]=>2
[6,5,4,3,2,1,8,7]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[5,6,4,3,2,1,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[4,6,5,3,2,1,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,4,6,3,2,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,5,6,3,2,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,6,5,4,2,1,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[3,5,6,4,2,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,3,6,5,2,1,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,4,6,5,2,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,4,3,6,2,1,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,5,3,6,2,1,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,5,6,2,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,6,2,1,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,6,5,4,3,1,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[2,5,6,4,3,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,4,6,5,3,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,2,6,5,4,1,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,2,5,6,4,1,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,6,5,4,1,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,3,5,6,4,1,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,6,5,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,4,2,6,5,1,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,6,5,1,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,3,2,6,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,5,3,2,6,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,4,2,6,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,5,2,6,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,5,2,6,1,8,7]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,4,3,6,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,5,3,6,1,8,7]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,5,4,6,1,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,2,5,6,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,4,2,5,6,1,8,7]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,5,6,1,8,7]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,4,5,6,1,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,5,4,3,2,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,5,6,4,3,2,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,5,4,6,3,2,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,6,5,4,2,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,3,4,5,6,2,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,6,5,4,3,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,1,5,6,4,3,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,6,5,3,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,1,5,4,6,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,4,5,6,3,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,4,5,6,3,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,1,6,5,4,8,7]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,1,6,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,2,6,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,2,5,6,4,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,3,5,6,4,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,6,5,4,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,5,6,4,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[4,3,2,1,6,5,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[3,4,2,1,6,5,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,1,6,5,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,4,1,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,4,1,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,4,2,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,4,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,1,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,3,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,4,6,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,3,2,1,6,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[4,5,3,2,1,6,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,5,4,2,1,6,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,3,5,2,1,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,4,5,2,1,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,5,4,3,1,6,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,4,5,3,1,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,2,5,4,1,6,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,5,4,1,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,4,3,5,1,6,8,7]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,4,5,1,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,5,3,2,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,3,5,4,2,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,5,3,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,5,4,3,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,1,3,5,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,5,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,1,5,6,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[3,2,4,1,5,6,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,3,4,1,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,3,2,5,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,3,4,2,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,3,5,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,4,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,1,4,5,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[2,3,1,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,3,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,3,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,2,3,4,5,6,8,7]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]=>[7,1]=>2
[5,7,6,4,3,2,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[4,7,6,5,3,2,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[4,6,7,5,3,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,4,7,6,3,2,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,5,7,6,3,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,6,5,7,3,2,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,5,7,6,4,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,5,6,7,4,2,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,3,7,6,5,2,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,4,7,6,5,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,4,3,7,6,2,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[4,5,3,7,6,2,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,5,4,7,6,2,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,5,7,6,2,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,6,5,4,7,2,1,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,4,7,2,1,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,6,5,7,2,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,6,5,4,3,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[2,6,7,5,4,3,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,5,7,6,4,3,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,5,6,7,4,3,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,6,7,5,3,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,5,4,7,6,3,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,6,4,7,3,1,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,4,6,7,3,1,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,5,6,7,3,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[3,2,7,6,5,4,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,2,6,7,5,4,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,2,5,7,6,4,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,2,6,5,7,4,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,6,7,4,1,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[2,3,7,6,5,4,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,3,6,7,5,4,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,3,5,7,6,4,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,3,6,5,7,4,1,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,5,6,7,4,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,3,2,6,7,5,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[3,4,2,7,6,5,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,4,2,6,7,5,1,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,2,4,6,7,5,1,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[2,3,4,7,6,5,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,3,4,6,7,5,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[5,4,3,2,7,6,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[4,5,3,2,7,6,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,4,2,7,6,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,5,2,7,6,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,5,2,7,6,1,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,4,7,6,1,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,2,5,7,6,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[3,4,2,5,7,6,1,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,4,5,7,6,1,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[3,6,5,4,2,7,1,8]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,4,2,7,1,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,5,2,7,1,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,4,6,2,7,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,4,6,3,7,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,6,5,4,7,1,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,6,4,7,1,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,6,5,7,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,2,6,5,7,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,6,5,7,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,4,6,5,7,1,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,4,2,6,7,1,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,5,4,3,6,7,1,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,5,4,6,7,1,8]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,6,5,4,3,2,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[1,6,7,5,4,3,2,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,6,5,7,4,3,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,5,6,7,4,3,2,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,4,7,6,5,3,2,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,4,6,7,5,3,2,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,5,6,4,7,3,2,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,6,5,7,3,2,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,4,6,7,3,2,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,5,6,7,3,2,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,3,6,7,5,4,2,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,3,5,7,6,4,2,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,3,6,5,7,4,2,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,6,7,4,2,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,3,4,6,7,5,2,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,3,5,4,7,6,2,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,3,5,7,6,2,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,4,5,7,6,2,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,5,4,6,3,7,2,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,6,5,4,7,2,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,6,4,7,2,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,3,6,5,7,2,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,3,6,7,2,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,3,6,7,2,8]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,4,5,6,7,2,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]=>[6,2]=>2
[2,1,7,6,5,4,3,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,1,6,7,5,4,3,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,1,5,6,7,4,3,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[2,1,4,5,6,7,3,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,2,7,6,5,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,2,6,7,5,4,3,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,5,7,6,4,3,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,5,6,7,4,3,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,4,6,7,5,3,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,5,6,4,7,3,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,4,6,7,3,8]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,5,6,7,3,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]=>[6,2]=>2
[3,2,1,7,6,5,4,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[3,2,1,5,7,6,4,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[2,3,1,6,7,5,4,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,6,5,7,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,5,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,7,6,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,3,2,6,7,5,4,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,2,5,7,6,4,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,2,6,5,7,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,5,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[2,1,3,6,7,5,4,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[1,2,3,7,6,5,4,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,3,6,7,5,4,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,3,5,7,6,4,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,3,6,5,7,4,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,5,6,7,4,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]=>[6,2]=>2
[4,3,2,1,7,6,5,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[4,3,2,1,6,7,5,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[3,2,4,1,7,6,5,8]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,4,1,6,7,5,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,1,7,6,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,1,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,2,7,6,5,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,3,2,6,7,5,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,2,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,3,6,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,1,4,7,6,5,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[2,3,1,4,6,7,5,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,4,7,6,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,2,3,4,7,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,3,4,6,7,5,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]=>[6,2]=>2
[5,4,3,2,1,7,6,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[4,5,3,2,1,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,5,4,2,1,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,4,5,2,1,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,3,1,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,3,1,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,4,1,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,4,1,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,4,2,5,1,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,5,1,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,4,5,1,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,4,3,2,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,3,2,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,4,2,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,5,2,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,4,5,2,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,4,3,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,5,3,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,5,4,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[2,3,1,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,3,5,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,1,5,7,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[3,2,4,1,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,1,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,2,5,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,2,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,1,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[2,1,3,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,2,3,4,5,7,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]=>[6,2]=>2
[3,6,5,4,2,1,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,3,6,5,2,1,7,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,4,6,5,3,1,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,4,5,6,3,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,3,6,5,4,1,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,3,5,6,4,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[4,3,2,6,5,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[2,4,3,6,5,1,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,3,4,6,5,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[3,5,4,2,6,1,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,3,5,4,6,1,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,5,4,3,2,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,5,6,4,3,2,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,4,6,5,3,2,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,5,4,6,3,2,7,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,4,5,6,3,2,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,3,5,6,4,2,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,4,3,6,5,2,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,5,4,3,6,2,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,4,5,3,6,2,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,4,3,5,6,2,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,3,4,5,6,2,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]=>[5,3]=>2
[2,1,5,6,4,3,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[2,1,4,6,5,3,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[1,2,6,5,4,3,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,2,5,6,4,3,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,2,4,6,5,3,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,2,4,5,6,3,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]=>[5,3]=>2
[3,2,1,6,5,4,7,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[3,2,1,5,6,4,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[2,3,1,6,5,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,3,1,5,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,3,2,6,5,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,3,2,5,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,3,6,5,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,2,3,5,6,4,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]=>[5,3]=>2
[4,3,2,1,6,5,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[2,4,3,1,6,5,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[3,2,4,1,6,5,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,1,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,1,4,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,4,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,3,2,4,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,3,4,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,2,3,4,6,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]=>[5,3]=>2
[3,5,4,2,1,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[2,5,4,3,1,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[2,4,5,3,1,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[3,2,5,4,1,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[2,3,5,4,1,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[2,4,3,5,1,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,5,4,3,2,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,4,5,3,2,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,3,4,5,2,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]=>[4,4]=>2
[2,1,5,4,3,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[2,1,4,5,3,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,2,5,4,3,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[3,2,1,5,4,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[2,3,1,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,3,2,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,2,3,5,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]=>[4,4]=>2
[2,4,3,1,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[1,4,3,2,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[1,3,4,2,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]=>[5,3]=>2
[2,1,4,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[1,2,4,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]=>[5,3]=>2
[1,3,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]=>[6,2]=>2
[1,2,3,4,8,6,7,5]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,5,8,6,7,4]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,7,5,6,4,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,7,5,6,8,4]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,8,5,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,8,5,7,6,4]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,8,6,5,7,4]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,8,6,7,5,4]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,4,5,8,6,7,3]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,4,7,5,6,8,3]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,4,8,5,6,7,3]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,4,8,6,5,7,3]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,5,4,8,6,7,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,6,4,5,3,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,6,4,5,7,8,3]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,4,5,6,8,3]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,8,4,5,6,7,3]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,8,4,6,7,5,3]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,4,7,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,5,4,6,3,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,5,4,6,8,3]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,8,5,4,6,7,3]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,8,5,4,7,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,5,6,4,7,3]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,8,5,6,7,4,3]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,6,5,4,7,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,8,6,5,7,4,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,7,5,6,4,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,2,4,8,6,7,5]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,2,7,5,6,8,4]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,2,8,5,7,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,8,6,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,2,8,6,7,5,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,4,2,8,6,7,5]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,4,5,8,6,7,2]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,4,8,5,6,7,2]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,6,4,5,2,8,7]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,6,4,5,7,2,8]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,6,4,5,7,8,2]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,6,4,5,8,7,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,4,5,6,2,8]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,4,5,6,8,2]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,4,5,6,7,2]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,4,6,5,7,2]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,8,5,4,6,7,2]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,5,4,7,6,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,5,6,7,4,2]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,5,7,6,4,2]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,3,8,6,5,7,4,2]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,7,5,6,4,2]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,5,8,6,7,2]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,3,8,5,6,7,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,3,8,5,7,6,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,3,8,6,5,7,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,3,8,6,7,5,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,4,2,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,5,3,4,2,7,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,3,4,2,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,4,6,2,8,7]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,3,4,6,7,2,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,5,3,4,6,7,8,2]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,5,3,4,8,6,7,2]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,3,4,5,2,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,4,5,8,7,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,3,4,5,6,2,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,3,4,5,6,8,2]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,3,4,5,6,7,2]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,3,4,6,7,5,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,3,5,4,2,7,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,3,5,4,8,7,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,5,4,6,2,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,5,4,6,7,2]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,3,5,6,4,7,2]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,5,6,7,4,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,3,5,7,6,4,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,6,5,4,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,3,6,5,4,8,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,3,6,5,4,7,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,3,7,5,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,3,5,2,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,6,4,3,5,8,7,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,3,5,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,4,3,5,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,3,6,5,8,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,3,6,7,5,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,4,5,3,2,7,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,5,3,2,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,5,3,8,7,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,4,5,3,6,8,2]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,4,5,3,6,7,2]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,4,5,6,3,8,2]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,5,6,3,7,2]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,5,6,7,3,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,6,5,3,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,4,6,5,3,7,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,4,6,5,7,3,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,7,6,5,3,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,7,5,4,3,6,2,8]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,4,3,6,8,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,5,4,3,6,7,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,5,4,6,3,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,4,6,7,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,4,7,6,3,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,6,4,5,3,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,4,5,3,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,6,4,5,7,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,4,5,6,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,4,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,5,4,3,7,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,6,5,4,7,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,5,4,6,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,5,6,4,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,1,3,4,8,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,3,5,8,6,7,4]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,3,8,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,3,8,5,7,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,3,8,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,3,8,6,7,5,4]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,4,3,8,6,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,4,5,8,6,7,3]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,4,8,5,6,7,3]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,8,5,7,6,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,4,8,6,5,7,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,8,6,7,5,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,4,8,6,7,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,4,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,4,5,7,8,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,6,4,5,8,7,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,4,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,4,5,7,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,4,6,5,8,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,4,6,5,7,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,4,6,7,5,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,4,7,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,8,5,4,6,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,5,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,5,6,4,8,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,5,6,4,7,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,5,6,7,4,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,5,7,6,4,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,8,6,5,4,7,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,6,5,7,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,7,5,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,1,7,5,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,8,5,6,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,1,8,6,7,5,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,4,1,8,6,7,5]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,4,5,8,6,7,1]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,4,7,5,6,1,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,7,5,6,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,8,5,6,7,1]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,8,5,7,6,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,8,6,5,7,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,8,6,7,5,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,5,4,8,6,7,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,6,4,5,1,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,6,4,5,1,8,7]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,6,4,5,7,8,1]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,6,4,5,8,7,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,7,4,5,6,8,1]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,8,4,5,6,7,1]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,7,4,6,5,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,8,4,6,7,5,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,7,5,4,6,1,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,7,5,4,6,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,8,5,4,6,7,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,7,5,6,4,1,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,7,5,6,4,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,8,5,6,4,7,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,8,5,6,7,4,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,5,7,6,4,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,3,8,6,5,4,7,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,3,5,8,6,7,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,7,5,6,8,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,8,5,6,7,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,8,5,7,6,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,8,6,5,7,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,3,4,1,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,5,3,4,1,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,3,4,6,7,1,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,5,3,4,6,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,5,3,4,6,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,3,4,7,6,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,3,4,8,6,7,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,3,4,8,7,6,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,4,5,1,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,4,5,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,6,3,4,5,8,7,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,3,4,5,6,1,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,3,4,5,6,7,1]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,3,4,5,7,6,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,3,5,4,1,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,5,4,7,8,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,5,4,8,7,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,3,5,4,6,8,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,3,5,4,7,6,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,3,5,6,4,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,3,5,6,7,4,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,3,5,7,6,4,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,7,3,6,5,4,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,8,3,7,5,6,4,1]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,7,6,5,4,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[2,5,4,3,8,6,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,3,5,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,3,5,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,6,4,3,5,8,7,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,4,3,5,6,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,4,3,5,6,7,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,4,3,5,7,6,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,4,3,6,5,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,3,6,5,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,3,6,7,5,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,4,3,7,6,5,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,6,4,5,3,1,7,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,4,5,3,7,8,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,5,3,6,7,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,4,5,6,3,1,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,4,5,6,3,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,5,6,3,7,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,5,6,7,3,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,4,6,5,3,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,7,4,6,5,3,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,6,5,3,7,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,7,6,5,3,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[2,7,5,4,3,6,8,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,5,4,3,6,7,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,5,4,3,7,6,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,5,4,6,3,8,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,5,4,6,7,3,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,4,7,6,3,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,7,6,4,5,3,8,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,7,4,5,6,3,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,4,6,5,3,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,5,4,6,3,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,5,6,4,3,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,2,1,4,8,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,1,5,8,6,7,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,1,7,5,6,8,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,8,5,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,8,5,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,8,6,5,7,4]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,8,6,7,5,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,4,1,8,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,4,5,8,6,7,1]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,4,7,5,6,8,1]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,4,8,5,6,7,1]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,4,8,6,7,5,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,5,4,8,6,7,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,4,5,1,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,4,5,6,1,8]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,4,5,6,7,1]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,7,4,6,5,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,4,6,5,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,4,6,5,7,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,5,4,6,1,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,5,4,6,7,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,5,4,7,6,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,5,6,4,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,5,6,4,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,5,6,4,7,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,5,7,6,4,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,2,8,6,5,7,4,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,7,5,6,4,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,3,1,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,2,3,1,5,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,2,3,1,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,3,1,6,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,2,3,1,6,8,7,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,3,1,7,6,8,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,3,1,8,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,3,1,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,2,3,5,1,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,2,3,5,1,7,8,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,2,3,5,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,3,5,6,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,2,3,5,6,8,7,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,2,3,5,8,7,6,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[4,2,3,6,5,8,7,1]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,3,7,5,6,1,8]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,3,7,5,6,8,1]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,3,8,5,6,7,1]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,3,8,5,7,6,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,3,7,6,5,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,3,8,7,6,5,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,2,3,4,1,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,2,3,4,1,7,8,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,2,3,4,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,3,4,6,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,2,3,4,7,6,1,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[5,2,3,4,8,6,7,1]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,3,4,8,7,6,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,2,3,4,5,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,2,3,4,5,8,7,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[8,2,3,4,5,7,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[7,2,3,4,6,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[6,2,3,5,4,1,7,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[6,2,3,5,4,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,2,3,5,4,7,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,3,5,4,7,8,1]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,3,5,4,6,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,3,5,4,6,7,1]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,3,5,6,4,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[8,2,3,5,6,7,4,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[8,2,3,5,7,6,4,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,2,3,6,5,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,3,6,5,4,7,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,3,7,5,6,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,4,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[5,2,4,3,1,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,2,4,3,1,7,6,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,3,1,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,3,6,1,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,2,4,3,6,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,4,3,6,7,1,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,3,7,6,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,4,3,7,6,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,4,3,8,7,6,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,3,5,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,4,3,6,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,3,6,5,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,3,6,5,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,3,6,7,5,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,5,3,1,7,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[7,2,4,5,3,6,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,4,5,3,6,8,1]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,4,5,3,7,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,4,5,6,7,3,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[8,2,4,5,7,6,3,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,2,4,6,5,3,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,2,4,6,5,3,8,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,4,7,5,6,3,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,4,7,6,5,3,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,2,5,4,3,1,7,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,2,5,4,3,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,2,5,4,3,7,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,5,4,3,7,8,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,5,4,3,6,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,5,4,3,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,5,4,3,7,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,5,4,6,3,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,5,4,7,6,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,4,5,3,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,4,5,3,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,4,5,3,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,4,5,7,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,4,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,5,4,3,8,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,6,5,4,3,7,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,6,5,4,7,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,5,4,6,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,5,6,4,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[4,3,2,1,8,6,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[4,3,2,7,5,6,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,8,5,6,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,8,5,7,6,1]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,8,6,7,5,1]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,4,1,6,8,7]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,3,2,4,1,7,6,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,4,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,4,6,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,4,7,6,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,3,2,4,6,7,5,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[6,3,2,5,4,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,3,2,5,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,2,5,4,7,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,5,4,7,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,2,5,4,8,7,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,2,5,4,6,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,2,5,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,2,5,6,4,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,3,2,5,6,4,7,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,3,2,5,6,7,4,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[8,3,2,5,7,6,4,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,3,2,6,5,7,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,3,2,7,5,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,3,2,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,3,4,2,1,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,3,4,2,1,7,8,6]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,3,4,2,1,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,3,4,2,6,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,4,2,7,6,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,4,2,7,6,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,4,2,8,6,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,4,2,5,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,4,2,6,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,4,2,6,5,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,4,2,6,5,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,4,5,2,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,4,5,2,8,7,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,3,4,5,2,7,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,3,4,5,7,6,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,3,4,6,5,2,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,4,7,6,5,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,3,5,4,2,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,3,5,4,2,7,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,4,2,7,8,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,5,4,2,8,7,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,4,2,6,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,4,2,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,5,4,2,7,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,4,6,2,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,5,4,6,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,4,6,7,2,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,4,7,6,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,3,6,4,5,2,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,6,4,5,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,6,4,5,2,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,4,5,6,2,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,4,6,5,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,3,6,5,4,2,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,3,6,5,4,2,8,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,6,5,4,2,7,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,6,5,4,7,2,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,5,4,6,2,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,5,6,4,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,6,5,4,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[5,4,3,2,8,6,7,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,2,5,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,2,5,8,7,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[7,4,3,2,6,5,8,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,3,2,6,7,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,4,3,2,7,6,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[6,4,3,5,2,1,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,3,5,2,7,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,5,7,6,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[7,4,3,6,5,2,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,3,6,5,2,8,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,3,7,5,6,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,7,6,5,2,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,5,3,4,2,1,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,3,4,2,7,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,3,4,7,6,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,3,4,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,6,3,5,4,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,6,3,5,4,2,8,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,3,5,4,7,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,5,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,5,6,4,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,3,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,5,4,3,2,7,6,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[8,5,4,3,7,6,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,4,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,4,6,5,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,4,1,3,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,4,6,3,5,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,1,6,3,5,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,6,1,3,5,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,3,6,8,5,7]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,3,6,8,5,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,1,4,6,3,8,5,7]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,1,6,3,8,5,7]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,6,1,3,8,5,7]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,6,8,3,5,7]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[2,4,1,6,8,3,5,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,6,1,8,3,5,7]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,8,1,3,5,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[2,4,1,3,6,5,7,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,4,6,3,5,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[2,4,1,6,3,5,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[2,4,6,1,3,5,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[2,1,4,6,3,7,5,8]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,1,6,3,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,6,1,3,7,5,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,7,1,3,5,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[2,4,1,3,6,7,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,4,6,3,7,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,1,6,3,7,8,5]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,4,6,7,3,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,1,6,7,3,8,5]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,6,1,7,3,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,6,7,1,3,8,5]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,6,7,8,3,5]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[2,4,1,6,7,8,3,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,6,7,8,1,3,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,1,4,3,7,5,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,1,3,7,5,8,6]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,4,7,3,5,8,6]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,1,7,3,5,8,6]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,7,1,3,5,8,6]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,3,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,3,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,1,7,3,8,5,6]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,4,7,8,3,5,6]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[2,4,1,7,8,3,5,6]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,7,1,8,3,5,6]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,7,8,1,3,5,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[2,4,1,5,3,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,5,1,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,1,7,3,6,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,1,3,5,7,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,4,1,5,3,7,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,5,1,3,7,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,5,7,3,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,1,5,7,3,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,5,1,7,3,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,4,5,7,8,3,6]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[2,4,5,1,7,8,3,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,7,1,8,3,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,5,7,8,1,3,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,1,4,3,8,5,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,1,3,8,5,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,4,8,3,5,6,7]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[2,4,1,8,3,5,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[2,4,8,1,3,5,6,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[2,1,4,3,5,8,6,7]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,5,3,8,6,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,4,5,8,3,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[2,4,1,5,8,3,6,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,5,1,8,3,6,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,1,5,3,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,1,5,6,3,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,5,1,6,3,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,5,6,1,3,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,5,6,8,3,7]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[2,4,1,5,6,8,3,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,1,6,8,3,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,6,1,8,3,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,5,6,8,1,3,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,4,1,3,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[2,4,1,5,3,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[2,4,5,1,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[2,4,1,5,6,3,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[2,4,5,1,6,3,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,5,6,1,3,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[2,4,1,5,6,7,3,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,6,1,7,3,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,5,6,7,1,3,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[2,4,1,5,6,7,8,3]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[2,4,5,1,6,7,8,3]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,5,6,1,7,8,3]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,5,6,7,1,8,3]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,5,6,7,8,1,3]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[2,1,5,3,6,4,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,1,3,6,4,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,5,6,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,1,6,3,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,6,1,3,4,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,5,3,6,8,4,7]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,1,3,6,8,4,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,6,1,3,8,4,7]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,6,8,3,4,7]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[2,5,1,6,8,3,4,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,6,8,1,3,4,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[2,5,1,3,6,4,7,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,5,6,3,4,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[2,5,1,6,3,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[2,1,5,3,6,7,4,8]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,6,3,7,4,8]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,1,6,3,7,4,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,6,1,3,7,4,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,6,7,3,4,8]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[2,5,1,6,7,3,4,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,6,1,7,3,4,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,5,3,6,7,8,4]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,1,3,6,7,8,4]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,5,6,3,7,8,4]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,1,6,3,7,8,4]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,6,1,3,7,8,4]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,5,6,7,3,8,4]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,5,1,6,7,3,8,4]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,6,7,1,3,8,4]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,5,6,7,8,3,4]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[2,5,1,6,7,8,3,4]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,6,1,7,8,3,4]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,6,7,1,8,3,4]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,6,7,8,1,3,4]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,1,5,3,7,4,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,1,3,7,4,8,6]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,5,7,3,4,8,6]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,1,7,3,4,8,6]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,7,1,3,4,8,6]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,5,3,7,8,4,6]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,1,3,7,8,4,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,1,5,7,3,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,7,8,3,4,6]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[2,5,1,7,8,3,4,6]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,7,1,8,3,4,6]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,7,8,1,3,4,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[2,5,1,3,7,4,6,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,5,7,3,4,6,8]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[2,3,5,1,4,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,7,1,4,6,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[2,3,5,1,7,4,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,5,7,1,4,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,1,5,7,8,4,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,5,7,1,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,5,7,8,1,4,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,1,5,3,8,4,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,5,1,3,8,4,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,5,8,3,4,6,7]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[2,5,1,8,3,4,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[2,5,8,1,3,4,6,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[2,3,5,1,4,8,6,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,3,5,8,4,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[2,3,5,1,8,4,6,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,5,8,1,4,6,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[2,1,5,3,4,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,5,1,6,4,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,5,6,1,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,3,5,6,8,4,7]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[2,3,1,5,6,8,4,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,5,1,6,8,4,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,6,1,8,4,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,5,6,8,1,4,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,1,5,3,4,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[2,5,1,3,4,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[2,3,5,1,4,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[2,3,5,1,6,4,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,5,6,1,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[2,3,5,6,7,1,4,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[2,3,5,1,6,7,8,4]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,5,6,1,7,8,4]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,5,6,7,1,8,4]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,5,6,7,8,1,4]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[2,1,6,3,7,4,8,5]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,1,3,7,4,8,5]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,6,7,3,4,8,5]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,1,7,3,4,8,5]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,7,1,3,4,8,5]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,6,3,7,8,4,5]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,1,3,7,8,4,5]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,1,7,3,8,4,5]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,7,1,3,8,4,5]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,7,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[2,6,1,7,8,3,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,6,7,1,8,3,4,5]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,6,7,8,1,3,4,5]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[2,1,6,3,7,4,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,7,3,4,5,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,7,1,3,4,5,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[2,6,1,3,4,7,5,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,1,6,4,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,6,1,4,7,5,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,3,4,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,1,3,4,7,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,3,6,1,4,7,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,3,6,7,4,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,3,6,7,8,4,5]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[2,3,1,6,7,8,4,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,6,1,7,8,4,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,6,7,1,8,4,5]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,6,7,8,1,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,1,6,3,8,4,5,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,3,8,4,5,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,6,8,3,4,5,7]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[2,6,1,8,3,4,5,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,8,1,3,4,5,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[2,1,6,3,4,8,5,7]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,1,3,4,8,5,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,1,6,4,8,5,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,6,1,4,8,5,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,1,6,8,4,5,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,6,1,8,4,5,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,6,3,4,5,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,1,3,4,5,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,3,6,4,5,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,6,1,4,5,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,4,1,6,8,5,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,6,1,8,5,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,6,8,1,5,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,6,1,3,4,5,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[2,1,3,6,4,5,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[2,3,1,6,4,5,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[2,3,6,1,4,5,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[2,3,4,6,1,5,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[2,3,4,6,1,7,5,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,6,7,1,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[2,3,4,6,1,7,8,5]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,6,7,8,1,5]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[2,1,7,3,8,4,5,6]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,7,1,3,8,4,5,6]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,7,8,3,4,5,6]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[2,7,1,8,3,4,5,6]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[2,7,8,1,3,4,5,6]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[2,1,7,3,4,8,5,6]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,3,7,4,8,5,6]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,1,7,4,8,5,6]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,7,1,4,8,5,6]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,3,7,8,4,5,6]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[2,3,1,7,8,4,5,6]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,7,8,1,4,5,6]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[2,1,7,3,4,5,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,1,3,4,5,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,3,1,7,4,5,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,7,1,4,5,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,3,4,7,5,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,4,1,7,5,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,4,7,1,5,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,3,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[2,3,1,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,4,1,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,7,1,8,5,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,7,8,1,5,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[2,1,7,3,4,5,6,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[2,7,1,3,4,5,6,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[2,3,7,1,4,5,6,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[2,1,3,4,7,5,6,8]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[2,3,1,4,7,5,6,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[2,3,4,1,7,5,6,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,7,1,5,6,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[2,3,4,5,7,1,6,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[2,3,4,5,7,1,8,6]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,4,5,7,8,1,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[2,1,8,3,4,5,6,7]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[2,8,1,3,4,5,6,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[2,1,3,8,4,5,6,7]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[2,3,1,8,4,5,6,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[2,3,8,1,4,5,6,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[2,1,3,4,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[2,3,1,4,8,5,6,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[2,3,4,1,8,5,6,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,8,1,5,6,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[2,1,3,4,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[2,3,1,4,5,8,6,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,4,1,5,8,6,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,5,1,8,6,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,5,8,1,6,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[2,3,4,5,6,8,1,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[3,1,4,2,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,1,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,4,6,2,5,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,1,6,2,5,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,6,1,2,5,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,4,2,6,8,5,7]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,1,2,6,8,5,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,4,6,2,8,5,7]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,1,6,2,8,5,7]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,4,6,8,2,5,7]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[3,4,1,6,8,2,5,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,6,8,1,2,5,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[3,1,4,2,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,1,2,6,5,7,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,4,2,6,7,5,8]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,1,2,6,7,5,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,1,6,2,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,6,1,2,7,5,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,1,6,7,2,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,6,7,1,2,5,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[3,1,4,2,6,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,1,2,6,7,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,4,6,2,7,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,1,6,2,7,8,5]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,6,1,2,7,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,4,6,7,2,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,1,6,7,2,8,5]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,6,1,7,2,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,6,7,1,2,8,5]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,6,7,8,2,5]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[3,4,1,6,7,8,2,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,6,1,7,8,2,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,7,1,8,2,5]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,7,8,1,2,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,1,4,2,7,5,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,1,2,7,5,8,6]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,4,7,2,5,8,6]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,7,1,2,5,8,6]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,4,2,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,1,2,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,7,1,8,2,5,6]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,7,8,1,2,5,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[3,1,4,2,7,5,6,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,1,2,7,5,6,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,4,1,2,5,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,4,5,2,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,1,5,2,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,5,7,2,6,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,5,7,1,2,6,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[3,1,4,2,5,7,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,1,2,5,7,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,4,5,2,7,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,1,2,7,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,4,5,7,2,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,1,5,7,2,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,5,7,1,2,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,5,7,8,2,6]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[3,4,1,5,7,8,2,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,5,1,7,8,2,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,7,1,8,2,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,7,8,1,2,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,1,4,2,8,5,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,1,2,8,5,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,4,8,2,5,6,7]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[3,4,1,8,2,5,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,8,1,2,5,6,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[3,1,4,2,5,8,6,7]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,1,2,5,8,6,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,1,5,2,8,6,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,5,1,2,8,6,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,4,5,8,2,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[3,4,1,5,8,2,6,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,5,8,1,2,6,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[3,4,1,2,5,6,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,4,5,1,2,6,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,4,5,6,2,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,1,5,6,2,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,5,1,6,2,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,5,6,1,2,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,5,6,8,2,7]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[3,4,1,5,6,8,2,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,5,6,1,8,2,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,6,8,1,2,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,1,4,2,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[3,1,4,5,2,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[3,4,1,5,2,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[3,4,1,5,6,2,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[3,4,5,1,6,2,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,4,5,6,7,2,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[3,4,1,5,6,7,2,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,5,1,6,7,2,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,6,1,7,2,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,4,5,6,7,8,2]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[3,4,1,5,6,7,8,2]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[3,4,5,1,6,7,8,2]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,5,6,1,7,8,2]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,6,7,1,8,2]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,5,2,6,4,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,1,2,6,4,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,5,6,2,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,1,6,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,6,1,2,4,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,5,2,6,8,4,7]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,2,6,8,4,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,5,6,2,8,4,7]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,1,2,8,4,7]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,5,6,8,2,4,7]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[3,5,1,6,8,2,4,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,1,8,2,4,7]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,8,1,2,4,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[3,1,5,6,2,4,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[3,5,1,6,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,5,6,1,2,4,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[3,5,1,2,6,7,4,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,1,6,2,7,4,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,6,1,2,7,4,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,6,7,2,4,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,1,7,2,4,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,7,1,2,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[3,1,5,2,6,7,8,4]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,1,2,6,7,8,4]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,5,6,2,7,8,4]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,1,6,2,7,8,4]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,6,1,2,7,8,4]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,5,6,7,2,8,4]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,5,1,6,7,2,8,4]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,6,1,7,2,8,4]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,6,7,1,2,8,4]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,5,6,7,8,2,4]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[3,5,1,6,7,8,2,4]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,1,7,8,2,4]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,7,1,8,2,4]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,7,8,1,2,4]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,1,5,2,7,4,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,1,2,7,4,8,6]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,5,7,2,4,8,6]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,1,7,2,4,8,6]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,7,1,2,4,8,6]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,5,2,7,8,4,6]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,2,7,8,4,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,5,7,2,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,1,7,2,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,5,7,8,2,4,6]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[3,5,1,7,8,2,4,6]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,7,8,1,2,4,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[3,1,5,2,7,4,6,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,1,2,7,4,6,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,5,7,2,4,6,8]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[3,5,1,7,2,4,6,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,5,7,1,2,4,6,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[3,1,5,2,4,7,6,8]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,2,4,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,2,5,4,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,2,4,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,2,5,7,4,6,8]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,3,2,5,7,4,6,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,5,2,7,4,6,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,7,2,4,6,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[3,5,1,2,4,7,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,2,5,7,4,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,5,2,7,4,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,5,7,2,4,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,2,5,7,8,4,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,5,2,7,8,4,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,7,2,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,7,8,2,4,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,1,5,2,8,4,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,1,2,8,4,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,5,8,2,4,6,7]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[3,5,1,8,2,4,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,1,5,2,4,8,6,7]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,2,4,8,6,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,5,4,8,6,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,5,2,4,8,6,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,2,5,8,4,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,3,2,5,8,4,6,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,5,2,8,4,6,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,8,2,4,6,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[3,5,1,2,4,6,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,2,5,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,5,2,4,6,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,5,6,2,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,5,6,8,4,7]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,3,5,2,6,8,4,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,6,2,8,4,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,6,8,2,4,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,5,1,2,4,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[1,3,5,2,4,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[1,3,5,6,2,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[3,1,2,5,6,7,4,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,3,5,2,6,7,4,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,6,2,7,4,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,6,7,2,4,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[3,1,2,5,6,7,8,4]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,3,5,6,2,7,8,4]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,5,6,7,2,8,4]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,5,6,7,8,2,4]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[3,1,6,2,7,4,8,5]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,1,2,7,4,8,5]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,1,7,2,4,8,5]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,7,1,2,4,8,5]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,1,2,7,8,4,5]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,6,7,2,8,4,5]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,1,7,2,8,4,5]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,7,1,2,8,4,5]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,7,8,2,4,5]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,6,7,8,1,2,4,5]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[3,1,6,2,7,4,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,6,7,2,4,5,8]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[3,6,7,1,2,4,5,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[3,1,6,2,4,7,5,8]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,2,4,7,5,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,2,6,4,7,5,8]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,2,6,4,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,6,2,4,7,5,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,2,6,7,4,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,6,2,7,4,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,1,6,2,4,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,1,2,4,7,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,2,6,4,7,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,6,2,4,7,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,6,7,4,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,2,6,7,4,8,5]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,6,2,7,4,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,2,6,7,8,4,5]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,3,2,6,7,8,4,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,6,2,7,8,4,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,6,7,8,2,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,1,6,2,8,4,5,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,1,2,8,4,5,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,8,2,4,5,7]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[3,6,1,8,2,4,5,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,6,8,1,2,4,5,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[3,1,6,2,4,8,5,7]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,2,4,8,5,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,6,4,8,5,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,6,2,4,8,5,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,2,6,8,4,5,7]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,3,2,6,8,4,5,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,2,4,5,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,1,2,4,5,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,2,6,4,5,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,6,2,4,5,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,4,6,2,5,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,4,6,8,5,7]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,3,2,4,6,8,5,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,6,8,2,5,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,1,6,2,4,5,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[3,6,1,2,4,5,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[1,3,2,6,4,5,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,3,6,2,4,5,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[1,3,4,6,2,5,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[3,1,2,4,6,7,5,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,3,4,6,2,7,5,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,4,6,7,2,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[3,1,2,4,6,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,3,4,6,7,2,8,5]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,7,2,8,4,5,6]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,2,8,4,5,6]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,7,8,2,4,5,6]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[3,7,1,8,2,4,5,6]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,8,1,2,4,5,6]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[3,7,1,2,4,8,5,6]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,2,7,4,8,5,6]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,2,7,4,8,5,6]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,7,2,4,8,5,6]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,2,7,8,4,5,6]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,3,7,2,8,4,5,6]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,7,8,2,4,5,6]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[3,1,7,2,4,5,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,1,2,4,5,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[1,3,7,2,4,5,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,4,7,5,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,2,4,7,5,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,4,2,7,5,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,2,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,3,2,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,2,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,4,7,8,2,5,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[3,1,7,2,4,5,6,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[3,7,1,2,4,5,6,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[3,1,2,7,4,5,6,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,3,2,7,4,5,6,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,3,7,2,4,5,6,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[3,1,2,4,7,5,6,8]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,3,4,7,2,5,6,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[3,1,2,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,3,4,5,7,2,6,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[3,1,2,4,5,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,3,4,5,7,8,2,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[3,1,8,2,4,5,6,7]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[3,8,1,2,4,5,6,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[3,1,2,8,4,5,6,7]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,3,2,8,4,5,6,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,3,8,2,4,5,6,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[3,1,2,4,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,3,2,4,8,5,6,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,3,4,2,8,5,6,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,3,4,8,2,5,6,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[3,1,2,4,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,3,2,4,5,8,6,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,2,5,8,6,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,4,5,2,8,6,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,4,5,8,2,6,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[3,1,2,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,3,4,5,6,8,2,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[4,1,5,2,6,3,8,7]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,1,2,6,3,8,7]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,5,6,2,3,8,7]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,1,6,2,3,8,7]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,6,1,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,5,2,6,8,3,7]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,2,6,8,3,7]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[4,1,5,6,2,8,3,7]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,1,6,2,8,3,7]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,6,1,2,8,3,7]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,5,6,8,2,3,7]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[4,5,1,6,8,2,3,7]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[4,5,6,1,8,2,3,7]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,5,6,8,1,2,3,7]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[4,1,5,2,6,3,7,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,1,5,6,2,3,7,8]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[4,5,1,6,2,3,7,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,5,1,2,6,7,3,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,5,1,6,2,7,3,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,6,1,2,7,3,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,5,6,7,2,3,8]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[4,5,1,6,7,2,3,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,6,1,7,2,3,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,5,2,6,7,8,3]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,1,2,6,7,8,3]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,5,1,6,2,7,8,3]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,6,1,2,7,8,3]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,5,6,7,2,8,3]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[4,5,1,6,7,2,8,3]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,6,1,7,2,8,3]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,6,7,1,2,8,3]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,5,6,7,8,2,3]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[4,5,1,6,7,8,2,3]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,6,1,7,8,2,3]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,7,1,8,2,3]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,2,7,3,8,6]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,1,7,2,3,8,6]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,5,2,7,8,3,6]=>[[1,3,5,6],[2,4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,2,7,8,3,6]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[4,1,5,7,2,8,3,6]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,1,7,2,8,3,6]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,7,1,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,7,8,2,3,6]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[4,5,7,8,1,2,3,6]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[4,1,5,2,7,3,6,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,1,2,7,3,6,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,5,2,3,7,6,8]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,2,3,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,2,5,3,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,2,5,3,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,5,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,5,7,3,6,8]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,4,2,5,7,3,6,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,5,2,7,3,6,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,5,7,2,3,6,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[4,1,5,2,3,7,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,2,5,3,7,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,5,2,3,7,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,2,5,7,3,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,2,5,7,3,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,5,2,7,3,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,5,7,2,3,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,2,5,7,8,3,6]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,4,2,5,7,8,3,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,2,7,8,3,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,7,8,2,3,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[4,1,5,2,8,3,6,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,1,2,8,3,6,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,5,1,8,2,3,6,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,5,8,1,2,3,6,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[4,1,5,2,3,8,6,7]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,2,3,8,6,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,2,5,3,8,6,7]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,2,5,3,8,6,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,5,2,3,8,6,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,5,8,3,6,7]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,4,2,5,8,3,6,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,5,2,8,3,6,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,2,5,3,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,2,5,6,3,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,5,2,6,3,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,2,5,6,8,3,7]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,4,2,5,6,8,3,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,2,6,8,3,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,6,8,2,3,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[4,1,5,2,3,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[4,1,2,5,3,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,4,2,5,3,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,4,5,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[4,1,2,5,6,3,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,4,5,2,6,3,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,4,5,6,2,3,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[4,1,2,5,6,7,3,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,4,2,5,6,7,3,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,2,6,7,3,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,6,2,7,3,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,5,6,7,2,3,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[4,1,2,5,6,7,8,3]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,4,2,5,6,7,8,3]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,4,5,2,6,7,8,3]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,5,6,2,7,8,3]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,5,6,7,2,8,3]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,5,6,7,8,2,3]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[4,1,6,2,7,3,8,5]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,7,2,3,8,5]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,7,1,2,3,8,5]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,1,2,7,8,3,5]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[4,6,1,7,2,8,3,5]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,7,1,2,8,3,5]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,7,8,2,3,5]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[4,6,1,7,8,2,3,5]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,7,1,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,8,1,2,3,5]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[4,4]=>2
[4,1,6,2,7,3,5,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,1,2,7,3,5,8]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,6,7,2,3,5,8]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[4,6,1,7,2,3,5,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,7,1,2,3,5,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[4,1,6,2,3,7,5,8]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,2,3,7,5,8]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,2,6,3,7,5,8]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,2,6,3,7,5,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,2,6,7,3,5,8]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,4,2,6,7,3,5,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,6,2,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,6,7,2,3,5,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[4,1,6,2,3,7,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,2,6,3,7,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,6,2,3,7,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,2,6,7,3,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,6,2,7,3,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,2,6,7,8,3,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,2,7,8,3,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,6,7,2,8,3,5]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,4,6,7,8,2,3,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[4,1,6,2,8,3,5,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,1,2,8,3,5,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,6,8,2,3,5,7]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[4,6,1,8,2,3,5,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,8,1,2,3,5,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[4,1,6,2,3,8,5,7]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,2,3,8,5,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,2,6,3,8,5,7]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,2,6,3,8,5,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,6,2,3,8,5,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,2,6,8,3,5,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,6,2,8,3,5,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,6,8,2,3,5,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[4,1,6,2,3,5,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,1,2,3,5,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,1,2,6,3,5,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,2,6,3,5,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,6,2,3,5,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,2,3,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,2,3,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,4,6,3,5,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,2,3,6,8,5,7]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,2,4,3,6,8,5,7]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,6,8,3,5,7]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[4,1,6,2,3,5,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[4,6,1,2,3,5,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[1,4,2,6,3,5,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,4,6,2,3,5,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[4,1,2,3,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,4,2,3,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,4,6,3,5,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[4,1,2,3,6,7,5,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,4,2,3,6,7,5,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,2,3,6,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,4,2,3,6,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,4,6,7,8,3,5]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[4,1,7,2,8,3,5,6]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,2,8,3,5,6]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,7,8,2,3,5,6]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[4,7,1,8,2,3,5,6]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,7,8,1,2,3,5,6]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[4,1,7,2,3,8,5,6]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,1,2,3,8,5,6]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,2,7,3,8,5,6]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,7,2,3,8,5,6]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,7,8,3,5,6]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,4,2,7,8,3,5,6]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,7,2,8,3,5,6]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,7,8,2,3,5,6]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[4,1,7,2,3,5,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,1,2,3,5,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,1,2,7,3,5,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,2,7,3,5,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,7,2,3,5,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,2,3,7,5,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,2,3,7,5,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,4,3,7,5,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,4,7,3,5,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,2,3,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,4,2,3,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,4,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,7,3,8,5,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,4,7,8,3,5,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[4,1,7,2,3,5,6,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[4,7,1,2,3,5,6,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[4,1,2,7,3,5,6,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,4,2,7,3,5,6,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,4,7,2,3,5,6,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[4,1,2,3,7,5,6,8]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,4,2,3,7,5,6,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,4,3,7,5,6,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,4,7,3,5,6,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[4,1,2,3,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,4,2,3,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,4,5,7,3,6,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[4,1,2,3,5,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,4,2,3,5,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,4,5,7,3,8,6]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,4,5,7,8,3,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[4,1,8,2,3,5,6,7]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[4,8,1,2,3,5,6,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[4,1,2,8,3,5,6,7]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,4,2,8,3,5,6,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,4,8,2,3,5,6,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[4,1,2,3,8,5,6,7]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,4,2,3,8,5,6,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,4,3,8,5,6,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,4,8,3,5,6,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[4,1,2,3,5,8,6,7]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,4,2,3,5,8,6,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,4,3,5,8,6,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,5,3,8,6,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,4,5,8,3,6,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[4,1,2,3,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,4,2,3,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,4,5,6,8,3,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[1,4,2,3,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]=>[6,2]=>2
[5,1,6,2,7,3,8,4]=>[[1,3,5,7],[2,4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,1,2,7,3,8,4]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,6,7,2,3,8,4]=>[[1,3,4,7],[2,5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,1,7,2,3,8,4]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,7,1,2,3,8,4]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,1,2,7,8,3,4]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,6,7,2,8,3,4]=>[[1,3,4,6],[2,5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,7,1,2,8,3,4]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,6,7,8,2,3,4]=>[[1,3,4,5],[2,6,7,8]]=>[5,3]=>[5,3]=>2
[5,6,1,7,8,2,3,4]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,7,1,8,2,3,4]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,2,7,3,4,8]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,1,7,2,3,4,8]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,1,6,2,3,7,4,8]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,2,6,3,7,4,8]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,2,6,3,7,4,8]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,2,6,7,3,4,8]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,5,2,6,7,3,4,8]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,6,7,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[5,1,6,2,3,7,8,4]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,1,2,3,7,8,4]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[5,1,2,6,3,7,8,4]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,2,6,3,7,8,4]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,6,2,3,7,8,4]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,2,6,7,3,8,4]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,6,7,2,3,8,4]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,6,7,8,3,4]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,5,2,6,7,8,3,4]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,5,6,2,7,8,3,4]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,7,2,8,3,4]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,6,7,8,2,3,4]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[5,1,6,2,8,3,4,7]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,1,2,8,3,4,7]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,1,8,2,3,4,7]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,6,8,1,2,3,4,7]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[5,1,6,2,3,8,4,7]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,1,2,3,8,4,7]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,1,2,6,3,8,4,7]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,2,6,3,8,4,7]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,6,2,3,8,4,7]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,2,6,8,3,4,7]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,5,2,6,8,3,4,7]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,6,2,8,3,4,7]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,6,8,2,3,4,7]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[5,1,6,2,3,4,8,7]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,1,2,3,4,8,7]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[5,1,2,6,3,4,8,7]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,2,6,3,4,8,7]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,6,2,3,4,8,7]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,2,3,6,4,8,7]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,5,3,6,4,8,7]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,5,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,3,6,8,4,7]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,5,2,3,6,8,4,7]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,5,6,3,8,4,7]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,2,3,4,7,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[5,1,2,6,3,4,7,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,5,2,6,3,4,7,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,5,6,2,3,4,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[5,1,2,3,6,4,7,8]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,5,2,3,6,4,7,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,5,3,6,4,7,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,5,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[5,1,2,3,6,7,4,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,5,2,3,6,7,4,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,5,3,6,7,4,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,6,3,7,4,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,2,3,6,7,8,4]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,5,2,3,6,7,8,4]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,5,3,6,7,8,4]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,5,6,3,7,8,4]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,5,6,7,3,8,4]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,5,6,7,8,3,4]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[5,1,7,2,8,3,4,6]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,1,2,8,3,4,6]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,7,8,2,3,4,6]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[5,7,1,8,2,3,4,6]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,7,8,1,2,3,4,6]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]=>[5,3]=>2
[5,1,7,2,3,8,4,6]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,2,3,8,4,6]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,1,2,7,3,8,4,6]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,2,7,3,8,4,6]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,7,2,3,8,4,6]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,2,7,8,3,4,6]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,5,2,7,8,3,4,6]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,7,2,8,3,4,6]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,7,8,2,3,4,6]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[5,1,7,2,3,4,8,6]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,1,2,3,4,8,6]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[5,1,2,7,3,4,8,6]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,2,7,3,4,8,6]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,7,2,3,4,8,6]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,2,3,7,4,8,6]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,2,3,7,4,8,6]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,5,3,7,4,8,6]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,5,7,3,4,8,6]=>[[1,2,3,4,7],[5,6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,3,7,8,4,6]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,5,2,3,7,8,4,6]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,5,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,7,8,3,4,6]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[5,1,7,2,3,4,6,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[5,7,1,2,3,4,6,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[5,1,2,7,3,4,6,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,5,2,7,3,4,6,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,5,2,3,7,4,6,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,5,3,7,4,6,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,5,7,3,4,6,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[1,5,2,3,4,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,5,3,4,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,5,7,4,6,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[5,1,2,3,4,7,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,5,2,3,4,7,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,5,3,4,7,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,3,5,7,4,8,6]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,5,7,8,4,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[5,1,8,2,3,4,6,7]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[5,8,1,2,3,4,6,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[5,1,2,8,3,4,6,7]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,5,2,8,3,4,6,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,5,8,2,3,4,6,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[5,1,2,3,8,4,6,7]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,5,2,3,8,4,6,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,5,3,8,4,6,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,5,8,3,4,6,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[5,1,2,3,4,8,6,7]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,5,2,3,4,8,6,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,5,3,4,8,6,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,5,4,8,6,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,5,8,4,6,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[5,1,2,3,4,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,5,2,3,4,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,5,3,4,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,3,5,6,8,4,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[1,5,2,3,4,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]=>[6,2]=>2
[1,2,5,3,4,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]=>[5,3]=>2
[6,1,7,2,8,3,4,5]=>[[1,3,5,7,8],[2,4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,1,2,8,3,4,5]=>[[1,2,5,7,8],[3,4,6]]=>[2,3,3]=>[3,3,2]=>3
[6,1,7,8,2,3,4,5]=>[[1,3,4,7,8],[2,5,6]]=>[4,4]=>[4,4]=>2
[6,7,1,8,2,3,4,5]=>[[1,2,4,7,8],[3,5,6]]=>[2,2,4]=>[4,2,2]=>3
[6,1,7,2,3,8,4,5]=>[[1,3,5,6,8],[2,4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,1,2,3,8,4,5]=>[[1,2,5,6,8],[3,4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,1,2,7,3,8,4,5]=>[[1,3,4,6,8],[2,5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,2,7,3,8,4,5]=>[[1,2,4,6,8],[3,5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,7,2,3,8,4,5]=>[[1,2,3,6,8],[4,5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,2,7,8,3,4,5]=>[[1,3,4,5,8],[2,6,7]]=>[5,3]=>[5,3]=>2
[1,6,2,7,8,3,4,5]=>[[1,2,4,5,8],[3,6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,2,8,3,4,5]=>[[1,2,3,5,8],[4,6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,8,2,3,4,5]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]=>[4,4]=>2
[6,1,7,2,3,4,8,5]=>[[1,3,5,6,7],[2,4,8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,1,2,3,4,8,5]=>[[1,2,5,6,7],[3,4,8]]=>[2,5,1]=>[5,2,1]=>3
[6,1,2,7,3,4,8,5]=>[[1,3,4,6,7],[2,5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,2,7,3,4,8,5]=>[[1,2,4,6,7],[3,5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,7,2,3,4,8,5]=>[[1,2,3,6,7],[4,5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,2,3,7,4,8,5]=>[[1,3,4,5,7],[2,6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,2,3,7,4,8,5]=>[[1,2,4,5,7],[3,6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,6,3,7,4,8,5]=>[[1,2,3,5,7],[4,6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,2,3,7,8,4,5]=>[[1,3,4,5,6],[2,7,8]]=>[6,2]=>[6,2]=>2
[1,6,2,3,7,8,4,5]=>[[1,2,4,5,6],[3,7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,6,3,7,8,4,5]=>[[1,2,3,5,6],[4,7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,7,3,8,4,5]=>[[1,2,3,4,6],[5,7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,6,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[5,3]=>2
[6,1,7,2,3,4,5,8]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[6,1,2,7,3,4,5,8]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,6,2,7,3,4,5,8]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,6,7,2,3,4,5,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[6,1,2,3,7,4,5,8]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,6,2,3,7,4,5,8]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,3,7,4,5,8]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,6,7,3,4,5,8]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[6,1,2,3,4,7,5,8]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,6,2,3,4,7,5,8]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,6,3,4,7,5,8]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,6,4,7,5,8]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,6,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[6,1,2,3,4,7,8,5]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,6,2,3,4,7,8,5]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,6,3,4,7,8,5]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,3,6,4,7,8,5]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,6,7,4,8,5]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,6,7,8,4,5]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[6,1,8,2,3,4,5,7]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[6,8,1,2,3,4,5,7]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]=>[6,2]=>2
[6,1,2,8,3,4,5,7]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,6,2,8,3,4,5,7]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,6,8,2,3,4,5,7]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[6,1,2,3,8,4,5,7]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,6,2,3,8,4,5,7]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,3,8,4,5,7]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,6,8,3,4,5,7]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[6,1,2,3,4,8,5,7]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,6,2,3,4,8,5,7]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,6,3,4,8,5,7]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,6,4,8,5,7]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,6,8,4,5,7]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[6,1,2,3,4,5,8,7]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,6,2,3,4,5,8,7]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,6,3,4,5,8,7]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,3,6,4,5,8,7]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,4,6,8,5,7]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[1,6,2,3,4,5,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]=>[6,2]=>2
[1,2,6,3,4,5,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]=>[5,3]=>2
[1,2,3,6,4,5,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]=>[4,4]=>2
[7,1,8,2,3,4,5,6]=>[[1,3,5,6,7,8],[2,4]]=>[3,5]=>[5,3]=>2
[7,1,2,8,3,4,5,6]=>[[1,3,4,6,7,8],[2,5]]=>[4,4]=>[4,4]=>2
[1,7,2,8,3,4,5,6]=>[[1,2,4,6,7,8],[3,5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,8,2,3,4,5,6]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]=>[5,3]=>2
[7,1,2,3,8,4,5,6]=>[[1,3,4,5,7,8],[2,6]]=>[5,3]=>[5,3]=>2
[1,7,2,3,8,4,5,6]=>[[1,2,4,5,7,8],[3,6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,7,3,8,4,5,6]=>[[1,2,3,5,7,8],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,8,3,4,5,6]=>[[1,2,3,4,7,8],[5,6]]=>[4,4]=>[4,4]=>2
[7,1,2,3,4,8,5,6]=>[[1,3,4,5,6,8],[2,7]]=>[6,2]=>[6,2]=>2
[1,7,2,3,4,8,5,6]=>[[1,2,4,5,6,8],[3,7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,7,3,4,8,5,6]=>[[1,2,3,5,6,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,7,4,8,5,6]=>[[1,2,3,4,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,7,8,4,5,6]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]=>[5,3]=>2
[7,1,2,3,4,5,8,6]=>[[1,3,4,5,6,7],[2,8]]=>[7,1]=>[7,1]=>2
[1,7,2,3,4,5,8,6]=>[[1,2,4,5,6,7],[3,8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,7,3,4,5,8,6]=>[[1,2,3,5,6,7],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,3,7,4,5,8,6]=>[[1,2,3,4,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,4,7,5,8,6]=>[[1,2,3,4,5,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,4,7,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[6,2]=>2
[1,7,2,3,4,5,6,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]=>[6,2]=>2
[1,2,7,3,4,5,6,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]=>[5,3]=>2
[1,2,3,7,4,5,6,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]=>[4,4]=>2
[1,2,3,4,7,5,6,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,8,2,3,4,5,6,7]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]=>[6,2]=>2
[1,2,8,3,4,5,6,7]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]=>[5,3]=>2
[1,2,3,8,4,5,6,7]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]=>[4,4]=>2
[1,2,3,4,8,5,6,7]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,2,3,4,5,8,6,7]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]=>[6,2]=>2
[5,3,2,6,1,4,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,5,4,8,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,5,2,3,7,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,5,2,3,8,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,5,2,3,1,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,2,1,3,8,7]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,6,1,5,4,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,5,1,3,2,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,4,3,1,2,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,5,4,3,2,8,1,6]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,6,4,3,7,2,5,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,4,3,8,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[6,7,4,3,8,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,4,3,1,8,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,7,5,1,3,8,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,5,4,8,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,7,5,4,8,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,1,5,4,7,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,5,1,3,7,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,3,1,7,6,2]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,4,3,7,1,5,2]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,4,3,6,5,1,2]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,7,3,1,4,2]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,6,7,1,3,4,2]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,1,7,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,1,6,7,4,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,8,6,7,4,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,7,6,8,4,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,6,8,4,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,6,1,8,3,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,6,8,1,3,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,7,2,1,8,3,6]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,2,8,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,2,8,3,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,6,2,7,3,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,2,6,7,4,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,3,2,6,8,4,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[6,3,2,7,8,1,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[5,3,2,7,1,8,4,6]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,1,7,8,5,6]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[3,4,1,2,8,7,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,3,2,8,1,7,6,4]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,8,7,1,5,4]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,8,6,5,1,4]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[8,4,7,2,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,2,6,5,1,3]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,2,7,1,5,3]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,2,1,7,6,3]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,1,2,7,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,8,2,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,5,8,3,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,8,7,3,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,1,8,7,2,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,8,1,7,2,5,3]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,8,7,1,2,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,8,7,2,1,4,3]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,6,2,4,1,3]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,6,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,6,1,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,8,1,6,5,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,8,6,5,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,1,7,8,6,5,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,8,1,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,8,7,1,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,6,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,5,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[3,4,1,2,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[2,3,2,2,1]=>[3,2,2,2,1]=>5
[8,9,5,6,3,4,10,1,2,7]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>[2,2,3,3]=>[3,3,2,2]=>4
[9,7,6,5,4,3,2,10,1,8]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[8,2]=>[8,2]=>2
[10,8,9,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[6,7,8,9,10,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[7,3,2,8,9,10,1,4,5,6]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[6,4]=>[6,4]=>2
[8,5,4,3,2,9,10,1,6,7]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[7,3]=>[7,3]=>2
[9,7,5,10,3,8,2,6,1,4]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10]=>[10]=>1
[4,2,5,1,3,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[5,2,4,1,3,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[3,2,6,1,4,5,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[4,2,6,1,3,5,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[5,3,6,1,2,4,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,2,4,1,3,5,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,3,5,1,2,4,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[5,3,7,1,2,4,6,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[5,4,7,1,2,3,6,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,2,7,1,3,4,5,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,3,7,1,2,4,5,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,4,7,1,2,3,5,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,3,5,1,2,4,6,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,3,6,1,2,4,5,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,4,6,1,2,3,5,8]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[3,2,8,1,4,5,6,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[4,2,8,1,3,5,6,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[5,4,8,1,2,3,6,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,2,8,1,3,4,5,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,3,8,1,2,4,5,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,4,8,1,2,3,5,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[6,5,8,1,2,3,4,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,2,8,1,3,4,5,6]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,3,8,1,2,4,5,6]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,4,8,1,2,3,5,6]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[7,5,8,1,2,3,4,6]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,2,4,1,3,5,6,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,3,5,1,2,4,6,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,3,6,1,2,4,5,7]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,3,7,1,2,4,5,6]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,4,7,1,2,3,5,6]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[8,5,7,1,2,3,4,6]=>[[1,3,6,7,8],[2,5],[4]]=>[3,5]=>[5,3]=>2
[3,2,5,7,1,4,6,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[4,2,5,7,1,3,6,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[5,2,4,7,1,3,6,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[4,2,6,7,1,3,5,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[5,2,6,7,1,3,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,2,5,7,1,3,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,3,5,7,1,2,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[3,2,5,8,1,4,6,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[4,2,5,8,1,3,6,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[4,3,5,8,1,2,6,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[5,2,4,8,1,3,6,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[3,2,6,8,1,4,5,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[4,2,6,8,1,3,5,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[5,2,6,8,1,3,4,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,2,4,8,1,3,5,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,3,4,8,1,2,5,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,2,5,8,1,3,4,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,3,5,8,1,2,4,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,4,5,8,1,2,3,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[3,2,7,8,1,4,5,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[4,3,7,8,1,2,5,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[5,3,7,8,1,2,4,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[5,4,7,8,1,2,3,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,2,7,8,1,3,4,5]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,3,7,8,1,2,4,5]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[6,4,7,8,1,2,3,5]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[7,2,4,8,1,3,5,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[7,3,4,8,1,2,5,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[7,3,5,8,1,2,4,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[7,4,5,8,1,2,3,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[7,4,6,8,1,2,3,5]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[8,3,4,6,1,2,5,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[8,3,5,6,1,2,4,7]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[8,2,4,7,1,3,5,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[8,2,5,7,1,3,4,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[8,3,5,7,1,2,4,6]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[8,2,6,7,1,3,4,5]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[8,4,6,7,1,2,3,5]=>[[1,3,4,8],[2,6,7],[5]]=>[4,4]=>[4,4]=>2
[4,6,2,5,1,3,7,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,3,5,1,2,7,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,2,5,1,4,6,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,7,3,5,1,2,6,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,7,2,4,1,3,6,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,2,6,1,4,5,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,7,3,6,1,2,5,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,7,2,6,1,3,4,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[6,7,2,5,1,3,4,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,2,5,1,3,6,7]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,2,4,1,3,6,7]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,3,4,1,2,6,7]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,8,2,6,1,4,5,7]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,3,6,1,2,4,7]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,4,6,1,2,3,7]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,3,5,1,2,4,7]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[3,8,2,7,1,4,5,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,2,7,1,3,5,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,3,7,1,2,5,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,2,7,1,3,4,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,3,7,1,2,4,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,2,7,1,3,4,5]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,3,7,1,2,4,5]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,5,7,1,2,3,4]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,2,4,1,3,5,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,2,5,1,3,4,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,3,5,1,2,4,6]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,4,6,1,2,3,5]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]=>[4,2,2]=>3
[4,3,2,6,1,5,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[5,3,2,6,1,4,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,3,2,5,1,4,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,5,2,4,1,3,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[4,3,2,7,1,5,6,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[5,3,2,7,1,4,6,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[5,4,3,7,1,2,6,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,3,2,7,1,4,5,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,4,2,7,1,3,5,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,4,3,7,1,2,5,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,5,2,7,1,3,4,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,5,3,7,1,2,4,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,3,2,5,1,4,6,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,4,2,5,1,3,6,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,3,2,6,1,4,5,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,4,2,6,1,3,5,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,4,3,6,1,2,5,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,5,2,6,1,3,4,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,5,3,6,1,2,4,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,6,3,5,1,2,4,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[4,3,2,8,1,5,6,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[5,3,2,8,1,4,6,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[5,4,3,8,1,2,6,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,3,2,8,1,4,5,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,4,2,8,1,3,5,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,4,3,8,1,2,5,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,5,2,8,1,3,4,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[6,5,3,8,1,2,4,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,3,2,8,1,4,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,4,2,8,1,3,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,4,3,8,1,2,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,5,3,8,1,2,4,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,5,4,8,1,2,3,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[7,6,2,8,1,3,4,5]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,3,2,5,1,4,6,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,4,2,5,1,3,6,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,3,2,6,1,4,5,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,4,2,6,1,3,5,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,5,3,6,1,2,4,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,6,2,4,1,3,5,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,6,2,5,1,3,4,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,3,2,7,1,4,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,4,2,7,1,3,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,4,3,7,1,2,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,5,2,7,1,3,4,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,5,3,7,1,2,4,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,6,3,7,1,2,4,5]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,7,2,4,1,3,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,7,2,5,1,3,4,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,7,3,5,1,2,4,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,7,2,6,1,3,4,5]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,7,3,6,1,2,4,5]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[8,7,4,6,1,2,3,5]=>[[1,4,7,8],[2,6],[3],[5]]=>[4,4]=>[4,4]=>2
[4,6,3,5,8,1,2,7]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,4,8,1,3,7]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,5,8,1,3,6]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,5,8,1,2,6]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,2,4,8,1,3,6]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,3,4,8,1,2,6]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,6,8,1,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,2,6,8,1,3,4]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,4,6,8,1,2,3]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,3,4,8,1,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,3,5,8,1,2,4]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,2,5,7,1,4,6]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,3,5,7,1,2,6]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,2,4,7,1,3,6]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,2,6,7,1,4,5]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,2,6,7,1,3,4]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,3,6,7,1,2,4]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,5,7,1,3,4]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,5,7,1,2,3]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,2,4,6,1,3,5]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,2,5,6,1,3,4]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,5,6,1,2,4]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,2,6,8,1,5,7]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[5,3,2,6,8,1,4,7]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[5,4,2,6,8,1,3,7]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[5,4,3,6,8,1,2,7]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[6,3,2,5,8,1,4,7]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[6,4,3,5,8,1,2,7]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[6,5,2,4,8,1,3,7]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[4,3,2,7,8,1,5,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[5,3,2,7,8,1,4,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[5,4,2,7,8,1,3,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[5,4,3,7,8,1,2,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[6,4,2,7,8,1,3,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[6,4,3,7,8,1,2,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[6,5,2,7,8,1,3,4]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[7,4,2,5,8,1,3,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[7,4,3,5,8,1,2,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[7,5,2,6,8,1,3,4]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[7,5,3,6,8,1,2,4]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[7,6,2,4,8,1,3,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[7,6,3,5,8,1,2,4]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,3,2,5,7,1,4,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,4,2,5,7,1,3,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,5,2,4,7,1,3,6]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,3,2,6,7,1,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,5,2,6,7,1,3,4]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,5,3,6,7,1,2,4]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,6,2,4,7,1,3,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,7,2,4,6,1,3,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,7,3,4,6,1,2,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[8,7,2,5,6,1,3,4]=>[[1,4,5],[2,7,8],[3],[6]]=>[5,3]=>[5,3]=>2
[4,3,7,2,6,1,5,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,2,6,1,4,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,7,2,6,1,3,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,3,7,2,5,1,4,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,4,7,2,5,1,3,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,4,7,3,5,1,2,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,3,6,2,5,1,4,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,2,6,1,5,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,2,6,1,4,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,2,6,1,3,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,3,6,1,2,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,2,5,1,3,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,3,5,1,2,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,2,4,1,3,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,3,4,1,2,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,2,7,1,5,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,2,7,1,4,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,2,7,1,3,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,3,7,1,2,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,2,7,1,4,5]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,2,7,1,3,5]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,3,8,2,5,1,4,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,3,5,1,2,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,2,4,1,3,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,2,6,1,3,4]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,4,6,1,2,3]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,8,2,5,1,3,4]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,8,3,5,1,2,4]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,6,2,5,1,4,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,6,2,4,1,3,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,2,5,1,4,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,3,5,1,2,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,2,4,1,3,6]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,2,6,1,4,5]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,2,6,1,3,5]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,3,6,1,2,5]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,2,6,1,3,4]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,7,2,4,1,3,5]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,7,2,5,1,3,4]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,7,3,5,1,2,4]=>[[1,3,8],[2,5],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,3,2,7,1,6,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,4,3,2,7,1,5,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,5,3,2,7,1,4,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,5,4,2,7,1,3,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,5,3,2,6,1,4,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,5,4,2,6,1,3,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[5,4,3,2,8,1,6,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,5,3,2,8,1,4,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,5,4,2,8,1,3,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,5,4,3,8,1,2,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,5,3,2,8,1,4,6]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,5,4,2,8,1,3,6]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,6,3,2,8,1,4,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,6,4,3,8,1,2,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,6,5,2,8,1,3,4]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,5,3,2,6,1,4,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,5,4,2,6,1,3,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,6,5,2,4,1,3,7]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,5,3,2,7,1,4,6]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,6,3,2,7,1,4,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,6,4,3,7,1,2,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,3,2,6,1,4,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,4,2,6,1,3,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,4,3,6,1,2,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,5,2,6,1,3,4]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,6,2,4,1,3,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,6,2,5,1,3,4]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,6,3,5,1,2,4]=>[[1,5,8],[2,7],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[4,8,3,7,2,6,1,5]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,7,2,6,1,4]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,7,2,6,1,3]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,7,3,6,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,7,2,5,1,4]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,7,2,5,1,3]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,7,3,5,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,5,7,2,4,1,3]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,5,7,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,6,2,5,1,4]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,4,6,2,5,1,3]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,4,6,3,5,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,5,6,2,4,1,3]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,3,8,2,7,1,6]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,8,2,7,1,5]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,8,2,7,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,4,8,3,7,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,3,8,2,6,1,5]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,8,2,6,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,4,8,2,6,1,3]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,8,2,5,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,4,8,2,5,1,3]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,8,2,4,1,3]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,7,2,6,1,5]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,3,7,2,6,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,7,2,6,1,3]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,7,3,6,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,3,7,2,5,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,4,7,2,5,1,3]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,4,7,3,5,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,5,7,2,4,1,3]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,6,2,5,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,4,6,2,5,1,3]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,4,6,3,5,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,5,6,2,4,1,3]=>[[1,4],[2,6],[3,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,4,3,2,8,1,7]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,6,5,4,2,8,1,3]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,5,4,3,2,7,1,6]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,6,5,3,2,7,1,4]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,7,4,3,2,6,1,5]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,7,5,3,2,6,1,4]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,7,5,4,2,6,1,3]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,7,6,3,2,5,1,4]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,7,6,4,2,5,1,3]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,7,6,5,2,4,1,3]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,1,2,3,4,7,5,6]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[8,1,2,3,6,4,5,7]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[8,1,2,3,7,4,5,6]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[7,1,2,3,6,4,8,5]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,1,2,3,8,7,4,6]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[8,1,2,3,6,7,4,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[4,1,2,8,3,7,5,6]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,5,3,4,6,7]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[7,1,2,5,3,4,8,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,2,6,3,4,5,7]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[7,1,2,6,3,4,8,5]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,5,3,8,4,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,5,3,7,4,6]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,6,3,7,4,5]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,2,5,3,7,8,4]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,1,2,8,6,3,5,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[4,1,2,8,7,3,5,6]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[4,1,2,7,6,3,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,1,2,5,6,3,4,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[8,1,2,5,7,3,4,6]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[8,1,2,7,6,3,4,5]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[7,1,2,5,6,3,8,4]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,1,2,5,8,7,3,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,1,2,8,6,7,3,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,5,6,7,3,4]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[3,1,8,2,4,7,5,6]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,2,6,4,5,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,8,2,7,4,5,6]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,7,2,6,4,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,5,2,8,7,4,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,1,8,2,6,7,4,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,2,3,5,6,7]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[7,1,4,2,3,5,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,1,4,2,3,8,5,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,2,3,7,5,6]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,2,3,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,1,5,2,3,4,6,7]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[7,1,5,2,3,4,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,1,7,2,3,4,5,6]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[6,1,5,2,3,8,4,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,2,3,7,4,6]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,2,3,7,4,5]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,5,2,3,7,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,1,4,2,8,3,6,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[5,1,4,2,7,3,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,2,6,3,5,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,2,7,3,5,6]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,2,6,3,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,5,2,6,3,4,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,1,5,2,7,3,4,6]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,2,6,3,4,5]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,2,6,3,8,4]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,4,2,6,8,3,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,2,8,7,3,6]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,2,6,7,3,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,2,6,7,3,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,2,6,7,8,3]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,1,4,8,2,7,5,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,8,5,2,4,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[3,1,7,5,2,4,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,1,8,6,2,4,5,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[3,1,7,6,2,4,8,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,1,6,5,2,8,4,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,5,2,7,4,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,6,2,7,4,5]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,5,2,7,8,4]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,1,4,5,2,3,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[7,1,4,5,2,3,8,6]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,4,6,2,3,5,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[7,1,4,8,2,3,5,6]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[7,1,4,6,2,3,8,5]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,6,5,2,3,4,7]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[7,1,8,5,2,3,4,6]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[7,1,8,6,2,3,4,5]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[7,1,6,5,2,3,8,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,1,4,5,2,8,3,7]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,5,2,7,3,6]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,6,2,7,3,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,6,5,2,7,3,4]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,5,2,7,8,3]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,8,6,2,5,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,1,4,8,7,2,5,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,1,4,7,6,2,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,1,8,5,6,2,4,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,8,5,7,2,4,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,8,7,6,2,4,5]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,1,7,5,6,2,8,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,5,6,2,3,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[8,1,4,5,7,2,3,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[8,1,4,7,6,2,3,5]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,7,5,6,2,3,4]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,5,6,2,8,3]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,1,4,5,8,7,2,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,1,4,8,6,7,2,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,8,5,6,7,2,4]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,5,6,7,2,3]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[2,8,1,3,4,7,5,6]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,1,3,6,4,5,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,1,3,7,4,5,6]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,7,1,3,6,4,8,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,1,3,8,7,4,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,1,3,6,7,4,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,4,1,8,3,7,5,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,5,3,4,6,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,7,1,5,3,4,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,1,6,3,4,5,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,7,1,6,3,4,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,1,5,3,8,4,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,5,3,7,4,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,1,5,3,7,8,4]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,1,8,6,3,5,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,4,1,8,7,3,5,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,4,1,7,6,3,8,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,1,5,6,3,4,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,1,5,7,3,4,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,1,7,6,3,4,5]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,7,1,5,6,3,8,4]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,1,5,8,7,3,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,1,8,6,7,3,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,5,6,7,3,4]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,3,1,2,4,5,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[6,3,1,2,4,8,5,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[8,3,1,2,4,7,5,6]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[6,3,1,2,4,7,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[5,3,1,2,8,4,6,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[5,3,1,2,7,4,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[8,3,1,2,6,4,5,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[8,3,1,2,7,4,5,6]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[7,3,1,2,6,4,8,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[5,3,1,2,6,8,4,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,3,1,2,8,7,4,6]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[8,3,1,2,6,7,4,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,3,1,2,6,7,8,4]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[7,4,1,2,3,5,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[6,4,1,2,3,8,5,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[8,4,1,2,3,7,5,6]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[6,4,1,2,3,7,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[7,6,1,2,3,4,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[5,8,1,2,3,7,4,6]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,1,2,3,7,4,5]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[5,4,1,2,8,3,6,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[5,4,1,2,7,3,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[8,4,1,2,6,3,5,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[8,4,1,2,7,3,5,6]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[7,4,1,2,6,3,8,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[5,8,1,2,6,3,4,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,1,2,7,3,4,6]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,1,2,6,3,4,5]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[5,7,1,2,6,3,8,4]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,1,2,6,8,3,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,4,1,2,8,7,3,6]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[8,4,1,2,6,7,3,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,8,1,2,6,7,3,4]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,4,1,2,6,7,8,3]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[4,3,1,8,2,5,6,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[4,3,1,7,2,5,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[4,3,1,6,2,8,5,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,8,2,7,5,6]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,6,2,7,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[8,3,1,5,2,4,6,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,3,1,5,2,4,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[8,3,1,6,2,4,5,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,3,1,8,2,4,5,6]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,3,1,6,2,4,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,3,1,5,2,8,4,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,3,1,5,2,7,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,3,1,6,2,7,4,5]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,3,1,5,2,7,8,4]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,5,2,3,6,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,4,1,5,2,3,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,6,2,3,5,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,4,1,8,2,3,5,6]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,4,1,6,2,3,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,8,1,5,2,3,4,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,7,1,5,2,3,4,6]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[8,7,1,6,2,3,4,5]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[6,7,1,5,2,3,8,4]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,1,5,2,8,3,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,5,2,7,3,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,6,2,7,3,5]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,8,1,5,2,7,3,4]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,1,5,2,7,8,3]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[4,3,1,5,8,2,6,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[4,3,1,5,7,2,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[4,3,1,8,6,2,5,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[4,3,1,8,7,2,5,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[4,3,1,7,6,2,8,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[8,3,1,5,6,2,4,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[8,3,1,5,7,2,4,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[8,3,1,7,6,2,4,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,3,1,5,6,2,8,4]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[8,4,1,5,6,2,3,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[8,4,1,5,7,2,3,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[8,4,1,7,6,2,3,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,8,1,5,6,2,3,4]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[7,4,1,5,6,2,8,3]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[4,3,1,5,6,8,2,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[4,3,1,5,8,7,2,6]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[4,3,1,8,6,7,2,5]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,1,5,6,7,2,4]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[8,4,1,5,6,7,2,3]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[4,3,1,5,6,7,8,2]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[2,3,8,1,4,7,5,6]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,1,6,4,5,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,8,1,7,4,5,6]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,7,1,6,4,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,5,1,8,7,4,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,8,1,6,7,4,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,1,3,5,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[2,7,4,1,3,5,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,6,4,1,3,8,5,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,8,4,1,3,7,5,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,6,4,1,3,7,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,8,5,1,3,4,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[2,7,5,1,3,4,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,8,7,1,3,4,5,6]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[2,6,5,1,3,8,4,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,1,3,7,4,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,6,8,1,3,7,4,5]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,1,3,7,8,4]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,5,4,1,8,3,6,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,5,4,1,7,3,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,1,6,3,5,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,1,7,3,5,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,7,4,1,6,3,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,5,1,6,3,4,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,8,5,1,7,3,4,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,7,8,1,6,3,4,5]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,7,5,1,6,3,8,4]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,4,1,6,8,3,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,5,4,1,8,7,3,6]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,1,6,7,3,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,1,6,7,3,4]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,5,4,1,6,7,8,3]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[7,3,4,1,2,5,8,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,3,4,1,2,8,5,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,3,4,1,2,7,5,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,3,4,1,2,7,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,3,5,1,2,4,8,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,3,7,1,2,4,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,3,5,1,2,8,4,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,1,2,7,4,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,1,2,7,4,5]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,1,2,7,8,4]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,5,4,1,2,3,8,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,8,4,1,2,3,5,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[6,7,4,1,2,3,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,8,5,1,2,3,4,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[6,7,5,1,2,3,8,4]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,5,4,1,2,8,3,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,5,4,1,2,7,3,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,8,4,1,2,7,3,5]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,5,1,2,7,3,4]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,4,1,2,7,8,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[5,3,4,1,8,2,6,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[5,3,4,1,7,2,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,4,1,6,2,5,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,3,4,1,7,2,5,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,3,4,1,6,2,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,1,6,2,4,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,3,5,1,7,2,4,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,3,8,1,6,2,4,5]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[7,3,5,1,6,2,8,4]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,4,1,6,2,3,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,5,4,1,7,2,3,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,8,4,1,6,2,3,5]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,5,1,6,2,3,4]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[7,5,4,1,6,2,8,3]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,3,4,1,6,8,2,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,3,4,1,8,7,2,6]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,4,1,6,7,2,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,1,6,7,2,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,5,4,1,6,7,2,3]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[5,3,4,1,6,7,8,2]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,3,4,8,1,7,5,6]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,8,5,1,4,6,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[2,3,7,5,1,4,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,8,6,1,4,5,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[2,3,7,6,1,4,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,6,5,1,8,4,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,5,1,7,4,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,6,1,7,4,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,3,6,5,1,7,8,4]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,8,4,5,1,3,6,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,7,4,5,1,3,8,6]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,6,1,3,5,7]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,7,4,8,1,3,5,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,7,4,6,1,3,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,6,5,1,3,4,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[2,7,8,5,1,3,4,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[2,7,8,6,1,3,4,5]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[2,7,6,5,1,3,8,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,6,4,5,1,8,3,7]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,5,1,7,3,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,6,1,7,3,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,5,1,7,3,4]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,6,4,5,1,7,8,3]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,4,5,1,2,8,6]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,3,4,6,1,2,8,5]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,3,6,5,1,2,4,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[7,3,8,5,1,2,4,6]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[7,3,8,6,1,2,4,5]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[7,3,6,5,1,2,8,4]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,6,4,5,1,2,8,3]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,3,4,5,1,8,2,7]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,3,4,5,1,7,2,6]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,3,4,6,1,7,2,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,3,6,5,1,7,2,4]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,6,4,5,1,7,2,3]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,5,1,7,8,2]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,8,6,1,5,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[2,3,4,8,7,1,5,6]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[2,3,4,7,6,1,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,8,5,6,1,4,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,8,5,7,1,4,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,8,7,6,1,4,5]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[2,3,7,5,6,1,8,4]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,4,5,6,1,3,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,5,7,1,3,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,7,6,1,3,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,8,7,5,6,1,3,4]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,7,4,5,6,1,8,3]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,4,5,7,1,2,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[8,3,4,7,6,1,2,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[8,3,7,5,6,1,2,4]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,3,4,5,6,1,8,2]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,3,4,5,8,7,1,6]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[2,3,4,8,6,7,1,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,8,5,6,7,1,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,5,6,7,1,3]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[9,1,2,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8,9],[2]]=>[9]=>[9]=>1
[8,1,2,3,4,5,6,9,7]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[7,1,2,3,4,5,8,9,6]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[6,1,2,3,4,7,9,5,8]=>[[1,3,4,5,6,7],[2,8,9]]=>[7,2]=>[7,2]=>2
[9,1,2,3,4,7,8,5,6]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[6,1,2,3,4,7,8,9,5]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[5,1,2,3,6,7,8,9,4]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[4,1,2,5,6,7,9,3,8]=>[[1,3,4,5,6,7],[2,8,9]]=>[7,2]=>[7,2]=>2
[9,1,2,5,6,7,8,3,4]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[4,1,2,5,6,7,8,9,3]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[9,1,8,2,3,4,5,6,7]=>[[1,3,5,6,7,8,9],[2],[4]]=>[3,6]=>[6,3]=>2
[3,1,4,5,6,7,9,2,8]=>[[1,3,4,5,6,7],[2,8,9]]=>[7,2]=>[7,2]=>2
[9,1,4,5,6,7,8,2,3]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[3,1,4,5,6,7,8,9,2]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[2,9,1,3,4,5,6,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[2,8,1,3,4,5,6,9,7]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[2,7,1,3,4,5,8,9,6]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[2,5,1,3,6,7,8,9,4]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[9,3,1,2,4,5,6,7,8]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[9,4,1,2,3,5,6,7,8]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[5,9,1,2,3,4,6,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[5,8,1,2,3,4,6,9,7]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[5,7,1,2,3,4,8,9,6]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[9,6,1,2,3,4,5,7,8]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[9,7,1,2,3,4,5,6,8]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[8,9,1,2,3,4,5,6,7]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[5,6,1,2,3,7,8,9,4]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[9,7,1,6,2,3,4,5,8]=>[[1,4,6,7,8,9],[2],[3],[5]]=>[4,5]=>[5,4]=>2
[2,3,9,1,4,5,6,7,8]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]=>[6,3]=>2
[2,6,9,1,3,4,5,7,8]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[2,6,7,1,3,4,8,9,5]=>[[1,2,3,7,8],[4,5,6,9]]=>[3,5,1]=>[5,3,1]=>3
[9,3,4,1,2,5,6,7,8]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[9,3,7,1,2,4,5,6,8]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[9,3,8,1,2,4,5,6,7]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[9,5,4,1,2,3,6,7,8]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[9]=>[9]=>1
[9,7,4,1,2,3,5,6,8]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[9]=>[9]=>1
[9,8,4,1,2,3,5,6,7]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[9]=>[9]=>1
[6,7,9,1,2,3,4,5,8]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[9,7,8,1,2,3,4,5,6]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[6,7,8,1,2,3,4,9,5]=>[[1,2,3,7,8],[4,5,6,9]]=>[3,5,1]=>[5,3,1]=>3
[2,3,4,9,1,5,6,7,8]=>[[1,2,3,4,7,8,9],[5,6]]=>[4,5]=>[5,4]=>2
[2,3,7,9,1,4,5,6,8]=>[[1,2,3,4,8,9],[5,6,7]]=>[4,5]=>[5,4]=>2
[2,9,4,5,1,3,6,7,8]=>[[1,2,4,7,8,9],[3,6],[5]]=>[2,2,5]=>[5,2,2]=>3
[2,7,8,9,1,3,4,5,6]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]=>[5,4]=>2
[9,3,4,8,1,2,5,6,7]=>[[1,3,4,8,9],[2,6,7],[5]]=>[4,5]=>[5,4]=>2
[7,3,8,9,1,2,4,5,6]=>[[1,3,4,8,9],[2,6,7],[5]]=>[4,5]=>[5,4]=>2
[9,8,4,5,1,2,3,6,7]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[4,5]=>[5,4]=>2
[9,8,6,5,1,2,3,4,7]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[8,3,6,5,1,7,2,9,4]=>[[1,3,6,8],[2,7,9],[4],[5]]=>[3,3,2,1]=>[3,3,2,1]=>4
[2,3,4,5,9,1,8,6,7]=>[[1,2,3,4,5,9],[6,7],[8]]=>[5,2,2]=>[5,2,2]=>3
[9,7,4,5,6,1,2,3,8]=>[[1,4,5,9],[2,7,8],[3],[6]]=>[5,4]=>[5,4]=>2
[8,9,4,5,6,1,2,3,7]=>[[1,2,5,9],[3,4,8],[6,7]]=>[2,3,4]=>[4,3,2]=>3
[2,3,4,5,6,9,1,7,8]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[2,9,8,5,6,7,1,3,4]=>[[1,2,5,6],[3,8,9],[4],[7]]=>[2,4,3]=>[4,3,2]=>3
[9,3,4,5,6,8,1,2,7]=>[[1,3,4,5,6],[2,8,9],[7]]=>[6,3]=>[6,3]=>2
[2,3,4,5,6,7,9,1,8]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[2,9,4,5,6,7,8,1,3]=>[[1,2,4,5,6,7],[3,9],[8]]=>[2,5,2]=>[5,2,2]=>3
[9,3,4,5,6,7,8,1,2]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[2,3,4,5,6,7,8,9,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[8,1]=>2
[3,5,2,6,1,4,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,2,6,4,1,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,2,7,4,8,1,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,2,7,4,8,6,1]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,7,2,3,8,6,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,2,3,8,1,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,2,3,1,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,6,2,1,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,5,1,6,4,2,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,6,1,3,2,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,6,3,1,2,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,5,7,3,2,8,1,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,3,2,8,6,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,3,8,2,5,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,3,8,2,1,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,3,8,1,2,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,7,3,1,8,2,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,1,3,8,2,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,7,4,8,2,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,5,7,4,8,3,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,7,4,8,6,3]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,1,7,4,8,6,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,7,1,3,8,6,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,3,1,8,6,2]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,3,8,1,5,2]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,3,8,5,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,3,8,5,2,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,8,3,1,4,2]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,7,8,1,3,4,2]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,7,1,8,3,5,2]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,1,7,8,4,5,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,6,7,8,4,5,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,6,7,8,4,3,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,6,1,7,8,4,2,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,7,1,8,3,2,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,8,1,3,2,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,7,2,1,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,2,8,1,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,2,8,3,1,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,2,8,3,5,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,2,7,8,4,5,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,2,7,8,4,1,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,2,7,8,1,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,7,1,8,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,1,7,8,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,4,1,2,7,8,6,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,2,7,1,8,6,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,2,7,8,1,5,4]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,2,7,8,5,1,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,6,2,7,8,5,4,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,7,2,8,5,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,2,8,5,1,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,2,8,1,5,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,7,2,1,8,6,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,1,2,8,6,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,7,2,8,6,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,5,7,3,8,6,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,7,8,3,5,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,1,7,8,2,5,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,7,1,8,2,5,3]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,7,8,1,2,4,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,7,8,2,1,4,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,7,8,2,4,1,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,7,8,2,4,3,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,7,8,1,4,2,3]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,7,1,8,5,2,3]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,1,7,8,5,2,4]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,1,6,7,8,5,3,4]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,6,1,7,8,5,4,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,7,1,8,5,3,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,8,1,4,3,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,7,8,4,1,3,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,8,9,10,1,4,5,3,2]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[5,3,2]=>[5,3,2]=>3
[6,7,8,9,10,1,4,5,2,3]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[5,3,2]=>[5,3,2]=>3
[6,7,8,9,10,1,3,4,5,2]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[5,4,1]=>[5,4,1]=>3
[6,7,8,9,10,1,5,4,3,2]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[5,2,3]=>[5,3,2]=>3
[6,7,8,9,10,5,4,3,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,5]=>[5,5]=>2
[6,5,8,7,3,4,1,2]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,7,4,5,8,1,2]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,7,4,5,1,8,3]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,7,4,5,2,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,4,7,6,2,3,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,4,7,6,1,8,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,4,7,6,8,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,7,8,6,1,2]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,4,3,8,7,6,1,2]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[6,4,8,3,7,5,1,2]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,4,5,7,1,2]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,4,8,6,7,1,2]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,5,6,8,7,1,2]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[3,2,5,6,1,8,7,4]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,6,8,1,7,3]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,4,8,6,1,7,3]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,8,4,5,1,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,2,4,5,1,6,3]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,1,4,5,2,3,6]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,8,4,5,2,3,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,4,8,6,2,3,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[4,1,3,2,8,6,5,7]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,3,8,2,6,4,7]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,3,2,5,4,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,3,2,5,4,6]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,3,1,5,6,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,8,3,1,5,7,4]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,2,3,8,1,6,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,2,1,7,5,4]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,3,2,1,6,5,4]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,2,6,1,5,3]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,2,8,7,1,6,3]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,2,7,8,1,6,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,3,7,1,6,8,4]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,3,7,2,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,7,3,2,5,4,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,7,3,1,5,8,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,2,1,8,5,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,5,6,2,1,4,3]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,8,7,1,2,3,4]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[5,4,1,8,7,2,3,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[6,4,8,1,7,2,3,5]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[7,8,3,1,2,6,4,5]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,1,8,2,7,4,6]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,2,8,7,5,6]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[4,2,1,3,8,5,7,6]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,1,8,3,4,7,6]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,8,1,3,4,7,5]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[7,8,2,1,3,4,6,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,3,1,2,6,5,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[5,3,1,6,2,4,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,3,1,5,2,4,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,3,1,5,2,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,4,5,1,2,7,3,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,4,5,1,2,8,3,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,4,5,1,2,3,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,4,6,1,2,3,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,1,6,5,3,4,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,6,1,5,2,4,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,5,1,2,3,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[5,6,4,1,2,3,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,5,4,1,2,3,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,5,4,1,2,8,3,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,6,4,1,7,2,3,5]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,6,4,1,8,2,3,5]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[6,7,4,1,8,2,3,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[5,7,4,1,2,8,3,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,7,5,1,2,8,3,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,5,2,8,4,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,7,5,3,8,4,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,5,3,7,4,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,8,1,5,2,7,4,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,5,1,2,7,3,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,1,2,7,3,6]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,4,1,7,2,3,5]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,4,1,6,2,3,5]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[5,8,6,7,1,2,3,4]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,8,6,1,7,2,3,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[3,8,1,6,7,2,4,5]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,8,6,7,3,4,5]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,1,7,6,8,3,4,5]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,6,8,2,4,5]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,6,1,8,2,3,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[5,7,6,8,1,2,3,4]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,4,7,1,2,8,3,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,1,8,2,3,5]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,1,8,2,3,5]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,4,6,1,7,2,3,5]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,3,1,6,7,2,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,3,1,6,8,2,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,3,1,7,8,2,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,3,1,7,2,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,2,7,8,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[2,1,4,3,8,7,5,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,1,2,8,7,5,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,1,8,7,2,4,5]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[7,3,1,8,6,2,4,5]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[8,4,7,1,6,2,3,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,1,6,2,3,5]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,1,2,7,3,6]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,1,2,7,3,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,8,2,7,4,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,5,8,3,7,4,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,8,7,3,4,5]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,6,1,8,7,2,4,5]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,8,1,7,2,3,5]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,7,1,2,3,4]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[7,5,8,6,1,2,3,4]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[8,5,7,6,1,2,3,4]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,7,8,6,1,2,3,4]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,7,8,1,6,2,3,5]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,8,6,2,4,5]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,1,7,8,6,3,4,5]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[2,1,8,7,6,3,4,5]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,8,1,7,6,2,4,5]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,7,1,6,2,3,5]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,6,1,2,3,4]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[6,8,7,5,1,2,3,4]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[6,4,7,3,8,5,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,7,3,5,8,1,2]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,2,5,1,8,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,2,7,6,1,3,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[5,4,2,7,6,1,8,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,4,3,7,6,8,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,7,8,6,1,2]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,4,8,3,5,7,1,2]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,3,8,6,7,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,6,8,7,1,2]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[5,4,2,6,7,1,8,3]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,4,2,6,7,1,3,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[5,3,2,6,1,7,4,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,6,1,7,8,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,3,2,6,1,8,7,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,6,8,1,7,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,4,2,8,6,1,7,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,2,5,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,4,2,5,1,6,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,4,2,5,1,3,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,4,2,8,6,1,3,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[5,3,2,6,1,8,4,7]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,1,6,8,5,7]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[4,3,2,1,8,6,5,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[5,3,2,8,1,6,4,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,3,8,2,1,5,4,7]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,8,3,2,1,5,4,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,8,3,2,1,5,6,4]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,3,8,2,1,5,7,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,3,2,8,1,6,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,7,8,1,6,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,7,1,8,6,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,7,1,6,8,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,3,2,7,1,6,4,8]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,3,7,2,1,5,4,8]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,2,1,5,8,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,3,7,2,1,8,5,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,2,8,1,5,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,7,8,2,1,4,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,5,8,7,2,1,3,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,3,7,2,1,8,4,5]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,2,1,4,8,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,3,7,2,1,4,5,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,3,2,7,1,4,8,6]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,8,7,1,3,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,8,4,2,6,1,3,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,2,1,6,4,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,3,8,2,1,7,4,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,3,2,8,1,7,4,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,1,8,7,5,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[4,3,2,1,7,5,8,6]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[4,3,2,1,7,5,6,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[4,3,2,1,8,5,7,6]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,8,1,4,7,6]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,2,1,4,7,5]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,8,3,2,1,4,6,5]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,3,8,2,1,4,5,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[4,3,2,1,8,5,6,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[4,3,2,1,5,8,6,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,8,5,6,1,2,4,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,4,1,6,2,5,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,1,4,6,2,5,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,8,4,7,2,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,8,4,7,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,8,3,2,7,5,4]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,3,2,7,5,4]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,3,2,6,5,4]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,1,2,6,5,4]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,3,4,6,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,2,4,6,1,5,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,2,3,1,6,5,4]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,1,3,6,5,4]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,1,2,3,6,5,4]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,1,8,2,3,7,5,4]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,2,3,7,5,4]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,2,8,3,7,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,2,8,3,7,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,1,8,3,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,8,1,3,7,5,4]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,3,1,7,5,4]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,8,4,7,5,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,4,7,5,1,2]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,8,4,7,1,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,8,3,1,7,5,4]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,1,3,7,5,4]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,1,8,3,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,5,8,3,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,1,3,8,7,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,3,8,1,7,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,4,8,7,1,6,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,4,8,7,6,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,3,4,8,7,6,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[5,2,4,8,7,1,6,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,2,3,8,1,7,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,3,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,1,2,3,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,4,2,3,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,1,3,2,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,3,1,2,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[6,3,8,1,2,7,5,4]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,1,8,2,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,3,8,2,7,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,3,8,2,7,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,8,7,2,6,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,4,8,7,2,6,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,1,8,7,2,6,3]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,1,7,2,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,7,1,2,4,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,7,3,4,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,7,2,1,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,5,1,8,7,2,6,3]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,5,8,7,2,6,3]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,5,8,7,2,6,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,5,8,2,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,5,8,2,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,8,1,2,7,5,4]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,2,1,7,5,4]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,2,7,1,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,8,3,7,5,1,2]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,3,8,7,6,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,5,2,8,7,1,6,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,2,8,1,7,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,4,2,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,1,2,4,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,2,5,8,1,7,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,8,7,1,6,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,5,8,7,6,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[3,4,5,8,7,6,1,2]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,5,8,7,1,6,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,5,8,1,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,3,2,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,3,2,6,4,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,3,2,5,4,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,3,2,5,4,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,3,2,5,4,7,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,2,5,3,7,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,4,2,5,3,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,4,2,5,3,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,4,2,6,3,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,3,5,4,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,2,5,4,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,2,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,5,1,4,3,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,1,4,3,8,7]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,7,1,4,3,8,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,8,1,4,3,7,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,8,1,4,3,7,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,1,4,3,8,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,6,1,4,3,8,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,5,1,4,3,8,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,2,5,3,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,2,5,4,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,7,3,5,4,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,3,5,4,7,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,2,5,4,7,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,2,5,3,7,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,5,1,4,3,7,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,1,4,3,7,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,4,3,8,2,6,5]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,3,7,2,6,5]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,5,3,7,2,6,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,5,3,8,2,6,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,1,5,3,7,4]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,2,6,3,7,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,2,6,3,7,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,2,6,4,7,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,3,6,4,7,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,7,3,6,4,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,2,6,3,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,2,6,3,8,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,6,1,5,3,8,4]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,1,5,3,8,4]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,8,1,5,3,7,4]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,5,2,6,3,7,4]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,5,2,7,3,8,4]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,4,2,7,3,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,2,6,3,7,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,3,2,6,4,7,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,3,2,6,4,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,3,2,7,4,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,3,2,7,4,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,3,2,7,5,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,4,3,8,5,7,6]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,4,2,8,5,7,6]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,3,2,8,5,7,6]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,3,2,8,4,7,6]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,3,2,8,4,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,1,3,2,6,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,1,3,2,6,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,1,4,2,6,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,1,4,2,6,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,4,2,8,3,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,4,2,8,3,7,6]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,5,2,8,3,7,6]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,5,2,8,4,7,6]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,5,3,8,4,7,6]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,3,8,4,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,2,8,4,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,2,8,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,6,2,8,3,7,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,5,2,8,3,7,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,1,5,2,6,4]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,1,5,2,6,4]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,3,8,1,5,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,8,3,7,1,5,4]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,2,6,1,5,4]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,3,7,2,6,4]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,3,7,2,6,5]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,4,7,2,6,5]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,4,7,3,6,5]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,7,4,8,3,6,5]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,4,8,2,6,5]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,3,8,2,6,5]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,3,8,2,6,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,2,6,1,5,4]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,3,7,1,5,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,6,3,8,1,5,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,2,6,8,1,5,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,3,6,2,8,1,4,7]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,6,2,4,8,1,7]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,8,2,4,1,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,8,2,4,6,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,2,5,8,3,6,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,2,5,8,3,1,6]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[4,5,2,6,3,8,1,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,1,6,8,3,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,3,1,6,8,2,4,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,6,2,8,1,3,4,7]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,5,6,1,4,8,2,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,5,6,3,8,2,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,1,6,3,8,2,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,6,3,2,8,1,7]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,5,3,8,2,1,6]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,5,3,8,2,6,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,4,8,3,2,5,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,8,3,2,1,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,7,4,1,8,3,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,4,5,3,1,8,2,6]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,7,1,5,8,3,2,6]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,3,7,8,1,4,2,6]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,8,2,4,6,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,8,1,4,6,2]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,1,7,8,3,6,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,1,5,8,3,6,2]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,7,4,3,8,1,5,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,4,8,3,1,5,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,8,3,5,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,7,3,8,4,2,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,3,1,8,4,2]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,1,7,3,8,4,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,6,7,3,8,4,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,7,1,8,3,5,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,8,3,1,4,5,2]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,2,8,4,5,1,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,8,4,1,3,5]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,7,4,8,3,2,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,7,3,2,8,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,6,1,7,3,2,8,4]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,7,3,2,1,8,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,6,7,3,2,8,4,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,2,7,3,8,4,1]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,7,3,1,8,4]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,2,1,7,3,8,4]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,7,4,2,8,3,5]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,7,2,1,8,3,4,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,5,8,2,1,3,4,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,7,3,1,8,2,4,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[4,7,1,5,2,8,3,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,2,5,1,8,3,6]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,7,4,2,1,8,3,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,7,4,2,8,3,1,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,4,2,8,3,5,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,7,2,8,4,5,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,7,2,8,4,1,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,7,2,1,8,4,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,8,2,1,4,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,7,8,2,1,5,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[3,7,8,1,4,6,2,5]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,8,2,6,1,5]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,3,8,2,6,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,7,2,8,5,1,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,6,7,8,5,2,1,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,6,7,8,5,2,4,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,7,8,2,5,3,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,7,8,2,1,5,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,1,5,7,8,2,6,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,7,8,1,6,2,4]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,2,8,5,1,3,4]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,4,1,7,8,2,5,3]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,6,2,7,8,4,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,2,1,7,8,4,3]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,2,7,1,8,4,3]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,7,8,4,3,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,7,2,8,4,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,2,1,8,4,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,1,7,2,8,4,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,6,7,2,8,4,3]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,7,1,8,2,5,3]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,7,1,8,5,2,4]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,5,2,4,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,3,5,1,4,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,8,1,5,3,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,7,8,4,3,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,6,1,7,8,4,3,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,7,1,8,4,3,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,3,4,2,5,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[8,3,2,5,1,6,4,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,3,6,2,4,1,7]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,7,4,1,8,6]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,8,2,4,6,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,4,5,8,3,6,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,5,3,7,1,8,6]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,5,6,3,1,7]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[8,2,4,5,6,1,3,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[8,1,2,4,5,6,3,7]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[8,2,5,1,3,6,4,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,5,6,2,1,4,3,7]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,3,6,4,1,2,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[8,4,1,5,6,3,2,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,1,4,5,6,3,2,7]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[4,5,3,7,2,1,8,6]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,5,8,3,2,6,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,6,7,2,8,5,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,7,2,8,1,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,3,6,7,2,8,5]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,3,7,1,8,2,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,5,3,7,2,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,4,7,1,2,8,6]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,2,1,4,6,3]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,3,8,4,1,6,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,5,8,3,6,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,7,8,1,5,2]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,4,7,8,3,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,7,8,3,5,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,7,8,4,1,2]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,1,5,6,7,8,4,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,6,1,7,8,3,5,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,7,1,4,8,5,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,1,7,8,5,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,7,1,4,8,3,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,7,8,1,2,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,5,3,6,7,8,2,4]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,7,8,2,1,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,5,6,7,8,2,4,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,7,1,3,8,4,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,3,1,7,8,2,4,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[4,5,2,7,8,1,3,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,6,7,8,3,1,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,2,6,7,8,3,5,1]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,2,7,4,8,5,1]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,2,7,4,8,1,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,1,6,4,7,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[3,7,4,2,1,5,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,7,3,4,2,5,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,2,1,3,5,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[7,8,4,2,1,3,6,5]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,8,1,3,4,2,6,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,3,4,2,1,6,5]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,2,7,1,8,5,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,6,2,7,1,8,5,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,8,2,5,4,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,7,8,5,2,3,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,4,7,8,1,5,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,2,7,8,1,5,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,5,8,6,2,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[7,4,1,5,8,6,2,3]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[7,5,3,8,6,1,2,4]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,5,8,2,1,6,3,4]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,2,7,1,3,8,5,4]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,1,7,8,2,5,4]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,6,1,7,8,5,2,3]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,2,6,7,8,4,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[5,2,6,7,8,4,1,3]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,2,6,7,8,4,3,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,5,6,7,8,4,1,3]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,5,2,6,7,8,4,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,4,7,8,5,2,3]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,6,7,1,3,8,5,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,2,1,5,4,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,3,8,5,1,4,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,7,8,5,3,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,5,2,3,7,6,1,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,3,7,2,5,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,6,5,1,2,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[1,5,6,3,4,8,7,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,2,7,3,5,1,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,6,7,4,5,1,8]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,2,6,5,3,1,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,6,2,4,3,1,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,5,4,8,3,6,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,5,4,1,3,2,6]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[6,8,5,4,2,1,3,7]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[5,8,6,2,4,1,3,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,6,5,1,3,7]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,2,8,6,5,1,4,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[4,1,2,6,5,8,7,3]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,2,4,8,7,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,5,4,2,8,7,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,5,4,8,2,6,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,5,4,7,6,2,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,6,7,4,5,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,6,7,4,5,2,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,6,8,4,2,5,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,1,7,8,2,4,5,3]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,7,2,8,4,6,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,2,7,8,5,6,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,1,7,8,5,6,4]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,8,7,1,5,4,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,7,1,5,3,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,7,2,1,4,3,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,1,2,4,3,5]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,6,1,4,2,3,5]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,6,1,4,3,2,5]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[1,7,6,8,4,3,5,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,7,8,3,4,5,2]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,7,1,3,4,2,5]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,1,3,2,4,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,8,2,1,3,4,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,7,2,8,1,3,5,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,2,6,8,4,1,5,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,6,2,8,3,1,5,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,6,8,2,3,1,4,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,3,2,1,4,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,5,8,3,1,2,4,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,5,7,3,1,4,2,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,5,7,3,8,4,6,2]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,3,7,8,5,6,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,3,7,1,5,2,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,8,2,1,5,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[4,5,2,3,8,1,6,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,5,4,8,1,6,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,2,3,1,8,7,6]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,3,1,2,8,7,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,4,3,1,8,2,6,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,4,3,1,7,6,2,5]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[1,5,8,3,7,6,4,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,1,3,7,6,2,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[7,5,1,3,8,2,6,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,5,1,3,2,8,7,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,6,1,2,3,8,7,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,6,2,1,3,8,7,5]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,2,6,1,4,8,7,5]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,1,8,4,6,5]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,2,1,8,3,6,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,1,2,8,3,6,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,1,8,2,3,5,4]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,1,8,3,2,5,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,6,1,7,3,5,2,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,8,7,3,5,4,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,6,5,3,4,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,1,6,5,3,2,4]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,8,1,6,5,2,3,4]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,1,7,2,5,3,4]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,2,7,6,3,4]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,1,7,6,3,5]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,2,8,1,7,6,4,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,2,8,7,6,5,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,1,8,2,7,6,4,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,8,7,2,5,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,6,5,2,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,7,6,5,4,2,3]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,1,2,6,5,8,7,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,6,2,4,8,7,5]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,5,2,4,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,2,3,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,6,1,2,3,8,7,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,5,3,4,8,7,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,1,5,2,4,8,7,3]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,1,2,3,8,7,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[6,4,1,2,3,8,7,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,4,1,2,3,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,4,1,2,7,3,6,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[6,4,1,7,2,3,5,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[6,4,1,8,2,3,5,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,4,1,2,8,3,6,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,1,2,8,3,6,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,5,2,8,4,6,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,5,3,8,4,6,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,3,7,4,6,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,5,2,7,4,6,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,1,2,7,3,6,4]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,1,2,7,3,6,5]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,1,7,2,3,5,6]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,4,1,6,2,3,5,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[8,6,1,7,2,3,5,4]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,6,7,2,4,5,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,6,7,3,4,5,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,6,8,3,4,5,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,6,8,2,4,5,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,1,8,2,3,5,4]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,7,1,2,8,3,6,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,7,2,8,4,6,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,2,7,8,5,6,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,3,8,7,5,6,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,2,8,7,5,6,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,8,7,5,6,4]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,8,2,7,4,6,5]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,7,2,4,5,6]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[3,1,7,6,2,4,5,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[4,7,1,6,2,3,5,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,8,1,6,2,3,5,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,8,1,7,2,3,5,6]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,8,1,2,7,3,6,5]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,1,2,7,3,6,4]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,8,2,7,4,6,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,8,3,7,4,6,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,8,7,3,4,5,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,8,7,2,4,5,3]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,1,7,2,3,5,4]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,7,1,2,3,4,5]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[5,8,7,1,2,3,4,6]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[5,8,6,1,2,3,4,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[5,7,6,1,2,3,4,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[7,8,1,6,2,3,5,4]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,8,6,2,4,5,3]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,8,6,3,4,5,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,7,6,3,4,5,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,1,7,6,2,4,5,3]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,1,6,2,3,5,4]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,1,6,4,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,5,4,7,1,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,3,7,6,8,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,3,7,1,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,3,6,1,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,1,6,3,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,5,4,6,2,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,5,3,6,2,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,5,1,6,2,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,5,2,7,1,8,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,2,7,5,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,2,7,1,8,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,1,7,2,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,5,1,7,2,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,5,4,7,2,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,5,4,7,3,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,5,4,7,6,8,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,5,3,7,6,8,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,5,1,7,6,8,2]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,1,7,5,8,2]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,5,7,1,8,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,4,7,2,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,4,7,1,8,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,1,7,4,8,2]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,6,3,7,4,8,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,3,7,5,8,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,4,7,5,8,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,4,7,5,8,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,4,7,3,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,4,7,2,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,3,7,2,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,6,3,7,2,8,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,1,7,2,8,4]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,2,7,1,8,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,2,7,4,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,3,7,4,8,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,3,7,1,8,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,1,7,3,8,4]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,1,7,3,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,1,7,3,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,3,7,1,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,3,7,5,8,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,4,7,5,8,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,4,7,1,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,1,7,4,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,5,1,7,4,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,4,1,7,5,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,4,2,7,6,8,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,5,1,7,6,8,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,1,7,5,8,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,5,7,1,8,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,5,7,3,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,5,7,1,8,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,1,7,5,8,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,1,7,6,8,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,5,2,7,6,8,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,5,2,7,6,8,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,5,3,7,6,8,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,3,7,5,8,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,2,7,5,8,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,2,7,5,8,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,6,2,7,4,8,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,1,7,4,8,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,4,7,1,8,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,4,7,3,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,2,7,3,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,2,7,1,8,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,1,7,2,8,3]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,6,4,7,2,8,3]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,5,7,2,8,3]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,5,7,2,8,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,5,7,3,8,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,5,7,4,8,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,5,7,3,8,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,6,4,7,3,8,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,1,7,3,8,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,3,7,1,8,2]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,2,1,6,4,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,5,2,4,1,7]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,7,5,2,4,1,8,6]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,7,5,2,4,6,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,4,5,7,3,6,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,5,7,3,1,8,6]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,2,4,6,5,3,1,7]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,5,4,6,1,3,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,3,5,1,4,2,7]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,1,4,5,3,2,7]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,1,5,6,4,3,2,7]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,7,4,3,2,1,8,6]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[8,5,7,4,3,2,6,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,3,2,7,5,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,3,2,8,1,5]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,7,3,2,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,4,7,3,1,8,2,6]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,7,4,5,3,2,8,6]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,5,1,4,2,8,6]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,4,2,1,3,8,6]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,5,7,4,2,1,6,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,5,1,4,6,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,1,7,5,3,6,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,8,7,1,5,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,4,8,6,3,5,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,7,6,3,5,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,5,8,7,4,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,1,5,8,6,7,4,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,6,7,3,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,4,1,8,7,5,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,2,6,1,4,7,5,3]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,6,8,1,4,3,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,6,4,8,2,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,5,6,8,2,4]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,6,7,5,8,2,4]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,7,6,5,8,2,1,4]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,8,5,7,2,4,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,5,7,6,8,1,4]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,5,7,8,3,4]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,6,8,3,1,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,8,7,3,5,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,2,4,6,7,5,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,2,6,4,8,1,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,6,1,4,7,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,3,7,2,1,8,4,6]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,2,1,5,8,6]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,7,6,1,3,4,2,5]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,7,3,2,1,6,4]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,6,7,2,1,5,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,7,8,6,2,1,5,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,3,5,2,4,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,7,4,8,1,6,5,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,8,2,1,7,5,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,1,5,7,2,6,3]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,3,7,1,6,2,4]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,2,1,3,6,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,2,6,7,1,3,5,4]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,6,1,7,5,2,4]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,1,8,7,2,5,3]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,2,5,6,7,4,3]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[8,2,6,5,7,4,1,3]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,7,8,5,6,4,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,5,7,6,4,3,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,7,6,8,5,4,1,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,5,8,6,4,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,4,8,2,6,5,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,8,1,6,5,2,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,8,6,1,3,5,4]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,3,5,1,4,2]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,7,6,5,1,3,2]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,1,5,6,4,3,2]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,1,6,7,5,4,3,2]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,5,3,1,2,4,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[4,6,3,5,1,2,8,7]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,5,3,7,2,1,4,6]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,8,1,4,5,7,3,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,2,4,5,1,3,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,6,2,4,5,1,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,1,4,5,3,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,2,4,5,3,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,6,3,2,1,4,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,4,3,6,1,2,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,3,1,4,5,2,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[3,1,6,4,5,2,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,4,5,1,2,6]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,8,7,4,2,6,3,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,4,1,6,3,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,1,7,4,2,6,3,5]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,4,5,1,2,6]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,8,7,5,3,4,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,1,6,8,5,7,3,4]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,3,8,1,7,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,1,4,5,8,3,2]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[3,7,6,4,5,8,2,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,5,7,4,1,6,3,2]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,4,7,6,2,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,4,7,6,1,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,3,5,6,7,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,8,3,5,6,7,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,4,2,5,6,7,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,4,1,3,5,6,7,2]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[7,5,8,4,3,6,1,2]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,3,8,4,1,7,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,1,5,8,4,6,7,3]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,8,3,6,7,5]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,8,2,1,7,5]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,8,4,2,6,1,5]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,1,2,5,6,7,4]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[3,1,8,2,5,6,7,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,8,1,5,6,7,4]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,8,2,5,6,7,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,2,3,5,6,7,1]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,2,1,5,6,7,4]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,1,3,5,6,7,4]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,1,2,3,5,6,7,4]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[7,8,2,4,3,6,1,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,2,4,1,7,5]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,8,3,4,6,7,5]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,7,8,5,4,3,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,7,3,8,1,4,2,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,8,4,5,3,2,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,8,4,5,3,1,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,1,4,3,6,2,5]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,8,7,4,2,6,1,5]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,8,4,3,6,2,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,8,4,2,7,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,3,6,2,1,7,5]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,6,3,1,4,2,7,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,3,8,2,4,1,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,3,1,8,5,7,6]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,3,2,6,8,7,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,3,6,2,8,1,4]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,3,5,1,2,7,4]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,8,3,2,6,1,7,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,3,8,6,2,7,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,8,4,7,6,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,8,2,4,7,6,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,5,4,1,6,2,3]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[2,7,6,4,5,8,1,3]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,1,6,4,5,8,2,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,6,1,8,2,4]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,7,6,5,8,3,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,5,3,6,7,4]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,8,3,5,2,1,7,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,5,4,2,6,1,3]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,4,2,5,6,7,3]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,8,4,1,5,6,7,3]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,8,1,2,5,6,7,3]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,4,8,1,5,6,7,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,2,8,5,6,7,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,1,8,5,6,7,3]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,2,8,5,6,7,3]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,2,1,5,6,7,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,5,2,4,8,6,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,5,3,2,8,1,7,4]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,1,5,3,8,6,7,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,3,5,8,1,7,2]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,3,5,4,8,6,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,4,1,5,6,7,2]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,3,1,8,5,6,7,2]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,8,5,6,7,2]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,3,7,2,8,4,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,7,4,5,8,2,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,2,4,5,8,3,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,7,4,8,6,3,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,7,4,8,6,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,6,3,7,1,8,4,2]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,7,4,5,2,1,6]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,4,8,6,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,4,8,6,2,3]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,3,1,8,2,7,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,3,5,8,2,7,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,3,8,1,2,7,5]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,8,4,1,6,2,5]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,1,6,8,4,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,6,2,5,4,8,1,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,2,4,7,1,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,8,2,4,7,6,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,5,8,3,7,6,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,5,3,8,1,7]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,1,6,8,3,7]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[6,3,5,1,4,8,2,7]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,5,3,8,2,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,6,4,3,8,2,7]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,3,2,7,1,8,6]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,4,3,8,2,7,6,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,2,8,7,5,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,3,7,6,2,1,8,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,4,3,1,7,2,8,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,4,3,1,8,2,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[1,4,7,5,8,3,2,6]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,3,5,8,4,2,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,2,5,8,4,1,3,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,8,5,7,4,6,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,8,7,1,4,6,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,5,8,7,3,6,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,4,8,7,3,6,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,3,8,1,7,5,2]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,7,1,8,6,5,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,8,3,7,6,5,2,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[5,3,8,7,6,4,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[7,5,3,1,8,6,4,2]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[1,8,6,5,3,7,4,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,5,8,6,3,7,4,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,8,7,3,5,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,7,3,1,4,5,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,2,8,7,4,5,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,2,8,4,1,3,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,3,1,6,8,4,2,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[1,7,6,4,8,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,6,3,2,8,4]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,7,5,3,2,8,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,6,5,3,2,1,8,4]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[6,5,3,2,8,7,4,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[5,2,6,3,8,7,4,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,6,3,1,8,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,5,2,1,7,3,8,4]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,2,7,4,1,8,3,6]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,2,6,3,1,8,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,8,6,3,7,5,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,2,4,7,5,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,3,6,2,4,1,8,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,7,2,1,4,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,7,8,2,1,5,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[8,3,7,1,4,6,2,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,2,5,7,1,6,4]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,6,2,7,1,5,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,3,6,2,1,5,4]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,3,6,2,5,4,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,8,2,1,6,5,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,8,1,7,5,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,8,2,7,1,6,3]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,1,5,7,2,6,3]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,3,7,1,6,2,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,7,2,6,1,3,4]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,6,2,7,5,1,3,4]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[3,6,8,1,7,5,2,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,8,2,7,4,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,2,8,1,7,4,3]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,7,1,8,6,4,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,8,2,7,6,4,3,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,2,8,7,5,4,3,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[7,6,2,1,8,5,4,3]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[6,1,7,2,8,5,4,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,5,1,8,2,6,4,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,1,8,6,2,5,3]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,3,1,6,5,2,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,4,6,1,5,3,2]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,1,6,4,3,2]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,8,1,7,5,4,3,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,1,8,6,5,4,3,2]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[5,4,2,3,7,6,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[6,4,2,7,3,5,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,2,6,3,5,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,2,6,3,1,5,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,2,7,6,4,5,1,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,2,6,3,5,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,6,2,3,4,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,5,2,3,8,4,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,2,8,3,4,6]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,2,3,1,4,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,6,2,3,1,4,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,6,3,1,5,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,2,8,6,4,1,5,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,2,1,6,4,8,5,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[7,1,5,2,8,3,4,6]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,8,5,2,7,3,4,6]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,7,2,3,4,5]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,1,6,7,2,3,4,5]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[7,1,6,8,2,3,4,5]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[3,2,1,7,8,4,5,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[3,2,8,7,1,4,5,6]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[5,8,7,2,1,3,4,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[1,7,6,8,2,3,4,5]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,5,8,2,3,1,4,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,2,1,3,4,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[6,4,2,8,3,1,5,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[5,4,2,3,8,1,6,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,2,5,4,1,8,6,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,5,2,3,1,8,6,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,2,3,1,8,6,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,1,3,8,5,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,4,2,1,8,3,5,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,4,2,1,7,3,5,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[1,4,2,8,7,3,5,6]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,5,8,2,7,3,4,6]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,1,2,7,3,4,6]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[7,5,1,2,8,3,4,6]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[6,5,1,2,3,8,4,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[4,6,2,1,3,8,5,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,2,6,1,4,8,5,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,1,8,4,5,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,7,2,1,8,3,5,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,6,1,8,2,3,4,5]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[8,6,1,7,2,3,4,5]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[1,6,8,7,2,3,4,5]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,7,8,6,2,3,4,5]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[7,8,1,6,2,3,4,5]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,8,1,7,2,3,4,5]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,8,2,1,7,3,5,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,8,1,7,4,5,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,1,8,7,4,5,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[5,1,8,2,7,3,4,6]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,8,7,2,3,4,5]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[8,1,7,6,2,3,4,5]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[1,8,7,6,2,3,4,5]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[6,3,5,1,2,4,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,3,5,6,1,2,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,5,2,1,4,6]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,3,7,5,1,8,4,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,7,1,8,3,4]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,2,7,4,1,3,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[2,6,1,5,4,3,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,3,5,1,2,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,3,1,4,6,2,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[3,1,4,6,5,2,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,7,4,6,2,8,3,1]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,4,7,2,6,3,5]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,7,8,5,2,1,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,1,8,5,7,3,4,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,3,5,1,7,4,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,2,4,6,7,3,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,8,6,5,7,1,2]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,4,8,1,6,3,2]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,4,6,8,2,7,3]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,5,4,6,7,1,8,3]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,6,3,7,5,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,3,8,5,7,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,4,2,8,6,5,1]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,4,1,3,5,8,6,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[6,5,8,4,1,7,3,2]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,3,7,4,1,6,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,8,3,7,6,5]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,3,8,2,1,6,5]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,4,1,8,2,5]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,1,2,5,7,6,4]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[3,1,8,2,7,6,5,4]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,3,8,1,6,7,5,4]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,2,6,8,5,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,2,3,8,5,6,1]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,2,1,7,5,6,4]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,1,3,6,5,7,4]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,8,5,4,3,1,6]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,7,1,6,3,4,2,5]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,8,6,7,2,4,1,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,8,7,4,2,6,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,8,7,2,1,6,5]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,6,1,4,2,7,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,5,8,2,4,1,6]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,1,8,5,7,6]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,3,2,6,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,3,5,6,2,7,1,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,6,1,8,7,2,4]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,2,8,7,4,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,5,6,1,4,2,3]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,5,4,7,1,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,4,5,7,2,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,6,1,7,2,4]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,8,6,5,7,3,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,5,3,6,8,4]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,5,2,1,8,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,4,2,5,6,8,3]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,7,4,1,6,5,8,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,1,2,8,7,3,5]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,1,5,8,7,6,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,1,2,5,8,6,7,3]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,2,1,5,8,7,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[8,5,2,4,6,1,7,3]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,5,3,2,6,8,1,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[2,1,5,3,6,8,7,4]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,4,6,1,8,2]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,4,1,5,7,8,2]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,3,1,5,7,6,8,2]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,4,5,6,8,7,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,5,2,6,3,1,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,2,1,4,3,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,5,2,7,4,8,3,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,2,7,4,1,6,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,5,2,1,6,4]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,3,7,5,2,8,4,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,5,4,2,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,6,3,2,4,1,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,2,4,1,5,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,1,3,5,4,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,2,3,4,8,5,1]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,2,3,4,1,6,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,1,7,3,8,4,6,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,7,3,8,6,4,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,6,1,3,5,8,4,2]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[3,6,7,4,1,8,5,2]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,7,4,8,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,6,7,4,8,5,3]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,8,7,4,3,6,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,8,3,7,4,2,6,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,7,4,1,2,6,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,8,1,3,5,2,6,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,7,3,2,6,1,4]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,6,3,1,5,7,4]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,1,6,3,2,5,4,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,1,6,3,7,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,1,2,7,6,3,5]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,4,2,5,7,1,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,3,5,2,7,4,1]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,5,3,8,7,6,4]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,5,3,2,8,7,1,4]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[7,5,2,4,8,1,6,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,4,2,8,5,7,6,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,1,8,7,6,5,3]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[8,4,2,1,7,5,3,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[4,3,1,8,6,7,5,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,4,8,6,5,7,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,6,5,4,8,2,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,6,8,4,2,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,6,8,2,4,3]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,2,5,1,7,4,3]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,2,1,8,7,3,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,2,5,8,3,7,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,2,6,3,8,1,4]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,2,3,6,8,7,5]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,4,3,1,8,5,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,5,2,8,3,4,6,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,2,8,4,3,1,7]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,2,8,1,5,3,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,2,1,4,5,6,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[3,6,8,7,1,5,4,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,6,3,4,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,5,4,3,6,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,8,4,5,3,6,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,3,8,1,4,6,2]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,7,8,5,4,6,3]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,5,8,4,6,3,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,8,4,1,2,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,5,8,4,3,6,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,3,5,6,1,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,3,6,5,2,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,8,1,7,2,5,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,1,3,7,2,6,5]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,1,8,2,4,7,6,5]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,1,4,6,7,5]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,8,2,5,1,7,6]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,8,4,2,5,7,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,4,3,8,2,5,1,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,4,8,3,5,7,6]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,2,4,3,5,1,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,3,5,1,6,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,2,1,4,6,5,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,1,3,4,5,7,6]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,4,1,6,5,3,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,1,6,5,7,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,7,6,1,4,3,5]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,6,7,4,3,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,5,8,6,1,4,2,3]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,6,1,4,2,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,2,4,1,6,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,2,4,1,6,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,5,3,4,7,6,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,3,4,1,7,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,5,3,4,1,6,7]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,6,1,4,5,3]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,5,3,6,1,7,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,5,6,7,4,1,3]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,5,3,4,7,1,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,3,4,6,1,7]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,3,4,6,7,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,5,7,2,4,6,1,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,7,3,1,4,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,5,2,8,3,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,5,2,8,3,1,4,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,5,8,2,4,6,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,6,1,4,3,2]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,8,2,1,3,7,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,5,6,2,1,8,7,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,6,1,4,8,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,2,4,1,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,7,2,4,6,8,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,2,7,3,1,8,4]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,5,2,6,3,1,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,1,2,3,7,6,8,5]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,2,7,3,4,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,6,7,4,3,8,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,6,4,8,7,3]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,2,8,6,4,7,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,6,8,7,3,4,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,2,8,3,7,4,1]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,2,3,8,7,5,6]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,1,2,3,8,6,5,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,1,2,3,8,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,2,3,7,6,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,1,2,3,8,5,7,6]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,6,8,4,3,5,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,8,4,5,7,3]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,8,2,3,1,7,4]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,2,4,3,1,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,2,4,3,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,2,8,3,4,1,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,2,8,3,7,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,2,7,3,4,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,7,4,3,2,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,1,6,8,7,3,2,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,1,6,8,4,3,2,5]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,7,8,6,3,4,2,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,3,6,5,7,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,3,6,2,7,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,4,8,6,2,7,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,8,6,5,2,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,1,6,5,8,3,2,4]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,6,7,8,3,2,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,1,6,5,7,3,2,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,2,6,3,7,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,7,3,8,1,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,6,2,4,8,7,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,2,4,8,1,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,6,8,4,1,2]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,5,2,8,1,7,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,2,5,8,4,7,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,6,5,8,3,4,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,2,6,3,8,4,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,2,3,5,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,1,2,3,7,8,6,5]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,5,2,7,3,8,6,1]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,6,7,8,3,5,2]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,2,6,8,5,7,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,2,5,6,8,7,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,5,2,6,3,7,8,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,5,6,1,4,3,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,4,2,1,5,3,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,8,2,1,6,5,3,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,1,2,5,7,3,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[2,4,8,1,5,7,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,8,1,7,2,5,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,3,1,4,7,2,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,8,3,4,5,1,6,2]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,3,5,4,2,1,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,4,1,2,3,6,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,3,6,5,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,2,1,5,3,4,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,2,6,4,1,3,5]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,2,5,6,4,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,1,6,5,4,3,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,2,1,7,5,4,3,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[2,1,8,7,5,4,3,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,3,8,2,6,4,7,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,7,1,6,4,8,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,2,7,4,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,2,5,8,7,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,3,1,8,4,2,7,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,2,1,5,3,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,7,5,8,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,8,7,5,6,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,7,1,5,3,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,3,7,6,4,2,8,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,1,7,5,6,8,4,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,2,8,6,4,1,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,8,1,7,6,4,5,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,5,7,3,6,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,5,8,3,6,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,6,8,2,4,7,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,8,5,3,1,4,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[2,6,1,4,7,3,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,7,3,8,4,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,1,4,7,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,5,2,1,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[4,5,6,7,2,8,1,3]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,7,6,1,8,3,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,6,2,7,3,4]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,8,3,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,5,7,1,2,8,3]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,5,6,3,1,8,2]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,6,3,4,2,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,1,4,2,3,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,6,4,3,8,1,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,3,4,5,8,7,1,2]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[6,2,4,1,8,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,3,5,4,8,1,7]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,3,4,5,8,7,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[5,1,4,2,7,6,8,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,2,4,7,8,3,5]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,2,4,1,6,3,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,4,2,8,5,3,7]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,5,8,1,4,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,7,6,3,4,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,6,2,3,1,4]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,7,2,6,5,3,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,2,1,5,6,3,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,2,7,8,1,6,3,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,8,7,6,5,3,4]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,1,4,7,8,2,6,5]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,7,4,5,6,8,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,7,1,6,3,8,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,5,6,8,1,2]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,6,3,5,7,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,2,5,3,7,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,6,5,2,4,1,7]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,5,6,1,4,7,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,7,8,2,1,6,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,2,8,7,1,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,7,5,2,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,8,5,1,4,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,6,8,5,2,1,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,8,5,1,2,4,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[3,7,1,6,4,2,5,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,1,8,6,2,3,5,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[4,7,8,6,3,5,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,7,6,5,4,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[2,1,7,6,5,3,4,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,8,1,6,4,5,3,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,7,5,1,4,3,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,6,7,5,1,3,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,7,8,6,5,4,1,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,4,2,7,1,3,8,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,4,2,5,1,3,8,6]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,5,3,6,1,7,2,4]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,3,6,2,4,8,1,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,1,2,5,8,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,6,2,7,1,4,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,6,7,1,2,8,4]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,4,1,2,8,5]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[4,7,1,5,2,3,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,5,1,2,4,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[7,6,4,2,3,8,1,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,6,4,2,3,7,1,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[4,7,6,3,8,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,4,2,3,8,1,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,1,4,8,2,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,7,5,2,8,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,5,2,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,6,3,7,1,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,6,2,4,7,1,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,6,2,7,1,3,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,8,1,3,4,7]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,5,7,4,8,1,3,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,6,7,2,8,1,3]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,7,1,4,8,2,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,2,4,8,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,7,3,8,1,2,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,3,8,1,2,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,6,3,7,1,2,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,1,6,7,2,3,5]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,4,1,6,8,2,3,5]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,5,3,7,1,8,2,4]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,2,7,8,3,4]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,3,6,4,7,8,1,2]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,4,8,5,1,2]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,5,8,6,2,3]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,5,1,2,8,6,3,4]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[7,6,1,8,5,2,3,4]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,6,1,7,5,2,3,4]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[5,7,2,8,1,6,3,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,7,8,5,1,2,4]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[3,6,8,2,7,1,4,5]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,7,1,3,5,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,3,8,7,1,2,5,6]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[5,3,8,7,1,2,4,6]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[8,3,7,6,1,2,4,5]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,4,7,6,1,2,3,5]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[3,5,8,7,1,2,4,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[2,5,8,7,1,3,4,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[6,8,4,7,5,1,2,3]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,7,1,6,2,3,4]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,6,1,3,4,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,8,7,6,1,2,4,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[4,8,7,6,1,2,3,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,6,3,1,4,2,8,7]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,3,8,2,1,6,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,8,7,4,5,1,6,2]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,7,8,5,3,6,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,3,8,1,2,6,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,1,4,5,3,2,6]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[2,7,8,4,1,6,5,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,4,2,6,5,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,4,8,6,3,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[6,5,3,1,8,4,7,2]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,6,3,1,2,5,7,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,7,1,4,2,6,5,3]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,5,6,7,8,1,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]=>[7,2]=>2
[2,3,4,5,6,8,9,1,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[2,3,4,5,7,8,9,1,6]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[2,3,4,6,7,8,9,1,5]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[2,3,5,6,7,8,9,1,4]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[2,4,5,6,7,8,9,1,3]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[3,4,5,6,7,8,9,1,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[2,3,4,5,6,7,8,9,10,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[2,3,4,5,6,7,8,9,1,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]=>[8,2]=>2
[2,3,4,5,6,7,8,10,1,9]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[2,3,4,5,6,7,9,10,1,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[2,3,4,5,6,8,9,10,1,7]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[2,3,4,5,7,8,9,10,1,6]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[2,3,4,6,7,8,9,10,1,5]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[2,1,5,6,7,8,9,3,4]=>[[1,3,4,5,6,7],[2,8,9]]=>[7,2]=>[7,2]=>2
[2,3,5,6,7,8,9,10,1,4]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[1,4,5,6,7,8,9,2,3]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[2,4,5,6,7,8,9,10,1,3]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[3,4,5,6,7,8,9,10,1,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[3,6,4,5,7,2,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,2,7,4,6,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,6,2,4,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,2,5,1,8,4,7]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,3,6,2,7,1,4]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,6,3,4,7,1,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,6,3,4,5,8,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,7,3,4,5,8,1]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,5,7,3,6,8,1]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,7,6,2,3,8,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,5,2,4,8,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,6,2,4,5,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,7,6,3,4,5,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,5,3,1,2,8,4,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,6,5,2,3,7,1,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,2,1,7,3,4,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,5,2,1,8,3,4,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[1,6,3,2,8,4,5,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,3,1,8,4,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,8,6,2,7,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,5,2,7,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,5,2,3,6,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,1,7,3,4,5]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,3,7,2,4,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,7,3,4,5,6]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,8,1,7,3,4,5,6]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,8,6,1,7,2,4,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[4,8,1,5,7,2,3,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,8,3,7,1,5,6]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,2,7,3,4,5,6]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[3,6,2,7,1,8,4,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,7,1,2,8,4,5]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,2,6,1,8,3,4,5]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,3,1,5,8,2,4,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[3,2,1,5,8,4,6,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,4,1,3,6,8,2,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[1,5,3,4,6,8,2,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,3,5,1,6,8,2,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,3,8,7,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,4,5,8,7,1,2]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,5,3,4,8,7,1,2]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[5,3,2,8,7,1,4,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[5,3,1,8,7,2,4,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[8,5,3,7,6,1,2,4]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,1,8,3,7,2,4,5]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,1,7,2,4,5]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,8,2,3,5,1,4]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,2,4,6,1,5]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,3,8,2,5,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,7,8,2,6,1,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,8,7,1,3,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[2,3,8,7,1,4,5,6]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[7,2,8,6,1,3,4,5]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[2,1,8,7,3,4,5,6]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[8,2,7,6,1,3,4,5]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[1,2,8,7,3,4,5,6]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,3,8,7,2,4,5,6]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,7,8,3,6,2,4,5]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,5,8,7,2,3,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[5,4,8,7,6,1,2,3]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,8,3,7,5,1,2,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,6,2,5,1,3,4]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,1,6,7,3,2,5,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,1,6,7,3,2,4,5]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,5,3,7,2,4,6]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,5,3,6,2,4,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,1,3,6,2,4,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,5,8,3,6,2,4,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,3,2,6,5,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,1,3,2,6,5,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,3,2,6,5,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,3,2,7,5,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,3,2,7,6,5]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,4,6,7,2,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,3,6,2,7,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,3,2,6,7,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,1,4,3,2,5,7,6]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,1,4,3,2,5,6,7]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[7,4,1,3,2,5,6,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[7,4,8,3,2,5,6,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,3,8,2,5,7,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,1,2,5,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,4,1,3,2,5,8,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,4,1,3,2,6,8,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,1,3,6,2,8,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,5,1,4,6,8,2,3]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,5,8,3,6,2,1,4]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,3,2,6,1,5]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,3,2,5,1,6]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,3,8,2,5,1,7]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,7,2,5,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,3,2,8,6,1,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[5,4,3,2,8,7,1,6]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[6,5,3,8,7,2,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,4,8,7,1,2,3]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,5,4,1,7,8,2,3]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[6,5,3,1,7,2,8,4]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,1,2,7,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[5,4,3,2,1,8,6,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[6,5,3,1,8,2,7,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,5,4,1,8,7,2,3]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,5,1,4,8,6,2,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[7,4,1,3,2,8,6,5]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,4,1,3,2,8,5,6]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,1,2,8,5,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,4,3,1,2,7,5,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,4,3,8,2,7,5,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,8,7,2,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,3,1,7,2,4,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[6,5,3,1,8,2,4,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,5,1,3,8,2,4,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,6,1,8,3,2,4,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,6,1,8,4,5,2,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,8,1,4,5,2,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,1,3,2,5,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,3,7,8,2,4,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,7,2,8,5,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,7,2,1,5,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,4,8,3,2,1,5,6]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,4,8,3,2,1,6,5]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,3,1,2,6,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,4,1,6,2,3]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,5,4,8,1,7,2,3]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,8,1,2,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,4,3,2,8,1,7,6]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,7,2,1,8,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,5,3,7,1,2,8,4]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,7,1,8,2,3]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,7,8,2,1,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[6,4,3,7,2,8,1,5]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,2,7,8,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[5,4,3,2,6,8,1,7]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[5,6,2,1,3,4,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[5,3,7,8,2,1,4,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[7,6,1,2,5,8,3,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[2,1,7,8,4,3,5,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[7,8,1,2,5,4,6,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,1,3,7,6,2,5]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,5,2,1,8,7,4,3]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[4,7,2,8,1,3,6,5]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,8,6,1,2,5,4]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,7,1,8,2,6,5]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,2,4,3,5,6,7]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,4,3,5,6,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,6,2,4,3,5,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,5,2,4,3,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,6,2,5,3,4,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,5,3,4,6,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,8,2,5,3,4,6,7]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,8,2,6,3,4,5,7]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,6,3,4,5,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,8,2,7,3,5,4,6]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,8,3,5,4,6]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,8,3,5,4,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,8,3,6,4,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,8,3,6,5,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,8,4,6,5,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,3,8,4,6,5,7]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,7,4,6,5,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,2,7,4,6,5,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,7,3,6,5,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,7,3,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,7,3,5,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,6,3,5,4,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,6,3,5,4,7]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,5,3,6,4,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,5,3,6,4,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,5,3,7,4,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,4,3,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,4,3,7,5,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,4,3,6,5,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,4,3,6,5,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,3,4,6,5,7]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,2,3,4,6,5,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,2,3,4,7,5,6]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,2,4,3,7,5,6]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,4,3,8,5,6]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,4,3,8,5,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,4,3,8,6,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,5,3,8,4,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,5,3,8,4,6]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,5,3,7,4,6]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,6,3,7,4,5]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,6,3,8,4,5]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,3,8,4,7,5,6]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,2,8,4,7,5,6]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,8,3,7,5,6]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,8,3,7,4,6]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,8,3,7,4,5]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,8,3,6,4,5]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,7,3,6,4,5]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,7,2,5,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,7,5,2,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,6,3,8,5,1,7,2]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,3,8,5,1,2,7]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,8,3,4,1,2,7]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,3,4,1,7,2]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,2,7,5,3,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,7,2,4,3,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,4,3,1,7,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,4,3,1,2,7]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[5,7,8,4,1,6,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,4,1,6,3,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,4,1,3,6,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,4,2,1,7,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,2,4,1,7,3]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,2,8,5,1,7,3]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,6,8,5,1,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,8,5,1,4,7]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[4,6,2,8,5,1,3,7]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,8,2,4,1,3,7]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,4,2,1,3,7]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[5,7,8,4,1,3,2,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,4,1,2,6,3]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,4,1,2,3,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[6,7,8,1,5,2,3,4]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,1,5,2,4,3]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,8,1,5,3,2,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,1,3,5,2,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,2,1,6,3,4]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,2,8,1,6,3,5]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,7,8,1,6,4,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,7,8,1,6,5,4]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,2,8,1,6,5,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,8,2,1,6,4,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,3,5,4,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,5,3,4,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,8,1,5,4,3,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,1,5,4,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,1,4,5,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,4,5,3,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,4,3,5,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,8,1,3,4,5,2]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,2,1,4,6,3]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,2,8,1,5,6,3]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,7,8,1,5,6,4]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,8,4,1,7,5]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,2,8,3,1,7,5]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,8,3,2,1,7,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,3,1,4,6,2]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,3,1,6,4,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,3,1,6,2,4]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,8,1,6,2,5]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,8,1,6,5,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,8,1,5,6,2]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,3,8,2,1,7,5]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,3,2,8,1,7,6]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,2,3,8,1,7,6]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,5,4,8,1,7,6]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,3,2,8,1,6,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,3,8,2,1,5,7]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,7,3,8,1,5,2,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,8,1,2,6,5]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,3,8,1,2,5,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,7,8,3,1,2,4,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[5,7,8,3,1,2,6,4]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,3,1,4,2,6]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,3,2,1,4,7]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[3,2,7,8,1,5,4,6]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,8,2,1,4,3,6]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,3,4,2,5]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,4,3,2,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,1,4,2,5,3]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,8,1,4,2,3,5]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,1,2,5,3,4]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,2,5,4,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,2,4,5,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,8,1,3,2,5,4]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,8,2,1,3,6,4]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,7,8,1,4,6,5]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,8,1,3,2,4,5]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,1,2,4,3,5]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,1,2,3,5,4]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,8,5,1,6,4,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,5,2,6,4,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,5,4,2,6,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,2,8,5,4,1,6,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,8,5,4,3,1,7,6]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[2,8,4,5,6,1,7,3]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,6,5,7,3,1,4]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,5,3,7,1,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,3,5,6,1,7]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,2,8,4,5,6,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,7,5,2,4,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,2,3,8,5,1,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,2,8,5,1,4,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,4,8,2,5,6,3,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,5,2,1,3,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,4,8,5,1,3,7,2]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,7,5,2,1,8,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,3,7,5,1,2,8,6]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[4,3,7,1,5,6,8,2]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,1,7,5,2,8,4]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,1,2,7,6,8,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,2,1,7,5,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,5,7,1,4,8,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,2,7,4,1,8,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,5,2,6,4,8,7,1]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,1,8,6,4,7,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,1,8,7,2,4,3]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,5,8,2,7,4,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,8,4,2,3,7,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,5,8,3,7,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,5,7,3,4,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,7,4,6,3,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,1,8,7,6,3,4]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[7,1,3,8,4,6,2,5]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,8,6,1,7,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,8,6,5,1,7]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,7,3,5,8,6,1,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,2,4,7,8,6,1,5]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[1,5,4,6,2,7,3,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,4,7,1,8,3,6]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,6,4,1,8,7,2]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,1,4,8,2,7]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,6,8,4,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,3,5,1,8,2,7,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,1,5,8,4,7,3]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,6,5,8,3,4,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,1,6,3,8,4,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,4,1,7,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,1,4,2,7,8,6,5]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,7,2,8,6,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,4,7,8,2,5,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,4,6,8,5,7,2]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,4,5,7,1,8,2]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,5,4,6,1,7,8,3]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,1,4,3,6,5,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[7,3,4,1,2,6,5,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,4,3,2,1,6,5,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,6,3,2,5,4,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[6,7,3,2,5,4,8,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,2,5,4,7,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,5,2,3,7,6]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,5,1,6,2,4,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,2,1,5,6,3,4,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,2,1,6,5,4,3,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,6,1,5,4,2,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,5,1,3,2,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,4,3,2,7,6]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,8,6,4,3,7,2,5]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,7,4,3,1,8,2]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,4,7,5,1,3,8,2]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,7,1,5,4,8,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,1,7,5,4,8,3]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,8,5,4,7,6]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[2,5,8,4,3,1,7,6]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,6,8,4,3,7,1,5]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,4,3,6,5,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,7,4,3,6,5,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,5,6,3,4,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,8,5,6,3,4,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,8,5,7,3,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,6,7,1,3,4]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,6,1,7,3,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,2,1,8,6,7,4,5]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,1,6,8,4,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,7,6,1,8,3,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,6,8,1,3,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,5,8,3,1,2]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,6,5,7,3,2,4]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,5,6,7,2,3,4]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,5,7,8,2,1,3]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,6,7,1,8,2,3]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,6,1,7,8,2,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,2,1,6,7,8,3,4]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[6,2,1,5,7,3,8,4]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[6,3,5,1,7,2,8,4]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,5,7,1,2,8,3]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,7,2,1,8,3]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,6,4,7,2,8,1,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,6,2,7,3,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,2,6,7,4,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,2,6,8,4,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,3,2,7,8,1,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,3,2,7,1,8,4]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,2,1,7,8,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[6,2,1,4,3,7,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,2,8,7,1,5]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,2,8,6,5,1]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,3,2,7,6,5,4]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,4,7,2,6,5,3]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,4,8,2,7,1,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,5,8,1,2,7,6]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,5,1,8,2,7,6]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,1,5,8,3,7,6]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,2,1,6,8,7,3,5]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[3,4,6,8,1,7,2,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,8,7,1,2,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[3,6,5,8,7,2,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,5,7,6,2,4,3]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,6,7,5,4,2,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,7,8,5,4,1,2]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,5,7,8,6,1,4,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,7,8,1,6,5,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,7,8,6,5,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[2,3,8,1,7,6,5,4]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,7,1,6,5,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,3,6,5,8,7,10,9,12,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[3,2,2,2,2,1]=>[3,2,2,2,2,1]=>6
[7,4,6,1,8,3,5,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,1,7,4,6,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,4,1,7,5,6,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,3,1,7,5,6,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,2,1,7,5,8,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,6,2,7,5,8,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,5,2,6,8,4,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,2,1,6,8,4,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[6,8,4,3,1,7,5,2]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,8,4,1,7,5,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,7,5,1,8,4,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,6,1,8,3,4,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,6,5,7,1,8,2]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,5,6,1,8,3,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,5,1,8,4,3,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,1,7,5,3,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,5,3,1,8,4,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,4,2,1,6,7,5,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[1,8,4,2,6,7,5,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,5,3,2,7,6,8,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,2,1,7,6,8,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[2,5,3,1,7,6,8,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,1,6,7,5,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,5,1,6,8,4,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,6,1,7,5,8,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,1,6,5,8,2,3]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,6,5,7,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,1,2,7,5,8,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,1,2,6,8,4,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[8,4,1,2,6,7,5,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[5,3,1,2,7,6,8,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,5,3,7,6,8,4]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,1,2,7,6,8,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,5,1,2,7,6,8,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,1,5,8,2,3,4]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,7,6,1,5,8,3,4]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,5,1,7,6,8,4]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,1,5,8,3,2,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[3,6,7,1,5,8,2,4]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,6,5,8,2,4,3]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,1,6,8,4,2,3]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[8,4,1,6,7,5,2,3]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,2,3,1,7,6,8,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,2,1,7,6,8,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,5,2,7,6,8,4]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,6,2,5,8,3,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,2,1,5,8,3,4]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[8,3,1,5,7,6,2,4]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[6,2,4,1,7,5,8,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,5,1,7,4,8,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,4,8,2,5,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,4,7,1,5,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,5,2,7,4,8,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,2,5,8,3,1,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,3,5,7,6,2,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,3,5,7,6,2,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,2,3,7,6,8,4]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,1,3,7,6,8,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,2,6,8,4,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,4,2,6,7,5,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,1,4,2,7,5,8,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,5,7,1,4,3]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,8,2,5,7,1,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,5,7,6,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[5,1,3,2,7,6,8,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,3,2,7,6,8,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,1,3,7,6,8,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,2,3,7,6,8,5]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,1,3,7,6,8,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,1,3,7,6,8,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,3,5,7,6,1,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,3,5,7,1,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,1,3,5,8,2,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[8,3,5,7,6,1,2,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[5,1,2,3,7,6,8,4]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,2,4,7,6,8,5]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[10,8,9,5,6,7,1,2,3,4]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[10,8,9,4,5,6,1,2,3,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[10,7,8,5,6,9,1,2,3,4]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[10,7,8,4,5,9,1,2,3,6]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[10,6,7,4,5,8,1,2,3,9]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[10,7,8,3,4,9,1,2,5,6]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[10,6,7,3,4,8,1,2,5,9]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,8,10,5,6,7,1,2,3,4]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,8,10,4,5,6,1,2,3,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,7,10,5,6,8,1,2,3,4]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,7,10,4,5,8,1,2,3,6]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,6,10,4,5,7,1,2,3,8]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,7,10,3,4,8,1,2,5,6]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,6,10,3,4,7,1,2,5,8]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,7,9,5,6,10,1,2,3,4]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,7,9,4,5,10,1,2,3,6]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,6,9,4,5,10,1,2,3,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[7,6,8,4,5,9,1,2,3,10]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,7,9,3,4,10,1,2,5,6]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,6,9,3,4,10,1,2,5,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[7,6,8,3,4,9,1,2,5,10]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,6,10,5,7,8,1,2,3,4]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,6,10,4,7,8,1,2,3,5]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,5,10,4,6,7,1,2,3,8]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,6,10,3,7,8,1,2,4,5]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,5,10,3,6,7,1,2,4,8]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,6,9,5,7,10,1,2,3,4]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,6,9,4,7,10,1,2,3,5]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,5,9,4,6,10,1,2,3,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[7,5,8,4,6,9,1,2,3,10]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,6,9,3,7,10,1,2,4,5]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,5,9,3,6,10,1,2,4,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[7,5,8,3,6,9,1,2,4,10]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,4,9,3,5,10,1,2,6,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[7,4,8,3,5,9,1,2,6,10]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,6,10,2,7,8,1,3,4,5]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[9,5,10,2,6,7,1,3,4,8]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,6,9,2,7,10,1,3,4,5]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,5,9,2,6,10,1,3,4,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[7,5,8,2,6,9,1,3,4,10]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,4,9,2,5,10,1,3,6,7]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[7,4,8,2,5,9,1,3,6,10]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[8,1,2,4,3,6,5,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,5,6,2,7,4]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,1,3,4,2,6,7,5]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,3,2,4,5,7,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,7,8,3,4,5,6,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,3,8,4,5,7,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,2,1,4,5,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,3,1,4,2,6,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,4,1,5,6,8,2,3]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[4,7,8,5,6,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,8,5,6,2,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,8,4,2,6,1,5]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,2,4,5,1,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,2,8,4,5,1,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,6,7,4,5,8,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,2,4,8,6,1,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,4,2,8,7,1,6]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,5,8,7,1,2,3]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,4,5,1,7,8,2,3]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,4,1,2,3,8,5,6]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[6,2,4,1,3,7,5,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,6,4,8,3,7,5,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,8,7,3,4,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,5,1,7,3,4,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,5,2,1,8,3,4,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[2,5,6,7,8,3,4,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,6,7,3,8,5,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,7,3,1,5,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,7,8,2,3,1,5,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,8,3,2,1,6,5]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,6,4,8,1,7,2,3]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,8,1,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,5,3,7,1,6,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,6,7,2,1,8,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,4,6,7,2,8,1,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,2,7,8,1,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,2,5,6,8,1,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,7,8,6,4,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[5,1,2,7,8,6,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[4,7,1,8,6,5,2,3]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,1,2,8,6,5,3]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,8,1,2,7,5,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,1,5,3,2,4]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,3,5,1,2,4]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,1,6,3,5,2,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,3,6,5,2,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,6,5,2,1,4]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,2,8,6,1,5,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,3,4,8,6,5,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,2,7,1,8,6,5,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,8,2,3,6,5,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,5,7,1,6,2,3,4]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,1,2,6,3,4]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,2,7,1,3,5,4]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,7,2,5,3,1,4]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,2,4,8,7,1,5,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,8,3,7,4,5,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,8,3,4,7,5,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,8,1,7,5,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,7,2,3,5,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,1,7,3,5,4]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,5,7,2,1,6,3,4]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,1,2,3,6,4]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,2,1,4,3,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,5,7,2,3,1,6,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,4,2,7,1,6,3]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,7,5,3,4,6,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,3,5,4,6,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,5,4,7,1,6,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,2,7,3,1,6,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,7,6,2,4,3,1,5]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,6,1,2,4,3,5]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,7,6,1,4,2,3,5]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,7,6,4,1,3,2,5]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[5,8,4,7,2,1,6,3]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,7,5,4,3,6,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,6,8,4,3,7,5,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,3,2,5,1,4]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,1,7,3,2,5,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,5,7,3,1,6,2,4]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,1,3,2,6,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,3,1,2,6,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,8,4,7,1,2,6,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,4,1,7,2,6,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,4,7,1,6,2,3]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,2,6,5,7,4,3]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,5,6,7,4,1,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,8,5,7,1,6,2,3]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,5,7,1,2,6,3]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,5,1,7,2,6,3]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,5,3,1,7,2,6,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,5,3,7,1,2,6,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,8,1,3,7,2,5,4]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,2,8,1,7,5,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,4,8,3,7,5,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,7,4,5,3,6,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,5,7,2,1,6,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,5,3,7,2,1,6,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,7,6,3,1,4,2,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,7,6,1,3,2,4,5]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,5,3,2,7,1,6,4]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,8,5,2,7,1,6,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,7,4,3,5,6,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,3,4,5,6,2]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,2,4,5,7,1,6,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,2,3,7,1,6,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,3,1,5,4,2,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,3,1,5,2,7,6,4]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,2,1,7,3,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,5,4,2,1,7,6,3]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[6,5,4,2,1,3,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[6,5,4,2,3,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,3,2,5,1,4,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,3,1,2,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[6,5,4,1,3,2,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,5,4,1,2,7,6,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[8,7,4,1,6,3,2,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,7,4,1,6,3,5,2]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,4,1,6,5,3,2]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,5,4,1,3,7,6,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,5,4,3,1,7,6,2]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[8,3,2,5,1,7,6,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,1,8,5,3,7,6,4]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,5,1,7,4,6]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,3,1,7,2,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,5,4,1,3,7,2,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,7,4,1,6,5,2,3]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,7,4,1,6,2,5,3]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,6,5,2,1,4,3]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[8,7,4,3,6,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,3,2,7,6,4,1,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[2,1,8,7,6,4,3,5]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,1,8,7,6,4,5,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,2,7,6,4,5,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,4,3,6,2,5,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,6,5,2,4,3,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[6,2]=>[6,2]=>2
[8,5,4,2,3,7,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,7,4,2,6,5,3,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,4,2,6,3,5,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,4,2,6,3,1,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,3,1,7,6,4,2,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,1,7,6,4,5,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,1,7,6,5,4,2]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,3,1,5,4,7,6,2]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,3,1,5,4,7,2,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,1,7,6,5,2,4]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,1,7,6,2,5,4]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,4,2,6,1,5,3]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,7,4,2,6,5,1,3]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[8,5,4,2,3,7,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,3,2,5,4,7,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,8,5,4,7,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,7,6,5,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,4,3,6,5,1,2]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[8,7,6,5,3,1,4,2]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[8,7,6,5,1,3,2,4]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,7,6,5,1,3,4,2]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[8,7,6,5,1,4,3,2]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[6,2]=>[6,2]=>2
[8,7,6,5,4,1,3,2]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[7,1]=>[7,1]=>2
[8,7,4,3,6,1,5,2]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,3,2,7,6,1,5,4]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,8,7,6,3,5,4]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,2,7,6,1,4,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[8,7,6,5,1,4,2,3]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[8,7,6,5,1,2,4,3]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[7,1]=>[7,1]=>2
[7,3,5,1,8,4,6,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,4,1,8,5,6,2]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,6,2,1,8,7,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,2,7,4,3,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,4,3,1,8,6,5,2]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[7,6,5,1,8,4,3,2]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[7,6,4,1,8,5,3,2]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[6,4,2,1,8,7,5,3]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[1,6,4,2,7,5,3,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,3,2,7,6,4,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[5,3,2,1,8,7,6,4]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[2,5,3,1,7,8,6,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,4,1,7,8,5,3]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,5,1,7,8,4,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,7,1,6,8,2,3]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,1,2,8,4,3,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[6,4,1,2,8,5,3,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[5,3,1,2,8,6,4,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[4,3,1,2,8,6,5,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[6,1,2,5,8,3,4,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[7,1,3,4,8,2,5,6]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[7,1,5,6,8,2,3,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[2,6,1,5,7,8,3,4]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,4,1,6,8,5,2,3]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,2,3,1,8,6,7,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,2,1,6,8,7,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,2,5,7,3,4,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,2,1,5,8,7,3,4]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[7,3,1,5,8,6,2,4]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[6,2,4,1,8,5,7,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,5,1,8,4,7,3]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,1,4,8,6,2,5]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[6,2,1,4,8,7,3,5]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[1,6,2,4,7,3,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,2,1,3,8,7,4,6]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[7,4,1,3,8,5,2,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[7,5,1,3,8,4,2,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[3,6,7,1,4,8,2,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,1,4,8,3,2,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[4,2,1,3,8,7,5,6]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[2,6,1,4,7,8,3,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,1,4,6,8,2,3,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[7,1,3,5,8,2,4,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[6,1,2,4,8,3,5,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[5,2,3,1,6,4,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,5,2,3,1,8,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,3,5,2,4,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,5,2,4,1,8,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,5,2,4,1,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,4,1,6,3,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,3,5,2,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,4,1,5,2,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,3,4,1,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,7,3,4,1,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,8,6,7,3,4,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,8,5,7,3,4,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,3,4,1,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,4,1,5,2,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,3,5,2,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,4,5,2,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,7,4,5,3,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,6,7,4,5,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,6,7,3,5,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,3,4,1,5,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,3,4,1,6,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,6,2,7,3,4,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,3,5,1,6,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,4,7,3,6,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,5,7,3,6,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,5,7,4,6,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,5,7,4,6,3]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,7,4,6,3,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,4,6,2,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,3,6,2,8,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,3,6,2,8,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,3,5,1,8,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,8,4,7,3,5,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,3,6,2,5,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,6,2,5,1,8,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,5,1,7,3,8,4]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,4,1,7,3,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,4,1,7,3,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,3,6,2,4,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,4,6,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,2,3,1,8,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,3,1,7,4,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,3,1,7,4,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,3,1,7,5,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,4,2,8,6,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,3,1,8,5,7,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,6,2,3,1,7,4]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,5,6,2,3,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,5,6,2,4,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,6,2,4,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,4,1,8,6,7,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,5,2,8,6,7,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,5,2,8,6,7,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,3,8,5,7,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,2,8,5,7,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,2,8,5,7,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,6,2,8,4,7,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,6,2,5,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,4,6,2,5,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,3,8,4,5,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,5,1,6,2,7,3]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,4,6,2,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,5,6,2,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,5,6,2,7,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,5,6,3,7,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,7,4,8,5,6,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,4,8,5,6,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,3,8,5,6,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,4,5,1,6,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,5,1,7,3,6,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,6,2,8,4,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,5,6,1,3,4,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,1,3,6,2,5,4]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,8,4,7,2,5,6]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,1,4,7,2,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,1,2,5,7,3,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,8,2,5,7,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,2,4,5,6,1,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,1,5,4,6,3,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,1,6,3,4,5]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,5,6,4,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,1,4,2,3,6,5]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,5,1,4,2,6,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,4,5,3,1,6,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,8,4,3,2,7,6]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,6,1,4,3,2,7,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,4,8,3,7,1,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,6,8,3,7,5,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,8,5,3,1,6,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,5,8,1,4,7,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,8,4,7,6,1,2]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,2,4,7,3,8,5]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,2,1,4,7,8,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,6,2,5,3,1,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,5,1,3,6,8,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,5,3,6,2,4,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,3,6,1,4,8,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,6,7,2,1,8,4]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,1,7,5,2,4,8,3]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,1,2,4,5,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[1,4,7,2,5,3,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,8,3,5,1,2]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,1,8,4,2,5,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,7,5,8,2,4,3]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,6,7,8,1,4,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,5,7,8,2,1,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,2,7,6,1,4,3,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,6,8,1,3,4]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,7,5,6,8,4,1,3]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,1,6,8,4,5,3,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,1,8,5,3,4,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,6,8,5,4,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,8,5,6,7,1,2]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,1,6,3,7,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,5,4,6,7,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,4,5,6,1,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,2,8,6,1,7,5]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,7,1,5,2,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,7,8,1,2,6,5]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,3,8,5,2,6,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,8,3,6,2,5,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,8,6,3,2,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,7,8,6,1,3,4,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,5,8,1,3,4,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,4,3,8,2,5,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,1,3,4,8,2,6,5]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,5,4,1,2,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[2,4,5,1,7,8,6,3]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,3,4,5,8,1,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,6,4,1,8,3,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,6,4,8,5,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,1,4,8,3,5,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,1,6,5,3,8,4,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,5,6,3,8,1,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,2,7,1,8,4,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,6,2,7,3,1,4,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,6,7,4,2,8,1,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,6,4,1,8,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,1,5,2,8,3,4]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,5,2,4,8,3,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,1,5,2,8,3,4,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,7,5,3,8,4,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,5,4,2,3,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,1,5,3,4,2,8,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,1,5,3,2,8,4]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,5,6,4,1,2,8,3]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,7,5,4,3,1,8,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[7,5,2,4,3,1,6,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,4,6,1,2,5,3,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,4,2,5,3,6,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,8,1,4,2,5,7,3]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,2,5,7,3,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,6,3,7,5,4,2,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,8,1,3,7,5,4,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,1,3,5,6,4,2,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[7,3,1,6,4,5,2,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,2,6,5,1,3,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,4,6,3,1,5,2,8]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,2,4,1,5,3,6,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,2,3,5,4,1,6,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[6,8,1,2,3,4,7,5]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,5,7,2,3,8,6,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,2,3,6,7,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,2,3,7,6,4,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,2,8,1,3,7,4,5]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,2,3,5,4,7,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,2,4,1,5,7,3]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,3,1,2,4,7,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,6,4,1,5,7,3,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,6,3,5,7,1,4,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,7,8,3,6,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,3,6,8,4,7,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,4,7,8,5,6,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,7,6,8,5,1,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,3,7,6,1,8,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,7,8,1,4,6,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,7,4,1,6,2,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,4,1,8,6,7,2]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,8,4,6,1,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,1,8,6,3,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[4,2,8,6,5,3,7,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,5,7,6,3,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,4,2,7,5,8,6,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,8,6,7,5,3,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,7,6,2,4,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,4,7,6,2,1,3]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,8,7,4,3,6,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,8,3,1,7,2,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,8,7,1,3,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,3,8,7,2,5,1,4]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,7,1,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,3,8,6,7,2,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,3,7,8,6,2,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,5,7,6,4,2,8,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,8,7,4,1,6,2,3]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,4,8,1,2,7,3,5]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,1,2,3,7,4]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[6,8,5,2,4,3,7,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,5,3,1,2,7,4]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,5,1,2,7,6,3,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,1,2,6,8,7,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,1,8,4,7,2]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,7,1,2,8,6,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,2,7,5,1,4,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[4,2,6,1,7,3,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,6,3,1,2,7,5,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,5,3,1,7,6,2,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,5,7,1,6,3,8]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,2,7,8,1,6,4]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,4,7,5,6,2,8]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,5,8,7,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,1,4,5,8,6,7,2]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,6,8,5,2,7,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,6,2,8,4,7,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,6,1,8,7,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,3,1,6,8,7,2]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,1,7,5,8,6,4,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,5,3,8,6,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,7,3,8,6,5]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,1,7,5,2,3,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[6,1,3,7,5,2,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[3,1,2,6,8,5,4,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,7,1,2,5,4,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,7,2,4,8,6,5]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,7,8,6,5,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,7,5,1,8,6,2]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,4,1,5,8,6,3]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,7,1,5,8,6,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,1,3,7,4,6]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,8,3,4,7,5]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,8,3,1,5,7,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,6,4,1,5,7,3]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,6,4,8,5,1,7,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,7,4,5,1,8,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,3,7,5,8,1,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,1,7,8,3,4,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[4,7,2,3,6,8,1,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[5,2,7,3,6,8,1,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,6,2,8,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,4,6,1,8,2]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,8,4,6,1,7,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,2,4,1,6,7,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,2,3,5,1,6,7,4]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,2,8,3,6,7,1,5]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,1,7,3,5,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,1,3,6,2,5,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[4,8,3,1,7,2,5,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[5,2,8,4,7,1,6,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,4,7,3,1,6,2]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,8,3,1,7,5,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,2,7,1,5,4]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,1,8,2,4,7,5]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,8,1,2,6,4,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,1,6,2,3,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[8,5,4,1,2,6,3,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[5,1,8,4,2,7,3,6]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,2,8,5,3,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,5,3,1,7,4,2]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[8,4,5,1,2,6,3,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,7,1,2,4,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,6,3,7,2,8,4,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,2,7,8,5,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[4,5,7,8,3,1,6,2]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,7,2,5,8,1,6,3]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,3,4,6,2,5,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[3,8,2,4,6,7,1,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,8,2,7,1,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,5,6,8,1,7,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,8,3,5,6,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,2,3,7,8,1,4]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,3,4,1,2,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,3,4,1,2,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,7,1,5,3,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,7,2,5,3,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,8,7,2,6,3,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,8,7,1,6,3,2]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,7,6,1,2,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[4,3,8,7,6,1,2,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[4,8,3,7,5,1,2,6]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,3,4,6,5,1,2,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[3,8,4,7,5,1,2,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,8,7,6,1,2,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[3,5,8,7,6,1,2,4]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[4,5,8,7,6,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[4,5,8,7,1,6,3,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,7,2,6,3,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,8,2,7,6,4,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,8,1,7,6,4,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,1,7,6,4,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,7,1,6,3,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,7,1,6,3,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,7,1,5,3,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,4,6,1,5,3,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,6,2,5,3,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,8,4,7,2,5,3,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,8,7,2,6,3,5]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,7,2,6,3,4]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,2,7,6,4,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,3,7,6,4,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,4,2,8,7,6,5,3]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,3,8,2,7,6,4,5]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,3,2,7,5,4,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,3,2,6,5,4,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,3,1,6,5,4,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,3,1,7,5,4,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,8,1,7,6,4,5]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,1,8,7,6,5,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,3,1,8,7,6,5,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,2,1,8,7,6,5,3]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,8,2,1,7,5,4,6]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,3,2,1,6,5,4,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[8,4,2,6,1,5,3,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,2,8,7,1,6,3,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,7,1,6,3,4]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,1,7,6,4,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,1,7,6,4,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,2,7,6,4,1]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,8,3,2,7,5,4,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,3,1,7,5,4,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,1,7,5,4,3]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,7,1,5,3,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,7,2,1,4,3,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,5,6,1,2,4,3,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,1,2,4,3,6]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,1,2,7,5,4,3]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,3,7,5,4,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,2,8,3,7,6,4,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,3,7,6,4,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,7,2,6,3,4]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,7,2,6,3,5]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,1,7,2,5,3,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,1,6,2,5,3,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,1,2,6,5,4,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[3,8,1,2,7,5,4,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,1,8,2,7,6,4,5]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,1,2,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,1,3,8,7,6,5,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,1,4,8,7,6,5,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,1,8,3,7,6,4,5]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,1,3,7,5,4,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,1,3,6,5,4,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,1,2,3,6,5,4,7]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[1,8,2,3,7,5,4,6]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,2,8,3,7,6,4,5]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,3,6,8,2,5,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,2,5,8,4,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,8,2,4,7,6]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,5,2,8,3,7,6]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,2,6,5,8,3,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,2,6,8,3,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,1,6,5,8,2,4,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,2,5,8,3,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,5,2,6,4,8,3,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,6,5,4,8,3,7]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,4,7,3,8,6]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,2,6,3,8,7,5]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,5,4,2,8,3,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,4,7,5,2,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,5,2,8,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,2,5,1,8,3,4,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,4,5,2,8,7,3,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,2,8,3,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,2,8,3,7,6,5]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,5,3,8,7,6,4]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,6,5,3,7,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,5,2,8,6,3,7,4]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,2,8,7,3,5]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[6,2,1,8,7,3,4,5]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[7,6,2,1,8,3,4,5]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,3,1,6,2,8,4,5]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[1,7,6,4,2,8,3,5]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,2,6,3,8,4]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,2,7,5,3,8,4]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,7,6,5,3,8,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,2,6,5,3,8,7,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,2,6,3,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,7,6,3,8,4]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,5,2,7,3,8,4]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,7,4,2,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,8,6,3,7,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,1,8,6,2,4,7,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,7,1,8,2,5,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,3,1,6,2,4,7,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,1,8,3,2,4,6,5]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,7,3,2,4,6,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,4,2,8,7,3,6,5]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,4,2,8,3,6,5]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,5,4,2,7,3,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,5,2,7,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,3,1,7,2,4,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,6,2,1,7,3,4,5]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[1,8,6,4,2,7,3,5]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,2,6,3,7,4]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,2,7,3,8,6,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,8,5,3,7,6,4]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,3,8,7,5,4]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,6,3,8,5,4]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,2,7,3,8,5,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,8,5,3,6,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,4,2,8,6,3,5]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,8,3,2,6,4,5]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,1,8,6,3,4,5]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[1,8,7,3,2,6,4,5]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,4,2,8,7,6,3,5]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,2,8,7,5,3,6,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,2,8,6,3,7,5,4]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,3,8,6,5,4]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,7,3,6,5,8,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,7,6,2,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,7,6,3,4,5,2]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,6,2,4,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,6,2,4,3,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,1,5,2,7,3,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,5,3,7,6,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,4,5,3,8,7,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,4,5,3,7,8,2]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,7,8,6,2,4,3]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,4,8,3,5,7,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,8,6,3,4,5,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,4,5,3,8,6,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,4,5,3,6,8,2]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,4,5,3,6,7,2]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,1,5,2,6,3,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,7,2,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[6,3,5,8,2,1,7,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,5,7,2,1,8,4]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,5,7,3,6,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,5,8,3,7,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,7,6,2,4,1,3]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,4,8,6,3,1,7,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,4,1,8,2,3,7,6]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,1,6,2,4,3,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,1,5,2,6,3,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,8,2,1,4,7]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,3,4,1,8,6,5,7]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,5,6,2,1,4,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[2,3,8,5,1,4,7,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,8,6,1,5,7,4]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,6,7,1,3,5,4]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,3,5,7,2,1,6,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,8,5,6,1,7,4]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,5,6,3,1,8,2]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,5,6,3,1,7,2]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,5,6,2,8,1,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,5,8,2,1,6,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,5,6,2,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[2,7,6,5,1,3,4,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[2,7,6,8,1,3,5,4]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,6,5,8,3,1,4]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,5,6,1,4,2,3]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,6,4,1,8,5,7,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,1,3,8,5,7,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,1,3,6,5,8,4]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,6,8,4,3,1,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,7,6,1,8,3,4,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,7,6,1,4,3,5,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,5,1,2,8,4,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,4,1,5,2,3,7,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,8,1,6,3,4,2,5]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,1,8,3,2,7,5]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,8,6,4,1,7,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,8,6,7,4,3,1,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,3,5,7,2,4,1,6]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,1,8,7,5,6]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,6,1,7,3,4,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,3,8,1,6,4,7,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,8,1,4,5,7,6]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,6,1,4,3,5,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,3,4,5,6,7,9,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[8,1]=>2
[2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[9]=>[9]=>1
[1,2,3,4,5,6,7,8,10,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[2,1,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[9,1,2,3,4,5,6,7,10,8]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[7,1,2,3,4,5,6,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[2,8,1,3,4,5,6,7,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[2,10,1,3,4,5,6,7,8,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[8,4,3,6,5,1,7,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,6,3,4,1,7,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,5,4,3,1,7,2]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[1,7,6,5,4,2,3,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,8,6,5,2,7,3,4]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,7,5,4,1,6,3,2]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[7,8,5,4,1,3,6,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,8,5,4,2,1,7,3]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,8,6,2,4,1,7,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,2,6,5,1,7,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,8,6,5,1,7,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,2,1,7,6,4,5,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[4,1,3,7,6,2,5,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[5,1,7,3,6,2,4,8]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,7,5,3,2,4,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,1,6,5,2,4,3,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,6,5,2,3,7,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,6,3,4,5,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,2,8,3,7,4,5,6]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,2,6,3,5,4]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,2,6,4,3,5]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,8,2,4,7,3,5]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,3,2,7,4,6]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,3,8,2,7,5,6]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,8,4,7,5,6]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,8,7,1,6,5,4]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,7,1,6,5,3]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,7,2,1,6,4,3]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,1,3,5,4,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,6,1,5,3,4,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,6,1,5,4,3,2]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,8,7,2,6,5,3,4]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,8,2,5,6,3,4]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,7,1,4,5,3,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,1,4,3,5,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,3,2,1,7,4]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,3,1,4,6,2]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,5,7,3,1,6,4,2]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,4,2,7,3,5]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,4,8,2,7,3,6]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,3,7,1,6,5,2]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,3,8,1,5,6,2]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,1,5,2,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,4,3,1,2,6,5,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,4,3,1,2,5,7,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[1,5,4,2,3,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[8,5,1,4,2,3,7,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,1,4,2,6,3,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,4,3,2,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,6,1,3,4,2,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,2,1,5,3,7,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,6,1,5,4,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,1,4,6,5,8]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,2,1,3,6,5,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,1,3,2,6,4,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,2,4,5,3,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,1,2,5,4,3,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,6,1,2,5,3,7,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,7,2,3,6,4,5,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,1,2,3,6,5,4]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[7,8,1,2,3,5,6,4]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,8,1,2,4,3,7,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,1,3,2,4,7,6]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,2,1,3,5,7,6]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,2,8,1,4,5,7,6]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,3,2,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[5,1,2,4,3,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[6,1,2,3,5,4,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[7,1,2,3,4,6,5,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[8,1,2,3,4,5,7,6]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[6,7,3,8,5,1,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,7,4,5,1,8,3,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,7,6,8,1,2,3]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,8,6,1,2,4]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[3,8,4,5,7,1,2,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,4,8,6,7,1,2,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,6,7,1,8,3,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,2,7,4,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,6,1,7,8,4,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,6,1,8,7,4,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,6,8,1,7,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,4,5,1,6,3,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,4,8,6,2,3,7,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,5,6,8,2,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,6,2,8,4,7,3]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,6,3,4,7,8,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,2,6,8,5,7,3]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,3,2,5,4,6,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,2,3,1,5,6,4,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,8,3,1,5,7,4,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,4,1,6,8,7,5,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,1,6,7,8,5,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,3,1,7,6,8,5,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,7,8,1,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,2,6,4,8,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,3,1,5,8,4,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,2,1,8,5,4,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,2,8,1,5,3,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,8,2,1,4,3,5]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,1,2,8,4,5,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,1,3,4,8,5,2]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,2,7,3,4,6,8,1]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,7,3,4,8,6,2]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,7,8,2,3,6,4]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,8,7,2,3,6,5]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,1,2,7,4,5,6]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,3,7,5,8,6,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,4,5,7,8,6,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,1,8,3,4,7,6,5]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,1,3,4,6,5,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[1,8,2,3,4,5,7,6]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,8,3,4,6,7,5]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,1,6,5,8,7,3]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,6,1,4,8,7,3]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,6,4,1,8,7,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,7,4,8,1,6,3]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,7,4,8,6,1,3]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,7,2,3,8,6,1,4]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,2,3,8,1,6,4]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,2,3,1,8,7,4]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,1,3,8,7,4]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,6,4,2,8,7,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,1,3,2,8,7,4]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,1,2,8,7,4]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,3,2,1,8,7,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,2,8,1,6,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,3,2,8,6,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,3,8,2,1,5,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,3,8,1,2,5,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,3,1,8,2,6,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,1,3,8,2,6,4]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,7,4,8,2,6,3]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,7,4,8,3,6,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,7,4,8,6,3,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,4,8,6,2,3]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,7,1,3,8,6,2,4]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,3,1,8,6,2,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,3,8,1,5,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,8,5,2,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,7,8,3,1,4,2,5]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,1,8,3,5,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,7,8,4,5,2,3]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,7,8,4,5,3,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,7,8,4,3,5,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,7,8,4,2,5,3]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,1,8,3,2,5,4]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,2,1,8,3,6,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,2,8,1,3,5,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,2,8,3,1,5,4]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,2,8,3,5,1,4]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,7,8,4,5,1,3]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,8,4,1,5,3]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,7,8,1,4,5,3]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[5,2,7,1,8,4,6,3]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,1,7,8,5,6,3]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,2,7,8,6,5,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,2,7,8,1,5,4,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,8,5,1,4,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,7,8,5,4,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[6,7,2,8,5,3,1,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,2,1,8,6,3,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,2,8,6,3,4]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,7,2,8,6,4,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,5,7,3,8,6,4,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,8,3,5,4,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,7,8,2,5,4,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,7,1,8,2,5,3,4]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,8,2,4,1,3,5]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,2,4,3,1,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,1,8,5,2,3,4]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,1,7,8,5,2,4,3]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,7,8,5,3,4,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,7,8,5,4,2,3]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,7,1,8,5,3,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,7,8,4,1,3,2,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,5,2,7,4,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,8,4,7,3,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,5,8,7,2,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,6,1,4,8,7,3,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,6,4,8,5,7,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,4,8,6,3,7,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,7,1,8,6,5,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,4,2,7,1,5]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,7,1,4,2,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,1,6,8,2,4]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,8,5,6,7,2,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,2,7,8,5,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,4,2,8,7,5,1]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,3,7,5,2,8,1,4]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,7,4,8,1,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,1,4,8,3,2,6]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,5,1,4,6,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,1,4,6,7,2,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[6,5,8,4,3,7,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,4,2,8,5,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,1,6,2,4,5,3]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,6,7,1,4,5,2]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,8,7,4,1,2,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[4,3,8,7,1,5,6,2]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,6,1,2,5,7,4]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,1,8,7,3,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,4,2,7,3,6,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,6,4,2,8,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,1,5,3,8,2,7]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,6,3,4,7,5,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,6,3,5,4,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,4,3,5,8,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,6,4,5,2,8,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,6,5,3,4,8,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,5,4,3,1,8,2,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,6,5,4,2,7,3,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[8,5,4,1,7,2,6,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,4,1,8,3,2,6]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[1,6,5,2,8,3,4,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,6,5,3,4,8,2,7]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,3,1,8,2,7]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,5,8,4,2,7,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,6,4,7,3,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,5,3,2,6,4,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,3,1,7,2,5,4]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,6,3,7,5,2,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,5,2,6,4,3,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,1,6,2,5,4,3]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,8,1,6,3,2,5,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,1,7,3,5,6,4]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,1,3,7,2,6,5]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,8,5,7,3,6,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,6,8,3,2,4]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,3,1,8,4,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,8,4,5,2,6]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,8,5,3,4,6]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,1,8,4,3,2,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,6,1,7,4,2,5,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,1,2,7,3,4,6,5]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,2,8,3,5,4,6]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,6,1,7,3,5,4]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,1,5,8,3,6,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,4,3,1,6,8,2,7]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[4,7,5,6,8,3,2,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,5,4,8,2,7,3,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,8,7,4,2,3]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[8,6,4,7,5,3,2,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,1,8,3,7,6,2,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,1,7,2,6,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,8,2,4,7,5,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,8,2,6,4,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,2,8,6,3,5,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,8,7,4,5,6,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,8,6,4,3,5,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,7,5,6,3,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,6,3,5,4,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,6,5,2,4,3]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,8,6,5,3,2,4]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,2,8,7,6,3,4,5]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,3,8,7,4,6,2,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,6,8,7,4,2,3]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,8,7,2,5,4,3,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,6,4,5,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,6,5,3,4,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,6,5,4,2,3]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[5,8,6,7,3,4,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,6,7,3,5,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,6,7,4,5,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,7,4,5,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,6,7,4,5,2,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,7,4,6,2,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,7,4,6,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,5,7,3,6,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,6,4,5,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,7,4,5,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,7,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,4,8,5,6,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,8,5,6,1,2]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,2,8,5,6,1,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,8,5,6,2,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,8,5,6,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,8,5,6,1,4]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,3,8,5,6,1,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,4,8,5,6,1,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,7,4,6,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,7,4,5,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,6,4,5,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,6,4,5,2,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,1,7,4,5,2,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,7,4,6,2,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,4,8,5,6,2,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,8,5,6,2,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,5,6,1,7,3,4]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,6,2,7,3,4]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,8,4,6,2,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,7,3,6,2,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,7,3,6,2,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,1,7,3,5,2,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,6,3,5,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,7,3,5,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,7,3,6,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,7,3,6,1,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,3,8,4,6,1,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,8,4,6,1,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,8,4,6,2,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,7,3,6,2,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,7,3,6,1,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,4,7,2,6,1,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,5,7,2,6,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,7,2,6,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,5,7,3,6,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,7,3,6,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,6,7,3,5,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,7,3,5,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,6,7,2,5,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,6,7,2,5,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,2,4,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,5,7,1,4,2,3]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,1,4,2,3]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,6,7,1,5,2,3]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,6,7,1,5,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,8,6,7,3,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,1,8,6,7,3,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,1,8,5,7,3,4]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,8,5,7,3,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,7,1,6,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,7,1,5,2,3]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,4,6,1,5,2,3]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,6,1,5,2,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,7,1,5,2,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,7,1,6,2,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,4,7,1,6,2,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,8,4,7,3,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,1,8,4,7,3,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,6,1,8,4,5]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,6,2,8,4,5]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,6,2,7,3,5]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,6,2,7,3,4]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,5,2,6,3,4]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,5,1,6,3,4]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,5,1,7,3,4]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,6,1,7,3,4]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,6,1,7,3,5]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,6,2,8,4,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,3,6,1,8,4,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9]]=>[9]=>[9]=>1
[1,2,3,4,5,6,8,9,7]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[8,1]=>2
[1,2,3,4,5,7,8,9,6]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[8,1]=>2
[1,2,3,4,6,7,8,9,5]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[8,1]=>2
[1,2,3,5,6,7,8,9,4]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[8,1]=>2
[1,2,4,5,6,7,8,9,3]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[8,1]=>2
[1,3,4,5,6,7,8,9,2]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[8,1]=>2
[1,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[10]=>[10]=>1
[1,2,3,4,5,6,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,2,3,4,5,6,7,9,10,8]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[1,2,3,4,5,6,8,9,10,7]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[1,2,3,4,5,7,8,9,10,6]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[1,2,3,4,6,7,8,9,10,5]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[1,2,3,5,6,7,8,9,10,4]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[1,2,4,5,6,7,8,9,10,3]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[3,2,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8],[2],[9]]=>[8,1]=>[8,1]=>2
[1,3,4,5,6,7,8,9,10,2]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[9,1]=>2
[6,7,4,8,3,5,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,4,5,2,8,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,4,6,2,3,1,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,4,6,3,8,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,4,8,3,6,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,5,3,7,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,6,3,7,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,4,8,3,7,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,7,2,4,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,7,2,8,1,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,8,2,7,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,4,8,2,7,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,6,2,7,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,5,2,7,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,4,5,2,6,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,5,2,3,1,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,6,2,3,1,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,4,8,2,3,1,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,8,2,4,1,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,4,2,8,1,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,5,2,7,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,5,2,8,1,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,8,2,5,1,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,6,2,5,1,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,6,2,4,1,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,5,2,4,1,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,5,2,4,1,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,5,2,6,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,6,2,7,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,6,2,7,1,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,8,2,7,1,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,7,2,8,1,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,6,2,5,1,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,6,2,8,1,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,8,2,6,1,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,4,8,2,6,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,6,2,8,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,6,2,4,1,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,5,2,4,1,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,5,2,8,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,4,8,2,5,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,5,8,2,4,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,5,7,2,3,1,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,4,8,2,3,1,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,8,2,4,1,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,4,2,8,1,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,4,2,6,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,4,2,8,1,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,4,8,2,3,1,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,7,2,3,1,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,7,2,3,1,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,4,6,2,3,1,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,6,2,4,1,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,7,2,4,1,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,7,2,4,1,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,7,2,5,1,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,8,2,5,1,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,5,2,8,1,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,5,2,6,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,7,2,6,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,7,2,8,1,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,8,2,7,1,6]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,5,2,7,1,6]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,4,2,7,1,6]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,4,2,7,1,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,4,2,6,1,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,4,2,5,1,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,4,2,6,1,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,5,2,6,1,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,8,2,6,1,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,6,2,8,1,7]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,5,2,1,8,3,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,8,5,2,1,7,6,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,6,5,2,1,3,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,6,4,2,3,1,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,5,3,1,2,8,7]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,4,6,1,3,2,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,8,1,7,3,2,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,8,1,6,3,5,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,1,6,5,3,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,1,3,7,6,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,5,3,1,7,6,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,4,7,1,3,8,2,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,8,1,7,5,2,3]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,7,2,1,3,4]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[8,5,7,6,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,4,6,3,7,2,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,8,7,4,1,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[2,1,6,8,7,4,3,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,1,7,8,6,4,5,3]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,8,6,4,5,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,8,5,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,6,2,3,1,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,6,3,2,1,4]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[6,8,7,5,3,2,4,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,4,2,3,7,6,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,2,6,5,3,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,2,6,3,5,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,6,2,7,3,1,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,1,8,7,4,2,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,1,8,6,4,5,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,1,6,7,5,2,4]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,6,8,2,5,4]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,6,2,8,1,3,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,7,4,2,8,1,5,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,4,2,7,5,1,3]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,1,8,6,7,5,3,4]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,2,6,7,5,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,6,4,3,7,5,1,2]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[5,8,6,7,3,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,7,5,8,1,3,4,2]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,5,8,1,4,3,2]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,5,7,4,1,3,2]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,4,3,8,1,5,2]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,3,2,6,8,1,5,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,1,7,6,8,3,5,4]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,6,8,1,4,2,3]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,7,8,1,2,4,3]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,3,7,4,6,5,2]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,7,4,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,2,5,4,7,3,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,7,5,4,8,3,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,3,5,4,7,6,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,4,3,8,7,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,3,4,5,7,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,5,3,4,8,6,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,4,3,5,6,8,2]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,3,4,5,6,7,2]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[1,7,2,4,5,6,3,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,3,2,7,5,1,8,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,7,2,5,6,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,8,2,4,7,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,2,1,4,3,7,6]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,5,2,8,4,1,3,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[5,6,2,1,4,8,3,7]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,1,8,5,2,4,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,2,6,3,5,4,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,1,2,8,6,5,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,1,2,6,8,5,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,8,1,6,3,2,4,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,3,8,5,2,1,4,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[8,3,1,5,2,4,7,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[3,8,2,6,1,5,7,4]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,6,7,2,1,5,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,5,6,4,2,1,7,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,2,5,8,3,1,6,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,7,5,6,3,2,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,1,2,3,8,5,7,4]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,2,3,6,5,8,4]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,1,3,8,6,4,5]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[1,5,7,3,2,4,6,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[5,2,7,3,1,8,4,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,4,1,3,7,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,2,6,3,4,1,5]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,6,3,2,7,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,8,6,4,2,7,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,7,4,3,2,5]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,5,8,7,2,4,1,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,3,7,8,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[2,4,1,3,8,7,5,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,8,3,1,7,4,6]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,3,7,2,4,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[2,8,1,3,6,4,7,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,2,3,4,1,5,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,8,3,2,4,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9]=>[9]=>1
[8,9,7,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,7]=>[7,2]=>2
[8,7,9,6,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[8,7,6,5,4,3,2,9,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[8,1]=>[8,1]=>2
[8,7,6,5,4,3,2,1,9]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[9]=>[9]=>1
[9,10,8,7,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[7,8,9,6,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[9,8,10,7,6,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[8,6,7,9,5,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[8,7,6,5,4,2,3,9,1]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[8,1]=>[8,1]=>2
[8,7,6,5,4,3,1,2,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[9,8,7,6,5,4,3,2,10,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[9,1]=>[9,1]=>2
[9,8,7,6,5,4,3,2,1,10]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[1,4,2,7,8,6,3,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,2,4,8,5,3,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,2,4,7,5,3,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,8,5,2,4,6]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,3,2,8,6,4,5]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,5,7,8,6,1,3]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[7,2,3,1,8,5,6,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,5,1,7,3,4,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,2,1,8,3,4,7,5]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,8,3,5,1,7,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,4,8,5,7,1,3]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,4,8,5,7,2]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,6,4,7,5,8,2]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,4,7,5,8,1,3]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,1,3,7,8,4,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[7,8,2,1,4,3,5,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[7,6,4,2,3,1,8,5]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,7,2,3,1,6,8,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,4,2,6,8,1,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[1,7,5,3,4,6,8,2]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,2,5,4,6,7,1,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,6,3,1,8,7,4]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,6,4,3,1,7,5]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,2,7,4,1,3,5,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[1,2,8,4,3,5,6,7]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,7,4,2,3,5,6,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[6,8,4,1,3,2,5,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,7,4,3,2,5,6]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,6,3,8,2,4,7,5]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,8,1,2,7,4,6]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,3,2,6,4,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,1,2,6,4,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,4,2,6,3,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,5,8,2,4,6,3,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,4,2,7,3,6]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,6,2,8,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,1,6,7,2,4,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,3,6,1,2,8,4,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,2,7,8,4,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,5,3,8,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,4,1,2,5,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,3,1,4,2,7,5,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[1,8,3,2,4,5,6,7]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[8,6,3,2,4,1,7,5]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,5,3,2,6,7,1,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[4,5,2,6,8,1,7,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,5,6,7,8,1,3]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[5,2,3,6,7,1,8,4]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,2,3,4,1,7,8,5]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,2,3,1,4,5,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,6,1,4,3,2,5,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,3,1,6,5,2,4,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,7,5,1,8,2,4,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[4,1,5,2,8,7,3,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,2,4,6,5,3,7]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[8,1,2,5,4,6,3,7]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,6,5,1,3,4,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,3,1,6,2,5,4,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,6,4,5,3,7]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,5,6,4,3,7]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[8,1,2,6,5,4,3,7]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,7,5,4,2,8,3,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,1,4,8,2,7,3,6]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,6,8,2,7,3,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,7,6,2,8,3,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,7,2,8,3,6]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,7,4,5,2,8,3,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,5,1,2,8,4,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,7,2,8,1,3,4,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,2,8,7,1,3,4,6]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[4,1,5,8,2,7,3,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,6,2,8,7,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,2,8,6,7,3,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,2,6,4,8,7,5]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,7,6,3,4,8,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,7,4,6,8,5]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,7,2,6,8,3,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,6,8,5,7,4]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,4,2,7,8,3,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,4,2,7,6,8,3,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,6,8,7,3,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,1,2,8,4,6,7,5]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,7,6,4,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,3,7,1,8,2,4,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,7,4,3,2,5,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,8,7,2,1,3,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[1,8,7,3,4,2,5,6]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,7,8,2,6,4,5]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,2,7,8,3,6,5]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,8,1,3,4,7,6]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,6,3,4,7,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,4,2,6,8,3,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,3,7,8,5,6,4]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,7,5,8,6,4]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,4,2,7,3,8,6,5]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,7,2,8,6,4,5]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,7,8,3,4,6,5]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,8,7,5,6,4]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[10,1,2,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[10,9,1,2,3,4,5,6,7,8]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[8,1,2,3,4,5,6,9,10,7]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[2,9,10,1,3,4,5,6,7,8]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]=>[7,3]=>2
[4,7,8,5,6,2,1,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,8,4,2,6,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,4,2,5,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,7,2,1,5,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,6,3,8,2,1,5,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,7,8,3,2,1,5,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,3,2,1,6,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,7,8,4,3,5,6,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,8,4,2,5,1,6]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,8,3,2,1,5,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[5,7,8,3,2,1,4,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[7,6,3,8,2,1,4,5]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,6,3,7,2,1,4,5]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,6,3,8,2,1,4,7]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,6,4,8,2,5,1,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,4,8,3,5,7,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,4,7,3,5,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,4,7,2,5,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,7,2,1,5,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,6,3,7,2,1,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,4,3,2,1,6,5,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[6,4,3,2,1,7,5,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[4,5,3,2,7,1,6,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,5,4,2,8,6,1,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,3,2,1,8,5,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,4,3,2,1,8,5,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,4,3,2,1,7,5,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,4,3,2,1,7,6,5]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[7,4,3,2,1,8,6,5]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[6,4,3,2,1,8,7,5]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[5,6,3,8,2,1,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,3,2,8,1,6,4]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,5,4,2,7,6,1,3]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[7,5,4,2,8,6,1,3]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[6,5,4,2,8,7,1,3]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[4,6,5,8,7,2,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,6,5,7,8,3,4,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,4,2,7,8,1,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,4,2,6,7,1,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,3,2,6,1,7,4]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,5,3,2,6,1,8,4]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,6,3,7,2,1,8,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,3,7,2,1,8,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,4,7,2,8,1,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,4,7,3,8,5,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,4,2,7,8,1,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,5,3,2,7,1,8,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,3,2,1,6,8,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,4,3,2,1,6,7,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,4,3,2,1,5,7,6]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[7,4,3,2,1,5,8,6]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[6,4,3,2,1,5,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[3,5,4,2,6,8,1,7]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,3,7,2,6,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,4,2,6,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,7,5,1,4,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,3,8,1,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,6,4,8,5,1,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,2,4,1,7,6,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,5,8,3,1,6,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,1,5,4,2,8,6,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,1,5,8,3,2,6,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,3,8,5,2,1,6,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,7,3,5,2,1,6,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,3,2,7,5,1,6,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[4,3,6,2,5,1,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,3,2,5,1,7,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,3,1,5,7,2,6,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[4,3,6,1,5,2,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,3,1,5,2,7,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[5,3,6,4,1,2,7,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[4,3,6,1,7,2,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,1,3,7,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,6,4,1,2,7,5,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,6,3,1,7,2,5,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,7,1,3,4,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,5,2,7,3,1,6,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,2,1,7,3,5,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[3,2,6,1,4,7,5,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,7,4,6,1,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,4,8,5,1,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,1,4,6,8,2,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[3,2,6,1,5,7,4,8]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,2,1,5,7,4,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,4,2,1,5,3,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[4,2,6,1,5,3,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,1,7,5,3,6,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[7,4,1,5,6,2,3,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,3,1,5,2,6,4,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,1,2,7,4,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,2,6,4,1,3,7,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[3,6,5,1,2,7,4,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[6,5,2,1,4,7,8,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,5,3,1,4,7,2,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[2,3,1,8,5,4,7,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,1,5,8,3,7,6]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,1,5,3,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,5,1,2,8,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,1,8,2,7,6]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,5,8,2,1,7,6]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,2,8,1,7,6]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,6,2,1,7,8,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,4,6,2,1,7,5,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,2,7,1,4,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,2,7,1,8,4]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,6,2,7,8,1,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,6,3,7,2,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,6,8,2,7,5,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,2,8,7,5,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,2,7,8,4,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,2,7,4,1,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,6,7,2,8,3,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,8,7,2,4,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,8,6,7,3,4,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,8,6,7,3,1,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,8,7,2,1,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,5,6,7,2,1,8,3]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,1,8,6,7,4,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,2,6,7,5,4]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,1,6,7,8,4,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,1,6,7,4,8,3]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,1,6,7,4,3,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,1,7,4,2,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,1,7,4,8,2]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,6,8,1,7,5,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,8,6,1,7,5,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,8,7,1,4,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,6,7,8,1,3,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,5,6,7,1,3,8,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,6,7,1,3,2,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,6,7,3,1,8,2]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,5,6,8,7,4,1,2]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,5,8,6,7,4,1,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,5,6,7,4,3,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,8,6,7,4,3,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,5,3,7,1,6,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,3,7,1,6,5]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,2,4,3,7,1,6]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,5,6,1,8,3,7]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,6,1,7,3,8]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,7,3,2,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[6,1,5,8,3,2,4,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[3,8,2,4,7,1,5,6]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,8,2,4,7,1,5]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,5,6,7,1,8,2]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,7,1,5,6,8,2,4]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,5,8,2,4,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,3,2,4,6,1,5,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,3,2,4,6,1,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,2,5,1,7,4,6,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,1,8,4,6,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,1,7,8,4,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,8,3,2,4,6,1,5]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,1,5,7,8,3,2,4]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,2,5,6,1,7,8,3]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,7,6,1,8,3,4,2]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,6,1,7,3,4,2]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,5,8,7,3,2,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[8,7,3,2,4,6,1,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[3,2,5,1,8,7,4,6]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,1,6,4,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,2,4,1,8,7,5,6]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,1,6,8,7,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,5,1,7,4,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,5,1,8,4,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,5,1,7,8,4,2,3]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[3,2,5,1,6,7,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,2,4,1,8,5,6,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,2,4,1,7,5,6,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,2,4,1,6,8,5,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,1,8,5,7,6]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,2,4,7,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[3,2,5,1,8,4,7,6]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,5,1,6,7,4,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,5,1,7,4,2,3,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,5,1,8,4,2,3,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,4,2,3,7,5,1,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[4,2,6,1,8,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,1,8,3,7,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,6,1,7,3,5,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,1,8,4,7,3]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,2,3,8,5,1,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,5,1,6,4,2,3,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,5,1,6,4,2,3,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,2,5,1,7,6,4,8]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,1,8,6,4,7]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,2,4,8,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,6,1,5,7,3,2,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[4,2,6,1,8,5,7,3]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,6,1,7,3,4,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,8,5,1,7,4,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,1,6,7,4,2,3]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[3,2,5,1,8,6,7,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,4,1,8,6,5,7]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,4,1,5,8,6,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,1,7,8,6,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,5,1,6,4,2,3]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,5,1,7,6,4,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,1,8,6,4,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,5,1,6,4,2,3]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[3,2,5,1,8,7,6,4]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,5,7,3,1,8,4,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,3,7,1,8,5,2]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,7,5,1,8,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,6,1,7,5,3,8]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,7,4,1,6,3,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,4,1,6,8,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,7,3,6,1,8,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,7,8,3,1,6,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,3,7,5,1,8,6,2]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,3,8,5,1,7,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,8,4,3,6,1,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,8,3,6,1,7,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,3,6,7,1,8,2]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,5,4,6,1,7,3,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,5,8,1,6,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,4,6,8,1,7,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,8,4,1,6,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,2,1,8,5,7,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,1,7,5,8,6,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,1,7,5,3,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,4,1,8,5,3,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,8,2,1,6,3,7]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,5,8,4,1,6,3,7]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,6,1,8,4,7]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,8,3,2,6,1,5,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,8,1,6,4,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,1,6,8,5,4,7]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[3,2,7,1,5,4,8,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,1,5,8,6,4]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,2,5,1,6,7,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,3,2,6,7,1,5]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,3,8,2,6,7,1,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,2,6,7,8,1,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[4,3,2,6,7,1,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[4,3,7,2,6,8,1,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,8,2,6,1,5]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,7,4,8,1,6,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,5,7,8,1,6,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,5,7,1,6,8,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,7,1,6,4,8]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,7,1,5,4,8]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,7,1,5,8,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,3,2,7,8,1,5,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,2,6,1,7,8,5,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,1,7,8,4,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[2,1,7,5,3,8,6,4]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,1,8,5,3,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,2,7,1,4,8,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,3,2,1,4,7,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,3,2,1,4,7,5,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[3,5,2,1,7,4,6,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,1,7,8,4,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,2,1,7,3,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,6,2,1,8,3,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,1,7,3,8,6,5]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,7,1,4,8,6,5]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,8,2,1,7,4,6]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,3,7,2,1,5,6]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,3,7,2,8,1,5,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,7,2,1,5,6,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[4,8,3,2,7,1,5,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,8,1,7,4,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,2,8,1,4,7,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,4,7,5,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,1,8,4,6,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[4,8,3,2,1,5,6,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[4,3,8,2,1,5,6,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[1,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,7]=>[7,2]=>2
[1,10,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[6,2,3,1,5,4,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,5,2,3,1,7,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,2,5,3,4,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,5,3,4,1,7,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,5,3,4,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,5,2,4,3,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,5,1,3,2,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,5,3,4,2,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,5,1,4,2,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,2,4,1,7,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,5,6,2,4,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,2,4,1,6,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,1,4,2,7,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,5,3,4,2,7,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,5,1,3,2,7,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,4,5,3,7,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,4,5,1,3,2]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,1,5,3,4,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,3,5,1,4,2]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,5,6,1,4,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,3,6,1,4,2]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,4,6,2,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,4,6,1,5,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,1,6,4,5,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,3,6,4,5,2]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,5,6,3,4,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,5,6,1,3,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,4,7,5,6,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,3,4,2,6,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,3,6,2,5,4]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,1,6,2,5,4]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,2,6,4,5,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,3,6,4,5,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,3,6,1,5,4]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,1,6,3,5,4]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,2,4,3,6,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,3,2,7,4,6,5]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,3,7,4,6,5]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,5,2,4,3,7,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,1,4,3,6,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,3,4,1,6,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,5,6,3,4,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,5,6,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,2,3,1,6,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,3,1,7,4,6,5]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,3,1,5,4,7,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,3,1,8,5,7,6]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,3,2,8,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,2,3,1,5,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,3,1,7,5,6,4]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,2,6,3,4,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,2,6,1,4,3]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,5,6,1,4,3]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,2,5,1,4,3]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,1,5,2,4,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,1,3,2,5,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,6,7,3,5,4]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,3,7,5,6,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,3,2,7,5,6,4]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,5,6,2,4,3]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,2,6,4,5,3]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,1,6,4,5,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,4,6,1,5,3]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,4,6,3,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,2,6,3,5,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,2,6,1,5,3]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,1,6,2,5,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,4,6,2,5,3]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,1,6,2,4,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,5,7,3,6,4]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,4,6,1,3,2]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,1,6,3,4,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,4,6,3,5,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,1,6,3,5,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,3,6,1,5,2]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,8,3,6,1,7,5]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,1,3,2,7,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,8,6,3,2,7,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,8,7,3,1,2,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[1,5,8,7,3,6,2,4]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,8,4,6,5,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,8,4,1,5,3]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,2,8,4,5,7,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,1,8,4,5,7,3]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,6,1,5,7,3]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,1,8,4,5,7,2]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,6,8,4,5,7,2]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,6,8,4,5,7,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,8,4,1,5,2]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,7,8,4,6,5,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,7,8,2,4,6,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,7,8,2,4,6,3]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,7,8,4,2,5,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,1,8,4,2,5,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,6,8,7,3,2,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,8,3,7,1,6,5,4]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,8,7,3,6,1,4]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,1,8,4,6,5,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,7,8,4,6,5,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,7,8,1,4,6,3]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,7,8,5,4,6,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,1,3,8,5,6,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[7,2,5,8,3,4,6,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,8,5,4,3,1,7]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,8,3,5,4,1,6,7]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,8,4,5,3,1,6,7]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,4,8,5,2,3,1,7]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,8,2,4,6,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,1,2,8,5,6,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[3,4,2,1,8,5,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,7,6,8,4,3,5,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,1,8,3,4,6,2]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,5,8,1,4,6,2]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,5,8,3,4,6,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,8,5,4,3,2,7]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,6,8,5,1,3,2,7]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,1,4,3,2,7]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,6,3,4,2,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,3,6,5,1,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,4,1,5,6,3,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,1,8,3,5,6,2,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,4,1,3,2,7]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,1,5,3,2,7]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,8,4,5,3,2,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,8,5,4,6,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,1,8,5,4,6,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,3,8,4,6,5,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,3,8,4,6,5,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,8,4,3,6,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,7,4,1,6,5,3]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,4,3,1,6,7]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[6,5,8,4,2,3,1,7]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,3,2,8,5,6,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,4,3,2,8,5,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,3,2,8,5,4,6,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,2,5,3,1,7]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,4,3,5,1,6,7]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,3,4,5,1,6,7]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,2,8,4,5,3,1,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,3,8,5,4,6,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,3,1,8,5,6,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,2,1,4,8,5,6,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[5,1,3,2,4,8,6,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,8,1,5,3,4,7,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,8,4,5,3,7,6]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,2,8,5,3,6,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,8,4,2,5,3,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[8,1,5,3,2,4,6,7]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[3,8,1,5,2,4,6,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,5,1,4,8,2,6,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,5,2,8,4,3,6,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,2,8,5,4,3,6,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,2,5,4,3,8,6,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,8,5,3,7,6]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,2,7,4,8,5,3,6]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,2,7,8,4,3,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,2,7,4,8,3,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,5,1,4,7,2,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,1,5,4,7,3,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,8,5,7,4,3,6]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,4,8,7,5,3,6]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,8,1,4,3,7,6,5]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,2,8,7,4,3,5]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,4,1,2,8,7,3,5]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[3,6,4,8,1,7,2,5]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,1,4,2,8,3,5]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,1,6,2,8,4,3,5]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,2,8,4,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,1,4,2,8,3,5]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,7,1,4,8,2,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,1,5,2,4,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,2,8,5,3,4,6]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[1,7,2,8,4,5,3,6]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,7,8,5,3,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,2,8,4,3,7,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,1,2,8,3,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,1,3,2,4,8,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,7,1,3,2,4,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,7,3,5,8,4,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,5,8,3,4,6]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,8,1,3,7,2,4,6]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,2,5,8,7,3,4,6]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[1,2,5,8,3,7,4,6]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,8,1,7,3,5,4,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,1,3,2,4,7,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,2,8,1,7,3,6,5]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,1,7,4,3,6,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,2,8,4,3,6,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,8,4,7,5,3,6]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,7,4,5,3,6]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,1,7,5,3,4,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,3,7,1,5,2,4,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,8,6,1,4,7,2,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,1,4,2,7,3,5]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,6,2,7,4,3,5]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,2,8,6,4,3,5]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,1,2,8,6,3,5]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[3,7,4,8,1,6,2,5]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,8,7,1,6,2,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,1,7,6,3,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,1,7,6,4,3,5]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,3,4,1,5,2,6]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,4,1,6,2,5]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,4,1,7,2,5]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,4,1,8,2,5]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,4,1,8,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,4,1,7,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,4,1,6,2,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,4,1,5,2,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,4,1,5,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,4,1,6,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,8,3,4,1,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,7,3,4,1,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,2,8,3,5,1,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,5,1,6,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,5,1,6,2,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,5,1,7,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,5,1,8,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,3,1,7,4,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,4,1,8,3,7]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,4,1,7,3,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,2,5,1,7,3,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,2,5,1,8,3,7]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,8,3,7,2,6]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,7,3,8,2,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,2,7,3,8,1,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,7,3,8,1,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,7,4,8,1,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,8,4,7,1,2]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,8,4,7,1,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,8,3,7,1,4]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,2,8,3,7,1,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,7,3,6,2,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,8,3,6,2,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[9,2,1,3,4,5,6,7,8]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[10,2,1,3,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[9,2,3,1,4,5,6,7,8]=>[[1,3,5,6,7,8,9],[2],[4]]=>[3,6]=>[6,3]=>2
[4,2,3,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8],[2],[9]]=>[8,1]=>[8,1]=>2
[3,2,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[9,1]=>[9,1]=>2
[6,5,3,2,1,4,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[4,6,3,5,2,1,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,3,5,2,4,1,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,8,2,4,5,7,3,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,2,4,5,3,1,6]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[3,6,1,4,5,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,7,4,5,2,1,6]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,4,5,7,2,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,4,3,6,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,4,3,6,1,5]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,7,4,3,6,2,5]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,3,5,1,4,2,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,8,5,7,4,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,3,5,1,7,4,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,8,4,7,6,3,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,4,7,6,3,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,1,5,6,7,2]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,1,3,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,4,1,6,3,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,3,6,1,4,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,3,6,1,2,7,5]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,7,4,1,6,2,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,2,5,6,7,4]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,7,1,4,2,6,3,5]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,6,3,1,2,4,7,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,1,7,4,5,2,3,6]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,8,7,4,5,1,3,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,2,4,1,6,3,5]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,8,3,6,2,4,7,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,6,3,2,1,4,7,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,7,3,5,2,1,4,6]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,8,3,6,2,1,7,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,7,4,2,6,1,3]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,6,8,4,5,7,1,3]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,4,5,7,2,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,5,1,7,2,4]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,5,8,3,6,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,3,6,1,2,7,4]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,8,2,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,8,1,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,2,1,5,6,7,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,4,8,2,5,6,7,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,1,4,7,6,2,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,3,1,6,2,7,4]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,3,8,6,1,7,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,1,8,5,6,7,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,6,8,10,1,3,5,7,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,4,6,9,10,1,3,5,7,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,4,7,8,10,1,3,5,6,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,4,7,9,10,1,3,5,6,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,4,8,9,10,1,3,5,6,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,5,6,8,10,1,3,4,7,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,5,6,9,10,1,3,4,7,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,5,7,8,10,1,3,4,6,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,5,7,9,10,1,3,4,6,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,5,8,9,10,1,3,4,6,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,6,7,8,10,1,3,4,5,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,6,7,9,10,1,3,4,5,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,6,8,9,10,1,3,4,5,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,7,8,9,10,1,3,4,5,6]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,4,6,8,10,1,2,5,7,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,4,6,9,10,1,2,5,7,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,4,7,8,10,1,2,5,6,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,4,7,9,10,1,2,5,6,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,4,8,9,10,1,2,5,6,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,5,6,8,10,1,2,4,7,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,5,6,9,10,1,2,4,7,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,5,7,8,10,1,2,4,6,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,5,7,9,10,1,2,4,6,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,5,8,9,10,1,2,4,6,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,6,7,8,10,1,2,4,5,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,6,7,9,10,1,2,4,5,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,6,8,9,10,1,2,4,5,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[3,7,8,9,10,1,2,4,5,6]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,5,6,8,10,1,2,3,7,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,5,6,9,10,1,2,3,7,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,5,7,8,10,1,2,3,6,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,5,7,9,10,1,2,3,6,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,5,8,9,10,1,2,3,6,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,6,7,8,10,1,2,3,5,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,6,7,9,10,1,2,3,5,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,6,8,9,10,1,2,3,5,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[4,7,8,9,10,1,2,3,5,6]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[5,6,7,8,10,1,2,3,4,9]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[5,6,7,9,10,1,2,3,4,8]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[5,6,8,9,10,1,2,3,4,7]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[5,7,8,9,10,1,2,3,4,6]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[5,5]=>2
[2,4,6,8,10,12,1,3,5,7,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,6,8,11,12,1,3,5,7,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,6,9,10,12,1,3,5,7,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,6,9,11,12,1,3,5,7,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,6,10,11,12,1,3,5,7,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,7,8,10,12,1,3,5,6,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,7,8,11,12,1,3,5,6,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,7,9,10,12,1,3,5,6,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,7,9,11,12,1,3,5,6,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,7,10,11,12,1,3,5,6,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,8,9,10,12,1,3,5,6,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,8,9,11,12,1,3,5,6,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,8,10,11,12,1,3,5,6,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,4,9,10,11,12,1,3,5,6,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,6,8,10,12,1,3,4,7,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,6,8,11,12,1,3,4,7,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,6,9,10,12,1,3,4,7,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,6,9,11,12,1,3,4,7,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,6,10,11,12,1,3,4,7,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,7,8,10,12,1,3,4,6,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,7,8,11,12,1,3,4,6,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,7,9,10,12,1,3,4,6,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,7,9,11,12,1,3,4,6,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,7,10,11,12,1,3,4,6,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,8,9,10,12,1,3,4,6,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,8,9,11,12,1,3,4,6,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,8,10,11,12,1,3,4,6,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,5,9,10,11,12,1,3,4,6,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,7,8,10,12,1,3,4,5,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,7,8,11,12,1,3,4,5,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,7,9,10,12,1,3,4,5,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,7,9,11,12,1,3,4,5,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,7,10,11,12,1,3,4,5,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,8,9,10,12,1,3,4,5,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,8,9,11,12,1,3,4,5,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,8,10,11,12,1,3,4,5,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,6,9,10,11,12,1,3,4,5,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,7,8,9,10,12,1,3,4,5,6,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,7,8,9,11,12,1,3,4,5,6,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,7,8,10,11,12,1,3,4,5,6,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,7,9,10,11,12,1,3,4,5,6,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[2,8,9,10,11,12,1,3,4,5,6,7]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,6,8,10,12,1,2,5,7,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,6,8,11,12,1,2,5,7,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,6,9,10,12,1,2,5,7,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,6,9,11,12,1,2,5,7,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,6,10,11,12,1,2,5,7,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,7,8,10,12,1,2,5,6,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,7,8,11,12,1,2,5,6,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,7,9,10,12,1,2,5,6,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,7,9,11,12,1,2,5,6,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,7,10,11,12,1,2,5,6,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,8,9,10,12,1,2,5,6,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,8,9,11,12,1,2,5,6,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,8,10,11,12,1,2,5,6,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,4,9,10,11,12,1,2,5,6,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,6,8,10,12,1,2,4,7,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,6,8,11,12,1,2,4,7,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,6,9,10,12,1,2,4,7,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,6,9,11,12,1,2,4,7,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,6,10,11,12,1,2,4,7,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,7,8,10,12,1,2,4,6,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,7,8,11,12,1,2,4,6,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,7,9,10,12,1,2,4,6,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,7,9,11,12,1,2,4,6,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,7,10,11,12,1,2,4,6,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,8,9,10,12,1,2,4,6,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,8,9,11,12,1,2,4,6,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,8,10,11,12,1,2,4,6,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,5,9,10,11,12,1,2,4,6,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,7,8,10,12,1,2,4,5,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,7,8,11,12,1,2,4,5,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,7,9,10,12,1,2,4,5,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,7,9,11,12,1,2,4,5,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,7,10,11,12,1,2,4,5,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,8,9,10,12,1,2,4,5,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,8,9,11,12,1,2,4,5,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,8,10,11,12,1,2,4,5,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,6,9,10,11,12,1,2,4,5,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,7,8,9,10,12,1,2,4,5,6,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,7,8,9,11,12,1,2,4,5,6,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,7,8,10,11,12,1,2,4,5,6,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,7,9,10,11,12,1,2,4,5,6,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[3,8,9,10,11,12,1,2,4,5,6,7]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,6,8,10,12,1,2,3,7,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,6,8,11,12,1,2,3,7,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,6,9,10,12,1,2,3,7,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,6,9,11,12,1,2,3,7,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,6,10,11,12,1,2,3,7,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,7,8,10,12,1,2,3,6,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,7,8,11,12,1,2,3,6,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,7,9,10,12,1,2,3,6,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,7,9,11,12,1,2,3,6,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,7,10,11,12,1,2,3,6,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,8,9,10,12,1,2,3,6,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,8,9,11,12,1,2,3,6,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,8,10,11,12,1,2,3,6,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,9,10,11,12,1,2,3,6,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,7,8,10,12,1,2,3,5,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,7,8,11,12,1,2,3,5,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,7,9,10,12,1,2,3,5,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,7,9,11,12,1,2,3,5,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,7,10,11,12,1,2,3,5,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,8,9,10,12,1,2,3,5,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,8,9,11,12,1,2,3,5,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,8,10,11,12,1,2,3,5,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,6,9,10,11,12,1,2,3,5,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,7,8,9,10,12,1,2,3,5,6,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,7,8,9,11,12,1,2,3,5,6,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,7,8,10,11,12,1,2,3,5,6,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,7,9,10,11,12,1,2,3,5,6,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,8,9,10,11,12,1,2,3,5,6,7]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,7,8,10,12,1,2,3,4,9,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,7,8,11,12,1,2,3,4,9,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,7,9,10,12,1,2,3,4,8,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,7,9,11,12,1,2,3,4,8,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,7,10,11,12,1,2,3,4,8,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,8,9,10,12,1,2,3,4,7,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,8,9,11,12,1,2,3,4,7,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,8,10,11,12,1,2,3,4,7,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,6,9,10,11,12,1,2,3,4,7,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,7,8,9,10,12,1,2,3,4,6,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,7,8,9,11,12,1,2,3,4,6,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,7,8,10,11,12,1,2,3,4,6,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,7,9,10,11,12,1,2,3,4,6,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[5,8,9,10,11,12,1,2,3,4,6,7]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[6,7,8,9,10,12,1,2,3,4,5,11]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[6,7,8,9,11,12,1,2,3,4,5,10]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[6,7,8,10,11,12,1,2,3,4,5,9]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[6,7,9,10,11,12,1,2,3,4,5,8]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[6,8,9,10,11,12,1,2,3,4,5,7]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[7,8,9,10,11,12,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[6,6]=>2
[4,5,7,6,2,3,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,2,6,4,8,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,7,3,6,4,8,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,7,3,6,8,4,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,3,7,6,1,5,2]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,2,3,5,4,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,7,3,6,4,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,4,7,6,1,5,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,4,7,1,6,5,3]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,4,7,6,8,5,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,3,7,6,8,5,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,7,3,6,8,4,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,1,3,5,8,4,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,3,6,1,4,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,7,6,1,5,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,4,7,6,1,5,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,7,1,6,5,3]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,4,7,2,6,5,3]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,2,7,6,5,4]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,8,3,1,7,6,5,4]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,2,1,7,6,5,4]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,1,2,8,5,4,3]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,2,3,1,7,6,5,4]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,3,2,1,7,6,5,4]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[3,4,1,7,6,8,5,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,7,8,6,5,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,4,2,7,1,6,5,3]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,2,1,6,4,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,7,2,8,6,4,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,7,1,8,6,4,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,7,1,6,8,4,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,4,5,8,1,3,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,7,6,8,1,3,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,7,8,1,6,4,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,7,8,2,6,4,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,1,2,6,4,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,1,7,2,6,5,3]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,4,8,7,2,6,5,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,8,7,6,1,5,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,8,7,6,1,5,2]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,7,8,6,1,4,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,2,8,1,5,4,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,7,8,1,6,4,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,8,7,1,6,5,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,1,7,6,5,4]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,3,8,2,7,6,5,4]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,3,1,2,7,6,5,4]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,2,1,3,7,6,5,4]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,8,3,7,6,5,4]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,8,3,7,6,5,4]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,8,7,2,6,5,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,7,8,2,6,4,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,7,1,8,2,5,4,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,7,1,2,6,4,3]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,7,2,6,5,3]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,1,2,7,6,5,4]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,1,3,7,6,5,4]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,3,7,6,5,4]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,1,2,3,7,6,5,4]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,1,4,5,6,7,8,9,10,2]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[10,1,4,5,6,7,8,9,2,3]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[6,7,1,8,4,5,2,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,5,8,2,6,4]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,1,5,8,3,6,4]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,5,1,8,3,7,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,5,1,8,2,7,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,5,1,8,7,2,3]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,4,1,8,7,2,3]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,4,5,7,6,2,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[6,4,5,1,8,7,2,3]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,6,1,8,7,2,3]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,6,1,8,7,2,3]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,1,8,2,7,4]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,6,1,8,3,7,4]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,6,1,3,8,7,5]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,1,2,8,7,5]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,1,2,8,7,5]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,1,8,2,7,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,1,5,8,2,6,4]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,3,5,7,2,6,4]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,2,5,7,3,6,4]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,1,5,8,3,6,4]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,5,1,8,3,7,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,1,3,8,7,5]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,6,1,4,8,7,5]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,5,3,1,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,1,3,8,7,5]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,1,4,3,8,6,5]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,4,3,7,6,5]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,4,2,7,6,5]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,1,4,2,8,6,5]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,1,2,8,7,5]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,3,1,2,8,7,5]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,4,1,2,8,7,5]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,4,1,3,8,7,5]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,1,4,3,8,6,5]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,4,2,8,6,5]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,3,2,8,6,5]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,6,7,2,3,5,4]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,7,1,2,3,8,6,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,2,4,8,6,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,1,3,4,8,6,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,3,1,4,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,2,1,4,8,7,5]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,2,1,8,3,7,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,2,1,8,3,7,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,1,5,2,7,3,6,4]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,2,3,7,6,5]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,1,2,3,8,6,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[6,4,2,1,3,8,7,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[5,4,2,3,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,5,2,4,1,8,7,6]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,2,1,4,8,7,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,3,1,2,4,8,6,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[8,1,3,2,4,7,6,5]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,3,4,7,6,5]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[7,2,1,3,4,8,6,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[6,2,3,1,4,8,7,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,3,6,1,5,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,6,5,8,1,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,6,3,5,8,7,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,3,5,8,1,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,1,5,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,5,3,1,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,2,6,5,1,8,7,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,5,8,1,7,3]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,5,8,1,3,7]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,5,8,3,1,7]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,1,5,8,3,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,6,5,8,3,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,4,6,5,8,3,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,1,6,5,8,7,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,6,1,5,8,7,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,5,8,3,7,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,4,3,8,7,5,1]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,2,6,8,5,3,7,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,8,1,5,7,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,1,8,5,7,3]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,1,6,8,5,7,3]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,4,6,8,5,7,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,4,6,8,5,3,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[2,4,1,6,8,5,3,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,6,1,8,5,3,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,8,1,5,3,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,8,5,1,3,7]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[2,4,6,8,3,5,7,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,8,3,5,1,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,8,3,1,5,7]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,4,6,3,1,8,5,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,3,8,1,5,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,3,8,5,1,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,3,8,5,7,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,3,6,8,5,7,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,6,8,5,1,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,6,8,1,5,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,1,6,8,5,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,4,1,3,6,8,7,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,3,6,1,8,7,5]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,6,8,1,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,5,2,8,7,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,6,3,8,1,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,4,6,8,3,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,1,6,8,3,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,6,1,8,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,6,8,1,3,7,5]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,8,3,1,7,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,2,8,5,7,1,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,4,8,7,1,3,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[6,4,2,8,7,5,3,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,6,4,8,1,7,5,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,4,1,8,7,5,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,6,1,4,8,7,5,3]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,1,6,4,8,7,5,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,4,8,7,3,5]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,4,2,8,7,5,1,3]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[1,6,4,7,3,8,2,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,7,4,5,8,2,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,7,3,6,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,6,3,4,8,2,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,3,7,2,4,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,6,3,8,2,4,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,4,8,3,5,6]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,7,3,4,8,2,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,4,5,8,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,7,3,8,2,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,7,5,8,2,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[2,8,6,3,7,1,4,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,1,3,7,2,4,5]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,2,1,7,3,4,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,2,1,8,3,4,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,7,1,3,8,2,4,5]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,2,4,8,3,6,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[4,3,6,1,5,8,2,7]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,1,4,5,8,3,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,1,3,4,8,2,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[1,6,2,4,8,3,5,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,5,1,3,7,2,4,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[1,5,3,2,8,4,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,4,2,1,5,8,3,7]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[2,5,3,4,1,8,6,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,5,2,1,8,6,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,4,8,7,1,3,5]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,8,7,2,3,5]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[2,7,8,3,6,1,4,5]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,2,8,7,1,5,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[5,2,4,8,7,1,3,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[6,2,8,3,7,1,4,5]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,4,8,7,2,3,6]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[4,8,2,5,1,3,7,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,2,5,1,3,8,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,2,1,5,4,8,6]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,2,1,5,4,7,6]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,2,1,5,4,6,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,3,2,1,6,4,5,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,4,2,5,1,6,3,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,3,2,1,5,6,4,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,3,2,1,4,6,5,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[3,8,2,1,4,5,7,6]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,2,1,4,5,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,2,7,1,4,6,8,5]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,1,4,6,7,5]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,1,4,7,6,5]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,2,1,4,7,5,6]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,1,5,7,4,6]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,2,5,1,7,3,6]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,2,5,1,8,3,6]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,1,5,8,4,6]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,2,1,4,8,5,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,2,1,7,5,8,6,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,7,1,6,8,4,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,6,1,8,3,5]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,6,8,1,2,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,6,7,1,2,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,6,1,7,3,5]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,1,6,7,4,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,1,8,7,5,6,4]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,2,1,7,4,5,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,8,1,7,4,6,5]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,1,6,4,7,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,1,6,4,8,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,7,6,1,3,8,5]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,6,1,3,7,5]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,7,1,3,6,5]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,3,4,1,2,6]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,8,1,3,6,5]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,6,8,1,3,7,5]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,6,7,1,3,8,5]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,1,8,4,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,2,1,8,4,5,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[3,7,2,1,8,5,4,6]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,8,5,1,2,6]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,7,8,6,1,2,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[3,2,7,1,8,6,4,5]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,1,6,8,5,7,4]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,6,1,8,7,4,5]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,8,1,7,3,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,8,7,1,2,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[4,2,6,7,1,8,3,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,2,6,1,7,8,4,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,8,7,5,1,2]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,3,6,4,8,7,1,2]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,4,6,2,7,8,5,3]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,5,4,2,6,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,2,7,5,4,8,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,5,4,8,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,5,4,6,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,7,5,4,6,1,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,3,6,7,8,5,1,2]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[4,5,6,3,8,7,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,5,4,7,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,5,4,7,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,3,5,4,8,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,2,5,4,8,7,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,2,5,8,3,6,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,8,2,5,7,3,6,4]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,1,5,4,8,7,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,6,2,8,7,5,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,8,1,2,4,6,5,3]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,3,1,4,2,6,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,6,1,8,2,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,8,5,4,1,6,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,8,1,5,2,3,7,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,1,6,4,3,2,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[5,8,1,6,4,3,2,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,5,7,4,3,2,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,5,8,6,4,3,2,7]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,4,6,1,5,8,2,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,4,1,5,3,2,6]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,5,1,6,3,2,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,1,5,7,3,8,4]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,7,4,3,2,5]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,8,1,7,4,3,2,5]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,1,7,4,3,2,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,1,7,6,4,3,2,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,1,7,8,4,3,2,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,1,8,6,4,3,2,5]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,8,7,6,4,3,2,5]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[2,1,7,5,6,3,8,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,7,5,8,2,4]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,8,1,6,5,3,2,4]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,2,1,4,5,6,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,1,5,4,6,7,3]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,1,5,4,6,8,3]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,8,5,6,3,7,4]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,2,5,7,3,8,4]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,2,1,5,6,3,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[4,3,6,1,5,7,2,8]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,6,3,7,8,2,4]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,6,8,5,7,2,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,3,7,1,8,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,6,4,8,7,2,5]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,6,7,3,8,2,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,6,1,3,7,2,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,1,5,2,3,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[4,1,7,5,2,3,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,4,5,8,3,7,6]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,3,5,4,1,8,6]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,8,3,5,4,1,7,6]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,6,3,8,1,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,2,3,4,1,6,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,1,4,6,3,2,5]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,4,7,8,2,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,7,4,3,2,6]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,1,5,8,4,3,2,6]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,1,8,7,4,3,2,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,5,1,8,4,3,2,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,7,1,4,3,2,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,1,4,3,2,6]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,7,1,4,3,2,6]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,7,8,4,3,2,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,7,5,1,3,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,8,4,6,1,3,2,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,5,4,1,3,2,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,4,1,8,2,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,4,5,1,3,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,5,8,4,3,2,7]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,8,5,1,4,3,2,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,5,1,4,3,2,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,3,4,5,6,9,7,8]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]=>[7,2]=>2
[9,8,1,2,3,4,5,6,7]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[7,8,9,1,2,3,4,5,6]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[9,8,7,1,2,3,4,5,6]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[9]=>[9]=>1
[6,7,8,9,1,2,3,4,5]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]=>[5,4]=>2
[9,6,7,8,1,2,3,4,5]=>[[1,3,4,8,9],[2,6,7],[5]]=>[4,5]=>[5,4]=>2
[8,9,6,7,1,2,3,4,5]=>[[1,2,7,8,9],[3,4],[5,6]]=>[2,2,5]=>[5,2,2]=>3
[9,8,6,7,1,2,3,4,5]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[4,5]=>[5,4]=>2
[9,8,7,6,1,2,3,4,5]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[9,5,6,7,8,1,2,3,4]=>[[1,3,4,5],[2,7,8,9],[6]]=>[5,4]=>[5,4]=>2
[8,9,5,6,7,1,2,3,4]=>[[1,2,5,9],[3,4,8],[6,7]]=>[2,3,4]=>[4,3,2]=>3
[9,8,5,6,7,1,2,3,4]=>[[1,4,5,9],[2,7,8],[3],[6]]=>[5,4]=>[5,4]=>2
[9,7,8,5,6,1,2,3,4]=>[[1,3,8,9],[2,5],[4,7],[6]]=>[3,2,4]=>[4,3,2]=>3
[9,8,7,5,6,1,2,3,4]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[9,8,7,6,5,1,2,3,4]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[9]=>[9]=>1
[7,8,9,4,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[3,3,3]=>[3,3,3]=>3
[9,7,8,4,5,6,1,2,3]=>[[1,3,6],[2,5,9],[4,8],[7]]=>[3,3,3]=>[3,3,3]=>3
[9,8,7,4,5,6,1,2,3]=>[[1,5,6],[2,8,9],[3],[4],[7]]=>[6,3]=>[6,3]=>2
[8,9,6,7,4,5,1,2,3]=>[[1,2,9],[3,4],[5,6],[7,8]]=>[2,2,2,3]=>[3,2,2,2]=>4
[9,8,6,7,4,5,1,2,3]=>[[1,4,9],[2,6],[3,8],[5],[7]]=>[4,2,3]=>[4,3,2]=>3
[9,8,7,6,4,5,1,2,3]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[6,3]=>[6,3]=>2
[9,8,7,6,5,4,1,2,3]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[9,7,8,5,6,3,4,1,2]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[3,2,2,2]=>[3,2,2,2]=>4
[9,8,7,5,6,3,4,1,2]=>[[1,5],[2,7],[3,9],[4],[6],[8]]=>[5,2,2]=>[5,2,2]=>3
[9,8,7,6,5,3,4,1,2]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[9,8,7,6,5,4,3,1,2]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[9]=>[9]=>1
[9,10,1,2,3,4,5,6,7,8]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[8,9,10,1,2,3,4,5,6,7]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]=>[7,3]=>2
[10,8,9,1,2,3,4,5,6,7]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[3,7]=>[7,3]=>2
[10,9,8,1,2,3,4,5,6,7]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[10]=>[10]=>1
[7,8,9,10,1,2,3,4,5,6]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]=>[6,4]=>2
[10,7,8,9,1,2,3,4,5,6]=>[[1,3,4,8,9,10],[2,6,7],[5]]=>[4,6]=>[6,4]=>2
[9,10,7,8,1,2,3,4,5,6]=>[[1,2,7,8,9,10],[3,4],[5,6]]=>[2,2,6]=>[6,2,2]=>3
[10,9,7,8,1,2,3,4,5,6]=>[[1,4,7,8,9,10],[2,6],[3],[5]]=>[4,6]=>[6,4]=>2
[10,9,8,7,1,2,3,4,5,6]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[10]=>[10]=>1
[10,6,7,8,9,1,2,3,4,5]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[5,5]=>[5,5]=>2
[9,10,6,7,8,1,2,3,4,5]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>[2,3,5]=>[5,3,2]=>3
[10,9,6,7,8,1,2,3,4,5]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>[5,5]=>[5,5]=>2
[10,8,9,6,7,1,2,3,4,5]=>[[1,3,8,9,10],[2,5],[4,7],[6]]=>[3,2,5]=>[5,3,2]=>3
[10,9,8,6,7,1,2,3,4,5]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[5,5]=>[5,5]=>2
[10,9,8,7,6,1,2,3,4,5]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[10]=>[10]=>1
[9,10,5,6,7,8,1,2,3,4]=>[[1,2,5,6],[3,4,9,10],[7,8]]=>[2,4,4]=>[4,4,2]=>3
[10,9,5,6,7,8,1,2,3,4]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[6,4]=>[6,4]=>2
[8,9,10,5,6,7,1,2,3,4]=>[[1,2,3,10],[4,5,6],[7,8,9]]=>[3,3,4]=>[4,3,3]=>3
[10,9,8,5,6,7,1,2,3,4]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[6,4]=>[6,4]=>2
[9,10,7,8,5,6,1,2,3,4]=>[[1,2,9,10],[3,4],[5,6],[7,8]]=>[2,2,2,4]=>[4,2,2,2]=>4
[10,9,7,8,5,6,1,2,3,4]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[4,2,4]=>[4,4,2]=>3
[10,9,8,7,5,6,1,2,3,4]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[6,4]=>[6,4]=>2
[10,9,8,7,6,5,1,2,3,4]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[10]=>[10]=>1
[10,7,8,9,4,5,6,1,2,3]=>[[1,3,4],[2,6,7],[5,9,10],[8]]=>[4,3,3]=>[4,3,3]=>3
[9,10,7,8,4,5,6,1,2,3]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>[2,2,3,3]=>[3,3,2,2]=>4
[10,9,7,8,4,5,6,1,2,3]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[4,3,3]=>[4,3,3]=>3
[10,9,8,7,4,5,6,1,2,3]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[7,3]=>[7,3]=>2
[10,8,9,6,7,4,5,1,2,3]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[3,2,2,3]=>[3,3,2,2]=>4
[10,9,8,6,7,4,5,1,2,3]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[5,2,3]=>[5,3,2]=>3
[10,9,8,7,6,4,5,1,2,3]=>[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[7,3]=>[7,3]=>2
[10,9,8,7,6,5,4,1,2,3]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[9,10,7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[10,9,7,8,5,6,3,4,1,2]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[10,9,8,7,5,6,3,4,1,2]=>[[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>[6,2,2]=>[6,2,2]=>3
[10,9,8,7,6,5,3,4,1,2]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[8,2]=>[8,2]=>2
[10,9,8,7,6,5,4,3,1,2]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[3,4,6,2,7,1,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,2,5,4,1,7,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,2,7,5,4,1,6,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,3,6,2,8,1,5,7]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,2,5,4,7,8,3]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,4,5,1,3,7,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[4,2,8,5,1,3,7,6]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[4,3,6,8,1,7,2,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,6,4,1,7,2,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,1,5,8,3,7,4]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,7,4,8,3,5,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,6,3,7,5,8,2]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,2,5,8,1,3]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,1,7,5,3,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,5,4,1,6,3,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,5,4,6,2,8,1,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,5,4,3,8,6,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,3,5,8,7,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,4,3,6,7,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,6,2,7,8,1,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,1,6,7,3,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,6,3,2,7,1,4,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,3,2,7,1,8,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,5,6,3,2,7,1,4]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,2,8,1,7,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,1,7,8,5,3,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,4,1,6,3,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,3,2,1,8,4,7]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,5,2,1,6,4,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,3,2,1,5,7]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[5,3,8,2,1,6,4,7]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,8,2,1,4,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,3,2,8,5,1,6,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,3,2,1,7,5]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,6,4,3,2,1,7,5]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[7,6,4,3,2,1,8,5]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[7,8,4,3,2,1,6,5]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,4,7,2,1,8,6,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,3,2,6,1,4]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,2,1,6,8,4]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,7,3,2,1,6,4,8]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,3,7,2,5,1,8,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,8,3,5,2,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,5,7,8,4,1,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[2,1,5,7,8,6,3,4]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,6,7,2,8,1,4,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,3,7,2,8,1,4,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,6,1,7,4,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,5,2,1,4,7,6,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,3,5,2,1,8,4,6]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,1,3,7,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,5,8,4,1,3,7,6]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,1,7,8,3,6,5]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,2,8,6,1,4,5]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,8,2,1,7,4,5]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,2,1,4,7,6]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,8,7,3,2,1,5,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,7,3,2,1,5,6,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,4,7,3,2,1,5,6]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,3,5,2,1,4,7,6]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,3,2,8,6,1,4,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[3,5,2,1,4,6,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[7,8,6,5,4,3,2,1,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,8,9,7,6,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[8,9,7,6,5,4,3,2,1,10]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[6,8,7,5,4,3,2,1,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,7,9,8,6,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[1,9,10,8,7,6,5,4,3,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[7,8,3,5,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,3,7,5,2,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,1,6,3,2,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,4,1,6,2,3,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[5,7,1,6,2,8,3,4]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,1,6,2,8,4,3]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,6,5,1,8,3,4]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,7,6,5,1,8,4,3]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,6,5,1,4,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,6,4,1,5,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,6,1,5,4,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,6,1,4,8,5,3]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,6,1,4,8,3,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,3,5,1,8,4,2,6]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,5,1,8,6,4,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,7,6,1,5,8,4,3]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,6,4,1,8,5,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,1,7,6,3,8,5,4]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,6,3,8,4,5]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,6,2,8,4,1]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,6,4,1,8,3,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,3,5,1,8,6,2,4]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,5,1,8,2,4,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,8,7,6,1,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,3,4,8,5,7,1,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,5,4,8,1,2,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,4,3,5,8,7,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,4,5,8,7,3,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[6,4,3,5,8,7,1,2]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[7,3,5,4,8,1,6,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,4,8,7,5,6,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,8,7,5,1,6]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,7,6,5,4,8,1,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,3,5,6,8,4,1,2]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,3,5,6,8,1,4,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,3,5,6,8,1,2,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[6,4,1,5,8,7,2,3]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[6,4,1,5,8,7,3,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[6,4,1,5,8,3,7,2]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,7,1,6,3,8,2,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,1,5,8,3,2,7]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[7,4,1,5,8,2,3,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,4,1,5,8,2,6,3]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,5,7,8,2,1,4]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[6,3,5,7,8,2,4,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,7,6,4,5,8,3,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,6,1,8,4,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,4,5,8,6,3,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[7,3,5,4,8,6,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,8,5,6,1,7]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,8,7,1,6,5]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,8,1,7,6,5]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,8,1,6,7,5]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,8,5,1,7,6]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,5,4,8,2,7,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,3,5,8,2,1,6]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[2,1,4,5,8,3,7,6]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,3,5,8,2,6,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,5,4,8,2,1,7]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,8,5,1,6,7]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,3,4,8,1,6,5,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,8,1,5,7,6]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,8,2,6,1,5,3,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,6,2,5,3,4]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,6,7,2,5,3,4]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,7,2,6,3,4]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,7,2,6,3,4]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,7,1,6,3,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,7,1,5,3,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,5,7,1,6,3,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,7,5,6,3,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,7,5,6,3,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,7,4,6,3,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,7,4,6,3,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,7,1,6,3,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,7,1,6,3,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,7,2,6,3,5]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,7,2,6,3,5]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,7,5,6,2,3]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,7,5,6,2,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,7,5,6,2,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,1,7,5,6,2,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,1,7,4,6,2,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,7,4,6,2,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,7,2,6,4,5]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,1,7,2,6,4,5]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,2,7,1,6,4,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,2,7,4,6,1,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,2,7,5,6,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,7,5,6,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,7,5,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,4,7,5,6,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,7,5,6,1,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,7,5,6,1,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,7,4,6,1,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,7,1,6,4,5]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,7,3,6,4,5]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,2,8,6,4,1,3]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[7,5,1,8,6,2,3,4]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[7,4,8,6,1,5,2,3]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,4,5,2,6,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,1,7,4,2,5,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,7,4,2,8,5,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,7,3,8,5,2,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,3,5,6,2,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,6,2,5,1,4]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,2,8,6,1,3,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,3,1,8,4,2,5,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[7,2,8,4,1,5,3,6]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,3,5,1,6,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,8,3,4,6,1,5]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,7,8,2,6,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,3,8,5,7,4,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,4,8,5,3,1,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,3,1,4,8,5,2,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[2,6,3,7,8,5,4,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,7,8,4,5,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,7,3,5,6,8,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,7,3,6,8,5,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,3,7,8,1,6,4]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,5,4,7,8,2,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,1,4,8,2,6,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,2,4,8,6,1,3,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[5,2,3,8,4,6,7,1]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,2,3,6,1,7,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,2,3,5,7,1,6]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,7,8,3,6,2,5]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,3,6,7,2,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,8,2,4,7,1,6]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,3,8,1,2,7,6]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,4,2,8,1,3,7,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,2,5,1,7,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,8,1,4,7,2,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,1,3,6,2,7,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,7,4,2,6,8,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,1,4,2,6,3,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,1,2,7,6,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,5,1,2,8,7,3,4]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[6,5,3,1,4,2,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,3,1,6,4,2,7,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[5,2,6,4,1,7,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,7,5,2,8,3]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,1,7,2,6,3,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,6,1,2,8,7,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,1,8,6,2,4]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,2,7,5,1,8,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,5,7,1,8,6,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,7,2,8,6,1,5]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,5,8,2,7,1,6]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,2,8,1,5,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,2,6,8,1,7,4]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,5,6,1,3,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,3,1,2,5,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[5,3,6,8,4,7,2,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,7,2,5,4,8,6,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,2,5,7,3,6,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,6,5,4,8,2,7]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,5,8,3,2,7]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,8,4,3,2,7]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,5,4,7,6,3,2,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,7,1,5,4,3,8,6]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,1,5,4,3,7,6]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,5,7,3,2,6]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[8,4,6,1,7,3,2,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,6,1,4,7,2,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,6,1,4,3,8,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,8,5,1,3,2,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,2,4,3,5,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,6,2,8,3,5,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,6,2,4,7,5,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,6,2,4,8,5,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,8,4,6,2,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,5,8,6,2,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,2,1,4,3,6,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,7,3,1,4,6,2,5]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[8,7,6,3,2,5,4,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[8,7,3,5,1,6,2,4]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,7,2,5,1,3,6,4]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,5,7,1,2,3]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,6,5,1,8,2,4]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,1,2,3,4,5,6,7,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[9]=>[9]=>1
[1,9,2,3,4,5,6,7,8]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]=>[7,2]=>2
[9,1,2,3,4,5,6,7,8,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[7,8,1,2,3,4,5,6,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[1,8,9,2,3,4,5,6,7]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]=>[6,3]=>2
[1,10,2,3,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]=>[8,2]=>2
[8,9,1,2,3,4,5,6,7,10]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[6,8,1,2,3,4,5,7,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[1,7,9,2,3,4,5,6,8]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]=>[6,3]=>2
[1,9,10,2,3,4,5,6,7,8]=>[[1,2,3,6,7,8,9,10],[4,5]]=>[3,7]=>[7,3]=>2
[3,6,4,8,7,5,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,4,3,8,7,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,2,4,7,8,5,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,2,4,8,1,5,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,4,7,2,8,1,6,5]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,7,2,5,8,6,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,4,5,6,1,2]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,4,8,7,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,8,5,3,7,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,3,4,7,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,5,4,2,8,7,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,2,7,3,6,4]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,7,5,1,8,6,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,4,2,6,5,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,6,4,8,2,5,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,1,7,5,3,2,6,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,5,1,3,4,2,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,8,5,3,1,7,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,4,5,3,2,8,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,6,1,4,2,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,8,6,4,1,3,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,4,6,2,5,8,3,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,2,5,8,1,7,4]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,7,4,2,3,5]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[6,1,7,8,2,4,3,5]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,8,6,3,4,2,5]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,1,4,5,6,8,3]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[1,2,8,3,6,5,7,4]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,3,2,7,5,8,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,3,8,5,7,2,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,4,1,7,5,8,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,6,5,8,1,4,2,3]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,8,6,7,3,2,1,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,3,7,2,8,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,3,4,8,7,1,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,1,3,4,5,2,8,6]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,8,3,5,4,2,7,6]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,6,3,8,2,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,2,4,6,3,1,5]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,2,6,4,7,8,1,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,5,7,4,3,1,6]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,2,5,8,3,4,1,6]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,8,7,1,2,6,4]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,3,8,2,1,7,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,4,1,2,3,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,8,7,4,1,3,2,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,7,8,4,1,2,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,4,7,5,3,8,2,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,7,3,1,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,8,4,6,3,1,2,5]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,4,5,3,8,1,7]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,5,8,4,2,1,7]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,8,4,2,3,1,7]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,4,3,1,2,7]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[6,1,4,2,8,5,7,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,6,5,3,2,7,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,6,5,1,2,4,7,3]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[6,7,5,8,2,1,4,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,5,8,2,6,4,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,8,5,7,6,2,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,5,7,1,2,4]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,1,5,6,2,7,4]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[6,8,5,2,1,4,7,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,8,2,5,6,1,7,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,1,5,6,3,7,4]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,2,5,6,3,7,4]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,8,2,5,7,6,3,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,8,6,2,7,3,4]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,5,8,6,1,7,3,4]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,5,7,2,3,4]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,8,6,5,7,1,2,4]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,6,5,8,1,2,4,3]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,7,6,8,4,2,3]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,3,7,8,6,2,4]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[7,2,5,8,1,6,4,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,8,5,7,6,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,1,5,7,6,3,4]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,2,8,6,1,7,3,4]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,6,5,7,3,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,3,6,7,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[8,2,5,6,3,7,1,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,6,5,4,1,8,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,1,3,5,4,7,8,2]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,5,3,4,7,8,2]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,6,2,4,1,8,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,2,6,3,7,1,4]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,2,6,7,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[8,1,6,5,7,3,2,4]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,8,6,2,7,1,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,1,6,3,7,2,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,6,3,7,2,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,6,5,4,2,8,3]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,7,6,1,4,2,8,3]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,4,2,6,5,8,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,3,5,6,8,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,4,1,5,6,8,3]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[5,7,6,4,1,2,8,3]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,7,6,1,5,2,8,3]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,6,4,5,2,8,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,6,5,7,2,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,1,6,5,7,2,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,3,5,7,6,2,4]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,8,5,4,1,6,2,3]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,1,5,4,3,7,8,2]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,6,4,2,1,8,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,2,6,5,7,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,2,5,1,8,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,4,3,5,7,8,2]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,3,4,5,7,8,2]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[7,2,6,4,5,1,8,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,3,6,5,7,1,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,7,3,6,8,1,2]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,8,5,6,1,2]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,7,2,5,1,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,4,7,2,5,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,2,4,7,1,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,3,4,5,7,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[4,3,6,7,5,8,1,2]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,7,5,8,4,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,8,6,4,5,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,6,5,1,4,8]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[1,2,7,6,5,8,3,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,6,1,5,3,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,8,6,4,1,5,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,3,6,2,5,1,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,3,2,5,1,4,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,1,2,5,6,3,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[4,1,6,2,5,7,3,8]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,2,5,8,7,3,4]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[2,1,8,6,4,7,3,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,6,8,4,2,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,8,3,6,7,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,5,8,3,6,2,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,8,7,2,3,6,4]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,5,7,4,2,8,3]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,1,6,4,7,2,5,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,7,5,1,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,1,4,2,3,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,1,3,2,4,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,5,1,3,4,2,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,3,4,5,1,7,6]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,4,3,1,5,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[4,2,8,3,1,7,5,6]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,4,8,2,5,6]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,4,1,6,2,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,7,3,6,1,8,5]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,7,6,3,1,2,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,5,6,8,1,4,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,7,1,6,5,3,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,8,5,4,3,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,3,1,2,8,4,5,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[4,2,1,3,6,5,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[2,8,1,4,5,6,3,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,2,1,5,4,6,3,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,1,8,5,3,7]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,2,1,4,5,3,6]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,1,5,3,6,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,6,1,5,8,7,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,6,4,3,8,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,1,6,3,4,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,1,8,2,7,4,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,1,7,5,2,3,4]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,1,8,5,3,2,4]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[5,6,1,7,4,8,2,3]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,1,5,7,4,2,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,6,1,7,4,8,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,5,6,4,8,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,6,4,8,3,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,7,8,5,3,4,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,8,6,5,4,2,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,6,5,7,3,4,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,7,5,8,2,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,3,6,2,7,4,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,7,4,6,8,2,5]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,6,3,2,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,6,5,4,8,2,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,5,7,2,4,3]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,7,6,8,3,4,5]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,7,5,3,8,2,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,5,6,8,3,4]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,1,7,6,8,2,3]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,5,6,2,7,3,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,6,4,2,7,5,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,5,2,4,6,3,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,6,3,7,4,5,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,1,6,2,4,5,3]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,1,4,7,2,5,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,1,7,2,6,5]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,7,1,8,3,2,6]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,4,1,8,5,2,6]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,1,4,8,3,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,1,8,4,5,3,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,2,8,4,3,5,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[6,5,1,4,3,8,2,7]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,2,5,8,3,4,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,5,1,3,7,2,6,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,4,2,1,7,3,6,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,4,2,1,8,5,3,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[1,5,4,2,8,3,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,4,3,1,5,8,2,7]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[3,7,6,8,4,5,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,6,8,5,3,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,6,8,5,4,2,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,4,8,6,7,5,2,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,6,7,3,5,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,5,4,6,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,8,5,6,7,2,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,8,4,7,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,8,6,7,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,8,7,3,6,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,5,8,7,3,4,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,8,5,7,4,6,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,8,7,5,6,2,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,7,4,6,3,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,5,7,6,2,4]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,8,7,4,2,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[5,4,1,8,7,6,2,3]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[5,8,6,7,4,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,8,7,5,6,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,2,1,6,3,5,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,2,1,4,3,5,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,2,1,4,3,8,5,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,2,1,4,3,6,5,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,2,4,1,3,8,5,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,1,3,5,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,1,6,4,3,5,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,6,1,4,3,5,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,4,1,3,5,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,6,2,1,3,5,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,4,2,1,3,5,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,4,2,1,3,6,5,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,4,2,1,6,3,5,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[6,4,2,1,8,3,5,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[2,6,1,4,3,8,5,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,6,4,3,8,5,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,4,3,6,5,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,8,1,4,3,6,5,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,1,3,6,5,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,8,2,1,3,6,5,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,1,4,3,5,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[8,6,2,1,4,3,5,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[2,8,1,4,6,3,5,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,1,4,8,3,5,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,4,1,8,3,5,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,6,4,8,1,3,5,7]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,6,2,8,1,3,5,7]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,2,6,1,8,3,5,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,1,8,3,5,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,2,1,6,8,3,5,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[4,2,1,6,3,8,5,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,3,6,8,5,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[2,1,4,3,8,6,5,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,1,3,8,6,5,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,1,3,8,6,5,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[4,2,1,8,3,6,5,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,8,6,3,5,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[8,2,1,6,4,3,5,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,2,6,1,4,3,5,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,1,3,6,5,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,1,3,6,5,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,8,3,6,5,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,4,8,3,6,5,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,4,8,6,3,5,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[2,4,8,1,6,3,5,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,6,1,3,5,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,2,8,6,1,3,5,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[8,4,6,2,1,3,5,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[4,6,8,2,1,3,5,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[2,6,8,4,1,3,5,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[2,6,8,1,4,3,5,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,8,4,3,5,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,1,6,8,4,3,5,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[2,1,8,6,4,3,5,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,8,6,4,1,3,5,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[4,8,6,2,1,3,5,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[6,8,4,2,1,3,5,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,2,6,1,5,4,8,7]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,4,3,8,1,7,6]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,4,1,5,3,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,1,5,2,8,7]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,5,2,8,1,7,6]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,2,6,5,8,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,8,2,6,1,7,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,8,1,7,2,6,5]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,8,1,5,2,7,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,3,4,2,7,6]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,1,3,2,7,6]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,5,4,8,3,7,6]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,6,8,3,4,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,6,8,1,5,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,1,8,5,6,2]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,5,8,1,7,2]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,5,4,7,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,5,4,8,1,7,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,3,8,4,5,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,5,8,1,3,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,8,4,6,3,7,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,6,1,3,2,7,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,6,3,4,2,7,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,6,3,7,2,5,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,1,7,2,6,4]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,2,6,1,7,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,5,2,6,4,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,3,5,1,7,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,1,5,3,6,4]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,1,5,3,7,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,1,7,3,6,5]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,3,6,1,7,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,4,6,1,7,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,1,5,4,7,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,6,8,1,5,4]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,1,8,5,6,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,5,8,1,7,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,7,2,4,3,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,2,4,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,4,1,8,5,6,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,2,4,1,5,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,1,5,2,4,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,7,3,8,5,6,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,3,2,8,5,6,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,5,6,2,4,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,2,6,4,5,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,8,1,5,4,6,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,4,5,3,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,7,2,6,3,8,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,2,6,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,1,7,2,4,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,5,8,3,7,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,7,4,8,1,3,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,7,1,8,3,4,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,7,4,8,3,5,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,7,1,8,3,6,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,3,8,1,7,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,3,1,5,4,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,5,3,4,7,1,8,6]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,8,3,5,7,6,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,5,3,1,8,6,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,8,5,3,6,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[5,4,1,3,8,2,6,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[5,1,4,8,3,2,6,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[1,5,8,4,3,2,6,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,8,5,4,3,2,6,7]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,7,4,3,8,5,2,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,7,3,8,4,2,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,4,7,8,3,2,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,8,1,5,7,3,6,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,5,3,7,4,6,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,4,7,6,5,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,6,8,5,3,7,4,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,7,4,3,5,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,8,1,7,3,5,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,8,7,1,5,2,3]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,1,3,8,2,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[1,7,5,6,3,2,8,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,1,7,8,5,3,6]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[2,7,4,6,3,1,8,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,8,4,3,7,5,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,8,3,7,5,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,6,3,4,1,8,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,7,3,1,4,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,7,1,8,3,5,4,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,7,3,5,8,4,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,1,3,6,2,4,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,2,1,7,3,5,6,4]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,8,2,6,3,1,5,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,2,6,3,5,4,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,8,7,4,5,6,3]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,1,5,6,2,4]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,2,7,5,3,4]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,1,6,2,7,4,5,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,5,2,6,7,4,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,2,1,8,6,7,4,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,5,7,6,4,3,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,7,8,5,2,6,4,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,6,4,2,5,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,6,1,5,3,2,4]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,6,1,5,2,4]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,1,5,3,4,2]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,1,6,4,5,3,2]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,7,5,6,4,3,2]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,8,6,7,5,4,3,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,3,5,2,1,4,8,7]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,3,5,7,2,8,4,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,2,7,4,3,1,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[4,5,3,6,1,2,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,1,4,6,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,4,5,7,2,1,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[5,7,4,6,3,8,2,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,6,3,7,1,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,4,7,3,6,2,5]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,4,7,5,1,2,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,5,1,4,7,3,2,6]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,5,3,7,1,4,2,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,1,8,5,7,4,3,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,3,7,1,8,4,2]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,4,7,8,3,2]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[6,3,4,7,5,8,1,2]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,4,6,8,3,7,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,7,1,3,5,8,6,2]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,3,7,1,2,6,5]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,6,4,1,7,2,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,2,5,7,6,4]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,5,4,1,3,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,7,2,6,4,1,3,5]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[3,8,6,7,4,2,1,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,6,8,4,2,3,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,7,8,2,4,6,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,6,2,1,4,7,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,3,7,6,2,1,8,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,3,6,2,8,7,1,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,8,6,4,2,1,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,6,7,5,4,8,1,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,7,4,5,8,2,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,3,5,1,8,2,4]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,6,7,5,8,3,4]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,7,3,6,8,4]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,3,6,1,2,8,4]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,7,2,5,6,8,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,7,1,6,5,8,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,2,1,8,7,5,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,6,2,7,8,5,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,2,5,8,7,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,1,4,8,2,7,3]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,3,1,8,7,2,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,4,7,1,8,2]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,6,1,5,7,8,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,1,5,7,6,8,2]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,2,7,1,6,5,4]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,2,7,6,1,5,4]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,2,7,6,5,1,4]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,8,2,7,6,5,4,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,8,7,2,6,5,3,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,2,6,5,1,3]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,2,6,1,5,3]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,7,2,1,6,5,3]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,3,1,6,5,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,3,2,1,6,5]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[4,8,7,3,2,6,1,5]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,3,2,6,5,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,3,6,2,5,1]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,7,3,6,2,1,5]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,3,6,1,5,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,7,3,6,5,1,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,3,6,5,2,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,6,3,4,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,6,3,1,4,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,6,3,2,4,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,6,2,4,3,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,6,2,1,4,3]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,6,4,2,3,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,6,4,2,1,3]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[5,8,7,6,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,6,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[7,3,5,2,6,4,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,1,5,6,4,3,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[1,4,6,7,3,8,2,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,5,7,1,3,8,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,5,1,7,4,8,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,1,5,7,4,8,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,1,5,7,4,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[2,4,6,7,3,8,1,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,6,7,3,8,5,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,6,7,8,3,4,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,5,6,7,8,3,1,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,2,1,6,7,8,4,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,2,1,6,7,8,4,3]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,3,6,1,7,8,4,2]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,7,1,8,3,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,6,7,8,3,2,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[6,4,5,7,2,1,8,3]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,4,6,7,2,8,3,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,2,1,7,8,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,6,2,7,8,5,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,7,2,8,5,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,5,7,3,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[1,5,6,7,8,2,4,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,6,7,8,4,2,3]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,4,6,7,1,8,5,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,1,7,8,5,2]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,3,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[2,3,2,2,1]=>[3,2,2,2,1]=>5
[2,4,1,6,3,5,8,7,10,9]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[2,2,3,2,1]=>[3,2,2,2,1]=>5
[2,4,1,6,3,8,5,7,10,9]=>[[1,2,4,6,9],[3,5,7,8,10]]=>[2,2,2,3,1]=>[3,2,2,2,1]=>5
[2,4,1,6,3,8,5,10,7,9]=>[[1,2,4,6,8],[3,5,7,9,10]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[2,4,1,6,3,8,5,9,7,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[2,4,1,6,3,7,5,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[2,4,1,5,3,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[2,3,1,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[1,3,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[7,1,2,3,4,5,6,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[9]=>[9]=>1
[1,4,3,6,2,5,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,4,3,7,2,5,6,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,4,3,7,6,8,2,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,3,7,5,8,2,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,3,7,2,6,5,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,7,4,8,2,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,6,5,8,4,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,8,2,6,3,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,8,3,7,2,6]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,3,6,5,8,4,7]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,8,2,4,5,7,1,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,8,4,5,2,6,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,1,4,5,3,6,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,7,4,1,6,5,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,3,6,1,5,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,3,1,6,4,7,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,1,4,7,6,3,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,5,1,8,6,2,4,3]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,1,8,2,6,3,5]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,8,4,2,6,3,5]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,8,5,2,4,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,3,8,5,2,4,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[7,1,8,3,6,2,5,4]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,1,8,4,2,6,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[7,2,8,4,1,6,5,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,3,6,5,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,8,3,6,1,5,4]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,2,3,6,5,4]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,2,8,3,5,4,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,2,3,8,4,7,6]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,2,3,8,4,7,6]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,3,8,1,4,7,6]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,8,1,3,5,4,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,1,8,7,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,1,4,2,8,5,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[3,1,6,4,2,8,5,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,3,8,7,1,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,8,5,1,4,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,1,8,3,4,7,6]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,1,3,8,4,7,6]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,5,3,8,4,7,6]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,4,8,3,7,6,5]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,8,1,3,7,6,5]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,3,7,1,6,5]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,8,3,7,6,1,5]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,3,8,1,7,4,6]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,4,1,3,8,7,6]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,5,4,8,2,7,6]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,1,4,8,2,7,6]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,3,8,4,7,1,6]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,2,3,7,6,1,5]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,3,7,1,6,5]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,1,2,3,7,6,5]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,8,2,3,7,6,5]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,3,7,2,6,5]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,8,1,5,2,4,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,1,2,4,7,6]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,3,8,2,4,7,6]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,3,8,2,4,7,6]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,4,8,2,7,6,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,4,8,2,7,6,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,8,1,2,7,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,1,2,8,7,4,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[5,3,1,6,4,2,8,7]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[5,1,6,2,8,7,4,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,5,8,2,7,6,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,2,5,8,7,6,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,4,2,5,8,7,6,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,3,5,2,8,7,4,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,1,2,8,7,4,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,2,8,7,5,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,2,6,1,8,7,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,1,5,8,2,7,6]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,5,2,8,7,1,4,6]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,4,8,7,2,6,1,5]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,8,7,1,2,6,5]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,8,1,7,2,6,5]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,4,8,7,2,6,5]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,4,8,2,7,6,5]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,8,1,2,7,6,5]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,8,2,7,1,6,5]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,8,2,7,6,1,5]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,8,1,7,6,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,2,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[3,1,4,2,5,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,1,8,7,6,4]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,8,2,1,5,3,6,4]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,1,2,7,3,5,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[2,3,7,5,4,1,8,6]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,3,1,5,4,2,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,8,1,5,4,2,6,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,3,5,4,1,6,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,2,5,4,1,3,6]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,2,5,4,6,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,1,5,4,7,3,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,6,1,4,7,8,2]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,6,2,4,7,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,1,7,3,8,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[4,3,7,5,8,6,1,2]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,1,8,3,6,5]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,7,4,8,1,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,6,7,4,8,5,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,7,6,5,3,8,4,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,6,5,3,8,1,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,5,2,4,8,3]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,7,6,5,3,1,4,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[2,7,1,4,8,3,5,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,6,4,8,5,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,6,3,8,4,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,6,2,4,8,3,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,5,2,1,3,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,7,6,5,2,8,1,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,7,6,5,1,8,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,5,2,8,3,4]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,5,3,2,8,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[4,7,6,5,1,2,8,3]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,7,6,5,3,1,8,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[6,1,3,5,4,8,7,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,6,3,4,1,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,2,4,7,8,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,6,3,4,8,7,5]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,4,8,3,6,5]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,4,2,8,3,5,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,1,8,2,6,3,5,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,2,1,5,3,6,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,1,6,2,3,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,2,6,8,3,5,4]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,6,7,4,8,5,3]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,6,7,4,2,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,2,8,5,4,6,1,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,3,5,8,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,7,1,2,5,3,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,6,5,2,4,1,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,5,1,4,8,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,6,5,2,1,8,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,7,6,5,8,2,4,3]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,6,5,8,1,4,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,6,5,1,2,4,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,1,6,8,4,2,5,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,7,6,8,3,5,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,6,5,1,4,3,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,7,6,5,8,1,3,4]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,7,6,5,8,4,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,2,1,7,4,8,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[4,2,1,7,3,5,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,3,1,5,4,2,8,6]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,5,2,7,6,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,5,1,3,7,6,4]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,2,1,5,8,6]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,7,2,5,3,1,8,6]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,5,4,1,3,8,6]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,5,4,3,2,1,8,6]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[6,5,2,1,8,4,3,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[5,7,4,3,2,8,1,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,2,4,8,3,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,7,3,6,4,8,1,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,7,5,3,8,1,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,5,3,6,4,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,2,7,1,6,4]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,3,1,6,5,4,2]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,2,6,1,5,4,3]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,8,5,7,4,3,6,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,5,7,2,4,6,3]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,6,1,7,2,5,4]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,8,5,6,1,4,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,7,5,8,2,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,2,6,8,4,1,5]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,5,8,1,4,2,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,8,4,1,3,7]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,5,4,8,3,2,1,7]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,3,5,1,8,4,2,7]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,1,5,7,3,6,2]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,1,6,8,2,3,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,3,7,4,8,5,2,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,7,2,5,8,6,3,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,3,1,8,4,7,5,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,8,7,4,1,2]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[5,4,8,1,7,6,2,3]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,1,7,3,6,4]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,8,1,5,3,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,8,7,1,3,6,4]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,8,7,2,1,6,4]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,6,1,5,4,2]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,6,5,1,4,3]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,8,7,6,2,1,5]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[2,4,8,7,6,1,3,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[3,5,8,7,2,6,1,4]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,8,6,5,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,5,8,6,4,3,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[5,8,7,3,6,4,2,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,6,2,5,3,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,6,5,1,4,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,7,6,5,4,1,3]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[3,4,1,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[3,2,1,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[4,5,6,1,2,3,7,8,9]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[4,2,5,1,3,6,7,8,9]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[4,3,2,1,5,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[9]=>[9]=>1
[5,6,7,8,1,2,3,4,9]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]=>[5,4]=>2
[5,2,6,7,1,3,4,8,9]=>[[1,3,4,8,9],[2,6,7],[5]]=>[4,5]=>[5,4]=>2
[5,6,3,4,1,2,7,8,9]=>[[1,2,7,8,9],[3,4],[5,6]]=>[2,2,5]=>[5,2,2]=>3
[5,3,2,6,1,4,7,8,9]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[4,5]=>[5,4]=>2
[5,4,3,2,1,6,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[6,2,7,8,9,1,3,4,5]=>[[1,3,4,5],[2,7,8,9],[6]]=>[5,4]=>[5,4]=>2
[6,7,3,4,8,1,2,5,9]=>[[1,2,5,9],[3,4,8],[6,7]]=>[2,3,4]=>[4,3,2]=>3
[6,3,2,7,8,1,4,5,9]=>[[1,4,5,9],[2,7,8],[3],[6]]=>[5,4]=>[5,4]=>2
[6,4,7,2,5,1,3,8,9]=>[[1,3,8,9],[2,5],[4,7],[6]]=>[3,2,4]=>[4,3,2]=>3
[6,4,3,2,7,1,5,8,9]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[6,5,4,3,2,1,7,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[9]=>[9]=>1
[7,4,8,2,5,9,1,3,6]=>[[1,3,6],[2,5,9],[4,8],[7]]=>[3,3,3]=>[3,3,3]=>3
[7,4,3,2,8,9,1,5,6]=>[[1,5,6],[2,8,9],[3],[4],[7]]=>[6,3]=>[6,3]=>2
[7,8,5,6,3,4,1,2,9]=>[[1,2,9],[3,4],[5,6],[7,8]]=>[2,2,2,3]=>[3,2,2,2]=>4
[7,5,3,8,2,6,1,4,9]=>[[1,4,9],[2,6],[3,8],[5],[7]]=>[4,2,3]=>[4,3,2]=>3
[7,5,4,3,2,8,1,6,9]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[6,3]=>[6,3]=>2
[7,6,5,4,3,2,1,8,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[8,6,9,4,7,2,5,1,3]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[3,2,2,2]=>[3,2,2,2]=>4
[8,6,4,3,9,2,7,1,5]=>[[1,5],[2,7],[3,9],[4],[6],[8]]=>[5,2,2]=>[5,2,2]=>3
[8,6,5,4,3,2,9,1,7]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[3,4,1,2,5,6,7,8,9,10]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[3,2,1,4,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[4,5,6,1,2,3,7,8,9,10]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]=>[7,3]=>2
[4,2,5,1,3,6,7,8,9,10]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[3,7]=>[7,3]=>2
[4,3,2,1,5,6,7,8,9,10]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[10]=>[10]=>1
[5,6,7,8,1,2,3,4,9,10]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]=>[6,4]=>2
[5,2,6,7,1,3,4,8,9,10]=>[[1,3,4,8,9,10],[2,6,7],[5]]=>[4,6]=>[6,4]=>2
[5,6,3,4,1,2,7,8,9,10]=>[[1,2,7,8,9,10],[3,4],[5,6]]=>[2,2,6]=>[6,2,2]=>3
[5,3,2,6,1,4,7,8,9,10]=>[[1,4,7,8,9,10],[2,6],[3],[5]]=>[4,6]=>[6,4]=>2
[5,4,3,2,1,6,7,8,9,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[10]=>[10]=>1
[6,2,7,8,9,1,3,4,5,10]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[5,5]=>[5,5]=>2
[6,7,3,4,8,1,2,5,9,10]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>[2,3,5]=>[5,3,2]=>3
[6,3,2,7,8,1,4,5,9,10]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>[5,5]=>[5,5]=>2
[6,4,7,2,5,1,3,8,9,10]=>[[1,3,8,9,10],[2,5],[4,7],[6]]=>[3,2,5]=>[5,3,2]=>3
[6,4,3,2,7,1,5,8,9,10]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[5,5]=>[5,5]=>2
[6,5,4,3,2,1,7,8,9,10]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[10]=>[10]=>1
[7,8,3,4,9,10,1,2,5,6]=>[[1,2,5,6],[3,4,9,10],[7,8]]=>[2,4,4]=>[4,4,2]=>3
[7,8,9,4,5,6,1,2,3,10]=>[[1,2,3,10],[4,5,6],[7,8,9]]=>[3,3,4]=>[4,3,3]=>3
[7,4,3,2,8,9,1,5,6,10]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[6,4]=>[6,4]=>2
[7,8,5,6,3,4,1,2,9,10]=>[[1,2,9,10],[3,4],[5,6],[7,8]]=>[2,2,2,4]=>[4,2,2,2]=>4
[7,5,3,8,2,6,1,4,9,10]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[4,2,4]=>[4,4,2]=>3
[7,5,4,3,2,8,1,6,9,10]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[6,4]=>[6,4]=>2
[7,6,5,4,3,2,1,8,9,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[10]=>[10]=>1
[8,5,9,10,2,6,7,1,3,4]=>[[1,3,4],[2,6,7],[5,9,10],[8]]=>[4,3,3]=>[4,3,3]=>3
[8,5,3,9,2,6,10,1,4,7]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[4,3,3]=>[4,3,3]=>3
[8,6,9,4,7,2,5,1,3,10]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[3,2,2,3]=>[3,3,2,2]=>4
[8,6,4,3,9,2,7,1,5,10]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[5,2,3]=>[5,3,2]=>3
[8,6,5,4,3,2,9,1,7,10]=>[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[7,3]=>[7,3]=>2
[8,7,6,5,4,3,2,1,9,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[9,7,5,4,3,10,2,8,1,6]=>[[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>[6,2,2]=>[6,2,2]=>3
[3,6,5,1,2,4,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,7,5,8,2,4,1,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,7,2,4,1,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,7,8,4,3,2,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,1,2,6,4,3,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,5,4,3,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,4,6,3,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,1,2,6,5,3,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,1,5,7,8,3,2,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,1,5,8,7,3,2,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,7,1,8,3,6,2,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,7,8,5,2,3,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[5,1,7,4,8,2,3,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,3,8,1,4,2,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,8,7,3,4,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[5,1,8,4,7,2,3,6]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,8,7,5,2,3,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,7,1,6,3,2,8,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,2,3,7,5,8,4]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,2,3,8,6,5,4]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,1,2,3,5,8,6,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[6,8,1,4,3,7,2,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,3,2,4,1,6,5]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,1,7,3,4,8,6,5]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,3,2,4,1,6,5]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,1,4,3,8,2,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,2,3,5,7,6,4]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[8,1,2,3,6,7,5,4]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[7,1,2,3,6,8,5,4]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[7,1,2,3,8,5,6,4]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,2,3,7,5,6,4]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,2,3,6,5,7,4]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,8,5,4,3,2,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,8,2,6,3,4,1,5]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,7,3,4,1,5]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,8,3,4,1,5]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,7,1,4,2,6,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,8,1,4,2,6,5]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,8,1,4,2,7,5]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,7,8,2,4,1,6]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,6,7,1,4,2,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,2,8,3,1,4,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,6,2,7,3,1,4,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,1,7,5,4,3,2,6]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,1,7,4,5,3,2,6]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,3,7,1,4,2,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,7,3,4,6,8,5]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,2,4,1,8,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,2,4,3,6,1,5]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,2,3,5,6,8,4]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[6,1,2,3,8,7,4,5]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[5,1,2,3,7,8,6,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[5,1,2,3,8,7,6,4]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,1,2,3,8,6,7,4]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,2,3,5,8,7,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[8,6,2,4,3,1,7,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,6,3,2,4,8,1,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[2,1,6,3,4,8,7,5]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,2,4,7,1,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,2,4,3,1,8,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,3,5,7,8,4]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[5,1,2,3,6,8,7,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[7,8,1,2,6,3,5,4]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,8,2,7,3,5,6]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,5,4,7,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,5,4,2,7,6]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,3,6,8,4,7,1,5]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,8,4,7,5,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,8,1,7,3,6,5]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,8,5,7,6,1,2]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,6,8,4,5,7,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,1,2,4,3,6,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[7,4,6,1,5,2,3,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,2,6,3,5,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,8,1,4,7,2,3,5]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,4,2,8,3,5,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,8,5,4,2,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,8,1,7,3,5,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,3,6,5,4,2,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,1,6,5,4,2,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,2,1,4,6,3,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,2,3,6,5,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,1,2,3,6,5,4,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[6,8,1,2,7,3,5,4]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,2,3,8,5,4,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,8,2,7,6,3,4]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,2,7,6,3,4]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,2,7,6,3,4,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,8,1,7,3,5,4]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,2,1,7,4,3,5]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,4,1,2,8,5,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,1,6,3,8,5,4,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,1,8,7,6,3,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,3,8,7,4,6,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,5,3,8,7,4,6]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,7,6,5,1,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,5,3,8,7,1,6,4]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,8,4,1,7,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,8,7,1,4,2,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,4,1,7,6,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,7,6,3,5,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,7,6,5,3,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[4,1,8,7,6,5,3,2]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[4,3,8,7,6,5,1,2]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[6,3,1,8,7,2,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,3,7,6,1,4,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,3,8,7,6,2,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[1,5,3,8,7,6,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,5,8,4,7,2,6,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,4,7,2,6,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,7,4,6,1,2,3]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,1,2,4,7,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,6,3,1,2,4,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[5,6,2,4,3,1,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,1,2,4,3,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,8,1,7,2,3,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,8,1,7,2,6,3]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,2,5,8,7,4,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,1,8,7,4,6,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,1,8,7,2,6,4]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,6,1,2,8,5,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,3,1,7,2,6]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,2,8,7,1,3,6]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,2,5,8,7,1,6,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,8,7,6,2,1,5]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,1,4,8,7,6,2,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,4,8,7,6,5,1,2]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,3,4,8,7,6,2,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,4,8,7,6,2,5,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,5,8,7,4,6,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,8,3,1,7,6,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,3,5,8,7,4,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,7,5,8,6,4,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,8,2,6,5,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,1,3,7,5,2,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,8,1,2,6,5,4]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,8,2,6,5,4]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,7,8,1,6,5,4]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,7,8,1,3,6,5,4]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,6,7,3,5,4]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,2,6,7,5,3,4]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[8,2,5,7,1,3,6,4]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,8,1,6,7,3,5,4]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,8,3,7,1,5,4]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,6,4,7,1,5,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,3,4,1,7,5,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,7,4,1,5,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,8,3,7,5,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,1,6,7,5,3,4]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,5,7,1,6,3,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,7,2,3,6,1,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,4,2,6,1,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,7,4,1,6,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,2,4,7,1,6,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,2,3,5,7,1,6,4]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,2,4,7,3,6,1,5]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,7,1,4,6,3,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,1,2,4,6,3,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,7,1,4,6,2,3,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,4,7,1,3,6,2,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,3,7,2,5,4]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,7,1,2,6,4]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,7,1,3,6,2,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,4,7,1,6,2,3]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,7,1,2,6,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,5,1,4,7,2,6,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,4,6,8,2,7,5,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,5,8,2,7,4,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,6,3,1,7,4,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,6,2,8,1,7,4,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,5,7,2,6,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,7,3,6,1,2,4]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,3,5,7,1,6,2,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,8,3,7,5,2,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,2,7,5,1,4]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,8,4,2,7,1,5,3]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,4,7,3,1,5,2]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,5,7,3,1,6,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,2,5,7,1,6,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,3,4,7,2,6,1,5]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,1,3,4,6,2,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,3,7,2,4,6,1,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,5,7,1,6,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,3,4,5,1,6,2]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,7,4,5,2,6,1,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,8,7,2,3,6,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,2,3,4,6,1,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,7,2,3,6,1,4,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[1,3,2,8,5,4,7,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,8,5,3,7,1,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,1,8,4,3,7,6]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[6,2,8,4,3,7,5,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,4,3,1,6,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,3,4,8,2,1,6,5]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,4,8,2,7,5,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,4,1,8,2,7,6]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,5,2,3,7,6]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,5,4,3,2,7,6]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,5,4,2,8,1,7,6]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,3,2,8,7,1,6]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,3,2,8,7,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[6,5,3,2,1,7,8,4]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[5,6,3,2,7,8,4,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,1,6,3,2,7,8,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,6,4,2,7,8,1,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,4,3,7,2,5]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,4,3,6,5,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,4,1,3,6,5,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,7,4,2,6,1,5,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,7,3,2,6,5,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,2,6,4,8,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,3,2,5,4,1,8]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,3,2,1,5,4,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[4,7,5,6,2,3,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,7,5,6,2,4,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,7,5,6,1,3,4,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,6,5,7,1,3,8,4]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,5,7,2,8,1,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,4,7,2,8,3,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,5,4,1,7,2,8,3]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,4,6,2,1,8,3]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,5,7,1,8,2,3]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,4,6,1,7,8,2,3]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,6,7,2,3,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[2,1,4,6,8,7,3,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,4,6,8,7,1,2,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,3,1,6,8,7,2,5]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[5,3,6,8,7,2,4,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,5,1,8,7,2,4]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,5,8,6,2,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[7,2,8,5,6,3,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,8,5,1,7,3,4]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,8,6,7,3,5]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,2,8,6,7,4,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,8,6,7,1,4,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,3,2,6,7,4,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,7,1,6,5,4]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,7,6,1,5,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,2,8,7,6,4,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[7,2,1,8,6,5,4,3]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,3,6,1,8,5,4,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,7,8,5,4,2,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,3,7,8,6,4,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,3,1,7,8,6,5,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,4,7,8,6,1,5,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,5,7,6,2,4,3]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,7,6,8,1,4,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,7,6,8,3,1,2]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,1,7,6,8,3,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,7,5,8,3,2,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,5,1,8,3,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,6,4,3,1,8,2]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,5,1,7,4,3,8,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,7,5,3,8,1,2]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,7,5,1,4,8,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,7,5,4,2,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,1,7,6,5,4,3,2]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[2,7,6,1,5,4,3,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,6,5,1,4,2,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,7,6,5,3,1,2,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,6,4,3,1,5,7,2]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,6,4,1,5,2,7,3]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,6,5,1,3,2,7,4]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,6,3,1,7,2,4,5]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,7,3,1,5,2,4,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[5,3,1,7,2,4,6,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[8,7,1,2,4,5,3,6]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[8,6,1,2,4,7,3,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,5,1,2,6,7,3,4]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[8,5,1,6,4,2,7,3]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,1,3,6,4,7,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,1,5,3,4,7,2]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,1,5,2,4,7,3]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,1,2,5,7,3,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,6,1,2,7,4,3,5]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,7,1,2,5,4,3,6]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[5,1,4,2,3,8,6,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,2,7,3,6,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,8,2,6,3,4]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,8,1,2,4,6,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,1,3,4,6,2]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,1,7,3,4,6,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,5,7,2,4,6,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,2,7,6,3,5]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[1,4,2,3,8,7,5,6]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,2,7,6,3,5,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,1,2,8,7,5,3,4]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,1,2,4,8,7,5,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,1,8,4,6,7,5,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,7,6,4,8,5,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,2,4,6,8,5,3]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[7,1,2,6,8,5,3,4]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[6,1,2,7,8,5,3,4]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[6,1,2,7,4,8,5,3]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,6,4,7,8,5,2]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,3,8,4,6,2]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,1,8,4,2,6,3]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,5,3,2,8,6,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,4,5,2,8,6,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,3,1,5,8,6,2]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,3,1,5,6,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,1,7,4,5,2,6,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,5,3,2,6,4]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,1,2,6,4,5]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,2,8,4,7,5,6]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,2,8,6,4,5,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[3,1,7,2,6,4,5,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,4,2,3,8,6,5,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,2,3,8,5,7,6]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,1,7,2,4,6,3]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,1,3,4,7,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,8,6,4,7,5,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,6,7,4,5,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,2,8,7,3,5,4]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,5,8,4,7,6]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,5,8,6,4,7]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,1,2,8,3,6,5,4]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,2,8,6,4,5,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,7,8,4,6,5,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,8,7,6,4,5,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,2,7,4,6,5,3]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,7,3,6,5,4]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,5,8,7,4,6]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,3,6,8,5,4,7]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[7,8,5,6,3,1,4,2]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,6,3,1,4,2,8]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,3,1,4,2,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,8,5,3,1,4,2,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,8,5,3,1,6,2,4]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,8,5,3,1,6,4,2]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,5,3,6,1,4,2]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,5,3,6,4,1,2]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,5,8,3,4,1,6,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,6,3,4,1,8,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,6,3,1,2,8,4]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,3,6,1,2,8,4]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,1,4,2,6,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,5,3,1,6,4,8,2]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,3,6,4,1,8,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,6,4,8,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,8,4,6,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,8,1,4,6,2]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,1,8,4,6,2]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,3,1,8,2,6,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,3,1,6,4,2,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,5,3,1,8,4,2,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,5,3,1,8,6,2,4]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,5,3,8,1,6,4,2]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,8,6,1,4,2]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,8,6,4,1,2]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[7,5,8,3,6,4,1,2]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,3,6,1,4,2]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,8,3,1,6,4,2]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,3,6,1,4,2,8]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,8,4,1,2,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,5,8,6,3,1,2,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[7,5,8,6,3,1,4,2]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,6,3,4,1,2]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,6,8,3,1,4,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,5,6,3,8,1,2,4]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,3,4,1,8,2,6]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,6,3,1,8,2,4]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,5,6,3,1,8,4,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,5,6,3,8,1,4,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,6,3,8,4,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,3,6,1,8,4,2]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,1,6,8,2,4]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[7,5,3,1,2,8,4,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,5,3,1,2,8,6,4]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,5,3,1,4,8,6,2]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,5,3,4,8,1,6,2]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,5,3,4,1,6,8,2]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,1,4,6,8,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[3,6,2,5,4,1,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,2,8,4,7,6,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,7,3,2,8,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,8,3,2,7,6,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,5,3,2,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,3,2,6,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,5,8,3,2,7,6,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,3,8,5,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,6,3,7,5,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,5,3,2,7,6,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,3,2,7,6,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,2,8,4,7,6,1]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,8,4,7,6,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,7,4,8,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,4,3,2,8,6,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,5,3,2,8,6,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,8,3,6,5,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,8,3,7,5,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,6,4,3,8,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[7,3,2,6,8,5,4,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,8,6,7,5,4,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,3,2,6,7,5,4,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,6,4,3,7,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,5,7,6,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[8,4,5,3,2,7,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,3,6,5,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,4,6,3,7,5,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,3,8,5,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,7,2,6,8,5,4,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,2,6,7,5,4,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,2,5,4,7,6,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,8,6,5,4,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,6,2,8,7,5,4,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,4,7,3,8,5,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,3,7,5,2,1]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,3,6,5,2,1]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,5,3,2,8,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,4,3,2,8,6,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[7,3,2,5,4,8,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,7,5,4,8,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,2,8,6,5,4,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,8,4,3,6,5,2,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,7,4,3,2,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,8,4,3,7,5,2,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,3,2,8,7,5,4,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,3,2,7,8,5,4,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[6,7,4,3,8,5,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]=>[7,2]=>2
[2,3,1,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]=>[8,2]=>2
[2,4,3,1,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]=>[2,7]=>[7,2]=>2
[2,3,4,1,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[3,7]=>[7,3]=>2
[2,3,4,5,1,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[4,6]=>[6,4]=>2
[2,3,4,5,6,1,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]=>[5,5]=>2
[2,3,4,5,6,7,1,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[6,4]=>[6,4]=>2
[2,3,4,5,6,8,7,1,9]=>[[1,2,3,4,5,6,9],[7],[8]]=>[6,3]=>[6,3]=>2
[2,3,4,5,6,7,8,1,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]=>[7,3]=>2
[2,3,4,5,6,7,9,8,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[4,6,8,3,5,7,1,2]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,2,4,5,7,3]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,5,8,2,4,7,1,6]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,2,4,1,6,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,7,3,6,1,8]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,2,8,3,1,6,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,2,5,8,3,7,1,6]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,8,4,7,3,5]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,8,3,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,6,8,4,7,1,2]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,5,8,2,4,7,3]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,2,6,8,5,7,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,3,8,2,6,7,5]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,8,3,2,1,6,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,4,3,7,2,6,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,2,7,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,3,2,1,8,5,7]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,1,7,3,2,5,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,1,7,8,2,6,5]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[3,5,1,2,7,8,6,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,1,4,8,2,6,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,4,7,3,8,6,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,4,7,6,3,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,8,7,1,4,2,6,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,5,1,2,7,6,4]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,3,1,7,2,6,5]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,3,5,2,7,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,3,1,5,2,8,7]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,3,6,5,2,1,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,3,7,6,4,2,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,6,3,4,2,8,7,5]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,6,2,7,5,4]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,8,7,4,2,5,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,4,8,7,5,3,1,2]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[7,6,4,3,8,5,1,2]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[1,7,6,2,8,4,5,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,3,2,6,8,5,4]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,2,7,4,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,2,1,8,5,4,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[6,5,3,2,7,4,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[5,2,6,3,7,4,1,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,5,3,1,6,4,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,1,7,3,8,5,4,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,2,3,7,8,5,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,7,2,8,4,5,3]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,1,8,2,4,6,3]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,2,7,8,3,6,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,1,7,8,6,3,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,1,7,3,8,5,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,2,8,4,3,1,5,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,3,2,1,8,4,5,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,8,3,2,5,6,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,1,8,2,4,5,6,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,1,2,4,5,3]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[8,3,7,6,2,1,4,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,2,8,7,5,1,4,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[8,3,6,5,2,1,4,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,6,3,5,2,4,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,2,5,3,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,4,1,6,5,3,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,1,7,5,3,6]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,4,1,7,6,3,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,1,5,6,2,4,3]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,7,3,6,4,1,2]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,3,7,5,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,1,6,7,5,2,4,3]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,2,6,4,3,7,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,8,1,7,5,4,3,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,1,8,6,4,3,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,2,6,4,3,1,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,2,7,5,4,3,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,1,8,6,5,4,3,7]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,2,7,5,4,3,8,6]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,7,2,4,3,8,6,5]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,8,3,6,5,4]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,8,6,5,2,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,8,6,5,4,1,2]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[1,8,7,6,5,2,4,3]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,1,7,3,2,6,5,4]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,3,2,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,6,5,3,2,1,7,4]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[8,6,3,2,1,7,4,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,6,5,4,1,7,2,3]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,6,5,1,7,3,2,4]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,6,1,7,4,3,2,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[4,6,3,2,7,5,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,3,7,2,5,8,6]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,8,3,1,6,2,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,5,8,3,2,6,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,7,4,1,8,2,6,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,4,3,1,8,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,2,5,4,6,3]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,3,7,2,6,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,1,8,7,5,2,6]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[1,4,8,6,3,5,2,7]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,6,3,5,2,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,6,8,4,2,7]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,5,4,8,7,1,2,6]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,1,4,6,8,7,2,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[1,6,3,8,7,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,2,4,8,7,5,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,4,1,6,7,5,3,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[7,1,6,4,8,5,2,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,6,8,5,1,2,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,3,7,2,6,8,4,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,5,2,8,1,4,7]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,6,5,7,2,4,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,6,3,8,1,5,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,7,3,5,1,8]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,6,2,4,7,5,1,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,2,4,1,8,5,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,8,2,1,6,4,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,2,1,8,6,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,4,3,1,5,2]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[8,7,6,4,1,5,2,3]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[3,8,7,2,1,4,6,5]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,8,2,7,1,5,4,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,8,2,1,5,4,7]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,1,6,5,3,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,1,5,7,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,6,1,4,2,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,7,3,5,4,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,1,7,5,4,2,3]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[1,6,2,8,7,3,5,4]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,2,4,6,7,3,5]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,4,7,1,3,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,5,8,6,4,3,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,2,5,6,4,3,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,5,7,8,4,3,6]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,7,4,8,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,8,3,6,5,4]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,8,6,3,5,4,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,7,6,3,5,2,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,4,6,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,5,8,3,4,6,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,6,4,2,3,5,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[8,6,2,4,7,3,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,2,4,5,7,3,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[2,7,1,4,5,8,3,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,1,6,4,5,2,3,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,5,6,8,2,3]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[7,1,4,6,5,8,3,2]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,2,3,8,5,4,6]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[7,1,5,4,3,8,2,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,4,2,6,8,5]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,1,5,4,6,2,8,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,5,6,4,3,8,2]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,6,5,4,3,2,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,6,2,5,4,3,7,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,1,7,4,3,6,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,5,1,4,7,8,6,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,1,4,8,6,2,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,2,4,7,8,1,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,6,2,4,8,7,1,3]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,3,8,2,4,7,1,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,8,7,2,3,1,4]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,8,2,4,1,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,2,8,5,1,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,7,2,5,8,1,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,1,3,5,2,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,8,1,2,7,5,6]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,4,1,7,2,5,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,8,3,1,5,6,4,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,1,5,4,2,6]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,1,7,6,8,2,5]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,1,7,5,6,8,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,1,5,7,6,2,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,4,1,6,2,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,7,2,5,3,6,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,8,1,2,3,6,5]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,6,1,5,3,7,4]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,6,5,1,3,8,2,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,5,1,3,4,8,2]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,2,6,4,1,3,8,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,7,5,2,1,3,8,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,4,5,3,7,2,6,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,5,2,8,1,6,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,3,1,5,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[7,3,8,4,1,5,2,6]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,3,4,1,6,5,8]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,2,8,3,6,1,5,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,5,7,2,1,3,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,5,2,7,1,3,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,3,5,2,1,7,4,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,3,1,4,2,7]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,6,5,4,2,8,1,7]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,4,7,2,5,3,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,4,8,2,5,3,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,5,8,2,4,3,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,8,2,4,3,7,5]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,2,4,3,7,8,5]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,6,2,4,7,3,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,2,4,7,8,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,2,4,7,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,7,2,4,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,7,2,4,3,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,7,2,4,3,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,6,7,2,4,8,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,8,2,4,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,7,2,4,6,8,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,7,8,3,2,4,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,5,8,3,2,4,6,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,5,6,2,4,8,3,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,6,2,8,3,4,5]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,4,2,8,6,5]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,4,3,8,7,5]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,6,2,4,8,7,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,7,3,2,4,6]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,4,2,3,5,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,5,2,3,4,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,5,2,3,8,7,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,2,8,6,5,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,6,5,2,8,4,3]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,7,5,2,3,8,4]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,7,5,2,8,4,3,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,5,6,2,8,3,4]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,7,6,2,4,8,3]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,3,2,4,7,6]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,5,2,3,7,4,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,6,5,2,3,7,8,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,6,8,4,2,3,7,5]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,4,6,2,8,3,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,5,2,8,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,8,5,2,3,7,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,4,2,3,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,6,4,2,3,7,5,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,5,8,6,2,4,7,3]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,7,3,2,4,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,7,3,4,2,8,5,6]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,4,2,8,5,3,6]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,4,2,3,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,6,4,2,3,8,5,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,4,2,8,5,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,2,8,6,4,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,6,4,2,3,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[7,3,5,6,1,4,8,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,5,6,1,4,8,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,4,1,6,7,5,3]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,4,2,7,5,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,6,1,4,2,8,5,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,7,4,3,5,8,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,1,4,3,5,8,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,1,4,3,5,8,2]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,4,1,6,7,8,2]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,7,1,6,3,5,8,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,4,7,6,5,8,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,7,4,3,5,8,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,6,4,3,5,8,2]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,6,4,3,5,8,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,1,6,4,2,7,5,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,4,1,3,7,2,5,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[4,7,1,3,8,2,5,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,4,1,3,8,2,5,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[1,3,6,4,2,8,5,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,1,2,8,5,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,7,8,1,2,6,5,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,4,2,7,5,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,6,4,2,7,5,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,3,7,2,5,6]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,1,3,6,2,5,4]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,8,5,7,3,2,1,4]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,4,3,7,2,5,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,3,4,7,6,1,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,8,4,6,2,1,5]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,4,6,8,2,1,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,7,8,6,1,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,4,7,3,8,2,5,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,6,8,3,2,1,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,3,4,8,6,1,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,4,8,2,1,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,3,4,2,8,5,6]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,4,3,8,2,5,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,1,7,3,8,2,5,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,3,7,2,5,6]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,2,3,4,7,6,1,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,2,3,7,8,6,1,5]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,2,3,4,8,6,1,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[2,7,5,6,3,8,1,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,2,6,3,8,1,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,2,6,8,4,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,2,5,6,8,4,1,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,2,3,8,5,6,1,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,2,3,8,7,6,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[8,2,3,7,5,6,1,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,3,7,2,5,4]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,8,4,2,6,5,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,1,8,2,5,6,3]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,4,8,5,2,1,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,4,3,8,5,6,1,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,8,3,6,2,5,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,6,3,2,1,4]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[6,5,8,7,3,2,1,4]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[8,5,7,6,3,2,1,4]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,5,3,8,7,6,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,5,8,6,2,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,8,6,5,2,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,8,7,3,6,2,5,4]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,7,5,3,2,1,4]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[5,7,6,8,3,4,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,6,8,4,5,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,7,6,8,2,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,4,6,5,8,2,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,4,6,5,8,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,4,8,6,7,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,4,6,5,7,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,4,7,5,8,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,7,5,8,3,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,4,8,5,7,2,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,6,5,7,2,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,8,6,7,2,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,5,4,6,2,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,5,2,4,3,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,6,5,7,3,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,8,5,6,3,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,6,5,8,3,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,7,6,8,3,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,6,8,2,5,3,4]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,6,8,4,5,2,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,6,8,1,4,2,3]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,5,6,1,3,2,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,1,3,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,7,6,8,4,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,6,8,2,4,3,5]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,3,2,6,4,5]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,6,2,4,3,5]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,6,7,2,4,3,5]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,4,2,6,3,5]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,4,2,5,3,6]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,1,4,3,6,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,1,2,4,3,5,6]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,3,6,5,8,7,1,2]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,6,5,7,8,1,2]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,2,5,6,7,8,9,4]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[3,4,1,2,6,7,8,9,5]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[3,4,5,6,7,8,1,2,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[1,6,2,3,8,7,4,5]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,4,3,2,8,6,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,4,7,6,2,5,8,3]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,6,5,3,7,4,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,5,3,7,8,4]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,3,7,5,2,6,8,4]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,3,7,4,2,6,8,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,6,4,3,7,8,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,6,4,3,7,5,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,4,7,3,2,5,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,4,3,2,5,8,6,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,5,3,2,4,8,6,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,3,2,8,6,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,5,3,2,4,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,5,4,3,1,8,2]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[6,8,5,4,3,2,1,7]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[7,1,5,4,3,8,6,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,5,4,8,1,7,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,1,4,3,2,7,5]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,5,4,3,7,1,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,1,4,3,8,5,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,5,8,3,1,7,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,5,1,3,2,7,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,2,4,3,7,6,5]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,4,7,2,1,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,9,6,5,4,3,8,1,7]=>[[1,2,7],[3,9],[4],[5],[6],[8]]=>[2,5,2]=>[5,2,2]=>3
[7,6,5,1,3,8,4,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[1,6,3,4,8,7,5,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,4,5,8,3,7,6,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,5,4,1,2,7,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,8,5,2,3,7,6,4]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,4,3,7,1,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,4,7,2,6,5]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,8,4,3,2,1,6]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,8,5,7,3,2,1,6]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,10,7,6,5,4,3,9,1,8]=>[[1,2,8],[3,10],[4],[5],[6],[7],[9]]=>[2,6,2]=>[6,2,2]=>3
[5,1,7,6,8,4,3,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,5,2,6,1,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,8,2,1,7,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,5,2,1,7,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,7,5,6,1,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,5,1,8,4,3,6]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,8,7,4,2,3,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,8,6,7,4,3,5,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,5,2,4,1,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,3,6,4,1,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,1,4,5,3,2,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,8,7,1,4,6,5,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,7,1,2,4,3,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,7,6,8,2,5,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,8,1,7,2,4]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,6,8,5,7,1,4]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,7,2,4,8,5,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,6,5,2,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[7,1,8,2,5,4,3,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,3,7,4,1,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,4,7,5,1,8,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,7,6,2,3,1,5]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,1,2,5,6,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,7,3,5,6,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,7,4,2,5,6,3]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,4,3,8,2,5,6,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,1,5,8,2,7,3]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[2,5,8,7,3,6,1,4]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,8,7,4,6,3]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,5,6,7,4,1,2]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,4,3,2,8,5,6,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,2,7,1,8,5,6,3]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,2,8,5,6,3]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,8,7,3,5,6,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,8,3,1,5,6,2]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,7,2,8,5,6,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,1,4,8,5,6,2]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,3,4,8,5,6,1]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,8,5,2,7,4,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,4,5,8,6,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,3,6,7,5,4]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,1,6,4,7,5,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,8,2,6,4,1,5,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,5,8,7,1,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,6,2,1,5,8,4,3]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[4,5,2,7,6,1,8,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,6,8,4,7,2,3]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,8,7,5,2,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,4,8,6,5,2,3,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,4,7,3,2,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,4,1,2,3,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[2,6,4,8,5,3,7,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,5,8,4,2,1,6]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,2,5,8,4,1,7,6]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,7,1,5,2,3,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,8,7,5,6,1,2,3]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,1,4,8,7,3,5,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,8,4,3,5,6,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,8,1,3,5,6,2]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,3,4,1,5,6,2]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,8,2,7,3,5,6,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,8,7,2,5,6,4]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,1,7,2,5,6,4]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,3,7,1,5,6,4]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,7,1,3,2,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,6,7,3,1,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,8,2,7,6,1,5]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,8,4,2,1,3,7,5]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,8,2,4,3,5,6,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,3,7,1,5,6,4]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,2,7,3,5,6,4]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,1,3,2,8,5,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,8,6,2,1,4,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[4,6,5,2,8,3,1,7]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,7,5,1,8,2,6]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,2,7,4,3,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,2,5,4,3,8,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,1,4,5,2,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,2,4,5,3,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,2,4,5,3,7]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,1,2,5,4,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,1,6,2,3,4,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,1,6,5,8,2,3,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,6,2,5,1,7]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,6,1,4,5,2,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,6,8,4,5,1,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,5,4,3,8,1,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,3,8,7,4,2,5,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,4,3,7,6,1,2]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,4,3,1,6,2,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[1,7,4,3,8,6,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,5,3,4,8,2,6]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,6,1,7,4,5,3]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,6,5,7,2,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,6,8,2,1,5,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,8,7,4,3,5,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,4,3,1,6,7,2]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[1,5,8,6,3,4,7,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,8,6,3,4,7,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,3,8,5,6,7,2]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,8,4,3,1,7,2]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,6,5,2,8,1,7,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,8,1,3,6,4,5]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,2,3,6,7,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,8,3,2,5,6,7,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,8,3,1,5,6,7,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,8,3,2,5,6,7,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,2,3,1,5,6,7,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,3,5,6,7,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,8,2,3,6,7,5]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,7,8,6,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[7,5,1,8,2,4,3,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,8,1,2,4,7,6]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,8,1,2,3,7,6]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,7,1,8,6,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,4,1,2,6,7,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[5,4,8,2,3,6,7,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,3,6,7,4,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,6,8,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,7,1,8,5,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,7,3,2,8,5,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,7,1,4,3,8,5,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,1,8,6,3,7,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,1,3,6,2,7,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,8,5,1,7,2,3,4]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,6,5,8,2,1,4]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,3,5,8,2,1,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[4,5,8,7,3,6,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,8,6,1,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,5,6,1,4,7,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,5,4,1,2,7,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[2,6,1,8,3,7,5,4]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,6,2,8,5,3]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,5,3,8,7,2,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,6,3,7,1,5,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,6,1,5,8,2,3,4]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,6,8,5,1,2,7,4]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,2,4,8,1,7,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,1,4,8,2,6,7,3]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,2,5,1,6,7,3]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,8,5,2,6,7,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,1,8,5,6,7,3]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,4,8,2,6,7,3]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,1,5,8,6,3,4]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[2,8,4,5,1,6,7,3]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,8,3,7,6,1,2]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,1,5,8,6,2,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,4,8,5,1,7,2]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,4,8,1,6,7,2]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,1,2,8,3,5,4]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,8,4,1,2,6,3]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,4,6,1,3,2]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,4,8,7,1,3,2]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,8,1,2,7,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,1,6,2,3,8,4]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,5,1,6,8,2,4,3]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,4,1,8,2,7,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,5,4,7,1,2,8,3]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,7,8,1,3,2]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,3,7,1,4,2,8]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,1,8,4,2,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,5,1,4,8,3,2,6]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,1,6,4,7,3,5,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,1,4,8,3,6,2]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,3,7,1,4,8,2]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,1,5,8,7,2]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,4,1,5,3,8,6,2]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,5,4,3,7,6,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,4,3,7,2,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,1,5,3,8,2,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,1,5,3,2,6,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,1,5,4,3,2,6,7]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,1,6,4,2,5,3,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,5,3,1,2,7,4,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,5,3,8,1,4,2,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,6,8,1,4,3,2,5]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,2,5,4,3,6]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,2,5,4,6,3]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,1,2,5,4,8,3]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,3,8,1,4,7,2]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,5,3,1,2,7,8,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,5,1,4,2,6,8,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,6,4,2,5,7,3]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,4,1,5,3,2,8,6]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,1,5,2,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,1,5,7,2,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,4,1,5,3,6,2,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,5,4,3,6,2,7]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,4,3,6,7,2]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,4,1,5,3,6,8,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,1,5,7,8,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,7,3,8,4,5,1,2]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,4,5,1,8,2,3]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,5,6,2,3,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,5,6,1,8,2,3]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,5,6,3,8,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,5,8,4,6,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,8,6,7,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,6,5,7,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,4,7,1,8,2,3]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,7,3,8,2,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,8,2,7,3,4]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,8,4,7,2,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,6,5,7,2,3]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,8,6,7,2,3]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,4,5,1,6,2,3]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,3,1,6,5,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,8,1,4,3,7]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,4,1,8,2,7]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,4,5,2,7,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,4,5,1,8,2,7]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,4,8,1,5,3,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,6,1,5,4,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,4,1,6,5,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,5,3,4,1,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,5,3,6,2,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,8,6,7,2,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,6,2,7,4,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,4,8,2,7,3,5]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,4,7,3,5,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,3,6,4,5,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,6,4,8,2,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,8,4,6,3,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,5,8,4,6,2,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,5,8,2,6,3,4]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,5,6,3,8,2,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,5,6,3,4,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,5,3,4,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,5,3,8,2,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,5,8,1,4,2,3]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,2,3,1,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,3,1,8,4,5]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,8,1,4,3,5]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,7,5,6,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,7,5,8,2,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,5,8,1,4,3,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,7,5,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,8,4,7,5,6]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,3,1,6,4,5]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,6,1,4,3,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,7,1,4,3,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,4,3,7,5,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,5,4,6,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,7,3,6,1,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,8,2,7,3,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,8,2,7,5,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,8,6,7,2,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,5,1,8,6,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,8,1,6,5,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,2,5,1,6,4,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,8,1,6,3,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,6,1,8,2,7]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,7,1,4,2,5,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,3,7,5,1,2,4]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,6,1,8,3,5,2,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,2,8,3,5,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,2,3,8,5,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,6,2,7,3,1,5,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,7,2,5,1,6,3,4]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,4,2,1,7,6,3,5]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[8,5,7,2,1,4,3,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,3,1,4,2,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,3,1,4,6,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,5,7,2,1,4,6,3]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,4,2,1,3,7,6,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[8,4,3,1,7,2,6,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,5,1,3,2,7,6,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,6,4,1,3,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[8,4,7,5,1,6,2,3]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,5,1,2,3,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,7,3,5,1,2,6,4]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,3,2,6,5,1,4,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[4,8,6,3,5,1,2,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,3,1,5,2,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,4,7,2,1,5,3,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,7,1,5,4,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,1,4,2,6,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,7,3,1,2,6,4,5]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,7,3,1,2,4,6,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,3,2,1,4,7,6,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[8,3,2,1,7,4,6,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,3,2,7,1,5,6,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,4,7,2,1,5,6,3]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,7,2,1,6,3,4,5]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[3,6,5,4,1,2,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,8,5,6,7,4,1,2]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,5,8,6,2,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,7,8,6,3,4,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,5,7,6,3,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,6,3,2,1,5,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,2,1,5,3,4,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[5,8,1,3,7,6,4,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,3,6,1,8,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,4,2,8,1,5,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,6,8,5,7,3,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,7,3,8,5,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,6,7,5,3,4,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,5,8,7,6,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,1,4,7,6,3,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,7,8,5,3,2,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,1,3,7,6,2,8,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,1,6,3,2,7,4]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,1,5,2,8,4]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,8,4,7,5,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,6,1,3,2,5,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,6,7,3,1,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,3,8,2,1,5,6]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[4,7,5,8,1,6,3,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,3,2,7,8,1,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[4,2,5,1,6,7,8,3]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,4,8,5,7,1,3,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,4,6,8,5,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,2,5,6,1,4,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,8,7,5,6,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,7,3,5,1,8,4]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,4,2,5,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,1,6,3,2,4]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,7,2,8,4,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,8,6,5,2,1,7]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,7,6,1,4,5,8,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,5,8,2,1,7,3,4]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,4,3,5,1,6,8,2]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,1,6,3,5,8,7,2]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,5,8,4,3,7,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,7,1,5,4,3,2]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,6,5,8,4,7,3]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,8,5,4,3,7]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,1,8,5,6,2,3,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,6,4,8,7,3,5,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,8,4,3,5,1,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,7,6,1,3,5]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,1,8,2,7,5,4,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,1,2,6,7,4,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,3,2,7,1,6]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,4,8,6,3,2,5,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,4,7,2,1,3,6]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,1,8,4,3,7,5,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,2,4,5,7,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,4,2,3,6,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,2,4,3,1,6,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,8,3,1,6,4,5,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[8,2,1,3,4,7,5,6]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[1,4,8,2,6,3,5,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,3,5,4,8,6]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,3,8,4,5,7,6]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,8,3,4,5,7,6]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,2,6,4,5,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,5,7,2,3,6,4,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,3,5,4,8,6]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,8,2,4,5,7,6]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,3,8,4,6,7,5]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,2,3,5,4,6,7]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,7,8,2,3,6,4,5]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,7,8,2,3,5,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,8,2,5,3,6,4]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,8,2,4,5,3,6]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,3,6,4,5,7]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,2,3,6,4,5,7]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,8,3,5,4,6,7]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,8,3,6,4,5]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,2,7,8,3,6,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,2,8,4,6,7,5]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,2,3,4,6,7,5]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,7,8,2,4,3,6,5]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,3,1,5,2,8,4]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,3,1,5,2,7,4]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,4,5,1,2,8,3]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,6,1,5,2,4,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,5,4,1,2,8,3]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,8,6,4,1,7,2,3]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,4,1,8,2,3]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,4,7,5,1,2,8,3]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[6,2,1,7,5,3,8,4]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,1,5,2,7,4]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,8,4,1,7,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,5,7,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,8,6,7,1,2,3]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,6,1,7,2,3]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,1,6,7,2,4]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,1,7,6,8,3,4]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,7,6,1,8,2,3]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,6,5,7,1,2,3]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,5,6,8,1,2,3]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,5,7,8,1,2,3]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,4,6,1,8,2,3]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,6,1,7,2,3]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,1,6,7,2,4]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,1,6,8,2,4]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,6,3,1,7,8,2,4]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,8,3,1,7,6,2,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,4,8,1,6,2,3]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,6,8,1,7,2,3]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,6,7,5,1,2,3]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,2,1,7,8,6,3,4]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[5,3,8,1,7,6,2,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,7,1,6,2,3]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,7,5,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[4,7,8,6,5,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[4,8,7,6,5,1,2,3]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[2,5,4,7,3,6,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,6,3,7,5,1,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,3,6,5,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,3,1,5,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,5,3,1,6,4,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,3,7,6,4,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,6,5,3,7,4,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,7,6,3,5,1,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,5,3,6,4,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,7,5,4,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,5,2,3,8,4,6]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,1,3,7,5,4,8,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,1,8,6,5,4,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,3,1,8,6,4,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,8,3,1,6,5,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,6,4,1,5,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,6,8,2,1,4,5,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[1,5,2,8,3,4,7,6]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,6,3,8,7,4,5]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,3,6,4,7,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,7,6,3,4,8,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,1,3,8,7,5,4,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,3,8,6,4,7,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,7,4,8,6,5]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,6,3,8,4,5]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,6,4,8,7,5]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,7,6,4,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,6,3,1,8,5,4,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,1,3,8,5,4,7,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,1,8,4,2,3,5,6]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[2,1,8,4,3,5,7,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,2,6,3,1,8,5,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,8,3,1,6,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,5,8,2,4,1,6,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,5,4,8,3,1,6,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,2,1,8,3,5,7,6]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,7,4,2,3,5,6]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,5,2,8,7,3,4,6]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,2,7,3,6,4,8,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,8,6,3,7,4,5]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,3,8,6,4,5]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,3,8,4,7,6,5]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,3,4,8,6,5]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,3,8,4,7,5]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,2,3,8,7,4,6]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,1,8,3,7,5,6]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,2,1,7,4,5,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[1,8,4,2,7,3,5,6]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,2,8,6,3,4,7,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,3,8,4,6,5]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,3,8,7,4,6,5]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,8,7,6,4,5]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,5,3,8,1,6,4,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,4,7,1,5,3,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,7,1,4,3,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,7,1,2,6,4]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,5,7,2,6,4,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,8,6,2,5,7,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,8,6,1,2,5,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[2,5,7,1,4,8,6,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,1,5,7,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,3,8,1,6,5,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,7,5,6,4,3]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,8,1,6,5,7,4]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,8,1,3,5,7,6]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,6,1,2,4,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[3,5,7,6,2,4,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,6,7,2,3,5,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,7,1,2,3,5]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,8,6,7,1,3,5,2]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,8,6,1,5,7,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,5,7,1,6,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,8,5,6,1,7,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,5,7,2,1,6,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,8,6,2,1,5,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[3,5,7,6,2,1,4,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[4,8,6,7,2,1,3,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,6,7,3,5,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,3,4,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,2,1,3,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,6,7,2,1,4,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,7,2,1,5,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,1,7,5,2,8,6]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,8,5,1,7,6]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,3,8,5,1,6,7,2]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,6,7,1,5,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,1,4,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,2,3,4,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,6,7,2,4,3,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,1,2,4,3]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,3,8,5,1,6,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[4,2,8,5,1,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,2,8,5,6,1,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,4,8,6,1,5,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[3,2,5,7,6,1,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[4,8,6,7,1,3,2,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,6,7,1,2,5,3]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,7,2,5,3,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,8,5,2,6,7,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,8,5,1,2,6,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[4,2,6,7,5,1,3,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[3,8,5,7,1,4,2,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,4,7,1,5,2,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,2,8,4,6,1,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,1,7,4,6,2,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,4,7,2,5,1,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,3,8,5,2,6,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[4,1,2,6,7,5,3,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,2,6,7,5,3,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,6,7,3,2,5,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,7,3,1,2,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,1,5,7,6,2,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,4,1,7,5,6,2,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,7,5,2,8,6,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,7,5,2,3,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,8,6,7,2,3,1,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,7,3,2,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,6,7,4,2,3,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,6,7,4,1,2,3]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,6,7,4,1,3,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,6,7,3,1,4,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,7,3,1,5,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,6,7,5,3,8,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,7,5,3,2,8,6]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,5,3,1,7,6]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,2,1,6,7,5,3,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[4,8,6,7,3,2,1,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,8,6,7,4,2,1,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,8,6,7,4,3,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,3,5,8,1,4,2,6]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,8,7,6,1,4,2,5]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,1,8,3,6,7,2,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,7,8,5,6,2,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,7,1,5,8,6,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,4,7,8,5,2]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,8,4,7,5,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,1,3,5,7,2,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,1,4,3,8,2,5]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,8,1,6,5,4,2,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,1,3,7,5,8,2,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,7,3,8,4,2,5]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,6,3,5,2,4]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,7,6,5,8,4,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,6,5,3,4,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,2,6,7,5,3,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[4,8,1,6,7,5,3,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,4,1,6,8,2,5,3]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,8,6,2,7,5,4]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,2,7,8,4,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,8,6,2,5,3,4,7]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,6,8,1,5,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,3,6,4,5,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,8,6,2,1,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,7,4,1,6,8,3,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,7,2,4,5,1,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,4,5,2,3,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,6,5,1,3,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,1,7,5,2,6,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,5,8,6,1,2,4,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,7,3,1,4,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,5,4,3,6,8,1,7]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,5,4,6,2,1,7]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,1,3,7,5,6]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,1,2,7,5,8,3]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,8,3,6,7,5,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,4,5,2,6,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,8,5,1,6,2]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,8,2,7,6,1,3]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,3,6,5,8,4]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,7,6,3,4,1,5]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,2,6,3,4,1,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,7,5,8,6,2,3]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,8,4,3,6,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,7,5,4,3,6,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,8,1,4,7,5,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,4,5,6,1,2,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,4,3,5,7,8,2,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,8,7,1,3,4,2]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,2,4,8,1,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,2,7,4,3,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,5,6,4,3,1,7]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,6,5,4,3,2,7]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[6,1,5,2,8,4,7,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,1,8,5,7,2,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,2,8,5,6,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,7,2,8,5,6,3]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,3,5,8,6,2,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,3,5,8,6,1,2,4]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[3,6,8,1,5,7,2,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,5,8,1,7,2]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,1,5,7,2,3,4]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,2,5,8,6,3,4]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[1,7,2,5,8,6,3,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,6,8,2,3,5,4]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,8,1,2,3,5,4]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,1,5,8,6,3,4]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,7,1,8,5,6,3]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,5,8,3,1,6,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,2,1,8,5,6,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,6,8,2,1,3,5,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,6,8,3,5,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,6,8,2,1,5,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,2,1,6,8,5,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[6,7,4,1,8,5,3,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,4,3,1,8,5,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,7,4,1,6,8,5,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,7,6,8,1,5,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,2,6,8,5,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[7,3,2,5,8,6,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[3,1,7,6,8,2,5,4]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,6,8,1,2,5,4]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,7,6,8,2,5,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,4,2,6,8,5,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,4,1,2,6,8,5,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[7,1,4,2,8,5,6,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,2,5,4,6,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,4,6,1,5,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,8,1,6,4,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,8,5,4,2,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,1,2,6,8,5,4,3]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,7,2,6,8,5,4,3]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,6,8,3,2,5,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,8,3,1,2,5,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,1,5,8,6,3,2,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[7,2,5,8,6,3,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[3,6,7,1,8,5,4,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,8,5,4,1,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,6,8,2,3,1,5,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,6,8,3,1,5,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,1,6,8,5,4,3]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,3,1,8,5,4,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,1,8,5,4,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,2,1,6,8,5,4,3]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[7,6,8,3,2,1,5,4]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,7,8,5,6,1,3,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,5,8,7,1,3,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,4,8,1,2,7,3]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,5,6,7,2,4,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,5,1,8,2,7,3]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,7,1,2,8,3]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,3,6,7,2,1,5,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[5,3,6,7,1,4,2,8]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,6,7,3,2,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[8,1,3,6,7,4,5,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,1,6,8,4,5,3]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,6,7,1,4,8,3]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,6,7,3,1,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,2,4,1,5,8,7,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,1,5,4,8,6,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,5,3,7,2,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,1,5,4,8,2,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,1,5,8,2,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,3,4,2,1,8,6,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,3,5,2,7,1,6,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,3,8,1,4,2,7]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,7,2,4,5,6,3]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,1,2,4,5,8,3]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[4,7,8,2,3,1,6,5]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,2,8,1,4,7,3]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,2,1,3,7,8,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,5,1,3,2,6,8,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,6,3,2,5,7,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,4,1,3,5,2,8,6]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,4,2,3,1,6,8,7]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,3,1,4,5,6,2,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[8,1,4,3,5,6,2,7]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,3,1,5,7,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,8,4,2,1,6,5,3]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,2,1,5,6,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,2,3,4,8,7,1,5]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[6,2,3,4,7,8,1,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[7,8,3,4,6,2,1,5]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,6,4,2,1,5]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,3,5,6,2,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,2,3,8,7,5,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[6,2,3,7,8,5,1,4]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,2,6,3,8,1,7,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,2,5,8,7,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,3,2,8,4,7,1,5]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,8,7,5,1,2]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[6,4,3,7,8,5,1,2]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,2,4,1,7,3,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,7,4,8,1,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,5,7,8,1,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[5,7,2,3,6,1,8,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,2,3,6,1,7,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,5,8,3,2,1,6]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,5,6,8,3,2,1,7]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,6,8,5,3,2,1,7]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,6,1,4,2,3,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,6,8,4,3,7,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,1,4,2,3,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,8,3,4,1,7,6]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,8,6,3,2,1,7]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,6,5,8,3,2,1,7]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,5,6,3,2,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,2,3,4,5,8,1,7]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[5,1,4,3,6,2,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,4,3,7,2,8,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,4,3,8,2,7,6]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,2,4,1,7,8,3]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,2,4,1,8,7,3]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,2,4,1,8,6,3]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,4,2,8,7,5,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,4,2,7,8,5,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,4,1,7,6,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,7,4,1,6,8,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,1,3,7,2,6,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[5,1,4,3,6,2,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,8,6,4,3,7,1,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,1,4,2,3,7,6]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,6,3,4,2,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,8,6,5,3,2,1,7]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[4,8,5,6,3,2,1,7]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,4,7,8,3,2,1,6]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,4,8,7,3,2,1,6]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[4,6,8,7,3,2,1,5]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,6,7,8,3,2,1,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,7,6,8,3,2,1,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,8,5,3,2,1,6]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,7,1,3,4,2,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,8,4,2,3,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[5,1,7,4,2,3,6,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[5,8,1,3,4,2,6,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,5,3,2,1,6]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[4,7,8,6,3,2,1,5]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,8,7,6,3,2,1,5]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[4,8,2,6,3,7,5,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,8,1,6,2,5,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,7,2,5,1,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,4,3,7,1,6,2]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,1,2,4,3,5,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,1,3,4,2,6]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,6,3,1,2,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,3,8,2,7,5,6,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,3,8,2,6,5,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,2,8,1,6,5,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,1,3,8,2,6,5,7]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,8,3,7,5,6,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,8,1,5,4,2,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,8,1,5,4,6,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,8,1,6,2,5,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,2,1,8,6,5,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,7,8,4,1,2,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,1,7,8,5,3,2,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,7,6,8,4,2,1,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,8,2,6,4,5,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,3,8,1,6,5,7]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,8,2,6,5,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[2,6,8,4,7,3,1,5]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,6,8,4,2,1,5]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,6,2,8,3,5,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,4,8,1,6,5,7]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,8,3,6,1,5,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,1,8,5,2,6,3]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[1,3,2,4,8,6,5,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,1,2,4,8,6,5,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[3,1,4,8,2,6,5,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,7,4,8,5,1,2,6]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,7,2,8,3,5,4,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,3,4,8,6,5,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[1,2,3,4,8,6,5,7]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,8,3,6,2,1,5,7]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,5,8,2,6,1,4,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,5,8,2,4,1,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,8,7,2,4,6,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,4,5,7,3,6,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,5,7,3,8,1,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,4,5,8,3,1,7]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,8,1,2,5,6,3,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,3,5,2,6,4,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,2,1,6,3,8,4,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,2,5,1,8,4,3,7]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,1,5,8,4,2,7]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,4,5,8,3,2,7]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[5,6,4,8,1,3,2,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,5,4,3,8,2,1,7]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[5,4,3,7,2,8,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,8,4,3,7,2,6,1]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,8,3,7,2,5,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,3,2,8,1,5]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,6,2,7,8,5]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,4,3,7,2,8,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,8,5,3,1,2,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[5,7,3,4,1,2,8,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,5,4,7,6,2,1,3]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,5,7,4,3,6,1,2]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,8,1,6,7,5,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,8,3,6,1,5,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,8,6,7,4,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,8,6,4,7,5,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,2,7,4,1,5,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,6,2,1,4,3,8,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,6,1,3,4,2,8,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,5,7,3,2,6,8,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,7,3,2,5,8,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,6,8,5,7,4,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,2,3,6,7,4,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,2,3,1,6,8,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,6,4,7,2,3,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,7,5,2,8,4,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,4,1,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,1,7,8,3,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,6,3,8,1,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,8,7,2,3,5,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,6,8,7,4,5,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,7,4,1,6,8,5]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,2,1,7,8,4,5]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[3,7,1,8,4,2,5,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,2,1,3,7,5,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[8,1,3,7,4,2,6,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,3,7,6,2,1,5]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,5,2,7,6,1,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,2,8,7,1,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,2,8,1,6,5,4]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,8,7,2,6,5,4,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,2,7,8,6,1,5,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,2,4,7,1,5,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,1,8,7,3,6,4]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,1,6,3,7,5,4]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,3,1,7,5,2,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,1,6,7,2,4,3]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,8,1,5,7,4,3]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,2,6,1,4,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,2,5,6,4,3,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,6,7,5,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,6,8,1,5,4,3]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,8,5,6,4,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,8,1,6,2,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,1,8,2,6,5,4]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,7,3,8,6,5,4]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,1,7,6,5,4,3]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,1,4,7,6,5,3,2]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,6,7,5,1,4,3,2]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,6,5,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,4,3,2,1,6,7]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[6,4,7,3,2,1,8,5]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,4,7,3,2,1,6,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,5,3,7,2,1,4,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,8,3,6,2,1,4,7]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,3,7,8,2,1,4,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[5,3,7,6,2,1,4,8]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[3,8,7,6,2,1,4,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[5,8,4,2,6,1,3,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,2,5,1,3,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,3,2,6,1,4,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,3,2,5,1,7,6]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,7,2,5,1,8,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,7,2,5,1,4,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,4,2,7,5,1,3,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,3,2,7,5,1,4,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[5,3,2,6,7,1,4,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,8,2,6,5,1,4,7]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,2,7,8,5,1,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[5,2,7,6,8,1,3,4]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,6,5,1,3,8]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,8,7,6,5,1,3,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[6,5,4,3,1,7,8,2]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[6,4,7,3,1,5,8,2]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,4,7,3,1,8,6,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,3,7,1,5,8,2]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,4,3,6,1,8,7,2]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,3,7,8,1,4,5,2]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,7,6,1,4,8,2]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,7,6,1,5,8,2]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,7,6,1,4,5,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,5,4,2,1,7,3,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[6,4,7,2,1,5,3,8]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,2,1,5,3,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,8,3,2,1,4,7,6]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,8,3,2,1,5,7,6]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,3,7,2,1,4,8,6]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,8,7,2,1,4,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[6,5,2,7,1,4,3,8]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,8,2,6,1,4,3,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,2,7,1,5,3,8]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,6,1,8,3,7]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,6,1,5,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,2,7,8,1,4,3,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,7,6,1,5,3,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,6,1,4,5,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[6,5,4,1,8,7,3,2]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[5,8,4,1,6,7,3,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,4,7,1,5,8,3,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,7,1,6,8,3,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,1,5,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,3,1,6,8,7,2]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[4,8,3,1,5,6,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,7,1,5,4,6,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,2,1,6,4,3,7]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,2,1,5,4,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,1,6,4,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[3,8,2,1,5,4,6,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[6,2,7,1,5,4,3,8]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,1,6,4,3,8]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,1,5,6,3,8]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,1,5,4,6,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[2,8,7,1,5,4,3,6]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,1,7,8,4,3,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[5,8,1,6,7,4,3,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,4,1,7,5,8,3,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,1,6,7,8,3,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[4,8,1,6,5,7,3,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,1,7,5,4,8,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,1,6,7,4,8,2]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,3,1,6,5,7,8,2]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,1,6,5,4,7,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,1,6,7,4,3,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[4,2,1,6,5,7,3,8]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[2,8,1,6,5,4,3,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,7,8,5,4,3,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,1,7,6,5,8,3,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,7,6,5,4,8,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,8,1,2,6,3,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,7,2,6,3,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,3,5,6,2,4,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,1,3,5,7,2,4,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[3,6,8,1,7,2,4,5]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,5,6,8,1,7,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,5,8,2,6,7,1,3]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,5,6,7,1,4]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[1,7,2,3,5,4,6,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,1,2,3,5,4,6,7]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[2,7,8,1,3,5,4,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,3,5,6,1,4]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,7,8,1,6,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,5,8,1,7,6,3,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,5,8,7,2,1,6,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,7,3,5,6,2,1,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,2,1,3,5,4,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[3,6,8,7,2,1,5,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,6,4,1,7,5,3,2]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[7,6,4,3,1,8,5,2]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[2,3,6,7,8,1,5,4]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,8,1,2,5,4,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,6,7,2,5,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,1,8,5,2,3,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[7,1,4,2,8,3,6,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,2,5,3,6,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,5,4,2,3,6]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,7,2,6,5,4,3,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,6,3,2,5,4,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,6,3,1,2,5,4,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,1,7,6,3,2,4,5]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,2,5,7,6,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,6,8,1,7,5,4,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,6,7,5,4,1,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,7,8,6,3,1,5,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,7,8,1,6,5,4,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,3,1,8,6,5,4,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,7,2,1,6,5,4,3]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,6,3,2,1,5,4]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[2,1,8,6,3,7,4,5]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,5,2,7,4,3]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,1,7,4,2,6,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,1,7,5,4,3,8,6]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,1,7,8,3,6,5,4]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,4,8,5,7,3,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,3,1,6,2,4,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[6,4,1,5,2,3,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,5,2,6,1,4]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,4,6,8,1,2]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,7,6,2,1,4]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,2,6,3,8,5,1,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,2,1,7,6,4,3]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,3,2,4,1,7,5,6]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,2,8,1,4,6,5,3]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,4,5,3,2,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,6,1,4,7,3,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,6,1,7,4,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,4,1,2,8,7]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,7,3,6,5,1,4,2]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,4,3,6,1,8,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,7,2,8,1,5,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,3,5,8,1,6,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[3,8,4,7,1,6,5,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,4,6,1,5,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,3,4,5,7,6,1,2]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[3,2,4,5,6,8,1,7]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[5,6,8,1,4,2,7,3]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,7,8,4,6,2,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,7,8,6,2,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,5,7,8,6,1,2,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[3,5,1,6,8,2,7,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,5,6,8,2,7,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,5,6,8,1,7,4]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,6,4,8,2,1,7,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,6,3,8,4,7,2]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,1,6,8,3,7,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,2,6,8,3,7,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,7,1,8,6,2,3,4]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,5,2,7,8,6,3,4]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,5,2,8,3,4]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,1,7,5,2,8,3,4]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,7,5,1,8,3,4]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,7,2,8,6,1,3,4]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,5,7,8,6,2,1,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,1,7,8,6,3,4,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,3,7,8,6,4,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,2,7,8,4,6,1,3]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,5,7,8,6,1,4]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[6,2,7,5,1,8,3,4]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,7,5,8,3,4]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,5,4,1,8,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,7,5,2,4,1,8,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,2,5,3,8,1,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,4,5,2,1,8,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,7,8,6,4,3,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,5,7,8,6,3,1,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,1,7,8,6,3,2,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,3,7,5,1,8,2,4]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,7,5,3,8,2,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,7,5,4,2,8,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,7,5,1,4,2,8,3]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,8,6,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[4,1,7,2,6,5,8,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,7,1,5,6,8,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,4,1,5,2,8,3]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,7,4,5,2,8,3]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,3,7,5,8,2,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,1,7,5,8,2,4]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,3,7,8,6,1,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,5,4,2,1,8,3]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[6,3,2,7,5,8,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,4,2,5,1,8,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,7,4,5,1,8,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,3,7,5,8,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,1,6,3,8,2,4]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,6,1,3,8,5,4]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,3,5,1,8,2,6,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,5,1,8,2,4,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,7,5,1,8,6,2,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,7,4,1,8,3,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,7,3,8,5,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,5,1,8,4,7,2]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,5,1,8,4,2,7]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,4,8,1,6,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,1,5,8,7,3,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,5,1,6,2,8,4,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,7,8,1,6,5]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,8,5,4,3,2,7,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,9,6,5,4,3,2,8,1]=>[[1,2],[3,8],[4],[5],[6],[7],[9]]=>[2,6,1]=>[6,2,1]=>3
[6,8,5,4,3,7,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,3,2,1,7,6]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[6,5,4,3,1,8,7,2]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[8,7,6,5,4,3,9,1,2]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[8,7,5,4,3,1,6,2]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[8,3,4,6,2,1,5,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[3,5,6,2,1,8,4,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,6,8,4,1,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,5,3,2,8,4,1,6]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[7,5,3,2,8,4,6,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,5,7,3,8,6,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,6,8,3,1,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,2,8,1,5,6,3,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,6,1,8,4,3,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,6,8,1,4,2,7]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,6,8,1,3,2,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,5,6,8,3,2,7]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[4,5,6,3,8,2,1,7]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,3,7,2,8,6,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,7,3,2,8,5,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,7,3,2,8,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,7,8,4,5,3,2,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,3,8,4,2,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,1,7,4,3,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,7,4,1,8,6,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,1,4,8,6,2]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,3,1,7,8,5,2]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[6,4,1,7,3,8,5,2]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,3,7,8,4,2,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,1,6,3,7,8,4,2]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,1,3,7,8,4,2]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,1,7,8,3,4,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,3,7,4,8,5,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,4,1,8,5,3]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,1,4,3,8,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,7,3,1,2,8,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,6,3,1,2,7,8,4]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[5,6,1,3,2,7,8,4]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,3,2,1,7,8,4]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,5,6,3,7,8,4,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,6,3,1,7,8,4]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,6,4,7,3,1,8,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,7,2,8,4,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,7,2,8,4,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,7,1,8,4,5]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,2,1,8,4,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,3,8,4,2,1,5,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,7,2,1,3,8,6,5]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,7,8,6,4,2,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,8,4,6,2,1,5]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,3,8,2,1,6,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,7,8,5,2,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,6,2,7,8,5,3,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,2,1,7,8,5,3]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[7,4,5,8,1,2,6,3]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,1,7,3,8,6,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,1,3,8,5,4]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,6,7,8,2,4,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,7,1,8,5,2,4]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,1,7,3,8,5,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,1,8,5,4,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,1,7,8,5,4,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,1,3,6,8,2,5,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[4,2,3,6,8,1,5,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[5,3,2,1,8,4,7,6]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[3,6,5,8,2,1,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,2,1,3,8,7,6]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,2,6,4,5,8,1,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,5,8,1,3,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,2,4,5,8,3,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,2,1,6,8,4,7]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[6,2,4,5,8,1,3,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,3,4,6,5,8,2,7]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,3,4,5,8,2,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,1,8,5,2,7,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,1,7,6,3,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,4,2,7,3,6,5]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,3,2,8,7,4,6]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,1,7,5,3,4,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[1,7,6,4,5,8,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,4,1,2,6,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,4,6,2,1,3]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,2,5,8,6,7,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,3,5,6,8,7,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[2,4,8,6,7,1,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,6,2,8,1,7,5]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,4,8,2,1,6,5]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,5,8,6,7,1,4]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,5,6,8,7,1,4]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[2,1,8,5,6,7,3,4]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,3,5,6,7,4]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,3,7,1,8,6,5]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,6,4,8,1,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,1,6,7,3,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[2,7,8,5,4,1,3,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[1,7,5,3,8,4,2,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,5,3,1,2,8,6]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,2,4,8,5,3,1,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,8,3,1,2,7,6,5]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,2,7,4,1,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,2,3,7,1,5,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[2,8,4,7,1,3,5,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,2,4,6,7,1,3,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[4,8,2,3,6,7,1,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,2,7,6,1,8,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,3,2,5,8,7,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,3,2,1,6,7,4]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,3,4,6,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,2,7,4,1,6,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,4,2,8,7,6,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,7,6,5,8,2,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,3,7,1,6,2,8,4]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,8,7,1,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[6,3,2,1,8,5,7,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[2,7,5,4,1,8,6,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,2,5,6,8,7,1,3]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[1,8,4,2,5,6,7,3]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,8,4,1,5,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,2,8,5,6,7,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,7,1,8,6,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,4,7,1,8,6,2]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,4,1,3,2,5,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,1,3,6,5,2,4,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,4,3,6,5,2,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,5,2,1,8,7,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,3,2,4,6,5,1,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,4,2,1,6,5,3,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[8,4,1,2,6,5,3,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,6,4,2,1,5,3,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,3,6,4,1,5,2,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,2,6,3,4,5,1,7]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,4,8,5,7,2,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,8,4,7,6,2,3,1]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,4,7,5,8,2,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,2,4,8,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,1,3,8,7,4]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,1,6,5,8,3,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,8,7,6,3,1,2]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[2,8,5,1,4,7,6,3]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,3,1,5,8,6,7,2]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,3,5,8,6,7,2]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,3,8,4,7,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,1,6,8,7,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[6,8,4,3,2,7,1,5]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,7,8,2,1,6,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,3,2,8,6,7,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,1,2,8,6,7,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,3,1,6,8,7,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,2,1,8,6,7,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,2,1,3,6,8,7,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[2,4,7,3,8,1,6,5]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,8,2,7,4,1,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,1,3,6,4,7,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[3,5,1,7,8,4,2,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,4,5,8,3,1,6]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,4,3,7,2,6,5]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,8,7,2,1,6,5]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,4,7,8,3,6,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,8,7,2,1,5]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,3,8,7,4,1,2,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[3,5,7,2,4,8,1,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,2,3,1,5,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,1,3,2,5,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,2,1,3,5,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,6,4,2,1,3,7,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,6,4,1,3,2,7,5]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,6,4,2,3,1,7,5]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,5,7,2,6,1,8,4]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,3,8,5,7,2,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,3,2,6,7,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,5,3,6,2,7,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,1,5,4,7,6,3]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,8,7,4,6,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,6,4,5,8,3]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,2,4,6,5,8,3]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,1,7,6,8,2,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,6,1,3,7,4]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,5,8,7,2,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[2,5,7,8,4,1,6,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,8,1,5,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,5,2,6,8,7,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,1,6,8,7,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,5,1,6,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,8,5,2,6,7,3]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,7,1,8,5,4,6,3]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,6,2,1,3,7,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,2,4,1,5,6,7,3]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,6,3,5,8,1,7,2]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,8,3,5,4,6,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,5,1,8,6,7,2]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,4,5,7,8,2,6,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,6,2,8,5,1,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,6,8,1,5,2,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,7,2,1,8,6,5]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,8,2,1,5,6,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[3,5,2,7,8,4,6,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,6,2,8,4,1,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,8,4,1,2,7]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[3,5,7,2,4,8,6,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,2,8,4,6,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,7,8,4,1,6,2]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,2,1,8,5,4,7]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,7,2,8,5,4,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,2,4,5,1,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,2,1,4,8,6,5]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,2,8,4,5,6,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,2,1,4,5,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[4,1,5,6,7,8,3,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,1,5,7,3,8,6,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,6,3,7,8,5,2]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,3,8,5,2,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,6,7,3,8,5,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,6,8,3,5,2,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,7,3,2,8,6,5]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,3,2,5,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[4,5,2,6,8,1,3,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,5,7,3,8,1,6,2]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,8,3,2,1,6,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[4,6,2,7,8,5,1,3]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,7,3,2,8,5,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,2,8,3,5,6,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,8,3,2,5,6,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,2,3,1,5,6,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,1,2,6,8,4,3,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[5,1,6,3,8,4,2,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,7,4,8,2,3]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,2,3,8,4,1,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,7,8,4,1,3]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,8,3,4,2,1,7]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,2,3,4,8,6,1]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,7,8,3,4,2,6,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,2,3,4,1,6,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,1,2,3,7,8,5,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[6,1,2,3,8,5,4,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[6,1,2,7,8,5,4,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,1,7,3,8,5,4,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,7,8,4,5,3,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,3,4,5,2,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,2,3,8,5,4,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,2,8,4,5,3,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,2,3,4,8,6,5]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[7,1,2,8,4,5,6,3]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,8,3,4,5,6,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,1,8,2,3,7,5]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,1,2,4,3,7,6]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,5,7,2,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,8,6,1,2,4,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[3,1,6,8,2,4,7,5]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,2,8,1,5,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,1,3,8,4,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,5,2,3,4,6,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[2,7,5,1,3,8,4,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,2,5,7,4,6,1,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,1,3,7,6,4,5]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,2,5,1,3,7,4,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,5,3,1,6,4]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,2,6,5,4,7,1,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,5,2,4,8,1,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,8,2,5,3,1,6,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,8,6,3,2,4,5]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,8,1,5,3,2,4,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,7,5,3,2,4,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[6,5,1,2,4,8,3,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,8,1,6,4,2,3,5]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,4,1,2,5,6,3,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[1,7,3,6,5,2,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,1,3,7,2,6,4,5]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,2,6,5,1,8,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,8,4,2,5,6,1,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,2,7,4,5,6,1,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,6,5,1,7,4]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,9,8,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,7]=>[7,2]=>2
[6,9,8,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,7]=>[7,2]=>2
[5,9,8,7,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,7]=>[7,2]=>2
[4,9,8,7,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,7]=>[7,2]=>2
[3,9,8,7,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,7]=>[7,2]=>2
[2,9,8,7,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,7]=>[7,2]=>2
[8,10,9,7,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[7,10,9,8,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[4,8,6,5,7,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,10,9,8,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[3,8,7,5,4,6,2,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,5,6,7,3,2,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,10,9,8,7,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[2,8,7,6,4,3,5,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,7,4,5,6,2,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,10,9,8,7,6,5,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[1,8,7,6,5,3,2,4]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[2,8,7,6,3,4,5,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,10,9,8,7,6,5,4,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[1,8,7,6,5,2,3,4]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,9,8,7,6,5,4,2,3]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[2,10,9,8,7,6,5,4,3,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,8]=>[8,2]=>2
[7,2,8,6,5,4,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[7,2,8,5,4,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,2,8,5,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,8,5,4,3,1,7,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,8,6,4,1,3,7,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,6,1,8,5,2,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,1,2,8,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,3,5,4,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,5,8,3,6,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,8,5,2,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,2,6,4,8,3,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,3,1,7,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,4,1,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,4,5,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,3,2,5,8,4,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,3,2,1,5,4,7,6]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,3,7,1,5,8,4,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,1,8,4,3,7,6]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,5,4,8,1,3,7]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,1,6,5,8,2,7]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,4,6,8,2,7]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,4,5,8,2,7]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[8,3,4,1,5,2,7,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,4,2,6,8,3,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,2,6,4,1,7,3,5]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,4,5,2,1,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,5,1,8,4,3,6]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,2,5,4,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,2,1,5,3,4,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[3,6,1,5,8,7,4,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,3,6,4,5,1,7,2]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,8,1,2,7,3]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,7,2,3,5,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,4,1,3,5,7,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,4,7,8,6,2,5,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,3,5,7,8,6,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[6,5,1,8,4,7,3,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,1,8,4,7,6,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,7,4,6,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,3,2,8,1,6,5]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,1,4,7,2,8,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[8,7,3,6,1,5,2,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,3,6,8,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,7,3,8,5,6,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,6,1,5,7,3,4]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,2,5,4,3,1,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,3,4,2,7,6,5]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,3,7,4,2,6,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,3,2,4,1,8,6]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,3,4,7,1,5,6]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,3,6,7,8,2,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[1,7,6,3,2,5,8,4]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,8,1,5,6,2,7,4]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,5,6,1,7,4,3]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,5,2,8,6,4,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,5,4,8,7,2,1,3]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,6,4,5,2,7,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,3,6,2,7,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,2,1,7,5,8,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,4,1,8,7,6,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,6,5,8,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,1,4,2,7,3,5]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,4,7,1,8,2,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,4,7,8,2,5,6,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,2,4,5,6,7,3]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,2,4,1,6,8,7,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,7,6,1,8,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,5,6,1,8,7,2]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,4,1,7,6,8,2]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,4,6,5,7,8,2]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,7,3,5,6,8,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,2,7,5,8,6,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,5,8,3,7,6]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,2,6,8,5,3,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[1,5,2,4,8,7,6,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,4,8,7,5,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,4,8,6,5,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,3,2,7,5,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,8,5,7,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,4,8,7,3,6]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,4,8,7,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,8,5,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,8,2,6,7,4,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,7,8,2,5,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,7,8,2,3,6,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,2,7,8,4,6,3]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,6,2,4,8,7,5]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,7,3,4,8,5,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,7,4,8,6,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,4,1,5,3,7,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,8,4,2,7,6,5]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,4,8,3,6,5]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,6,4,8,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,2,4,8,3,7,6]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,5,2,7,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,8,6,2,7,4,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,8,5,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,7,8,6,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,7,8,5,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,5,7,8,6,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,4,7,6,8,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,8,7,4,1,6,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,2,6,8,7,5,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,7,8,6,5,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,2,6,7,3,4,8,1]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,2,4,7,6,3,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,2,1,7,8,3,4]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,6,2,1,4,8,7,3]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,1,4,5,8,7,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,2,7,6,3,8,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,7,6,4,5,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,1,7,5,8,3,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,1,7,4,8,5,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,2,7,8,4,3,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[2,6,1,7,4,8,3,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,4,1,7,8,2,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,1,3,8,7,2]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,4,1,5,8,7,2]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,1,5,4,8,7,3]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,1,4,7,8,5,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,2,4,8,6,7,3]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,2,4,8,7,3,6]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,1,2,4,8,7,6,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,3,8,5,4,7,6]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,3,1,2,8,5,7,6]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,5,3,8,6,4,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,3,8,5,6,4,7]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,8,6,4,5,7]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,2,3,8,6,5,4,7]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,3,8,5,4,6,7]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,6,1,5,4,8,3,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,2,4,8,6,3,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[5,1,2,4,8,3,7,6]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[5,6,3,1,4,8,2,7]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[2,5,4,3,1,8,6,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,3,1,8,7,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,6,4,5,1,8,7,2]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,5,4,1,8,7,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,2,6,1,7,8,4,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,6,2,8,7,3,4]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,3,7,8,6,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[2,1,3,7,8,5,6,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,4,1,7,8,6,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,1,2,8,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,4,2,8,6,7,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,3,6,8,5,7,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,8,6,7,4,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,8,7,5,4,6]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,3,8,7,4,5,6]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,2,3,8,5,7,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,3,6,8,7,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[5,4,1,2,8,7,6,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,1,6,2,8,7,5,4]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,3,4,5,6,7,10,8,9]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]=>[8,2]=>2
[1,2,3,4,5,9,7,6,8]=>[[1,2,3,4,5,6,9],[7],[8]]=>[6,3]=>[6,3]=>2
[1,2,3,4,5,6,10,7,8,9]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]=>[7,3]=>2
[1,2,3,4,5,10,6,7,8,9]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[6,4]=>[6,4]=>2
[1,2,3,4,10,5,6,7,8,9]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]=>[5,5]=>2
[1,8,3,4,2,5,6,7]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,2,3,10,4,5,6,7,8,9]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[4,6]=>[6,4]=>2
[1,8,4,3,2,5,6,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,9,3,2,4,5,6,7,8]=>[[1,2,5,6,7,8,9],[3],[4]]=>[2,7]=>[7,2]=>2
[1,2,10,3,4,5,6,7,8,9]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[3,7]=>[7,3]=>2
[8,4,7,6,5,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[8,4,7,5,6,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,4,6,3,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,7,6,3,5,4,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,6,7,3,5,4,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,3,6,4,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,4,6,5,3,2]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,3,6,5,4,2]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,3,6,5,4,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,2,6,5,4,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,2,6,4,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,6,7,2,5,4,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,7,6,2,5,4,3,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,4,7,1,6,5,3,2]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,1,6,5,4,2]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,1,6,5,4,3]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,2,6,5,4,3]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,7,6,2,5,3,4,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,7,6,5,3,4,2]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,6,5,2,4,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,7,6,5,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,7,6,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,7,5,4,1,3,2]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,7,6,4,1,3,2]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,6,5,1,4,2]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,4,5,1,3,2]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,6,2,5,1,4,3]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,6,1,5,2,4,3]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,8,1,3,2,5,4,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,1,4,2,5,3,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,6,1,4,2,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,5,3,6,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,5,1,4,3,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,4,3,6,2,5]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,4,3,7,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,5,1,4,3,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,5,3,7,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,5,4,7,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,4,7,6,8,1,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,3,7,6,8,1,4]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,1,4,3,7,6,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,1,4,3,7,5,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,8,1,4,3,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,1,5,3,7,4,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,3,7,4,8,1,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,4,7,5,8,1,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,6,4,7,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,6,4,7,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,6,3,7,1,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,5,3,7,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,5,2,6,3,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,7,1,5,2,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,7,1,4,2,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,3,2,6,4,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,7,1,3,2,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,7,1,3,2,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,5,7,1,3,2,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,6,8,2,4,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,6,8,1,3,2,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,5,8,1,3,2,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,3,2,6,5,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,4,2,6,5,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,5,8,1,4,2,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,6,8,1,4,2,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,6,8,2,5,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,6,8,2,5,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,5,8,3,6,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,5,8,2,6,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,5,8,2,6,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,4,8,2,6,1,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,4,8,1,5,2,6]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,5,2,6,4,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,6,1,5,4,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,6,5,8,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,6,5,8,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,5,8,4,7,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,8,4,7,1,3]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,8,3,7,1,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,3,7,1,5,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,4,2,8,5,3,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[7,6,4,3,8,2,5,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,4,8,5,2,3,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,4,3,7,2,1,5]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,4,3,5,1,8,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,3,5,4,8,2,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,7,5,2,4,1]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,8,3,5,2,4,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,3,5,8,2,4,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,3,5,2,4,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,4,2,5,1,8,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,2,8,4,1,5,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,6,3,8,2,4,1,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,4,8,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,8,3,7,4,5,2,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,5,8,4,2,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,8,3,6,2,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,3,6,7,2,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,4,8,7,2,5,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,4,7,2,1,5]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,8,4,1,7,5,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,7,4,1,5,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,4,7,5,8,2,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,7,8,4,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,7,3,6,8,2,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,8,3,7,2,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,3,4,1,8,2]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,8,3,5,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,8,3,5,7,2,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,5,6,8,2,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,3,5,8,2,6,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,4,7,8,2,1,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[5,3,8,2,4,1,6,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,4,8,2,6,1,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,3,6,2,5,7,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,3,5,7,2,6,1]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,5,6,7,2,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,8,3,5,6,2,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,8,3,6,2,5,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,3,6,7,2,5,1]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,7,2,5,6,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,4,8,2,7,6,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,8,2,4,1,7,6]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,8,4,1,7,3,6]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,5,1,8,7,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,5,8,2,1,7]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[6,3,5,8,7,2,4,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,3,7,2,6,4,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,4,8,2,1,6]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,4,2,3,1,6,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,4,2,3,1,7,6]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,5,3,8,2,1,7]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,5,3,7,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,3,8,5,7,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,8,5,3,1,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[6,4,2,7,3,1,8,5]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,7,8,5,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[6,4,5,3,7,1,8,2]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,4,2,3,1,6,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,3,7,1,8,2,4]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,4,7,1,8,2]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,3,4,8,2,1,7]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,5,7,4,8,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,4,7,8,2,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,3,5,7,1,8,2]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,4,2,5,1,7,3,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,2,4,1,6,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,4,7,2,6,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,3,6,2,5,8,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,3,6,8,2,5,1]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,7,3,5,8,2,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,8,3,6,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,3,6,7,2,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,3,7,2,6,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,4,6,8,2,1,7]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[5,3,6,8,2,1,4,7]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[5,3,6,7,1,8,2,4]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,4,6,7,1,8,2]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,6,3,5,7,8,2,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,7,3,6,8,2,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,8,3,7,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,4,8,6,3,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,2,6,5,1,8,7,4]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,7,2,8,4,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,7,8,9,5,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[5,6,7,8,9,4,3,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[4,5,6,7,8,9,3,2,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[3,2,1,6,5,4,9,8,7]=>[[1,4,7],[2,5,8],[3,6,9]]=>[4,3,2]=>[4,3,2]=>3
[3,4,5,6,7,8,9,2,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[8,9,10,7,6,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[7,8,9,10,6,5,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[4,6]=>[6,4]=>2
[5,4,3,2,1,10,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[5,6,7,8,9,10,4,3,2,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[4,7,3,9,6,2,10,8,5,1]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,5,6,7,8,9,10,3,2,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[3,4,5,6,7,8,9,10,2,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,6,2,5,3,4,8,7]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,8,2,4,6,5,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,3,6,4,8,5]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,2,5,3,7,4]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,2,5,3,4,7,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,2,3,6,4,7,5]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,5,2,8,4,7,6]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,7,3,5,4,6,8]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,2,7,3,4,6,5]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,8,2,3,7,4,6]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,2,3,5,4,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,1,2,4,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,1,5,8,4,2,3,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,5,7,4,2,3,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,1,4,5,8,2,3,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[7,4,1,6,2,8,3,5]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,7,2,6,3,5]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,7,5,2,3,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,5,4,7,2,3,6]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,1,7,5,8,3,4,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,4,8,2,3,6]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,8,5,2,3,6]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[6,4,1,7,2,3,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,8,3,1,2,4,6,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[8,7,1,6,4,2,3,5]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,6,1,7,4,2,3,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,6,1,8,4,2,3,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,3,8,1,2,4,6,5]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,1,2,4,6,5]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,6,1,2,4,7,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,5,1,2,4,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[7,3,6,1,2,4,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,7,1,8,4,2,3,5]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,1,7,4,2,3,5]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,1,8,5,4,2,3,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,1,8,4,5,2,3,6]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,7,8,5,3,4,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[7,6,3,1,2,4,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,1,2,3,8,7,5,4]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,8,1,4,2,3,7,5]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,3,1,2,7,4,5]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,7,3,1,2,8,4,5]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[6,7,1,4,2,3,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,6,8,5,7,1,2]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,2,5,4,8,3,7]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,1,5,8,3,4,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[1,3,6,8,7,4,2,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,8,5,7,3,4,6]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,5,8,3,4,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,6,8,4,3,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,1,2,5,7,3,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,4,6,2,5,7,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,6,4,7,2,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,1,4,7,2,5,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,7,8,4,6,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,4,8,5,1,6,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,1,6,5,4,8,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,3,1,5,8,4,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,7,4,6,8,1,3,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,7,5,8,6,4,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,2,6,7,5,4,3,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,8,7,1,6,4,5,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,8,2,7,4,1,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,2,8,7,4,6,3]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,2,7,8,1,6,5]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,3,7,5,6,8,2]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,1,7,4,2,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,7,1,4,2,3]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,7,3,8,5,2,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,1,4,5,8,2,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,7,4,5,3,8,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,7,3,5,4,8,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,1,2,5,8,4,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[1,4,7,2,8,5,3,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,7,2,4,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,7,1,2,4,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,1,7,5,6,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,4,3,7,5,6,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,2,1,5,7,3,4]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[7,2,8,4,1,6,3,5]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,8,6,5,3,7]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,1,5,6,8,4,3,2]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,7,8,1,4,6,3,5]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,5,7,1,6,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,6,8,5,3,7,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,2,6,4,8,3,1,7]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,1,3,4,5,8,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,7,3,2,4,8,5,6]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,3,6,5,2,8,4,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,6,5,3,4,8,2]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,4,2,8,7,5,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,7,5,2,6,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,7,4,2,3,5,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,6,4,5,2,8,7,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,1,3,5,4,2,7]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[5,3,8,6,1,2,4,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[2,5,6,3,4,8,7,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,3,6,8,7,4,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,3,5,2,6,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,7,2,6,4,5,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,5,4,8,7,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,6,1,5,2,7]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,2,5,3,8,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,2,6,8,1,4,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,5,2,7,1,4,3,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,8,5,3,6,2,4,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,7,2,4,3,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,3,4,8,6,2,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,1,3,8,6,2,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[5,1,8,6,3,4,2,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,2,8,3,7,6,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,3,7,6,4,5,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,2,4,7,6,3,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,5,3,4,7,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,5,6,4,8,1,3]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,7,4,8,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,3,5,8,2,6,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[8,2,1,3,5,6,7,4]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[6,3,1,4,7,5,8,2]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,3,8,2,6,7,5]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,8,3,6,7,5,4,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,1,7,2,8,5,4,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,1,4,7,2,8,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,8,4,7,2,3,6]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,3,6,2,8,4,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,4,5,8,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,4,5,7,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,7,3,2,4,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,1,8,5,4,3,6,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,7,4,1,5,3,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,8,6,2,3,1,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,1,4,6,3,8,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,5,6,8,1,3,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,3,2,8,5,4,6]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,5,4,1,3,6,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,1,7,4,2,3,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,8,6,5,1,4,2,7]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,8,6,5,2,7]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,1,8,6,5,3,2,7]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,8,5,2,7,3,6,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,8,5,3,6,4,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,4,3,7,6,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,5,2,3,6,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,2,8,4,6,1,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,4,3,6,2,8,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,5,1,2,8,3,4]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,2,6,8,3,4,7,1]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,2,4,5,8,3,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[3,6,8,4,7,2,5,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,3,8,4,2,5,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,3,8,4,7,5,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,2,3,6,5,8,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,5,8,3,1,4]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,3,6,4,5,7,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,5,6,8,3,7,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,8,1,2,6,4,7,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,3,2,7,4,5]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,2,8,4,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,1,2,8,4,6,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,8,3,6,2,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,2,7,4,3,6,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,5,8,2,7,3,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,3,6,4,8,2,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,6,4,8,2,7,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,5,6,4,8,7,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,1,6,4,7,8,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,1,4,2,7,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,6,4,3,8,5,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,3,5,8,7,4]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,1,8,4,7,6]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,6,1,8,5,4,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,1,7,5,4,8,6,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,6,4,8,5,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,3,6,8,5,4]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,6,1,8,5,7,4]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,5,8,4,7,3,6]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,8,5,2,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,6,8,5,4,3,7]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,3,5,8,2,4,7,6]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,6,8,3,2,5,7]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,3,7,5,6,8,2,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,7,3,8,5,4]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,7,3,8,6,4]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,5,7,6,8,4,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,4,6,8,2,7,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,6,5,8,7,1,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,5,6,8,4,3]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,7,5,8,4,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,2,7,5,8,3,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,7,4,8,2,6,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,7,6,8,3,5,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,6,8,3,5,7,2]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,5,8,2,7,4,6]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,8,4,7,6,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,8,7,4,3,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,3,5,8,7,2,4,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[5,7,1,2,8,6,4,3]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,4,5,7,2,8,1,3]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,4,7,2,8,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,7,4,6,8,1,5]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,2,7,1,4,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,6,3,4,7,1,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,7,3,4,5,8,1,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,4,5,6,8,1,2]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,5,7,3,6,8,1,4]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,2,3,8,1,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,3,5,2,4,8,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,2,4,5,8,1,3]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[6,5,2,3,4,8,1,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[5,3,1,2,8,4,7,6]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,2,3,7,1,4,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[5,2,1,7,3,4,6,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[5,2,1,8,3,4,6,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[6,3,2,8,4,5,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,1,2,8,4,6,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,1,3,8,5,7,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,3,1,8,4,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,2,7,1,4,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,2,4,7,1,5,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,5,2,3,6,1,4,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,2,1,7,3,4,5,6]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[8,6,3,7,2,4,5,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,6,2,3,4,5,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[8,2,7,3,4,5,6,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,2,3,4,5,7]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[8,1,7,3,4,5,6,2]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,1,7,2,4,5,3]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,5,7,2,3,6,4]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,5,8,2,3,6,4]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,1,8,3,4,5,6]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,3,8,2,4,5,6,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,8,3,4,5,6,1]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,8,3,4,5,6,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,5,8,3,6,7,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,7,1,8,3,6,4]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,1,8,4,5,3]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,1,3,8,5,6,2]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,2,8,4,5,7,3]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,3,6,8,2,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,4,6,8,2,7,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,6,3,8,7,1,2,5]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,4,5,8,7,1,2,3]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[5,3,4,8,7,1,2,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[3,2,8,7,1,4,6,5]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,8,7,2,4,6,5]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,7,6,1,2,4,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[1,8,3,7,2,4,5,6]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,8,1,7,2,4,5,6]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,8,2,3,5,1,4,7]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,8,2,6,1,3,5]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,8,7,1,4,5,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,7,1,4,5,6,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,6,1,3,4,5,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[2,7,6,1,3,4,5,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[1,7,6,2,3,4,5,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[1,8,6,2,3,4,5,7]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[2,8,7,3,4,5,6,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,7,2,4,5,6,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,3,6,2,4,5,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,8,7,2,3,6,4]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,1,3,4,5,2]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[3,6,2,4,7,1,8,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,7,2,5,1,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,4,8,5,3,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,8,5,3,2,7,6]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,6,2,5,7,1,4,8]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,2,8,3,7,5,4,6]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,3,2,8,5,4,7]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,1,2,8,4,3,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,8,7,4,2,5]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,8,1,2,6,7,5]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[9,10,7,8,5,6,1,2,4,3]=>[[1,2,9],[3,4],[5,6],[7,8],[10]]=>[2,2,2,3,1]=>[3,2,2,2,1]=>5
[1,8,10,6,9,4,7,2,5,3]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[1,2,7,10,5,9,3,8,6,4]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[4,2,2,2]=>[4,2,2,2]=>4
[1,2,3,6,10,4,9,8,7,5]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[5,2,3]=>[5,3,2]=>3
[1,2,3,4,5,10,9,8,7,6]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[3,1,2,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[9]=>[9]=>1
[2,4,1,3,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[2,3,5,1,4,6,7,8,9]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]=>[6,3]=>2
[2,3,4,6,1,5,7,8,9]=>[[1,2,3,4,7,8,9],[5,6]]=>[4,5]=>[5,4]=>2
[2,3,4,5,6,8,1,7,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[3,6,8,7,1,2,5,4]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,7,2,4,8,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,1,6,5,8,7,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,1,2,4,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,5,2,1,4,6,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,8,5,2,7,4,1,6]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,2,8,4,7,3,1,6]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,4,1,3,6,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[4,3,5,1,2,8,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,4,6,2,8,7,5]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,4,6,5,2,8,7,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,6,1,8,7,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,8,7,2,1,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,4,7,2,6,3,5,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,5,2,1,6,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,1,4,7,2,3,6,5]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,5,7,3,4,6,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,5,1,7,4,2,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,4,8,7,3,2,5]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[6,4,8,5,7,1,2,3]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,1,6,3,2,7]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,8,6,3,7,2,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,7,6,3,8,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,3,7,5,8,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,3,5,8,6,2,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[5,7,4,3,8,1,2,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,4,8,3,7,6,5,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,2,1,6,5,7]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,8,4,2,7,1,5,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,2,5,7,6,4,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[1,8,2,7,6,5,4,3]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,8,1,6,7,5,4,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,7,2,6,8,5,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,2,3,8,5,6,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,1,7,5,6,4,3]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,6,5,7,4,2]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,4,3,6,1,5,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,8,5,4,3,6,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,4,5,3,2,6,7]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,5,4,3,1,6,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[7,1,6,3,4,2,5,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,7,1,4,2,5,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,1,4,2,7,5,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,8,5,7,6,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,5,1,2,8,4,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,8,5,6,7,2,1,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,7,6,2,4,3,5]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,5,6,1,4,2,3,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,5,4,7,1,3,2]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,4,5,7,2,3,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,3,6,1,7,2,4,5]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,8,6,5,7,3,4,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,5,3,6,8,4,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,4,1,6,5,8,3,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,8,7,6,3,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,2,5,8,6,7,3,4]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,5,8,7,3,6]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[5,2,4,6,1,7,3,8]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,5,3,6,8,7,4,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,4,6,1,8,2,7]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,5,7,6,8,2,4]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,5,6,8,7,2,3]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,4,6,3,7,2,8,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,3,6,5,2,8,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,6,2,5,4,1,7,3]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,7,2,6,5,4,1,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,6,2,5,4,3,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,7,5,2,6,3,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,2,6,4,7,5,1,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,3,7,5,4,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,3,4,7,6,2,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,8,3,6,1,7,5,4]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,2,5,1,6,4,3]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,8,2,6,5,1,7,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,2,5,4,1,6,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,5,2,6,1,7,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,1,3,7,2,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,3,7,5,2,8,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,3,6,2,8,5,4]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,6,2,7,5,4]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,4,7,3,8,6,5]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,8,2,6,5,4,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,1,8,6,2,7,5,4]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,7,8,2,6,5,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,1,8,2,7,4,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,7,8,1,6,5,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,8,6,1,7,5,4]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,1,6,5,4,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,8,7,2,6,5,4,3]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,1,6,5,4,3]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,1,6,5,4,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,5,1,6,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,8,5,1,4,3,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,8,4,1,7,2]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,8,5,4,1,6,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,4,8,6,5,1,7,2]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,5,1,6,4,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,6,2,7,5,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,6,7,1,5,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,4,7,8,1,3,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,6,5,1,2,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,3,5,1,2,8,6,4]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,6,2,3,8,7,5]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,2,7,4,8,6,5]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,2,1,6,3,8,5,4]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,1,7,6,4,8,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,2,1,7,3,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,7,1,2,8,4,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,1,2,8,6,3]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,6,2,8,5,4]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,1,2,8,5,4,3]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[2,7,1,3,8,6,5,4]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,6,1,2,7,5,4,3]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[1,7,2,3,8,6,5,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,1,2,6,5,4,3]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,8,1,2,6,5,4,3]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,1,6,2,7,5,4]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,5,1,2,7,6,3]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,8,1,2,7,4,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,3,7,4,8,6,5]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,7,3,6,8,1,5]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,4,2,8,1,7]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,5,3,8,2,7,6]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,4,7,3,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,3,4,7,5,1,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,5,4,8,1,7]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,4,3,5,8,1,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,3,6,4,2,8,1,5]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,5,2,8,1,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,1,8,2,7,6]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,5,4,2,7,3,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[5,4,1,7,2,6,3,8]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,1,8,3,2,6,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,5,2,8,3,4,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,2,1,8,3,6,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,5,3,4,8,2,7,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,5,3,8,2,7,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,3,1,8,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,4,2,7,3,1,6]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,6,4,7,3,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,2,5,7,4,1,3]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,5,3,2,6,4,1,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,3,1,7,2,5,4,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,2,6,4,3,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,1,6,2,5,4,3,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,3,5,6,4,2]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,7,4,5,2,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,7,2,6,5,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,7,6,8,3,2,4,5]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,1,5,8,4,2,6,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,8,4,5,2,6,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,8,5,3,4,6,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,8,4,3,2,5,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,1,7,4,2,5,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,3,4,6,5,8]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,4,3,5,6,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,2,8,3,5,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,1,7,3,5,4,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,5,8,4,2,6,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,3,1,6,8,2,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,7,4,8,3,2,1,6]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,4,8,2,7,3,1,6]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,7,3,4,1,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,5,3,2,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,8,3,7,6,2,4,5]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,3,2,6,4,1,7]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,4,7,5,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,2,6,4,1,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,8,2,7,3,1,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,8,7,3,4,1,5]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,6,3,5,1,4]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,7,2,5,4,3]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,7,4,5,6,1,2]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,6,4,3,5,1,7]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,7,6,3,5,4,1,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,6,5,2,4,3,8]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,6,5,3,2,4,7]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[3,8,7,4,6,2,5,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,3,7,6,2,4,1]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,8,6,5,2,3,4]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,4,7,5,3,2,1,6]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,7,2,5,4,3,1,6]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,8,3,2,5,4,7,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,7,8,4,3,6,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,1,5,4,7,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,1,8,5,4,7,3]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,5,7,4,1,3,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,5,6,8,4,3,7,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,4,7,1,8,6,3]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,1,8,7,6,4,3]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,8,6,7,5,3,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,5,4,8,2,1,7,3]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,8,4,7,2,6,3,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,2,7,6,4,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,2,1,4,3,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[3,5,7,4,2,6,1,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,6,5,3,7,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[4,2,1,5,7,6,3,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[3,5,4,7,1,6,2,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,5,8,6,7,1,2]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,5,1,6,8,7,2]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,8,1,3,5,7,9]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]=>[5,4]=>2
[8,7,6,5,4,3,2,10,1,9]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[8,2]=>[8,2]=>2
[6,5,4,10,3,9,2,8,1,7]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[6,5,4,3,2,8,10,1,7,9]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[7,3]=>[7,3]=>2
[4,8,3,7,2,6,10,1,5,9]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,3,2,6,8,10,1,5,7,9]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[6,4]=>[6,4]=>2
[2,1,7,3,8,4,6,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,2,7,3,6,5]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,2,8,3,6,5]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,3,2,8,4,6,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,2,4,3,6,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,7,2,5,3,6,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,5,2,8,3,6,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,2,8,3,6,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,2,7,3,6,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,2,4,3,7,6]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,6,2,4,3,7,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,8,2,4,3,7,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,8,2,5,3,7,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,6,2,5,3,7,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,6,2,7,3,5,4]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,8,2,7,3,5,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,7,2,8,3,5,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,7,2,5,3,8,4]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,7,2,4,3,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,6,2,4,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,5,2,4,3,8,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,2,4,3,8,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,2,5,3,8,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,2,8,3,5,4]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,2,6,3,5,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,2,7,5,4,6,3]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,2,7,4,3,5,6]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,8,6,4,7,2,3,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,4,2,6,3,5,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,4,8,1,5,2,3,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,1,7,2,6,3,5,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,4,3,6,2,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,3,2,4,1,6]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,4,3,6,2,7]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,4,3,7,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,4,7,2,6,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,2,5,3,7,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,4,2,6,7,3]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,4,8,2,1,3,5,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[4,1,7,3,2,5,6,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[7,5,4,8,2,3,6,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,7,2,6,8,4,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,7,4,2,6,8,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,6,3,2,5,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,1,6,2,5,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[6,5,4,3,7,1,8,2]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,5,1,7,3,8,2,4]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,8,5,7,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,4,3,8,2,7,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,4,3,8,7,1,2]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[7,6,3,8,5,4,1,2]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,4,8,2,1,7,3,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,8,5,1,3,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,6,4,8,5,1,2,3]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,2,8,6,3,1,4,5]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,2,8,6,1,5,3,4]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,8,3,6,4,5]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,1,7,8,2,3,5]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[4,2,1,6,7,3,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[4,3,1,5,2,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,7,3,8,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,3,2,8,6,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,2,8,7,4,5]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,1,7,8,5,2,4]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[6,5,4,1,7,8,3,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[5,4,3,1,6,7,2,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,5,4,2,7,8,3,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[5,4,2,6,3,8,7,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,5,2,6,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,1,6,7,8,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[5,4,3,1,6,7,8,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,3,8,1,2,5,7,4]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,1,2,5,8,4]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,8,3,1,2,5,6,4]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,1,3,2,4,6,5]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,2,1,3,5,4,6]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,3,7,1,8,6,4]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,3,6,1,8,7,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,7,3,1,8,4,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,7,1,3,5,4,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,3,1,7,4,5]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,7,1,8,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,2,7,8,6,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,1,2,7,3,6,4,8]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,4,7,8,2,3,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[5,3,4,7,8,6,1,2]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[3,5,4,6,8,7,1,2]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,5,4,6,8,2,3,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,3,2,4,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,5,3,6,2,7,8,4]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,3,7,2,6,8,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[5,2,4,7,8,1,6,3]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[4,2,5,7,6,1,8,3]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,2,8,6,1,7,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,1,8,2,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,8,3,2,4,7,5]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,5,7,6,8,1,2]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,7,6,2,3,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,5,1,8,6,2,3,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,2,1,8,3,6,4,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,2,1,8,7,5,6]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,5,4,2,1,8,3]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[7,6,5,4,8,1,3,2]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,5,8,2,1,4,3]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,4,3,2,1,7,6]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[7,6,5,4,1,8,3,2]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[8,7,6,5,4,9,1,3,2]=>[[1,6],[2,8],[3],[4],[5],[7],[9]]=>[6,2,1]=>[6,2,1]=>3
[7,6,5,2,8,1,4,3]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,5,8,4,1,3,2]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,8,5,2,1,4,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,8,6,3,2,1,5,4]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[8,7,4,3,2,1,6,5]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[7,8,4,5,9,2,3,6,10,1]=>[[1,2,5,9],[3,4,8],[6,7],[10]]=>[2,3,4,1]=>[4,3,2,1]=>4
[7,8,2,4,5,1,3,6]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,7,2,5,1,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,1,3,2,4,5,6]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,8,4,1,5,2,3,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,6,7,2,1,4,5,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[5,2,3,6,1,4,7,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[2,5,3,6,1,4,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,6,7,3,1,4,5,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[4,6,7,1,5,2,3,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,3,5,8,1,2]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,1,5,2,3,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,2,7,3,1,4,5,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[3,2,5,6,1,4,7,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[3,5,2,6,1,4,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,1,4,6,7,2,3,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[3,5,4,6,7,8,1,2]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,5,4,6,7,2,3,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,3,2,4,5,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,5,3,6,2,4,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,1,3,6,2,4,7,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[5,2,4,6,7,1,3,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[2,5,4,6,7,1,3,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,7,4,5,1,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,7,4,5,1,3,8]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,6,7,1,3,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[4,5,2,6,7,1,3,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,3,1,6,2,4,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[6,1,7,3,2,4,5,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[6,1,7,4,5,2,3,8]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,7,4,5,8,1,2]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,1,6,7,2,3,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,2,1,6,3,4,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,3,2,5,4,1,6,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,3,5,4,2,1,6,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,3,5,2,4,1,6,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,5,2,1,4,3,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[1,3,6,7,5,2,8,4]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,4,1,6,2,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,3,4,1,6,5,2,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,4,1,5,6,2,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,3,2,5,1,6,4,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,4,1,3,2,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[7,3,4,1,5,2,6,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,3,6,7,2,5,8,4]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,4,6,2,8,5,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,1,7,2,6,8,5]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,1,4,7,3,8,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,2,1,7,4,8,6]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[1,3,4,5,8,7,2,6]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[6,3,4,5,8,1,7,2]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,5,1,6,8,7,3]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,2,5,6,8,7,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,3,2,5,6,8,1,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[3,7,5,4,6,8,1,2]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,4,6,5,8,2,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,5,8,6,1,7]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[2,3,4,5,8,1,7,6]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,4,6,5,8,7,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,7,5,4,6,8,2,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,1,4,7,2,8,3]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,1,7,5,6,8,2]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,1,7,6,5,8,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,6,7,8,5,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[1,4,5,2,6,8,7,3]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,2,6,8,1,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,5,2,6,8,4,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,1,2,7,4,8,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,5,2,4,7,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,2,1,4,7,8,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[5,3,1,4,2,7,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[5,3,1,2,4,7,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[7,1,5,2,6,8,4,3]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,5,2,6,8,3,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,7,4,6,5,8,3,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,4,6,1,8,3,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,4,6,1,8,5,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,6,7,1,5,8,4]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,6,7,5,1,8,4]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,6,7,1,8,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,3,2,5,6,8,1,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,1,5,4,6,8,2,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,4,6,5,8,1,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,4,5,8,6,1,2]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[7,3,4,5,8,1,6,2]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[7,3,4,5,8,1,2,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,3,4,5,8,6,2,7]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,3,4,5,8,2,7,6]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,4,5,8,2,1,7]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[6,3,4,5,8,2,7,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,3,4,5,8,6,2,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,7,4,6,5,8,3,1]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,5,4,6,8,3,2]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,2,5,6,8,4,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[5,7,4,6,1,8,3,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,4,5,8,1,2,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[7,3,4,5,8,2,1,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,3,4,5,8,2,6,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,8,6,1,7,5,2,3]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,8,2,6,1,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,4,2,8,3,5,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,4,2,7,5,3,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[8,4,7,3,6,5,1,2]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,6,1,7,5,3,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,4,7,1,8,3,2,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,3,6,1,5,2]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,1,7,3,5,4,8]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,8,6,3,5,4,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,3,5,8,6,4]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,1,5,4,6,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,1,4,8,5,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,2,1,8,3,6,7,5]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,8,6,3,5,7,4]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,1,7,3,5,8,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,3,1,4,8,5,6]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,2,1,6,4,5,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[3,2,1,5,7,8,4,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[2,1,7,3,6,8,4,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,1,5,6,8,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,4,7,5,1,6,8,3]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,7,5,6,1,8,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,8,5,1,7,2]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,1,8,3,5,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,6,8,3,7,4,5]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,8,3,5,7,4,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,1,5,6,8,4,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[3,2,1,5,7,4,6,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[2,1,7,3,6,4,5,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,1,6,3,5,8,4,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,4,1,7,5,6,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,4,7,5,1,6,2]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,3,6,1,7,5,2]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,2,1,7,3,5,4,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,6,1,8,3,5,4,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,3,1,5,6,4,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,4,7,5,1,6,3,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,2,4,1,7,5,3,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,6,3,1,7,4,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,4,7,1,8,5,3,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,5,1,6,3,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,2,1,7,3,4,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,2,1,7,8,3,5,4]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[2,7,1,8,3,5,6,4]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,8,3,6,4,5,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,1,6,7,4,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[3,2,1,7,4,5,6,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[3,2,1,6,8,4,5,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[2,1,8,3,7,4,5,6]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,1,8,3,6,7,4,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,5,1,6,7,3]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,8,5,6,1,7,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,1,8,4,5,6,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[1,6,8,3,7,2,4,5]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,1,5,7,2,4,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,8,4,7,3,5]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,8,2,4,7,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,4,8,3,6,7,5]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,2,7,8,3,6,5]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,5,7,4,8,6,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,4,7,6,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,1,2,5,4,6,3]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,8,1,2,3,7,6,4]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,8,4,3,5,7,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,5,3,7,6,4,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,2,8,7,4,5,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,6,2,8,4,5,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,6,3,8,5,4,7]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,5,3,6,4,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,3,8,5,4,6]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,2,7,8,6,3,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[1,6,2,8,4,3,5,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,2,7,3,5,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,3,2,4,5,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,7,3,2,8,4,5,6]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[3,1,7,8,6,2,4,5]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[1,8,7,2,4,5,6,3]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,3,5,6,2,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,8,7,4,5,6]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,8,3,2,6,4,5,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,7,6,3,2,4,5,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,2,8,4,3,7,5,6]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,1,7,2,4,6,3]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,8,7,4,6,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,4,7,5,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,8,2,7,4,5,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,5,3,8,6,4,7]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,5,3,6,4,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,3,7,5,4,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,3,7,5,4,8,6]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,7,4,8,6,5,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,2,7,6,4,5,3]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,7,6,5,1,4,3]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,1,6,3,2,5,4,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,7,6,3,1,5,8,4]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,8,4,3,6,5,2,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,4,6,5,3,2,7]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,4,2,1,6,5,3,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,6,1,4,3,5,2,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,1,3,5,2,6,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[7,3,1,2,4,6,5,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[1,8,6,3,4,5,2,7]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,6,7,4,2,5,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,2,1,4,8,5,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,1,7,2,4,6,8,5]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,7,1,5,2,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,7,4,1,5,8,2]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,2,7,1,5,8,6]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,8,6,5,4,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,4,8,6,1,2,3,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[5,6,8,7,4,3,1,2]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,8,2,7,4,3,6,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,8,2,3,7,1,4]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,8,5,3,1,7,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,6,1,3,2,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,1,6,3,7,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,2,8,6,4,7,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,3,2,6,4,8,1,7]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,6,3,5,8,2,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,3,8,6,1,7]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,5,3,2,7,6,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,5,2,6,7,3]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,2,7,6,5,8,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,1,6,7,8,5,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,3,6,2,7,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,7,3,2,8,1,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,3,6,8,4,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,2,1,4,8,6,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[5,3,1,4,2,8,6,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[7,6,1,3,8,5,4,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[3,4,7,8,1,2,6,5]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,7,8,1,4,5,2]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,2,8,1,5,4,7]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,6,8,5,1,4,7]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[3,1,6,4,8,2,5,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,3,2,6,8,5,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[7,3,5,8,4,6,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,2,8,4,1,6,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,5,8,2,1,3,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,8,5,2,4,6,3,7]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,2,3,5,7,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,4,2,8,3,5,1,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,8,2,5,7,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,4,8,3,6,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,7,4,8,5,3,6,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,5,4,8,3,6,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,2,5,8,4,6,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,6,3,7,2,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,3,8,5,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,6,8,3,4,1,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,6,2,7,5,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,6,7,2,4,3,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,6,8,4,3,1,7]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,5,7,8,4,1,3,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[6,5,7,8,4,1,3,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,6,8,2,4,1,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,2,8,5,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,2,6,8,5,1,7]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[3,5,6,8,2,4,1,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,8,4,2,1,7]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,6,7,8,1,4,5,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,7,8,1,4,2,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,7,8,2,1,4,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,6,7,8,1,4,3,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,7,8,3,1,4,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,5,7,8,3,1,4,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,4,7,3,8,1,5,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,4,7,3,8,1,5,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,3,8,1,2,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,3,8,2,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,5,4,8,1,7]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,5,2,3,8,1,7]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,5,3,2,8,1,7]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,3,8,2,1,7]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,7,3,8,1,6,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,7,8,3,1,6,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,7,8,3,1,2,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,5,6,8,2,3,1,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,6,2,8,3,1,7]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,2,6,8,4,1,7]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,4,7,2,8,1,3,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,7,8,2,1,3,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,6,7,8,1,3,2,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,7,8,1,3,5,2]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,7,8,1,3,5,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,7,8,1,5,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,7,8,1,5,2,3]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,7,8,1,2,5,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,7,8,2,1,6,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,7,2,8,1,6,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,2,7,8,1,6,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,3,2,7,8,1,6,5]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,5,7,8,2,1,6,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,7,8,1,2,5,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,7,8,1,5,2,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,6,7,8,1,5,4,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,7,8,1,5,4,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,6,7,8,9,1,2,10]=>[[1,2,3,4,5,6,7,10],[8,9]]=>[7,3]=>[7,3]=>2
[2,4,5,6,7,8,1,3,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[1,4,5,6,7,8,9,10,2,3]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[4,2,7,1,5,3,8,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,8,6,1,5,3,7]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,6,7,5,1,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[2,7,1,3,5,4,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,2,1,5,8,6,3]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[7,2,1,3,5,8,6,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[2,3,6,4,7,1,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,3,4,8,2,7,5,6]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,4,8,2,6,7,5]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,1,6,2,5,7,4]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,6,2,1,5,7,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,8,3,6,5,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,7,3,5,1,8,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,5,1,8,2,3]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,7,5,8,2,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,5,1,6,8,2,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,5,6,1,8,2]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,6,8,5,1,7,2]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,8,2,1,5,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,2,1,3,5,7,4]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,2,3,5,7,4,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,7,3,6,1,4,5,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,6,1,3,5,8,4,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,3,2,5,6,1,4,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[4,7,5,2,6,1,3,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,2,8,1,5,3,7]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,1,2,7,5,3,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[4,5,6,2,7,1,3,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,1,2,6,3,4,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[1,6,2,7,4,8,3,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,1,7,8,5,3,4]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[6,7,3,8,4,1,5,2]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,8,4,1,5,6,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,1,8,5,6,3,4]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,5,1,6,7,3,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,2,4,5,1,6,7,3]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,8,4,5,6,1,7,2]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,8,3,6,7,1,2]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,3,7,6,1,2]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,3,7,1,6,5]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,3,4,8,1,6,5]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,3,4,8,1,5,6]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[7,6,3,4,8,5,1,2]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[7,6,3,5,8,4,1,2]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,6,3,8,4,5,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,8,5,1,4,6]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[7,2,3,8,5,1,6,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,4,8,1,5,7,3]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,3,8,4,1,5,6]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[7,2,3,5,8,1,4,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[7,8,2,3,6,1,4,5]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,2,3,6,1,5,4]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,6,3,7,1,5,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,2,3,5,8,1,6,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,3,8,4,1,6,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,4,8,1,3,7,5]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,4,8,1,7,5,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,5,1,2,3,8,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,6,5,1,4,2,8,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,6,4,5,1,8,7,3]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,6,4,1,2,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[7,8,5,4,1,2,6,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,5,6,4,1,2,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,6,5,1,4,2,3,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,6,5,1,2,4,3,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,5,1,2,4,8,3]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,6,5,1,3,2,8,4]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,5,1,3,2,4,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,6,5,1,3,4,2,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,2,3,4,5,1,8,6]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,6,4,3,1,5,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,6,4,3,1,8,5,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,6,4,3,1,8,7,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,5,8,4,1,2,7,6]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,8,4,1,2,6,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[3,5,8,4,1,6,2,7]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,3,6,1,7,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,8,4,1,6,7,2]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,8,4,1,7,3,6]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,4,2,1,7,8,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,6,4,2,1,7,5,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,4,1,8,7,2]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,4,5,1,3,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,6,5,1,4,3,8,2]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,5,1,2,8,4,3]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[7,6,5,1,2,8,3,4]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,6,5,1,8,2,4,3]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,5,1,8,2,3,4]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,6,5,1,8,3,2,4]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[7,6,5,1,4,8,2,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[3,6,4,5,1,7,2,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,6,4,1,7,8,3]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,8,5,4,1,6,3,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,6,4,1,7,3,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,6,4,5,1,7,8,2]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,5,1,4,8,3,2]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[7,6,5,1,8,3,4,2]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,5,1,8,4,2,3]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[4,1,7,6,2,8,5,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,6,2,1,3,5,4]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,7,6,1,2,8,4,5]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,6,5,3,1,4,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,6,1,5,3,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,1,4,2,5,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,4,5,7,8,1,3]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,1,6,5,2,4,3]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,5,6,8,1,3,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[6,1,3,4,2,8,7,5]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,5,6,1,8,7,3]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,6,5,7,3,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,3,4,7,5,1,6]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,7,4,3,5,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,8,5,1,6,3,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,6,4,7,3,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,6,1,7,3,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,3,2,1,5,4,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[3,8,5,1,7,2,4,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,1,3,2,4,5]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,8,7,4,6,3]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,1,8,4,5,6,2]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,3,8,4,7,5,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,4,3,1,7,2,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,3,7,4,6,1,2,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,3,8,6,4,5,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,5,8,6,7,4,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,2,1,8,6,5,3]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[4,6,7,2,5,8,3,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,2,5,3,8,1,4]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,1,3,4,8,7,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[6,5,4,2,8,3,1,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[5,4,3,1,8,7,2,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[6,1,4,3,8,5,2,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,6,2,8,1,5,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,5,1,7,8,3,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,3,1,7,8,6,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,2,1,8,6,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,6,8,1,5,3,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,5,8,3,1,2,7]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,3,2,5,6,7,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,6,8,1,5,2,4,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,8,7,4,5,1,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,5,7,4,2,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,8,5,1,2,3]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,1,4,8,7,5,3,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,1,6,8,3,7,5,4]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,8,2,4,1,5,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,2,8,1,7,5,4,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,6,5,4,8,1,3,7]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,5,3,4,8,1,7,2]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,4,3,2,5,1,7,6]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,2,8,1,5,3,6,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,2,6,4,3,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,6,2,1,3,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[4,6,2,8,3,7,5,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,5,8,3,6,4,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,8,5,3,6,7,1,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,5,6,4,1,3,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,4,1,6,3,7,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,1,3,5,7,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,4,5,6,2,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,9,5,8,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]=>5
[7,6,8,3,5,1,4,2]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,9,5,7,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]=>5
[8,9,6,7,3,5,1,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]=>5
[8,9,6,7,4,5,1,3,2]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]=>5
[8,9,6,7,4,5,2,3,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]=>5
[9,7,10,5,8,3,6,1,4,2]=>[[1,3],[2,5],[4,7],[6,9],[8,10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[7,8,6,3,5,1,4,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,8,7,6,1,4,2]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[9,8,5,7,3,6,1,4,2]=>[[1,4],[2,6],[3,8],[5],[7],[9]]=>[4,2,2,1]=>[4,2,2,1]=>4
[10,7,9,5,8,3,6,1,4,2]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[7,9,6,8,3,5,1,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]=>5
[10,8,9,5,7,3,6,1,4,2]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[6,5,8,4,7,1,3,2]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,9,5,7,4,6,1,3,2]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]=>5
[10,8,9,6,7,3,5,1,4,2]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[8,9,6,7,3,5,2,4,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]=>5
[10,8,9,6,7,4,5,1,3,2]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[6,7,4,2,5,3,1,8]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,4,8,3,1,5,2]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,8,5,6,1,3,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,2,5,6,3,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[4,2,7,5,6,3,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,7,5,6,2,1,8]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,3,5,6,2,1,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,2,5,6,4,1,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,5,6,1,4,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,5,2,7,4,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,5,1,7,4,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,4,8,2,1,5,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,7,8,6,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,4,1,2,3,7,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,1,8,5,6,3,2,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,2,5,6,4,3,7]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,8,5,3,7,4,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,1,5,2,7,6,4]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,1,5,3,7,6,4]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,2,4,6,7,8,3]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,1,5,3,6,7,8,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,5,3,7,2,4]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,4,6,3,2,8,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,4,1,7,8,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,6,4,3,1,2,8,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,6,3,5,1,7,2,4]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,5,3,1,6,7,8,2]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,5,2,1,6,7,8,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[5,2,3,1,6,7,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[1,5,3,2,6,7,8,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[8,4,6,5,1,7,2,3]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,5,4,6,1,2,8,3]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,6,1,7,8,4]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,2,8,7,6,1,4,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,8,4,7,2,1,3,5]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,8,7,5,6,1,2,4]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,2,7,5,6,1,3,4]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,8,6,5,1,7,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,6,2,3,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,4,2,1,5,8,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[5,7,4,6,1,3,8,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,6,4,7,3,1,2,5]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,2,4,3,7,1,8,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,4,2,7,1,8,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,4,1,3,5,2,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,7,4,1,5,3,8,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,4,1,2,6,8,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[1,7,4,2,3,6,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,8,2,5,3,7,6,4]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,1,5,4,7,3,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,1,5,6,4,3,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[3,8,1,5,6,4,2,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,1,2,5,3,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,2,8,1,6,5,4,7]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,6,1,5,7,8,4]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,4,1,5,2,8,3]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,6,1,5,4,7,2,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,1,4,6,7,8,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,2,1,4,6,7,8,3]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[5,4,1,3,6,7,8,2]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[8,4,1,5,3,7,2,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,4,1,3,2,8,6]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,2,5,1,4,7,8,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,1,4,3,5,2,8,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,3,5,4,7,2,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,3,4,6,7,8,2]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[3,1,8,2,5,7,4,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,6,1,4,7,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,8,1,6,4,3,7,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,1,3,8,7,5,4]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,7,1,3,8,6,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,1,5,7,4,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,1,5,8,4,6,3]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,1,6,4,8,3,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,1,6,5,3,8,4]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,1,7,6,5,4,3]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[8,3,2,7,1,6,5,4]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,8,7,3,2,6,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,1,7,2,8,6,5,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,8,6,5,4,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,7,6,1,4,2,5,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,1,4,6,8,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,6,8,5,1,4,7,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,5,8,2,1,4,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[7,3,6,2,1,4,5,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[7,3,6,2,1,5,4,8]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,4,2,8,1,6,5,3]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,5,3,2,1,6,4]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[7,5,2,6,3,1,4,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,4,6,2,1,8,3,5]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,8,4,5,2,1,7,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,8,5,1,7,3,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,1,3,8,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,6,1,5,3,2,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,7,6,3,8,2,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,7,6,4,2,8,3]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,1,8,7,6,4,3,2]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[8,5,2,1,7,6,4,3]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[8,5,2,1,6,3,7,4]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,1,8,6,3,2,7,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,6,1,7,4,8,2,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,8,6,3,7,2,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,2,5,7,3,1,6]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[3,4,6,8,5,7,1,2]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,8,2,7,3,6,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,7,3,6,1,2]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,4,7,3,6,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,3,8,7,1,2,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,3,7,2,4,8,1,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,4,2,7,3,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,2,8,1,3,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,5,2,7,1,3,8,4]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,6,5,4,2,1,7,3]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[6,4,7,3,1,8,2,5]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,3,8,6,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,5,8,4,6,3,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,6,4,8,3,5,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,3,8,2,4,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,6,3,7,4,2,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,6,3,8,5,1,4,2]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,1,3,2,5,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,6,3,1,5,2]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,7,6,5,3,1,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,7,2,4,6,5,1,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,3,4,5,2,6,7]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[1,6,8,4,2,5,3,7]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,4,1,5,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,4,8,5,1,2,3]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,2,7,8,5,1,6,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,8,1,5,4,6,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,4,8,5,3,7,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,8,5,2,6,7,3]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,1,8,4,3,7,2,5]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,1,4,2,5,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,1,4,3,5,6,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[4,1,5,3,6,8,2,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,5,3,2,7,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,1,4,6,3,8,5,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,6,4,1,8,7,5]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,3,1,8,2,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[3,5,2,1,8,7,6,4]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,5,3,2,8,6,4,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,2,1,7,8,6,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[8,2,7,6,5,1,3,4]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,6,2,7,1,4,5,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,7,3,6,2,8,5,4]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,3,2,1,8,5,4]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[8,6,3,7,4,1,2,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[5,2,3,4,7,1,8,6]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,6,3,1,4,5,7,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,7,3,1,5,4,2,8]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,3,1,2,4,7,6]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[8,1,3,2,4,5,6,7]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[8,4,1,7,2,3,6,5]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,1,6,5,4,7,3]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,1,5,6,4,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,4,1,2,5,7,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,2,8,1,6,5,7,4]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,4,1,5,2,3,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,6,1,5,4,7,3,2]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,1,4,6,7,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,1,4,7,6,3,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[4,5,8,2,1,3,7,6]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,2,3,1,4,6,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,2,1,3,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,4,1,3,6,2,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,5,4,1,3,6,2,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[3,2,5,1,4,6,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,1,4,3,5,6,7,2]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,3,5,4,6,2,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,3,4,6,2,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[4,1,3,2,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,1,4,2,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[4,6,7,3,1,5,2,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,3,5,2,7,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,3,1,4,5,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[7,5,1,8,2,3,6,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,8,4,2,6,7,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,8,3,5,7,2,6]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,2,3,6,8,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,3,4,7,5,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,2,7,1,6,8,3]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,1,6,5,8,2,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,1,4,8,5,6,2]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,2,8,7,1,5,3]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,4,8,1,5,3,6]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,3,1,7,8,5,2]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,1,6,7,8,4,2]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[4,1,6,2,7,8,5,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,3,4,8,7,5,6]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,5,6,7,8,9,1,2,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[4,5,6,7,8,9,2,3,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[5,6,7,8,9,1,2,3,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[6,7,8,9,2,3,4,5,1]=>[[1,2,3,4],[5,6,7,8],[9]]=>[4,4,1]=>[4,4,1]=>3
[8,9,6,7,5,4,3,2,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[2,2,5]=>[5,2,2]=>3
[4,5,6,7,8,9,10,1,2,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[4,5,6,7,8,9,10,2,3,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[5,6,7,8,9,10,1,2,3,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[6,4]=>2
[5,6,7,8,9,10,3,4,1,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[6,2,2]=>[6,2,2]=>3
[7,8,9,10,3,4,5,6,1,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[4,4,2]=>[4,4,2]=>3
[7,8,9,10,5,6,3,4,1,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[4,2,2,2]=>[4,2,2,2]=>4
[8,9,10,5,6,7,2,3,4,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[3,3,3,1]=>[3,3,3,1]=>4
[4,8,3,7,6,5,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,3,8,7,5,4,1,2]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[5,3,8,7,6,4,1,2]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[2,8,7,6,1,5,4,3]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,2,8,7,6,1,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,8,7,5,1,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,8,2,6,5,1,4,3]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,8,7,5,4,3,2]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[3,1,8,7,6,5,4,2]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[7,8,2,6,1,5,4,3]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,8,7,1,5,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,1,7,6,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,8,2,7,6,1,5,3]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,7,2,1,6,5,4]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,5,8,7,1,4,3,2]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,1,7,6,5,3,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[5,4,1,8,7,6,3,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,4,8,1,7,5,3,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,8,4,1,6,5,3,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,1,6,5,4,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,3,8,1,7,5,4,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,1,8,7,6,4,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,8,2,1,6,5,4,3]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,5,3,1,8,7,4,2]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[6,4,3,1,8,7,5,2]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[5,4,3,1,8,7,6,2]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[7,5,2,1,8,6,4,3]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[5,4,2,1,8,7,6,3]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[7,3,2,1,8,6,5,4]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[6,3,2,1,8,7,5,4]=>[[1,5],[2,6],[3,7],[4,8]]=>[5,3]=>[5,3]=>2
[9,7,5,3,1,10,8,6,4,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,7,5,3,1,10,9,6,4,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,6,5,3,1,10,8,7,4,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,6,5,3,1,10,9,7,4,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,6,5,3,1,10,9,8,4,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,7,4,3,1,10,8,6,5,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,7,4,3,1,10,9,6,5,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,6,4,3,1,10,8,7,5,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,6,4,3,1,10,9,7,5,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,6,4,3,1,10,9,8,5,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,5,4,3,1,10,8,7,6,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,5,4,3,1,10,9,7,6,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,5,4,3,1,10,9,8,6,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[6,5,4,3,1,10,9,8,7,2]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,7,5,2,1,10,8,6,4,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,7,5,2,1,10,9,6,4,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,6,5,2,1,10,8,7,4,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,6,5,2,1,10,9,7,4,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,6,5,2,1,10,9,8,4,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,7,4,2,1,10,8,6,5,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,7,4,2,1,10,9,6,5,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,6,4,2,1,10,8,7,5,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,6,4,2,1,10,9,7,5,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,6,4,2,1,10,9,8,5,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,5,4,2,1,10,8,7,6,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,5,4,2,1,10,9,7,6,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,5,4,2,1,10,9,8,6,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[6,5,4,2,1,10,9,8,7,3]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,7,3,2,1,10,8,6,5,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,7,3,2,1,10,9,6,5,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,6,3,2,1,10,8,7,5,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,6,3,2,1,10,9,7,5,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,6,3,2,1,10,9,8,5,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,5,3,2,1,10,8,7,6,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,5,3,2,1,10,9,7,6,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,5,3,2,1,10,9,8,6,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[6,5,3,2,1,10,9,8,7,4]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[9,4,3,2,1,10,8,7,6,5]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[8,4,3,2,1,10,9,7,6,5]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[7,4,3,2,1,10,9,8,6,5]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[6,4,3,2,1,10,9,8,7,5]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[6,4]=>[6,4]=>2
[6,1,4,2,3,5,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,6,1,4,2,3,5,7]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[6,8,1,4,2,3,5,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,1,4,2,3,6,5,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,2,3,6,5,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,6,1,4,5,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[6,2,3,8,1,4,5,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[4,6,2,3,8,1,5,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,3,6,1,5,7]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,3,6,4,1,5,7]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[8,4,3,6,2,1,5,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,2,3,8,4,1,5,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[8,4,2,3,6,1,5,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[6,4,2,3,8,1,5,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[2,6,4,3,8,1,5,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,3,6,1,5,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,8,4,1,5,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,3,8,4,2,1,5,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,6,3,8,1,4,5,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,8,3,6,1,4,5,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,3,6,4,2,1,5,7]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,8,3,6,4,1,5,7]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,3,6,2,4,1,5,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,6,2,1,4,5,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[6,2,1,3,8,4,5,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[8,2,1,3,6,4,5,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[6,3,8,2,4,1,5,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,3,8,1,5,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,4,7,8,5,1,2]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,6,4,2,7,5,8,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,4,2,7,1,5,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,4,7,2,5,6,8,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,8,5,3,7,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,4,2,7,8,3]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,2,5,3,6,1,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,3,6,2,8,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,5,2,4,8,7,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,2,8,5,7,3]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,1,4,2,5,6,3]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,8,5,2,1,6,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,8,5,3,1,6,2,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,1,3,5,8,2,7,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,8,7,4,2,3,5]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,2,8,5,7,3,6,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,6,8,7,5,2,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,2,5,4,7,6,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,2,4,5,8,6,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[1,2,7,3,5,8,6,4]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,2,5,7,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,6,2,1,7,5,3,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,7,8,5,2,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,2,3,7,8,1,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,6,3,7,1,2,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,1,3,5,7,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[7,3,2,4,5,1,8,6]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,8,2,5,4,1,7,6]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,4,2,6,3,1,5]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,6,3,8,7,1,5]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,8,2,7,4,3,1,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,8,5,1,7,2,6]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,8,1,2,7,5]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,5,2,8,1,7]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,8,4,2,1,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[6,1,7,2,8,3,9,4,10,5]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[6,1,7,8,9,10,2,3,4,5]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[6,4]=>[6,4]=>2
[7,1,8,2,9,3,10,4,11,5,12,6]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[3,2,2,2,2,1]=>[3,2,2,2,2,1]=>6
[1,8,6,7,5,3,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,8,7,2,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,8,6,2,3,7,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,6,1,3,5,4,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,1,8,2,5,7,3]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[2,8,6,1,3,5,4,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,3,6,5,8,7,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,3,5,8,7,4]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,3,8,5,7,6]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,1,3,5,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,1,3,5,8,7,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,6,1,3,5,8,7,2]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,1,4,3,5,8,7,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,1,3,5,8,7,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[6,2,1,3,5,8,7,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[4,2,1,3,6,5,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[4,2,1,6,3,5,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[6,2,1,8,3,5,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,1,3,8,5,7,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,4,3,8,5,7,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,4,3,8,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,4,3,6,5,7,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,1,3,6,5,7,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,2,1,3,6,5,7,4]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,2,1,6,3,5,7,4]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,1,4,3,5,7,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,2,1,4,3,5,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[8,2,4,1,3,5,7,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,2,6,1,3,5,7,4]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,6,1,3,5,7,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,1,6,3,5,7,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,4,6,3,5,7,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,4,6,3,5,7,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,8,3,5,7,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,1,8,3,5,7,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,1,3,5,7,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,8,1,3,5,7,4]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,1,3,5,7,6]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,8,1,3,5,7,4]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,1,3,5,7,2]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,1,8,3,5,7,2]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,6,8,3,5,7,2]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,6,3,8,5,7,2]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,1,3,8,5,7,2]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,1,8,3,5,7,6]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,6,8,3,5,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,3,6,8,5,7,2]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,3,6,8,5,7,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,3,8,6,5,7,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,8,3,6,5,7,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,4,3,5,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[2,6,1,4,3,5,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,8,1,4,3,5,7,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,1,6,3,5,7,4]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,1,3,6,5,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,8,3,6,5,7,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,8,6,3,5,7,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,8,6,3,5,7,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,1,6,3,5,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,1,3,5,7,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,6,1,3,5,7,4]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,4,1,3,5,7,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,6,4,1,3,5,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[4,6,2,1,3,5,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[6,8,1,4,3,5,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,8,4,3,5,7,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,8,4,3,5,7,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,6,4,3,5,7,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,1,6,4,3,5,7,2]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,1,4,3,5,7,2]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,4,1,3,5,7,2]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[8,6,2,1,3,5,7,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,4,2,1,3,5,7,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,8,6,5,2,1,4,3]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,7,4,1,8,6,3,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,4,2,8,3,7,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,4,2,7,3,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,4,6,3,2,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,1,4,6,3,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,7,4,5,8,2,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,4,6,8,2,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,4,1,7,2,5,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,6,1,7,8,3,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,4,1,8,7,3,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,8,4,6,7,2,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,4,5,7,2,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,4,5,6,2,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,4,5,3,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,1,4,5,3,2,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,5,4,6,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,1,5,4,6,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,1,5,4,6,8,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,1,4,5,3,8,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,1,4,6,3,8,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,4,2,7,3,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,7,2,8,3,1,6]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,7,2,8,3,6,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,4,2,8,3,1,7]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,1,4,6,3,2,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,1,5,4,6,2,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,1,5,4,2,7,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,6,1,5,4,8,2,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,3,1,4,2,5,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,1,4,2,5,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,3,1,4,2,8,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,1,5,4,7,8,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,1,2,7,6,5,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,1,2,6,8,7,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,3,1,4,7,2,5]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,7,2,8,5,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,1,4,7,3,2,6]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,1,4,5,3,2,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,1,5,4,7,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,1,5,4,8,7,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,1,5,4,7,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,1,4,2,5,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,3,1,4,2,7,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,3,1,4,6,2,5]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,2,6,5,1,3]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,5,8,7,3,4,2,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,3,1,4,6,5,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,3,1,4,5,2,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,5,4,2,6,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,8,1,5,4,2,7,6]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,1,4,7,3,6,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,4,2,7,5,3,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,4,7,2,8,5,3,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,7,1,4,8,5,2]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,1,4,7,5,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,5,4,8,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,2,8,5,7,6]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,1,2,5,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,5,4,2,8,6]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,3,1,4,5,8,2]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[7,3,8,1,4,5,2,6]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,1,4,5,6,2]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,3,1,4,5,2,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,5,4,2,6,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[9,8,7,6,5,4,2,1,3]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[9]=>[9]=>1
[9,8,7,6,5,3,2,1,4]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[9]=>[9]=>1
[8,7,6,3,5,2,1,4]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[9,8,7,6,4,3,2,1,5]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[9]=>[9]=>1
[8,7,4,6,3,2,1,5]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[9,8,7,5,4,3,2,1,6]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[9]=>[9]=>1
[8,5,7,4,3,2,1,6]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[9,8,6,5,4,3,2,1,7]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[9]=>[9]=>1
[9,7,6,5,4,3,2,1,8]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[9]=>[9]=>1
[9,8,7,6,5,4,1,3,2]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[8,1]=>[8,1]=>2
[10,9,8,7,6,5,4,2,1,3]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[9,8,7,6,5,2,4,1,3]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[10,9,8,7,6,5,3,2,1,4]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[10,9,8,7,6,4,3,2,1,5]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[8,7,6,2,5,4,1,3]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[10,9,8,7,5,4,3,2,1,6]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[8,5,4,7,3,2,1,6]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,3,6,5,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[10,9,8,6,5,4,3,2,1,7]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[6,5,8,4,3,2,1,7]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,4,7,6,3,2,1,5]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[9,6,8,5,4,3,2,1,7]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[10,9,7,6,5,4,3,2,1,8]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[5,8,7,4,3,2,1,6]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[10,8,7,6,5,4,3,2,1,9]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[10]=>[10]=>1
[5,8,6,2,3,4,7,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,5,2,7,3,1,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,2,6,3,5,7,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,7,2,5,8,6,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,2,5,8,4,3,7]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,1,6,8,5,2,4]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,2,7,1,8,6,3,4]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,2,8,1,7,3,4]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,8,3,5,1,7,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,3,8,7,1,6,2]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,4,3,7,2,6,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,3,7,4,2,6,5,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,6,5,1,7,4,3]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,3,2,8,4,1,7,5]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,8,3,4,1,7,5,6]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,2,8,3,1,7,6]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,8,4,3,1,7,6,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,3,1,7,6,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,8,6,4,1,7,5,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,5,1,6,4,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,3,7,5,2,6,4,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,6,2,5,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,6,1,5,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,4,8,6,2,1,5,3]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,8,5,2,1,6,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,3,8,4,2,1,6,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,5,4,3,8,2,1,6]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[3,7,8,4,1,2,6,5]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,8,5,1,2,6,4]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,8,6,1,2,5,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,4,6,3,5,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,8,6,1,2,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,7,8,3,1,2,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[7,3,4,8,2,1,5,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,6,4,8,3,2,1,5]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,5,8,6,2,1,4,3]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,8,7,3,1,4,2]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,8,3,1,5,7,6]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,2,4,8,1,5,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[2,3,8,4,1,6,7,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,8,5,1,6,7,4]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,4,8,7,3,1,5,2]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,4,7,3,2,5,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,4,7,2,5,6,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,8,7,1,5,6,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,8,6,1,5,7,3]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,8,6,1,4,7,3]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,5,7,2,4,6,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,7,2,3,5,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,8,7,1,3,5,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,8,5,1,3,7,4]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,8,4,1,3,7,5]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,8,3,1,4,7,6]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,7,1,3,4,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,4,6,8,2,1,3,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,3,5,4,1,8,6,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,3,6,4,8,1,5,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,4,6,3,5,2,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,8,6,2,1,3,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,3,6,8,1,5,4,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,6,1,4,7,8,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,6,1,4,7,3,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,1,6,8,4,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,6,1,8,5,4,3]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,7,6,8,1,4,5,3]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,7,6,3,2,5,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,6,3,2,4,5]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[5,7,8,6,2,3,4,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,6,1,8,5,3,4]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,5,1,7,2,4,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,7,6,1,5,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[7,3,5,8,4,1,2,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,8,4,5,2,7,3,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,5,2,7,6,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,5,8,4,1,6,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,7,6,4,8,5,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,5,4,6,8,1,2]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,4,7,1,8,2]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,5,4,7,1,2,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,1,5,6,8,7,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,1,6,8,5,2,4]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,8,6,4,7,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,4,3,6,2,5,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,8,6,4,5,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,1,6,8,5,4,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,3,5,4,7,2,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,5,4,6,8,2,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,6,4,8,5,3,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,4,5,2,6,3,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,8,5,3,1,2,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[7,3,5,8,4,6,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,6,5,8,1,7]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,7,5,1,8,6]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,7,5,1,6,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,3,4,7,1,6,5,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,7,1,6,8,5]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,6,1,8,7,5]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,8,4,2,7,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,8,5,3,2,1,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,8,4,5,2,3,6,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,4,8,5,3,2,6,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,5,8,4,2,1,7]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,2,4,6,8,3,7,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,7,4,6,3,2,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,4,6,3,7,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,5,4,6,7,2,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,3,4,5,7,2,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,7,4,6,3,8,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,1,7,8,3,2,6]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,4,2,7,8,3,6,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,4,6,8,3,2,7]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[5,1,8,4,6,3,2,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,6,4,5,3,2,7]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,3,5,4,6,2,7]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,6,2,4,3,5,7]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,7,1,2,4,3,5,6]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[1,7,6,2,4,3,5,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,3,2,4,6,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,2,6,3,4,5,7,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,6,3,4,5,2,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,2,5,4,3,6,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,7,2,4,5,3,6,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,8,2,4,7,3,6,1]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,3,2,4,7,5,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,1,3,4,5,2,6]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[8,1,6,3,4,5,2,7]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,5,4,3,6,7]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[3,4,8,7,5,2,6,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,6,1,5,4,7]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,2,4,3,5,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[8,7,3,6,4,2,5,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,7,2,5,4,6,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,2,4,5,6,3,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[5,3,6,2,4,8,7,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,8,6,1,4,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,2,5,1,4,8,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,8,6,2,3,4,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[2,5,4,1,8,6,3,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,6,1,8,2,5,4]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,6,3,1,8,2,4,5]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,2,3,6,1,4,7,5]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,8,2,6,3,4,7,5]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,3,6,4,7,2,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,3,6,4,8,2,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,1,3,5,7,4,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[8,2,6,3,1,4,7,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,4,1,3,8,2,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[2,7,5,8,3,4,1,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,8,5,4,1,2,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[7,2,3,6,1,4,8,5]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,3,7,2,5,8,4,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,3,5,8,4,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,4,8,1,3,6,2,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,3,5,7,4,6]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[7,1,2,3,5,8,4,6]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[8,6,1,4,7,3,2,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[2,6,3,7,1,4,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,8,1,4,7,5]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,4,8,1,3,2,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,7,1,3,2,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,1,8,5,4,6,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,6,5,1,3,4,2,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,5,1,7,6,3,4,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,7,6,1,8,5,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,6,7,1,8,4]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,8,4,7,5,1,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,5,1,3,2,6]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,1,6,5,2,7,4]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,2,8,3,4,7,5]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,3,1,7,2,4,5]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,2,5,6,1,8,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,4,2,5,1,7,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,5,3,8,4,1,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,3,1,4,7,2,6,5]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,3,2,1,5,7,4,6]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[2,8,3,6,4,7,1,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,6,4,8,1,2,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,6,4,7,1,2,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,3,5,7,4,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,3,2,5,7,4,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[6,5,1,7,4,2,8,3]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,6,4,8,2,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,1,7,3,5,2,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,7,3,4,2,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,7,3,4,2,8,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,1,6,5,2,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,1,6,5,2,4]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,4,2,8,6,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,1,7,6,5,3,4]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,2,8,6,5,1,7,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,4,2,8,5,1,7,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,6,4,7,1,5,2,3]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,6,4,8,1,5,2,3]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,4,2,3,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,2,3,8,7,5,1,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,8,7,1,6,5,2,4]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,8,1,6,7,5]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,7,1,6,8,5]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,3,7,8,5,1,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[5,1,6,4,2,3,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[6,4,7,8,1,5,2,3]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,4,6,1,5,2,3]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,7,8,1,4,2,3]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,8,6,1,5,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,7,8,1,5,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[3,2,4,8,7,1,5,6]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[4,8,7,6,1,5,2,3]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,6,1,4,2,3]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,5,7,1,4,2,3]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,7,4,2,3,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[6,7,4,8,1,5,2,3]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,7,6,1,5,2,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,4,7,1,5,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,3,2,4,8,1,5,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[2,5,3,7,1,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,6,7,1,5,2,3]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,8,1,5,2,3]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,8,4,2,3,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,2,3,7,5,1,6,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[3,7,5,8,1,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,7,1,6,5,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,7,1,5,8,6,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,7,6,1,5,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[4,7,6,8,1,5,2,3]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,6,7,1,4,2,3]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,7,5,1,4,2,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,5,1,4,2,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,5,1,4,2,3]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,6,8,7,1,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,7,1,5,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,7,1,5,8,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,4,6,1,5,7,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[6,7,8,5,1,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,6,5,1,4,2,3]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,7,5,4,2,8,6]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,5,4,6,3,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,5,2,3,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[5,4,1,3,6,7,2,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[8,4,1,2,6,3,7,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[8,2,7,1,5,3,4,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,1,5,8,4,6]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,1,5,4,2,8]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,8,1,5,4,2,6]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,3,8,4,2,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,1,3,6,8,2,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,8,1,5,4,2,7]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,3,1,5,4,2,7]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,3,1,5,4,2,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[3,6,2,1,5,8,4,7]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,2,1,5,3,4,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[4,8,2,1,7,5,3,6]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,8,1,5,7,4,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,2,8,6,4,5]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,6,2,8,3,4,5]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,2,6,3,8,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,8,1,5,3,4,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,2,1,5,3,4,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,1,8,5,3,6]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,2,1,4,5,3,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,7,5,6,1,4,3,2]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,8,6,1,4,3,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,4,1,6,5,3,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,4,5,6,8,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,1,6,4,5,8,3,2]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,4,7,6,8,2]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,1,7,5,3,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,8,7,1,4,3,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,7,1,4,3,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,5,7,1,4,3,2]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,6,1,4,3,2]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,8,1,4,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,1,5,6,4,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,1,6,5,3,7]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,1,8,5,3,7]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,1,4,5,6,7,2]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[5,3,1,4,8,6,7,2]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,1,6,3,4,8,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,5,8,4,3,6,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,1,6,4,3,7,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,1,8,4,6,7,2]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,1,5,4,6,7,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,6,1,4,5,3,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,1,4,5,3,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,6,1,5,3,4,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,8,6,1,5,3,4,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,1,5,6,3,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[7,1,2,5,8,3,4,6]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[7,1,4,5,6,8,3,2]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[8,5,6,7,1,4,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,8,5,1,4,3,2]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,5,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,7,1,4,5,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,7,4,6,8,2]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,5,6,4,8,3,2]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,6,5,4,8,3,2]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,6,1,4,5,3,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,8,1,4,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,6,5,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,3,1,6,5,8,7,2]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,1,2,4,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,3,6,2,1,8,7,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,2,1,4,6,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,3,7,2,8,4,1,6]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,5,8,3,1,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,2,4,5,1,3,6,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[6,2,4,5,1,8,7,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,4,5,2,8,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,4,5,2,8,7,3]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,4,5,1,2,6,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,7,4,5,8,2,1,6]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,4,2,6,3,5,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[8,7,4,5,2,1,6,3]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,1,8,4,2,5]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,4,1,6,3,2,8]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,4,8,6,3,2,5]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,4,8,6,3,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,8,3,5,6,7,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,3,5,6,7,2,4]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,5,6,7,2,3]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,3,5,6,7,2,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[5,8,4,3,6,1,2,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,3,8,4,1,7,2,6]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,4,6,7,3,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,3,6,7,5,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,8,2,1,7,5,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,8,4,2,6,1,5,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,5,6,7,4,3]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,5,6,7,4,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,5,6,7,1,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[8,2,1,5,6,7,4,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[8,1,3,5,6,7,4,2]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[7,1,4,3,6,2,5,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,8,4,3,6,2,1,5]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,1,8,5,7,6,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,6,8,7,5,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[6,3,1,8,2,7,4,5]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,8,2,7,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,4,8,6,2,1,3]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,1,4,8,6,2,3,5]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[7,5,4,1,6,2,3,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,6,4,5,8,1,3,2]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,4,5,8,2,3,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,6,1,8,2,4,5]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,7,6,5,8,3,4,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,3,6,7,4,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,3,5,2,1,7,4,6]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,4,1,5,6,7,3,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[8,4,2,5,6,7,1,3]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[4,1,8,5,6,7,3,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,5,6,7,3,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,5,6,7,3,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[1,5,3,8,6,7,4,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,5,8,6,7,3,2]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,5,8,1,7,2,6]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,4,8,6,1,2,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[1,4,8,5,6,7,2,3]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,8,5,6,7,1,2]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,1,5,6,3,4,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,7,1,4,3,6,5,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,7,2,5,6,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,3,1,4,5,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,7,1,4,2,6,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,1,5,6,2,8,4]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,1,5,6,8,2,3]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,2,6,7,3,1,4]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[8,4,2,6,3,7,1,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,2,3,5,7,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[4,7,3,2,5,6,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,4,6,2,8,1,7]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,4,2,8,1,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,2,3,8,1,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,2,8,3,1,4]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,2,4,8,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,1,8,3,4,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[8,7,6,1,4,5,2,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,7,6,1,3,2,5,4]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,7,2,4,3,1,6,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,7,4,5,1,6,2,3]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,6,4,1,7,2,3]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,6,3,1,2,7,4]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,4,6,2,3,1,7,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,4,2,1,7,6]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,7,3,4,2,1,8,6]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,2,3,1,8,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,5,3,1,2,8,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,7,5,4,1,8,2,3]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[10,3,1,2,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[10,4,1,2,3,5,6,7,8,9]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[5,10,1,2,3,4,6,7,8,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[10,6,1,2,3,4,5,7,8,9]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[10,7,1,2,3,4,5,6,8,9]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[8,10,1,2,3,4,5,6,7,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[2,3,10,1,4,5,6,7,8,9]=>[[1,2,3,6,7,8,9,10],[4,5]]=>[3,7]=>[7,3]=>2
[8,9,1,2,3,4,5,6,10,7]=>[[1,2,5,6,7,8,9],[3,4,10]]=>[2,7,1]=>[7,2,1]=>3
[7,3,5,4,1,8,6,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,7,3,1,8,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,2,4,7,5,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[4,2,1,6,3,7,5,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,6,3,7,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[4,2,1,3,7,8,6,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,8,1,7,4,3,2,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,2,1,8,3,5,6,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[4,2,1,6,3,8,7,5]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,4,2,6,8,1,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,7,5,2,4,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,5,2,4,1,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,7,3,6,5,8]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,7,6,8,4,2,5,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,1,7,4,2,6,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,8,6,2,4,5,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,1,3,5,8,6,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[4,2,1,8,3,7,6,5]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,1,5,4,7,8,3]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,3,5,8,7,1,2]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,1,4,8,7,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,5,1,8,3,4,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[4,7,5,2,1,3,6,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,5,6,2,4,1,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,5,6,1,4,8,3,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,4,1,5,3,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,6,8,4,5,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,5,2,8,1,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,5,6,4,2,3,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[5,7,4,6,8,1,3,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,8,1,4,6,3,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,7,4,6,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,8,4,6,7,5,3,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,1,8,4,7,5,3,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,5,8,6,1,7,3,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,5,1,6,7,3,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,4,5,6,7,3,2]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[5,6,7,1,4,2,3,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,2,6,1,5,7,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,8,5,2,1,6,7,3]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,1,8,4,2,6,3,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,6,2,5,3,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,5,2,3,4,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[8,3,1,4,6,2,5,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[3,1,8,2,5,6,4,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,8,2,6,4,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,1,2,8,4,7,6]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,5,8,6,1,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,2,4,3,6,7,1,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,5,7,1,6,4]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,2,8,5,1,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,1,8,4,7,5,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,7,1,4,6,5,3]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,2,7,1,5,4,6,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,5,3,6,8,1,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,1,5,6,2,4,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[3,7,5,1,6,2,4,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,7,3,6,5,8,1,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,2,4,1,6,5,3]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,8,7,2,3,6,5,4]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,8,2,6,4,3,5]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,8,2,6,4,5]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,7,3,6,4,5,8]=>[[1,2,3,5,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,8,3,2,4,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[1,6,2,8,4,3,7,5]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,8,7,2,4,6,5]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,3,7,2,5,4,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,4,7,3,2,5,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[4,7,8,1,3,2,5,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,2,3,5,6,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[8,2,1,4,7,3,5,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[2,1,3,8,4,6,7,5]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,4,8,5,7,6]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,7,5,6,8,3,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,7,5,6,3,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,3,8,4,7,6,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,5,7,3,6,4,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,8,5,2,7,6,4]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,6,3,4,5,7,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,5,7,3,4,8,6,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,6,1,4,5,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,7,8,2,5,6,4]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,8,5,1,6,4,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,2,3,4,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[4,8,1,5,2,7,3,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,2,5,3,8,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,8,7,5,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[5,4,1,8,2,7,6,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,8,1,2,5,3,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,3,1,4,8,5,2]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,1,6,8,2,7,3]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,7,1,2,8,6,3]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,4,1,2,8,3,5]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[6,5,1,2,3,7,8,4]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[6,5,1,2,3,4,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[6,7,4,1,2,5,3,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[2,4,6,3,5,7,1,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,6,3,7,2,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,2,5,3,1,7,4]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,2,3,4,5,1,7,6]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,8,3,4,2,7,5,6]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,4,1,6,7,5]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,2,3,1,6,5,4]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,8,2,4,6,1,7,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,2,4,3,1,6,5]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,8,2,3,1,7,6]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,4,3,7,2,6,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,3,5,7,2,4,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[2,1,4,7,5,3,6,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[7,1,3,6,2,5,4,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,6,2,4,7,5]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,1,8,3,7,5,4,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,2,5,6,3,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,5,8,2,7,3,4]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,2,8,1,6,7,3]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,5,8,1,4,7,3]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,8,5,1,6,7,4]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,7,1,4,6,5,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,2,5,7,4,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,7,1,6,4,5,3]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,7,1,5,6,4,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,8,5,6,1,7,2]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,4,1,6,5,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,6,2,7,3,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,4,5,7,1,6,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,8,4,1,7,2]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,3,1,5,4,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,2,3,1,4,6,5,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,1,4,5,7,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,5,1,3,2,4,7,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,1,3,2,6,4,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,6,1,4,5,3,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,6,4,1,5,2,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[4,5,6,1,3,2,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,7,1,2,6,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,4,1,2,6,5,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[6,7,1,4,2,5,3,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,1,3,5,6,4,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,1,2,4,3,7,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,8,1,3,4,6,7,5]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,1,2,5,3,6,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,1,2,5,7,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,2,6,7,5,3,8,4]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,7,5,3,2,8,4,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,6,7,5,3,8,4,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,7,2,3,8,4]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,8,2,6,5,7,4]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,5,7,6,3,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[1,3,4,8,2,5,7,6]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,7,6,2,3,4,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,5,3,8,2,6,4,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,8,3,2,5,7,6]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,8,3,5,7,6,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,8,3,5,7,6]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,8,4,2,6,7,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,4,8,2,3,5,7,6]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,7,3,8,2,4,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,7,5,8,3,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,7,5,2,1,8,4,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,4,8,7,5,2,1,6]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,7,5,2,8,4,6,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,8,3,1,7,2,4]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,8,3,2,7,5]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,4,7,1,8,6,2,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,6,8,2,1,5,7]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[3,8,2,5,6,1,4,7]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,8,6,4,1,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,2,5,7,3,8,6,1]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,2,5,3,8,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,2,8,5,6,4,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,2,1,6,8,3,4,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,2,6,8,4,1,3,7]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[1,5,6,8,3,4,2,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,1,6,3,2,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,1,6,8,3,2,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,7,3,8,2,6,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,3,7,8,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,3,1,7,8,2,5]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[4,5,3,1,7,8,2,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,1,3,5,4,8,2,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,5,2,8,1,4,3,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,7,3,8,4,6,1,2]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,5,7,3,8,6,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,3,7,8,5,2,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,3,6,7,8,4,2,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,5,3,6,7,8,4,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,6,1,7,3,8,5,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,7,1,8,4,5,2]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,2,4,8,1,5,3]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,1,4,7,3,8,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,5,6,7,8,1,4]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[5,2,3,6,7,8,4,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[6,7,1,3,2,8,4,5]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,7,1,3,4,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,2,1,7,3,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,7,1,8,3,5]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,3,7,8,1,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,3,7,8,5,1]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,3,8,2,4,5,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,2,7,4,1,8,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,3,2,1,4,8,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,1,8,3,4,2,5,6]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,1,8,3,5,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,8,6,1,3,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[7,3,4,8,6,2,1,5]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[3,5,7,2,1,8,6,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,3,2,5,1,4]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,8,2,5,4,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,7,4,8,5,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,7,1,8,5,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,2,7,1,8,5,3]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,4,8,5,2,6,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,7,8,5,2,6,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,7,8,1,6,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,7,1,8,2,5,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,4,7,8,2,5,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,6,1,7,8,4,3]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,1,2,7,8,4,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,2,1,8,5,3,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,2,8,5,4,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,6,7,4,8,5,3,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,8,2,4,6,3,5,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,5,7,4,3,6,2,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,5,3,6,2,7]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,3,4,7,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,2,4,6,3,7,5]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,2,5,4,6,7,3]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,2,7,1,4,5,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,4,7,5,2,6,8,3]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,6,5,3,7,1,8,2]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,3,8,6,7,1,5]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,4,8,1,3,7,6]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,5,4,8,3,7,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,3,5,8,2,7,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,3,4,8,1,6,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[3,5,2,4,7,1,6,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,3,4,8,1,6,2,7]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,3,7,1,6,2,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,3,8,5,1,2,4]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[4,2,6,7,3,8,1,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,7,4,2,8,6,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,2,8,6,4,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,3,7,8,6,2,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,5,3,6,8,2,7,4]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,6,5,7,8,1,2]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,3,5,6,8,1,7]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[4,2,6,7,3,8,5,1]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,5,6,8,1,7,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,5,2,3,8,7,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,5,3,8,7,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,4,7,5,2,3,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,2,7,4,5,3,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,2,5,3,8,7,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,2,3,8,7,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,7,4,5,3,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,7,2,4,5,3,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,4,5,8,7,3,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,6,4,8,7,5,3,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[8,2,4,6,7,5,3,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[4,2,6,8,7,5,3,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,2,6,5,8,7,3,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,2,3,6,8,7,5,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,4,8,7,2,5,3,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,8,7,5,2,3,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,5,8,7,2,3,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,6,4,7,5,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,8,2,7,5,3,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,5,8,2,7,3,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,8,6,4,7,5,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,4,2,5,3,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[9,2,4,6,8,1,3,5,7]=>[[1,3,4,5],[2,7,8,9],[6]]=>[5,4]=>[5,4]=>2
[9,4,6,8,1,2,3,5,7]=>[[1,3,4,8,9],[2,6,7],[5]]=>[4,5]=>[5,4]=>2
[9,6,8,1,2,3,4,5,7]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[3,5,7,9,1,2,4,6,8]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]=>[5,4]=>2
[5,7,9,1,2,3,4,6,8]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[7,9,1,2,3,4,5,6,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[10,9,8,7,6,5,2,4,1,3]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[8,2]=>[8,2]=>2
[10,9,4,8,3,7,2,6,1,5]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[10,9,8,7,2,4,6,1,3,5]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[7,3]=>[7,3]=>2
[6,10,5,9,2,4,8,1,3,7]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>[2,2,3,3]=>[3,3,2,2]=>4
[10,9,2,4,6,8,1,3,5,7]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[6,4]=>[6,4]=>2
[10,3,5,7,9,1,2,4,6,8]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[5,5]=>[5,5]=>2
[10,5,7,9,1,2,3,4,6,8]=>[[1,3,4,8,9,10],[2,6,7],[5]]=>[4,6]=>[6,4]=>2
[10,7,9,1,2,3,4,5,6,8]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[3,7]=>[7,3]=>2
[4,2,5,6,3,8,1,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,5,7,4,8,3,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,2,1,4,7,6,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[6,7,3,2,5,8,4,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,2,6,4,8,1,5,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,6,4,7,8,5,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,8,3,4,6,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,8,2,6,3,4,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,3,5,8,4,2]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,1,7,8,4,5,2]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,6,7,4,1,8,2]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,1,2,5,8,6,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[1,6,3,5,2,4,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,8,2,7,5,1,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,8,5,7,4,1]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,8,4,7,2,5,6,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,8,1,5,3,7,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,8,1,6,2,7,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,4,6,7,3,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,6,3,4,5,7,2]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,5,4,1,2,8,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[5,7,6,8,3,4,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,1,6,5,7,4,3]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,8,2,5,3,7,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,3,7,6,1,8,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,2,4,6,7,3,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[5,2,3,7,4,8,6,1]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,6,8,4,3,1,7]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,8,1,5,4,3,6,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,4,8,5,3,6,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,5,1,8,4,6,2]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,8,5,4,6,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,3,8,6,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,1,6,3,5,2,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,3,1,7,4,2,5,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,1,8,2,4,5,7,6]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,3,7,6,2,4,5]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[2,3,6,8,7,1,4,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,3,2,8,5,7,1,6]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,6,4,2,8,5,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,3,2,5,1,8,6]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,4,7,5,8,6,1]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,3,8,6,5,1,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,3,5,1,8,6,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,8,1,4,6,5,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,8,3,1,2,6,5]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,8,2,1,3,6,5]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,6,8,2,3,7,5]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,1,2,8,3,7,6]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,2,8,1,3,7,5]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,2,8,4,7,1,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,6,8,4,7,1,5]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,8,3,1,7,5]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,5,1,8,3,7,6]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,2,5,8,3,7,6]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,4,1,3,8,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,5,3,8,1,7,6]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,5,4,8,7,1,6]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,1,4,2,3,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,1,3,2,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,1,2,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[3,5,1,4,8,7,2,6]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,6,8,7,3,4,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,1,8,7,2,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,6,8,2,1,7,5]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,8,3,7,5,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,2,8,7,1,6]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,1,4,2,8,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,1,4,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[4,3,2,5,8,1,7,6]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,2,4,5,8,7,1,6]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,2,1,3,4,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,1,2,3,4,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[8,6,2,5,4,1,3,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,5,7,4,2,8,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,5,3,8,2,4,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,1,6,3,4,5,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[8,3,5,6,2,4,1,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,2,1,3,5,4,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,1,2,3,4,6,5,7]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[6,2,3,7,8,4,5,1]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,8,2,6,3,4,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,1,6,5,8,4,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,6,7,3,4,8,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,8,2,1,4,5,3]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,7,6,2,1,3,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,3,8,4,7,2,6,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,3,7,6,4,2,5]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,3,1,7,8,6,2,4]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[3,5,8,2,7,1,6,4]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,8,5,3,1,7,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,2,6,4,7,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,2,8,5,1,7,6]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,6,5,2,1,7,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[8,3,7,4,2,5,6,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,5,7,2,1,3,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,1,8,2,6,7,5]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,6,3,7,1,5,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,3,4,1,5,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,7,6,2,8,4,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,2,5,7,4,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,5,6,7,1,3,4]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,7,6,3,1,8,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,3,1,5,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[2,5,7,3,8,4,6,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,7,1,8,5,3,6]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,1,8,7,5,6,3]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,6,7,1,5,4,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,7,5,8,6,4,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,7,8,4,3,1,6,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,7,4,5,8,3,6,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,7,1,4,8,6,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,5,1,4,6,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,5,3,8,4,2,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,4,8,3,6,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,6,1,3,5,2,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,3,2,4,7,5,6]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,4,3,2,5,7,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[3,6,4,8,2,5,7,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,7,2,5,8,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,7,8,5,6,1]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,6,4,3,8,5,1,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,2,1,6,4,5,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[8,2,1,3,4,5,7,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[4,6,8,3,2,1,5,7]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[3,2,6,8,5,4,1,7]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,8,2,5,4,1,6]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,3,8,7,6,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,8,2,6,5,3,1,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,6,8,5,4,1,3,7]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[3,1,8,6,5,4,2,7]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,4,8,7,3,2,6,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,8,3,7,2,5,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,3,6,2,1,8,5]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,3,7,1,8,2,6]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,3,8,5,1,4,2,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,8,7,6,2,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[3,8,1,5,7,4,6,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,5,7,3,1,6,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,4,8,3,7,6,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,6,7,1,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,8,3,1,6,5,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,5,3,6,4,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[4,6,1,3,8,7,5,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,1,7,4,5,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,1,6,4,2,8,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,2,7,5,6,8,4]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,1,2,7,5,8,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,6,2,5,8,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,2,5,8,7,4,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,5,2,3,6,7,4,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[4,7,2,6,3,8,1,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,2,4,8,7,5,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,7,2,4,6,1,8,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,7,2,8,1,4,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,8,7,5,1,4]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[7,3,8,2,6,5,1,4]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,7,2,5,1,3]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,8,1,7,6,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,8,1,7,6,3,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,1,3,8,7,5,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,6,1,8,7,5,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,1,2,8,7,4,3]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,5,2,8,1,6,4,3]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[2,7,6,8,1,5,4,3]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,5,1,6,2,4,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,8,6,1,2,5,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,1,8,3,6,5,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,7,1,6,4,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[9,6,5,4,3,2,8,1,7]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[8,5,4,3,7,2,1,6]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[6,5,4,8,3,2,7,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,5,4,3,9,2,8,1]=>[[1,6],[2,8],[3],[4],[5],[7],[9]]=>[6,2,1]=>[6,2,1]=>3
[7,6,4,3,2,8,5,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[7,3,1,4,8,2,5,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,4,1,2,5,8,3,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[6,7,4,2,5,1,3,8]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,2,4,6,8,1,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,5,1,6,2,8,3]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,4,6,3,1,8,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,1,4,3,2,8,6]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,6,4,2,3,7,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[6,4,7,1,3,8,5,2]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,7,3,1,6,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[4,5,1,2,7,6,8,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,6,8,3,1,2,7]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[6,4,8,1,3,7,2,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,3,8,5,2,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,8,4,5,7,2,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,7,4,5,3,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,8,4,3,5,1,7]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,4,2,8,5,6]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,3,7,2,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,5,8,6,2,1,3,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,8,1,3,6,5,4,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,3,5,4,1,6]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,2,6,8,7,1,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,4,2,3,6,1,8,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,4,2,3,6,5,7,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,3,8,4,1,2,6,5]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[6,8,3,2,7,1,5,4]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,5,6,3,7,1,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,2,5,8,1,6,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,7,8,3,4,5,1,6]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,1,2,4,6,5,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,5,6,8,2,1,4,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,1,6,5,2,7,4,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,8,6,5,3,4,1,7]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,2,3,5,6,8,4]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,4,2,1,5,6,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[3,4,6,2,8,5,7,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,1,7,5,8,3,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,2,6,5,1,3,8]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,4,1,2,5,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,7,1,6,5,2,8,3]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,3,6,5,1,8,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,7,1,6,8,5,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,7,5,6,8,3]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,4,8,6,7,1,5]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,8,7,3,1,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,4,6,1,8,5,2,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,6,7,5,8,2,3]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,7,5,1,2,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[4,3,7,1,6,8,2,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,5,6,8,2,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,7,3,6,5,2,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,7,4,5,3,1,6]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,4,3,5,1,6]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,4,2,6,5,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,7,3,6,2,5,8]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,7,6,1,2,4,3]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,6,2,1,3,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,1,7,2,6,8,5,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,3,6,1,8,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,7,3,6,5,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,2,4,5,6,7,1]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,2,4,1,6,7,5]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,5,6,2,4,1,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,5,3,7,1,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,6,5,1,4,7,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,2,1,4,6,7,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,2,5,4,6,7,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,7,5,6,3,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,7,5,6,1,8,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,6,7,5,3,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,2,6,1,4,5,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,8,7,3,4,5,1,6]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,2,4,6,5,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,6,1,3,4,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,6,2,3,4,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,1,7,5,6,2,3,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,8,1,5,2,6,4,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,7,5,3,4,1,6]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,5,4,3,1,6]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[4,1,7,5,6,3,2,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,7,6,1,3,2,4]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,6,4,1,2,3]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[5,4,2,3,7,6,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,3,5,2,8,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,7,5,1,6,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,7,2,5,1,6,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,2,3,5,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,7,2,4,6,8,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,7,1,2,6,8,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,1,7,3,6,8,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,4,7,5,2,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,7,6,2,5,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,5,6,1,3,8,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,6,4,3,1,8,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,7,6,3,1,4,8,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,5,2,3,4,8,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,7,5,3,4,1,6,2]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,7,1,3,8,4,2,5]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,1,3,4,8,5,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[3,6,5,2,7,8,1,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,2,8,6,7,1,4,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,3,6,5,2,1,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,6,5,4,2,3,7]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,8,7,2,3,5,4,6]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,2,5,3,4,6]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,6,8,5,1,2,4,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[3,7,5,1,8,2,6,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,2,8,3,5,6,4]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,7,8,2,5,3,4]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,5,2,8,1,4,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,4,5,8,6,2,3]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,7,6,4,2,8,1,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,5,6,1,2,8,4,3]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,3,7,8,6,2,5]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,1,4,3,6,8,7,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,6,8,2,1,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,6,8,4,2,1,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,1,6,8,4,2,7,3]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,8,2,3,6,5,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,4,7,3,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,4,7,8,5,2,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[3,6,4,8,5,1,2,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,4,8,1,2,5,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,4,3,8,2,6,5,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,8,3,2,5,4,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,1,3,5,4,6,2]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,8,3,4,2,6,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,3,1,4,5,2]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,1,4,8,2,5,7,6]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,5,2,1,3,6,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,8,2,6,3,1,4,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,2,3,7,4,1,5]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,2,3,4,6,5,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,7,2,4,5,3,6]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,3,6,2,5,4,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,1,6,3,5,4,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,1,6,3,5,4,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,1,5,4,3,6,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,2,1,5,4,3,6,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,1,3,5,4,2,6,7]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,5,3,4,2,6,7]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,5,6,2,3,7,4]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,4,5,3,2,6,7]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,4,3,5,2,6,7]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,2,1,4,5,3,6,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[2,7,1,4,5,3,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,1,5,4,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,3,2,1,5,4,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,3,1,4,5,2,6,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[7,3,1,5,4,2,6,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,3,1,6,2,5,4,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,7,1,6,2,5,4,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,4,5,2,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,6,2,1,5,4,7,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,3,6,1,5,4,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,2,4,1,6,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,3,4,1,5,2,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,1,5,3,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,6,4,1,5,3,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,1,3,7,4,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[6,2,5,1,3,7,4,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,1,3,7,4,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,6,1,2,4,5,3,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[6,7,1,2,8,3,5,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,1,2,5,4,3,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,1,3,7,4,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,2,6,1,3,7,4,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,1,5,3,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,3,5,2,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,1,5,3,2,6,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,7,1,4,2,6,3,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,1,6,2,3,8,4]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,3,1,2,7,4,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,2,5,3,1,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[5,3,6,1,2,7,4,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,1,5,2,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,5,1,8,7,3,4,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,7,5,4,1,3,6]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,8,5,2,3,4,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,6,2,7,1,4,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,1,2,7,8,4,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[4,7,6,1,5,3,8,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,6,4,1,3,8,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,6,2,4,5,3,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,7,5,3,8,4,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,7,5,3,1,4,2]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,5,2,7,1,6,4,3]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,1,5,3,8,4,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,2,4,7,8,1,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,6,1,7,8,5,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,8,6,7,1,5,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,5,6,7,2,3,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,6,4,1,2,7,3]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,8,6,1,7,2,4,3]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,7,3,2,6,4,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,1,7,2,6,4,3]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,5,7,2,6,4,3]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,7,2,5,6,3,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,2,5,1,3,4]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,2,1,6,3,4]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,5,2,6,7,3]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,8,5,1,6,2,4]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,7,8,1,4,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,2,8,5,6,3,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,2,1,5,6,3,4]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[8,6,7,1,5,2,3,4]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,7,8,5,2,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[7,5,6,2,1,8,4,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,7,5,2,1,6,4,3]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[7,1,3,5,8,6,2,4]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,1,3,4,6,8,7,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,5,3,6,8,2,7,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,3,4,8,1,7,2]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,7,8,5,1,3,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,3,1,2,6,7,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,5,1,6,3,4,7,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,8,6,3,4,7,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,1,5,3,7,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,5,8,3,2,7,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,4,8,7,1,5,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,8,1,3,4,7,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,3,1,2,7,4]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,8,3,5,2,7,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,3,5,2,1,4]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,3,5,2,7,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,7,1,3,5,6,2,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[6,7,8,3,5,1,2,4]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,8,1,2,6,7,5]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,2,4,3,6,7,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,2,3,1,6,7,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,2,3,5,1,7,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,2,3,5,6,1,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[8,6,5,1,4,3,7,2]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,6,5,4,1,3,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,1,7,6,3,8,2,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,5,7,6,3,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,6,5,1,8,2,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,3,4,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,1,5,2,3,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,3,5,1,4,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,6,7,5,1,8,4,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,2,5,3,4,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[6,2,5,1,8,3,4,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,6,5,2,8,3,4,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,6,3,5,1,8,7,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,7,6,5,8,1,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,4,8,7,6,3,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,6,8,5,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,1,3,5,7,4,6,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,2,8,7,5,1,6,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,5,1,6,7,2,3]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,8,5,1,6,7,2,4]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,8,6,1,3,5,2,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,6,7,2,8,1,3,4]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,5,1,8,6,7,4,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,1,8,6,7,4,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,3,8,6,7,4,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,3,5,4,6,7,1,2]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,3,8,6,7,4,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,5,8,6,7,4,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,1,5,3,8,7,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,3,2,8,1,4,7]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,1,6,3,5,2,7,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,6,2,5,3,1,4]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[4,7,6,8,3,2,5,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,5,8,1,3,4,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,6,2,8,5,1,4,3]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,3,7,5,2,6,4]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,4,8,7,5,1,6,2]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,3,8,1,4,2,5,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,5,7,4,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,8,5,1,3,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,4,8,7,5,6,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,5,8,2,6,4,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,8,2,4,1,7,5]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,8,2,6,7,3,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,1,6,7,3,4]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,8,4,6,7,3,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,4,6,7,2,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,4,3,2,6,7,1,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[4,2,8,1,6,7,3,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,1,6,7,3,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,2,6,7,3,4]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,8,7,2,1,5,6]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,8,5,3,6,4,2,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,5,7,4,1,3,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,4,1,6,7,2,3]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,4,6,7,2,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,2,3,4,6,7,1,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[6,2,7,3,8,4,1,5]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,3,2,8,5,1,6]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[5,3,2,8,4,6,1,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,2,6,5,3,1,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,2,5,3,1,6,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,3,6,2,5,4,1,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,3,2,6,1,7]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,8,2,4,6,1,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,8,2,3,1,5]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,8,3,6,4,2,1,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,8,6,2,5,3,1,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,4,3,2,8,7,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,5,3,2,8,4,7,6]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,4,3,1,2,6,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[2,8,7,3,5,1,4,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,6,4,1,2,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,1,2,7,3,8,5,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,7,4,3,8,6,5]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,3,8,2,7,5]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,3,2,8,7,4,6]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,4,2,7,6,5,3]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,3,7,2,6,5,4]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,4,8,3,7,2,6]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,6,8,5,4,7,3]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,5,7,8,2,4,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,3,1,6,7,2,5,4]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,8,6,1,3,2,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,1,2,5,3,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,1,5,2,4,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,5,4,8,3,2,7,6]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,6,1,2,5,4,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,7,1,3,2,6,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,4,8,2,1,3,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,8,2,5,1,3,7]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,2,1,5,3,8]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,3,8,5,7,4]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,2,6,8,4,7,3]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,2,3,8,1,4,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,4,7,5,8,1,2,3]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,5,1,6,3,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,6,1,7,4,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,4,2,1,7,5,3]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[7,4,2,1,5,8,6,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,6,4,1,8,5,2,3]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[1,6,4,8,7,5,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,3,1,2,8,4,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,1,3,2,8,6,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,7,1,2,5,8,6,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,4,1,2,7,5,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,8,1,2,6,4,3]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,1,6,3,5,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,2,1,7,3,6,4]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,1,8,2,4,7,5]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,8,7,6,2,5,4]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,1,8,7,3,2,6]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[3,5,1,8,7,2,4,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,1,8,3,7,2,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,2,8,6,3,5]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,4,1,7,6,2,3]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,8,1,5,4,2,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,7,5,4,3,2]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,1,5,8,6,4,3,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,1,8,7,3,6,4,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,7,6,2,5,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,8,7,6,5,2,4]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,6,4,5,2,3,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,4,5,2,3,6,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,3,5,2,4,6,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,6,3,5,2,4,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,6,3,4,2,5,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,3,4,2,5,6,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,8,6,7,3,4,2,5]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,7,3,4,2,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,4,2,6,5,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,8,4,7,3,6]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,8,5,7,3,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,5,2,6,4,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,7,3,5,2,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,6,2,5,4,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,6,2,4,5,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,4,6,2,3,5,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,8,5,6,2,3,4,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,8,5,6,2,4,3,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,8,5,6,4,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,8,5,6,3,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,8,4,6,3,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,8,4,5,3,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,2,4,5,3,6,7]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[3,4,7,8,5,6,9,10,1,2]=>[[1,2,3,4,7,8],[5,6],[9,10]]=>[4,4,2]=>[4,4,2]=>3
[1,8,9,6,7,4,5,2,3,10]=>[[1,2,3,10],[4,5],[6,7],[8,9]]=>[3,2,2,3]=>[3,3,2,2]=>4
[1,6,7,8,9,4,5,2,3,10]=>[[1,2,3,4,5,10],[6,7],[8,9]]=>[5,2,3]=>[5,3,2]=>3
[1,4,5,6,7,8,9,2,3,10]=>[[1,2,3,4,5,6,7,10],[8,9]]=>[7,3]=>[7,3]=>2
[1,8,9,6,7,2,3,4,5,10]=>[[1,2,3,8,9,10],[4,5],[6,7]]=>[3,2,5]=>[5,3,2]=>3
[1,6,7,8,9,2,3,4,5,10]=>[[1,2,3,4,5,10],[6,7,8,9]]=>[5,5]=>[5,5]=>2
[1,2,7,8,5,6,3,4,9,10]=>[[1,2,3,4,9,10],[5,6],[7,8]]=>[4,2,4]=>[4,4,2]=>3
[1,2,5,6,7,8,3,4,9,10]=>[[1,2,3,4,5,6,9,10],[7,8]]=>[6,4]=>[6,4]=>2
[1,8,9,2,3,4,5,6,7,10]=>[[1,2,3,6,7,8,9,10],[4,5]]=>[3,7]=>[7,3]=>2
[1,2,7,8,3,4,5,6,9,10]=>[[1,2,3,4,7,8,9,10],[5,6]]=>[4,6]=>[6,4]=>2
[1,2,3,6,7,4,5,8,9,10]=>[[1,2,3,4,5,8,9,10],[6,7]]=>[5,5]=>[5,5]=>2
[9,10,11,12,5,6,7,8,3,4,1,2]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[4,4,2,2]=>[4,4,2,2]=>4
[7,8,9,10,11,12,3,4,5,6,1,2]=>[[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[6,4,2]=>[6,4,2]=>3
[11,12,9,10,5,6,7,8,1,2,3,4]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[2,2,4,4]=>[4,4,2,2]=>4
[1,2,3,6,7,8,9,4,5,10,11,12]=>[[1,2,3,4,5,6,7,10,11,12],[8,9]]=>[7,5]=>[7,5]=>2
[1,2,3,4,7,8,5,6,9,10,11,12]=>[[1,2,3,4,5,6,9,10,11,12],[7,8]]=>[6,6]=>[6,6]=>2
[1,2,3,4,5,6,7,8,9,10,11,12]=>[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[12]=>[12]=>1
[8,6,4,7,2,1,3,5]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[1,6,4,7,2,8,3,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,7,3,5,8,2,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,6,2,3,5,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,8,2,3,6,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,5,2,3,1,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,2,4,5,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,6,2,3,5,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,3,4,8,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,4,8,2,3,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,4,1,2,3,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[6,8,5,3,4,1,2,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,3,7,2,1,4,5]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,5,1,6,3,7,2,4]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,3,7,4,8,2,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,7,3,5,8,2,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,6,4,8,2,3,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,5,7,2,3,4,6]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,1,5,8,2,3,4,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[5,1,7,3,8,2,4,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,7,8,2,3,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[7,4,8,6,1,2,3,5]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[3,8,7,5,1,2,4,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,7,6,1,2,4,5,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[4,7,6,1,2,3,5,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[1,6,5,8,2,3,4,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,5,8,4,1,2,3,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,5,7,4,1,2,3,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[1,5,7,4,8,2,3,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,4,8,2,1,3,5]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,6,2,3,8,1,4,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,4,8,5,1,6,2,3]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,2,3,1,7,4,5]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,6,4,1,2,7,3,5]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[1,7,2,8,6,3,4,5]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,1,3,8,2,4,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,5,8,1,3,6,2,4]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,1,8,2,3,6,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[1,4,8,7,2,3,5,6]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,5,8,7,2,3,4,6]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[6,5,1,8,2,3,4,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[5,7,1,3,8,2,4,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,6,8,1,5,2,3,4]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,8,6,2,3,4]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[6,1,8,2,7,3,4,5]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,1,8,7,2,3,5,6]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[5,1,8,7,2,3,4,6]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[1,8,7,6,4,5,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,3,6,5,4,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,1,5,8,3,4,2,6]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,4,3,2,5,6,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[6,4,2,3,8,5,7,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,2,7,5,8,3,1]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,1,7,5,8,3,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,4,6,5,2,3,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,1,4,6,5,8,2,3]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,4,6,3,8,2,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,4,3,2,5,8,6]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,1,4,6,5,2,8,3]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,1,4,6,5,3,8,2]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,4,6,5,3,2,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,4,2,7,5,3,8,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,7,2,6,8,5,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,1,6,8,2,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,1,6,8,5,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,7,5,3,6,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,1,7,8,6,2,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,2,3,8,5,1,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[6,4,2,7,5,8,1,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,7,5,3,1,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[3,4,7,2,6,8,1,5]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,7,3,6,8,2,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,2,6,5,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,3,2,5,6,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,3,5,1,2,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,1,3,5,2,6]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,3,1,2,6,5,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,7,1,6,2,5,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,7,1,6,2,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,7,2,6,5,8,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,3,1,2,6,7,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,1,6,3,4,2,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,5,1,3,7,2,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,5,1,3,4,7,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,3,4,2,6,7,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,7,3,6,2,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,7,2,6,1,8,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,3,7,5,1,2,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,4,3,7,5,1,8,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,2,4,3,1,5,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,8,7,4,1,5,2,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,4,7,3,6,1,5,8]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,3,2,1,6,4,7]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,4,3,1,2,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[5,4,7,3,6,2,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,8,2,1,6,5,4]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,3,8,5,2,1,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,2,8,4,3,1,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[4,3,2,8,6,5,1,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[4,3,8,7,5,1,6,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,2,5,8,6,1,4,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[8,4,3,7,5,2,6,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,7,8,5,1,2,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[5,3,7,8,4,1,2,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[6,2,5,8,3,1,4,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[6,2,4,8,3,1,5,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[5,2,3,8,4,1,6,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[5,3,8,7,4,1,6,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,3,2,8,6,4,1,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[7,5,3,8,4,2,1,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,5,3,6,2,4,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,5,3,7,2,4,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,4,3,8,2,6,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,5,3,8,2,7,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,3,8,2,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,6,3,8,2,4,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,6,3,7,2,4,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,3,5,2,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,6,3,5,2,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,3,5,2,6,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,3,4,2,6,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,8,4,3,2,6,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,8,4,3,2,7,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,8,3,4,2,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,8,3,4,2,6,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,8,4,6,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,3,6,2,5,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,3,5,2,6,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,8,3,5,2,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,3,5,2,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,3,7,2,6,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,3,7,2,4,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,4,7,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,4,7,3,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,4,7,3,8,2,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,7,3,8,2,6,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,3,8,2,7,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,6,2,4,7,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,6,1,4,8,7,2]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,2,4,6,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,1,5,6,8,7,2]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[4,2,1,5,8,6,3,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[4,2,1,5,8,6,7,3]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,2,1,5,8,7,6,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,3,1,5,7,8,6,2]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[4,3,1,7,5,8,6,2]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[6,7,3,1,4,8,2,5]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,7,1,4,8,2,6]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,1,5,7,8,2,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[3,2,1,8,5,4,6,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[3,2,1,8,5,7,4,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,8,7,5,4,6]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[5,2,7,1,8,4,3,6]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,2,1,8,4,3,5]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,2,1,8,4,5,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,1,8,5,6,4,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,8,6,5,4,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[4,3,1,6,7,8,5,2]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[4,2,1,6,8,7,5,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,2,1,6,8,5,7,3]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,2,1,6,8,5,3,7]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[5,2,6,1,8,4,3,7]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,6,1,8,7,4,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,2,6,1,8,7,3,4]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,6,1,8,3,4,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,2,1,6,8,3,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,3,1,6,7,8,2,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[6,7,3,1,5,8,2,4]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,2,1,7,8,6,3,5]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[3,2,1,8,7,6,4,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[3,2,1,8,6,4,7,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,8,6,4,5,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[3,2,1,8,4,6,5,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,8,4,6,7,5]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,8,4,7,6,5]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,8,7,4,6,5]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,1,7,8,3,6,5]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,7,1,8,3,6,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,2,1,8,3,5,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,7,1,8,3,4,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,2,1,7,8,3,5,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[3,2,1,8,4,5,7,6]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,2,8,6,3,4,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,8,6,2,5,3,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,6,2,4,5,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,4,3,1,8,2,5,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,4,2,8,5,6,1,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,8,5,2,4,6,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,8,4,5,6,2,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,2,4,5,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,2,5,7,4,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,3,8,1,5,2,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,3,7,8,2,4,1,5]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,7,3,8,2,4,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,7,2,6,8,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,2,4,6,7,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,8,2,4,7,5,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,2,6,8,1,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,8,2,7,5,1,3]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,5,3,1,4,2,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[5,7,4,2,6,1,3,8]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,4,2,3,8,1,7]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,6,3,7,8,2,4,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,3,8,2,4,7,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,7,2,4,5,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,2,5,8,4,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,8,2,4,7,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,6,2,3,8,1,7]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,7,8,2,4,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,4,2,1,5,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,5,8,6,4,2,1,7]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,8,6,3,4,2,1,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,3,4,2,1,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,4,2,1,5,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,6,4,2,1,3,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,5,4,1,7,8,6,3]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,8,5,4,1,6,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,8,5,4,1,6,3,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,6,3,8,5,4,1,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,8,6,3,5,4,1,7]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,6,4,2,1,3,7]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,2,1,5,7,8,6,3]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[2,7,8,6,3,5,4,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,8,5,7,6,2,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,6,2,1,8,4,3,5]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[2,1,8,5,6,4,3,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,1,8,5,6,3,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,2,1,5,6,3,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[2,5,6,3,8,4,1,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,4,2,1,8,5,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,5,6,4,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,8,5,6,4,2,1,7]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,4,2,1,8,5,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,8,6,4,2,1,5,7]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[3,7,8,6,4,2,1,5]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,5,3,7,6,2,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,2,4,1,8,5,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,1,7,6,2,3]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,6,2,3,8,5,4,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[2,1,7,8,6,4,3,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,1,6,4,3,7,8,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,4,2,1,3,7,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,3,7,8,4,2,1,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,8,4,2,1,6,3,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,2,3,8,4,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,1,8,4,3,7,5]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,1,7,5,8,4,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,2,3,7,5,6,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,7,6,2,1,4,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,5,7,6,2,1,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,6,2,1,3,8,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,5,6,1,8,4,2,3]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,5,8,4,3,6,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,3,6,1,7,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,7,8,3,2,1,5]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,6,5,4,3,2,8,1,9]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[6,4,3,7,5,2,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,3,2,8,4,1,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[6,5,2,7,8,4,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,4,3,2,5,8,1,7]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,3,7,2,5,4,1,8]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,7,5,4,1,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[8,4,2,6,3,1,7,5]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,5,3,7,4,2,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,7,3,4,2,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,5,2,3,1,7,4]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,7,6,3,4,2,8,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,6,3,2,5,7,4]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,7,5,2,1,4,6,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[7,8,5,2,1,4,6,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,8,5,2,3,1,7,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,6,2,3,1,7,4]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,2,6,3,1,7,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,8,6,4,1,7,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,2,1,7,5,4,8,6]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[4,1,3,7,5,2,8,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,1,7,3,4,2,8,6]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,3,2,5,8,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,4,3,6,8,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,1,8,2,4,5,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,8,3,2,6,7,4]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,7,1,5,6,4]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,2,7,1,5,6,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,7,2,1,4,6,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,8,7,1,3,4,5,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,6,1,3,4,5,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,7,8,2,4,5,6,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,7,1,3,4,5,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,8,1,3,4,5,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,8,2,3,1,7,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,8,3,2,5,7,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,3,8,2,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,2,7,1,5,6,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,4,2,8,1,5,6,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,4,2,8,3,1,7,5]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,3,8,1,7,6]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,5,2,3,1,6,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,2,1,3,6,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,4,2,1,3,6,7,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[1,5,3,2,4,7,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[8,5,1,3,2,6,7,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,6,1,3,4,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,2,1,5,3,8,7]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,2,1,3,6,8,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[5,7,1,3,2,6,8,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,1,2,4,5,8,3]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,6,1,2,4,5,7,3]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[1,8,2,3,5,6,7,4]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,7,1,2,4,5,6,3]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[7,8,1,2,4,5,6,3]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,1,3,2,6,7,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,2,1,3,6,7,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,1,3,2,5,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,1,2,4,3,7,8,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,4,8,1,2,3,7,6]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,7,6,3,2,5,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[4,8,3,2,7,6,1,5]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[4,3,8,2,7,1,6,5]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,2,8,1,7,6,5]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,8,7,3,2,5,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,7,8,1,2,5,3,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,6,7,4,1,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,6,3,4,7,8,1,5]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,7,8,4,2,5,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,7,8,2,6,4,1,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,2,4,8,6,1,5]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,3,6,4,7,2,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,5,8,2,3,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,5,2,6,3,4,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,5,2,7,3,4,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,8,5,6,3,2,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,6,7,8,5,1,2]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,6,4,7,5,8,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,5,4,2,6,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,3,8,5,4,7,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,2,5,4,7,8,3]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,2,5,6,3,7,4]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,6,4,8,5,7,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,3,1,4,2,5,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,1,5,2,3,6,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,4,1,5,2,3,6,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[5,6,1,8,4,3,2,7]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,1,8,6,4,3,2,7]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,1,6,3,8,7,2,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,2,5,8,3,7,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,8,7,4,3,2,5]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,1,2,5,4,8,6,3]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,5,8,3,6,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,3,7,5,2,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,6,7,8,5,2,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,6,4,7,8,5,3]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,3,7,8,2,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,4,8,2,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,4,1,6,3,2,5]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,6,3,8,7,2,5]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[7,5,1,8,4,3,2,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,1,7,4,3,2,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[4,1,8,5,2,3,7,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,1,6,8,3,7,2,5]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,6,1,3,8,2,7]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,8,1,4,3,2,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,7,4,6,8,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,5,4,7,2,6,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,4,7,8,2,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,4,7,2,8,6]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,5,7,4,8,2,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,7,4,8,6,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,5,7,8,4,2,6]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,6,3,2,7,4,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,1,6,2,8,7,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,7,2,5,4,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,7,5,2,4,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,5,7,4,3,8,1,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,3,7,4,8,1,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,6,7,8,1,5,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,5,2,7,8,4,1,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,7,4,8,3,2,6]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,2,6,8,4,7,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,7,4,3,8,6,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,7,2,4,8,6,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,3,7,2,8,5,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,7,3,8,6,2,5]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,8,2,4,3,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,8,2,4,1,6]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,3,7,2,4,1,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,4,7,3,1,5,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[2,4,7,8,3,1,5,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[6,3,1,5,8,2,4,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,5,3,4,2,8,1,7]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,2,4,3,8,1,6,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,4,8,1,5,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[3,2,4,6,8,1,5,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[8,1,5,7,3,2,4,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,4,6,7,2,3,1,5]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,7,8,2,3,1,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,8,2,3,1,5]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,4,8,3,1,5,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[5,3,8,7,2,4,1,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,7,3,1,5,6]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[4,6,8,7,2,3,1,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,4,6,2,3,1,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,8,7,2,3,1,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,8,7,2,3,1,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,7,4,2,8,6,5]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,4,1,7,6,5]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,8,2,3,1,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,6,8,2,3,1,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,6,8,2,3,1,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,4,7,2,3,1,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,3,7,4,1,6,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,7,8,4,1,6,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,4,8,2,5,1,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,7,4,1,6,8,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,4,2,3,7,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,7,8,6,2,3,1,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,7,3,1,5,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,3,1,7,4,2,8,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,7,6,2,3,1,4]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,6,2,3,1,4]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,6,4,2,3,8,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,1,7,6,4,2,8,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,7,6,2,3,1,5]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,5,2,3,1,4]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,3,6,1,5,8,7,2]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,5,1,8,7,2]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,3,5,1,8,7,2]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,1,5,8,7,2]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[4,1,6,5,3,8,7,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,5,3,8,7,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,3,1,8,7,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,6,5,1,8,7,3,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,8,1,7,3,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,8,1,3,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,5,8,3,1,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,5,3,8,1,7,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,1,5,8,3,7,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,6,5,8,3,7,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,6,5,8,3,7,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,5,8,7,3,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,6,5,3,8,7,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,3,8,7,1,5,2]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,3,7,1,5,2]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,8,5,3,7,1,4]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,1,5,7,3,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,8,5,7,3,2]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,6,8,5,7,3,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,4,6,8,5,7,3,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,4,6,8,5,3,7,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,1,8,5,3,7,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,8,5,3,1,7,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,6,8,5,1,7,3,4]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,3,5,1,7,2]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,8,3,1,5,7,2]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,3,1,8,5,7,2]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,3,8,1,5,7,2]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,3,8,5,7,1,2]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,6,8,1,5,7,2]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,6,1,8,5,7,2]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,1,6,8,5,7,2]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,3,6,8,7,5,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[4,3,6,1,8,7,5,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,3,6,8,1,7,5,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,2,8,7,3,1,4]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[6,5,2,8,7,1,3,4]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,2,5,8,7,1,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[6,2,5,8,7,3,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,6,3,8,1,7,5,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,1,8,7,5,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,1,6,3,8,7,5,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,4,6,3,8,7,5,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,6,8,3,7,5,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,1,8,3,7,5,2]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,8,1,3,7,5,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,5,7,3,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,8,5,7,1,3,4]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,7,1,5,3,6]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,7,5,3,1,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,4,1,8,7,5,3,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,1,4,8,7,5,3,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,6,4,8,7,3,5,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,1,8,7,3,5,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,8,7,5,1,3,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,4,8,7,3,5,1,6]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,5,6,8,9,7,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[2,3,4,5,7,8,9,6,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[2,4,5,6,7,8,9,3,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[2,3,4,7,8,5,6,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,7,1,4,8,6,5]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,1,3,7,8,5,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,4,5,6,7,10,1,8,9]=>[[1,2,3,4,5,6,7,10],[8,9]]=>[7,3]=>[7,3]=>2
[1,5,3,2,6,4,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,5,3,2,6,7,4,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,7,3,2,8,5,4,6]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,2,7,5,4,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,2,4,3,7,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,5,3,7,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,7,6,2,3,1,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,4,8,2,1,5,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,2,8,5,3,4,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,2,3,7,5,1,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,3,6,5,1,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,3,5,6,1,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,2,7,4,6,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,6,4,7,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,2,3,5,7,1,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,2,1,6,8,4,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,5,2,6,8,4,3,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,7,2,8,4,3,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,2,1,8,6,4,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,8,4,2,1,5,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[4,3,2,6,1,8,5,7]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,5,8,2,7,4,3,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,2,3,4,8,6,5]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,3,4,1,7,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,8,2,3,5,7,6]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,1,8,4,5,7,6]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,2,1,4,5,8,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,8,1,4,3,5,2,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,2,3,4,6,8,5]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[6,1,2,3,4,8,7,5]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[1,8,2,3,4,7,6,5]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,2,3,4,6,7,5]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[2,8,1,3,5,4,7,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,1,4,3,5,2,6]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,2,1,4,5,7,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[3,8,2,1,5,6,4,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,1,6,5,4,7]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,8,3,5,4,2,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,1,8,3,5,2,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,7,3,5,2,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,8,4,6,2,1,5,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,4,2,5,3,1,6,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,5,2,4,3,1,6,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,3,2,5,4,1,6,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[4,3,2,5,1,8,6,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,5,2,4,1,8,6,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,7,8,1,5,3,6]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,8,7,3,5,4,2,6]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,8,2,7,4,3,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,2,8,4,3,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,2,8,5,3,4,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[6,3,2,1,8,4,5,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,3,2,8,4,5,1,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,8,4,3,5,1,6]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,3,5,4,2,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,2,3,4,6,1,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,1,3,4,8,2,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,1,3,4,7,2,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,2,3,4,6,8,5]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,6,2,3,4,8,7,5]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,2,3,4,1,8,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,6,2,3,4,1,7,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,1,7,3,5,4,2,6]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,2,7,4,5,1,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,2,3,4,1,8,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,6,2,3,4,8,1,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,6,2,3,4,7,1,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[6,3,4,8,7,5,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,8,7,3,5,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,5,3,6,1,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,3,4,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,2,1,6,7,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,8,4,1,2,6,7,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[5,3,7,2,6,1,8,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,8,1,6,3,7,4]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,2,1,4,7,6,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,2,5,1,7,6,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,4,1,2,6,5,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,5,2,7,6,3]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,2,4,7,6,3]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,2,8,3,6,7,1,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,7,6,2,4,1,5]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,6,4,1,3,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,8,2,6,5,1,3,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,8,7,6,4,2,3,5]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[2,8,7,6,3,1,4,5]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,8,7,6,2,4,3,5]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,6,3,4,2,5]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,1,4,5,6,7,3]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,7,3,6,5,8,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,2,6,5,8,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,1,6,5,8,4]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,2,8,5,7,3,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,1,8,5,7,3,4]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,1,8,5,7,2,4]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,1,7,5,8,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,1,3,8,5,2,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,7,1,6,8,5,4]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,2,6,8,5,4]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,2,6,5,3,1,4]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,2,6,7,5,8,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,5,6,3,8,4]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,7,6,4,3,1,5]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[3,8,7,6,1,2,5,4]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,7,6,2,1,5,4]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[4,8,7,6,2,1,3,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,8,7,6,1,3,2,5]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,6,4,1,2,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,8,3,6,5,1,2,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,3,7,5,6,8,1,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,7,6,4,2,1,5]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[5,1,4,6,8,2,3,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,7,6,3,5,4,8,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,7,2,6,5,1,8]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,6,1,5,7,2,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,5,7,3,4,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,1,5,8,6,3,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,1,2,5,8,3,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,6,7,2,1,4,8,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[7,8,6,5,1,2,4,3]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,3,6,5,7,8,2,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,5,3,1,6,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,8,5,2,4,1,7,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,1,6,8,5,7,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,2,5,1,4,8,6]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,1,4,2,3,6,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,3,4,6,7,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,1,2,4,7,6,5]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[2,3,8,1,6,5,4,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,7,2,5,3,6]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,2,4,1,7,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,7,8,6,2,1,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,4,8,6,2,7,1,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,1,6,7,3,4]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,2,8,6,4,3,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,1,2,7,5,3,8,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,8,6,4,1,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[2,7,8,4,6,3,1,5]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,5,7,2,6,8,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,5,2,6,1,8,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,2,3,6,1,7,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,1,6,3,5,7,2,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,6,4,3,7,1,5]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,3,2,6,4,7,1,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,8,7,6,5,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,2,8,7,3,6,5,4]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,7,3,6,1,5]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,7,1,2,6,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,7,3,2,6,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,5,8,7,3,2,1,6]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,6,8,1,7,5,4,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,4,7,2,1,5]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,3,7,6,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,8,4,7,6,1,5]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,8,3,7,2,6,4]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,8,4,7,2,1,6]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,2,3,7,1,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,4,2,7,5,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,4,2,7,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,2,3,7,6,4]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,4,3,7,6,5]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,8,4,3,7,1,6]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,4,1,2,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,1,3,2,7,4]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,8,4,3,2,7,5]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,4,3,2,1,7]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,1,2,8,6,5,4,3]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,1,4,8,6,2,5,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,1,8,6,2,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,4,8,3,6,1,5]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,4,8,3,2,6,5]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,5,8,3,2,1,6]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,6,2,8,7,5,4,3]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,8,7,2,5,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,4,8,7,2,1,5]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,2,5,8,7,6,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[3,2,4,8,7,6,1,5]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[3,1,5,8,7,2,6,4]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,8,7,2,6,5]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,4,8,2,7,5,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,5,8,2,7,6,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,5,8,3,7,1,6]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,5,8,1,2,7,3]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,8,3,2,7,5]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,5,8,3,2,7,6]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,1,4,8,2,5,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,1,3,8,2,5,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,3,4,8,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,2,5,1,8,6,4,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,2,5,3,8,6,1,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,1,4,8,6,5,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[7,2,1,3,8,6,5,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[7,2,3,4,8,6,1,5]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[7,3,5,4,8,2,1,6]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,5,1,8,7,4,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,3,5,4,8,7,1,6]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,6,5,4,8,2,7,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,5,3,8,2,7,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,3,4,8,2,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,5,4,8,2,7,6]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,5,4,8,2,1,7]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,5,2,3,8,1,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,1,4,2,8,5,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,6,1,2,3,8,5,4]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[7,6,2,4,3,8,1,5]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,5,4,2,8,6,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,5,2,3,8,6,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,2,4,3,8,6,5]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,5,4,3,8,1,7]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,1,4,3,2,8,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,1,5,4,3,2,8,6]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,4,2,6,7,8,1,5]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,4,2,6,8,7,5]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,4,2,6,1,7,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,7,3,5,4,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,8,3,5,4,1,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,8,3,5,4,1,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,2,8,5,3,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,1,2,7,5,3,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,1,6,3,7,5,4,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,1,3,6,8,4,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,7,3,2,8,1,4,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,4,2,6,1,8,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,1,2,8,5,3,6]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[8,7,4,2,1,5,3,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,4,1,2,6,5,3,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[7,4,3,1,5,6,8,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,7,4,1,5,8,3,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,5,1,6,8,3,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,3,1,7,6,8,2]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,1,2,7,5,3,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,1,3,6,5,4,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,8,2,6,5,3,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,1,2,8,5,3,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,4,3,1,5,6,7,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[4,5,3,1,8,6,7,2]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,5,6,3,1,7,2]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,3,4,8,6,7,2]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,3,8,1,6,7,2]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,5,3,4,1,6,7,2]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,2,1,5,3,7]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,7,3,2,5,1,4,8]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,3,2,5,1,4,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,4,6,8,3,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,3,4,7,6,8,2]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,4,2,7,5,3,8]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,3,7,1,6,8,2]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,7,5,4,1,8,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,4,2,1,5,3,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,2,7,6,5,4,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,2,8,6,5,4,3,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[9,2,8,7,6,5,4,1,3]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[8,7,2,6,5,4,1,3]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,2,8,7,6,5,1,4]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[4,8,7,6,5,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[7,8,6,1,5,4,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,9,1,7,6,5,4,3,2]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[2,2,5]=>[5,2,2]=>3
[7,3,8,6,5,4,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[4,8,5,7,6,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,8,7,4,6,5,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,6,3,5,4,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,5,6,1,3,2,4,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,5,3,2,4,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,8,1,5,3,2,4,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,1,7,5,3,2,4,6]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,6,1,4,5,2,3,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,6,3,1,5,2,4,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,4,6,1,5,2,3,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,2,1,5,4,3,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,5,2,6,1,4,3,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,2,1,7,4,3,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,8,2,1,5,4,3,6]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,3,1,5,2,4,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[8,2,7,5,1,3,4,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,4,1,7,5,2,3,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,2,7,1,5,4,3,6]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,6,1,7,4,3,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,4,3,2,6,5]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,1,5,7,3,2,6,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,7,8,1,3,2,6,4]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,1,5,7,3,4]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,1,6,7,2,3,4]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,6,1,8,2,3,4]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,7,2,5,1,8,3,4]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,1,6,8,2,3,4]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,5,7,1,8,2,3,4]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,7,3,8,1,2,4,5]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,5,4,1,8,2,3,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,6,1,4,8,2,3,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,1,6,4,7,2,3,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,1,3,2,4,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,8,4,1,3,2,5,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,3,7,4,1,2,5,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,5,1,7,3,2,4,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,8,1,7,3,2,4,5]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,1,8,4,3,6,2,5]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,1,8,6,4,2,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[8,3,1,7,4,6,2,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,5,1,7,2,3,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,1,7,2,3,4]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,1,2,7,3,4]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,1,8,5,6,2,4]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,8,3,1,5,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,1,7,3,2,6,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,1,7,3,2,6,5]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,3,4,7,1,2,6,5]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,7,4,1,3,6,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,4,8,2,1,3,6,5]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,4,3,8,1,2,6,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,2,3,6,7,1,5,4]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,8,5,2,3,6,4,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,5,2,3,4,7,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,5,2,6,8,1,4,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,4,6,8,1,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,7,3,6,8,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,5,3,6,8,1,7]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,6,8,1,3,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[5,1,3,4,6,8,2,7]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[4,3,5,2,6,8,1,7]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,5,7,2,8,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,5,7,2,6,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,7,2,5,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,3,1,7,8,2,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,3,5,1,7,8,2,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,3,4,8,2,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,1,3,4,6,8,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,5,7,1,3,6,8,2]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,6,7,1,5,8,2]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,5,1,7,8,2]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,3,5,7,2,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,6,4,1,7,8,2]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,1,5,6,7,4,8,2]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,6,7,3,4,8,2]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,7,1,3,5,8,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,7,3,4,5,8,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,7,4,5,8,1,3]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,7,4,8,1,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,6,1,2,7,8,4]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,5,2,6,1,7,8,4]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,2,6,7,4,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,3,6,7,4,8,1]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,3,6,1,7,8,4]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,2,6,1,3,7,8,4]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,2,6,7,3,5,8,1]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,2,4,5,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,2,8,1,4,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,2,4,8,1,5,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,2,4,6,8,1,3,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[7,1,3,4,6,8,2,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[3,7,2,4,6,8,1,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,7,2,6,8,1,4]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,2,5,8,1,4]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,7,2,8,1,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,7,2,4,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,4,5,7,3,8,1]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,4,5,1,7,8,3]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,7,1,2,5,6,8,3]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,6,7,5,8,1,3,4]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,1,2,5,8,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,2,4,7,3,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,2,6,7,3,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,2,6,1,7,8,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,5,4,6,2,7,8,3]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,4,1,2,7,8,3]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,4,5,1,2,7,8,3]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,3,5,1,7,8,2,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,2,8,1,3,4]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,5,7,1,3,4,8,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,4,7,1,3,8,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,6,3,1,7,8,2]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,3,2,4,8,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,4,5,2,6,1,3,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,4,2,1,6,3,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,5,3,4,1,6,2,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,4,5,3,1,6,2,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,5,4,2,1,8,3,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,5,4,2,1,6,8,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[7,4,5,3,1,6,8,2]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,4,3,5,6,1,8,2]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,6,3,7,4,1,8,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,7,3,1,4,8,2]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,4,1,5,8,2]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,2,1,5,8,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,6,7,3,1,8,2,4]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,7,8,1,2,4]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,3,7,2,4,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,7,2,3,8,1,4]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,5,2,8,1,3,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,3,2,4,8,1,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,4,2,1,3,8,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[7,6,3,4,1,2,8,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,6,3,2,4,1,8,5]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,7,3,2,5,1,8,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,3,2,7,8,1,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,5,3,2,7,4,8,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,5,2,7,3,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,5,2,7,8,1,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,5,2,6,1,8,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,5,6,1,2,8,3]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,6,2,1,3,8,4]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,5,1,2,8,4]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,7,4,1,2,8,3]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,6,7,2,4,1,8,3]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,4,2,7,8,1,3]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,7,2,1,8,3,4]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,5,7,2,1,4,8,3]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,4,6,7,3,1,8,2]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,7,8,5,6,1,4,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,8,5,6,3,4,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,5,8,6,3,4,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,5,8,6,1,4,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,3,8,6,4,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,5,7,8,6,3,4,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,7,8,3,6,4,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,8,1,6,4,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,8,1,5,6,3,4,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,8,5,6,3,4,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,5,8,6,3,4,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,7,8,3,6,4,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,7,8,5,6,4,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,7,8,5,6,4,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,7,5,8,6,4,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,3,8,6,4,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,3,8,6,4,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,8,3,6,4,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,5,8,1,6,4,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,1,8,6,4,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,7,1,8,6,4,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,7,5,3,8,6,4,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,3,1,8,6,4,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,3,8,6,1,4,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,5,8,1,6,4,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,5,8,3,6,4,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,8,5,3,6,4,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,6,3,1,4,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,6,1,3,4,2]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,1,6,3,4,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,8,1,5,6,4,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,3,5,6,4,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,3,8,5,6,4,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,8,5,6,4,2]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,1,8,3,6,4,2]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,1,8,6,3,4,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,1,8,6,3,4,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,1,6,3,4,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,5,1,6,3,4,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,8,1,3,6,4,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,8,3,6,4,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,1,3,8,6,4,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[5,7,1,3,8,6,4,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,5,8,6,4,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,5,8,6,4,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,5,3,7,8,6,4,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,1,7,8,6,4,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,3,1,7,8,6,4,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[7,3,1,5,8,6,4,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[7,3,1,8,5,6,4,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,8,3,1,5,6,4,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,1,8,3,5,6,4,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,8,5,6,4,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,3,5,8,6,4,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,1,5,7,8,6,4,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,7,3,4,8,6,1,2]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,3,4,8,1,6,2]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,3,4,1,8,6,2]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,1,4,6,2,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,1,4,8,6,2]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,7,4,1,2,6,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[5,3,7,1,4,2,6,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,1,4,2,8,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,5,1,2,8,6,4]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,3,5,1,2,6,4]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,5,8,1,2,6,4]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,5,1,2,6,8,4]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,1,4,3,5,2,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,7,3,8,4,1,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,7,8,6,1,3,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,6,2,8,3,1,4]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,2,5,8,3,1,6]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,2,4,5,1,3,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,1,4,6,3,2,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,5,6,2,4,1,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,6,7,5,4,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,2,7,8,3,4,1,5]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,3,4,8,1,7,6]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,1,2,5,3,4,6]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[5,1,8,2,3,4,7,6]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,7,6,2,8,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,1,5,4,6,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,3,4,6,8,5,2]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[8,3,6,5,7,1,4,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,7,1,4,6,2,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,7,6,1,8,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,2,6,3,8,5,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,8,4,6,7,3,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,8,6,3,1,2,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[3,8,1,5,6,7,2,4]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,7,2,4,8,5,3,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,3,6,7,5,1,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,1,7,6,3,5,4]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,4,5,8,1,7,6]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,6,3,2,1,8,5]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,7,3,2,1,8,6,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,4,7,5,2,3,8,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,8,1,7,3,2,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,7,2,3,1,5,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,3,1,8,7,5,6]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,8,1,3,5,2,4]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,5,2,3,1,8,4]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,2,6,5,1,8,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,2,1,8,5,7,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,2,1,5,6,8,4,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[8,7,2,6,4,1,5,3]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,7,8,2,5,3,1,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,7,3,6,8,5,4]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,7,8,4,6,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,5,7,8,3,6,1,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,1,5,7,2,8,3]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[7,4,8,1,2,5,6,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,7,8,6,3,5,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,7,4,3,2,8,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,8,3,4,2,1,7,5]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,6,1,5,7,8,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,6,7,3,5,8,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,8,3,7,4,1,2]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,8,3,5,6,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,7,5,3,4,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,6,3,1,5,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,4,8,2,5,7,6,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,4,8,6,1,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,6,3,7,5,1,8,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,4,8,7,5,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,3,7,2,8,5,1,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,2,5,8,7,1,4]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,2,8,4,7,6,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,8,6,5,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[6,2,4,8,7,5,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[2,4,5,8,7,6,1,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,2,7,3,8,1,6,5]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,1,4,7,3,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,3,8,7,2,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,5,6,2,8,7,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,2,8,7,6,3]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,5,3,2,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,3,5,1,8,6,4]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,1,8,7,6,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,4,5,2,8,7,6,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,2,8,7,5,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,4,2,5,1,8,6,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,6,2,7,5,1,8,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,3,6,2,8,7,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,8,3,2,7,6,4]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,2,1,7,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,2,5,1,4,8,7]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,8,7,1,3,6,5]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,2,4,7,6,5]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,1,7,2,8,5,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,1,2,8,6,4,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[1,5,2,3,8,7,6,4]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,5,1,2,8,7,6,3]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,4,1,2,8,7,5,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[5,2,8,1,3,7,6,4]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,6,8,3,1,2]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,6,4,7,5,3,1,2]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,5,2,6,4,1,3,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[1,6,3,7,5,8,4,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,7,4,5,8,6,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,6,3,4,1,5,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,4,6,5,1,2]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,4,7,5,3,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,8,7,5,6,3,1,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,6,4,5,1,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,5,2,8,3,7,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,5,2,1,4,3,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[2,7,6,3,1,4,5,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[6,8,5,3,2,1,4,7]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[2,7,6,4,5,1,3,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,2,6,4,1,3,8]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,1,3,7,5,8,4,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,7,3,6,8,5,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,6,4,3,7,5,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,4,8,6,3,5]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,8,6,3,7,5,4,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,7,3,6,5,4]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,3,8,4,7,5,6]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,7,4,3,6,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,3,1,6,8,4,7,2]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,8,7,1,4,3,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,2,1,5,4,3,6]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,2,3,1,4,6,5,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,3,1,5,6,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[3,4,2,7,1,5,6,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,7,3,8,2,1,5,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,2,7,3,1,4,6,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[8,3,7,2,1,5,4,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,2,8,4,6,5]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,2,5,8,6,7,3]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,3,8,2,1,4,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[2,6,4,5,7,1,3,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,4,6,2,7,1,3,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,3,1,8,4,5,2]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,6,2,1,8,5,3,4]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[1,7,5,8,6,4,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,5,1,2,8,3,7,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,1,4,3,7,5,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,4,1,3,7,5,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,5,7,1,3,8,4,2]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,1,7,4,6,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,1,7,5,4,6,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,8,7,4,6,5,2]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,7,6,3,5,4]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,1,7,6,4,3,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[2,3,1,8,7,4,5,6]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,4,1,8,5,7,3,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,1,7,6,3,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,2,7,1,8,5,3,4]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,1,6,5,4,3,2]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,1,8,3,6,5,4,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,8,7,5,6,3,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,9,3,4,5,6,7]=>[[1,3,4,6,7,8,9],[2,5]]=>[4,5]=>[5,4]=>2
[3,5,8,7,2,6,4,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,7,1,6,4,3]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,6,4,5,8,3,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,7,5,2,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,6,3,8,5,2,1,7]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,6,3,7,5,2,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,7,8,2,6,1,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,4,6,8,5,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[4,8,3,7,5,1,6,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,3,4,8,7,1,6]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[5,2,3,4,6,8,1,7]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[4,2,8,5,7,6,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,6,4,5,1,8,2]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,7,5,2,1,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,7,3,6,5,1,2,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[4,2,7,5,8,6,3,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,8,1,7,3,6,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,7,8,4,6,3,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,3,7,6,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,3,1,6,4,5]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,2,3,4,8,5,1,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[6,2,3,4,1,8,5,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,4,1,8,6,5]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,4,1,5,8,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,4,8,7,5,6]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,8,5,3,4,6,7]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,8,4,2,3,5,6,7]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[8,6,7,4,1,5,3,2]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,6,7,5,1,3,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,8,4,6,5,2,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,1,5,4,6,2,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,1,4,6,3,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,8,5,1,7,3,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,5,7,1,6,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,7,1,5,6,3,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,1,4,5,6,3,2]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[8,7,4,5,6,1,3,2]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,5,1,4,6,2,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,7,2,5,1,4,6,3]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,7,2,5,1,6,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,4,8,5,2,7,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,1,4,2,5,6,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,7,5,1,2,4,6,3]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[7,1,8,5,6,2,3,4]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,7,1,2,5,6,4]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,5,8,7,1,2,6,4]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,8,5,7,1,6,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,7,1,5,6,2,4]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,8,7,1,6,2,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,6,7,5,1,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,8,6,7,5,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,8,6,2,7,5,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,4,1,2,6,5,3]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[1,3,8,6,7,5,2,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,1,8,2,6,3,4]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,7,1,5,6,3,4]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,1,5,2,4,6,3]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,8,2,4,6,5,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,2,8,4,7,5,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,8,5,7,2,6,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,3,7,2,5,6,4]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,7,1,3,5,6,4]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,7,1,8,2,3,6,4]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,8,2,3,5,6,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,3,7,4,1,5,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,2,8,6,7,5,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,2,7,5,6,1,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,3,6,1,7,5,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,3,4,7,5,1,6,2]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,4,5,1,6,2]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,4,2,5,6,1,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,7,5,1,6,2,3,4]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,7,2,4,1,5,6,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,8,6,1,7,2,5,3]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,1,8,2,6,5,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,8,6,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,4,1,2,5,6,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,2,7,1,6,3,4,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,1,3,6,4,5]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,3,6,7,1,5,4]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,2,1,3,5,6,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[1,8,7,2,3,6,4,5]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,2,6,3,4,5]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,2,7,3,6,1,4,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,7,3,6,2,4,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,7,6,3,4,5]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,2,7,4,1,5,6,3]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,2,1,7,5,6,3,4]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,1,5,6,2,4]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[2,8,7,3,5,6,1,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,3,1,6,7,5,2,4]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[8,5,2,1,6,7,4,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[1,5,2,8,6,7,4,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,8,6,7,5,3,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,3,6,7,5,2,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,3,6,7,5,1,4]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[8,3,7,2,5,6,1,4]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,3,7,5,6,2,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,2,7,5,6,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,4,2,6,7,5,3]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,6,7,3,5,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,2,7,3,6,4,5]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,7,3,6,2,4,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,2,6,3,4,5]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,2,3,6,4,5]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,3,7,2,5,6,4]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,3,6,7,2,5,4]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,8,2,3,6,5,4]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,1,2,5,6,4]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,1,2,3,6,4,5]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[2,8,5,7,4,6,3,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,8,5,7,4,2,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,5,7,4,2,6,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,6,2,4,5,7,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,6,4,3,5,7,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,6,8,3,5,4,7,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,5,8,4,6,3,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,2,7,6,1,3,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[4,8,1,7,6,3,2,5]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,1,7,6,2,3,5,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[3,7,1,8,6,2,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,7,6,4,5,2,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,7,5,8,4,2,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,1,6,8,7,5,2,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,3,8,7,5,2,4,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,5,8,4,2,6,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,6,4,2,8,5,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,3,6,2,5,4,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,8,2,1,6,3,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,7,4,6,3,2,5,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,8,5,2,1,4,3,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,5,2,3,1,4,8,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,4,6,2,3,8,1,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,5,8,3,7,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,6,5,8,1,3,2,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,5,3,8,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,8,1,3,6,2,5]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,3,4,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,1,4,2,3,6,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,8,1,3,2,4,6,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,8,6,1,3,2,7,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,6,2,1,3,7,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,4,8,7,2,3,6,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,8,7,3,1,2,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,8,3,7,2,5,4,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,6,8,2,3,7,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,4,2,8,3,6,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,7,2,1,8,3,5]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,5,3,4,1,2,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,8,5,4,1,3,2,7]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,3,7,1,5,2,8]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[9,8,7,6,5,2,3,1,4]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[7,4,2,6,1,5,3,8]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,4,2,5,6,1,3,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[6,4,2,8,1,5,7,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,8,2,5,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,5,6,4,2,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,3,1,5,6,2,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,4,5,2,6,1,3,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,2,8,6,4,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,2,6,7,4,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,2,5,4,7,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,8,2,1,5,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,4,3,1,8,2,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,3,7,8,2,6,4,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,8,5,6,3,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,6,8,2,4,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,8,4,6,2,1,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,4,3,6,7,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,6,4,7,2,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,3,8,6,2,7,4,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,8,6,3,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,8,6,7,5,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,3,8,7,2,4,1,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,7,2,6,4,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,6,7,2,4,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,7,8,6,2,4,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,6,4,8,2,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,4,6,7,2,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,2,8,1,7,3,5]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,5,2,4,3,7,8,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,6,2,8,7,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,3,8,7,2,4,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,3,1,8,2,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,7,4,3,6,8,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,8,6,2,4,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,8,6,7,3,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,8,5,7,3,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,3,7,2,4,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,8,2,7,1,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,8,2,6,4,1,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,5,7,1,4,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,4,8,6,2,3,5]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,2,5,7,8,1,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[5,2,7,4,6,8,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,7,1,8,4,2]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,6,7,1,8,3]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,1,3,6,7,2,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[8,1,4,2,7,5,3,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,3,8,2,7,4,5]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,5,2,8,6,3,4]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,4,8,1,5,7,2]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,8,4,2,6,3,7]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,4,1,6,8,2]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,1,2,6,4,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,8,2,3,7,6]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,1,8,2,6,3,5]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,1,2,3,8,6,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[5,2,6,1,3,4,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,8,4,5,1,3,2,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,3,2,5,4,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,4,3,5,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,3,1,5,4,6]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,4,3,5,1,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,4,1,5,3,6]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,6,5,7,3,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,4,2,7,3,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,4,1,5,3,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,4,3,5,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,3,1,5,4,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,5,4,8,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,1,6,5,7,3,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,6,4,7,3,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,1,6,4,7,3,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,5,7,4,8,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,4,3,7,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,6,1,7,3,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,6,3,7,2,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,6,1,7,2,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,4,1,7,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,4,3,7,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,3,2,7,4,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,4,7,1,3,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,4,5,1,3,2,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,5,8,1,3,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,3,2,7,6,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,7,1,3,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,1,3,2,7,5,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,3,6,2,7,5,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,6,5,7,2,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,3,1,7,6,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,7,6,8,1,2]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,7,3,8,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,7,2,3,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,4,6,1,7,2,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,1,6,4,7,2,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,6,4,7,2,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,6,2,7,4,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,2,6,1,7,4,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,2,6,4,7,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,6,1,7,5,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,2,3,1,7,5,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,6,1,7,5,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,3,6,4,7,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,3,6,1,7,4,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,2,7,5,4,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,1,7,3,8,2,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,6,7,4,3,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,2,7,6,4,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,7,2,8,3,6,4]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,7,3,1,8,4,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,6,8,4,3,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[1,3,7,2,8,5,4,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,2,7,1,8,3,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,3,6,8,2,7]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,4,5,7,8,3,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,1,5,6,8,4,7,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,5,6,8,7,3,4]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,6,5,2,7,8,4,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,2,4,7,5,8,3,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,7,8,4,2,6,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,4,1,8,6,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,6,8,5,7,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,7,3,1,8,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,5,6,2,8,7,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,6,8,1,7,4,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,6,1,8,7,3,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,5,6,3,1,8,7,2]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,2,1,7,5,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,3,2,1,7,5,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,6,3,1,7,5,2,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,3,7,6,1,8,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,1,7,3,8,6,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,7,1,4,3,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,5,7,6,1,8,2]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,6,1,7,5,2,8]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,2,6,1,7,5,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,1,6,4,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[5,3,1,6,2,7,4,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,3,2,7,4,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,1,4,7,5,3,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,1,7,4,2,5,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,1,7,5,3,2,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,1,6,3,7,4,2,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,6,4,2,1,7,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,3,2,6,4,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[5,2,1,6,3,7,4,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[5,2,6,3,1,7,4,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,3,1,7,8,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,6,2,1,7,4,5,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[3,6,2,7,4,1,5,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,5,7,2,8,6,4,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,7,1,3,6,5,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,1,3,7,5,4,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,1,7,5,2,4,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,1,6,2,7,4,3,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,6,4,3,1,7,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,2,1,6,4,3,7,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[5,4,2,1,6,3,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[5,4,2,6,3,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[5,4,1,6,2,7,3,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,4,2,7,3,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,7,5,4,8,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,1,5,4,3,7,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,1,6,2,5,4,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,4,3,2,7,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,4,1,6,3,2,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[5,4,3,1,6,2,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,3,1,6,5,4,8,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,8,1,5,4,3,6]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,6,5,8,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,2,6,5,4,1,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,3,2,1,5,4,6,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,2,8,6,1,4,3,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,7,6,8,4,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,7,2,5,4,1,6]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,9,2,7,6,5,4,1,8]=>[[1,2,9],[3,4],[5],[6],[7],[8]]=>[2,2,5]=>[5,2,2]=>3
[7,5,1,6,8,4,3,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[7,4,2,1,5,6,3,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,2,8,6,5,1,3,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[5,3,2,6,7,4,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[4,3,7,2,5,6,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,10,2,8,7,6,5,4,1,9]=>[[1,2,10],[3,4],[5],[6],[7],[8],[9]]=>[2,2,6]=>[6,2,2]=>3
[6,7,1,4,3,2,5,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,2,6,7,1,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,6,5,2,4,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,5,6,2,4,7,1,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,8,7,2,4,6,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,8,2,5,4,3,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,2,5,4,3,6,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,6,4,7,1,3,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,6,3,5,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,3,8,7,2,6,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,5,3,7,8,2,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,2,7,6,3,5]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,3,5,1,8,6,2]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,3,6,1,5,4,2]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,8,7,4,6,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,1,7,8,3,6]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[4,7,8,3,5,2,1,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,6,2,1,8,3,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,7,3,5,8,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,6,2,1,7,5,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,6,4,2,1,5]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,3,1,8,4,7,6,5]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,4,8,6,5,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,6,5,1,4,7,3,2]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[8,5,4,1,7,3,6,2]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,7,2,8,5,4,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,6,3,8,2,7,5,4]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,5,3,8,2,6,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,7,4,1,8,5,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,2,7,5,1,4]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[2,7,5,1,3,8,6,4]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,4,3,8,2,5]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,2,4,8,6,5,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,2,8,7,6,1,5]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,1,4,3,2,7,8,6]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,7,8,5,2,4,1,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,6,2,4,1,8,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,2,5,7,4,3]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,2,5,8,4,3,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,2,7,8,4,3,1,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,3,1,7,8,4,2,6]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[2,7,6,4,1,3,8,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,1,7,6,3,2,8,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,4,2,7,6,3,1,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[6,3,1,7,5,2,8,4]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[6,2,7,5,3,1,8,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,2,7,4,6,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,2,8,4,6,3,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,1,8,4,6,2]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,7,3,1,6,5,2]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,5,7,4,1,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,2,1,7,4,8,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,7,4,6,2,1,8,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,4,8,3,7,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,8,3,4,2,5]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,3,5,1,4,2,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,7,1,8,3,4]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,4,3,8,1,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,8,6,7,1,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,7,4,5,3,6]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,4,8,3,6,1,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,8,5,6,4,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,6,4,7,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,6,4,8,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,2,3,1,6,4,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,2,4,3,6,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,2,7,1,5,3,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,6,2,5,3,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,5,3,6,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,3,5,1,7,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,5,1,4,2,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,7,1,4,2,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,1,6,3,4,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,6,3,4,2,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,6,4,7,2,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,1,6,4,8,2,3]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,8,1,7,2,3]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,1,4,2,8,5,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,1,4,2,8,6,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,8,3,7,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,8,2,3,1,7]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,6,5,8,1,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,4,6,2,8,1,7]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,5,4,7,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,7,1,8,5,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,2,3,1,8,5,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,3,8,1,7,5,6]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,3,8,4,7,1,6]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,3,8,1,7,4,5]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,1,8,3,6,4,5]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,1,8,7,6,2,3]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,5,7,8,2,6,3,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,6,8,3,7,4,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,6,8,7,4,5,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,4,8,7,2,5,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,8,4,7,3,5,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,3,5,7,1,4,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,7,8,2,5,3,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,5,2,8,6,3,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,8,2,5,3,7,4,1]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,8,4,2,7,5,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,5,8,6,2,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,7,5,3,8,6,4,1]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,8,3,7,4,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,8,2,7,3,6,4]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,4,8,1,5,3,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,4,8,6,2,5,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,5,3,7,2,4,1]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,5,2,3,7,4,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,3,8,2,6,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,2,3,8,6,4,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[6,7,3,4,8,5,2,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,6,4,7,8,5,2,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,4,2,5,8,6,3,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[7,4,5,8,1,6,3,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,7,8,5,2,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,1,2,7,4,5,8,3]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,8,3,4,1,6,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,2,7,4,3,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,7,3,2,5,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,7,3,8,5,4,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,8,4,5,3,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,7,8,4,3,6,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,8,4,5,7,1,2]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,4,7,2,3,5]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,5,7,8,2,6,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,5,7,8,6,1,2]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,4,5,7,6,8,1,2]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,6,7,4,8,5,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,5,6,8,7,1,2]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,4,5,8,7,2,3,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,2,5,8,3,6,4,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,5,8,6,2,3,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[7,8,1,4,6,2,3,5]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,4,8,2,5,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,5,6,8,2,7,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,5,8,6,2,7,3]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,2,5,8,3,4,7,6]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,7,2,3,5,8,4]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,8,1,2,3,5,4,6]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,7,2,3,5,4,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,7,6,2,3,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[1,2,5,7,3,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,7,3,6,8,4]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,8,2,3,5,7,4]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,8,4,5,2,3,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,8,4,5,2,7,3]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,8,2,3,4,7,5]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,8,2,3,7,4,5]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,7,6,2,8,3]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,8,1,4,5,2,6,3]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,1,2,3,4,6,5]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,1,2,3,6,4,5]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,7,2,3,8,5,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,6,3,8,7,4]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,6,5,3,8,7]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[6,8,2,1,4,3,7,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,2,4,3,1,5,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[4,6,5,2,8,3,7,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,5,8,3,7,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,2,6,3,5,1,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,3,5,8,7,1]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,3,8,5,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,3,6,5,1,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,1,8,4,3,7,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,5,2,1,7,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,7,5,2,1,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,6,8,7,4,5,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,6,5,7,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,6,4,5,1,3,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,8,5,3,1,4,6,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[2,7,4,8,3,5,1,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,4,8,3,5,6,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,8,4,3,5,1,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,2,1,5,3,6,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,5,1,4,2,3,6,7]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[8,4,1,5,3,2,6,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,7,3,8,4,2,5,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,3,8,4,2,1,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,1,8,4,3,5,2,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,4,3,5,2,6]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,4,8,3,5,2,6]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,8,1,5,6,2,3]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,4,3,5,6,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,1,8,4,5,2]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,3,8,4,5,2,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,4,8,3,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,4,1,3,8,2,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,7,8,4,3,2,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,2,1,8,4,5,3,6]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,1,8,4,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,7,8,4,3,1,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,2,7,8,4,3,5,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,7,4,8,3,5,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,7,4,8,3,1,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,1,3,6,2,4,5]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,2,7,8,6,3,4,5]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[2,6,7,1,8,5,3,4]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,7,8,5,3,1,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,6,7,8,5,3,4,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,7,8,4,5,3,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,1,8,4,5,6,3]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,2,8,4,5,6,3]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,8,1,5,6,2,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,8,1,5,2,4]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,1,2,8,5,3,4]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,8,4,2,5,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,7,6,5,8,4]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,4,7,3,8,5]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,7,5,3,6,4,8,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,2,6,7,4,8,3]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,5,7,3,2,6,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,6,1,7,3,2,5,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,6,1,8,3,2,5,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,7,1,8,3,5,2,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,7,8,6,2,3,5]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[1,6,5,7,8,3,4,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,5,8,7,3,4,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,8,7,6,2,3,5]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,8,1,7,3,5,2,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,6,3,2,5,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,7,1,6,3,2,5,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,1,2,3,7,5,4,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[6,8,1,5,3,7,2,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,5,2,4,1,6,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,5,7,3,4,8,6,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,3,4,7,6,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,5,2,4,1,6,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,2,3,5,6,4,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[8,1,2,3,5,6,4,7]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[8,1,2,3,5,4,7,6]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,8,4,6,3,2,5]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,2,4,3,1,5,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,7,2,4,3,1,5,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,8,1,2,4,5,7,6]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,1,8,6,4,2,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,3,7,5,8,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,2,6,7,5,8,4]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,8,1,7,6,4,2,5]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,6,2,4,3,1,5,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,7,2,4,3,5,1,6]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,7,4,6,3,2,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,6,5,3,2,4]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,5,7,3,4,6,8,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,2,5,3,6,1,4]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,2,3,5,4,8,6]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,1,2,3,5,8,4,7]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[6,1,2,3,5,7,4,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[5,1,2,3,7,6,4,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[5,1,2,3,8,6,4,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[1,5,6,3,4,7,8,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,5,2,4,7,1,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,2,5,3,1,8,4]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,5,2,3,8,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,7,4,5,1,6]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,7,3,2,5,1,6]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,3,1,2,8,7]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,6,2,3,1,5,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,3,4,5,8,6,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[8,2,3,4,5,7,1,6]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[7,3,4,6,8,5,1,2]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,7,3,2,8,6,1,5]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,4,5,1,8,6,2]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,2,6,7,4,5,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,1,5,6,7,3,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,2,4,6,7,1,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,1,3,4,2,7,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,2,4,3,1,7,6]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,7,6,8,5,3,4]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,6,1,8,5,2,4]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,3,8,5,1,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,3,6,4,8,5,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,1,4,8,5,2,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,2,3,7,8,5,4,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,2,3,8,4,5,1,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,6,8,4,1,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[8,2,3,5,7,1,4,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[6,4,8,3,5,1,7,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,3,6,7,1,2]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,8,4,6,7,2]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,1,8,4,5,2,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,8,3,5,2,7,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,8,3,2,4,1,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,3,5,6,1,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,3,1,4,5,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,2,7,4,8,3,1,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,8,2,1,4,6,5]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,5,2,8,4,1,6]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,2,4,1,8,7,5]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,4,8,5,1,6]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[5,7,3,1,4,2,6,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,4,1,8,2,5,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,3,7,4,8,1,2,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,4,2,6,1,5]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,4,1,5,6,2,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,8,3,2,4,5,7,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[8,4,1,6,3,7,5,2]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,4,2,1,6,3,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,3,5,2,7,4,1,6]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,3,8,7,6,4,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,2,4,8,1,3,6,5]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,8,7,5,6,3,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,6,7,5,2,4]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,8,6,5,7,2,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,4,8,2,3,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,6,8,3,4,2,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,5,1,7,4,3,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,1,8,7,4,3,6]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[5,2,6,3,8,1,4,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,3,4,6,1,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,4,3,1,7,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,2,8,1,3,6,5,4]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,1,4,6,2,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,5,4,6,3,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,4,6,3,7,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,8,4,1,2,7,6]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[5,8,4,3,6,2,1,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,3,6,5,2,7,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,2,4,7,6,5,3]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,1,4,6,7,5,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,5,1,7,6,4]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,8,2,5,1,6,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,2,4,3,5,1,7,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,1,4,6,5,7,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,3,4,5,7,6,2]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[6,1,5,2,4,7,8,3]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,8,5,2,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,2,3,7,5,6]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,7,2,1,4,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,7,3,5,1,4,8,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,7,5,8,2,3,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,8,4,2,6,3,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,1,6,8,3,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,6,1,7,3,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,4,7,8,3,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,6,7,4,8,2,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,8,6,2,7,3,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,5,6,2,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,3,8,4,7,2,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,8,2,7,4,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,7,2,8,6,5,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,7,3,8,5,2,4,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,7,5,1,4,8,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,8,4,6,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,8,4,6,2,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,8,4,3,7,6,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,4,8,6,2,1,5]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,4,8,7,2,5,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,4,8,2,7,6,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,7,3,8,6,2,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,8,4,7,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,1,8,7,5,4,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,4,8,1,7,6,3,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,4,1,7,6,3,2]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[1,8,2,5,6,3,4,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,2,8,4,5,1,3,6]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,7,5,6,2,4,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,4,3,5,2,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,2,3,7,4,6]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,8,2,5,3,6,7,4]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,8,4,3,5,7,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,3,2,1,6,4]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,2,8,4,1,5,6,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,1,2,6,3,4]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,7,4,3,2,8,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,5,2,6,4,7,8,3]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,4,6,2,3,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,2,5,7,1,4,8,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,3,8,1,7,2]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,3,6,8,5,2,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,8,3,6,5,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,8,5,4,6,3,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,8,3,4,1,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,7,3,4,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,5,7,4,1,3,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[6,2,5,8,4,1,3,7]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,7,8,4,6,1,3,5]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,2,8,3,7,4,5]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,2,8,5,4,7,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,5,7,8,1,3,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,5,4,2,6,7,3,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,6,5,7,3,8,1,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,7,5,8,4,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,7,8,5,6,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,2,4,8,7,3,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,5,2,1,8,7,3,4]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[2,6,5,3,7,8,4,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,2,5,3,8,4,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,2,3,8,7,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[5,4,1,2,3,8,6,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[5,1,4,2,3,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[1,5,4,2,6,3,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,6,3,8,2,7,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[9,8,7,6,5,4,3,1,2,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[8,7,6,5,4,2,1,3,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[1,9,8,7,6,5,3,2,4]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,8,7,6,2,5,4,3]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,10,9,8,7,6,5,4,2,3]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[1,2,9,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[1,2,3,9,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[1,2,3,4,9,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[1,2,3,4,5,9,8,7,6]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[1,2,10,9,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[1,2,3,10,9,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[4,6]=>[6,4]=>2
[1,2,3,4,10,9,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,5]=>[5,5]=>2
[1,3,2,6,5,4,10,9,8,7]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[1,2,3,4,5,6,10,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,3,4,5,6,7,10,9,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[5,2,7,4,1,6,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,1,5,6,2,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,3,4,1,6,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,8,4,5,6,2,3]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,4,2,6,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,3,8,5,2,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,3,7,5,1,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[1,7,3,4,8,6,2,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,3,2,1,6,5,4]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[8,7,6,3,1,5,2,4]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,5,1,7,2,3,4,6]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[2,4,8,5,3,7,1,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,8,5,3,7,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,8,6,3,1,7,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,4,6,8,2,1,7,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,1,5,8,2,7,6]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,4,5,3,2,7,6]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,4,1,5,2,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,6,2,1,8,7,5]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,2,1,7,8,4]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,4,6,2,7,8,1,5]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,6,3,7,2,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,6,3,7,5,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,2,1,7,4,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,6,7,3,4,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,5,6,7,3,2,4]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[3,4,1,6,8,7,2,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,1,8,7,2,4]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,3,8,6,7,4,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,2,6,7,5,4]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,6,7,1,5,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,1,8,6,7,5,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,8,6,1,7,4,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,1,8,7,4,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,1,6,8,7,5,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,4,6,8,7,1,5,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,4,6,2,7,5,3]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,1,6,7,8,4,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,6,1,7,8,3,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,1,7,3,8,2]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,1,6,7,4,8,2]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,5,6,7,4,2,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[8,1,5,6,7,4,3,2]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,5,1,6,7,4,2,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,6,1,7,3,2,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,7,4,3,1,2]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[6,4,2,7,8,5,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,1,4,8,7,5,2,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[1,6,4,8,7,5,2,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,6,2,4,7,3,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,2,4,7,3,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,2,1,4,8,3,5]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[6,4,1,7,8,5,2,3]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[7,6,1,2,4,8,3,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,6,1,3,4,8,2,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,1,6,3,4,7,2,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,6,3,4,7,2,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,2,5,4,8,3,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,2,5,4,8,3,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,1,5,4,8,3,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,3,4,7,1,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,6,1,4,7,3,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,2,1,5,4,8,3,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,5,4,8,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,5,4,8,1,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,8,4,7,3,1,6]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,7,5,4,8,1,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,2,4,7,1,5]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,2,5,4,8,1,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,7,5,4,8,2,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,5,4,8,2,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,4,7,3,2,6]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,4,7,3,2,6]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,2,4,7,3,1,6]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,3,7,5,1,2]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,5,6,2,1,4,3]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,2,4,7,3,1,6]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,1,5,4,7,3,2,6]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,5,4,7,3,2,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,5,4,8,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,3,1,4,7,2,5]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[8,6,4,2,7,5,1,3]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[8,6,4,1,7,2,5,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,3,7,4,6,8,2,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,3,2,7,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,2,7,8,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,4,3,1,7,8,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,7,3,5,4,8,1,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,5,4,7,3,1,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,3,4,6,8,2,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,2,5,4,7,3,1,6]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,3,5,4,8,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,4,7,8,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[8,1,7,6,4,3,5,2]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,4,5,2,7,1,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,8,6,4,3,5,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,4,2,5,1,6,3,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,3,6,5,2,1,4,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,3,6,5,2,1,7,4]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,3,6,5,2,1,8,4]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,6,4,2,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[5,4,2,8,1,3,7,6]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,8,2,6,4,1,3,7]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,4,2,5,1,8,3,7]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,2,1,4,7,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[2,5,8,6,3,1,4,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[2,3,5,8,1,4,7,6]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,6,8,1,5,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,5,2,7,1,4]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,5,2,1,4,8]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,5,7,6,3,1,4,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[2,8,7,6,3,1,5,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[2,5,8,7,6,3,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,4,8,1,6,5,7,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,7,3,6,1,4,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,5,2,1,4,6,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,4,2,5,1,3,7,6]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,3,6,8,1,4,7,5]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,8,6,3,1,4,5]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,3,8,5,2,1,4,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,3,6,1,8,4,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,6,3,1,4,5,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[8,3,5,2,1,4,6,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[2,4,8,1,3,7,5,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,8,1,7,3,6,4]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,1,5,7,3,6,4]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,6,1,4,7,5,2]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,8,1,5,7,3,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,1,5,8,3,4,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,8,1,2,6,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,6,1,2,8,4,5]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,4,8,1,6,5,2,3]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,5,8,6,1,2,3]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[6,8,4,5,1,7,2,3]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,8,7,6,2,3,4]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,6,1,8,7,5,2,3]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,5,1,8,7,2,3,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,8,7,1,2,5,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[6,4,8,7,1,2,5,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,3,7,1,4,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,1,2,7,3,8,4]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[6,5,1,8,2,7,3,4]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,8,7,2,3,4]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[6,5,1,7,2,8,3,4]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,7,2,3,8,4]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[5,6,8,7,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[6,8,5,7,4,1,2,3]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,3,8,1,5,2,4,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,1,7,5,3,6,2,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,2,3,6,7,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,5,8,3,4,6,7,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,7,2,3,6,8,5]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,2,1,5,7,8,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,5,2,3,1,7,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,6,7,4,1,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,6,2,7,1,4,8,3]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,3,8,1,7,4,5]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,6,8,3,4,7,1,5]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,2,7,5,1,3,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[2,6,3,1,8,4,5,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,7,8,1,5,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,3,2,7,4,8,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,2,7,6,8,4,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,3,1,8,7,4,5]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,4,7,8,1,2]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,4,2,8,7,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,3,7,8,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[4,1,8,2,5,7,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,4,7,2,5,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,2,3,8,4,1,7,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,4,1,5,3,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,7,6,4,1,8,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,5,4,1,7,6,8,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,1,4,7,8,3,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[2,6,5,1,7,8,3,4]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,7,5,2,1,6,3,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,2,3,7,8,1,6,5]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[5,8,3,1,7,2,4,6]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,3,1,5,2,4,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,7,4,2,6,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,2,5,1,7,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,4,3,1,5,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,8,4,2,1,5,7,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,1,7,3,2,4,6,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[5,2,1,8,3,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,8,1,6,2,7,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,1,8,5,7,3,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,1,7,4,5,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[6,4,2,1,7,5,3,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,5,2,1,8,6,3,4]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[5,3,2,7,6,1,4,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[5,3,2,8,6,1,4,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,3,2,8,7,1,4,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[4,2,8,1,7,3,5,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,7,2,1,5,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,1,5,8,4,7,3,6]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,6,2,7,5,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[5,4,1,7,2,8,6,3]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,1,7,8,4,2]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[6,4,2,1,7,8,5,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[5,3,2,1,6,7,8,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,6,1,4,5,7,2,3]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[5,2,8,3,7,4,6,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,8,5,4,7,3,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,6,3,7,4,2,5]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,5,7,2,3,4]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,2,8,4,3,6,7,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,2,7,3,6,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,8,3,6,1,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,8,4,7,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,4,3,7,1,6]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,3,7,4,1,5]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,2,7,3,1,8,6]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,7,1,2,8,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,8,1,2,7,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,6,3,8,4,2,1,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,2,8,5,1,6,3,4]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,4,3,1,5,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,5,3,8,4,2,6,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,2,7,3,1,5,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,6,4,8,2,3,5,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,8,1,2,5,3,4]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,1,7,8,4,6,2]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,7,8,4,6,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,1,6,3,8,7,2]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,7,8,2,3,4]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,3,1,7,8,4,2,5]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[5,4,1,7,3,8,2,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,7,8,4,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[6,1,5,4,3,2,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,1,3,5,2,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,1,6,5,7,3,4,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,1,5,7,6,2,3]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[7,8,6,2,5,3,1,4]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,3,5,2,8,4,7]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,7,4,2,5,6]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[4,3,8,7,5,2,1,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,7,1,8,5,3,4,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,6,4,8,3,5,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,2,7,1,4,8,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,4,6,1,3,2,8,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,2,1,3,8,4,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,4,7,6,3,1,5,2]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,4,1,5,6,3,8,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,7,5,6,1,8,2]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,7,5,6,3,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,1,7,6,2,8,3]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[3,5,6,7,1,4,8,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,6,1,3,4,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[5,7,2,1,6,3,8,4]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,2,5,6,3,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,2,5,7,1,4,3]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,7,4,5,3,8,1,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,7,1,3,2,5,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,6,5,7,1,4,3]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,4,3,2,6,7,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,5,6,2,4,7,3]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,5,6,2,4,7,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,1,3,2,7,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,5,2,8,6,7,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,1,7,8,6,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,7,6,2,8,1,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,1,2,8,7,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,1,2,8,6,7,3]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,5,2,1,6,7,3]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,6,8,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,3,2,7,8,4,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,5,4,2,7,8,3,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,6,7,8,3,1,5,2]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,2,8,4,3,1,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[5,2,8,6,3,4,7,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,8,4,3,2,7,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,8,1,7,2,4,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,7,8,4,2,1,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,1,8,4,3,7,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,4,2,1,7,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,5,8,3,1,6,7,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,8,1,2,6,7,4]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,1,5,6,7,4]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,3,2,6,7,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,6,2,4,7,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,2,7,8,4,6,1,5]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,8,3,4,6,7,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,7,2,1,6,3,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,8,1,6,3,4,7,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,3,4,2,1,6,5,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,2,5,8,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,5,2,6,3,1,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,5,8,3,6,1,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,8,1,2,6,4,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,3,5,2,4,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,5,1,2,6,4,3,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[5,8,6,1,3,4,2,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,6,1,3,2,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,4,5,2,8,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,4,3,6,1,8,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,3,7,8,5,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,4,1,8,3,2,5,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,2,1,7,8,4,5,3]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,3,1,5,4,8,2]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,6,5,1,7,8,3]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,4,7,5,6,8,2,3]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,7,6,5,8,2,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,2,4,6,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,6,1,7,4,2,8,3]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,4,8,1,2,6,5]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,5,7,8,1,4,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,5,7,1,8,4,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,7,8,2,1,3,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[6,7,3,8,4,1,2,5]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[2,7,8,3,4,6,1,5]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,4,1,3,2,6]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,8,3,1,2,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,6,7,4,8,1,2,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,3,1,6,8,4,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,3,1,8,6,4,5]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,3,1,5,7,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,8,1,2,3,5,7,6]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,6,8,1,2,4,3,5]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,5,1,3,2,4]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,5,4,6,1,7,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,5,2,7,6,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,6,4,1,2,5,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[6,7,1,3,5,2,8,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,2,3,6,8,1,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[8,5,3,2,7,6,1,4]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[3,4,6,7,5,8,1,2]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,7,6,1,8,2]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,6,4,5,7,8,3,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,5,1,6,2,7,4]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,1,3,6,8,7,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,1,3,7,8,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,5,7,1,4,8,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,4,6,8,1,5,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,7,8,4,1,5,6,2]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,5,4,2,1,6,3]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[6,7,2,5,1,8,4,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,1,2,5,8,4,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,8,2,3,7,6]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,6,4,5,8,3,7]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,2,4,6,8,3,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,1,5,8,2,4,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,1,4,8,3,7]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,6,1,4,8,3,7]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,1,8,4,7,3,6]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,1,4,3,6,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,7,5,8,2,4,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,2,1,5,7,3,4,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[2,5,4,8,1,3,7,6]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,1,3,8,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,3,7,1,2,6,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,7,3,5,8,2,6,4]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,2,6,7,3,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,1,6,8,7,2,4,5]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[7,2,1,6,8,3,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[3,1,7,6,8,2,4,5]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,1,7,2,6,8,3,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,7,2,3,6,8,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,1,6,3,5,8,4]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,1,7,3,5,8,4]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,2,5,3,6,8,4]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,4,1,2,7,8,3,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[8,1,3,2,4,6,7,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,3,1,2,4,6,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[1,8,3,4,7,2,5,6]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,5,8,1,2,7,4,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,1,2,4,7,5]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,3,8,7,2,6,5]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,7,4,8,2,6,5]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,6,8,2,3,7,5]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,8,1,7,2,4,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,6,8,1,7,3,4,5]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,8,2,3,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,3,2,7,5,6,4]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,7,2,8,5,6,4]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,7,3,8,1,5,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,1,7,3,6,2,5]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,7,2,8,6,1,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,3,8,7,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,7,8,4,2,6,3]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,8,7,4,2,6,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,7,2,8,3,6,5,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,7,8,5,3,6,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,7,4,8,3,6,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,7,5,3,6,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,2,7,3,6,5,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,2,6,3,5,8,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,2,4,3,7,5,1]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,4,3,8,5,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,7,3,5,4,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,7,2,4,1,5,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,8,2,4,1,5,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,2,4,5,7,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,2,4,5,8,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,1,4,2,3,8,7]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,6,1,7,2,5,4,3]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,6,1,2,3,5,4]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[5,4,3,1,6,2,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,3,4,7,1,6,2,5]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,1,8,5,2,7]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,5,2,7,1,6,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,6,7,5,3,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,8,7,3,6,4,5]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,5,8,2,4,7,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,1,8,7,3,4,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[6,5,2,7,4,3,8,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,5,2,7,3,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,7,1,8,3,5,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,5,4,8,3,6,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,5,1,2,6,4,3]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,4,3,2,7,1,6,5]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,6,2,3,8,5,4]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,1,3,2,7,5,6]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,1,4,7,5,2,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,8,7,4,5,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,8,5,2,3,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[8,5,7,4,6,2,1,3]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,8,2,3,5,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,4,6,2,1,5,3]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,6,1,3,5,2,8,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,8,3,2,4,6,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,2,6,5,3,1,7,4]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,7,6,5,2,3,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,1,8,6,4,3,7,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,1,7,6,5,3,8,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,7,6,1,3,5,8,4]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,2,5,4,6,1,8,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,6,1,2,5,8,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,4,1,7,6,8,5,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,7,8,5,6,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,4,3,1,8,6,2]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[8,5,6,2,7,3,1,4]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,2,5,6,1,7,3]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,3,5,4,1,7,8,2]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,1,3,6,7,5,8,2]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,7,2,4,5,8,3,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,5,8,3,2,6]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,4,7,8,3,5,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,6,4,7,8,3,5]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,7,8,3,5,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,4,7,8,1,5,2]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,6,7,1,8,2,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,6,4,7,8,1,2,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,1,5,3,8,6]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,6,4,7,2,8,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,4,7,2,8,5,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,3,4,2,7,8,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,1,3,7,8,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[1,6,7,3,8,2,5,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,4,7,8,5,2,3]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[6,3,2,1,7,8,5,4]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[8,6,5,1,3,2,4,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[6,4,7,8,3,2,5,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,4,7,1,2,5,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,6,1,2,5,4,3,7]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[4,8,6,1,5,3,2,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,6,4,1,3,2,7]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,3,6,4,5,2,1,7]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,5,7,4,2,3,1]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,8,7,1,6,4,5]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,8,1,6,2,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,8,7,4,1,2,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[7,3,8,4,1,2,5,6]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[4,8,1,2,7,3,5,6]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,1,2,7,4,5,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,8,4,1,3,7,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,4,7,1,6,3,2]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,8,7,3,6,4,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,7,5,6,1,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,4,8,5,6,2,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,8,7,5,1,2,3]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[3,8,5,2,4,6,7,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,7,1,8,4,6,2,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,8,7,2,1,4,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,3,7,8,5,6,1,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,7,6,8,5,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,7,8,5,1,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,4,7,8,1,6,3,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,7,8,2,6,3,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,3,4,1,5,7,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,3,4,1,2,7,5]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,7,1,5,2,3,4]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,3,2,7,6,1,4]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,3,1,8,6,7,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,3,2,8,6,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,8,6,1,4,7,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,5,6,1,4,7,3]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,1,5,2,7,3]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,2,3,7,6,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,8,5,3,2,7,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,4,8,5,1,7,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,4,8,5,2,1,3]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,4,8,6,5,2,7,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,8,7,5,6,2,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,3,2,8,6,1,4]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[2,5,1,3,8,6,7,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,1,2,8,6,7,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,8,1,3,6,7,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,5,4,1,6,7,2]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,3,4,8,5,6,1,2]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,7,2,4,8,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,5,1,2,3,8,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,4,3,1,2,8,5,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,4,7,6,2,1,5,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,4,6,5,7,1,3,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,1,4,5,8,3,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[7,4,1,6,3,5,8,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,7,6,4,1,8,2]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,7,5,2,1,3,8,6]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,7,2,3,6,4,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,2,3,7,1,4,5]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[5,7,2,4,8,3,6,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,2,4,8,6,3,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,6,1,5,4,8,3,2]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,3,2,1,8,5,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,1,7,2,5,8,4,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,6,1,2,5,3]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,6,1,3,2,5,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,6,7,4,1,3,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,8,6,4,2,3,1,7]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,3,1,6,5,4,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,1,2,5,7,4,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,5,4,2,7,3,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,3,1,2,4,5,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[4,6,8,7,3,1,5,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,5,3,7,8,4,1,2]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[4,1,3,8,7,5,6,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,7,4,8,1,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,5,2,1,6,3,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,3,2,6,8,1,7,5]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,5,6,3,8,2,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,2,4,7,8,3,6]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[3,5,4,2,8,1,6,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,3,8,4,2,7,6]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,8,7,3,5,4,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,4,3,6,5,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,7,4,1,2,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[5,6,8,1,7,3,2,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,1,6,8,7,4,2,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,6,8,2,1,5,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,5,8,4,3,1,2,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,5,8,3,6,7,4,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,1,3,7,4,6,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,8,3,7,4,2,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,2,7,1,5,6,4]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,2,3,6,4,1,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,3,4,7,5,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,1,8,4,2,6,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,6,8,5,2,7,4,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,5,4,8,3,7]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,8,4,6,5,3]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,7,4,3,5,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,8,4,6,1,2]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,2,8,4,6,3,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,8,2,4,3,1,5,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,3,8,1,5,4,2]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,1,7,5,2,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,3,1,4,6,8,5,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[4,3,8,7,1,6,5,2]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,3,6,8,1,7]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,5,4,1,2,7]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,7,5,6,3,8,2,1]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,7,5,8,3,6,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,2,7,3,4,6,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,2,4,5,3,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,2,1,4,8,5,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,2,3,1,4,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,2,1,3,6,4,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[7,1,8,3,5,4,6,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,2,4,8,5,6,3]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,1,3,4,5,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[8,7,3,5,4,2,1,6]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,4,6,5,3,2,1,7]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,1,6,4,3,2,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,1,4,6,5,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,3,6,4,7,5,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,1,7,5,8,3,4]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,8,7,5,2,1,4]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[6,7,2,1,5,8,4,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[9,1,8,7,6,5,4,3,2]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[7,6,8,1,5,4,3,2]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,7,6,1,3,2]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[10,1,9,8,7,6,5,4,3,2]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[7,6,1,8,5,4,3,2]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,7,9,1,6,5,4,3,2]=>[[1,3],[2,5],[4],[6],[7],[8],[9]]=>[3,2,4]=>[4,3,2]=>3
[6,5,8,1,7,4,3,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,7,4,1,3,2]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,4,8,3,2,5,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,8,3,5,6,2,4,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,4,8,5,6,2,3,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,5,3,7,4,6]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,8,2,3,5,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[8,7,2,5,6,1,4,3]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,8,2,5,4,7,3,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,4,1,2,3,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,7,4,2,5,3,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,4,2,1,3,8,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,4,3,8,5,7,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,3,6,2,1,5,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,2,5,3,4,1,6,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,4,5,6,1,2]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,4,3,1,5,6,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[6,8,4,2,3,1,5,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,2,4,1,6,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,1,3,2,8,4,5,6]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,1,7,4,8,3,5,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,6,1,3,4,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[2,8,3,1,4,5,6,7]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[7,4,8,2,3,1,5,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,3,1,5,6,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[8,3,7,2,1,4,5,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[6,5,2,4,7,1,3,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[6,5,7,4,1,8,2,3]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,5,1,8,2,3]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,6,4,1,3,7,2,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,4,3,1,8,2,5,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,4,1,2,8,3,5,6]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[4,8,1,3,5,7,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,1,3,6,2,5]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,8,1,3,7,2,4]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,1,8,2,4,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,7,3,1,8,2,5,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[8,3,1,7,2,4,5,6]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[2,8,1,4,7,3,5,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,8,5,4,7,6,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,5,8,3,7,6,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,3,8,7,6,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,5,1,8,2,7,6,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,5,3,1,7,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,5,2,8,1,7,6,3]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,1,8,7,6,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,7,8,1,4,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,2,8,7,1,5,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,3,7,1,5,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,6,3,7,5,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,8,2,7,5,1,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,2,8,7,5,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,2,7,4,1,8,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,7,2,3,1,8,4]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,7,2,8,3,1,4]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,2,1,8,3,4]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,2,1,3,8,4]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,6,1,7,8,2,4,3]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,1,7,2,4,8,3]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,6,7,8,3,4,2]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,6,8,7,3,5,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,8,6,7,5,4,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,6,8,7,5,3,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,1,6,7,4,8,3,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,1,7,8,4,2,3]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,8,1,7,5,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,6,1,7,5,3,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,7,1,8,3,2,4]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,7,1,3,8,2,4]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,1,3,2,8,4]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,7,3,1,2,8,4]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,6,7,3,8,1,2,4]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,8,7,4,2,1,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,6,7,3,8,2,1,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,2,3,5,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,6,3,2,5,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,4,1,6,3,8,5,2]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,1,5,8,4,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[6,4,2,5,7,3,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[4,2,5,7,6,3,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,5,6,1,8,3,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,8,6,3,2,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,2,7,6,1,8,5,4]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,1,6,8,2,3]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,6,5,1,2,7,4,3]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[3,2,5,1,4,8,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,4,1,3,2,7,6]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,4,2,3,6,8,7,5]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,8,3,7,1,6,2]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,1,8,2,5,3,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,1,8,5,3,7,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,1,3,5,2,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,4,7,8,1,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,3,7,8,1,6]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,6,7,2,5,3,4]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,7,6,5,8,2,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,5,6,8,3,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,7,2,8,3,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,7,6,8,4,5]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,8,6,4,7,1,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,4,6,3,2,1,5]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,6,5,3,7,2,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,2,5,3,6,7,1,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,5,2,7,6,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,5,3,1,8,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,5,3,6,8,1,7,2]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,2,6,1,8,7,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,3,5,7,2,8,4]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,4,6,7,8,2,3]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,4,6,5,7,2,1,3]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,5,2,6,8,1,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,6,8,7,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,5,1,4,3,2,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,6,4,5,2,1,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,4,2,3,8,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,8,1,3,5,6,2,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,8,3,5,6,2,4]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,7,8,5,2,6,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,7,5,8,2,6,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,7,5,8,2,6,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,7,1,8,4,6,2]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,7,8,1,4,6,2]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,7,8,4,6,1,2]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,1,8,4,6,2]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,3,7,8,4,2,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,6,2,1,4,5,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,6,2,5,1,3,8,7]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,2,5,1,3,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,6,1,7,3,2,4,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[2,5,8,1,7,3,4,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,2,7,3,1,4,5]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,2,3,7,1,4,5]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[8,6,2,7,4,5,1,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,1,7,3,4,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,3,8,1,5,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[5,2,8,3,7,1,4,6]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,4,6,1,3,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,5,8,4,3,6,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[5,8,3,2,7,1,4,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,3,8,2,5,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[3,5,8,2,7,1,4,6]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,8,2,6,1,3,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,8,3,7,1,4,5]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,3,7,2,4,6]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,4,6,2,3,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,4,1,6,2,3,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,5,8,1,6,2,3,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,1,6,2,3,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,8,5,1,6,2,3,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,1,5,4,8,3,6,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,3,8,1,5,6,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,1,8,4,2,5,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[3,8,4,2,1,5,6,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[2,3,8,4,1,5,6,7]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[3,4,2,8,1,5,6,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,8,5,2,7,1,4,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,5,2,6,1,3,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,4,8,5,3,6,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[3,2,8,4,1,5,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[2,8,4,3,1,5,6,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[4,1,7,5,6,2,8,3]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,4,3,8,1,6,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,4,3,8,2,6,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,2,6,7,5,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,4,1,6,7,5,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,1,7,5,2,8,4,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,4,3,2,8,1,7]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,6,7,5,3,8,4,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,4,8,2,5,3,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,6,7,5,3,8,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,8,4,2,1,6,7,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,7,4,3,8,2,1,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,4,8,1,2,5,3]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,5,8,1,2,4,3]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,8,3,1,2,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,8,1,2,5,7,6]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,3,4,8,2,5,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[6,2,3,4,8,1,5,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[3,4,8,2,1,5,7,6]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,5,8,2,4,3,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,5,8,3,1,4,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,8,1,5,7,6,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,6,1,4,8,3]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,4,8,2,3,5,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,8,1,3,5,2]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,7,5,1,3,8,4]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,3,1,4,8,2,5,7]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,7,4,8,1,3,2,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,5,8,4,1,3,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,8,2,1,3,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,7,4,8,1,2,3,5]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,5,6,3,4,8,2,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,6,5,8,2,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,3,4,7,2,6,5]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,7,3,4,8,2,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,2,3,5,4,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,6,2,3,7,4,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,3,4,7,5,6,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,4,7,6,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,2,3,6,5,4,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,8,1,7,5,2,6,4]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,1,6,7,2,5,3]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,3,8,4,6,5,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,1,7,4,3,6,5]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,3,2,8,5,4,6,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,3,1,5,7,2,6,4]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,5,1,7,2,6,3]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,6,8,7,4,2,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,4,5,7,6,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,4,8,5,7,6,2,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,5,7,3,6,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,8,6,5,7,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,2,8,5,3,4,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,7,8,6,3,4,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,8,6,7,3,5,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,7,5,4,6,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,8,7,5,6,2,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,6,7,5,2,3]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,8,6,4,2,3]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,7,1,8,5,4,2,3]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,3,2,6,1,4,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,4,8,2,6,1,7,5]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,4,1,5,6,3,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,1,4,5,6,3,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,1,2,6,3,4,5]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,5,1,4,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,5,1,6,3,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,8,4,1,6,7,2]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,4,8,1,5,3,7]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,8,5,1,6,7,2]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,5,8,1,4,6,7,2]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,8,2,6,3,7,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,8,1,4,6,7,2]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,6,8,1,5,3,7]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,2,8,1,5,3,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,7,5,8,4,3,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,2,1,8,4,5,3,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,8,5,3,4,6]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[6,3,7,8,5,4,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[6,1,5,7,8,4,3,2]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,7,5,6,8,4,3,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,1,8,4,5,6,7,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,8,6,5,3,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,1,8,6,5,3,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,2,1,8,6,5,3,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[3,2,7,8,5,1,4,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[2,3,7,8,5,1,4,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,7,3,8,5,1,4,6]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,2,8,5,1,4,7]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[4,1,2,8,7,5,3,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,4,2,8,7,5,3,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,3,6,8,5,4,1,2]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,2,1,8,5,3,4,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[1,2,6,8,4,5,3,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,6,5,8,4,3,2]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,5,7,1,8,4,3,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,7,6,1,8,4,3,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,1,5,8,4,3,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,3,8,5,4,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,1,2,8,4,5,3,6]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,1,5,8,4,3,2]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,5,6,1,8,4,3,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,7,9,10,5,6,3,4,1,2]=>[[1,3,4],[2,6],[5,8],[7,10],[9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[7,1,6,5,3,2,4,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,8,7,5,3,2,4,6]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,8,7,4,2,5,3,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,7,4,2,5,3,6,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,6,4,2,5,3,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,4,7,1,3,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,1,5,3,6,4,2,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,1,6,4,2,8]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,6,4,2,7,1,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,8,7,4,2,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,4,2,8,6,3,5,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,6,1,8,7,4,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,3,8,7,4,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,8,7,5,4,6,1,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,1,8,7,5,4,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,3,8,7,4,2,1,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,4,2,1,8,6,3,5]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[8,6,3,5,7,4,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,8,6,3,5,7,4,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,3,8,5,2,1,7,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,6,3,7,4,2,1,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[2,8,6,4,7,5,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,8,6,3,7,4,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,4,1,8,5,2]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,2,6,3,7,4,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,7,4,2,5,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,6,3,7,4,2,5,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,6,3,2,4,7,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,6,3,2,4,7,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[7,5,1,8,6,3,2,4]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[6,1,8,7,5,3,2,4]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,3,2,8,7,6,1,5]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[2,4,5,1,3,8,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,6,3,2,4,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,5,8,6,3,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,4,2,5,8,6,3]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[8,6,3,1,7,4,2,5]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[8,7,4,2,5,3,1,6]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[5,3,1,8,7,4,2,6]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[4,1,8,7,5,3,2,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,8,6,4,1,3,7,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,1,8,6,3,2,7,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,4,2,8,6,3,1,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[6,3,1,8,5,2,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,2,6,3,1,7,4]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,8,5,2,6,3,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,2,7,4,6,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,5,2,7,4,6,3,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,3,1,8,5,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,3,1,7,4,8,5,2]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,3,1,5,7,4,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[4,1,7,5,8,6,3,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,3,1,7,5,8,6,4]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,8,5,2,1,6,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,5,2,1,7,4,6,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[1,7,4,6,3,8,5,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,8,5,7,3,2,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,5,7,8,4,3,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[5,1,7,4,8,3,2,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,2,8,3,6,1,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,2,7,3,1,8,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,2,7,6,5,10,9,8,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[1,4,3,6,5,2,10,9,8,7]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[1,4,3,7,6,2,10,9,8,5]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[1,5,4,7,6,3,10,9,8,2]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[1,4,3,8,7,2,10,9,6,5]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[1,5,4,8,7,3,10,9,6,2]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,3,1,6,5,4,10,9,8,7]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,3,1,7,6,5,10,9,8,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,4,1,6,5,3,10,9,8,7]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,4,1,7,6,3,10,9,8,5]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,5,1,7,6,4,10,9,8,3]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,4,1,8,7,3,10,9,6,5]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,5,1,8,7,4,10,9,6,3]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,4,2,6,5,1,10,9,8,7]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,4,2,7,6,1,10,9,8,5]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,5,2,7,6,1,10,9,8,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,5,3,7,6,2,10,9,8,1]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,4,2,8,7,1,10,9,6,5]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,5,2,8,7,1,10,9,6,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,5,3,8,7,2,10,9,6,1]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,5,1,6,4,3,10,9,8,7]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,5,1,7,4,3,10,9,8,6]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,6,1,7,5,4,10,9,8,3]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,5,1,8,4,3,10,9,7,6]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,6,1,8,5,4,10,9,7,3]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,5,2,6,4,1,10,9,8,7]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,5,2,7,4,1,10,9,8,6]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,6,2,7,5,1,10,9,8,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,6,3,7,5,2,10,9,8,1]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,5,2,8,4,1,10,9,7,6]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,6,2,8,5,1,10,9,7,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,6,3,8,5,2,10,9,7,1]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,7,2,8,6,1,10,9,5,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,7,3,8,6,2,10,9,5,1]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,5,1,9,4,3,10,8,7,6]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,6,1,9,5,4,10,8,7,3]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,5,2,9,4,1,10,8,7,6]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,6,2,9,5,1,10,8,7,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,6,3,9,5,2,10,8,7,1]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,7,2,9,6,1,10,8,5,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[6,2,8,4,1,7,3,5]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,4,8,1,7,2,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,8,5,4,2,3,7,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,5,4,8,1,2,7,6]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,3,8,7,1,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[2,6,8,4,1,7,3,5]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,7,4,2,6,3,5]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,3,5,8,7,1,2,4]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[5,2,8,6,7,1,3,4]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,8,7,5,1,3,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[1,8,5,7,6,2,3,4]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,6,7,8,5,1,2,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,8,6,7,5,2,3,4]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,7,6,4,8,1,2,3]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,3,8,7,5,1,2,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,8,7,4,1,3,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,4,8,7,1,3,2,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,6,1,3,2,5,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,4,2,7,6,8,1,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,8,7,1,4,5,3,6]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,2,1,8,7,3,5,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[5,1,6,3,2,8,7,4]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,8,7,3,2,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,7,2,3,5,4,1,6]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[5,3,1,4,8,7,2,6]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[4,3,5,2,8,7,1,6]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,2,8,6,1,5,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,6,8,1,5,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,4,2,3,6,7,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,7,2,1,8,6,4,5]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,6,1,7,3,5,4]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,6,3,5,8,2,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,5,1,6,8,2,4]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,6,5,8,1,4,7,2]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,5,6,4,7,2,3]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,6,7,4,1,8,2,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,7,4,6,8,2,5,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,8,2,6,3,1,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,1,6,5,4,8,3]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,2,6,1,8,5,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,7,2,3,1,8,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,1,8,4,6,2,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,8,1,6,7,4,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,4,3,6,8,1,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,4,6,1,5,3,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,1,6,3,2,5,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[4,7,3,8,5,2,1,6]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,1,7,4,8,5,2,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,1,6,3,2,8,5]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,8,6,2,7,4,1,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,1,4,5,2,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[6,1,4,8,5,3,2,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,1,2,4,6,7,5,3]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[8,1,3,6,7,5,4,2]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,5,2,3,8,6,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,6,2,4,1,3,7,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,7,5,1,8,6,3,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,2,8,5,6,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,5,7,6,1,3,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,4,2,3,6,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,4,6,1,7,5,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,4,6,5,2,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,7,6,1,5,8,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,1,4,5,7,6,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[3,5,1,6,8,4,7,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,5,7,3,8,4,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,4,7,3,2,6,1]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,6,5,8,4,1,3]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,2,5,1,6,7,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,6,8,3,7,4,1,5]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,5,6,4,7,3,2]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,8,1,6,4,7,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,1,8,3,2,6,5]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,4,2,1,6,5]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,2,6,8,3,1,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,5,8,4,1,7,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,6,1,8,4,5,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,3,4,6,5,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,2,5,6,4,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,3,1,6,4,8,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,3,2,4,8,7,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,4,2,3,6,1,5]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,7,1,5,4,2,3,6]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[3,7,1,5,2,8,6,4]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,2,5,4,1,3,6]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,7,2,5,3,1,4,6]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,2,8,7,1,4,3,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,6,2,4,3,5]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,6,2,7,5,3,4]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,6,2,8,5,3,4]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,4,1,7,2,8,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,4,3,5,1,8,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,2,3,8,6,4]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,5,1,7,6,4]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,1,4,8,2,5]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[6,1,8,2,7,5,3,4]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,8,1,6,5,3,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,4,3,8,1,5]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,7,4,3,8,2,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,1,7,4,8,2,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,8,2,1,5,3,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,2,4,1,6,3,7,5]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,5,1,6,4,3]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,7,3,2,8,5,4]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,2,1,6,3,8,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,1,5,3,8,4,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[5,3,1,6,2,8,4,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,2,8,4,3,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,3,8,1,5,2,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,4,8,1,5,3,2,6]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,3,2,8,4,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,3,2,8,4,1,5,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,3,4,2,8,5,1,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,6,3,4,2,8,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,1,3,7,4,2,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[3,8,6,1,5,2,7,4]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,1,3,7,5,2,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[4,8,5,6,1,7,3,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,3,8,5,2,4]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,6,7,1,5,2,8,4]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,3,8,4,2,6,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,2,7,1,3,8,4]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,2,8,1,3,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,8,3,7,5,2,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,2,1,5,8,3,6]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[7,4,1,5,8,3,2,6]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[7,3,2,6,4,8,1,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,7,3,8,1,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,8,3,7,4,2,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,3,1,5,2,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,2,1,7,4,8,3,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,4,5,2,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,6,4,5,2,8,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,2,7,1,6,8,4]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,7,3,1,6,8,2]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,7,2,8,6,1,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,1,7,2,6,8,4]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,7,2,8,1,3,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,2,1,5,8,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,7,1,3,8,5,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,5,7,8,4,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,6,7,1,5,8,3,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,7,4,8,5,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,7,4,8,5,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,2,7,6,3,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,1,3,7,6,4,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,4,3,8,6,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,2,1,5,8,6,4]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[6,2,7,1,4,8,5,3]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,4,2,1,8,5,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,2,5,3,1,8,6,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,4,2,8,6,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,4,1,3,8,6,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[5,3,2,1,7,6,4,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[6,3,2,8,1,5,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,4,3,2,8,1,6,5]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,2,4,8,3,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,3,6,4,8,1,5,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,5,3,8,1,4,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,5,3,6,4,2,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,6,2,3,7,5,4,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,6,3,2,7,5,4,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[8,3,2,7,1,6,4,5]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,2,6,1,5,4,3,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,4,3,6,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,2,4,6,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,6,7,1,3,2,5]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,8,5,6,1,4,3,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,2,6,8,4,1,5,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,6,4,8,3,2,5,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,8,1,4,2,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,4,1,3,7,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,8,3,2,1,7,6]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,3,7,2,1,6,5,8]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,5,8,1,4,3,7,6]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,8,2,1,5,7,4]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,4,8,1,3,6,2]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,1,4,8,2,6,3]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,4,1,8,3,6,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,1,8,4,2,7,6]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,5,7,3,6,2,8]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,8,3,1,7,6]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,7,8,3,5,4]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,1,8,6,4,2,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[3,1,8,4,7,5,2,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,7,3,5,1,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,1,7,6,2,3,5]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,1,4,7,5,2,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,1,6,4,2,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,8,1,5,3,2,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,6,2,5,3,4]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,1,3,6,4,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,2,1,6,4,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,1,6,3,5,4]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,6,1,5,4,2,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,6,1,3,5,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,2,6,1,4,3]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,1,7,5,2,4,3]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,8,6,5,1,2,4]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[5,7,8,4,3,1,2,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[5,8,6,4,3,2,1,7]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[8,7,3,6,4,2,1,5]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,1,4,2,5,3,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,3,7,5,4,2,8,6]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,1,3,5,4,2,7,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[6,1,2,5,4,7,3,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,6,3,4,7,8,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,2,6,3,4,7,1,8]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,5,8,6,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,7,1,5,3,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,6,7,4,8,1,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,7,4,8,5,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,7,6,5,3,1,8,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,2,6,1,4,7,8,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,6,5,2,1,8,3]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,3,6,2,4,1,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,4,2,1,3,6,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[6,3,1,5,4,7,8,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,6,1,4,2,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,4,2,6,3,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,4,1,2,3,6,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[6,4,1,2,5,3,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[4,7,6,3,8,5,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,6,5,2,8,1,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,5,1,2,8,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,7,2,6,1,3,8,5]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,1,6,8,3,5,4]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,6,5,8,1,4,3]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[9,1,2,3,4,5,6,8,7]=>[[1,3,4,5,6,7,8],[2],[9]]=>[8,1]=>[8,1]=>2
[10,1,2,3,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[9,1]=>[9,1]=>2
[9,1,2,3,4,5,7,8,6]=>[[1,3,4,5,6,7,8],[2],[9]]=>[8,1]=>[8,1]=>2
[2,3,4,5,6,7,8,10,9,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[3,9,2,8,7,6,5,4,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[2,2,5]=>[5,2,2]=>3
[5,2,8,7,6,4,3,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[8,2,7,6,1,5,4,3]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[9,2,8,1,7,6,5,4,3]=>[[1,3],[2,5],[4],[6],[7],[8],[9]]=>[3,2,4]=>[4,3,2]=>3
[8,4,1,7,6,5,3,2]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,5,6,2,3,8,1,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,3,2,7,8,1,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,7,3,8,4,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,8,7,2,4,3,5,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,7,4,5,8,1,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,5,2,4,3,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,3,4,6,1,5,2,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,7,5,8,1,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,7,8,2,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,7,4,8,6,1,2]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[8,3,6,4,1,7,2,5]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,4,8,6,2,5]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,7,8,5,4,1,2,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[5,4,3,1,7,8,2,6]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[5,7,6,2,8,4,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,7,5,8,3,4,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,6,4,1,3,8,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,6,8,4,7,3,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,3,7,6,5,8,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,1,7,5,8,6,2]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,7,4,3,1,6,2]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,8,5,1,7,2,4,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,4,1,3,7,6,5]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,3,6,2,1,4,5]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,1,7,4,2,3,6,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,8,7,2,3,5,6,4]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,3,1,6,7,5,4]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,2,3,1,5,7,6,4]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,4,1,2,7,6,5]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,7,2,3,6,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,2,1,8,4,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[2,3,7,4,1,8,5,6]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,1,3,2,7,8,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,7,8,5,1,3,6,4]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,5,6,7,1,3,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[2,8,5,4,7,6,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,1,5,8,2,4,3]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,7,6,2,3,5,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,1,5,3,2,6,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,7,3,8,2,1,4]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,7,2,5,6,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,4,6,1,5,8,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,4,5,7,1,6,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,2,6,8,3,1,5,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,7,6,2,4,5,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,6,5,8,1,4,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,5,8,6,1,4,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[4,2,3,8,6,1,5,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[6,4,1,2,8,3,5,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[1,2,3,7,4,6,8,5]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,7,1,4,5,8,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,1,5,3,8,7,4,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,3,2,4,1,6,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,7,1,8,3,5,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,1,8,2,7,3,5,6]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,5,3,8,4,6]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,1,4,8,5,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,7,6,8,4,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,6,8,7,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,3,7,8,4,6,5]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,6,8,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,7,8,6,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[6,2,8,3,7,5,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,3,7,5,6,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,4,8,6,5,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[5,3,4,8,7,2,6,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,5,8,7,2,6,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,8,5,7,2,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,3,8,6,2,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,8,3,7,4,5,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,4,3,7,5,6,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,8,3,7,4,6,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,3,8,6,2,5,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,4,8,7,2,6,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,3,8,6,7,2,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,7,8,4,5,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,8,5,4,7,3,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,6,4,7,3,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,8,6,4,7,3,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,6,5,8,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,7,8,4,5,2,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,7,8,5,6,2,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,6,4,7,3,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,6,5,7,3,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,6,7,4,5,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,8,7,5,4,6,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,2,7,4,5,6,3]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,8,6,3,4,5,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,8,4,5,7,3,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,4,6,7,3,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,5,6,7,3,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,8,5,7,2,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,8,7,2,5,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,5,8,6,2,4,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,3,5,7,4,6,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,8,4,5,6,3,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,8,4,6,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,4,6,8,3,2,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,6,5,8,4,7,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,8,4,5,7,3,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,1,3,8,5,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,2,5,1,3,8,6,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,1,7,2,4,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,2,5,8,6,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,4,1,2,8,5,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,5,1,3,4,8,6,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[7,5,1,2,4,8,6,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[6,4,2,3,7,1,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,6,3,8,1,2,5,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,4,2,3,8,1,6,5]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,7,5,2,8,1,3,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,2,6,3,7,1,4,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,2,7,4,5,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,7,1,2,3,6,5]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,7,1,2,4,6,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,7,1,3,4,6,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,2,7,1,3,5,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,8,5,6,1,2,4,7]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,7,5,8,1,2,4,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,6,4,8,1,3,5,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,8,1,2,4,7,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,8,1,2,5,7,4]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,2,4,8,1,6,5]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,3,8,1,2,5,7]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,6,3,7,1,2,5,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,1,7,8,2,3,6,5]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,8,6,3,4,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[5,3,8,1,6,2,4,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,8,5,2,3,4,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[6,1,7,5,2,3,4,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[6,8,1,3,7,4,5,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,8,1,6,3,4,5]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,8,2,5,1,3,6]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,2,7,1,4,5,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,7,1,3,5,6,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,7,1,2,4,6,5]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,8,7,1,2,3,6,5]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,1,2,4,6,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,1,3,4,6,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,1,8,6,2,3,5,4]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,6,4,1,2,3,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[7,8,4,1,2,5,3,6]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,1,2,6,5,3,4]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,8,2,7,5,3,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,3,4,7,2,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[7,8,2,1,6,3,5,4]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,2,7,5,4,3,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,8,7,5,4,3,6]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[5,1,7,3,6,4,8,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,1,5,7,4,3,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[6,2,3,7,4,1,5,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[3,4,8,7,5,6,1,2]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,7,4,1,5,6]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,7,3,8,6,4,1,5]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,3,7,6,4,5,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,7,1,4,6,8,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,7,5,2,1,8,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,3,1,4,5,7,8,2]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[5,3,1,4,6,2,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[5,1,2,4,7,6,8,3]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,7,4,1,2,6,3,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,2,6,7,3,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,7,8,2,6,3,5]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,8,7,6,5,3,4]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,1,2,4,6,8,7,5]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[3,1,8,4,5,7,6,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,5,4,7,1,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,1,5,3,7,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,8,5,7,6,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,2,1,6,3,7,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,6,5,2,7,1,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,5,6,1,7,4,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,7,8,1,2,6,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,8,5,2,1,6,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,7,2,8,4,1,6,5]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,1,7,4,6,5,3]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,7,5,1,6,4,3]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,6,7,5,1,4,3]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,3,4,6,7,2,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[1,3,4,8,7,5,2,6]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,4,1,7,3,5,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,4,2,3,7,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,6,1,4,2,8,7,5]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,8,4,3,7,2,5]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,4,7,8,5,2,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[6,1,7,4,3,8,2,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,7,4,3,6,2,5]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,4,1,3,8,2,6,5]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,8,2,3,1,5,7,6]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,2,1,3,7,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,7,4,1,8,3,5,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,7,8,4,2,3,6,5]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,1,3,8,2,6,5]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,1,3,4,2,6,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,7,4,3,6,2,8,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,6,4,5,2,1,7]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,4,6,5,2,1,7]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,4,3,7,5,8,1,6]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,7,3,6,2,8,5]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,3,4,2,6,7,5]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,1,3,7,2,8,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,1,4,3,6,2,7,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,3,8,5,7,1,6]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,5,7,3,4,1,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,6,4,3,1,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,2,5,8,4,3,1,6]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,2,3,5,8,7,1,6]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[8,2,3,5,4,7,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,3,4,2,7,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,6,4,2,3,7,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,8,4,5,6,2,1,7]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,3,5,7,8,1,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,6,5,4,2,1,7]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[6,3,1,4,2,8,7,5]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,8,1,2,6,4,5]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,4,5,3,2,6,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[1,8,4,2,6,5,3,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,4,8,6,3,2,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,3,1,8,4,7,2,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,8,1,5,7,2,6]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,1,2,5,7,4,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[7,1,4,2,6,5,3,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,4,1,6,5,2,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,6,4,5,8,2,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,2,4,5,1,6,3]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,5,4,8,6,3,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,8,7,5,3,6,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,8,3,7,4,1,6,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,1,4,8,6,3,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,7,4,8,6,2,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,4,8,6,2,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,4,1,6,3,2]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,4,5,1,6,3]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,3,8,4,1,6,2]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,3,8,1,4,7,2]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,8,4,1,6,5,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,3,1,5,4,2,6]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[3,6,2,1,5,4,8,7]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,2,6,1,3,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,5,1,4,8,7]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[2,5,8,1,7,4,3,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,2,7,4,3,1,5]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,8,2,3,7,5,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,2,5,4,8,1,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,6,5,1,8,4,3,7]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,7,3,1,8,5,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,2,3,7,1,5,8,6]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,2,7,3,8,6,1,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,1,5,8,4,3,7,6]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,4,2,6,7,1,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,2,4,8,1,5,7,6]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,8,3,1,7,5,6]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,3,2,1,7,6,5]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[4,1,3,7,2,6,8,5]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,8,2,1,6,5,7]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,7,2,1,5,4]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,8,1,7,2,6,4]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,7,4,6,8,3,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,8,1,5,3,2]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,1,8,2,6,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,6,3,8,1,4,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,7,6,4,8,3,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,4,8,7,3,6]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,7,2,6,1,3]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,3,8,7,1,5,6]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,4,1,8,6,2,7,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,5,4,2,1,7,6]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[4,8,6,5,2,7,1,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,2,8,7,5,4,1,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,8,6,5,4,3,1,7]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[5,4,2,6,3,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,6,5,2,8,4,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,2,3,4,8,5,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[8,7,5,3,1,4,2,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,1,5,3,8,4,6,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,6,4,2,8,5,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,1,8,7,4,3,5,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,8,7,4,2,1,5,6]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,5,2,6,1,7,3,4]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,6,8,3,7,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,2,8,1,4,3,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,7,8,4,5,1,3,6]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,8,1,5,2,7,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,1,2,5,3,6,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,1,2,4,3,5,6,7]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[5,8,7,4,6,3,2,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,7,6,3,5,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,6,5,2,4,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,9,6,8,5,4,3,2,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[2,2,5]=>[5,2,2]=>3
[5,8,4,7,6,3,2,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,8,5,4,7,3,2,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,6,2,5,4,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,6,3,2,5,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,9,8,7,6,5,2,4,1]=>[[1,2],[3,8],[4],[5],[6],[7],[9]]=>[2,6,1]=>[6,2,1]=>3
[3,8,7,6,5,2,1,4]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[8,6,9,4,7,3,5,1,2]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[3,2,2,2]=>[3,2,2,2]=>4
[8,6,9,5,7,3,4,1,2]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[3,2,2,2]=>[3,2,2,2]=>4
[8,7,9,5,6,3,4,1,2]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[3,2,2,2]=>[3,2,2,2]=>4
[7,5,8,4,6,3,1,2]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,9,4,7,3,5,2,1]=>[[1,3],[2,5],[4,7],[6],[8],[9]]=>[3,2,2,2]=>[3,2,2,2]=>4
[9,7,10,5,8,3,6,2,4,1]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[8,6,9,5,7,2,4,1,3]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[3,2,2,2]=>[3,2,2,2]=>4
[9,7,10,5,8,4,6,2,3,1]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[7,6,8,2,5,1,4,3]=>[[1,3],[2,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,9,4,6,3,5,1,2]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[3,2,2,2]=>[3,2,2,2]=>4
[9,7,10,6,8,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[9,6,8,5,7,3,4,1,2]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[3,2,2,2]=>[3,2,2,2]=>4
[9,8,10,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[3,5,2,4,7,6,1,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,4,7,2,6,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,4,7,6,1,2,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,5,4,7,6,1,8,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,7,4,6,1,8,2]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,7,4,6,1,2,8]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,7,4,6,2,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,7,4,6,1,8]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,2,7,6,4,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,5,7,2,6,4,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,6,2,4,1,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,6,1,2,8,4]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[5,3,7,6,1,4,2,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,6,4,1,2,8]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[3,5,7,2,6,1,4,8]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,2,7,6,1,4,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[5,3,7,6,4,1,8,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,7,5,4,1,8,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,7,5,4,1,8,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,7,5,1,4,8,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,5,1,4,8,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,7,1,2,6,8,4]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,2,1,6,8,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,2,7,1,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,7,2,1,6,4,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,1,6,2,4,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,7,1,4,6,8,2]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,1,4,6,2,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,1,4,2,6,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,7,2,1,4,6,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[3,5,2,7,1,4,6,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,2,5,7,4,1,6,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,5,2,7,4,1,6,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,5,7,4,2,1,6,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[3,5,7,4,1,2,6,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[3,5,4,7,1,6,8,2]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,4,7,1,2,6,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,5,4,7,2,1,6,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,5,4,2,7,1,6,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,5,4,7,1,6,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,4,7,2,1,8,6]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,4,7,1,2,8,6]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,6,3,1,8,4,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,3,1,8,2,4]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,5,7,4,1,2,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,4,2,1,8,6]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,2,5,7,4,1,8,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,7,1,4,8,6]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,5,2,7,1,4,8,6]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,7,2,1,4,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,5,7,1,4,2,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,5,2,1,8,6,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,7,2,5,1,8,6,4]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,7,5,1,8,6,4]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,5,1,8,4,6]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,2,5,1,8,4,6]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,5,2,1,8,4,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,1,7,5,8,4,6,3]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,4,5,6,7,9,2,8]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[2,1,4,5,6,7,8,9,3]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[5,8,3,4,1,7,6,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,7,2,4,1,6,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,6,4,1,7,5,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,3,5,6,8,1,7,2]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,7,6,4,1,8,5,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,7,4,1,8,6,5,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,8,4,1,7,6,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,2,7,6,1,5,4,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,7,6,1,5,4]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,2,4,1,6,3]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,8,1,6,7,3]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,5,8,1,7,3,6]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,8,2,4,1,6,3,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,2,6,5,1,3,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[3,2,6,8,1,5,4,7]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,2,5,6,1,4,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,2,8,6,7,1,5,4]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,6,8,7,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,7,1,5,4,8]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,2,5,6,1,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,2,8,1,5,3,6,4]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,2,7,5,1,3,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,4,2,8,5,1,3,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,2,4,1,8,3,6,5]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,5,7,1,4,6]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,5,7,1,8,3,4]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,1,8,7,4,3,6]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,1,4,6,3,5,2,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,5,4,1,6,2,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,4,1,5,2,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,4,7,6,8,2,3,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,2,3,7,6,5]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,5,3,4,7,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,2,4,6,8,7,3,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,6,8,3,4,5,7,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,4,8,6,1,3,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,2,6,7,8,1,3]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[6,4,2,7,3,5,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,1,8,3,5,6,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,8,7,3,1,2]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,4,2,1,3,6,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,7,1,3,2,5,6,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,8,2,3,1,7,5,4]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,3,2,6,8,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[2,7,4,3,8,5,6,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,7,2,1,5,6,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,2,4,3,1,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,3,2,6,1,5]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,1,6,7,4,2,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[3,2,5,7,4,8,1,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,7,3,4,1,5,6]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,6,3,5,8,2,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,5,6,7,1,4,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,2,7,8,6,4,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,6,8,5,1,4,7,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,2,8,6,5,7,3]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,1,6,8,7,2,4]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,6,2,1,3,8,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,5,8,7,4,1,6,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,1,7,5,2,6,8,3]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,6,2,4,5,1,8,3]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,3,4,2,5,8,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,4,2,5,1,6,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,1,4,5,2,6,7,3]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,2,4,8,6,7,1,3]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,6,2,1,3,7,4]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,2,1,5,6,7,8,3]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[3,4,6,5,1,7,8,2]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,3,5,2,4,6,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,7,2,4,6,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,2,4,6,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,2,4,6,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,5,3,2,4,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,5,3,2,7,4,6,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[5,7,3,2,1,4,6,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,7,3,2,4,1,6,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,2,5,4,1,6,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,1,3,2,4,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,1,3,2,7,4,6,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,1,3,2,5,4,6,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,2,5,4,6,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,1,3,5,2,4,6,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[5,1,3,7,2,4,6,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[3,2,7,5,1,4,6,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[3,7,5,1,2,4,6,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[5,7,3,1,2,4,6,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[1,5,3,7,2,4,6,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,3,2,7,4,1,6,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[5,3,2,4,7,1,6,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[5,3,2,1,4,7,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[5,3,2,1,7,4,6,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[1,3,2,7,5,4,6,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,3,7,2,5,4,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,3,1,2,5,4,6,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[5,3,1,2,7,4,6,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[5,3,1,2,4,7,6,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[3,2,5,1,4,7,6,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,3,1,5,2,4,6,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[1,3,7,5,2,4,6,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[7,5,1,3,2,4,6,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[5,7,1,3,2,4,6,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,7,1,5,2,4,6,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,7,1,2,5,4,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,2,1,5,4,6,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,1,7,5,4,6,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[3,1,2,7,5,4,6,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[3,1,7,2,5,4,6,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,7,5,2,4,6,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[7,1,5,3,2,4,6,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[1,7,5,3,2,4,6,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,2,3,4,5,7,9,6,8]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[1,2,3,4,6,9,5,7,8]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[1,2,4,9,3,5,6,7,8]=>[[1,2,3,4,7,8,9],[5,6]]=>[4,5]=>[5,4]=>2
[1,3,9,2,4,5,6,7,8]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]=>[6,3]=>2
[1,8,7,4,2,6,5,3]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,1,7,6,4,3]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,1,2,7,4,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,10,1,9,8,7,6,5,4,3]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[2,2,6]=>[6,2,2]=>3
[2,8,1,4,7,6,5,3]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,7,4,3,2,6,5]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,8,5,4,2,7,6,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,5,6,3,7,4,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,6,2,7,4,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,7,6,3,4,1,5,2]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,7,2,3,6,8,5,4]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,4,8,2,7,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,1,4,8,2,7,6]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,5,4,8,2,6,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,5,1,6,4,8,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,5,4,8,1,3,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,7,5,4,8,6,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,5,4,8,6,3,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,4,8,7,3,6]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,6,4,2,8,7,1,5]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,4,8,1,6,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,4,8,1,2,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,5,6,4,8,7,2,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,6,4,1,8,7,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,4,5,8,7,2,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,6,4,3,8,5,2,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,3,4,5,8,2,6]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[7,6,1,4,5,3,8,2]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,1,3,5,4,8,2]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,3,2,5,8,4,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,6,4,2,8,5,3,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,5,8,2,4,3,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,8,3,1,4,2]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,6,4,3,8,1,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,3,8,5,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,3,1,5,8,6,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,5,6,3,8,4,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,6,5,1,4,8,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,6,5,3,8,1,4]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,3,1,4,8,6,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,3,5,4,8,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,4,5,8,1,7,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,6,4,8,3,7,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,6,4,8,3,1,7]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,1,4,7,8,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,1,3,4,5,8,2]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[7,1,3,2,4,8,5,6]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,6,1,5,3,4,8,2]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,1,5,4,3,8,2]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,4,5,8,3,2,7]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,5,8,1,3,2,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,8,7,2,1,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,5,6,8,2,1,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,1,5,3,7,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[4,2,5,6,3,1,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,5,6,8,1,7,2,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,5,6,3,2,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,5,3,1,7,2,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,3,5,2,7,8,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,5,4,7,3,8,6,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,7,1,8,4,2,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,5,3,2,7,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,5,3,7,1,2,8,6]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,6,1,2,7,5,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,1,3,2,4,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[3,6,1,7,4,5,2,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,3,4,2,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[5,3,1,4,2,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[4,5,2,3,7,1,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,6,1,3,7,5,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,6,2,1,3,7,5,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,6,2,1,7,4,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,4,7,6,5,2,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,6,2,7,1,5,8,4]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,2,7,1,3,5,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,5,7,1,8,2,6,4]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,4,2,3,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[3,6,1,7,2,5,8,4]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,5,3,4,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,6,1,7,5,4,2,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,1,4,3,2,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[5,4,1,3,2,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[6,2,4,5,1,8,3,7]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,1,4,8,6,3,7,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,2,5,3,7,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,2,4,7,5,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[4,6,8,2,3,5,7,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,8,1,4,5,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,2,6,7,3,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[7,6,4,5,1,3,8,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,7,5,3,4,8,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,2,3,8,4,1,5]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[1,6,7,5,8,2,3,4]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,2,5,8,3,4,7,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,3,8,7,4,1,5]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,7,3,5,8,6,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,3,7,1,8,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,8,3,1,4,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[4,8,2,3,6,5,7,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,1,3,6,4,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,1,4,3,6,2,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,1,3,7,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,4,5,3,8,1,7,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,5,3,7,1,2,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,5,1,3,6,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,6,5,1,7,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,5,7,2,1,6,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[3,4,7,6,8,1,2,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,4,6,2,5,8,7,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,4,6,1,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,5,1,6,8,3,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,8,2,3,6,5,7,4]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,8,3,5,7,1,6]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,8,6,5,7,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,2,6,5,8,4]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,6,4,2,5,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,5,4,7,3,6,8,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,3,8,4,1,7,6]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,4,8,2,1,6]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,2,8,3,4,1,5,6]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,3,8,5,2,6,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,2,7,3,1,5,8]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,3,8,2,4,5,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,8,5,1,3,4,6]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[1,5,3,7,6,8,4,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,3,7,8,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,4,3,7,8,5,2,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,6,5,7,8,3,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,7,5,8,1,3]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,4,7,8,5,1,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,2,6,7,8,1,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[5,1,8,3,6,4,7,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,5,6,1,7,2,4]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,8,1,7,6,2,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,6,8,5,1,3,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,8,5,1,3,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,8,3,1,7,5,2]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,5,8,7,1,4,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,4,8,2,6,3,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,4,8,2,7,3,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,5,3,8,2,7,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,8,1,3,7,5,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,3,1,4,2,5,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[1,5,4,3,7,8,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,2,5,3,1,6]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,7,8,5,3,1,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,2,5,3,1,7,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,7,6,3,1,5]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,2,7,6,3,1,5,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,3,1,7,5,2,4,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[6,3,1,8,7,5,2,4]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[8,6,3,1,7,5,2,4]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[4,2,7,6,3,1,8,5]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,6,3,1,8,4,2,5]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,6,4,2,1,8,3,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[1,8,2,7,6,4,3,5]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,3,5,7,6,4,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,4,2,5,7,6,3,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[7,5,2,4,8,6,3,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,7,5,2,4,6,3,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[7,5,2,4,6,3,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[5,2,8,6,3,7,4,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,5,2,6,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,6,4,7,5,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,8,2,7,5,3,6,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,2,1,8,3,6,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,2,6,3,1,8,4]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,2,7,4,1,8,6,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,7,4,1,6,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,7,4,1,5,2,6,3]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,4,1,5,2,8,6,3]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,1,4,2,8,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,2,8,6,3,1,4]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[8,7,5,2,6,3,1,4]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[7,5,2,1,3,6,4,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,7,5,2,1,3,6,4]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[7,5,2,1,3,8,6,4]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[1,3,7,6,5,8,2,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,4,7,5,2,1,3]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,4,8,7,5,2,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[6,4,7,5,2,1,3,8]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,3,1,4,7,5,2,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[6,3,1,4,8,7,5,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[8,6,3,1,4,7,5,2]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[8,5,7,6,3,1,4,2]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,8,2,5,7,6,4,3]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,6,4,7,5,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,2,1,6,4,8,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,3,8,7,4,1,5,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,3,7,4,1,5,2,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,1,6,3,5,2,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,1,8,6,3,5,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,3,1,7,5,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,5,2,1,8,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,6,4,7,5,3,8,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,6,3,5,2,7,4,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,2,8,7,4,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,5,2,7,4,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,7,3,5,2,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,4,2,6,3,1,8]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,6,3,5,7,1,8]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,8,1,6,7,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,3,7,4,2,5,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[3,2,6,8,1,5,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,6,1,5,4,7,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,2,7,1,5,4,3]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,8,3,1,5,4,2]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,7,2,8,1,5,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,2,8,6,1,4,3]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,3,8,1,5,6,4]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,8,5,2,4,3,7]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,2,8,1,6,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,6,5,3,1,7,2]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,5,3,1,7,2,6,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,8,1,2,4,3,6,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,1,6,2,3,7,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,1,3,4,2,8,5,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,3,5,7,6,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,1,3,7,8,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[1,7,4,3,6,8,2,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,1,3,6,5,4,2]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,8,5,7,4,2,6,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,5,3,8,2,1,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,5,4,7,2,6,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,5,8,7,4,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[1,4,8,7,3,5,6,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,7,6,3,5,4,2]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,5,7,4,1,2]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,6,8,5,3,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,8,7,5,6,4,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,6,4,5,3,1]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,6,5,3,4,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,6,7,2,5,3,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,7,8,1,6,5,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,6,8,7,1,5,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,8,4,2,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,8,1,6,5,4]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,8,4,1,7,5,3]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,1,2,8,5,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,8,2,7,5,4]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,4,1,2,8,6,3]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[6,3,7,1,2,8,5,4]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,5,4,3,2,6]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,2,6,7,8,4,3,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[8,1,4,6,7,3,5,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,7,1,3,6,8,2,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,4,8,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,4,2,1,8,6]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,3,6,7,4,2,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,6,4,8,2,7,5,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,6,7,5,3,2,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,2,4,6,5,3,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,7,8,2,6,4,5,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,2,5,4,6,1,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,2,1,5,6,4]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[3,7,8,2,1,6,5,4]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,1,4,5,3,2]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[4,8,1,2,3,7,5,6]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,2,3,6,5,4,7]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,8,4,7,2,6,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,5,4,6,2,3,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,5,4,6,1,2,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,5,1,6,4,2,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,5,4,6,1,3,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,8,5,4,6,3,1,7]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,5,4,6,3,2,7]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,8,4,7,3,6,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,4,2,7,8,5,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,4,1,6,2,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[4,5,8,1,7,6,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,8,4,7,1,6,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,8,4,7,3,6,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,4,1,7,8,5,2]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,4,8,7,5,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,3,7,8,5,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,1,3,4,8,6,5,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,6,1,3,8,4,2,5]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[1,6,4,2,7,8,3,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,6,4,3,7,1,8,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,1,7,8,3,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,2,3,4,8,6,5,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,2,3,1,8,6,4,5]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,3,4,1,6,8,5]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,2,4,3,8,5,7,6]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,6,1,4,2,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,6,3,4,1,5]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,3,1,5,6,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,2,3,8,1,6,5,4]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,8,5,6,4,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,4,8,7,1,5,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,8,4,7,6,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,8,1,6,7,2,4]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,1,3,5,8,2,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,1,3,2,5,6,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,1,3,8,2,6,5,4]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,1,8,5,4,2,3]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[3,2,6,5,8,4,7,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,1,6,5,8,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,4,8,3,7,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,5,8,2,6,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,7,4,8,2,6,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,7,4,8,1,6,2]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,1,5,2,8,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,2,6,3,7,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,1,6,3,7,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,5,2,3,6,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[4,1,7,8,6,3,2,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,8,3,2,1,4,7,5]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,2,4,1,6,5,8,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,8,4,3,1,6,2]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,8,2,4,1,3,7,5]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,7,6,3,5,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,2,7,5,8,4,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,7,3,8,5,6,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,2,6,8,3,7,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,2,5,7,6,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,5,3,4,7,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,4,1,5,3,7,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,4,7,6,2,5,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,3,5,2,6,7,4]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,3,5,1,4,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,5,4,2,3,7,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,8,2,4,3,7,6,1]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,3,4,2,6,5,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,2,5,6,4,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,4,5,3,7,6]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[10,1,2,3,4,6,7,8,9,5]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[9,1]=>[9,1]=>2
[6,5,3,8,4,2,7,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,5,1,6,2,8,3]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,3,5,6,2,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,8,4,1,3,5,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,6,8,4,7,5,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,3,6,1,5,7,4,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,5,8,6,1,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,4,7,8,1,6,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,6,7,8,1,5,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,6,8,1,7,5,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,3,8,6,2,1,5]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,7,8,3,5,6,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,7,6,1,8,4,5]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,6,8,1,7,4,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,6,2,1,8,5,7]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,2,3,7,5,8,1]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,4,2,3,6,7,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,4,5,3,2,1,7,6]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,8,3,4,2,1,7,6]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,4,2,3,7,5,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,4,8,3,2,7,1,5]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,7,2,1,6,4]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,6,4,7,1,8,3]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,3,8,2,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,4,3,2,1,8,5]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[8,4,3,7,2,1,5,6]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[1,2,6,5,8,7,3,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,5,2,8,4,6,7,3]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,2,7,4,6,8,3]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,2,7,3,6,8,4]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,8,3,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,3,4,8,7,2,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,5,3,4,8,7,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[4,1,2,8,3,6,7,5]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,2,7,3,6,8,5]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,8,4,6,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,3,7,4,6,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,1,2,3,4,7,6]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,1,2,8,3,6,4,5]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,2,3,5,7,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,7,2,3,5,8,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,8,2,4,5,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,8,7,5,6,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,2,7,4,6,5,3]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,6,2,3,5,8,4]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,2,3,5,7,4]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,7,2,3,5,6,4]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,3,7,4,6,2,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,7,3,4,5,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,2,4,5,3,6]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,1,2,3,4,6,5]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[8,6,1,2,3,4,7,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[8,1,6,2,3,5,4,7]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,6,2,4,5,3,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,4,6,3,5,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,5,7,2,6,4]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,4,6,8,5,7,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,5,7,4,8,6,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,3,7,8,5,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,1,8,6,3,4]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,7,1,8,4,5,3]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,3,1,4,2,6,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,4,2,6,7,1,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,4,1,8,5,6,3,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,7,8,5,3,4]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,6,7,8,4,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,1,6,7,3,8,2]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,1,7,5,3,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,5,3,1,7,4,2,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[4,2,8,7,1,5,3,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,6,8,1,7,4,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,3,2,6,8,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,4,7,3,1,6,2,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,7,1,2,3,5,8,4]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,6,7,8,4,2,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[3,1,4,8,5,6,2,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,1,4,5,7,2,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[1,6,7,8,9,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[6,7,8,9,1,2,3,4,5,10]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]=>[6,4]=>2
[6,7,8,1,2,3,4,5,9]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[1,7,8,9,2,3,4,5,6]=>[[1,2,3,4,8,9],[5,6,7]]=>[4,5]=>[5,4]=>2
[1,7,8,9,10,2,3,4,5,6]=>[[1,2,3,4,5,10],[6,7,8,9]]=>[5,5]=>[5,5]=>2
[5,6,7,8,9,1,2,3,4,10]=>[[1,2,3,4,5,10],[6,7,8,9]]=>[5,5]=>[5,5]=>2
[4,6,7,8,1,2,3,5,9]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]=>[5,4]=>2
[1,5,7,8,9,2,3,4,6]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[1,6,7,8,9,10,2,3,4,5]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[6,4]=>2
[8,6,2,3,5,1,4,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[8,2,4,5,7,3,1,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[2,6,3,8,7,5,4,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[8,2,3,7,5,4,1,6]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,6,3,5,4,1,7]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,5,2,4,3,7]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,2,4,1,5,3,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,6,5,3,2,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,6,1,5,4,2,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,2,6,5,4,1,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,2,5,7,4,1,6]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[8,3,1,7,5,4,2,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,7,4,1,5,3,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,8,7,5,4,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,6,1,8,7,5,4,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,8,1,5,7,6,4,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,8,7,6,4,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,4,8,2,7,6,5,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,8,7,1,6,5,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,3,5,7,6,4,2]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[4,1,8,5,7,6,3,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,1,4,5,6,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,7,3,4,6,2,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,1,7,2,6,5,4]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,8,2,4,7,6,5,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,3,7,4,6,5,1]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,3,7,1,6,5,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,7,1,3,6,5,4]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,2,6,4,3,5]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,5,2,4,3,6]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,7,4,6,1,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,8,5,7,6,3,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,4,3,7,6,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,3,5,1,4,6]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,4,3,1,5,6]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,2,7,3,1,5,6,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,2,1,5,7,6,4,3]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[6,2,1,8,7,5,4,3]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,1,8,2,7,5,4,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,3,5,2,6,4]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,5,2,7,6,4,3]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,2,4,6,5,3]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,4,1,7,6,5,3]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,3,7,6,5,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,8,2,1,7,6,5,3]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,1,8,7,2,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,1,3,7,6,2,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,5,4,1,7,6,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,8,7,6,3,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,1,4,3,7,6,5,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,8,1,3,7,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,3,8,1,7,6,5,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,8,6,3,2,1,7,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,7,6,3,2,4,1,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,7,2,4,3,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,1,3,2,8,6,4]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,3,2,7,4,6]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,1,3,2,4,6,7]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[7,5,8,2,1,4,3,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,7,1,2,5,4,8,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,1,2,5,7,4,3]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,4,2,3,5,7]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[1,5,4,8,2,3,7,6]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,8,2,3,5,6,4]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,2,3,1,4,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,1,2,6,8,3,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[6,2,8,1,5,7,3,4]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,4,2,1,8,6]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,3,2,8,5,6,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,4,3,6,8,5,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,6,5,2,3,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,7,6,5,1,3,8,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,7,4,2,1,8,5,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,3,2,8,4,5]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,5,8,1,7,3,4,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,2,3,7,4,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,8,5,3,6,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[3,5,8,2,6,1,7,4]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,6,1,5,2,8,4]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,6,2,5,8,4,3]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,5,8,4,2,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,6,2,8,4,5,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,6,8,5,1,2,7]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[2,7,1,5,8,4,3,6]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,6,1,8,4,3,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,2,6,3,5,4,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,6,3,4,5,1,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,4,2,5,3,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,2,5,7,8,4,3]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[4,1,2,7,8,5,3,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,7,3,1,2,6,8,5]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,6,1,5,8,2,4]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,5,6,4,2,7,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,6,4,7,8,5,1]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,5,8,3,1,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,1,3,8,6,5]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,1,4,7,8,3,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,6,2,7,3,4,8,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,3,8,5,4,7,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,6,8,5,1,3,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,7,6,8,5,3,1,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,5,8,6,4,2,3,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[2,5,8,6,4,1,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,6,2,3,5,8,7,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,2,3,1,6,8,5]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,3,1,5,4,8,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,6,2,8,3,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,5,1,4,8,2,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,5,1,2,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[7,5,4,3,8,6,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[4,3,8,2,6,7,5,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,8,2,5,7,1,6]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,6,4,7,2,3]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,2,3,1,5,8,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,2,3,8,1,6,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,5,2,3,8,4,1,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[4,5,1,7,6,3,8,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,7,5,2,3,4,6]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[8,6,3,1,4,2,5,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[4,5,1,6,2,8,7,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,6,1,7,2,5]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,7,8,3,4,5,1]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[9,2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2],[9]]=>[8,1]=>[8,1]=>2
[4,2,3,1,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2],[4]]=>[3,6]=>[6,3]=>2
[1,2,4,6,8,9,7,5,3]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[1,2,4,3,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[3,7]=>[7,3]=>2
[1,2,4,6,8,10,9,7,5,3]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[1,2,4,6,8,5,7,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,7,5,8,6,3,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,7,3,8,6,5,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,8,7,4,6,5,1,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,4,6,5,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,3,6,5,8,1,2]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,7,2,6,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,7,5,1,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,7,6,5,8,3,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,8,5,2,3,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,3,8,2,7,6,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,4,1,7,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,4,7,2,5,8,3,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,7,5,1,4,2]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,6,4,1,2,8,7]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[6,8,4,3,5,7,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,4,8,7,6,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,2,5,1,7,8,3,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,1,3,8,6,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,3,8,2,6,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,2,4,3,6,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,5,4,8,2,3,6,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,8,3,1,6,7,2,5]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,8,2,6,5,7,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,2,4,8,7,1,5]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,2,6,8,1,5]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,3,4,6,8,1,2,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[3,6,7,2,5,8,1,4]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,8,3,7,2,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,8,3,4,7,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,8,1,3,4,7,2]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,5,6,3,4,7,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,1,3,5,4,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,6,3,5,4,7,2]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,2,5,8,4,6,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,4,8,1,7,3,5]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,7,8,5,4,6,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,2,7,4,8,5,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,1,8,4,3,5,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,7,1,8,3,2,4,5]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,7,6,3,5,8,1,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,7,5,6,8,1,3,4]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,7,2,8,1,3,4,5]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,1,6,8,7,2,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[1,5,7,6,8,2,3,4]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,8,5,3,1,2]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,8,6,7,5,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,7,5,8,6,3,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,6,8,3,2,5,4,7]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,1,5,4,7,3]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,4,7,6,2,8,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,7,6,5,1,8,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,1,5,8,3,2,7,4]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,4,8,5,7,6]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,5,8,4,6,3,1,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,4,8,3,2,6]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,1,7,5,3,2,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[2,7,6,4,8,1,5,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,5,4,8,1,6,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,2,5,3,8,6,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,2,3,8,6,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,5,8,1,6,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,3,8,4,1,2,6,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[2,4,8,3,7,1,5,6]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,4,1,6,3,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,5,2,1,8,4,3]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[2,7,5,1,8,3,6,4]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,8,7,4,3,6,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,7,2,4,6,1,5]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,1,3,2,4,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,7,6,3,5,8,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,7,6,3,5,1,2]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,4,2,3,5,6]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[6,5,1,3,8,7,4,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,7,8,3,2,5,1,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,5,3,7,2,4]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,6,8,3,7,4,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,5,1,7,4,3,2]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[7,6,4,1,3,5,8,2]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[8,2,3,7,1,4,5,6]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[2,8,3,7,1,4,5,6]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,6,2,7,4,3,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,6,2,7,4,1,3,5]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[3,7,8,5,2,1,4,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[6,8,4,7,3,1,5,2]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,6,5,1,2,7,3]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,8,6,5,1,2,3,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,4,5,1,7,6,8,2]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,7,6,5,1,2,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,4,6,7,1,2,5,3]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,2,6,1,8,4,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,2,6,1,3,8,4]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,2,6,1,4,7,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,7,5,6,1,4,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,4,7,2,1,5,3]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,6,5,1,3,8,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,3,4,5,2,8,6]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,2,1,3,5,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[1,7,2,5,4,3,8,6]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,7,3,4,8,1,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,7,4,3,8,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,1,8,7,5,6,2,3]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,7,4,3,6,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,1,3,8,7,5,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[2,1,7,4,6,8,3,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,4,6,8,3,5]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,4,2,7,3,5,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,6,1,2,3,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[1,8,6,2,7,3,5,4]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,8,6,2,3,5,4]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,3,5,7,6,4]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,8,1,7,6,2,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,1,3,6,7,5,4]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,2,4,8,6,1,5,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,2,5,6,7,8,9,10,3]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[8,2,1,3,4,5,6,7,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[9,2,1,3,4,5,6,7,8,10]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[8,3,1,2,4,5,6,7,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[8,2,3,1,4,5,6,7,9]=>[[1,3,5,6,7,8,9],[2],[4]]=>[3,6]=>[6,3]=>2
[5,8,4,3,1,6,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,7,2,4,6,10,1,3,5,9]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[6,4]=>[6,4]=>2
[2,10,7,9,4,6,8,1,3,5]=>[[1,2,4,7],[3,6,10],[5,9],[8]]=>[2,2,3,3]=>[3,3,2,2]=>4
[6,5,2,4,8,10,1,3,7,9]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[6,4]=>[6,4]=>2
[2,8,5,7,4,6,10,1,3,9]=>[[1,2,4,7],[3,6,10],[5,9],[8]]=>[2,2,3,3]=>[3,3,2,2]=>4
[8,7,6,5,2,4,10,1,3,9]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[7,3]=>[7,3]=>2
[4,10,3,9,2,6,8,1,5,7]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>[2,2,3,3]=>[3,3,2,2]=>4
[3,6,10,2,5,9,4,8,1,7]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[3,3,2,2]=>[3,3,2,2]=>4
[3,5,7,10,2,4,6,9,8,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[4,4,2]=>[4,4,2]=>3
[5,10,4,9,3,8,2,7,6,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[4,6,10,3,5,9,8,7,2,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[3,3,4]=>[4,3,3]=>3
[5,10,4,9,8,7,6,3,2,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[2,2,6]=>[6,2,2]=>3
[8,12,7,11,2,4,6,10,1,3,5,9]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[2,2,4,4]=>[4,4,2,2]=>4
[6,12,5,11,2,4,8,10,1,3,7,9]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[2,2,4,4]=>[4,4,2,2]=>4
[6,10,5,9,2,4,8,12,1,3,7,11]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[2,2,4,4]=>[4,4,2,2]=>4
[12,11,6,10,5,9,2,4,8,1,3,7]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[4,2,3,3]=>[4,3,3,2]=>4
[8,7,6,12,5,11,2,4,10,1,3,9]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[4,2,3,3]=>[4,3,3,2]=>4
[4,12,3,11,2,6,8,10,1,5,7,9]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[2,2,4,4]=>[4,4,2,2]=>4
[4,10,3,9,2,6,8,12,1,5,7,11]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[2,2,4,4]=>[4,4,2,2]=>4
[12,11,4,10,3,9,2,6,8,1,5,7]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[4,2,3,3]=>[4,3,3,2]=>4
[4,8,3,7,2,6,10,12,1,5,9,11]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[2,2,4,4]=>[4,4,2,2]=>4
[10,9,4,8,3,7,2,6,12,1,5,11]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[4,2,3,3]=>[4,3,3,2]=>4
[3,5,8,12,2,4,7,11,6,10,1,9]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[4,4,2,2]=>[4,4,2,2]=>4
[6,5,4,12,3,11,2,8,10,1,7,9]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[4,2,3,3]=>[4,3,3,2]=>4
[6,5,4,10,3,9,2,8,12,1,7,11]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[4,2,3,3]=>[4,3,3,2]=>4
[4,7,12,3,6,11,5,10,2,9,8,1]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]]=>[3,3,2,2,2]=>[3,3,2,2,2]=>5
[6,3,7,2,5,4,8,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,7,3,2,6,8,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,2,6,3,4,8,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,5,4,6,2,8,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,3,2,1,7,4,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,7,5,3,2,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,4,3,7,2,8,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,5,7,2,8,4,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,3,8,2,1,7]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,8,7,3,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,3,8,4,1,7,2,5]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,1,6,4,3,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,6,4,3,5,1,7]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,8,6,3,7,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,8,7,5,3,1,4,6]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[2,5,6,3,1,4,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,4,7,8,5,3,1,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,3,2,4,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,5,8,7,3,2,4,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,4,7,8,5,3,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[8,5,6,7,3,1,4,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,7,5,3,2,6,4,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[8,5,3,1,4,6,7,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,5,1,6,4,3,7,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,4,3,7,8,2,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,2,7,5,8,3,4]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,3,1,4,6,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,8,3,1,6,5,7,4]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,5,6,7,1,2,4]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,8,1,4,6,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,8,7,5,4,6,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,8,3,4,1,6,5,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,3,4,2,6,5,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,5,2,3,7,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,2,8,6,3,1,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,5,2,3,8,1,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,7,5,2,8,3,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,3,6,4,8,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,2,3,7,8,4,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[7,2,6,3,1,5,8,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,6,3,8,7,5,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,8,4,1,5,7,6,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,2,5,7,6,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,5,4,1,7,6,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,5,8,3,7,1,6,4]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,5,2,4,7,6,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,2,8,7,5,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,8,2,4,1,6,5,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,6,1,8,7,5,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,8,4,5,1,7,6,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,8,2,7,6,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,6,8,7,5,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,2,4,5,7,6,3]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,8,3,5,7,6,4]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,2,5,7,6,4]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,1,5,7,6,4]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,1,8,7,5,3,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,6,2,8,7,5,3,4]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,6,3,8,7,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,6,3,8,7,5,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,2,8,1,5,7,6,4]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,2,5,7,6,4]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,1,4,5,7,6,3]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,2,1,4,6,5,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,6,8,7,5,1,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,1,6,8,7,2,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,4,5,1,6,2,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,4,5,7,2,3,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[8,1,4,7,6,3,2,5]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,1,6,4,7,2,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,8,6,2,7,1,4]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,6,1,5,7,2,4]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,6,3,1,2,5,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[6,8,1,4,5,2,3,7]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,8,4,6,2,3,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,6,5,3,8,4,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,1,4,2,3,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,4,8,1,2,3,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,2,1,5,3,7,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[4,7,8,1,2,6,3,5]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,1,5,6,2,3,4]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[1,6,5,8,7,2,3,4]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,7,1,6,2,4,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,2,7,6,8,3,4]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,7,2,5,8,3,4]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,6,5,8,2,3,4]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,6,8,5,7,2,3,4]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,1,2,6,8,3,4]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[6,1,5,2,7,8,3,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,8,7,2,4,5]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,3,2,4,6,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[8,3,1,4,2,5,7,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,7,8,4,6,5]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,2,6,8,7,3,4]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[1,8,6,2,5,7,3,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,8,1,2,6,3,4]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,7,6,2,3,4]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,1,6,8,5,2,3,4]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[3,7,1,2,8,4,6,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,1,2,7,6,4,5]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[1,5,8,7,6,2,3,4]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,8,6,1,5,2,3,4]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,10,3,4,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8,9],[3],[10]]=>[2,7,1]=>[7,2,1]=>3
[7,8,6,3,1,5,2,4]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,8,1,3,4,5,2,6]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,8,2,5,3,6]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,6,1,4,2,7,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,8,2,4,6,3,5]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,4,1,5,3,2]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,2,8,1,5,4,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,5,4,1,7,2,6,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,4,7,3,2,5,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,5,3,8,4,1,2]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[6,4,5,7,8,1,3,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,7,4,1,6,8,5,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,2,7,6,8,5,4]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,8,4,5,1,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,3,5,4,2,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,5,2,4,6,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,4,8,3,5,2,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,4,8,6,3,7,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,2,5,3,7,1,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,4,5,2,6,7,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,8,6,5,3,7,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,4,6,3,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,2,8,6,4,7,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,1,2,7,4,3,5]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,3,6,2,4,1]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,2,3,4,8,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[7,3,5,4,2,8,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,1,3,2,4,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,5,1,3,7,8,6,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,3,7,2,1,8,6,5]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,2,1,3,5,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,6,2,3,1,5,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,6,4,2,5,1,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,4,7,5,2,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,2,7,5,4,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,4,7,5,3,6,1,8]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,3,4,1,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,5,8,6,4,7,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,7,3,8,6,5,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,2,7,5,8,6,1]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,5,4,7,8,6,2]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,2,3,1,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,8,1,4,6,5,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,8,7,4,1,3,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[2,6,4,7,5,3,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,4,7,1,3,8,5]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,3,5,1,4,2,8,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,7,1,3,2,8,6]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,4,7,5,3,8,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,4,3,1,5,6,2]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,7,1,4,3,5,6,2]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,8,4,7,3,2,5]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,3,6,1,2,8,5]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,1,7,4,3,8,6]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[4,7,6,2,3,1,8,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,6,8,2,5,3,4,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,6,1,8,7,5,4]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,6,8,7,5,3,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,4,1,7,5,2,8,3]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[5,7,8,2,3,6,1,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,1,2,5,6,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,7,4,1,5,6,3]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,6,2,1,5,7,4,3]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[3,8,6,7,5,2,1,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,3,7,5,8,2,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,3,1,8,5,6,2]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,7,5,3,4,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,4,5,7,3,8,1]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,4,5,8,3,7,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,8,5,3,4,7,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,5,6,8,3,7,2]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,1,8,7,2,5,3]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,2,3,4,5,6,7,10,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[6,9,1,2,3,4,5,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[1,3,8,5,2,7,4,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,6,7,2,4,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,8,3,7,6,1,4,5]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,2,7,8,6,1,3,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[1,3,8,7,6,2,4,5]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,4,6,8,5,2,3,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,2,6,7,8,1,3,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[4,5,6,8,1,2,7,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,8,6,1,2,7,4]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,2,6,8,7,1,3,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[1,4,6,8,7,2,3,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,5,3,8,1,7,2,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,8,4,1,7,2,6]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,7,8,2,3,4]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,5,4,8,1,3,7,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,4,8,5,1,3,2]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,5,2,4,8,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,2,7,4,5,3,6]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,7,4,6,1,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,7,4,5,3,8,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,3,1,5,4,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,4,8,3,1,7,5]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,3,7,5,6,4,2]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,5,3,8,6,7,4]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,5,7,8,2,3]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,7,4,2,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,7,2,4,1,3,8,5]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,8,4,2,6,5,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,3,4,2,7,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,8,2,5,6,7,4]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,6,7,2,5,4,3]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,8,3,5,4,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,3,8,5,4,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,7,2,4,6,1,5,3]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,8,6,5,2,4,3,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,7,5,2,8,4,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,7,8,1,3,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,6,7,8,1,4,2]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,7,6,8,4,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,3,2,8,6,4,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[5,4,8,6,7,2,3,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,6,3,1,2,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[4,5,7,3,6,2,8,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,6,3,8,2,7,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,7,2,1,3,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[2,5,4,7,8,1,3,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,3,6,4,8,2,7,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,7,4,6,2,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,3,7,4,5,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,4,7,3,5,6,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,6,5,7,3,4,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,6,2,7,3,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,6,2,8,3,7,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,6,1,7,2,5,3]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,1,6,3,8,7,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,6,3,7,1,8,2]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,2,8,5,4,1,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[4,3,1,5,2,8,6,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,1,3,2,6,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[3,8,4,1,5,2,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[2,5,4,3,8,1,6,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,7,4,3,1,6,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[5,3,4,2,7,1,6,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,5,4,1,2,6,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[4,3,5,1,2,7,6,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,3,5,2,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,1,8,6,3,7,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[3,1,7,2,5,6,4,8]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,4,2,1,6,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[3,7,2,4,1,6,5,8]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,2,1,6,4,5,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[2,8,6,1,7,4,3,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,4,6,1,3,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,5,6,4,1,3,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[8,5,2,6,1,3,7,4]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,1,5,6,3,2,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,1,2,5,4,6,3,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,1,6,5,3,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,1,2,7,5,6,3,8]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,2,6,5,4,3,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,1,5,6,3,7,4]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[2,8,5,1,6,4,7,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,4,5,3,2,7,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[3,1,6,5,4,2,7,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,1,4,6,5,2,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[2,1,8,6,3,7,5,4]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,3,1,7,6,4,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,6,3,2,8,5,1,4]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[5,6,3,8,7,4,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,2,6,8,7,4,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[6,3,8,5,4,1,2,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,3,8,4,5,1,2,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,3,1,4,8,6,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,4,1,3,2,8,6,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,1,3,4,2,8,6,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,2,1,4,3,8,6,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[4,2,7,3,8,5,1,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,3,2,8,5,1,6]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,7,2,8,5,6,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,1,2,4,8,6,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[5,4,3,1,2,8,6,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[5,3,4,1,2,8,6,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,2,3,4,1,8,6,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,1,7,3,4,6,8,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,7,4,3,1,6,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[6,8,1,3,4,5,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,7,8,2,5,4,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,3,7,4,1,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,4,1,2,5,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[7,2,6,8,4,3,1,5]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,7,2,8,6,5,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,7,5,1,2,4,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[7,4,5,1,8,2,3,6]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,2,3,1,8,4,5,6]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,1,4,8,3,7,5,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,6,7,3,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,2,7,8,4,3,6,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,1,3,5,6,2,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,7,8,4,2,6,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,7,8,2,4,5,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,2,4,3,1,7,6]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,5,4,2,3,1,8,6]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,5,4,6,7,1,8,2]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,2,6,5,8,7,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,2,6,4,8,7,5]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,5,3,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,6,4,8,7,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,2,5,3,8,7,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,1,4,3,8,7,6]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,5,4,8,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,6,3,7,5,4]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,6,4,7,5,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,6,4,8,5,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,6,3,8,5,4]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,2,7,4,8,6,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,2,8,5,7,6,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,1,3,2,6,5,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,8,4,7,6,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,7,3,6,5,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,3,8,1,5,4,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,3,1,4,2,6,5,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[4,8,7,3,5,2,1,6]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,3,5,2,4,1]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,5,1,2,6,4,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,1,5,4,2,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,6,4,1,5,3,2,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,6,5,4,1,3,2,7]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[6,2]=>[6,2]=>2
[5,3,8,7,4,6,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,8,7,4,6,1,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,7,4,1,2,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[4,8,5,3,1,2,7,6]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,8,7,3,1,5,4,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,5,4,1,3,7,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,5,8,7,4,6,3,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,6,5,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,7,5,1,6,2,4]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,3,8,7,5,6,1,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,7,1,3,6,4,5]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,4,7,2,1,3,6]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,8,7,3,5,2,1,4]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,8,6,4,2,7,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,4,1,5,2,7,3]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,2,1,7,5,3,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,4,6,1,2,7,3]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,8,6,5,1,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,7,6,5,2,1,3]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[4,8,7,5,1,6,2,3]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,5,2,1,8,6,7,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,8,3,1,6,7,2]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,2,8,4,6,1,3]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,3,2,4,8,5,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,2,8,6,4,5,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,2,6,5,1,3,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[5,2,7,8,4,1,3,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[2,7,8,6,4,1,3,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[7,6,3,5,2,8,4,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,4,8,5,3,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,6,5,1,7,2,4,3]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,8,5,1,7,3,2,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,8,3,7,4,2,5]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,3,4,8,2,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,6,4,8,1,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,2,4,8,1,7,6]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,8,2,4,1,7,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,3,8,7,5,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,3,8,7,5,4,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[6,8,4,2,1,7,5,3]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[5,2,6,4,3,8,1,7]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,3,1,4,8,2,7]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[3,1,7,8,6,4,2,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,8,1,7,6,2,5,4]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,7,6,4,2,5,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,2,6,3,8,5,4,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,3,8,6,4,1,5,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,7,5,8,2,4,3,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,5,2,4,8,3,7]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,3,8,2,4,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,7,1,3,6,5,2,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[2,6,7,4,3,8,5,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,7,3,8,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,8,7,2,4,6,3]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,8,7,3,6,5,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,2,5,1,6,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,2,8,1,5,4,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,6,1,5,8,4,7]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,1,5,8,4,3,6]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[7,2,8,1,4,3,6,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,8,3,2,6,5,4]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,4,8,3,2,6,5]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,5,4,8,3,2,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,5,4,3,8,2,7]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,4,5,6,8,2,3]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,3,4,5,6,7,9,8,2]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[2,3,4,5,6,7,9,8,1,10]=>[[1,2,3,4,5,6,7,10],[8],[9]]=>[7,3]=>[7,3]=>2
[1,8,4,5,6,7,9,2,3]=>[[1,2,4,5,6,7],[3,9],[8]]=>[2,5,2]=>[5,2,2]=>3
[1,3,4,5,6,7,8,10,9,2]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,6,4,2,3,5,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[1,8,7,2,3,4,5,6]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[1,5,8,6,2,3,4,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,6,5,7,2,3,4,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,5,6,2,3,4,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,3,2,7,6,4,5,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,2,3,7,6,4,5,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,5,4,2,3,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,5,4,2,3,8,6,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,8,6,4,5,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,7,5,8,2,3,4,6]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,8,7,5,2,3,4,6]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[2,1,5,8,6,3,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,5,8,4,6,1,7,3]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,3,8,6,1,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,5,8,1,7,4]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,2,5,8,1,7,4]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,8,6,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,8,4,6,1,3,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,8,6,1,4,7,2]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,5,4,8,1,7,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,5,7,2,6,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,8,5,3,7,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,8,1,7,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,1,5,7,6,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,4,1,5,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,3,6,8,5,2,7,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,4,7,2,6,3,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,8,5,4,2,7,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,4,8,5,2,7,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,4,1,8,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,4,1,5,2,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,6,5,1,3,7,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,3,5,6,7,1,4]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,6,2,4,7,1,8,3]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,5,4,6,1,8,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,7,4,6,1,8,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,7,4,1,3,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,5,7,4,1,3,8,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,6,3,5,7,8,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,6,3,5,7,8,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,4,2,5,7,8,1]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,3,6,1,5,7,8,4]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,6,2,5,7,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,1,2,5,7,8,3]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[2,6,4,1,5,7,8,3]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,4,1,6,5,7,8,3]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,4,2,6,1,8,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,7,3,1,8,6,5,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,4,2,7,1,8,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,7,5,3,1,8,6]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,3,6,4,8,2,1,7]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,2,5,4,1,8,6]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,5,1,8,6,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,6,3,8,7,2,1,5]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,6,3,8,2,1,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,8,6,2,1,5]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,3,2,6,1,8,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,3,2,6,4,1,8]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,5,3,1,8,6,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,5,2,8,4,3,1,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,2,4,1,8,6,5]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,2,7,5,1,6]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[4,3,7,5,8,2,1,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,5,3,7,2,1,6]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,5,2,8,6,1,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,6,4,5,7,3]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,5,3,4,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,9,4,3,5,6,7,8,2]=>[[1,2,5,6,7,8],[3],[4],[9]]=>[2,6,1]=>[6,2,1]=>3
[9,3,2,4,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3],[9]]=>[8,1]=>[8,1]=>2
[10,2,3,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[9,1]=>[9,1]=>2
[3,5,6,7,8,9,4,2,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[7,8,4,1,6,3,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,5,6,1,3,4,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,3,4,6,8,5,7,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[1,2,3,6,4,7,5,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[3,2,6,4,1,8,5,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,8,6,5,3,1,4,7]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[5,4,8,6,2,3,1,7]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,5,2,3,1,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,4,7,6,8,3,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,2,8,7,5,1,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,5,7,6,3,2,4,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,1,8,7,3,2,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[1,8,5,4,2,7,3,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,1,5,8,4,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,5,8,2,7,4,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,3,2,7,4,6,5,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,8,4,1,3,6,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,6,2,3,8,4,5]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,1,3,2,8,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,3,8,7,2,6,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,1,6,2,5,3,4]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,8,5,2,4,7,6,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,1,5,2,4,8,3,6]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,5,1,4,7,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,2,5,4,1,3,8,6]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,1,6,3,2,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,9,1,2,3,5,6,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[3,9,1,2,4,5,6,7,8]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]=>[7,2]=>2
[7,10,1,2,3,4,5,6,8,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[6,10,1,2,3,4,5,7,8,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[4,10,1,2,3,5,6,7,8,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[3,10,1,2,4,5,6,7,8,9]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]=>[8,2]=>2
[1,8,2,3,4,5,6,7,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]=>[7,2]=>2
[7,4,6,1,3,2,5,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,4,5,8,6,3,2,7]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,4,5,7,2,6,1,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,2,6,7,3,1,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,7,5,3,6,2,4]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,3,6,1,4,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,6,3,1,7,8,4]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,5,1,6,7,8,2]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,7,6,1,2,3,8,4]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,6,7,5,1,2,8,4]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,7,6,8,5,2,4,3]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,6,8,1,2,4,3]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,3,7,1,4,8,2]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,2,1,8,6,4,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[1,8,7,6,5,4,3,2,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,9,8,7,6,5,4,3,2,10]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[2,8,9,7,6,5,4,3,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[7,8,6,1,4,5,2,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,8,3,7,2,1,4]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,5,3,6,2,1,4]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,8,5,3,6,2,4,1]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,4,3,2,6,5,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,3,2,6,7,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,4,3,8,2,1,7,6]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,3,2,1,7,5]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,8,4,3,2,7,6,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,8,6,7,3,2,4,5]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,6,1,3,2,4,5]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,4,3,2,7,5,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,4,3,8,2,1,6,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[1,8,4,3,2,5,7,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,4,3,8,2,6,7,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,1,2,6,7,8,9,3]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[6,4,2,3,5,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,2,3,6,1,4,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,2,3,8,6,4,7,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,2,3,7,4,8,1,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,3,2,5,4,7,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,3,4,5,8,1,6]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[7,2,8,1,5,3,4,6]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,8,6,4,7,2,5,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,8,6,4,5,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,2,5,7,3,1,6]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,2,3,4,7,1,6]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[6,3,4,7,8,2,1,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[3,8,5,1,4,7,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,5,1,3,6,7,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,6,8,5,2,7,3,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,5,2,6,4,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,2,7,4,5,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,5,4,7,1,3,6,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,6,2,8,1,5,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,5,2,3,7,6,4]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,3,7,8,5,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[8,4,2,3,6,7,1,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[4,5,8,3,7,2,1,6]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,2,8,4,5,1,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,1,8,4,6,2,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,1,5,6,8,3,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[4,1,2,6,5,8,3,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,8,3,2,6,7,5]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,7,5,8,1,3,6]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,2,7,8,3,1,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,1,3,8,2,5,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,3,6,2,1,8,7,5]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,7,4,5,1,6,2,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,4,5,8,2,1,7]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,4,5,2,8,7,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,4,5,1,6,3,8]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,4,1,6,3,2,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[1,5,4,8,6,3,2,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,5,4,8,6,3,1,2]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,7,5,3,6,4,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,3,7,4,1,6,2,5]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,4,1,6,3,2,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[1,7,4,2,6,5,3,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,1,5,6,7,3,4]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[6,3,1,8,4,7,2,5]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,4,8,6,3,2,5]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,1,8,5,6,7,2,3]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,8,6,2,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,3,6,8,2,7,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,7,4,8,2,1,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,6,1,4,7,2,8]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,8,2,7,1,5]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,4,8,2,1,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,4,1,6,2,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,1,4,7,2,6]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,4,1,6,3,2,7]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,4,1,6,2,5]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,3,6,7,4,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,2,5,6,7,3,4]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,4,1,6,5,2,3]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,8,1,5,7,2,4]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,1,2,5,7,4,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[8,1,4,2,6,5,3,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,1,2,3,4,5,9,6]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[2,8,9,1,3,4,5,6,7]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[2,8,9,10,1,3,4,5,6,7]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]=>[6,4]=>2
[7,1,8,2,3,9,4,5,6]=>[[1,3,5,6,8,9],[2,4,7]]=>[3,3,3]=>[3,3,3]=>3
[6,1,7,2,8,3,4,9,5]=>[[1,3,5,7,8],[2,4,6,9]]=>[3,2,3,1]=>[3,3,2,1]=>4
[5,1,6,2,7,3,8,4,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[4,1,5,2,6,3,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[5,1,3,7,4,8,2,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,3,4,7,8,2,6]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[2,5,8,7,4,3,6,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,7,8,3,4,2,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,4,8,3,7,6,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,8,2,3,4,1,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,5,7,4,6,8,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,4,5,8,1,2,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,8,1,4,5,2,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,1,6,3,4,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,1,3,7,5,2,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,7,8,5,3,6,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,1,4,7,2,8,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[2,4,7,5,8,3,6,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,5,8,2,1,7,6]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,8,5,3,7,1,2,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,5,7,3,1,2,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,7,5,1,3,2,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,8,4,1,5,2,6]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,7,2,4,3,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,4,2,3,6,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,3,6,8,5,4,2,7]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,6,3,8,2,7,4,5]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,3,6,7,5,4]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,6,8,2,7,5,4]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,5,4,3,8,2,7]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,3,4,5,6,2,7]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,3,6,2,4,5,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,4,5,8,3,6,2,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,8,4,5,3,6]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,8,5,6,3,4,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,3,8,5,4,2,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,2,8,7,5,4,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[6,2,8,4,3,7,1,5]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,4,3,1,7,6]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,2,5,4,8,3,7,6]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,3,6,8,7,2,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[3,2,5,7,6,8,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,6,8,4,7,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,8,6,4,7,2,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,8,5,4,2,7]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,3,2,8,7,6,4,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,3,8,2,7,6,1,4]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,5,4,8,3,7,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,5,1,3,7,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,3,8,7,2,6,5,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,5,1,8,4,6,3]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,5,2,1,6,4,3]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,4,8,1,2,5,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,4,8,3,2,6,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,5,6,2,7,1,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,5,8,7,3,1,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,5,8,6,7,1,3]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,5,6,2,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[4,1,5,8,6,7,2,3]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,7,6,1,2,8,5]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[4,7,5,6,1,2,8,3]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,7,5,6,2,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,1,8,6,7,3,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,5,8,6,7,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,5,8,6,7,4,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,5,8,7,1,2,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,7,1,5,6,2,8,3]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,7,1,3,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,8,6,4,7,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,1,5,7,8,3,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[3,6,4,7,2,1,8,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,4,6,1,7,2,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,6,4,7,2,1]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,4,5,6,7,2,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,6,5,2,7,4,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,5,2,1,4,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[3,8,6,5,1,7,2,4]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,4,1,7,3,2,8,5]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,1,4,6,7,2,8,3]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,5,4,7,1,3,8,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,6,5,3,7,8,4]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,1,4,7,2,3,8,5]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,1,3,4,5,6,8,9,7]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[2,1,3,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[2,1,3,4,5,6,7,9,10,8]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[2,1,3,4,5,6,7,8,10,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[1,6,2,5,4,8,3,7]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,2,7,5,8,3,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,3,5,8,2,4,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[5,6,4,3,1,8,2,7]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,2,3,5,8,1,4,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[6,7,2,3,8,4,5,1]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,2,1,3,8,4,5]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,7,4,1,8,3,2,6]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,7,5,8,3,6,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,1,3,8,4,5,2]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,7,4,3,8,5,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,7,4,2,8,5,3]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,7,4,3,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,7,3,2,1,8,4,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,5,7,3,1,4,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,2,8,4,5,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,6,7,4,3,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,7,1,8,4,6,3,5]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,5,8,1,6,3,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,8,4,5,3,2]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,3,7,6,1,2,5,4]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,3,4,6,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,2,5,7,1,4,6,3]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,4,7,1,5,6,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,3,4,7,1,5,6]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[8,7,3,5,6,2,4,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,4,6,5,2,3,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,7,5,1,2,3]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[8,4,6,7,5,1,3,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,5,7,6,1,4,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,3,6,2,1,5,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,7,3,4,6,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,4,6,5,2,1,3]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,6,5,2,7,4,3,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[8,4,3,7,6,5,1,2]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,5,6,7,4,1,3,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,7,6,4,1,2,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,4,2,7,5,1,6,3]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,3,4,2,7,5,6,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,6,5,1,2,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,3,5,2,7,4,6,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,2,6,7,4,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,5,3,7,6,4,1,2]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,6,2,5,7,3,1,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,6,2,4,7,3,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,5,2,3,7,4,1,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,5,3,2,7,6,4,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[8,6,1,5,4,3,2,7]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,5,8,3,1,6,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[2,7,4,6,1,5,8,3]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,3,8,5,1,6,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,8,3,2,5,4,6,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,6,7,3,8,2,4]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,5,4,8,3,2,7]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,5,8,4,6,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,1,6,4,8,5,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,8,3,2,4,6,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,7,2,4,6,5,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,7,6,4,8,5,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,7,6,4,2,5]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,1,8,7,5,4,2,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,1,7,6,5,4,2,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,7,1,6,5,3,2,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,8,1,6,5,3,2,7]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,4,1,7,6,3,2,5]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[5,4,1,8,6,3,2,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[5,4,1,7,6,3,2,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[6,4,1,8,5,3,2,7]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[8,4,1,7,5,3,2,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,1,6,5,3,2,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[7,5,6,1,4,3,2,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,5,6,1,4,3,2,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,1,4,3,2,6]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,6,1,4,3,2,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,6,1,4,3,2,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,5,1,4,3,2,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,5,1,4,3,2,6]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,6,5,1,4,3,2,7]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,6,1,7,2,5,3,4]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,8,6,3,4,2,5,7]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,4,5,8,2,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,3,8,4,5,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,7,6,1,4,3,5]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,7,8,1,4,3,6]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,3,8,4,1,2,7]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[8,2,7,6,1,4,5,3]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,2,3,4,7,1,6,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[5,2,3,7,1,6,8,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,5,3,1,6,4,2]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[1,4,7,8,5,2,3,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[5,8,3,7,6,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,5,1,7,2,4,8,3]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,7,1,4,2,5,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,5,8,2,1,3,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,1,2,7,5,4,3,6]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,1,8,3,7,2,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,8,7,5,3,2,6,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[7,8,1,5,4,2,3,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,6,8,1,5,7,2]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,1,7,5,4,2,3]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,6,3,1,2,8,5,4]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[6,3,5,7,1,4,2,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,5,2,6,4,8,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,3,6,8,2,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,2,5,7,8,4,6,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,2,7,5,4,8,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,7,4,1,3,2,8,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,2,8,4,3,5,6]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,3,5,7,8,2,4]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,1,7,5,2,4,3]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,4,1,8,3,2,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,4,1,6,5,2,7,3]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,5,3,4,7,8,2,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,2,1,5,7,8,3,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,4,1,6,7,8,2,3]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[5,1,4,6,7,8,2,3]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[4,1,5,3,7,8,2,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,6,5,2,7,3]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,1,5,4,6,3,2,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,1,6,7,5,4,3]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[1,2,4,7,6,3,8,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,7,4,1,8,5,2,3]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[8,6,4,1,5,7,3,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[5,2,4,3,7,1,6,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,4,8,3,2,7]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,7,4,3,6,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,2,1,7,5,8,4,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,4,7,8,2,5]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,3,7,8,2,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,3,1,7,8,4,6]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,6,4,3,7,8,2,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,6,4,3,1,5,2,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,5,4,6,1,3,2,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,6,5,1,2,7,3]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,5,6,3,7,8,2,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,2,3,4,5,8,9,10,6]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[6,7,1,2,3,4,8,9,5]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[6,1,2,3,4,7,8,9,10,5]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[5,1,2,3,6,7,8,9,10,4]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[1,5,2,4,3,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,5,7,2,1,4,3]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,6,3,8,4,5,7,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,4,2,6,3,8,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[9,7,6,5,4,3,1,2,8]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[2,3,8,4,7,5,6,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,2,8,6,4,5,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,7,5,8,2,4,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,8,6,2,5,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,1,7,5,2,4,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,4,7,8,6,1,5,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,8,5,1,7,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,8,3,5,1,6,4,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,4,6,3,7,5,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,3,8,2,1,7,6]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,6,2,7,5,3,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,1,4,5,6,7,3]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[7,3,1,2,5,6,4,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[7,8,2,1,5,4,6,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,8,5,2,6,3,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,2,3,7,8,1,6,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,8,4,3,6,7,5]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,5,3,4,6,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,7,3,2,6,8,4,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,2,1,3,6,8,4,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[4,7,8,1,6,5,3,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,5,8,6,1,4,2,7]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,2,7,6,3,5]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,1,6,5,4,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,3,8,2,6,5,4,1]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,1,3,8,6,5,4,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,1,3,7,6,5,4,2]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[2,4,1,8,7,3,6,5]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,8,6,1,5,4,2]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,7,8,2,6,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,7,8,2,1,6,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,8,7,1,5,4,2]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,4,7,1,5,3,2]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,2,1,8,5,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,2,1,6,3,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,4,8,3,2,1,7]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,4,8,2,1,6,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,5,8,2,1,6,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,4,2,6,3,8,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,4,1,6,2,8,3]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,5,6,1,7,3,2,4]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,1,6,7,8,3,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,2,6,1,3,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,6,7,2,5,1,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,4,6,8,3,5,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,7,1,2,4,8,5,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,3,4,7,8,5,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,6,4,7,5,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,1,3,4,5,6,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,2,6,7,3,4,5]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,2,8,1,5,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,1,2,6,3,8,5,4]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,6,3,7,5,4]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,7,6,3,5,4]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,7,3,1,6,2,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,7,8,3,1,6,2,5]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,3,1,6,2,8,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,4,3,1,8,6,2,5]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[3,7,6,2,4,8,1,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,3,7,2,8,6,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,2,7,4,3,8,5]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,6,3,8,7,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,2,7,3,8,6,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,2,7,3,5,8,4]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,3,2,1,8,6,4]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[4,2,1,5,3,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,4,1,8,5,2,9,6,3]=>[[1,4,7],[2,5,8],[3,6,9]]=>[4,3,2]=>[4,3,2]=>3
[6,2,5,4,1,8,7,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,3,2,1,8,7,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,5,3,2,1,8,7,4]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[8,4,3,2,7,6,1,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[1,5,8,4,7,6,3,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,4,8,6,1,5]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,3,2,8,6,1,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[6,8,3,7,5,2,1,4]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,8,4,3,2,1,6]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,4,3,8,5,2,1,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,5,4,7,6,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,5,4,8,6,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,3,2,8,6,1,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,2,5,4,8,6,1,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,8,6,5,4,1,7]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,4,3,6,5,2,1,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,4,3,7,5,2,1,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[3,2,7,8,5,4,1,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,8,7,4,3,2,1,5]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[3,6,1,4,8,7,2,5]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,8,1,3,7,2,6,4]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,5,1,8,2,6,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,2,1,8,7,4,5]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[6,2,3,1,8,7,4,5]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,5,1,8,3,6,4]=>[[1,3,5],[2,6,7],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,1,5,8,4,6,3]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,2,8,1,7,5,6,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,1,5,2,8,6,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,6,4,2,8,5,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,7,4,1,5,8,6,2]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,6,1,2,7,4,3]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,1,4,3,7,5,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,4,3,8,5,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,1,5,3,8,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,1,2,4,7,5,3]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,1,6,4,8,3,5,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,4,1,3,7,5,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,5,3,6,1,7,4,2]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,2,1,4,5,8,6,3]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[8,5,6,1,2,7,4,3]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,2,5,4,7,3,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,3,2,4,6,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,2,1,4,3,6,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[2,8,4,1,3,6,7,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[8,1,2,4,5,6,7,3]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[6,1,4,3,2,7,8,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,8,3,6,7,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,8,3,7,4,6,5]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,9,2,3,4,5,6,7,8,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]=>[8,2]=>2
[1,7,2,3,4,5,6,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]=>[7,2]=>2
[8,2,6,5,4,3,1,7]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,2,7,6,4,5,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,3,5,4,2,6,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,7,2,1,8,3,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,7,1,8,2,5,4,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,8,6,1,3,7,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,8,6,2,7,3,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,1,5,3,8,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,2,1,8,5,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,5,6,7,8,3,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[4,1,3,5,6,7,8,2]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[3,7,8,4,5,1,6,2]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,8,3,2,7,1,5]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,2,3,7,1,5]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,1,7,4,5,2,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,8,3,7,1,2,6]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,8,4,6,2,5,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,1,5,7,8,2,4]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,5,4,7,1,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,6,2,5,1,7,4]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,8,6,2,1,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,5,8,6,1,2,7,3]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,5,2,7,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,5,2,6,1,4]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,5,4,1,6,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,5,3,1,7,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,8,2,3,5,4,1,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,5,2,7,8,1,3]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,5,2,3,4,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,6,5,1,7,3,8,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,3,1,2,4,8,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,3,2,5,1,7,4,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,2,4,8,5,3,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[6,3,1,7,2,5,8,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,5,8,1,7,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,3,4,5,6,8,7,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]=>[7,2]=>2
[1,2,3,4,5,6,7,9,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]=>[8,2]=>2
[5,2,7,3,4,6,1,8]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,8,6,4,7,2]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,5,8,6,7,2,4]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,7,4,8,5,3,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,7,4,1,3,6,8,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,4,3,1,6,5,8,2]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,8,1,4,6,5,3,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,8,6,1,4,5,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,2,7,3,8,5,4,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,7,5,3,4,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,2,8,3,6,4,5,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,8,3,1,4,5]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[1,7,8,2,5,3,4,6]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,7,3,4,6,5]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,7,4,5,1,6,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,1,5,7,2,6,4]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,4,8,6,1,2,3]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,1,8,6,4,5,2,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,5,1,4,3,6,2]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,8,4,3,1,7,2,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,4,1,3,7,5,6,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,8,1,3,7,5,6,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,6,8,5,3,4,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,5,1,3,8,6,7,2]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,6,8,5,3,4,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[5,6,8,7,3,1,2,4]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[6,7,5,3,8,1,2,4]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,7,3,1,2,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,1,4,2,6,8,7,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,2,4,7,1,8,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,5,8,6,2,4,3,7]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,6,2,4,3,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,6,3,7,1,2,4]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,6,3,8,1,2,4]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,5,3,1,2,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,2,5,3,6,8,7,4]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,2,1,5,3,4]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,3,6,1,4,8,2,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,6,5,3,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,3,2,1,4,6,5]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,3,5,1,7,4,2,6]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,8,4,2,7,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,2,6,4,3,7,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,6,3,4,1,7,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,2,3,5,8,6,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,3,7,5,1,6,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,8,7,2,1,5,3]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,2,3,7,5,6,4]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,3,6,7,1,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,3,2,5,6,1,8,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,6,7,8,2,4,3,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,2,8,5,3,7,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,8,4,2,5,1,7,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,6,4,3,2,7]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,8,3,5,6,4,1,7]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,8,3,2,5,1,4]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,1,4,5,3,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,2,7,4,3,6,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,1,3,8,4,6,2,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,8,7,1,3,2,4]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,5,1,6,8,4]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,6,8,2,1,4,3]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,6,5,2,7,4,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,5,3,4,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,7,2,5,6,8,3,4]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,2,4,8,3,5,6]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,6,2,4,5,3,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,3,2,8,4,5,7,6]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,8,2,4,3,5,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,2,5,3,4,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,3,6,7,4,5]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,5,3,4,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[10,3,4,5,6,7,8,9,1,2]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[3,1,4,5,6,7,8,10,2,9]=>[[1,3,4,5,6,7,8],[2,9,10]]=>[8,2]=>[8,2]=>2
[7,1,5,6,2,3,8,4]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,2,1,4,6,7,3,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[7,2,6,1,3,4,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,1,3,7,2,5,8,6]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,2,7,5,1,3,8,4]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[1,7,5,6,2,3,8,4]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,6,1,2,4,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[8,6,1,3,5,7,2,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[1,7,4,3,8,2,5,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,1,5,3,4,8,2,7]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,7,5,2,8,1,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,4,1,5,6,2,3]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,1,3,6,7,2,4]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,4,3,7,1,5,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,4,6,7,1,2,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,3,8,4,7,1,2,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,5,4,8,3,6,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,3,8,2,4,5,6]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[8,1,3,7,2,4,5,6]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[3,5,4,7,8,1,2,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,3,1,4,7,2,5,6]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[1,6,4,7,8,2,3,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,2,3,6,7,8,1,4]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[6,2,7,3,8,5,1,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,3,7,8,5,6,2,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,6,7,5,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,7,4,6,2,3,5]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,4,7,1,3,6]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,8,7,1,2,3,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,1,8,5,7,2,3,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,7,4,6,2,3,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,4,1,8,3,7]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,2,5,1,4,8,3,7]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,4,1,3,8,2,7]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,3,5,4,2,8,1,7]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,7,4,2,6,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,7,4,3,1,5,2,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,2,5,1,4,6,7,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,4,5,1,6,7,2]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,5,4,1,3,6,7,2]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[8,3,1,7,5,6,4,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,7,6,5,3,1,2]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,1,4,5,7,6,3,2]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,4,1,8,5,7,6,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,1,4,7,6,3,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[8,3,1,7,4,2,6,5]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,2,7,3,1,6,5,4]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,2,3,7,6,5]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,2,8,7,4,6,5]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,1,2,4,3,7,6]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,8,3,7,4,1,6,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,5,7,6,2,3,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,1,8,7,6,4,5]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,2,8,7,3,1,5,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,3,4,8,7,2,5,6]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[8,1,3,4,6,7,2,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[3,4,8,2,6,7,1,5]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,2,5,1,7,4]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,2,5,7,4,6,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,2,1,7,5,6,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,2,7,5,6,4,1,3]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,8,5,4,1,7,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,8,5,4,1,7,2,3]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,8,1,5,7,6,3,4]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,1,8,2,7,5,6,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,7,1,6,4,2,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,4,7,3,6,5,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,7,2,1,6,5,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,7,6,5,2,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,5,8,1,7,4,6,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,1,3,6,5,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,4,5,6,9,1,7]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[9,2,3,4,5,6,7,10,1,8]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[2,3,4,7,6,8,1,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,8,1,2,5,6,4,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,2,1,4,6,7,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[4,8,1,6,5,2,7,3]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,6,3,8,5,7,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,2,6,7,1,8,3]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,5,4,2,7,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,6,4,7,3,1,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,1,8,6,5,2,7,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,1,5,2,6,7,4]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[3,8,2,4,1,5,7,6]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,3,2,4,1,7,6]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,6,8,4,3,5,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,3,2,4,8,1,7]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[5,2,4,6,1,3,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,2,3,4,6,8,1,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[8,3,4,6,7,5,1,2]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[6,8,3,4,7,5,2,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,8,6,1,3,4,7,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,8,1,5,7,6,3,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,7,4,6,8,2,5,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,1,6,8,3,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,2,8,1,7,3,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,5,2,8,6,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,5,2,6,7,1,3]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,4,8,6,1,2,7,3]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[8,4,6,5,2,7,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,6,4,7,5,2,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,6,4,8,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,2,3,5,1,7,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,2,5,7,4,1,3,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[7,2,4,5,6,8,1,3]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[7,1,3,5,6,2,8,4]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,5,8,4,6,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,3,8,4,7,1,5,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,4,3,2,8,5,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,1,4,2,8,7]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,2,1,4,3,8,6]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,8,3,5,2,4,6]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,8,1,5,6,3]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,8,4,2,5,6,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,2,5,8,1,7,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,1,7,5,8,3,6,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,8,5,6,2,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,4,8,1,5,6,3]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,8,3,1,5,6,2]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,1,5,8,3,7,4,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,3,5,8,7,4,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,6,5,3,7,2,1,4]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[4,8,5,3,7,2,1,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,4,8,6,5,3,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[7,4,8,5,6,3,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,4,1,3,5,6,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,8,3,4,1,5,6,2]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,1,8,2,5,6,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,3,8,1,5,6,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,8,7,3,2,1,5]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[2,7,4,8,6,3,1,5]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,4,8,2,3,1,7,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,1,8,3,5,6,4]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,6,3,8,2,4,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,5,1,4,8,7,2]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,3,6,2,8,4,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,4,8,1,6,2,3]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,3,5,8,7,1,2,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[3,5,6,8,1,4,2,7]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,5,8,2,1,6,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[6,4,7,2,3,1,5,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,1,5,4,2,7,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,6,3,1,4,2,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,8,6,3,5,1,2,4]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,2,8,5,4,6,3,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,4,7,2,3,5]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,4,3,7,1,8,2]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,3,7,2,4,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,2,8,4,3,7,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,3,6,5,8,4,2]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,4,3,6,8,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,6,2,7,8,3,5,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,2,4,6,7,8,3]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[4,6,3,5,2,8,7,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,3,4,8,2,7,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,6,4,1,7,8,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,4,6,3,2,7,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,3,8,6,2,7,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,8,2,4,3,6,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,2,4,8,3,7,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,7,8,2,3,5,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,5,2,4,8,1,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,7,5,2,3,8,6,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,4,7,3,2,5,8,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,3,2,8,4,6,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,7,2,8,4,6,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,2,5,8,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,2,5,8,6,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,3,2,6,8,5,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,3,2,6,4,8,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,2,6,7,3,4,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,2,6,3,7,5,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,2,3,8,5,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,6,2,8,3,4,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,6,2,8,3,4,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,6,2,3,8,5,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,3,2,5,8,1,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,4,2,5,8,3,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[6,3,8,5,4,7,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]=>[7,2]=>2
[1,4,2,3,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]=>[7,2]=>2
[1,3,2,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]=>[8,2]=>2
[2,4,6,3,8,7,5,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,3,6,8,7,1,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,6,3,8,7,1,5]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,5,8,7,1,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,8,5,7,3,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,8,5,7,1,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,8,3,7,1,5]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,8,1,7,3,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,5,8,3,7,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,6,5,8,1,7,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,6,8,5,1,7,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,8,7,3,5,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,8,7,1,5,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,6,8,7,1,3,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,4,6,8,5,1,3,7]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,4,6,5,1,8,3,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,5,3,8,1,7]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,5,8,3,1,7]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,8,5,3,1,7]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,6,8,7,3,1,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,6,8,7,5,1,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,8,7,5,2,1,3,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[6,1,4,7,5,8,2,3]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,8,6,5,3,2,7,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,6,3,5,8,2,4,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,1,7,8,5,3,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,1,2,7,8,4,5,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,3,2,7,8,5,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,1,7,4,8,2]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,7,1,6,5,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,2,6,5,1,4,3]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,3,2,1,7,6,4]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,3,8,1,7,6,2]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,3,8,7,1,4,2]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,8,2,7,6,5,1]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,8,2,7,6,5,3,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,8,2,6,5,4,1,3]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,8,7,6,2,5,1,4]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,3,7,2,1,6,5]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,6,3,1,7,5,4,2]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[8,6,3,7,1,5,4,2]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,3,7,6,2,5,1]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,2,7,6,4,1,3]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,4,2,1,7,6,5,3]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[1,6,4,2,5,3,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,2,7,3,4,5]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,2,4,5,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[1,5,2,6,4,3,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,5,2,4,6,3,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,2,3,7,4,5]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,5,2,8,6,3,4,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,3,6,8,2,7,4,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,3,8,2,5,6,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,3,8,5,4,6]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,8,4,2,5,6,7]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,6,2,8,5,4,3,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,3,8,6,4,5]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,3,8,2,7,4,6]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,8,2,5,6,3,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,7,3,2,8,4,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,3,6,8,4,5]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,3,6,8,4,5]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,8,3,2,5,6,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,7,2,5,8,3,4,6]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,2,3,4,5,6,7,9,1]=>[[1,3,4,5,6,7,8],[2],[9]]=>[8,1]=>[8,1]=>2
[9,2,3,4,5,6,7,8,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[9,1]=>[9,1]=>2
[6,2,3,5,8,1,7,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,4,8,1,6,7,3]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,10,3,4,5,6,7,8,9,1]=>[[1,2,4,5,6,7,8,9],[3],[10]]=>[2,7,1]=>[7,2,1]=>3
[2,6,4,5,7,3,1,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,6,3,4,7,1,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,5,6,8,4,2]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,6,7,4,5,8,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,6,3,4,2,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,5,3,6,4,2,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,5,3,7,4,6,2,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,7,3,6,4,8,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,7,4,1,3,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,1,8,5,2,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,3,5,8,2,1,7]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,4,5,2,1,8,6,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,2,1,8,6,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,5,3,6,2,1,7,4]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,5,7,3,1,2,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,5,1,8,3,2,7,6]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,4,6,3,2,1,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,1,2,4,8,7,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,3,8,4,1,7,6]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,2,3,1,8,6,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,3,1,2,4,8,7,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[4,7,5,2,3,6,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,8,4,5,1,2,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,3,7,6,4,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,2,7,3,5,4,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,5,3,4,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,6,5,4,1,3,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,2,8,4,5,1,3,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,1,7,8,5,6,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,8,5,1,4,3,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,7,1,4,2,3,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,7,1,4,3,2,5]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,5,3,1,4,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,8,5,1,4,2,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,3,1,2,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[4,8,6,2,3,1,5,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,5,4,2,1,6,7]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,5,3,8,2,1,6,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,4,1,8,2,6,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,1,7,6,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,2,1,8,4,6,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,1,6,5,2,3,4]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,5,1,2,7,6,3,4]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[3,8,2,1,7,6,4,5]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,7,8,2,4,6,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,8,2,5,4,3,6,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,3,7,8,2,6,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,4,7,3,6,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,3,6,8,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,8,2,7,3,5,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,6,3,5,1,8,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,3,6,1,5,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,7,8,4,6,1,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,7,5,6,2,1,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,2,1,7,4,5,3,8]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,6,4,7,5,3,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,6,3,8,4,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,4,2,1,6,7,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[2,6,8,4,7,5,1,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,7,5,1,4,8,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,4,1,6,5,3,8,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,2,7,3,6,4,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,5,7,3,8,4,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,6,8,4,2,7,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,4,1,8,2,6,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,4,1,8,2,7,5,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,8,5,3,2,6,1,4]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,2,5,1,7,6,4,3]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,7,4,3,8,2,5,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,2,7,8,6,1,5]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,8,6,1,4,3,2,5]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,7,8,6,1,3,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[3,7,8,6,5,2,4,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,2,7,8,6,3,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,2,5,3,1,7,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,1,5,6,3,2,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[2,6,7,5,4,1,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[4,1,6,7,5,3,2,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,7,4,3,1,5,2,8]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,6,4,3,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,6,5,3,1,8,4,2]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[7,8,6,4,3,1,5,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[4,1,7,8,6,5,3,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,5,7,3,8,6,1,2]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,8,5,3,7,2,1,4]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,1,5,8,2,6,3]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,5,8,3,6,4,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,8,2,6,5,3,1]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,5,4,8,2,6,3,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,8,1,6,5,2,7]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,6,5,7,8,1,4]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,4,1,2,6,7,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,3,4,8,5,2,1,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,8,4,1,5,6,2]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,4,5,1,8,3,6]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,3,1,2,8,5,6,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,8,2,3,5,7,6,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,2,3,8,6,7,1]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,4,8,5,3,2,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[4,3,5,6,1,7,8,2]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,5,2,6,4,7,8,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,2,8,5,7,6,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,5,6,4,7,8,2]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,4,6,7,5,8,2]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,6,4,5,8,1,3,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,4,1,3,5,8,2,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[3,4,1,7,2,6,8,5]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,7,5,8,1,3,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,6,2,1,5,8,4]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,2,6,1,3,7,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,5,4,2,7,6,3,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[2,8,4,6,7,1,3,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,2,1,4,6,7,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[8,4,6,1,2,5,7,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,8,4,2,6,5,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,2,8,7,1,3,4]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[7,1,3,8,4,5,6,2]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,8,1,4,3,5,6,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,7,2,8,1,5,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,7,1,3,5,8,4]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,1,8,2,5,4]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,4,1,8,7,2,6,5]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,5,7,2,8,6,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,3,2,7,6,5]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,8,3,2,7,6,5]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,2,4,7,1,6,5]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,4,8,7,1,6,5]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,7,1,8,6,4]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,8,3,1,7,6,5]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,1,3,7,6,5]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,2,8,1,3,7,6,5]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,6,8,7,1,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[5,6,4,7,1,2,8,3]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,7,5,8,2,3,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,7,1,6,8,3,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,6,8,1,4,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,1,7,6,8,2,3]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,8,3,1,4,5]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,3,1,2,8,4,5]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,2,7,8,4,1,3,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[7,8,5,2,4,1,3,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,6,2,3,1,8,4,5]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,1,3,7,8,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,4,1,7,8,5,2,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,3,7,8,5,2,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,3,1,8,5,2,7,6]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[7,6,3,5,8,4,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[4,5,1,3,2,7,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,3,2,4,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,3,5,6,1,7,2,4]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,1,2,6,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,6,7,8,2,1,4]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,3,4,8,6,2,7,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,2,4,1,3,8,5,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,4,5,2,6,1,7,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,8,2,3,7,5,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,2,3,6,1,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,4,1,5,6,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,7,2,3,4,8,1,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,2,4,6,7,8,1]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,2,6,3,5,7,8,1]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,8,5,6,2,7,3]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,7,4,5,1,6,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,8,5,2,6,7,4]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,2,8,4,5,1,6,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,2,4,1,5,7,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,6,4,3,2,7,8,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,5,3,2,1,6,7,4]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[1,7,5,2,3,6,8,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[7,1,5,2,3,6,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,1,2,5,3,6,7,4]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,6,3,7,2,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,5,3,8,2,1,4]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,2,6,8,3,7,1,4]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,8,6,7,1,3]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,6,3,4,1,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,2,4,1,8,6,5]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,7,8,5,1,3,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,5,3,8,4,1,6,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,1,7,4,5,6,2,8]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,3,5,7,1,6]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,2,4,3,5,6]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,3,8,2,4,7,5,6]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,2,4,6,5,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,3,2,4,6,5,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,8,3,7,4,2,5,6]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,7,3,1,4,2,5,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[2,8,4,3,5,7,1,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,2,8,7,4,1,5,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,2,1,7,4,6,5,8]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,6,5,1,7,8,4]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,2,6,7,1,8,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,2,8,6,7,4,1,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,4,6,2,7,3,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,6,7,2,1,5]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,6,2,8,7,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,4,7,6,5,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,4,2,6,3,5,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,7,8,6,4,5,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,7,5,6,8,4,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,6,3,2,4,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,4,2,1,7,8,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[5,4,2,1,7,6,3,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[4,1,6,5,2,7,8,3]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,4,1,6,7,2,8,3]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[6,8,5,3,1,7,2,4]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,2,6,3,8,7,1,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,7,3,4,2,5]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,8,3,6,7,4,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,5,2,7,8,4]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,7,3,2,6,4,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,3,7,2,6,4,8]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,6,7,2,4,3,5]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,4,8,2,7,3,5]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,4,8,3,7,1,5]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,7,2,6,3,5,1,4]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,7,6,5,2,3,4]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,1,5,6,8,2,4,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,7,1,5,2,4,8,3]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,1,5,2,4,3,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,6,3,5,4,2,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,3,5,4,8,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,3,5,6,8,4,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,8,3,6,4,5,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,7,6,4,5,2,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,2,7,4,6,5,1,3]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,5,7,6,4,1,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,4,5,1,6,8,3,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,7,5,6,8,3,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,4,3,1,8,2]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,7,8,5,3,1,4,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,4,6,2,5,3,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,3,2,5,4,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,6,8,2,5,4,7,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,4,2,6,3,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,4,3,5,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,6,8,2,7,5,4,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,7,4,3,2,6,8,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,5,4,7,2,6,8,3]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,7,6,2,8,5,4]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,6,2,8,4,3,5]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,2,8,4,3,7,6]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,8,4,3,6,5,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,5,6,3,4,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,5,2,8,6,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,7,2,5,8,4,3]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,3,2,7,4,6]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,5,8,2,6,3,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,6,4,8,2,5,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,8,6,5,2,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,2,6,5,4,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,6,3,8,2,4,5]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,5,2,7,6,4,8,3]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,4,3,8,7,5,6]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,3,8,7,2,5,6]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[1,3,8,6,2,4,5,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,3,8,5,4,2,6,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,7,2,4,8,6,5,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,6,5,3,2,8,7,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,8,7,5,4,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,2,8,6,5,4,3,7]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,1,3,4,6,5,2,7]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[8,3,1,4,6,5,2,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[5,8,3,1,2,6,4,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,1,7,5,2,3,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,1,7,5,2,6,3]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,5,1,4,2,6,3,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,3,5,6,2,7]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[8,5,3,2,1,6,4,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,1,5,4,2,6,3,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,2,4,1,6,3,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,8,7,1,5,2,6,3]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,7,1,5,2,3,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,6,8,4,1,3,2,5]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,4,1,3,5,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,8,7,5,4,1,2,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,8,2,7,5,1,3,6]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,6,8,4,1,5,2,3]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,7,6,1,5,2,3,4]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[7,1,4,8,6,3,5,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,6,5,3,4,7,2]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,2,5,3,4,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,5,1,3,4,7,2]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[8,7,5,1,3,6,2,4]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,7,1,5,3,6,2,4]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,1,3,5,4,7,2]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,4,8,3,6,5,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,8,5,2,4,3,6,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,8,2,5,4,6,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,2,5,3,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,5,3,7,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,8,2,6,3,5,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,2,6,3,1,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,3,1,6,4,2,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,7,3,1,6,4,5,2]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,3,1,4,6,5,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,4,3,2,7,5,6,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,1,7,8,5,3,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[7,6,3,4,1,8,5,2]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,1,6,2,5,4]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,8,6,4,2,5,1,3]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,8,2,4,6,5,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,7,3,5,6,2,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,5,2,4,6,1,3]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,1,7,5,4,6,2,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,3,2,6,1,5,4]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,3,1,7,6,4,2,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[7,5,3,2,1,6,4,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,6,5,3,1,4,2,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[1,8,6,4,3,2,7,5]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,6,4,2,5,3]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[8,4,6,7,5,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,4,8,6,7,5,3,2]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,6,2,5,8,4,3,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,7,3,6,8,5,4,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,6,2,5,7,4,3,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,1,3,6,8,5,4,2]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[1,8,3,6,7,5,4,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,1,7,6,4,5,3,2]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,6,4,5,3,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,2,7,4,5,3,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,6,4,3,5,7]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,6,4,3,5,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,5,4,6,3,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,5,7,2,8,3,4,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,7,5,8,1,4,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,2,5,8,1,4,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,7,3,8,1,4,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,7,4,8,2,5,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,7,4,8,1,5,2]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,5,1,4,3,8,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,5,1,4,3,6,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,1,5,3,8,6,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,2,7,6,1,3,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,1,8,7,3,4,2,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,6,7,1,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[4,2,3,1,5,8,6,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,6,5,4,3,2,1,7,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[3,1,2,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[9,7,6,5,4,3,2,1,8,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[2,4,8,7,5,3,1,6]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,6,8,7,5,3,4,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,6,5,1,4,3,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,1,2,4,3,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,6,5,3,1,2,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,8,7,5,3,1,2,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[4,6,8,7,5,3,1,2]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,8,7,5,3,1,4,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[8,7,5,6,3,1,4,2]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,7,3,4,6,5,1,2]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[2,1,4,8,7,3,6,5]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,7,3,1,2,6,5]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,7,3,4,1,2,6,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,7,3,1,6,5,2,4]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,7,3,2,6,5,1,4]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[2,8,7,3,4,6,5,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,3,6,5,1,4]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,1,6,5,3,4]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,1,2,6,5,3,4]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,1,2,4,3,6,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,1,8,7,3,4,6,5]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,5,1,2,4,3,6]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[2,8,7,1,4,3,6,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,7,3,4,1,6,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,7,5,6,3,4,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,8,7,3,1,6,5]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,8,7,3,1,4,6,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,4,3,1,8,7,5,6]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,1,2,6,8,7,5]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[2,8,7,5,6,3,1,4]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,7,5,3,1,6,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[2,8,7,5,3,6,4,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,5,6,1,4,3]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,8,7,5,1,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,7,5,1,2,4,3]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,7,5,6,1,2,4,3]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,1,2,4,6,5,3]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[2,4,8,7,3,6,5,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,2,4,3,6,5,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,7,1,2,6,5,3]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,5,3,1,2,6,4]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,7,5,3,6,4,1,2]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[8,7,1,4,3,6,5,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,7,3,4,1,6,5,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[10,3,2,4,5,6,7,8,9,1]=>[[1,4,5,6,7,8,9],[2],[3],[10]]=>[9,1]=>[9,1]=>2
[9,4,3,2,5,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4],[9]]=>[8,1]=>[8,1]=>2
[7,1,2,3,5,4,6,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[7,1,2,6,4,5,3,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,2,4,3,5,6,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[1,10,2,3,4,5,6,7,9,8]=>[[1,2,4,5,6,7,8,9],[3],[10]]=>[2,7,1]=>[7,2,1]=>3
[4,7,3,6,5,1,2,8]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,5,4,2,8,3,1,6]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,3,6,1,5,2,4,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,6,8,5,7,2,4]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,7,2,1,8,4,6,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,8,6,4,3,1,5]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,3,8,7,4,2,1,5]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[7,6,3,2,8,4,1,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,6,1,3,2,4,5,7]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[5,8,3,7,4,2,1,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,1,7,3,5,8,6,2]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,3,5,2,1,6]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,1,3,2,6,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,8,2,1,3,6,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[8,1,3,5,2,4,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[1,8,3,5,7,2,4,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,1,4,2,7,6,3,5]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,4,5,6,7,8,2,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]=>[7,2]=>2
[1,3,4,5,6,7,8,10,2,9]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[2,1,4,5,6,7,9,3,8]=>[[1,3,4,5,6,7],[2,8,9]]=>[7,2]=>[7,2]=>2
[1,3,4,5,6,7,8,9,2,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]=>[8,2]=>2
[1,5,7,3,6,8,2,4]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,6,2,5,7,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,4,7,6,8,2,5]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,6,7,4,2,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,4,7,8,5,3,6]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,1,4,7,6,8,2,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,3,7,6,8,2,5]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,1,7,3,6,8,2,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,7,8,2,4,5,1,3]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,6,2,4,7,1,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,6,5,7,1,4]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,6,7,4,1,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,2,5,6,3,1,4]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,1,6,4,3,2,5]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,2,7,5,4,3,6]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,8,1,7,5,4,2,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,8,6,1,7,3,2,4]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,1,2,8,4,3,5]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,1,3,8,6,5,4,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,1,7,5,4,3,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[1,3,2,8,6,5,4,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,4,1,7,6,8,2,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,7,1,8,4,3,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,7,1,6,8,2,4]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,6,1,8,2,3]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,4,7,6,8,3,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,7,8,6,3,2,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,4,6,7,5,2,1,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,7,5,6,2,1,4]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,8,6,7,3,2,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,6,7,3,1,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,8,6,3,1,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,3,8,7,5,4,1,6]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,3,8,7,5,4,2,6]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,2,7,6,4,3,1,5]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,1,7,6,4,3,2,5]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,1,8,6,7,3,2,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,7,5,6,2,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,9,8,7,6,5,4,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[1,5,8,4,3,7,6,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,2,5,6,4,3]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,3,5,2,7,6,4]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,7,1,5,4,8,6,3]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,2,4,3,7,5,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,1,6,7,5,8,3]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,4,5,6,3,7,2]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,4,5,6,2,7,3]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,1,4,7,6,2,5,3]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,1,7,8,6,4,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,6,2,8,7,4,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,5,1,7,6,3,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,1,5,6,4,2,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,3,2,5,6,7,1,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,4,5,3,7,6,2,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,4,5,6,2,8,1,7]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,7,4,2,8,5,1,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,4,1,6,8,2,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,6,3,1,4,7,5,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,2,1,6,3,4,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,3,4,1,6,5,8,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,4,2,5,8,6,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,5,1,4,8,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,1,3,6,8,5,4]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,1,3,8,4,6,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,7,1,6,2,5,4]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,7,1,4,5,2,6]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,4,2,1,8,6,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,8,5,7,2,6,3,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,5,7,3,2,6,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,2,4,1,5,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,7,2,1,4,3,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,5,1,2,6,4]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,3,4,6,2,1,5,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[3,7,4,6,1,5,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,7,6,1,2,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,5,8,7,6,1,3,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,3,5,6,1,4,2]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,2,7,6,1,3,4]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[8,4,2,5,1,6,7,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,5,3,1,6,4,7,2]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,7,3,1,4,5,6,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,5,3,7,1,6,4,2]=>[[1,4],[2,6],[3,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,8,1,4,2,5]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,4,8,2,6,1,5,3]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,3,1,5,2,8]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,3,1,6,4,2,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[8,7,5,1,2,6,3,4]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,6,4,1,2,7,5,3]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[8,7,4,1,2,5,3,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[6,5,3,7,4,2,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[1,6,3,8,4,2,5,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,7,2,5,3,6,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,4,5,2,6,7]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,6,4,2,5,3,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,2,6,4,1,5,7,3]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,8,3,4,6,1,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,7,5,3,1,6,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[6,1,4,8,3,2,5,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[4,1,8,5,3,2,6,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,1,6,4,2,7,3,5]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,1,7,4,2,5,8,6]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,4,3,5,6,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[6,1,8,5,2,4,3,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,2,5,1,4,7,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,2,1,6,8,7,3]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[7,2,8,6,5,1,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,4,8,6,1,5,3,2]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,2,6,1,4,5,3]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,8,6,2,4,3,5]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,3,1,2,5,4,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[8,5,3,1,2,4,7,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,2,1,6,5,3,4,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,8,1,5,6,2,4,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,1,5,2,3,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,8,1,6,4,5,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,2,1,3,7,6,4,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[5,4,1,2,8,3,7,6]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,8,4,1,2,3,7,6]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[7,1,2,5,3,4,6,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[1,6,7,3,2,8,4,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,8,6,3,2,7,4,5]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,2,8,5,3,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,6,2,8,4,3,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,5,7,4,6,8,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,8,6,1,7,2,4]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,3,7,1,8,6,4,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,7,8,5,3,4]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,3,1,6,5,7,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,5,4,2,7,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,5,8,4,2,1,7,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,7,8,6,5,4,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,8,7,4,5,1,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,4,2,5,1,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,5,8,6,4,7,3]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,8,5,6,3,7,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,2,3,4,6,8,1]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,3,2,5,6,4]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,7,1,2,3,8,6,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,8,6,2,4,1,5,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,8,4,6,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,2,8,1,5,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,5,8,2,3,6,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,4,8,2,1,5,3]=>[[1,4],[2,7],[3,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,1,8,4,2,3,5,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[7,3,6,2,1,8,5,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,8,6,4,2,5,7,3]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,6,2,1,8,4,7,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,1,6,5,7,3,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,6,4,3,8,7,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,8,1,3,7,2]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,7,1,6,4,5,8,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,2,1,4,6,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[1,3,8,7,5,4,6,2]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,3,4,5,7,9,8,6]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,2,3,4,6,7,9,8,5]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,2,3,4,6,8,9,7,5]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,2,3,4,6,9,8,7,5]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[1,2,3,5,6,7,9,8,4]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,2,3,5,6,8,9,7,4]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,2,3,5,6,9,8,7,4]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[1,2,3,5,7,9,8,6,4]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[1,2,3,5,9,8,7,6,4]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[1,2,4,5,7,8,9,6,3]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,2,4,5,7,9,8,6,3]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[1,2,4,5,9,8,7,6,3]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[1,2,4,6,9,8,7,5,3]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[1,2,4,9,8,7,6,5,3]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[1,3,5,7,9,8,6,4,2]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[1,3,5,9,8,7,6,4,2]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[1,2,3,4,5,6,8,10,9,7]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,2,3,4,5,7,8,10,9,6]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,2,3,4,5,7,9,10,8,6]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,2,3,4,5,7,10,9,8,6]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,3,4,6,7,8,10,9,5]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,2,3,4,6,7,9,10,8,5]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,2,3,4,6,7,10,9,8,5]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,3,4,6,8,10,9,7,5]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,3,4,6,10,9,8,7,5]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[1,2,3,5,6,7,9,10,8,4]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,2,3,5,6,7,10,9,8,4]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,3,5,6,8,9,10,7,4]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,2,3,5,6,8,10,9,7,4]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,3,5,6,10,9,8,7,4]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[1,2,3,5,7,9,10,8,6,4]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,3,5,7,10,9,8,6,4]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[1,2,3,5,10,9,8,7,6,4]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,5]=>[5,5]=>2
[1,2,4,5,7,8,10,9,6,3]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,4,5,7,9,10,8,6,3]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,2,4,5,7,10,9,8,6,3]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[1,2,4,5,10,9,8,7,6,3]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,5]=>[5,5]=>2
[1,2,4,6,10,9,8,7,5,3]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,5]=>[5,5]=>2
[1,2,4,10,9,8,7,6,5,3]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[4,6]=>[6,4]=>2
[1,3,5,7,9,10,8,6,4,2]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[1,3,5,7,10,9,8,6,4,2]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,5]=>[5,5]=>2
[1,3,5,10,9,8,7,6,4,2]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[4,6]=>[6,4]=>2
[1,3,10,9,8,7,6,5,4,2]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[6,7,3,4,8,5,1,2]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,4,1,8,2,5,6,3]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,7,2,5,6,8,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,5,7,3,2,8,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,1,7,2,8,5,3]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,1,6,2,8,5,4]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,2,5,3,1,6,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,1,3,4,8,2,6,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[6,1,4,5,7,8,2,3]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[6,3,4,7,1,8,5,2]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,3,4,5,6,8,2]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[8,5,2,7,6,3,1,4]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,3,5,6,2,7,4]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,2,5,6,1,7,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,2,5,1,6,8,7,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,7,8,6,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,8,7,2,1,3,4,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,7,6,8,5,2,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,8,5,2,6,3,4]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,1,2,5,3,8,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,2,4,8,1,5,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,5,7,3,8,6,2,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,7,5,1,8,2,3,4]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,6,1,2,4,3,8,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,7,2,1,5,3,8,4]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,2,8,7,1,6,5]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,3,1,7,6,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,3,8,7,1,6,4,2]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,3,1,6,4,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,8,2,1,7,6,4]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,7,2,6,5,1,4]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,4,1,8,6,5,3,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,4,2,8,1,7,6,3]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,4,2,1,7,6,3]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,7,1,6,3,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,8,3,1,7,6,2]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,6,1,4,7,2,3]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,4,1,2,5,8,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[1,6,7,4,2,5,8,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,5,8,1,2,4]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,5,8,3,2,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,6,5,7,4,1,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,2,1,6,8,4,7,3]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,8,7,4,2,3,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,5,7,4,2,1,3]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,5,3,6,1,2,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,5,3,1,6,2,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,7,5,3,6,4,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,5,3,8,1,6,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,5,3,6,8,1,2]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,7,5,6,3,8,4,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,5,3,1,4,6,2]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[2,7,5,3,1,4,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,7,6,2,8,3,1,4]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,6,3,2,4,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,7,6,1,8,3,2,4]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,2,1,5,4,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,1,7,2,8,4,3,5]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,6,2,8,5,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,7,3,8,5,2,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,3,2,5,4,6]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,3,1,5,4,6]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,6,2,7,4,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,6,7,8,5,1,3]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[2,4,6,7,8,3,1,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[4,7,6,2,8,5,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,3,2,4,1,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,6,5,8,7,3,1,2]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,3,1,7,2,6,4,5]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,1,2,8,7,3,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,1,2,8,3,7,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,7,1,6,2,4,3]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,5,1,7,6,2,3]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,1,4,8,2,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,6,1,7,2,4,3]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,6,1,3,8,4,2]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,6,1,3,8,4,2]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,1,4,2,8,5,3]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,7,8,4,2,3,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,3,6,4,2,5,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[3,5]=>[5,3]=>2
[1,4,5,7,8,3,6,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,7,8,3,6,2,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,7,8,2,4,3,6]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,8,4,7,3,2,1,5]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,8,5,4,2,7,1,3]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,6,3,2,7,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,8,5,3,2,1,7]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[3,5,6,1,4,2,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,3,8,4,2,7,5]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,3,2,4,6,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,6,5,7,8,3,1,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,8,2,6,7,5,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,7,8,2,1,4,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,5,7,1,6,3,4,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,8,3,6,5,1,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,7,2,4,5,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,6,1,8,2,4,5,3]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,6,3,4,8,1,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,7,8,6,1,3]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[7,2,1,3,4,8,5,6]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[2,4,5,7,1,8,6,3]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,6,2,3,4,7,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,1,4,2,5,7,8,3]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[1,8,3,4,5,2,7,6]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,6,4,7,2,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,7,2,5,6,3,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,8,2,6,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,8,6,7,2,1,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,8,2,5,1,7,6]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,2,5,8,4,3,6]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,6,7,8,3,5,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,5,3,6,8,7,2]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,4,6,2,3,1]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,3,5,2,7,4]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,1,8,6,4,5,3]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,7,8,5,6,1,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,3,8,5,1,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,5,4,1,3,7,6]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,4,6,3,1,7,2,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,5,1,8,2,7]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,8,7,3,2,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,4,8,3,6,5,2,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,8,6,4,7,2,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,6,4,3,7,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,1,7,6,8,3,2,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,8,4,7,6,2,3,5]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,2,3,8,4,5,6,1]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,4,3,7,2,1,6]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,2,8,7,3,4,5]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[4,5,1,7,6,2,8,3]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,1,8,7,4,3,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,5,1,8,6,4,3,2]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,5,1,7,6,4,3,2]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,5,3,7,6,1,4,2]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,7,6,1,5,4,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,3,7,5,4,1,6,2]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,5,3,1,8,7,2,6]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,8,1,5,2,6,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,5,7,1,3,2,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,8,6,2,7,4,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,5,7,2,6,4]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,5,3,4,2,1,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,5,2,6,4,3,1,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,5,2,6,1,4,7,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,7,5,8,1,4,6,3]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,6,7,1,8,5,4]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,7,8,2,1,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,2,6,7,8,4,1,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[6,2,7,4,8,5,1,3]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,7,1,3,8,5,4,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,1,8,5,2,4,3]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,7,4,8,3,2,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,6,7,8,3,2,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[10,3,4,5,6,7,9,1,2,8]=>[[1,3,4,5,6,7],[2,9,10],[8]]=>[7,3]=>[7,3]=>2
[8,7,2,1,5,4,6,3]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,7,4,8,6,5,3,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,6,5,2,4,1,8,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,4,3,1,5,8,2]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[6,1,8,7,2,3,5,4]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,1,2,7,3,4,5]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[3,6,8,2,7,1,5,4]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,6,1,4,5,7,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,8,7,2,5,4,1,3]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,5,7,9,1,2,4,6,8,10]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]=>[6,4]=>2
[4,1,2,3,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[5,1,2,3,4,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[8,1,2,3,4,5,6,7,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[7,1,2,3,4,5,6,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[6,1,2,3,4,5,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[10]=>[10]=>1
[3,2,6,4,8,7,5,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,7,2,8,6,5,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,1,8,6,5,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[2,7,4,8,3,6,1,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,8,6,1,5,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,6,8,7,2,5,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,8,2,5,7,6,1]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,6,8,7,5,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,1,6,4,8,7,2,5]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,6,8,7,5,2,3]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,8,1,4,5,7,2,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,1,4,2,5,7,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,8,3,5,2,7,6]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,1,2,5,4,7,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,3,6,8,7,1,5]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[4,2,8,3,5,1,7,6]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,8,3,5,7,6,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,2,4,5,7,6,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,5,1,4,7,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,8,5,7,1,3,6]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,1,5,2,4,7,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,6,4,1,3,2,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,6,4,1,3,2,5]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,1,4,2,5,6,3,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,3,2,1,4,6,5,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,6,1,4,3,2,5,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,4,1,3,5,6,2,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[2,7,1,3,5,6,8,4]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,6,2,1,5,8,7,4]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,6,1,5,8,7,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,1,5,6,8,2]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,4,1,2,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,2,7,1,6,8,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,8,1,6,4,5]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,4,8,1,5,6,3,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,1,5,3,7,4]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,2,1,5,3,7,4]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,2,5,3,6,7,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,8,2,3,6,7,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,8,5,3,6,7,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,2,6,4,8,7,1]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,5,3,8,6,7,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,5,2,8,6,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,5,3,2,6,7,1]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,5,4,2,8,6,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,2,7,5,6,8,3]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,7,4,2,8,3,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,7,4,6,8,3,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,2,4,3,8,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,1,2,5,4,7,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,1,8,5,2,7,3]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[2,6,1,8,5,4,7,3]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,2,8,5,6,4,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,3,2,6,8,5,7,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,7,6,4,8,5,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,8,5,4,7,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,5,8,4,6,7,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,2,8,4,6,7,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,5,8,2,6,7,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,8,3,6,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,4,8,2,6,7,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,4,8,3,6,7,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,2,5,8,4,7,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,8,3,5,4,7,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,3,2,6,7,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,2,3,4,6,7,1]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,2,1,7,8,5,4,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[7,4,6,8,3,2,5,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,2,7,1,6,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,6,1,2,3,8,4]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[1,5,7,6,3,2,8,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,4,6,7,3,2,5,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,2,3,1,5,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,2,1,4,3,8,6]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[3,1,7,8,5,4,2,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,4,5,2,1,8,6,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,8,3,1,2,5]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,4,8,5,6,1,2,3]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,8,5,1,3,4,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[3,2,7,8,6,1,4,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[6,8,2,5,1,3,7,4]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,4,2,1,5,3,8]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,7,4,1,3,6,2,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,2,7,5,1,8,3,6]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,5,3,8,2,7]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,4,6,3,8,2,7]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,6,4,7,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,1,8,6,3,5,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,8,1,7,3,6,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,8,6,2,1,7,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,6,2,4,1,7,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,3,2,4,6,5,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,2,8,5,3,1,6,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,5,4,8,7,3,6,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,2,8,7,3,1,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[3,6,8,1,7,4,2,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,6,3,1,4,5,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[3,8,6,1,7,5,2,4]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,5,4,8,3,1,6]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,5,2,1,3,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,6,2,8,5,1,3,4]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[1,5,7,6,2,8,4,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,2,7,8,4,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,8,5,6,2,3,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,8,4,2,1,5,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,7,8,1,2,5,6,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,4,1,2,5,7,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[6,1,4,7,2,5,8,3]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,8,3,5,4,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,6,3,2,7,4,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,4,3,7,5,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,3,6,1,8,4,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,5,7,1,2,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,2,3,5,4,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,2,4,3,6,1,7]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,7,2,4,1,6,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,2,1,5,6,3]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,3,6,7,8,5,1,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[8,3,7,1,6,4,2,5]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,1,7,6,5,3,4]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[6,5,1,2,8,3,4,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[5,6,8,1,3,7,2,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,8,5,3,2,4,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[5,8,1,6,7,4,2,3]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,2,8,4,6,1,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,7,4,3,8,1,5]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,4,6,2,3,5]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,4,6,2,3,5]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,6,5,4,7,2,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,8,7,3,2,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,1,4,6,7,3,8,2]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,3,4,6,2,8,5]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,4,1,6,2,5,8,7,10,9]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[2,2,3,2,1]=>[3,2,2,2,1]=>5
[8,7,1,4,6,3,2,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[1,4,7,5,8,6,3,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,8,3,4,7,2,5]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,6,3,5,2,7,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,1,6,8,3,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,5,2,8,4,1,7]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,8,4,2,5,3,6]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,7,5,2,6,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,5,6,4,2,3,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[5,8,7,4,2,1,3,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[1,8,7,3,2,5,4,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,2,5,4,8,7,3,6]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,4,8,6,3,5,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[1,5,2,4,7,3,8,6]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,3,5,7,4,1,2]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,5,3,2,1,4,7,6]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[1,2,7,6,8,4,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,3,2,5,7,8,4]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,7,3,4,2,6,8,5]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,3,5,8,4,2,7]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,6,3,2,8,4,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,8,4,6,3,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,3,2,7,8,4,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,1,8,6,2,3,7,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,6,2,3,4,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,6,4,3,8,5,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,7,6,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,4,7,3,6,8,5,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,5,7,8,4,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,5,6,3,2,7,8,4]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,6,8,4,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,4,7,5,3,2,6]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,8,5,2,1,7,4,3]=>[[1,2],[3,6],[4,7],[5,8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,6,8,4,3,7,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,7,2,6,4,1,8]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,2,5,3,4,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,2,4,5,3,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,6,2,4,3,5,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,2,3,5,4,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,4,2,7,1,6,3,5]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,7,6,1,5,3,2,4]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,6,1,4,3,5,2]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,6,1,3,5,4,2]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[8,7,6,1,5,4,2,3]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[8,6,2,7,1,5,3,4]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,3,7,2,8,1,6,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,5,4,2,1,6,7]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,8,4,3,1,5,2,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,7,6,1,2,5,3,4]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[8,7,6,1,2,5,4,3]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[6,2]=>[6,2]=>2
[8,7,6,1,4,2,5,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,7,5,8,6,1,3,2]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,7,3,8,4,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,5,4,1,2,6,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,6,7,1,5,3,2,4]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,1,3,4,2,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,5,6,4,8,1,2]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,3,7,8,4,6,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,7,3,8,2,6,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,7,5,8,6,2,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,7,5,8,4,1,2,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,3,7,6,8,1,2,4]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,1,2,7,5,8,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,2,5,7,8,6,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[3,7,1,2,8,5,6,4]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,1,7,4,6,8,2]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,7,3,5,6,1,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,6,4,2,3,1,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,2,4,6,1,3,7]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,4,8,5,2,7,3]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,8,1,6,7,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,8,4,7,3,1,2]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,1,6,8,5,2,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,8,1,5,6,4,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,8,1,2,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,8,2,3,6,7,5]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,2,3,8,1,7,4,6]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,3,8,2,4,6,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,6,2,7,5,1,4,3]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,1,8,6,3,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,6,1,3,2,8,4]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,4,6,1,7,8,2]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,5,4,6,3,7,2]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,1,5,6,4,3,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,4,2,5,6,3,7,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,7,2,8,6,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,6,4,1,7,2,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,5,6,1,7,4,3,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,1,8,6,5,4,3]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[3,7,6,1,8,5,4,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,6,4,2,1,3,5,7,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[8,6,4,2,9,1,3,5,7]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[9,6,4,2,7,1,3,5,8]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[9,7,4,2,5,1,3,6,8]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[9,7,5,2,3,1,4,6,8]=>[[1,5,7,8,9],[2],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[9,7,5,3,1,2,4,6,8]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[10,8,6,4,2,1,3,5,7,9]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[10]=>[10]=>1
[6,4,2,7,1,3,5,8,9]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[4,5]=>[5,4]=>2
[8,6,4,2,9,1,3,5,7,10]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[5,5]=>[5,5]=>2
[6,2,8,3,1,4,5,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[9,6,4,2,7,1,3,5,8,10]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[5,5]=>[5,5]=>2
[2,7,8,3,1,4,5,6]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[9,7,4,2,5,1,3,6,8,10]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[5,5]=>[5,5]=>2
[9,7,4,5,1,2,3,6,8]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[4,5]=>[5,4]=>2
[9,7,5,2,3,1,4,6,8,10]=>[[1,5,7,8,9,10],[2],[3],[4],[6]]=>[5,5]=>[5,5]=>2
[9,7,5,3,1,2,4,6,8,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[10]=>[10]=>1
[1,5,3,2,8,6,7,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,3,2,6,7,4]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,5,6,7,3,2,8,4]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,7,5,2,3,4,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,7,5,2,4,8,6,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,7,8,3,2,4,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,4,8,6,2,3,5,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,8,4,5,6,7,2,3]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,8,6,3,5,7,4]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,8,4,3,5,6]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[1,8,6,7,4,2,3,5]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,7,8,4,2,3,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[1,6,7,8,3,4,2,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,4,2,3,8,5,6]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,7,8,4,2,3,5,6]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,7,3,5,6,2,8,4]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,8,3,4,2,5,6]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,2,3,7,8,5,4,6]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,7,4,6,3,8,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,8,4,5,2,3,6]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,8,3,4,5,2,6]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,4,5,6,3,7]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,5,6,2,3,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,2,7,3,4,1,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,7,2,3,4,1,5]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,5,2,6,1,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,3,2,5,1,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,8,1,6,7,4,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,1,3,7,6,4]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,8,3,6,7,4,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,4,6,2,7,5]=>[[1,3,5,7],[2,4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,1,6,5,2,3,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[1,8,7,6,4,3,5,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,1,8,7,5,3,4,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,7,3,2,4,1,5]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,7,5,6,8,4,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,7,5,8,1,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,8,7,6,4,5,1,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,7,6,3,1,5,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[3,5,2,4,7,6,8,1]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,2,6,4,7,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,2,6,7,4,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,7,6,4,8,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,5,2,8,4,6,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,2,7,4,6,8,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,5,7,4,6,8,1]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,7,5,4,8,6,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,2,4,8,6,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,3,7,5,4,8,6,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,6,8,2,5,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,8,4,1,3,6,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[3,8,5,2,1,4,6,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[7,6,4,1,8,2,5,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,5,4,2,1,6,3,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,1,6,7,3,4,2,5]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,1,6,7,4,3,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,2,8,6,3,7,1,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,8,1,2,5,4,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,3,4,8,5,7,6]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,3,9,4,5,6,10,7,8]=>[[1,2,3,4,6,7,8,10],[5,9]]=>[4,4,2]=>[4,4,2]=>3
[1,2,3,4,5,6,9,10,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[5,7,1,2,6,8,3,4]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,5,2,3,6,8,7,4]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,1,2,5,6,8,9,7]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[3,5,7,4,1,8,2,6]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,6,4,7,5,1,2,3]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[8,6,4,1,2,5,3,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[2,8,4,3,1,6,5,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,8,4,6,1,5,2,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,3,5,6,1,4,7,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,7,3,5,4,2,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,1,2,8,5,7,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,3,4,6,9,5,7]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[8,1,2,4,6,9,3,5,7]=>[[1,3,4,5,6],[2,8,9],[7]]=>[6,3]=>[6,3]=>2
[9,1,2,3,4,5,7,10,6,8]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[7,3,1,2,5,8,4,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[8,3,5,7,2,1,4,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,1,3,8,5,7,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[9,1,2,3,5,7,10,4,6,8]=>[[1,3,4,5,6,7],[2,9,10],[8]]=>[7,3]=>[7,3]=>2
[9,1,3,5,7,10,2,4,6,8]=>[[1,3,4,5,6],[2,8,9,10],[7]]=>[6,4]=>[6,4]=>2
[7,3,1,2,8,4,5,6]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[2,1,4,7,6,3,5,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[7,2,4,5,3,8,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,2,5,6,7,3,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[5,4,1,6,3,7,8,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,1,3,6,7,8,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,1,7,6,3,4,8,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,7,5,4,8,2,3]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,2,1,6,8,4,5]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[1,5,8,2,4,7,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,1,6,4,7,3,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,6,5,7,2,4,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,1,4,7,3,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,2,7,4,5,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,2,1,8,4,3,6]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,6,8,3,2,4]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,1,8,3,4,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,4,1,7,3,8,2,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,5,6,7,1,4,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,4,6,8,3,1,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[6,2,4,7,8,1,3,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[6,1,4,3,2,8,5,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,7,4,8,6,1,5,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,8,6,5,7,3,1]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,6,4,2,5,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,8,4,7,5,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,7,2,6,8,5,3]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,5,1,6,3,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,8,1,4,2,3,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,8,4,1,6,5,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,3,1,6,2,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,7,4,6,3,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,7,5,1,3,6]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[3,5,7,6,1,8,4,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,6,2,8,4,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,2,8,7,6,4]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,1,4,3,8,7,5,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,1,8,7,4,2,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[5,3,6,2,8,7,4,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,5,2,1,8,7,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,1,3,7,6,5]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,2,3,8,7,5,4,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,1,3,5,8,7,6,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,4,7,5,8,1,2,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,7,8,3,4,1,5,6]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,8,6,7,5,4,3,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,2,6,8,1,4,3,5]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,6,2,8,4,7,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,6,3,7,4,5,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,3,7,1,8,6,5]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,7,3,8,4,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,2,7,4,1,5,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,7,8,5,3,2,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,6,5,4,7,1,8,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,3,4,6,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,7,4,2,5,8,3]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,7,1,5,4,2,3]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,3,1,5,7,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,8,2,7,1,6,4]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,4,5,2,7,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,5,2,6,3,4,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[3,7,1,5,2,6,8,4]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,1,8,3,4,5,2]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,1,6,8,4,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,5,2,6,7,1,4]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,5,2,7,1,4,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,6,5,2,8,4]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,3,5,2,7,1,6,4]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,6,4,7,1,5,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,1,4,8,6,5,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,4,5,2,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,7,6,5,8,1,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,5,6,7,8,9,1,2]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[6,7,8,5,4,3,2,1,9]=>[[1,2,3,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[7,8,9,6,5,4,3,2,1,10]=>[[1,2,3,10],[4],[5],[6],[7],[8],[9]]=>[3,7]=>[7,3]=>2
[6,5,4,3,2,7,8,9,1]=>[[1,6,7,8],[2],[3],[4],[5],[9]]=>[8,1]=>[8,1]=>2
[3,5,7,6,8,2,1,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,3,7,6,1,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,3,7,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,6,4,7,5,2,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,5,3,6,4,1,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,5,3,6,4,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,5,3,7,4,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,3,7,5,1,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,3,6,4,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,6,2,5,4,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,8,2,5,4,1,7]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,1,4,6,5,2,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,3,7,2,5,4,1,6]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,3,6,4,1,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,8,4,6,5,1,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,7,3,6,5,2,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,5,4,1,6,3,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,2,6,4,1,5,3,7]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,3,7,5,2,6]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,1,4,8,5,3,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[5,2,1,4,8,6,3,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[3,2,1,5,8,6,4,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[4,2,8,3,7,5,1,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,8,3,7,4,1,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,2,6,4,1,5]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,1,4,8,5,2,6]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[1,3,7,4,8,5,2,6]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,6,3,7,4,1,5]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,3,8,4,1,5]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,3,8,4,1,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,4,8,5,1,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,6,3,8,4,1,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,5,3,8,4,1,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,5,3,8,4,1,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,5,3,7,4,1,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,6,4,8,5,2,7]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,4,8,6,2,7]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,4,3,7,5,1,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,3,8,5,1,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,3,8,5,1,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,4,3,8,6,1,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,3,8,6,1,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,3,1,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,3,1,7,5,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,2,4,3,1,6,5,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,1,3,6,4,2,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[8,4,1,3,6,5,2,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[1,5,2,4,7,6,3,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,2,5,3,1,6,4,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,2,5,3,1,7,4,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,3,1,7,5,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,2,6,4,1,7,5,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,4,1,6,5,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,3,1,6,5,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,7,3,1,6,4,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,7,3,1,5,4,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,6,3,1,5,4,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,5,2,4,8,6,3,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,4,1,3,7,5,2,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[6,2,1,5,3,7,4,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,6,4,7,5,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[3,2,8,5,1,6,4,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,4,1,5,3,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,4,1,5,2,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,2,5,6,4,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,2,4,8,1,7]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,2,8,7,4,3,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,2,8,1,4,3,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,3,1,5,2,7,6]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,5,3,2,6,8,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,5,3,2,1,4,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[8,7,6,4,3,2,1,5,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[8,7,5,4,3,2,1,6,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[8,7,6,5,4,1,2,3,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[9]=>[9]=>1
[9,8,7,6,5,4,2,1,3,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[8,7,6,5,2,3,1,4,9]=>[[1,6,8,9],[2],[3],[4],[5],[7]]=>[6,3]=>[6,3]=>2
[9,8,7,6,5,3,2,1,4,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[9,8,7,6,4,3,2,1,5,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[9,8,7,5,4,3,2,1,6,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[9,8,6,5,4,3,2,1,7,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[6,7,5,4,3,2,1,8,9]=>[[1,2,8,9],[3],[4],[5],[6],[7]]=>[2,7]=>[7,2]=>2
[8,6,2,3,1,5,7,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,4,2,7,3,6,8,5]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,2,1,7,8,5,4,6]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[7,3,4,2,1,5,8,6]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,7,6,3,2,4,8,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,1,6,4,7,8,5,3]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,2,4,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,2,3,7,5,8,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,8,5,3,2,4,7,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,7,8,1,5,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,7,1,8,4,2,5]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,7,6,2,4,5,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[2,7,3,8,4,5,6,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,4,3,8,5,6,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,2,7,8,3,4,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,1,8,5,6,2,3]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,5,8,1,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,8,1,5,7,2,3]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,4,1,3,6,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,2,1,4,7,5,8,3]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[2,6,1,5,4,7,3,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,6,8,4,1,7,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,2,8,6,3,5,4]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,2,3,7,1,6,5]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,2,4,8,7,3,1,6]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[3,2,4,6,7,8,1,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[5,2,6,8,1,3,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,1,6,3,7,5,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,5,2,6,4,3,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,5,2,6,1,4,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,5,6,2,7,4,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,7,6,1,8,5,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,4,8,6,3,5,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,1,8,5,4,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,3,2,1,6,4,8,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[3,6,5,2,1,8,4,7]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,7,2,4,3,5,8,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,8,2,1,5,7,6]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,3,2,8,1,6,7,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,5,8,3,2,7,1,6]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,2,7,3,4,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,7,8,2,3,6,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,8,2,1,6,7,5]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[9,1,3,4,5,6,7,8,2]=>[[1,3,4,5,6,7,8],[2],[9]]=>[8,1]=>[8,1]=>2
[3,5,7,4,6,2,8,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,7,6,2,4,8,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,7,2,5,3,8,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,8,3,1,5,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,7,3,1,5,6,2]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,8,1,7,6,4,2,3]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,6,7,1,8,3,4,2]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,6,2,5,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,1,7,6,4,2,3]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[1,5,8,2,6,4,7,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,7,4,6,8,3,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,7,5,6,8,3,2]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,7,4,8,1,3,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,2,6,4,5,7,3]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,1,7,2,5,6,3]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,7,1,5,4,8,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,6,5,8,1,4]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,3,4,5,8,2,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,1,8,4,5,6,3,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[10,1,3,4,5,6,7,8,9,2]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[9,1]=>[9,1]=>2
[1,8,3,4,5,6,9,2,7]=>[[1,2,4,5,6,7],[3,9],[8]]=>[2,5,2]=>[5,2,2]=>3
[1,2,7,4,5,8,3,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,4,5,6,7,8,9,12,10,11]=>[[1,2,3,4,5,6,7,8,9,10,12],[11]]=>[10,2]=>[10,2]=>2
[6,7,3,2,5,8,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,1,8,4,5,3,7,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,2,5,1,8,7,3]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,4,6,2,8,7,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,5,2,1,6,8,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,5,1,2,6,3,7,4]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[1,5,8,7,4,6,3,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,2,1,3,6,8,4]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,2,6,8,1,5,4]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,8,6,5,1,3,2]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,6,8,5,1,4,3]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,5,7,3,8,2]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,4,7,8,6,2,3]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,3,1,6,8,2,5,4]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,1,6,8,5,2,4,3]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,8,7,6,4,1,2]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,5,7,8,6,2,4,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,2,1,4,7,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,8,2,7,5,4,3,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[5,8,1,7,6,4,3,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[10,1,5,2,3,4,6,7,8,9]=>[[1,3,5,6,7,8,9,10],[2],[4]]=>[3,7]=>[7,3]=>2
[5,9,1,2,3,4,6,7,10,8]=>[[1,2,5,6,7,8,9],[3,4,10]]=>[2,7,1]=>[7,2,1]=>3
[10,8,4,9,1,2,3,5,6,7]=>[[1,4,7,8,9,10],[2,6],[3],[5]]=>[4,6]=>[6,4]=>2
[4,1,2,10,3,5,6,7,8,9]=>[[1,3,4,6,7,8,9,10],[2,5]]=>[4,6]=>[6,4]=>2
[4,1,5,6,7,8,9,2,3]=>[[1,3,4,5,6,7],[2,8,9]]=>[7,2]=>[7,2]=>2
[2,3,4,5,8,9,1,6,7]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[8,6,3,2,1,5,4,7]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,5,3,2,4,1,7,6]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,5,2,4,3,6,8,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,1,4,6,3,2,7]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,5,1,6,3,4,2,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,6,1,5,2,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,5,2,1,7,6]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,4,3,2,8,7,1,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[8,5,1,4,3,7,2,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,2,1,3,7,6]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[4,7,3,6,1,8,5,2]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,2,4,1,5,8,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,6,3,7,4,2,5]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,2,6,7,1,4]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,5,1,7,6,3,4]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,4,6,3,7,1,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,6,4,3,5,8,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,6,2,4,5,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,7,2,1,4,6,5]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,6,4,1,3,2,8,5]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,3,8,2,1,5,6,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,2,5,7,4,3,8,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,5,4,8,7,1,3]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,8,5,1,6,3]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,7,6,8,5,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,6,2,8,5,4,3]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,1,6,3,8,5,2,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,8,1,3,5,4]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,8,5,1,3,6,4]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[7,1,8,5,3,2,6,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,1,8,2,5,6,4,3]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,5,8,7,2,4,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,5,7,4,8,3,2]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,7,8,3,4,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,6,7,3,1,8,5,2]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,3,1,8,7,5]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,2,5,8,7,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,8,4,6,2,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,2,3,5,8,4,1,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[7,6,4,2,8,5,1,3]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[1,7,6,4,8,5,3,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,4,2,1,5,6,3]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[8,2,3,5,1,4,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[8,7,4,1,3,2,6,5]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,4,8,3,6,2,5]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,8,5,7,6,2,3]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,5,8,4,2,1,6]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,5,8,3,4,2,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,5,1,3,2,4,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,2,6,1,7,3,4,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,8,3,7,1,5]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[6,8,5,1,4,2,3,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,4,5,1,3,6,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,8,5,3,4,6,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,3,6,4,7,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,8,1,4,2,7,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,1,5,6,3,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,2,6,5,3,7,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,1,7,2,6,5,4]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,8,1,2,6,5,4]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,2,3,5,7,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,1,2,4,6,5,7,3]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,8,3,7,4,6,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,1,5,4,6,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,1,5,3,6,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,5,3,4,6,1,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,2,5,3,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[5,8,4,3,6,2,7,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,2,6,3,4,8,5]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,1,6,3,2,4,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,1,2,6,3,4,5,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[7,3,1,4,6,2,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,1,6,5,4,2,3,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,8,4,3,1,7,2,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,6,8,5,2,4,7,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,4,3,2,6,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,4,7,2,6,5]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,7,1,3,2,8,5,4]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,2,6,8,4,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,5,8,2,4,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,4,2,8,6,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,3,7,8,2,6,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,8,5,7,6,2,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,6,8,7,2,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,7,1,4,2,3,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,7,1,4,5,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[7,6,8,4,3,1,5,2]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,7,6,5,3,2,4,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[2,7,6,5,4,1,3,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[6,2,3,5,8,4,1,7]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,7,6,1,5,8,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[9,8,7,6,5,4,2,3,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[8,1]=>[8,1]=>2
[2,3,9,8,7,6,5,4,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[9,1,3,2,4,5,6,7,8]=>[[1,3,5,6,7,8,9],[2],[4]]=>[3,6]=>[6,3]=>2
[6,8,7,1,5,4,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,4,6,5,1,3,2]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[9,10,1,8,7,6,5,4,3,2]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[2,2,6]=>[6,2,2]=>3
[7,2,6,1,5,8,3,4]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,3,8,6,2,5,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,3,6,8,2,1,5]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,7,3,8,2,1,6]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,2,4,6,3,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,3,5,7,2,6,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,2,8,5,4,3,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,4,8,3,6,2,1,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,2,5,7,1,4,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,6,2,7,5,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,4,2,7,3,6,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,7,3,4,5,1,6]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,2,4,6,3,7]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,1,3,4,5,7,2]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[8,5,1,2,4,6,7,3]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[2,6,8,7,3,4,5,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,8,5,6,4,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,1,2,4,6,7,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[3,1,7,5,8,2,4,6]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,3,2,4,6,5,7]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,6,4,2,3,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,6,5,4,3,2,7]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,6,8,1,5,4,3,7]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,8,2,1,4,7,6]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,5,3,7,6,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,5,3,8,6,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,5,1,8,3,2,7]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,7,8,3,1,2,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[4,5,8,1,3,7,2,6]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,6,8,7,2,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,6,2,8,1,4,3,5]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,7,2,6,8,3,5,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,2,8,7,4,5,1]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,3,8,5,6,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,5,8,7,6,2,4]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,1,6,5,7,3,4]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,8,6,5,7,2,4]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,6,4,5,8,3]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,6,5,1,8,3,4]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,5,6,3,1,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,3,2,5,1,6,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,5,3,8,7,1,6]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[7,2,5,3,8,4,6,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,3,2,5,4,6,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,6,1,8,3,2,4]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,6,2,7,3,1,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,1,4,6,8,2,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,7,4,2,1,3,6]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,6,2,7,5,8,1,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,1,4,2,3,5,6]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,5,2,4,8,7,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,5,2,4,1,3,7,6]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,1,2,4,3,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,6,2,7,5,3,1,4]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[4,3,8,1,5,2,6,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,1,3,6,7,2,8,5]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,4,8,6,5,1,2,3]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[3,7,8,6,5,1,2,4]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[8,4,5,7,2,6,3,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,2,7,3,1,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,2,7,3,1,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,2,7,3,1,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,1,3,6,4,2,5]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,7,8,3,2,1,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,7,3,4,2,6,8,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,4,2,3,6,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,4,7,3,2,8,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,3,2,4,5,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,3,4,6,1,2,7]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,3,8,5,1,2,7]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[6,4,8,2,3,5,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,8,2,3,1,7]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,8,4,1,2,3,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[6,4,8,5,1,2,3,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[7,4,8,3,1,2,5,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,7,8,2,3,1,4,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,7,8,2,1,3,6]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[5,8,6,3,1,2,4,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[6,8,5,2,1,3,4,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,6,1,3,2,4,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,8,1,2,5,7,6]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,3,2,8,5,7,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,7,2,1,8,6,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,4,8,3,7,2,1,6]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,5,2,1,7,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,1,5,4,7,2,8,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,3,2,7,1,6]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,3,7,8,2,1,6]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[2,4,5,6,7,8,3,1,9]=>[[1,2,3,4,5,6,9],[7],[8]]=>[6,3]=>[6,3]=>2
[2,4,5,6,7,8,9,10,3,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[1,4,8,6,3,2,7,5]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,1,8,6,2,5,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,2,5,3,8,4,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,4,8,1,2,7,5]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,3,1,5,8,7,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[7,1,3,2,6,5,8,4]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,5,8,4,7,2,6]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,3,8,7,5,1,6,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,1,3,5,6,2,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,4,8,7,3,5,2,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,3,5,6,1,4,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[3,8,2,7,6,4,1,5]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,8,6,2,7,1,5]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,4,5,1,6,7,2]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,8,1,3,5,4,6,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,7,6,4,8,1,2]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,8,5,4,6,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,2,7,8,5,4,6]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,7,6,8,3,4,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,4,3,7,1,2]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,3,1,5,2,4,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[5,2,4,1,8,3,6,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,1,7,4,3,8,5,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,2,3,8,5,4,1,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,1,5,7,6,3,8,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,2,6,3,8,5,10,7,9]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[1,10,5,2,7,3,9,4,6,8]=>[[1,2,5,7,9,10],[3,6,8],[4]]=>[2,3,2,3]=>[3,3,2,2]=>4
[1,10,9,8,7,2,3,4,5,6]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[2,8]=>[8,2]=>2
[1,4,2,6,3,8,5,10,7,12,9,11]=>[[1,2,4,6,8,10,12],[3,5,7,9,11]]=>[2,2,2,2,2,2]=>[2,2,2,2,2,2]=>6
[1,4,8,2,3,6,5,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,6,7,3,5,2,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,8,2,6,7,5,3]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,3,2,4,5,6,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[1,7,3,2,4,5,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,6,4,3,2,5,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[4,2,6,5,3,1,7,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,2,1,6,8,7,4,3]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[1,3,5,8,6,2,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,7,8,5,4,2,6,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,3,2,7,5,6,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,8,5,7,4,2,6]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,3,7,5,4,6,8]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[1,4,2,8,6,3,5,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,8,6,3,5,7,4,1]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,1,8,2,5,3,4,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,5,4,2,3,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,1,5,2,3,4,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,4,8,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,2,5,8,7,4,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[6,5,2,1,8,4,7,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[5,6,2,4,3,8,1,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,5,2,8,1,4,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,4,7,3,2,8,6]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,1,5,8,6,2,3,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[5,4,8,6,3,7,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,3,1,8,7,4]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,7,5,3,8,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,4,8,3,1,6,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,5,1,8,7,2,6]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,3,6,1,8,4,7]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,6,8,3,1,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,4,5,3,6,2,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,2,4,5,3,6,8]=>[[1,2,4,5,7,8],[3],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,7,4,5,3,2,6,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,4,7,3,5,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,6,4,8,2,1,7]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,7,5,2,3,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[1,5,2,6,7,4,3,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,5,6,1,4,3,7,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,4,7,8,3,1,6]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,5,8,2,3,1,7]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,1,3,2,5,7,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,1,4,6,3,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,7,8,1,5,3]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,6,7,8,1,5,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,7,3,8,5,1,6,2]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,2,7,5,8,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,5,3,2,6,1,7]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,4,5,3,6,1,7]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,5,3,2,4,7,6]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,8,4,1,3,6,5,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,6,1,3,2,7,4,5]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,3,8,2,4,1,6,5]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,3,7,8,1,5,4]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,7,8,1,5,4,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,3,7,8,1,5,4]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,8,1,6,4,2,3]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,3,7,5,6,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,8,5,3,2,6,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,2,7,6,4,1,5,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,7,4,3,8,5,1,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,7,3,1,5,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,6,3,4,1,7,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,2,8,5,3,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,5,8,3,6,7,2]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,2,8,1,6,3,4]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,8,5,7,1,3,2,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,7,2,1,5,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,8,2,7,1,3,6,5]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,1,7,4,6,3,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,8,3,6,7,1]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,6,8,3,2,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,5,6,8,2,7,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,5,2,8,7,3,1,6]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,8,5,3,1,6,7,2]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[6,2,3,1,7,8,5,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,3,6,8,4,7,1]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,1,7,8,4,3,5]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[5,2,1,3,8,4,7,6]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,7,8,4,1,6,3]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,7,8,3,5,4,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,6,4,1,7,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,1,2,8,4,3,7,6]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,8,3,2,5,4,1]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,2,6,4,8,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,3,4,7,8,5,1]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[7,2,1,8,4,3,5,6]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[6,2,1,3,7,5,8,4]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,8,7,3,4,5,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,2,3,7,8,1,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[1,7,6,4,2,3,5,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,3,2,5,8,6,4,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,1,4,7,2,8,5,3]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,7,2,4,8,5,3]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,2,4,3,6,8,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,3,4,6,2,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,3,6,1,7,4,5]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,1,8,5,2,6,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[1,8,4,5,6,2,7,3]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,8,2,1,4,5,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,2,5,3,1,7,4,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,8,1,7,4,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,4,8,6,1,7,2]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,2,3,8,4,6,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,7,5,1,4,8,3,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,1,2,8,3,4]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,4,6,5,1,8,2,3]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,2,6,8,4,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,3,5,2,8,1,6,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,8,2,4,6,5]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,4,8,5,3,1,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,3,8,4,2,7,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,1,8,6,2,7,3]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[5,4,6,8,1,3,2,7]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,6,1,5,8,4,7,2]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,8,3,5,7,2,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,8,2,4,1,7,6]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,8,4,1,3,6,5]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[5,8,1,2,4,3,6,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,4,3,5,7,2,6,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,5,2,3,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,8,2,4,7,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,8,7,1,4,6,3,5]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,3,7,4,2,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,5,6,2,8,4,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,7,6,2,8,1,4,3]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,8,1,2,5,4,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,8,5,3,2,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[1,5,7,2,4,3,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,5,3,2,4,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,7,2,4,6,5,3,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,7,2,6,5,3,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,6,8,7,4,3,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,2,7,4,3,5,8,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,6,2,8,7,4,3,5]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,4,2,3,5,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,8,5,2,3,6,4,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,8,5,2,3,6]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[1,4,7,5,2,8,6,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,7,4,2,8,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,5,2,7,4,3,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,8,7,5,3,2,6]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,2,5,8,6,3,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,2,4,7,5,8,6,3]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,8,7,6,2,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,5,8,7,6,2,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,5,2,4,3,6,8,7]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,8,7,5,3,2,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,2,5,7,4,3,8,6]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,5,3,2,6,8,7,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,2,6,8,7,5,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,5,8,6,3,2,7,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,8,5,2,6,3,4,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,7,4,6,3,2,8,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,3,2,8,5,4,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,8,6,4,2,5,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,5,7,4,2,3,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,3,7,5,4,2,8,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,2,6,3,4,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,2,7,5,4,1,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,4,8,6,7,1,2,3]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,3,6,8,5,4,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,7,2,8,1,6,4,5]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,2,4,6,7,3,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[2,5,8,7,1,4,3,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,5,8,2,7,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,4,1,6,7,8,3]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[4,2,7,1,6,8,3,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,8,6,4,7,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,4,7,2,8,5]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,4,7,2,5,3,1,6]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,4,5,2,1,7,6]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,6,1,4,7,3,5,2]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,6,7,2,8,4,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,6,7,2,4,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,1,4,7,5,2,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[1,5,8,2,6,7,4,3]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,6,5,2,8,4]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,2,1,4,5,7,6,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[1,4,7,5,2,3,8,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,1,7,5,4,2,8,3]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,7,3,6,5,1,8,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,6,5,1,3,7,4,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[5,7,6,2,4,8,1,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,7,5,6,4,8,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,8,1,3,5,4,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,6,1,7,5,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,6,4,7,3,5,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,1,4,6,5,3,2]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,5,8,6,7,1,4,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,4,6,8,5,3,7]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,1,5,8,6,2,4,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[2,5,4,6,8,1,3,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,5,2,4,7,8,1,3]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,2,5,8,6,4,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[5,2,8,3,4,7,6,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,3,8,7,1,6,5]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,8,7,4,2,6,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,8,7,5,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[5,3,4,8,6,2,7,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,8,6,2,7,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,3,6,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,1,7,4,3,6,8,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,3,7,6,8,2,1,5]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,7,2,3,5,6]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[6,1,8,5,2,7,3,4]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,2,6,3,1,4,5]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,7,1,6,4,5,2,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,1,3,7,2,8,6]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,3,4,7,6,2,1,5]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[3,1,8,7,5,2,4,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,5,8,7,2,4,3,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,6,5,8,2,1,7]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,3,2,8,5,4,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[4,3,7,1,8,5,2,6]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,8,5,6,7,1,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,1,4,7,5,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[4,7,3,1,8,5,2,6]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,8,2,5,6,1,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,4,2,3,6,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[7,8,6,1,2,4,5,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,5,3,4,7,8,6,2]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,2,4,7,8,6,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[5,1,7,8,6,2,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[8,5,1,6,7,2,3,4]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[7,5,1,2,4,6,8,3]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[6,1,5,2,7,3,4,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,1,2,6,4,5,8,3]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,3,6,4,5,8,2]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,3,6,4,5,7,2]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,6,2,7,3,4,5]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,1,6,2,5,3,4,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,6,2,5,3,4,7]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,2,5,3,4,6]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,2,7,4,5,6,3]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,3,7,4,5,6,2]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,6,7,5,2,3,4]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,3,1,2,6,4,5,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[3,1,2,8,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,1,2,7,4,5,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[6,1,7,4,2,3,5,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[1,7,3,4,6,8,5,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,3,8,4,5,6,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,8,2,5,3,4,6]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,7,2,5,3,4,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,7,2,6,3,4,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,8,2,6,3,4,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,3,7,4,5,8,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,7,3,5,1,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,6,3,5,1,7]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,7,5,4,1,6,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,4,6,2,1,5,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,4,7,2,1,6,5,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,3,5,1,4,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,6,1,5,8,4,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,7,1,6,5,8,4]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,7,1,3,6,8,5]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,7,8,1,3,2,6]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,7,1,4,6,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,7,1,6,3,5,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,7,1,6,5,4,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,7,1,4,3,6,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,5,7,3,1,4,6,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[3,4,7,2,1,6,8,5]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,3,7,1,5,2,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,3,2,8,1,4,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,7,1,8,4,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,8,5,4,1,7,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,4,7,8,1,3,6,2]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,7,1,4,6,8,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,7,1,6,3,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,7,1,6,8,3,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,6,5,1,2,4,3,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[7,6,1,4,2,3,5,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[6,5,1,4,8,3,2,7]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,5,1,4,2,3,6]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[8,4,1,2,5,3,6,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[8,6,1,4,2,5,3,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,7,1,4,3,2,6,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,8,3,7,4,5,6,1]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,5,2,4,3,6,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,2,5,7,3,1,6,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[8,2,4,5,3,1,6,7]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[8,4,5,1,3,2,6,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,7,5,2,1,6,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,6,7,4,3,2,5,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,4,5,7,3,2,6,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[3,5,1,4,7,2,6,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,4,7,8,3,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,3,7,1,5,2,6,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,1,6,4,2,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,4,3,1,7,2,5,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[6,2,7,4,3,1,5,8]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,6,4,1,7,3,5,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,3,2,7,4,5,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,4,1,3,6,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,3,2,5,7,1,4,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,2,6,5,7,1,4,8]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,2,5,6,4,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,1,7,3,5,6,8,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,1,6,3,5,7,8,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,3,2,5,7,4,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,5,2,7,3,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,6,2,1,4,3,7,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,6,4,3,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,5,4,1,6,3,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[4,6,1,5,2,7,3,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,5,3,7,2,4,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,5,3,4,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,2,7,6,1,8,4,3]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,6,1,7,4,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,8,3,6,2,7,4]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,6,4,7,3,8,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,7,8,3,5,6,4]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,7,4,5,8,1,6,3]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,1,8,5,4,3,7]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,8,6,2,3,4,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,5,8,6,2,1,3,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[6,4,7,5,8,2,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,7,4,2,5,8,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,6,2,4,3,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,2,5,7,3,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,2,8,5,3,6,1,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,4,5,6,2,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,7,8,4,5,6,3]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,1,4,3,7,6,5]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,3,1,2,8,4]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[5,4,1,6,2,8,3,7]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[6,2,3,1,7,8,4,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,6,7,2,4,5]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,1,8,6,7,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,3,7,1,6,8,2]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,8,5,3,6,7,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,6,3,5,4,7,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,2,8,6,4,7,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,5,1,6,4,8,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,4,7,2,6,8,3]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,2,5,6,4,7,3]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,1,4,8,5,6,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,4,6,1,3,7,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,6,2,5,3,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,7,6,2,1,5,4]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,5,2,7,6,1,4,3]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,2,7,6,1,4,3]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,3,7,6,2,5,1,4]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,8,6,5,1,4,2]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[9,8,7,6,1,2,3,4,5,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[10]=>[10]=>1
[2,6,3,7,5,4,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,7,1,3,8,6,2]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,5,1,4,7,3,6]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,2,6,5,8,4,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,8,2,3,4,6,1,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,1,3,4,2,5,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[1,5,6,3,2,4,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[6,3,5,2,4,1,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,8,3,5,2,4,6,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,5,7,3,6,1,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,3,1,6,4,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,5,1,3,4,2,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[5,7,4,3,2,6,1,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,4,3,5,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,6,7,8,4,3,5,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,8,4,5,3,6,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,8,5,3,4,6,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,4,2,1,6,3,8]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,1,4,7,3,6,2,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,8,6,3,5,2,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,3,5,2,1,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,5,8,7,4,2,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,3,8,7,5,2,4]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[7,6,2,1,8,3,5,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,1,3,6,8,2,5,4]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,7,5,6,8,2,4,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,7,5,8,2,4,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,4,5,2,8,6,3]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,4,2,1,8,6,3]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[3,6,7,4,2,8,5,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,3,2,7,8,5,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,1,3,4,2,5,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[7,8,2,6,4,5,3,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,2,5,4,6,1,3,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,2,4,5,6,3,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[7,3,2,1,5,6,4,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[3,6,2,1,7,5,4,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,7,3,1,5,4,8]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,4,7,5,3,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,8,5,6,4,3,1]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,6,8,5,4,1,3,2]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,8,4,6,5,3,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,8,6,3,1,5,4,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,1,4,5,3,2,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,1,5,6,4,3,2,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,1,3,8,6,2,7,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,3,2,8,1,7,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,6,3,1,5,7,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,2,5,6,7,4,3,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,2,5,3,4,7,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,3,2,4,1,8,6]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,2,3,6,8,4,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[6,7,2,8,3,4,5,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,8,4,6,5,7,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,2,3,8,4,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,1,6,7,4,2,3,5]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,1,6,4,5,2,3,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,6,4,1,2,3,7,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,6,1,4,2,5,7,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,6,4,2,5,3,7,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,4,1,5,7,2,3]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[8,6,1,4,7,2,5,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,6,4,1,5,2,3,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,6,7,1,4,5,2,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,5,8,2,6,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,1,4,6,5,2,3]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,3,7,6,4,5,1,2]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,6,4,1,7,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,1,2,3,4,5,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[9]=>[9]=>1
[5,1,2,3,4,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[9]=>[9]=>1
[4,1,2,3,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[9]=>[9]=>1
[7,4,5,1,2,8,6,3]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,1,8,5,2,3]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,4,2,3,8,6,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,5,1,7,4,6]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,2,3,7,1,6]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,5,2,1,7,3,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,5,7,6,1,2,4,3]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,7,5,2,4,1,3]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,8,4,1,3,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,1,6,8,5,4,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[5,3,1,7,4,8,6,2]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,1,8,6,4,5,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,4,1,7,3,2,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[4,6,8,3,7,1,2,5]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,2,8,4,7,1,6]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,8,3,7,2,1,5]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,2,8,7,4,1,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,8,4,2,7,3,1,5]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[9,8,2,3,4,5,6,7,1]=>[[1,4,5,6,7,8],[2],[3],[9]]=>[8,1]=>[8,1]=>2
[8,9,2,3,4,5,6,7,1]=>[[1,2,5,6,7,8],[3,4],[9]]=>[2,6,1]=>[6,2,1]=>3
[5,6,7,9,8,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[5,6,7,8,9,1,4,3,2]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[5,2,2]=>[5,2,2]=>3
[10,9,2,3,4,5,6,7,8,1]=>[[1,4,5,6,7,8,9],[2],[3],[10]]=>[9,1]=>[9,1]=>2
[3,4,7,8,5,1,2,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,7,3,2,5,6,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,2,7,6,4,5,8,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,3,6,8,4,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,6,5,1,8,7,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[8,3,1,2,6,4,7,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[1,7,8,2,4,3,5,6]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,4,7,1,2,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,4,8,1,3,2,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,7,8,1,5,2,6]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,2,6,1,7,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,2,6,8,7,4,1,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,3,7,5,1,8,6,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,1,2,8,7,4,5]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[5,2,1,3,8,7,6,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[7,2,1,5,3,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[1,5,8,2,4,3,6,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,3,6,8,1,5,2,7]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,6,8,3,1,7,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,6,8,4,5,1,7,2]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,1,7,2,4,3,5]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,1,2,8,6,4,5]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[2,3,7,6,1,8,5,4]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,8,6,4,1,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,2,8,3,1,4,7,5]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,8,7,4,5,6]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[2,1,3,8,7,4,6,5]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,3,8,7,4,5,6]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[1,6,8,3,2,4,7,5]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,1,7,2,4,3,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,7,3,2,5,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,3,1,6,2,7,5,4]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,2,8,7,6,4,5]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,1,3,8,7,6,4,5]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,6,3,7,2,5,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,2,4,6,3,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,8,4,1,3,7]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,5,8,4,2,1,6,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[2,5,8,3,1,4,6,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[2,8,1,3,5,7,4,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,4,7,8,3,2,6,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,8,2,5,1,4,7]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,7,2,5,4,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,5,8,2,1,7]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,6,7,8,3,5,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,4,2,5,7,6,3,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,2,6,8,5,3,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,8,3,5,4,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,8,3,5,4,2,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,3,2,4,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,5,8,7,6,3,2,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,5,7,6,3,2,4,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,6,3,2,4,7,5,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,6,3,2,4,8,7,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,7,6,4,3,5,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,8,7,5,2,4,6,3]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,7,5,2,4,6,3,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,4,2,5,3,6,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,8,4,7,5,2,6,3]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,5,2,3,6,4,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,2,6,3,4,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,7,4,2,5,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,3,2,7,5,4,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,7,5,2,6,3,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,3,6,4,8,7,5,2]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,3,7,6,4,2,5,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,3,2,4,8,5,7,6]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,3,8,7,5,2,4,6]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,4,6,3,2,7,5,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,4,6,3,2,8,7,5]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,7,6,4,2,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,6,3,2,8,4,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,3,5,2,7,4,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,3,5,2,8,7,4]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,7,5,2,4,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,4,7,1,5,3,8,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,8,2,6,4,7,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,8,2,6,5,7,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,1,4,8,2,3,6]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,5,7,1,4,3,8,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,6,1,2,4,8,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,8,3,5,7,6,2,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,3,4,2,8,5,7,6]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,6,2,4,8,3,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,5,2,3,8,4,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,7,5,3,8,4,2,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,2,1,4,8,5,7,6]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[7,3,1,4,2,6,5,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[7,4,1,6,2,5,3,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,1,8,2,6,3,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[5,3,1,8,2,6,4,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,1,5,2,6,3,8]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,5,1,4,2,7,3,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,8,7,3,4,5,2,6]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,4,5,2,3,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,8,7,3,4,5]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[1,3,7,8,4,5,6,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,2,3,1,6,5,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,5,2,8,1,7,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,6,2,3,1,7,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,2,1,8,5,3,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[6,4,2,3,5,8,1,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[2,8,6,4,5,1,7,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,4,6,7,1,5,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,6,3,1,7,4,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,1,8,3,2,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,4,3,7,2,8,6,5]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,7,4,5,3,2,6]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,3,1,4,5,7,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[8,3,2,1,5,6,7,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[1,7,4,6,3,8,2,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,4,1,3,8,2,7]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,5,3,1,8,7,6,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,3,4,2,7,8,5,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,4,5,1,6,3,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,8,1,3,5,4]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,8,4,3,7,2,6]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,1,4,5,6,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,8,2,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,7,2,5,4,3]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,2,3,6,8,4,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[8,1,4,6,5,3,2,7]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,1,4,7,6,5,2,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,1,2,7,6,5,4,3]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[4,5,8,1,6,7,2,3]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,2,5,8,4,6,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,8,4,1,5,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,3,5,1,4,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,7,4,5,3,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,2,5,3,4,1,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,7,5,4,1,2,3]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[7,4,5,6,1,8,2,3]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,7,4,5,2,3]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,1,6,3,2,5]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,7,5,3,6,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,2,6,8,7,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,8,2,5,4,6,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,2,5,8,7,3,4]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,6,8,7,2,3,5,4]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,8,7,2,5,3,4]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,2,4,8,3,6,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,4,5,8,6,3,7]=>[[1,2,3,4,5,8],[6],[7]]=>[5,3]=>[5,3]=>2
[1,2,8,3,5,4,7,6]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,8,2,5,4,7,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,7,5,2,4,8,3]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,5,6,4,7,2,3,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,4,2,5,8,3,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,6,4,3,7,5,2,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,5,4,7,2,3,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,2,6,4,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,8,2,3,6,7,4]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,2,6,8,5,4,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,2,7,4,5,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,7,8,5,4,2,3,6]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,8,4,2,3,6,5,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,4,2,7,5,3,8,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,7,6,2,4,3,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,4,7,3,2,6,5]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,8,4,2,6,5,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,7,4,2,6,5,8,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,5,8,3,7,4,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,4,8,3,2,5,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,4,8,3,2,7,5,6]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,3,6,4,5,2,7]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,4,7,3,2,8,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,3,7,4,5,6,1]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,7,2,3,6,4,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,2,1,6,8,3,4]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[7,6,1,5,4,8,2,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,2,1,8,4,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[2,8,7,3,4,6,1,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,5,1,3,7,2,8,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,1,7,3,4,5,2,6]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,3,4,5,2,6]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,3,4,2,1,5]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,1,2,4,5,6]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[1,8,5,3,4,6,2,7]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[7,1,6,5,4,3,8,2]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,3,6,4,5,8,2]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,5,3,6,4,8,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,5,3,7,8,2,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,1,2,6,3,4]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,3,4,7,1,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,7,3,8,6,2,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,3,2,4,7,8,5]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,2,1,3,4,7,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[3,4,5,6,8,9,1,2,7]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[3,4,5,6,8,1,2,7,9]=>[[1,2,3,4,5,9],[6,7,8]]=>[5,4]=>[5,4]=>2
[3,2,5,8,7,4,1,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,2,5,8,7,3,1,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,4,1,6,5,2,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,4,8,5,7,2,1,6]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,4,8,5,7,2,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,7,3,6,2,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,8,7,3,1,6,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,5,8,2,1,7,4,3]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,3,8,7,2,5]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,3,2,6,8,7,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,8,7,2,4,5]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[1,2,8,4,5,7,3,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,1,8,7,6,3,5]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[3,2,5,8,7,1,4,6]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[5,6,3,8,7,2,1,4]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,5,8,4,7,1,6,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,2,4,8,5,7,3]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,6,5,8,7,2,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,8,5,3,6,7,1,2]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,3,4,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,1,3,6,4,5,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,1,7,3,5,4,6,2]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,6,3,2,5,4,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,2,4,8,5,7,1,6]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,4,7,5,6,3]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,5,8,3,1,7,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,6,2,1,5,7,3,4]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[4,6,2,8,5,3,7,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,2,4,1,5,3,6]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,4,8,6,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[2,8,3,1,4,6,7,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,3,6,5,1,2,7,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[5,8,3,7,6,4,2,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,3,8,7,6,5,2,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,8,7,2,6,3,1,5]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,7,2,6,3,5,4]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,2,1,4,3,5,6]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[2,8,7,1,6,3,4,5]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,8,7,6,5,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[1,2,5,7,4,8,6,3]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,1,8,7,5,3,4]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[6,3,8,7,4,5,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,3,4,1,5,6,7]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,3,7,5,4,8,6,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,3,1,8,2,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,3,8,4,2,7]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,5,3,8,4,1,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,3,8,4,2,6,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,6,2,8,4,1,7]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,6,5,4,8,1,7]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,4,8,2,6,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,7,1,2,8,4,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,7,2,5,4,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[9,7,8,5,4,3,2,1,6]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[6,8,4,1,7,5,2,3]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,4,6,7,5,2,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[2,6,8,1,4,7,5,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,8,1,2,7,5,3]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,1,6,7,5,3]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,6,4,7,5,3]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,6,2,7,5,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,2,6,7,5,3]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,2,1,6,7,5,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,2,4,6,1,7,5,3]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,1,4,5,6,7,8,9,10,3]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[4,3,5,6,7,8,9,10,1,2]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[6,3,4,5,7,8,9,10,1,2]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[8,3,4,5,6,7,9,10,1,2]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[5,4,7,6,3,1,2,8]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[3,6,4,8,1,5,2,7]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,8,4,1,5,2,7]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,1,4,2,3,5,6]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[3,8,6,4,1,5,2,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,2,6,5,7,1,3,4]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,1,3,2,8,7,5]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,4,8,2,3,6,5]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,3,6,7,1,8,2]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,7,8,3,5,2,6]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,1,3,5,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,1,4,8,3,7,6]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,1,2,5,4,8,7,3]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,7,3,5,6,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,2,5,7,3,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[2,4,5,6,8,3,1,7]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[3,4,5,8,6,2,1,7]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,5,1,8,6,3,7,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,4,5,6,8,9,2,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[8,3,7,2,1,6,5,4]=>[[1,3],[2,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,6,2,5,1,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,3,6,2,1,5]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,7,5,6,4,1,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,5,6,2,1,4]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,7,5,6,2,4,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,7,5,6,4,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,2,3,6,7,8,9,1]=>[[1,2,5,6,7,8],[3,4],[9]]=>[2,6,1]=>[6,2,1]=>3
[4,3,2,5,6,7,8,9,1]=>[[1,4,5,6,7,8],[2],[3],[9]]=>[8,1]=>[8,1]=>2
[5,6,7,2,3,4,8,9,1]=>[[1,2,3,7,8],[4,5,6],[9]]=>[3,5,1]=>[5,3,1]=>3
[5,3,6,2,4,7,8,9,1]=>[[1,3,6,7,8],[2,5],[4],[9]]=>[3,5,1]=>[5,3,1]=>3
[5,4,3,2,6,7,8,9,1]=>[[1,5,6,7,8],[2],[3],[4],[9]]=>[8,1]=>[8,1]=>2
[6,3,7,8,2,4,5,9,1]=>[[1,3,4,8],[2,6,7],[5],[9]]=>[4,4,1]=>[4,4,1]=>3
[6,7,4,5,2,3,8,9,1]=>[[1,2,7,8],[3,4],[5,6],[9]]=>[2,2,4,1]=>[4,2,2,1]=>4
[6,4,3,7,2,5,8,9,1]=>[[1,4,7,8],[2,6],[3],[5],[9]]=>[4,4,1]=>[4,4,1]=>3
[7,8,4,5,9,2,3,6,1]=>[[1,2,5],[3,4,8],[6,7],[9]]=>[2,3,3,1]=>[3,3,2,1]=>4
[7,4,3,8,9,2,5,6,1]=>[[1,4,5],[2,7,8],[3],[6],[9]]=>[5,3,1]=>[5,3,1]=>3
[7,5,8,3,6,2,4,9,1]=>[[1,3,8],[2,5],[4,7],[6],[9]]=>[3,2,3,1]=>[3,3,2,1]=>4
[7,5,4,3,8,2,6,9,1]=>[[1,5,8],[2,7],[3],[4],[6],[9]]=>[5,3,1]=>[5,3,1]=>3
[7,6,5,4,3,2,8,9,1]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[8,1]=>[8,1]=>2
[8,6,4,9,3,7,2,5,1]=>[[1,4],[2,6],[3,8],[5],[7],[9]]=>[4,2,2,1]=>[4,2,2,1]=>4
[8,6,5,4,3,9,2,7,1]=>[[1,6],[2,8],[3],[4],[5],[7],[9]]=>[6,2,1]=>[6,2,1]=>3
[4,5,2,3,6,7,8,9,10,1]=>[[1,2,5,6,7,8,9],[3,4],[10]]=>[2,7,1]=>[7,2,1]=>3
[4,3,2,5,6,7,8,9,10,1]=>[[1,4,5,6,7,8,9],[2],[3],[10]]=>[9,1]=>[9,1]=>2
[5,6,7,2,3,4,8,9,10,1]=>[[1,2,3,7,8,9],[4,5,6],[10]]=>[3,6,1]=>[6,3,1]=>3
[5,3,6,2,4,7,8,9,10,1]=>[[1,3,6,7,8,9],[2,5],[4],[10]]=>[3,6,1]=>[6,3,1]=>3
[5,4,3,2,6,7,8,9,10,1]=>[[1,5,6,7,8,9],[2],[3],[4],[10]]=>[9,1]=>[9,1]=>2
[6,7,8,9,2,3,4,5,10,1]=>[[1,2,3,4,9],[5,6,7,8],[10]]=>[4,5,1]=>[5,4,1]=>3
[6,3,7,8,2,4,5,9,10,1]=>[[1,3,4,8,9],[2,6,7],[5],[10]]=>[4,5,1]=>[5,4,1]=>3
[6,7,4,5,2,3,8,9,10,1]=>[[1,2,7,8,9],[3,4],[5,6],[10]]=>[2,2,5,1]=>[5,2,2,1]=>4
[6,4,3,7,2,5,8,9,10,1]=>[[1,4,7,8,9],[2,6],[3],[5],[10]]=>[4,5,1]=>[5,4,1]=>3
[6,5,4,3,2,7,8,9,10,1]=>[[1,6,7,8,9],[2],[3],[4],[5],[10]]=>[9,1]=>[9,1]=>2
[7,8,9,10,1,3,4,5,6,2]=>[[1,2,3,4,9],[5,6,7,8],[10]]=>[4,5,1]=>[5,4,1]=>3
[7,3,8,9,10,2,4,5,6,1]=>[[1,3,4,5],[2,7,8,9],[6],[10]]=>[5,4,1]=>[5,4,1]=>3
[7,4,3,8,9,2,5,6,10,1]=>[[1,4,5,9],[2,7,8],[3],[6],[10]]=>[5,4,1]=>[5,4,1]=>3
[7,5,8,3,6,2,4,9,10,1]=>[[1,3,8,9],[2,5],[4,7],[6],[10]]=>[3,2,4,1]=>[4,3,2,1]=>4
[7,5,4,3,8,2,6,9,10,1]=>[[1,5,8,9],[2,7],[3],[4],[6],[10]]=>[5,4,1]=>[5,4,1]=>3
[7,6,5,4,3,2,8,9,10,1]=>[[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>[9,1]=>[9,1]=>2
[8,5,9,3,6,10,2,4,7,1]=>[[1,3,6],[2,5,9],[4,8],[7],[10]]=>[3,3,3,1]=>[3,3,3,1]=>4
[8,5,4,3,9,10,2,6,7,1]=>[[1,5,6],[2,8,9],[3],[4],[7],[10]]=>[6,3,1]=>[6,3,1]=>3
[8,9,6,7,4,5,2,3,10,1]=>[[1,2,9],[3,4],[5,6],[7,8],[10]]=>[2,2,2,3,1]=>[3,2,2,2,1]=>5
[8,6,4,9,3,7,2,5,10,1]=>[[1,4,9],[2,6],[3,8],[5],[7],[10]]=>[4,2,3,1]=>[4,3,2,1]=>4
[8,6,5,4,3,9,2,7,10,1]=>[[1,6,9],[2,8],[3],[4],[5],[7],[10]]=>[6,3,1]=>[6,3,1]=>3
[8,7,6,5,4,3,2,9,10,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[9,1]=>[9,1]=>2
[9,7,5,4,10,3,8,2,6,1]=>[[1,5],[2,7],[3,9],[4],[6],[8],[10]]=>[5,2,2,1]=>[5,2,2,1]=>4
[9,7,6,5,4,3,10,2,8,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8],[10]]=>[7,2,1]=>[7,2,1]=>3
[1,5,6,3,8,2,7,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,3,8,4,7,1,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,3,5,7,8,1,4]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,5,6,3,7,2,8,4]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,5,3,6,2,8,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,7,3,4,2,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,8,3,4,2,7,6]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,5,3,7,2,8,6]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,5,3,8,2,7,6]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,1,4,2,7,8,3]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,5,1,4,2,8,7,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,7,5,4,2,8,6,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,1,6,8,3,7,2,4]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,7,1,8,6,3,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,4,8,2,6,5,3,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,5,1,3,6,2,4,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[7,5,1,8,3,4,2,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,1,7,4,3,6]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,2,5,6,8,7,3,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,5,6,8,2,7,4,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,7,3,4,1,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,5,7,8,2,4,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,6,7,2,8,4,3]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,7,6,1,8,2,4,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,3,7,2,6,4,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,8,6,7,3,4,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,5,8,7,2,4,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,7,6,2,8,3,4]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,5,8,6,7,4,3]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,2,6,5,7,3,8,4]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,5,8,6,4,2,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,6,5,8,1,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,7,8,1,6,3,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,6,8,1,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,6,8,1,2,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,5,8,3,2,7,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,6,8,2,3,7,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,8,7,1,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,5,8,3,6,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,6,8,5,2,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,3,6,7,5,2,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,5,7,3,6,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,4,7,8,5,6,3,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,8,7,5,2,4,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,7,8,5,1,3,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,8,4,6,5,3,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,8,4,7,5,1,3,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,7,8,9,1,2,3,4]=>[[1,3,4,5],[2,7,8,9],[6]]=>[5,4]=>[5,4]=>2
[7,6,1,2,3,5,4,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[2,8,7,5,1,6,3,4]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,7,6,4,2,1,5,3]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[7,1]=>[7,1]=>2
[3,8,7,5,2,6,4,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,7,5,1,2,6,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,8,3,7,1,4,6,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,7,4,2,6,5,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,3,2,4,7,6,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,8,2,4,6,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,3,2,6,1,7]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,1,4,6,3,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,5,8,3,6,2,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,3,6,1,2,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,1,8,5,4,6]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,8,5,2,3,1,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,7,8,1,5,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,1,3,8,5,4,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,7,8,4,1,3,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,6,7,8,4,3,1,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,1,2,5,3,6,7,8,9]=>[[1,3,4,6,7,8,9],[2,5]]=>[4,5]=>[5,4]=>2
[7,1,2,6,3,8,4,5]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,6,5,3,7,4]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,1,8,2,5,3,6]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[7,4,8,3,1,2,6,5]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,4,5,3,1,6,7,2]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,2,3,1,6,7,4,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,2,1,7,4,3,5,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,2,6,8,4,1,3,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[7,2,5,1,6,8,3,4]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,2,1,7,4,8,3,5]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,4,3,2,5,6,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,7,4,3,6,2,5,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,7,5,8,2,4,6,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,1,6,3,4,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[5,1,3,4,6,2,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,8,4,5,7,2,6,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,7,5,6,2,1]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,8,6,3,7,5,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,7,6,3,8,5,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,4,1,8,5,3,6,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,6,8,4,7,1,2]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,1,8,6,7,2,3]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,8,4,5,3,7,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,2,1,8,7,3,6]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,3,8,2,6,5,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,3,1,8,6,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[6,2,1,3,7,4,8,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[6,3,7,1,2,5,8,4]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,4,7,8,2,6,3]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,5,8,1,3,6,4]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,6,7,2,4,5,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,7,5,2,1,6,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[3,8,5,6,2,7,4,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,5,8,4,2,7,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,3,2,5,7,4,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,1,5,6,8,7,3,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,4,2,3,6,7,5,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[6,1,2,4,5,7,8,3]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[4,5,1,3,7,6,8,2]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,4,8,6,2,7,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,2,4,5,8,7,1]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,3,7,4,5,6,2]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,5,3,6,4,7,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,4,8,3,1,5,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,4,1,5,8,7,3]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,4,5,2,8,1,7]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,5,4,7,3,6,2]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,5,4,1,8,2,3]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[8,1,5,4,7,6,3,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,1,4,6,7,3,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,4,1,5,7,8,2]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[7,6,5,2,8,4,1,3]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[3,1,6,5,2,8,7,4]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,4,3,5,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,1,7,4,2,6,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,7,4,3,5,6,2]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,2,4,5,3,7,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,5,3,6,1,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,3,1,4,7,5,6]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,6,3,2,7,4,1,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[2,7,3,1,8,4,5,6]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,2,8,3,5,6,4,7]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,4,8,1,6,2]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,1,3,5,4,6,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,5,2,8,6,4,3,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,4,8,6,3,1,2,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[3,6,8,4,1,2,5,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,7,8,5,2,1,3,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[6,1,5,2,8,7,3,4]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,3,5,7,4,2,6]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[3,1,8,5,4,7,2,6]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,4,8,5,2,7]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,3,4,2,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,4,1,5,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[5,4,2,1,8,3,6,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[4,2,5,1,8,7,3,6]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[6,8,2,7,1,4,3,5]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,7,3,2,5,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,6,3,1,5,7,2,4]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[5,8,3,1,4,7,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,2,5,4,7,8,3,6]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,3,2,6,4,7,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,1,2,5,3,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,1,3,7,2,5]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,2,6,1,7,8,5,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,1,8,3,5,2]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,4,1,6,7,3,2,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[7,4,1,6,5,8,2,3]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,1,6,7,3,2]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[5,2,1,6,4,7,8,3]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,2,3,5,7,8,4]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,3,4,8,5,2,6,7]=>[[1,2,3,4,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[8,2,4,6,1,7,3,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,5,7,2,3,6,8,4]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,1,4,2,5,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,7,8,4,1,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,3,5,1,6,2,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[8,6,3,5,4,1,2,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,3,2,6,1,5,4,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,5,1,7,4,6,2,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,7,6,3,5,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,5,1,7,4,3,6,2]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,7,6,2,1,3,4]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,4,8,3,1,7,2,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,8,3,2,7,6]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,8,1,7,6,5,2,3]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,8,7,2,6,1,5]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,8,7,2,6,4,1,5]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,2,5,7,4,3,6,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,7,4,6,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,7,6,3,5,4,1,2]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[5,3]=>[5,3]=>2
[2,8,4,7,6,1,5,3]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,4,8,3,1,7,6]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,8,2,1,3,7,6]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,8,7,2,6,1,5,4]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,4,7,6,3,5,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,3,7,6,5,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,4,3,8,7,2,6,5]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,5,4,6,2,3,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,1,3,6,2,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[5,4,3,1,7,6,2,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[2,6,8,3,1,7,4,5]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,5,4,8,1,7,3,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,2,4,8,3,6,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,8,2,6,3,5,4,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,2,6,5,8,3,4,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,3,1,4,2,7,8]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,3,4,8,7,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,1,5,3,4,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,4,7,8,5,1,6,2]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,2,4,7,8,5,1]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,3,6,4,8,7,2,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,5,4,8,6,2,7,3]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,2,7,6,3,8,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,2,5,3,8,4,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,6,1,3,7,2,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,5,1,2,3,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[8,6,2,4,5,1,3,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[4,5,1,3,8,6,2,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,4,2,3,6,8,5,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[2,1,6,7,4,8,3,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,8,1,3,6,4,5,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,6,8,4,5,3,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,6,8,5,1,4,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,1,6,2,4,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,8,1,6,3,2,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,8,5,1,4,3]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,2,4,8,3,1,6]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,8,3,1,6,2,5,4]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,8,4,3,1,5,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,8,3,6,4,1,5,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,8,1,6,4,5,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,5,8,2,4,6,3]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,2,8,1,4,6,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,7,8,2,6,5,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,8,2,1,6,4,5]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,6,3,5,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,8,2,5,4,3,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,3,1,5,4,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,6,2,5,4,3]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,1,4,3,8,2,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,6,8,3,4,7,2]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,6,8,5,4,3,2]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,6,8,1,2,3,7,4]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,1,2,7,6,5,3]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,1,2,8,5,7,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,7,3,5,2,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,8,4,2,1,3,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[3,1,6,2,5,7,8,4]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,4,5,2,7,3,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,1,4,5,3,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[1,2,3,4,5,8,9,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[1,2,3,4,7,9,5,8,6]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[1,2,4,6,8,3,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,5,9,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6],[9]]=>[4,4,1]=>[4,4,1]=>3
[1,3,5,8,2,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,9,1,4,5,6,7,8,2]=>[[1,2,5,6,7,8],[3,4],[9]]=>[2,6,1]=>[6,2,1]=>3
[6,1,3,7,2,8,5,4]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,5,8,3,7,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,4,3,6,7,2,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,4,3,1,7,5]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,1,5,2,6,4,3,7]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,4,2,8,3,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,4,3,6,2,5]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,7,2,3,6,8,5]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,6,7,8,5,4]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[3,8,1,6,4,2,7,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,3,4,7,8,2,5]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,1,5,7,6,2,8,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,3,1,4,2,7,8,5]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[2,4,3,7,6,1,8,5]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,7,6,5,2,8,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,4,7,6,8,3,2,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,1,5,6,3,8,4]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[4,3,1,8,6,2,7,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[3,1,5,2,8,7,6,4]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,2,8,4,3,7,6,5]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,1,8,7,4,3,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,5,1,8,3,2,6,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,7,6,3,1,8,2,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,3,1,8,6,2,4,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[5,1,8,6,3,2,4,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,5,4,2,8,6,3,7]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,2,8,5,3,7,6]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,3,1,6,4,2,5,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[1,7,4,8,3,5,2,6]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,2,4,8,5,1,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[5,7,8,1,4,2,6,3]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,3,8,1,7,5,4]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,1,8,6,3,7,4]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,6,4,1,7,3,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,2,7,5,3,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,1,7,2,8,4,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,1,7,5,3,6,4]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,8,7,6,4,3,5]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,1,7,8,6,3,5,2]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,5,7,8,4,2,3]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,8,7,6,3,5,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,8,2,6,3,5,1,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,5,7,1,6,2,8]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,1,8,5,3,6,2,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,5,3,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,1,5,8,2,7,4,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,1,5,3,2,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,2,1,5,4,3,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[3,1,8,5,4,6,2,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,4,5,3,2,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,2,7,1,6,3,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,5,7,1,6,8,2]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,8,5,3,6,7,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,8,4,5,1,7,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,8,5,7,4,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,1,8,5,7,4,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,8,4,5,2,1,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,5,8,7,2,3,4,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,3,8,4,5,2,7,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,6,8,5,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,6,8,5,4,7,1]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,8,5,2,6,3,7]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,8,5,2,4,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[6,5,8,7,4,1,2,3]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[6,5,8,7,4,2,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[6,5,8,7,2,4,1,3]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,4,5,7,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,4,5,7,3,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,9,2,10,3,4,5,6,7,8]=>[[1,2,4,6,7,8,9,10],[3,5]]=>[2,2,6]=>[6,2,2]=>3
[4,2,7,3,5,8,6,1]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,2,4,8,5,7,1]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,1,8,4,7,6,2]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,1,8,5,4,7,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,8,3,7,6,5,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,6,8,2,5,7,4,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,5,4,3,7,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,8,2,5,4,7,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,8,3,2,5,7,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,2,8,3,5,7,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,1,8,5,7,4,2]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,6,8,4,1,7,3]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,8,7,2,5,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,8,2,7,4,6,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,8,5,7,4,3,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,8,7,6,3,5,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,1,6,3,2,8,4]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,7,6,3,4,1,8,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,6,3,1,2,8,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,8,2,1,7,5,6,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,8,5,7,2,4,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,4,8,6,2,3,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[8,2,1,7,5,3,6,4]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,2,1,6,7,3,5,4]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,8,1,7,5,3,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,1,8,7,6,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,7,8,3,5,6,1,2]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,4,5,7,8,6,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]=>[7,2]=>2
[3,2,5,6,8,4,7,1]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,5,2,6,3,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,6,4,8,3,7,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,5,7,3,8,1,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,3,1,6,8,2,5]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,2,7,6,8,1,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,4,6,8,3,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,2,5,6,3,1,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,4,1,3,7,8,2,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[6,1,5,8,3,7,2,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,1,6,8,3,5,4]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,6,4,1,8,3,2,7]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,7,8,5,1,6,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,6,7,4,3,5,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[5,8,6,3,4,1,2,7]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,10,1,4,5,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4],[10]]=>[2,7,1]=>[7,2,1]=>3
[6,2,3,1,8,5,4,7]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,2,6,4,8,3,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,2,3,7,5,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,7,9,1,2,3,4,5,6]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[4,5,2,8,6,1,3,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[3,4,8,2,5,6,1,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,2,7,5,3,1,4]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,3,2,5,8,4,1,7]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,6,7,2,8,4,1,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,8,3,6,4,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,8,5,2,7,1,6]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,5,1,6,3,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,5,8,4,7,1,6]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,8,1,3,4,7,6]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,1,8,7,4,2,6]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,6,1,3,8,2,7,5]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,1,2,3,5,7,4]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[5,1,7,8,3,2,4,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,1,7,6,2,8,5,4]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,7,4,2,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,8,6,7,3,1]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,1,4,2,8,7,3,5]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,2,6,8,4,5,1]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,5,2,7,8,3,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,2,7,8,3,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,6,4,2,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,2,1,8,5,7,4,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,6,2,3,1,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,7,8,1,3,4,2]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,7,6,8,4,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,2,8,3,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,7,8,4,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,7,3,1,5,2,8,6]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,6,3,1,5,8,2]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[2,7,3,1,8,5,4,6]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,3,1,7,4,5,6]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,6,8,9,1,2,3,4,5]=>[[1,3,4,8,9],[2,6,7],[5]]=>[4,5]=>[5,4]=>2
[5,4,6,7,8,9,1,2,3]=>[[1,3,4,5,6],[2,8,9],[7]]=>[6,3]=>[6,3]=>2
[1,8,2,7,3,5,6,4]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,4,8,6,5,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,6,3,5,7,4,8,2]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,4,7,2,8,3,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,5,2,6,1,7,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,4,8,5,2,6,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,2,6,5,3,4,7]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[3,7,4,2,5,6,1,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,1,3,4,2,5]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,2,8,6,7,5,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,8,6,1,4,2,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,1,5,2,7,8,4]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,2,6,3,5,7,4]=>[[1,3,4,6,7],[2],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,8,4,7,1,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,7,8,4,2,5,6,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,4,2,8,5,1,6,7]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,4,3,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]=>[2,7]=>[7,2]=>2
[6,8,2,7,5,4,1,3]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,4,3,7,6,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,8,7,1,2,6,5]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,8,4,5,7,6,2,3]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,8,5,7,1,6,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,4,8,7,2,1,5]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[5,3,8,4,7,1,6,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,8,7,1,4,6,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,7,1,6,4,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,3,1,6,4,5]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,5,1,4,6,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,8,7,4,1,6,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,4,6,8,3,5,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,8,1,3,6,4,5]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,1,5,4,6,3]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,8,1,4,5,6,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,8,2,4,1,5]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,7,8,6,3,1,2]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,4,6,8,7,3,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,5,8,6,7,1,3,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,6,8,2,1,3,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,6,8,2,4,1,5]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,7,8,6,3,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[4,5,7,8,2,6,1,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,6,8,7,3,1,2]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,1,5,3,8,4,7,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,6,2,5,4,7,3]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,1,7,5,2,6]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,2,7,4,8,3,1,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,5,1,4,3,7,6]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,2,7,5,1,4,3]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,3,4,5,6,1,7,2]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,3,6,4,7,2,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,5,7,3,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,4,6,2,7,3,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,6,5,8,4,1,7]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,6,5,8,7,1,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,5,8,7,1,3]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,2,6,4,8,7,1,3]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,4,7,6,8,2,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,7,5,8,3,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,5,8,6,1,3]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,5,8,4,1,6]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,7,2,8,5,1,6]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,6,2,8,5,1,7]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,7,6,8,5,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,6,8,2,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,2,8,6,1,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,6,4,8,7,1,5]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,3,8,6,1,5]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,6,8,3,1,4]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,6,8,4,1,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,6,8,5,1,4]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,2,7,5,8,4,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,1,7,3,2,5,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,4,8,2,1,5,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,7,8,2,5,4,6,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,5,8,3,2,6,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,1,3,2,5,8,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,6,4,1,5,3,2]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[6,2]=>[6,2]=>2
[3,8,5,2,6,4,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,5,3,4,8,1,6]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,5,3,7,8,6,1]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,2,4,1,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,6,2,3,5,4,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,2,6,3,7,4,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,2,3,7,5,6,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,5,6,2,3,8,4,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,5,6,4,3,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,3,7,5,6,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,5,7,6,4,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,8,6,3,5,4,2,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,7,6,3,8,5,4,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,4,2,5,6,3,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,7,5,3,8,4,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,8,3,7,5,6,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,8,3,7,5,6,2,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,5,8,3,7,4,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,3,8,2,5,6,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,5,6,3,7,4,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,3,7,1,2,6,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[8,5,6,4,1,3,2,7]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,2,8,4,3,1,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,7,3,2,8,4,1,5]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,8,3,1,5,2,6]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,1,3,2,6,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,7,8,1,6,3,2,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,3,8,6,5,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,7,2,8,3,4,6,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,2,8,5,6,4,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,1,5,8,6,4,7,2]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,8,6,4,5,7,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,6,1,8,7,3,4]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,2,8,4,7,5,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,6,3,1,4,2,7]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,3,4,6,2,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,1,8,6,4,2,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,5,3,8,6,4,2,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[5,1,3,8,6,4,2,7]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,5,8,3,6,4,2,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,3,6,4,2,1]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,5,8,6,3,4,2,7]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,8,2,6,4,1]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,8,1,4,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,8,4,2,6,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,5,3,4,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[1,4,6,5,7,2,3,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,6,7,3,5,4,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,5,1,3,7,6,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,3,2,6,8,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,7,5,4,2,6,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,2,6,4,7,3,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,3,7,2,5,8]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,8,3,2,6,1,4]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,3,4,5,6,9,8,7,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[2,3,4,5,6,7,10,9,8,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[2,3,4,5,8,9,7,6,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[8,4,5,1,3,7,6,2]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,4,3,7,1,5,2]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,3,1,8,6,5,2,4]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[2,7,3,1,4,8,6,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,6,5,7,8,4,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,1,5,8,7,6,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,7,1,3,2,5,6,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,7,2,5,6,8,4,3]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,7,6,8,3,1,5,2]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,4,7,1,8,6,2]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,5,4,2,3,6,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[7,1,3,6,4,5,2,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,3,8,4,5,2,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,8,7,3,6,5,4]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,6,3,1,2,7,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,8,2,7,1,3,6,4]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,5,4,1,3,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[4,1,5,7,6,3,2,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,5,1,7,6,3,2,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,4,2,1,8,7,3,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[6,2,1,5,4,3,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,4,2,6,7,8,5,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,2,5,6,8,7,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,3,6,7,8,4,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,6,2,4,3,5,7]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,4,5,7,8,1,6]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[2,3,4,7,5,8,6,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,2,8,7,4,3,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,8,5,4,2,1,6,3]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[7,5,2,8,6,4,3,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[7,8,3,2,6,5,4,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,2,6,3,7,5,1,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,7,2,5,3,1,4]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,2,7,8,4,5,3]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,6,2,7,5,4,1,3]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,6,8,2,7,5,3,4]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,3,2,8,1,5,4]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,1,7,4,3,8,6,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,7,2,4,1,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,8,6,4,2,3,5]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,2,8,6,4,1,3,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[1,5,3,7,4,2,6,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,7,6,4,3,2,8,5]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,7,6,3,4,2,5,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,7,4,3,8,6,5]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,4,2,3,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[1,5,3,2,4,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,6]=>[6,2]=>2
[1,5,4,2,3,7,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,2,7,6,3,5,8,4]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,3,2,6,5,7,4]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,5,6,1,8,4]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,5,1,6,3,8,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,6,1,4,3,8,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,3,5,2,7,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[10,5,9,4,8,3,7,2,6,1]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[3,2,2,2,1]=>[3,2,2,2,1]=>5
[1,4,2,5,3,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[8,3,6,5,4,1,2,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,7,5,8,4,6,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,5,7,1,2,8,3,4]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,1,4,2,3,8,6,5]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,5,3,7,6,4]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,5,2,4,1,7,3]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,6,5,2,4,1,7,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,2,4,3,1,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,4,2,8,6,7,1,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,7,2,5,1,8,3]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,2,5,1,7,8,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,2,7,8,1,5,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,1,4,2,5,8,6,3]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,5,1,2,4,3,6]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,1,4,3,6,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,3,8,6,4,1,5]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,2,3,8,7,4,1,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,7,6,3,1,2,4,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[4,2,6,8,1,3,5,7,9]=>[[1,3,4,8,9],[2,6,7],[5]]=>[4,5]=>[5,4]=>2
[4,6,2,7,8,1,3,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,2,3,7,1,4,5,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[4,2,5,7,9,1,3,6,8]=>[[1,3,4,5],[2,7,8,9],[6]]=>[5,4]=>[5,4]=>2
[2,3,5,7,9,1,4,6,8]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[4,2,6,8,10,1,3,5,7,9]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[5,5]=>[5,5]=>2
[6,4,2,8,1,3,5,7,9]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[4,5]=>[5,4]=>2
[4,6,7,8,2,1,3,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[4,8,2,5,9,1,3,6,7]=>[[1,2,5,9],[3,4,8],[6,7]]=>[2,3,4]=>[4,3,2]=>3
[4,2,5,7,9,1,3,6,8,10]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[5,5]=>[5,5]=>2
[1,4,5,7,9,2,3,6,8]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[2,3,5,7,9,1,4,6,8,10]=>[[1,2,3,4,5,10],[6,7,8,9]]=>[5,5]=>[5,5]=>2
[8,6,3,2,1,7,5,4]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[6,1,3,4,2,5,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,1,3,6,2,4,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,5,7,6,8,2,4,3]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,1,3,8,4,2,6]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,1,4,3,7,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,2,4,3,5,8,7]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,7,6,1,8,4,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,3,7,8,4,2]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,7,6,3,8,4,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,6,1,8,4,2]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,6,1,5,8,4,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,7,8,5,4,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,8,6,3,5,4,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,6,1,8,4,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,6,2,8,4,7,3,1]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,5,4,1,2,6,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[7,8,5,1,3,2,4,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,5,1,3,8,6,2,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[7,1,3,8,2,5,4,6]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,5,4,7,2,6,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,6,1,3,8,2,4]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,3,8,1,4,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,3,7,6,2,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[1,6,3,7,2,4,5,8]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,3,2,4,8,1,7,6]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,8,5,3,2,7,1,4]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,3,7,2,6,5,1,4]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,2,7,1,3,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,1,4,7,2,8,6]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,4,8,7,3,2,6]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[6,1,3,4,2,7,8,5]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,5,2,3,7,8,1,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[1,5,3,8,4,2,7,6]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,2,1,8,3,7,6]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[3,1,7,4,2,6,8,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,4,8,2,3,5,1,6]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,1,3,2,6,7,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,7,3,2,5,6,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,6,5,2,7,3,1,4]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[3,1,6,8,4,2,7,5]=>[[1,3,4],[2,5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,9,4,3,5,6,7,8,1]=>[[1,2,5,6,7,8],[3],[4],[9]]=>[2,6,1]=>[6,2,1]=>3
[5,6,2,3,7,4,1,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,2,4,7,3,5,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,4,8,5,3,6,7,2]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,6,3,1,8,4,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,5,1,2,7,8,6,3]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,5,1,2,6,7,3]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,6,7,5,1,2,8,3]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,2,8,1,4,5,3,6]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,7,3,8,2,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,6,3,4,8,2,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,8,4,6,3,1,5,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,2,6,3,5,1,4,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,7,4,1,5,8,2,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,8,4,1,7,2,5,6]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,7,5,1,3,8,2,4]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,1,3,6,7,2,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,8,6,2,4,1,3,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,2,4,1,3,6,7,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,1,3,6,2,5,7,4]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,6,3,8,4,7,2]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,6,1,3,7,2,8,4]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,1,8,2,3,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,1,2,8,4,7,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,8,1,6,4,2,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,8,6,3,4,2,5]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,3,8,6,4,2,5]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,1,8,6,4,2,3]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,8,1,5,6,4,2,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,8,5,6,4,2,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,8,6,4,2,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[8,1,3,5,6,4,2,7]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[1,3,8,5,6,4,2,7]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,8,6,4,2,7]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,5,7,8,6,4,2,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,2,6,5,3,4,7]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,6,1,5,2,3,4,7]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[8,5,1,6,2,3,4,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[7,6,1,2,3,8,4,5]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[2,7,8,4,1,3,5,6]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[6,8,1,2,3,7,4,5]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,3,5,6,7,2,4]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[8,1,2,5,3,4,7,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,2,7,3,4,8,1,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,5,4,1,3,6,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[2,7,4,6,5,1,8,3]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,7,5,2,1,4,3]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[2,8,6,3,5,1,4,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,8,6,4,5,3,7]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,7,6,3,4,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,4,8,5,7,3,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,8,5,2,7,3,4]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,6,4,2,5,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[5,4,2,3,6,8,1,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[8,2,6,3,5,7,1,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,7,8,6,2,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,8,1,6,5,3,7,4]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,5,7,6,3,8,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,3,5,1,7,8,6,2]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,2,3,4,7,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,5,8,2,3,4,7,6]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,7,8,4,5,6,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,5,6,9,10,1,7,8]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[4,3,8,7,6,2,5,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,8,2,7,6,3,1]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,3,6,1,7,5,8,4]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,5,2,1,7,8,3]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,6,1,7,5,8,3,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,5,7,6,8,3,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,2,1,4,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[4,3,6,5,1,7,8,2]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,5,3,1,7,8,2]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,2,3,4,5,7,6,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[6,4]=>[6,4]=>2
[1,2,3,5,4,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[4,6]=>[6,4]=>2
[1,2,3,5,4,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[5,8,1,4,2,3,6,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,5,8,2,3,1,6,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,5,4,8,1,7,2,6]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,6,8,1,4,7,2]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,1,8,6,4,7,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,2,8,3,1,6,5]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,5,6,8,3,7,4]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,8,4,6,2,7,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,1,5,2,6,3]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,2,1,6,5,7,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[4,1,5,6,8,7,2,3]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,5,6,8,4,7,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,6,8,4,7,2,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,8,1,2,4,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,1,4,5,7,2,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[4,3,5,1,8,6,7,2]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,5,6,8,4,7,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,6,8,2,3,4,7,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,1,2,4,8,7,3]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[5,8,7,2,1,3,6,4]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,1,7,2,8,6,3,4]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,3,4,8,7,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,6,3,2,1,4,7]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,7,1,6,3,5,4,2]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,1,7,8,6,4,5]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[8,6,7,1,2,5,3,4]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,4,2,8,7,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,4,8,2,3,6]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[3,2,8,1,7,5,6,4]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,3,1,7,5,6,2]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[6,1,7,8,4,2,3,5]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[7,4,3,1,8,5,2,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,8,1,6,3,4,5,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,1,7,3,4,2,5]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,6,7,8,9,2,3,4]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[1,8,9,10,2,3,4,5,6,7]=>[[1,2,3,4,8,9,10],[5,6,7]]=>[4,6]=>[6,4]=>2
[1,5,6,7,8,9,10,2,3,4]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[3,4,2,1,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]=>[2,7]=>[7,2]=>2
[4,3,1,2,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[3,4,2,1,5,6,7,8,9,10]=>[[1,2,5,6,7,8,9,10],[3],[4]]=>[2,8]=>[8,2]=>2
[5,3,1,2,4,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[9]=>[9]=>1
[4,3,5,1,2,6,7,8,9]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[4,3,1,2,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[10]=>[10]=>1
[4,6,5,3,8,2,7,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,6,3,8,1,7,2]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,8,3,5,2,1,6,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,3,7,5,2,4,1,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,5,7,3,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[7,8,1,5,6,4,3,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,3,7,5,1,4,2,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,2,4,6,7,5]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,7,3,4,2,5,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,1,7,2,5,8,6,4]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,7,6,3,5,1,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,1,5,6,4,3]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,6,2,8,1,7,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,5,7,3,8,2,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,6,8,2,5,3,4]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,5,7,4,2,3,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,2,8,4,5,6,3,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,3,1,2,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[9]=>[9]=>1
[6,5,4,3,1,2,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[8,5,4,3,9,1,2,6,7]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[6,5,4,3,1,2,7,8,9,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[10]=>[10]=>1
[7,6,5,4,3,1,2,8,9,10]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[10]=>[10]=>1
[9,6,5,4,3,10,1,2,7,8]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[6,4]=>[6,4]=>2
[6,8,7,3,2,4,5,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,8,6,1,4,5,7,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[7,5,8,6,4,1,3,2]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,6,3,8,5,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,1,8,4,6,5,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,7,6,8,4,5]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,8,4,6,7,5]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,3,5,1,8,6,7]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,5,6,10,1,7,8,9]=>[[1,2,3,4,5,6,9,10],[7,8]]=>[6,4]=>[6,4]=>2
[2,3,4,5,10,1,6,7,8,9]=>[[1,2,3,4,5,8,9,10],[6,7]]=>[5,5]=>[5,5]=>2
[2,3,4,10,1,5,6,7,8,9]=>[[1,2,3,4,7,8,9,10],[5,6]]=>[4,6]=>[6,4]=>2
[5,8,7,2,6,4,1,3]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,1,7,4,3,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,5,2,7,4,1,3]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,3,8,6,5,2,1,4]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[7,5,8,1,6,4,3,2]=>[[1,3],[2,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,5,8,2,6,4,1,3]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,3,2,8,1,7,5,4]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[2,6,8,7,1,3,5,4]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,8,7,6,2,1,4]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[3,7,6,1,4,5,2,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,6,2,7,5,3,8]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,2,5,3,1,4,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[4,3,1,7,6,2,5,8]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[4,5,3,1,2,8,6,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,3,1,8,6,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,7,6,2,3,1,4,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,3,7,5,2,6,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[4,1,6,3,2,7,5,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,5,4,1,3,2,6,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[5,3]=>[5,3]=>2
[2,4,8,5,6,3,1,7]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,7,4,1,3,6,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[5,7,4,1,3,2,6,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,8,4,5,3,1,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,3,7,4,1,6,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[4,5,1,6,3,2,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,1,6,3,2,4,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[4,2,5,1,6,3,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[5,1,6,2,4,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,4,8,7,6,2,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[8,3,1,6,7,5,4,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,4,6,5,7,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,2,6,7,4,5,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,5,7,2,4,3,6,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,3,6,4,7,2,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,2,5,3,6,7,4,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,8,3,4,7,6,5]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,5,2,7,1,3,4]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,6,4,5,2,1,8,3]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,2,4,7,6,3,1,5]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,8,5,4,2,1,6]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,3,4,7,2,8,5,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,7,3,6,4,2,5]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,5,3,4,2,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,4,3,1,5,2,7]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,8,3,2,6,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[1,5,2,4,7,8,6,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,2,7,4,3,8,6,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,4,8,5,6,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,6,8,3,5,4,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,4,5,3,8,6,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,3,7,4,5,8,1]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,3,2,7,5,8,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,5,2,6,8,1,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,7,1,5,8,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,5,3,6,4,7,8,1]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,5,3,6,7,8,1]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,5,2,4,7,3,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,2,4,6,3,5]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,2,5,4,3,6]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,4,2,7,3,6,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[1,5,4,2,8,7,3,6]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,8,3,5,2,4,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,6,2,3,5,8,4]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,2,8,3,6,5,4,7]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,8,6,5,2,4,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,4,7,3,2,8,6,5]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,8,6,5,2,4,7,3]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,6,8,4,3,2,5,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,7,5,3,2,6,4,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,2,6,5,3,8,4,7]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,7,3,2,8,4,6,5]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,5,2,8,4,7,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,7,2,4,6,5]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,2,8,7,6,1,3]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[8,6,3,2,5,7,4,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[7,3,2,1,6,5,8,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[7,3,2,6,1,5,8,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,8,5,2,7,1,4,3]=>[[1,2],[3,5],[4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,2,5,1,7,4,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,5,7,2,1,4,3]=>[[1,2],[3,4],[5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,8,2,7,4,1,3]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,2,1,7,5,8,4,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,6,4,8,5,3,7,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,6,7,8,1,3,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[4,6,5,1,3,7,8,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,1,7,2,6,4,8,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,6,5,8,2,3]=>[[1,3,6],[2,4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,3,6,7,8,1,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[4,7,2,1,6,5,8,3]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,3,6,7,8,1,5]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,5,2,7,3,1,4]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,1,3,7,8,2,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,2,1,4,3,5,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,4,3,7,8,5]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,5,4,2,3,6,7]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[7,1,2,4,6,3,8,5]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,1,2,6,5,3,8,4]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,5,6,1,2,4,8,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,4,5,2,3,6,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[6,1,4,8,7,2,3,5]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[6,1,8,5,7,2,3,4]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,5,8,3,4,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,7,5,8,2,3,4]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,4,7,8,2,3,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[8,1,2,3,7,5,4,6]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[5,8,6,1,2,4,7,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,6,8,7,5,3,4,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,8,7,5,2,3,4]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,3,1,2,4,6,5,7]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[8,3,1,2,4,5,7,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[6,3,1,2,4,7,5,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[6,7,1,4,2,3,5,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,1,7,4,8,2,3,5]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,7,8,5,1,2,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,6,5,4,3,2,7,9,1]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[8,1]=>[8,1]=>2
[9,6,5,4,3,2,7,1,8]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[8,7,6,5,4,3,2,9,1,10]=>[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[8,2]=>[8,2]=>2
[3,1,5,6,7,8,9,2,4]=>[[1,3,4,5,6,7],[2,8,9]]=>[7,2]=>[7,2]=>2
[2,1,3,5,6,7,8,9,4]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[4,3,8,5,6,2,7,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,8,6,7,2,5,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,1,5,3,4,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,6,1,5,3,8,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,8,1,7,2,5,4]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,5,4,8,2,7,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,2,5,4,7,1,8,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,6,7,5,1,2,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[2,7,1,8,5,6,4,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,8,2,3,5,1,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,2,1,3,5,4,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,5,1,6,4,8,2,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,8,6,2,1,4,7]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[2,4,8,5,6,1,3,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,8,2,5,6,1,3,7]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[5,3,8,4,2,7,6,1]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,5,3,1,4,7,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,7,8,4,6,3,2,5]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,2,4,6,3,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,7,3,2,1,6,4,5]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[7,8,3,4,6,5,2,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,3,6,5,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,8,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,2,7,5,4,6,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,1,4,5,3,6,2]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,8,7,4,6,3,5,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,7,4,6,3,1,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,3,4,1,2,5,7,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,4,1,3,2,5,7,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,3,8,6,2,1,4,5]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[7,2,8,4,6,5,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,6,4,7,2,3,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,2,6,5,8,3,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,8,5,7,4,2,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,7,5,2,4,8,3,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,2,7,5,6,3,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,7,3,4,6,1,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,7,5,4,8,1,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,5,6,4,7,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,6,2,4,3,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,1,3,4,2,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,4,5,1,3,2,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,8,7,5,3,2,1]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[3,5]=>[5,3]=>2
[6,7,1,4,3,2,8,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,5,1,4,8,3,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,1,3,4,2,7,6]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,6,3,2,8,7,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,6,8,4,2,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,3,2,8,5,4]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,7,6,8,4,5,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,8,5,2,7,6,4]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,1,5,2,8,7,3]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,5,3,1,8,2,4]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[2,5,1,4,7,3,6,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,5,7,2,4,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,5,7,4,8,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,7,1,6,3,8,4]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,1,5,7,4,3,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,1,6,5,2,4,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[3,6,5,1,4,2,7,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,6,5,1,7,2,4,8]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[3,6,5,2,1,4,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,4,3,6,1,7,2,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,5,2,7,6,1,3,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[4,6,5,3,1,2,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[5,4,1,6,3,7,2,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,6,3,7,8,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,5,7,1,4,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,5,1,4,7,2,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,3,6,5,7,1,2,8]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,6,5,1,3,7,8]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[4,1,6,5,3,7,8,2]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,5,7,6,1,3,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[3,4,7,6,1,2,5,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,2,5,7,6,3,8,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,6,5,2,7,3,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,6,5,7,2,1,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,5,7,6,2,4,1,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,4,2,6,3,7,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,5,2,7,3,1,8]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,5,2,1,7,3,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,5,8,2,1,4,6,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[3,5,8,2,4,6,7,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,8,2,1,4,6,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[5,3,1,8,2,4,6,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[5,1,3,8,2,4,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[1,5,8,4,2,3,6,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[5,8,2,1,4,3,6,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,2,4,1,6,7,3]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,2,4,6,3,1,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,2,4,3,6,1,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,4,6,2,3,7]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,8,4,6,7,2,3]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,4,6,7,2,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,4,6,3,7,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,6,7,2,1,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,8,4,6,7,2,5,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,3,6,7,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,4,3,6,7,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,6,2,4,5,3,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,8,6,4,5,7,2,3]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,2,4,5,3,1,7]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[1,8,6,4,2,3,5,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[3,8,1,6,2,4,5,7]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,8,6,2,1,4,5,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,8,6,2,4,1,5,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,6,2,4,5,7,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,3,6,2,4,5,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,3,6,2,4,5,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[8,3,6,7,2,1,4,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[3,8,6,7,2,1,4,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,2,6,4,5,1,7,3]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,4,6,7,5,2,3]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,4,6,2,3,7,5,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,2,1,3,6,5]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,7,1,6,3,5,8,4]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,4,2,1,5,3,7,6]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[8,2,1,4,7,3,6,5]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,2,5,8,4,7,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,5,8,7,3,6,4]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,1,6,7,4,8,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[4,3,1,7,8,5,2,6]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[5,6,8,2,4,3,7,1]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,5,3,6,4,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,8,6,4,7,3,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,2,7,8,6,4,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,2,7,8,3,5,6,1]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,8,3,7,1,4,6,5]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,7,1,5,3,6,4]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,5,6,4,2,8,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,8,4,2,7,6,5,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,3,2,7,5,6,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,4,8,7,5,6,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,8,1,5,3,4,7]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,5,6,8,1,4,7]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[3,8,1,6,4,5,2,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,3,6,5,4,2,7]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,3,6,2,1,8,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,2,4,8,6,3,7,5]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,2,1,5,3,4,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[5,7,2,3,1,4,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,5,2,4,6,8,3]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,2,7,3,5,6,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,6,4,7,5,3,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,4,1,5,8,6,3,2]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[4,5,8,7,3,1,2,6]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[1,3,8,7,6,4,2,5]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,8,5,1,7,4,6,3]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,6,4,7,5,2,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,4,6,3,8,5,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,8,6,4,7,5,3]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,6,7,9,1,2,8]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[3,4,5,7,8,9,1,2,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[3,5,6,7,8,9,1,2,4]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[3,4,5,6,8,9,10,1,2,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[3,5,6,7,8,9,10,1,2,4]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[3,4,5,6,7,8,1,2,9,10]=>[[1,2,3,4,5,6,9,10],[7,8]]=>[6,4]=>[6,4]=>2
[3,4,5,6,9,1,2,7,8]=>[[1,2,3,4,5,9],[6,7,8]]=>[5,4]=>[5,4]=>2
[3,4,5,6,1,2,7,8,9]=>[[1,2,3,4,7,8,9],[5,6]]=>[4,5]=>[5,4]=>2
[5,1,6,7,8,9,2,3,4]=>[[1,3,4,5,6],[2,7,8,9]]=>[6,3]=>[6,3]=>2
[4,1,8,6,3,7,5,2]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,3,1,6,2,5,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,5,4,3,8,1,6,2]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,3,1,6,2,8,7,4]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,4,1,7,8,2,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[6,4,2,1,5,7,3,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[3,1,5,8,7,2,4,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,2,5,7,8,4,6,1]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,7,4,2,6,8,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,7,4,2,6,1,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,4,2,1,6,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,2,8,4,3,1,6,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,1,8,4,3,2,6,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[5,2,7,4,3,6,1,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,7,4,3,6,8,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,3,7,4,1,6,8,2]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,5,7,8,4,6,2]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,1,5,7,8,4,2,6]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[5,2,7,4,1,3,8,6]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[6,2,3,7,4,8,5,1]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,3,7,4,8,1,5]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,3,7,4,5,1,8]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,3,7,4,5,8,2]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,8,6,4,3,5,7]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,1,3,7,4,5,2,8]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,8,6,3,5,4,2,7]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,1,8,5,3,4,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,5,7,8,1,6,3,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,5,7,8,4,6,3,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,8,2,7,5,3,4,6]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,5,4,1,8,6,7,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,5,1,4,8,6,2]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,3,2,4,5,6,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[3,8,7,1,4,2,5,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,1,7,8,2,4,3,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,4,6,1,7,3,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,2,1,4,6,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[5,3,2,4,8,1,6,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[5,3,2,4,7,1,8,6]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,4,5,3,7,1,2,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,8,1,7,3,5,6,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,2,4,6,8,1,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[4,6,8,3,7,1,5,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,6,4,2,5,3,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,6,4,2,8,3,1,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,5,2,4,3,7,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,1,4,3,7,6,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,4,1,3,6,8,2]=>[[1,5,6,7],[2],[3],[4],[8]]=>[7,1]=>[7,1]=>2
[3,6,7,2,5,1,8,4]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,5,7,1,4,8,3]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,1,7,8,4,6,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,2,4,6,8,7,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,2,4,7,6,5,3]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,4,1,8,6,7,5,2]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,8,5,1,7,6,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,2,8,5,7,4]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,2,4,5,6,7,9,8]=>[[1,3,4,5,6,7,8],[2,9]]=>[8,1]=>[8,1]=>2
[8,5,3,2,4,7,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[6,2]=>[6,2]=>2
[6,7,4,2,5,8,3,1]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,5,4,2,6,3,1,7]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,5,2,1,6,4,3,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[8,4,6,5,1,3,2,7]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,4,7,5,2,6]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,1,4,6,8,2]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,2,6,1,4,8,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,5,7,6,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,4,7,5,2,1,3,6]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[3,8,6,4,7,2,1,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,2,7,4,6,8,3,1]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,6,3,7,2,1,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,3,1,7,6,4,5]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,6,4,8,1,7,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,2,1,6,8,3,4]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,7,8,5,1,6,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,2,1,6,7,8,3]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,5,6,3,1,7,8,2]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,5,6,7,4,1,8,2]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,5,1,4,2,8,7,6]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,1,4,2,6,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,5,1,4,2,6,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[1,3,8,4,6,2,5,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,4,2,3,7,5,6]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,4,8,3,2,7,6,5]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,6,5,2,4,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,2,8,6,7,5,4,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,7,5,4,3,2,6,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[8,9,10,5,6,7,1,3,4,2]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[3,3,3,1]=>[3,3,3,1]=>4
[8,9,10,5,6,3,4,7,1,2]=>[[1,2,3],[4,5,8],[6,7],[9,10]]=>[3,2,3,2]=>[3,3,2,2]=>4
[8,9,5,6,10,1,3,4,7,2]=>[[1,2,5,9],[3,4,8],[6,7],[10]]=>[2,3,4,1]=>[4,3,2,1]=>4
[8,9,5,6,10,1,3,7,2,4]=>[[1,2,5],[3,4,8],[6,7,10],[9]]=>[2,3,3,2]=>[3,3,2,2]=>4
[8,5,9,10,3,6,7,1,2,4]=>[[1,3,4],[2,6,7],[5,9,10],[8]]=>[4,3,3]=>[4,3,3]=>3
[3,8,5,7,4,6,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,3,2,5,1,8,4]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,2,5,7,8,6,3,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,7,2,4,5,1,8,3]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,7,8,3,6,1,4]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,1,2,3,7,4,6]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[5,2,8,3,1,4,7,6]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,2,5,1,4,3,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,3,2,7,6,5]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,3,5,1,2,4,7,6]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,6,5,1,7,4,2,3]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[8,7,4,5,1,2,6,3]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,8,6,2,7,1,5,4]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,2,1,7,6,5]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,3,1,7,5,6,2,4]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,7,5,2,6,3]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,2,7,5,3,1,6]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,4,3,7,5,1,2,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[8,5,7,6,4,3,1,2]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,4,7,6,5,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,3,1,4,7,6,2,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[8,3,5,7,6,2,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,6,8,2,5,7,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,6,2,4,8,1,7,5]=>[[1,2,5],[3,4,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,3,8,2,4,6,1,5]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,2,6,8,3,7,4]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,3,1,8,2,6,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,2,8,4,1,3,5,6]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[6,1,7,3,2,8,4,5]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,2,1,7,3,8,4,5]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[5,8,2,1,3,4,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[4,2,5,1,8,3,6,7]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[7,4,2,8,3,1,5,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,4,2,8,3,5,1,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,8,5,2,1,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,6,2,7,8,4,3,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,3,4,1,8,6,2,5]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,6,3,5,8,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,6,5,2,4,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,4,7,8,6,2,5,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,7,8,3,2,5,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,3,2,7,8,4,6,5]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,1,4,6,2,8,3]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,1,4,7,8,2,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[9,1,7,8,6,5,4,3,2]=>[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[4,5,7,1,8,6,2,3]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,8,6,5,2,7,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,3,8,6,5,1,7,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,4,7,3,1,2,6,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[3,1,2,6,5,7,8,4]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,2,6,1,4,8,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,6,8,4,1,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[7,2,6,8,5,4,3,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,7,5,6,2,4,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,2,5,1,3,6,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,3,4,2,7,1,8,6]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,2,1,3,8,4,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[2,4,3,5,6,8,1,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,3,2,4,8,5,1,7]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[6,3,1,2,7,8,4,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[8,4,7,1,2,5,3,6]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,6,1,8,5,2,3]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,5,6,7,2,1,4,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,5,6,3,8,4,7,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,6,2,8,3,5,4]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,3,8,5,2,7,6]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,5,4,7,2,3,6]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,2,5,6,4,3,1,7]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[2,4,3,8,6,5,1,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,1,4,5,8,6,2,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[1,8,3,2,5,4,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[5,1,7,3,2,8,4,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,1,3,2,4,6]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,2,4,1,6,7,3,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,7,3,6,2,4,1,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,4,8,3,6,2,5]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,6,1,3,5,4,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,5,8,4,3,2,6]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,3,1,2,7,8,5,4]=>[[1,4,5,6],[2,7],[3,8]]=>[6,2]=>[6,2]=>2
[8,2,7,5,3,4,1,6]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,1,2,8,7,5,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[8,4,7,2,6,3,1,5]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,3,4,2,1,8,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,6,2,3,7,1,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,8,1,7,2,6]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,4,2,7,8,1,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,3,7,8,2,1,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,6,3,4,7,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[4,3,8,6,7,5,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,5,6,2,7,8,3,1]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,6,2,7,1,8,3]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,6,2,1,7,8,3]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,5,6,2,1,7,3,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,2,3,1,4,5]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,5,1,6,7,3,2,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,8,3,7,4,6]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,2,1,3,8,4,6]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,1,5,4,2,6,3,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[9,8,7,6,5,3,2,4,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[8,1]=>[8,1]=>2
[10,9,8,7,6,5,4,2,3,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[9,1]=>[9,1]=>2
[2,7,4,5,6,8,1,3]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,3,4,6,8,1,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,3,4,5,6,7,9,2,1]=>[[1,3,4,5,6,7],[2],[8],[9]]=>[7,2]=>[7,2]=>2
[2,3,4,5,7,9,1,8,6]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[2,3,5,8,1,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,4,7,5,6,8,1,3]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,5,6,7,9,1,8]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[9,3,4,5,6,7,8,10,1,2]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[2,3,4,5,6,8,10,1,9,7]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[7,3,4,6,2,8,1,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,6,5,2,8,3,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,4,8,6,7,3,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,4,1,6,8,2,3]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[4,2,3,5,6,7,9,1,8]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[8,5,2,1,7,6,3,4]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[2,7,3,6,4,1,8,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,1,8,5,6,4,3]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,5,1,4,8,2,7]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,3,5,4,8,1,2,7]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,5,1,4,6,3,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,5,6,4,2,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,6,4,3,1,7,2]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,3,5,6,7,1,2,4]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[2,1,4,7,3,6,8,5]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,7,6,4,8,2,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,6,4,2,8,1,5]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,1,4,3,7,2,5]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,7,5,1,6,3,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,5,3,7,8,6,4]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,7,6,8,2,3]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,3,7,6,5,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,3,4,1,6,7,5,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,2,6,5,7,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,1,4,3,2,6,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,6,4,3,8,2,7,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,4,3,8,2,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,1,4,3,2,5,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[7,1,8,4,5,3,6,2]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,1,8,6,5,7,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,7,5,1,8,6]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,2,3,7,4,1,8,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,1,7,4,3,6,8,5]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,1,2,4,5,6,8,3]=>[[1,3,4,5,6,7],[2],[8]]=>[7,1]=>[7,1]=>2
[2,8,7,1,4,5,6,3]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,7,1,3,4,5,6,2]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[5,8,3,1,4,6,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[1,7,2,5,4,6,8,3]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,3,8,1,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,2,5,7,8,3]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,5,3,4,1,7,8,2]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,6,3,4,1,7,8,2]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,3,1,4,7,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[6,8,2,3,1,5,7,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,1,5,2,7,8,6]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[5,2,3,1,4,7,8,6]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[7,2,1,3,5,6,8,4]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[5,2,4,7,8,6,3,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,4,8,7,2,3,1,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,5,3,6,2,7]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,5,1,4,6,2,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,2,1,7,4,3,6]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,7,2,1,8,4,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,5,4,7,3,8,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,1,3,8,5,6,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,8,4,1,7,2,5]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,4,7,6,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,5,6,8,4,3,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,2,4,7,8,6,1]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,5,6,3,8,2,1,4]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,2,7,4,5,8,3]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,2,6,1,5,8,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,6,2,5,7,3]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,3,4,5,1,6,8,2]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,4,2,7,6,1,5,3]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,7,1,2,6,5,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,6,1,2,5,3]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,6,2,1,5,3,4]=>[[1,6,8],[2,7],[3],[4],[5]]=>[6,2]=>[6,2]=>2
[5,7,8,1,6,2,4,3]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,7,4,2,5,1,3]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,8,4,5,7,2,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,4,3,2,7,1,8,9]=>[[1,6,8,9],[2],[3],[4],[5],[7]]=>[6,3]=>[6,3]=>2
[5,4,3,2,6,1,7,8,9]=>[[1,5,7,8,9],[2],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[4,3,2,5,1,6,7,8,9]=>[[1,4,6,7,8,9],[2],[3],[5]]=>[4,5]=>[5,4]=>2
[3,2,4,1,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2],[4]]=>[3,6]=>[6,3]=>2
[3,1,6,5,4,7,2,8]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,6,5,3,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[4,6,1,3,5,2,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,2,6,3,5,1,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,1,2,5,3,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,4,7,1,3,6,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,3,1,5,4,7,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,3,6,7,4,2,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,2,8,6,7,1,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[6,1,2,4,7,3,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[5,6,1,4,8,3,2,7]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,6,4,1,7,2,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,4,1,7,2,8,5,9]=>[[1,2,5,7,9],[3,6,8],[4]]=>[2,3,2,2]=>[3,2,2,2]=>4
[2,4,1,5,3,6,7,8,9,10]=>[[1,2,4,6,7,8,9,10],[3,5]]=>[2,2,6]=>[6,2,2]=>3
[3,6,4,1,7,2,8,5,9,10]=>[[1,2,5,7,9,10],[3,6,8],[4]]=>[2,3,2,3]=>[3,3,2,2]=>4
[5,2,6,3,7,8,4,1]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,4,1,3,7,8,6,5]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,1,5,7,8,4,3]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,1,6,4,7,8,2,3]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,6,3,7,5,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,6,8,2,3,5,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,4,8,1,2,6,3]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,7,5,8,1,4,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,5,6,8,2,4,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,1,6,8,4,5,3]=>[[1,2,5],[3,4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,4,7,2,6,3,8]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,5,8,3,1,7,6]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,7,5,8,3,6,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,8,7,3,5,1,4]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,7,8,6,2,5,1,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,3,5,6,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,3,5,4,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,8,1,6,5,7,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,3,6,2,5,8,7,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,1,4,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,2,5,1,3,4,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[2,6,5,1,3,4,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,6,5,1,2,7,3,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,6,4,1,2,7,3,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,1,5,6,2,4,3,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,5,1,2,7,3,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,4,6,1,3,2,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,1,4,3,2,6,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,4,1,3,7,5,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,8,5,3,2,1,6,4]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,2,6,7,8,4,5,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,1,4,8,2,7,5,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,1,8,4,6,5]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,1,7,3,2,8,6]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,4,5,1,8,6,2]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,6,7,4,8,2,3]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,2,5,7,4,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,5,2,7,6,3,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,5,2,1,7,6,3,8]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,7,8,3,1,4,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[6,3,2,5,1,7,8,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,7,8,2,1,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,7,1,8,4,2,3]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,2,8,6,5,4]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,2,8,6,5,4]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,7,8,1,6,5,3,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,5,7,3,4,6,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,8,2,7,6,3,1,4]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,8,4,7,6,3,1,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,8,2,4,7,6,3,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,8,7,1,6,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,2,4,6,7,5,3]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,5,1,8,4,7,6,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,2,8,1,7,6,5]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,5,8,1,7,6,3]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,8,2,6,7,5,4]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,8,1,4,3,7,5]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,5,2,8,7,3,4]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,1,5,8,7,3,4]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[8,1,7,3,5,2,4,6]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,3,2,7,6,4,5]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,4,8,6,2,5,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,1,6,2,3,4]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,4,5,3,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,5,3,2,8,4,1]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,2,5,3,8,1,4,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,6,1,3,5,2,4,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[6,2,4,5,3,8,1,7]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,4,7,2,3,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,5,4,7,1,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,8,4,2,5,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[7,5,8,1,3,4,2,6]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,2,8,3,5,7,6]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,5,4,8,7,2,6]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,6,2,4,8,3,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,8,5,4,2,6,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,5,2,8,6,4,7,3]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,5,2,7,4,8,3]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,6,7,4,2,8,3]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,5,4,2,8,6,7,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,5,4,6,2,7,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,5,4,6,2,8,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,4,1,6,2,7,3]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,1,3,7,6,2,5]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,3,1,2,8,7,6]=>[[1,2,6],[3,5,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[6,4,2,3,1,8,7,5]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,5,2,1,3,8,7,4]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,6,1,8,2,5,3,4]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,2,3,7,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[5,7,8,1,2,4,3,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,6,8,3,5,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,6,4,2,1,3,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[6,5,7,4,1,3,2,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,8,3,5,2,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,6,8,2,5,4,3]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,1,8,3,2,5,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,3,6,1,5,2,7]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,8,6,4,5,3,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,6,4,5,1,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,3,6,2,5,1,7]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,8,7,4,3,5,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,2,6,8,7,5,4]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[5,7,4,2,1,8,6,3]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,6,5,7,2,4,3,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,1,8,5,3,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,6,3,8,1,5,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,8,1,6,3,2,5]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,8,3,6,2,1,5]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,2,3,5,7,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,2,5,7,1,3]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,8,2,5,7,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,4,5,8,3,7,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,8,2,4,7,3,5,1]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,6,2,7,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,4,2,7,1,3,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,4,1,7,3,5]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,1,6,2,4,8,3]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,5,7,1,6,8,3]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,2,3,8,7,1,6]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,4,7,6,1,3,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[5,2,3,7,6,1,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[4,2,3,7,6,1,5,8]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[4,2,7,3,5,1,6,8]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,6,2,3,8,4,7,1]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,2,3,1,7,8,4]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,2,3,4,1,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,2,7,3,5,1,4,8]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,3,5,1,4,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,5,2,3,1,7,8,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,5,2,3,8,4,7,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,2,1,4,6,8,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,5,2,3,1,6,4,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,6,2,3,1,5,4,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,2,6,3,1,7,4,5]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,6,3,4,2,7,5,8]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,2,7,3,4,6,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,2,4,5,6,8,3]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,3,2,5,6,4,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,2,8,1,4,6,3,5]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,1,5,6,3,4]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,2,3,1,5,4,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,2,3,1,6,4,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,7,2,1,4,6,8,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[4,2,7,1,5,6,8,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,3,8,1,7,5,6]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,2,1,5,3,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[5,1,3,8,4,6,7,2]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,1,3,2,6,7,8,4]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,1,3,4,2,7,6,8]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,3,4,2,7,5,8]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,2,1,3,5,8,4,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[6,8,7,2,3,4,5,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,2,8,1,4,5,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[5,2,3,7,4,6,1,8]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,3,7,4,6,1,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,7,3,4,5,1,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,7,3,4,5,1,8]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,8,4,5,2,1,6,7]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,7,6,3,4,5,1,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,5,1,3,4,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[3,1,2,9,4,5,6,7,8]=>[[1,3,4,6,7,8,9],[2,5]]=>[4,5]=>[5,4]=>2
[3,1,2,10,4,5,6,7,8,9]=>[[1,3,4,6,7,8,9,10],[2,5]]=>[4,6]=>[6,4]=>2
[6,7,1,2,3,4,5,9,8]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[4,5,7,2,8,3,6,1]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,7,3,6,2,9,5,1]=>[[1,3,7],[2,5],[4,8],[6],[9]]=>[3,2,2,2]=>[3,2,2,2]=>4
[4,5,6,9,3,8,2,7,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[4,2,2,1]=>[4,2,2,1]=>4
[8,4,7,3,10,6,2,9,5,1]=>[[1,3,5],[2,6,8],[4,9],[7],[10]]=>[3,2,3,2]=>[3,3,2,2]=>4
[5,2,1,3,6,7,8,4]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[7,5,2,6,1,8,4,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,2,7,8,4,3]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,6,8,4,1,3,2]=>[[1,3,4],[2,7],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,5,1,4,2,6]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,7,3,6,2,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,3,2,6,4,5,1,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,3,7,4,1,2,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[8,5,6,2,7,1,3,4]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,2,6,5,1,3]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,3,2,6,1,4]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,3,6,4,7,5]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,2,3,5,8,1,4]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[4,5,3,7,8,1,6,2]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,2,8,1,6,7,5]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,3,4,1,5,7,6,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,5,1,6,2,8]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,6,1,4,3,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,7,4,2,8,6,1]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,5,8,6,1,4,3]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,1,4,6,7,8,2]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[4,6,2,1,3,7,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,5,4,1,3,6,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[4,2,5,6,7,8,9,1,3]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[3,1,6,7,8,4,5,2]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,5,6,2,1,8,3]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,2,5,6,7,8,9,10,1,3]=>[[1,3,4,5,6,7,8],[2,10],[9]]=>[8,2]=>[8,2]=>2
[3,7,5,6,2,1,8,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,6,3,8,4,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,1,2,7,8,3,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[6,4,1,3,5,2,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[5,1,8,3,4,6,2,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,2,3,7,1,6]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,4,8,2,5,1,6]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,2,5,1,6,8,3]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,2,8,1,5,6,4,3]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,6,4,2,1,8,3,7]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,4,3,5,8,1,6,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,5,3,8,1,4,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,1,2,4,3,5,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[4,4]=>[4,4]=>2
[6,5,8,2,7,3,4,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,6,8,4,3,2,5]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,7,6,5,3,8,2,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,1,2,4,3,5,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,6,1,3,7,8,5,2]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,4,1,5,2,6,7,3]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[1,5,6,3,8,7,2,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,2,6,8,7,1,4]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[6,3,5,2,7,1,4,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,5,2,6,7,1,4,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[5,3,8,7,1,4,2,6]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,5,3,1,8,7,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,1,2,3,6,7,4]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[2,8,6,1,5,4,7,3]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,2,6,1,5,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,8,6,4,7,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,7,5,4,3,2,6]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[8,6,4,7,1,3,2,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,4,7,6,2,5,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[5,3,4,1,6,2,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,7,1,4,6,3,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,1,6,5,2,4,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,1,5,2,4,6,3,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,5,2,7,3,8]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,1,5,8,2,7,4,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,1,2,3,6,4,5,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[2,8,4,6,5,1,7,3]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,1,3,6,5,2,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[5,7,2,8,1,3,6,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,1,4,7,3,2,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[2,7,8,4,1,3,6,5]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,6,5,7,8,1,3]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,6,7,5,8,1,3]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,4,6,3,7,8,1,5]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,6,8,7,1,3]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[2,4,5,6,8,3,7,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,5,6,3,8,1,7]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,4,6,8,5,1,7]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[5,2,8,3,4,1,6,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,4,1,2,7,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,1,7,3,8,6,2,5]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[8,4,1,2,5,3,7,6]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[1,5,2,7,6,8,4,3]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,6,8,3,1,2,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,2,7,6,5,1,3]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,4,2,8,6,5,1,3]=>[[1,4],[2,5],[3,6],[7,8]]=>[4,4]=>[4,4]=>2
[8,6,5,2,7,1,4,3]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,5,8,2,7,1,4,3]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,8,2,1,6,4,3]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,1,6,5,8,4,7]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[2,6,4,8,5,7,3,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,3,1,4,5,8,2,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[3,4,8,5,2,1,7,6]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,7,1,3,2,6,5]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,7,4,6,1,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,4,1,8,7,6,2,5]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,3,5,6,8,7,2,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[2,8,7,5,4,1,6,3]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[8,1,5,7,4,2,6,3]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,8,7,3,4,1,6,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,1,3,2,8,5,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,5,8,3,1,4,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,7,8,2,4,5,3,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,4,5,7,1,6]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,2,4,5,3,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,3,6,4,2,7,1,5]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,4,7,6,2,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,7,5,4,1,2,6]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[2,6,4,7,8,5,1,3]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,4,3,7,6,1,8,2]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,6,3,7,1,4,2,5]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,1,2,8,7,6,4,5]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,5,4,1,2,3,7,6]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[8,3,2,1,6,4,7,5]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[2,3,8,4,1,7,5,6]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,1,3,2,7,8,5]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,2,5,8,4,1,3]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,7,8,2,5,6,3]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,6,7,1,5,8,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,7,8,1,6,2]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,8,7,4,3,5,2,6]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,4,5,8,1,3,7,6]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,3,1,5,8,4,2,7]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[2,8,3,5,6,1,4,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,3,6,4,2,7,5,8]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,3,7,5,8,1,4,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,2,8,5,6,1,4,7]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,5,8,1,4,6,3]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,7,5,8,1,2,6,3]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,5,8,1,2,3,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,4,7,5,2,8,1,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,2,5,7,8,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[2,4,7,5,8,3,1,6]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,4,7,3,8,1,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,8,4,2,1,6,5]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,6,7,9,1,2,3,4,8]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]=>[5,4]=>2
[4,5,6,7,9,1,2,3,8]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[7,8,10,1,2,3,4,5,6,9]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]=>[7,3]=>2
[4,5,6,7,8,10,1,2,3,9]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[6,4]=>2
[8,5,4,7,6,3,1,2]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[1,5,4,8,7,6,2,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,2,4,5,8,1,6,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[3,6,8,4,2,7,1,5]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,5,1,7,2,8,4]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,4,1,6,2,8,5,3]=>[[1,4,6],[2,5,7],[3],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,8,2,4,7,5]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,7,4,3,8,2,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,3,1,6,5,2,8,4]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,5,4,1,6,2,7,3]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[4,7,2,8,5,1,6,3]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,6,2,1,5,4,3]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,1,3,8,7,5,6,4]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,7,3,6,5,2,4]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,7,3,8,5,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,3,4,5,6,8,10,7,9]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[8,2]=>2
[3,4,5,6,7,8,2,1,9]=>[[1,2,3,4,5,6,9],[7],[8]]=>[6,3]=>[6,3]=>2
[4,5,6,7,8,1,2,3,9]=>[[1,2,3,4,5,9],[6,7,8]]=>[5,4]=>[5,4]=>2
[4,8,1,6,3,7,2,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,4,1,6,3,7,2]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,7,6,2,4,8,5,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,2,4,8,6,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,4,6,3,5,1,7]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,8,3,6,4,5,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,1,4,6,5,2,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,5,4,1,8,3,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,6,1,8,5,3,2,7]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[3,8,5,2,1,6,4,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,1,4,8,2,6,3,7]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,1,3,7,6,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,7,1,4,3,2,5]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,7,8,6,3,5,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,2,6,3,4,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,6,1,2,7,4,5]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[3,8,6,1,2,5,7,4]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,6,2,1,8,5,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,3,7,6,1,8,5,2]=>[[1,3,6],[2,4],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,3,2,7,1,5,4]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,8,1,5,4,7,2,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,2,5,4,8,1,3]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,2,4,8,5,1,3]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[4,6,8,7,3,1,2,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[4,7,5,2,6,3,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,6,2,8,1,4,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,9,10,4,5,6,2,3,1,7]=>[[1,2,3,10],[4,5,6],[7,8],[9]]=>[3,3,2,2]=>[3,3,2,2]=>4
[8,4,2,5,9,10,1,3,6,7]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[6,4]=>[6,4]=>2
[4,8,9,2,5,6,10,1,3,7]=>[[1,2,3,7],[4,5,6,10],[8,9]]=>[3,4,3]=>[4,3,3]=>3
[4,8,2,5,9,10,1,3,6,7]=>[[1,2,5,6],[3,4,9,10],[7,8]]=>[2,4,4]=>[4,4,2]=>3
[6,1,8,2,4,3,5,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,8,2,5,3,4,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,8,7,1,2,6,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,6,4,3,8,1,7]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,3,5,1,4,6,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,3,5,2,1,4,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,7,3,5,2,4,6,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,2,7,6,5,1,3]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,6,3,8,5,2,7,1]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,3,8,5,6,2,7]=>[[1,3,4,6,8],[2,5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,2,8,3,1,6,7,4]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,7,8,6,3,2,5,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,1,5,7,4,6]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[3,4,6,7,2,1,5,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[2,6,7,1,4,3,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,7,4,8,5,6,1]=>[[1,3,5,7],[2,4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,2,7,4,6,3,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,8,3,7,1,6]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,5,1,6,4,3,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,7,5,1,6,4,3,2]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[5,3]=>[5,3]=>2
[4,5,8,3,1,2,7,6]=>[[1,2,3],[4,6,7],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[1,4,6,3,7,5,2,8]=>[[1,2,3,5,8],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,8,7,4,5,6,2]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,1,8,4,5,6,2]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,8,7,4,5,6,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,2,4,3,7,5,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,2,1,5,7,6,4]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,3,2,8,7,4,6,5]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,5,2,8,3,1,6,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,7,8,1,2,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,2,5,4,1,7,8,3]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,1,5,6,3,8,7,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,5,1,6,3,2,4,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[6,8,7,4,3,2,5,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[8,1,5,4,6,7,3,2]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,5,1,3,7,6,4]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,4,1,8,2,7,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,4,5,1,3,8,7,2]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,5,4,8,2,7]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,8,7,2,5,6,4]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,4,1,8,3,7,6]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,4,8,3,7,6,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,2,7,6,5,3]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[4,8,3,2,7,6,5,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,7,3,4,6,5,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,5,3,1,2,4,6,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[10,9,7,5,3,1,2,4,6,8]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[10]=>[10]=>1
[5,3,1,2,4,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[8,5,7,3,1,2,4,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[7,5,3,1,2,4,6,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[9]=>[9]=>1
[3,1,2,8,7,5,4,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,4,3,8,5,7,2,6]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,7,1,5,2,8,4,3]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,3,7,6,4,8,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,1,3,6,2,7,5]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,3,4,8,6,5,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,4,7,3,6,5]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,1,6,5,8,3,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,3,8,1,5,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[2,5,7,4,8,3,6,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,6,2,4,7,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,7,3,6,4,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,8,6,2,7,5,4,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,8,1,6,2,5,3,7]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,4,2,5,7,3,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,8,3,1,2,4,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[1,4,8,5,2,3,6,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,4,8,5,2,3,7,6]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,7,2,4,3,6]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,4,2,8,3,7,6]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,8,7,3,5,4,6]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,7,1,3,2,5,4,6]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,7,4,2,8,1,3,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,6,8,7,2,3,5]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,7,5,6,2,8,3,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,3,6,7,5,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[6,7,5,2,8,4,3,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,3,2,7,5,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,1,7,3,5,8,2,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,7,6,4,8,2,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,4,8,7,3,1,5]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,1,8,7,3,5,4,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,5,7,4,3,2]=>[[1,3,5],[2,4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,1,4,7,6,3,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,1,3,7,2,4,6,5]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,3,1,6,4,8,2,7]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,6,7,1,4,8,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,7,5,3,2,8,1,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,7,5,2,8,6,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,1,2,7,4,3,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,3,1,8,2,4,5,7]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[4,6,3,7,8,1,5,2]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,3,1,8,4,5,2,7]=>[[1,4,6,8],[2,5],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[7,6,2,4,8,3,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[6,5,8,1,4,3,7,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,2,7,5,6,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,2,8,3,9,4,10,5,6]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[7,1,8,2,9,3,4,10,5,6]=>[[1,3,5,7,8,10],[2,4,6,9]]=>[3,2,3,2]=>[3,3,2,2]=>4
[1,8,2,9,3,10,4,11,5,12,6,7]=>[[1,2,4,6,8,10,12],[3,5,7,9,11]]=>[2,2,2,2,2,2]=>[2,2,2,2,2,2]=>6
[8,6,3,5,2,1,7,4]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,8,3,1,2,5,4,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,6,4,7,1,2,3]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,8,7,3,4,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,8,4,3,5,1,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,7,3,6,8,2,5]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,1,4,6,8,2,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,4,7,3,6,8,1,5]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,6,1,3,2,4]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,5,6,1,8,4,3]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,6,7,4,5,8,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,2,8,7,1,4,3]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,3,6,8,1,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[2,6,1,3,8,5,4,7]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,1,8,3,2,5,7]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[5,8,1,4,2,7,3,6]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,3,1,6,8,7,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,8,2,1,7,3,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,3,1,8,7,5,6,4]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,6,7,2,4,3,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,8,6,4,1,5,3,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,7,4,5,1,3,8,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,5,3,8,2,4,7]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,1,2,4,8,3,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,4,5,1,3,2,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,5,1,2,7,4,3,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[4,1,8,7,2,5,3,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,4,6,1,8,7,5]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,7,4,1,2,5,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[1,4,7,5,8,2,3,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,8,4,7,3,2,5]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,6,7,5,4,8,1,2]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,2,6,3,8,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,5,7,4,6,8,3]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,5,7,8,1,6,4]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,5,7,4,2,3,6,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[2,4,7,5,3,6,8,1]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,7,2,4,6,3,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,4,7,8,6,3,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,3,6,2,5,8,4,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,6,8,2,4,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,1,2,6,3,7,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,1,2,6,3,7,4]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,2,3,7,5,8,4]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,2,6,5,7,8,3]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,4,2,7,3,6,5]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,5,2,3,8,6,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,4,7,3,5,2,6]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,3,6,1,7,2,5]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,6,1,8,3,7,4,5]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,2,1,3,7,5,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[2,5,1,7,6,8,3,4]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,1,8,2,4,7,6]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,6,3,7,5,8,4]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,8,3,2,4,7,6]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[3,1,5,4,6,7,8,2]=>[[1,3,5,6,7],[2,4],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,8,5,7,3,1,4,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,6,8,7,3,1,4,5]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,4,2,1,3,8,5,6]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[7,2,1,3,8,5,4,6]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[2,1,7,3,8,6,4,5]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,7,5,3,2,4,8,6]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,4,2,7,6,5,8,3]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,1,6,5,7,8,2]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,7,3,4,1,5,6]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,7,6,2,3,8,1,4]=>[[1,2,6],[3,5,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,5,7,6,2,8,1,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,7,5,2,6,4]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,5,6,8,7,2,1,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[2,8,3,1,5,4,7,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,1,5,2,7,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,6,2,4,3,7,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,1,6,2,7,5]=>[[1,2,7],[3,5,8],[4,6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,3,1,6,4,7,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,7,1,5,8,4,3]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,9,6,5,4,3,2]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[1,6,7,8,9,5,4,3,2]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[1,5,6,7,8,9,4,3,2]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[1,4,5,6,7,8,9,3,2]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,8,9,10,7,6,5,4,3,2]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[4,6]=>[6,4]=>2
[1,7,8,9,10,6,5,4,3,2]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,5]=>[5,5]=>2
[1,6,7,8,9,10,5,4,3,2]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[1,5,6,7,8,9,10,4,3,2]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[1,4,5,6,7,8,9,10,3,2]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,2]=>[8,2]=>2
[4,8,5,1,3,2,6,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,4,3,1,2,7,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[4,1,6,5,2,3,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[7,1,5,2,3,6,4,8]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[4,1,6,3,7,2,5,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,1,2,8,3,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,3,6,7,2,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[2,6,5,1,3,4,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[2,6,7,4,3,1,5,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[2,6,3,1,7,4,5,8]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[6,5,3,7,2,4,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,3,6,7,1,5,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,7,5,8,1,3,6,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,1,6,7,3,2,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[5,6,1,4,7,2,3,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,5,7,8,6,3,4]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[1,2,6,7,4,5,3,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,8,4,6,3,5]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[8,6,5,2,1,7,4,3]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[4,3,8,6,7,1,5,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,2,4,7,1,6,5]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,3,2,8,6,1,5,4]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,2,6,1,4,3]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,1,2,6,5,8,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,2,7,4,6,1,8,3]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,1,2,3,6,8,5]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[5,4,8,6,3,2,1,7]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,4,6,7,3,1,5,2]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,1,3,6,8,5,2,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[6,3,5,7,1,2,8,4]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,8,5,3,2,4,6,7]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[1,6,7,3,4,2,5,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,8,3,4,2,5,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,7,5,3,4,2,6]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,8,5,3,4,2,6]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,6,8,4,2,3,5]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,7,8,6,4,3,2,5]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[9,8,7,6,5,2,1,3,4]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[7,2,8,9,10,1,3,4,5,6]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[5,5]=>[5,5]=>2
[9,7,8,6,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[5,1,7,8,4,2,3,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[3,8,2,1,6,7,5,4]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,8,3,1,7,5,6,4]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[9,7,5,3,10,2,4,6,8,1]=>[[1,5,8,9],[2,7],[3],[4],[6],[10]]=>[5,4,1]=>[5,4,1]=>3
[7,5,8,9,10,4,6,3,2,1]=>[[1,3,4,5],[2,7],[6],[8],[9],[10]]=>[5,2,3]=>[5,3,2]=>3
[2,10,4,5,6,7,9,1,3,8]=>[[1,2,4,5,6,7],[3,9,10],[8]]=>[2,5,3]=>[5,3,2]=>3
[2,7,4,1,5,8,3,6]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,1,6,4,7,8,3,5]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,3,4,2,1,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,5,3,8,2,6,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,4,7,8,5,3,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,8,4,5,6,1,3,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,1,8,4,6,7,3]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,8,3,4,2,1,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,7,6,3,4,5,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,7,3,2,1,4,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[3,4,8,2,7,1,5,6]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,2,6,1,4,8,3,5]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,2,4,6,3,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[7,2,8,3,4,5,1,6]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,3,4,2,5,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,5,1,2,4,3,8,6]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,8,1,4,2,3,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,4,3,7,8,5,6,1]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,7,6,3,4,5,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[6,1,5,3,8,2,4,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,3,6,8,5,1,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,4,8,6,1,7,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,3,8,4,5,7,6]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,2,8,5,4,7,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,1,3,7,8,4,6,5]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,1,3,8,4,7,6,5]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,2,8,4,5,7,6]=>[[1,3,4,6,7],[2,5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,8,7,5,4,6,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,7,2,3,8,1,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,6,5,7,8,1,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,1,8,7,4,6,5,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,5,8,4,7,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,4,6,8,5,7,2,3]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,5,1,6,4,3,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,4,7,1,8,3,6,5]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,5,4,2,3,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,4,5,1,2,8,3,7]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,4,1,5,7,6,3,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,1,6,3,5,2,4,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,2,5,3,8,1,7]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,5,2,1,8,3,7]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,3,6,7,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,2,1,5,3,4,7]=>[[1,2,7,8],[3,5],[4,6]]=>[2,3,3]=>[3,3,2]=>3
[2,5,3,8,6,7,4,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,6,5,1,8,4,7]=>[[1,3,6],[2,4,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,5,8,1,6,2,3]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,1,6,7,3,2]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,4,6,7,3,2]=>[[1,3,5,6],[2,4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,5,3,8,1,7,2,4]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,3,7,1,6,2,4,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,6,5,7,2,3]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,7,5,6,4,2,3]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,1,5,3,7,2,4]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,6,8,1,5,4]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,6,3,7,8,1,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,3,8,7,2,1,5,4]=>[[1,3],[2,4],[5,7],[6,8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,5,6,3,4,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,8,6,3,1,5,4]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,2,4,5,8,6,3,1]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[6,3,8,4,7,2,5,1]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,3,6,8,5,4,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,2,8,5,4,1,3,6]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[7,4,5,2,8,1,6,3]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,5,4,2,8,1,6,3]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,3,2,8,4,5,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,3,6,8,4,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,5,4,8,3,6,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,8,3,6,1,4,5]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,5,2,8,3,6,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,1,3,2,4,6,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[6,5,3,4,1,8,2,7]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,5,3,8,1,2,7]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,6,3,8,5,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,3,7,6,1,5,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,4,2,6,8,7,3,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[3,7,2,5,8,6,4,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,6,5,3,8,1,7,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,8,7,6,1,5,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,2,8,7,4,6,5,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,6,5,1,4,3,7]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,5,2,7,6,3,1]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,8,6,5,7,1,3,4]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,4,7,2,1,6,5]=>[[1,2,4],[3,7],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,5,1,7,6,3,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,8,1,7,6,2,3,4]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[3,4,6,2,5,7,1,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,5,2,6,8,3,4]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[7,4,8,3,6,5,1,2]=>[[1,3],[2,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[1,5,4,3,8,7,2,6]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,8,2,6,4,3,7]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[10,9,8,6,4,2,1,3,5,7]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[10]=>[10]=>1
[10,8,7,6,4,2,1,3,5,9]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[10]=>[10]=>1
[10,9,8,7,6,4,2,1,3,5]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[10,8,6,5,4,2,1,3,7,9]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[10]=>[10]=>1
[10,9,8,6,5,4,2,1,3,7]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[10,8,7,6,5,4,2,1,3,9]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[10,8,6,4,3,2,1,5,7,9]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[10]=>[10]=>1
[10,9,8,6,4,3,2,1,5,7]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[10,8,7,6,4,3,2,1,5,9]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[10,9,8,7,6,3,5,2,4,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8],[10]]=>[7,2,1]=>[7,2,1]=>3
[10,8,6,5,4,3,2,1,7,9]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[3,5,6,2,4,7,8,1]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,6,7,2,4,8,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,7,6,8,2,4,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,5,7,2,6,8,4,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,7,6,8,4,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,7,4,2,6,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,4,7,2,6,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,5,7,2,6,8,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,7,2,8,6,1]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,4,7,8,2,6,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,4,7,2,8,6,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,5,7,4,8,6,1]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,7,4,2,8,6,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,7,8,4,2,6,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,5,7,8,4,6,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,5,2,7,8,6,4,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,5,7,8,2,6,4,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,7,8,6,2,4,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,5,6,7,8,9,1,4]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[4,2,5,6,7,3,8,1]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,1,4,3,5,2,7]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,8,4,3,5,2,7]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,6,4,8,2,3,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,1,4,2,5,3,6,7]=>[[1,3,5,7,8],[2,6],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,8,4,1,5,3,6,7]=>[[1,2,5,7,8],[3,6],[4]]=>[2,3,3]=>[3,3,2]=>3
[8,4,1,3,5,2,6,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[4,1,8,3,5,2,6,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,1,2,5,4,6,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[3,1,8,2,5,4,6,7]=>[[1,3,5,7,8],[2,4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,5,1,8,7,6,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,2,4,8,1,7,6,3]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,2,4,6,8,1,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[1,4,8,6,7,2,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,5,7,3,8,2,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,8,1,2,5,3,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,5,6,8,2,1,4,7]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[8,2,5,4,1,3,7,6]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,4,5,8,6,3,1,7]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[5,4,8,2,3,1,7,6]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,5,8,2,3,1,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,7,5,1,8,3,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,3,6,5,8,2,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,3,4,2,6,7,1,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,3,8,6,2,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,1,8,2,6,5,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,7,5,2,8,3,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,2,4,3,1,6]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,2,8,6,7,3,4]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,5,7,8,6,1,4,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,6,8,4,5,1,3]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,7,6,8,2,3,4]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,6,2,4,3,8,5]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,6,2,4,5,3,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,6,2,3,4,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[6,2,5,8,3,4,1,7]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,6,8,7,1,3,2,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,4,8,2,6,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,3,6,5,8,4,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,2,8,6,3,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,1,5,7,8,4,2,3]=>[[1,3,4,5],[2,8],[6],[7]]=>[5,3]=>[5,3]=>2
[4,6,1,5,7,2,8,3]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,8,4,6,3,7,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,1,2,6,8,5]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[8,1,6,5,2,7,4,3]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,5,2,7,4,3]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,8,2,3,7,6,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,3,2,4,8,6,5]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[4,3,1,8,2,6,7,5]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,1,3,2,5,7,6]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,5,3,8,6,2,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,3,8,1,4,7,6]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,2,5,8,1,3,7,6]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,2,4,3,5,7,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,4,3,8,1,5,7,6]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,7,4,8,6,5,2]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,4,5,3,2,8,7,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,8,5,1,6,4]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,3,2,5,6,4,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[3,1,8,2,6,5,4,7]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,6,2,8,1,4,5,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,3,8,4,1,5,7,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,4,2,3,1,5,7,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,2,3,4,1,5,7,6]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,1,6,2,4,8,3,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,8,1,4,3,6,5]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,1,3,2,4,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[2,1,8,5,3,4,6,7]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[8,4,1,3,2,5,6,7]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[8,6,1,2,3,5,4,7]=>[[1,4,5,6,8],[2],[3],[7]]=>[6,2]=>[6,2]=>2
[7,8,1,5,2,4,6,3]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,6,3,1,5,4,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,7,2,8,4,1,6,3]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,6,3,8,1,4,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,5,6,8,1,3,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,6,8,1,4,5,3,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,8,4,6,3,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,7,8,5,6,4,3,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,8,1,7,4,5,3,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,3,6,2,5,4,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,2,3,5,8,4,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,5,6,4,3,7,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,8,4,5,1,7,3]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,5,7,8,1,3,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,8,6,4,7,1,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,3,2,1,7,8,4,6]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[8,4,1,3,6,7,2,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[1,6,5,3,8,4,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,6,2,3,5,1,4,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[6,2,5,3,4,8,1,7]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,5,3,4,8,7,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,3,4,8,1,7]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,3,4,8,1,7,2,6]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,3,4,8,7,2,6]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[1,5,3,4,8,7,2,6]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[5,1,3,8,4,7,6,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,3,8,1,4,7,6,2]=>[[1,3,6],[2,5],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,3,5,8,1,7,6,2]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,5,4,8,1,2,7]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,6,5,4,8,2,7,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,2,4,8,7,6,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,5,3,6,8,4,1,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,6,2,5,1,7,8,3]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,1,7,4,8,6,5]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,3,6,4,2,7,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,7,4,8,5,3,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,7,3,2,5,4,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,8,5,2,6,4,3,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,1,2,5,7,4,6,3]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,2,5,3,6,1,4,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,7,4,1,5,2,3]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[8,6,4,7,5,1,3,2]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,4,7,8,3,5]=>[[1,3,4,5,6],[2,8],[7]]=>[6,2]=>[6,2]=>2
[2,4,6,5,7,1,8,3]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,9,10,1,4,5,6,7]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[5,5]=>[5,5]=>2
[3,5,2,1,7,8,6,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[4,2,7,8,6,5,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[1,2,7,8,6,4,5,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,1,2,6,5,3,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,1,6,3,2,4,8,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,4,8,1,2,3,7,5]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[7,4,1,3,6,8,5,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[7,2,5,1,6,4,3,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,2,7,1,4,6,3,8]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,8,5,7,1,4,2]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,3,8,5,7,1,6]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,1,4,6,5,7]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,5,7,6,1,3,8,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,1,6,5,8,2,4]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,3,6,8,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[3,8,5,4,7,6,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,6,8,7,3,5,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,5,1,3,8,7,2]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,4,6,2,1,8,7,3]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,5,1,4,6,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[3,5,4,1,2,8,6,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,3,8,1,4,2,6,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[5,3,8,1,4,2,7,6]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,7,5,8,6,2,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,6,3,4,1,2]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,2,6,1,4,8,3]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,4,5,1,8,3,7,6]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,8,5,3,4,1,6]=>[[1,3,6,8],[2,4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,4,5,3,1,7,8,2]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,3,5,6,4,1,8,2]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,4,7,8,9,1,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[2,3,6,7,8,9,1,4,5]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[2,5,6,7,8,9,1,3,4]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[2,3,4,5,8,9,10,1,6,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[2,3,4,7,8,9,10,1,5,6]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[2,1,6,7,8,9,3,4,5]=>[[1,3,4,5,6],[2,7,8,9]]=>[6,3]=>[6,3]=>2
[2,3,6,7,8,9,10,1,4,5]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[2,5,6,7,8,9,10,1,3,4]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[7,3]=>2
[2,5,6,3,4,1,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,2,1,5,8,3,7]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[4,6,7,2,3,8,5,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,3,7,8,1,2,6]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,3,5,8,1,6,4,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,4,5,8,3,6,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,5,6,3,1,4,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,2,6,1,5,7,3]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,7,8,1,5,4,6]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,2,6,7,8,3,1,4]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[5,6,2,7,8,3,1,4]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,3,7,5,8,4,6,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,8,5,1,4,6,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,6,7,1,8,4,3]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,7,8,1,2,5,3]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,8,1,2,3,6,4]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[1,2,8,7,4,6,5,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,4,8,7,3,6,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,1,8,7,5,6,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,2,7,6,1,5,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[7,2,6,5,3,1,4,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,3,7,6,2,4,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,2,7,4,6,5]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,1,6,4,3,5]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,3,2,8,1,7,5,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,4,1,6,3,8,2]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,5,3,2,4,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[1,7,3,5,2,4,8,6]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,3,7,2,5,1,6,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,4,3,2,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,2,1,3,5,4,6,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[8,3,7,5,4,2,6,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,6,8,7,5,2,3,4]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,3,6,2,5,4,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,7,6,3,1,8,2]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,6,7,5,1,3,8,2]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,6,5,1,4,7,8,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,6,7,3,1,5,8,2]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,4,1,8,7,3,6,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,4,7,5,3,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,2,5,1,8,7,3,4]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,6,1,5,8,7,4]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,3,6,7,5,1,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[6,2,3,5,7,4,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[5,3]=>[5,3]=>2
[1,6,3,8,4,7,2,5]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,5,2,4,7,3,6]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,1,4,2,3,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,3,4,8,5,6,2,7]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,2,7,1,8,6,5,4]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,2,4,1,5,7,8,3]=>[[1,3,5,6,7],[2,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,8,4,1,3,6,7,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,7,2,3,8,1,4,5]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,2,8,1,7,4,6,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,5,4,7,3,1,8,6]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,3,1,2,5,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[7,4,6,8,3,1,2,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[8,5,4,7,3,1,2,6]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[7,3,2,1,5,4,8,6]=>[[1,5,7],[2,6,8],[3],[4]]=>[5,2,1]=>[5,2,1]=>3
[2,5,6,4,8,1,3,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,4,1,6,2,3,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[1,3,6,5,2,4,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[5,4,1,2,7,6,3,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[5,8,7,3,1,2,4,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[2,7,8,1,4,5,3,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,8,7,3,6,5]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,4,3,8,7,5]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[3,7,8,1,2,4,6,5]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,4,1,2,6,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,4,3,1,2,6,5,7]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[3,8,2,7,4,5,1,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,2,3,5,4,1,7]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[8,2,6,1,3,5,4,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,3,7,2,5,6,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,1,7,4,5,2,6]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,4,5,1,7,3,6]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,8,2,4,5,1,7,3]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,8,1,7,5,6,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,3,7,1,5,6,2]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,3,4,7,2,6,5,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,3,7,6,4,5,2]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,1,4,5,6,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,3,6,1,2,5,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,6,2,4,5,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,2,3,6,1,5,4]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,2,7,1,3,4,6,5]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,1,8,4,2,3,7,6]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,4,7,3,1,6,5]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,2,7,6,3,1,4,5]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[6,8,1,4,7,3,2,5]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,5,7,2,6,3,1,4]=>[[1,3,8],[2,5],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,2,7,3,1,6,4]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,2,6,7,5,4,3]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[8,4,1,7,5,6,2,3]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,4,7,6,5,1,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,7,6,4,5,1,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,2,3,6,5,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,4,7,3,6,5,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,7,6,4,5,2,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,7,6,4,5,3]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,1,4,7,3,6,5,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[2,8,1,5,3,7,6,4]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,2,4,7,5,6,3]=>[[1,2,4,5,7],[3],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,3,8,4,7,1,6,5]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,8,2,3,5,6,4,7]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,7,6,2,3,5,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[1,7,6,2,3,8,4,5]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[1,8,2,3,7,6,4,5]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,8,6,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,2,3,7,4,1,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,2,8,3,7,6,1,5]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,3,5,6,4,8,2,7]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,1,8,2,7,5,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,8,5,6,1,2,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,6,2,5,4,8,3]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,1,7,4,3,8,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,2,1,5,6,8,4]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[3,1,5,6,4,2,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[8,1,6,4,3,5,2,7]=>[[1,3,6,8],[2],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,1,6,5,3,8,7,4]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,5,6,4,2,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[6,1,4,3,7,5,8,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,8,6,4,5,2,7,1]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,8,6,2,3,7,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,5,3,7,2,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,7,2,8,6,3,1]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,7,4,5,1,6,8,2]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,6,8,1,2,5,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,8,5,1,3,7,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,7,4,5,2,8,6,1]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,7,8,4,6,1,5,2]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,7,2,1,6,8,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,1,6,8,3,7,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,5,4,6,1,2,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,4,5,2,6,8,3]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,2,6,5,3,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,1,5,8,4,6,2,7]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,2,6,3,4,1,5,7]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,6,5,8,2,1,3,7]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,4,8,3,5,6,2,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,7,4,2,3,6,5]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,3,1,8,5,7,2,6]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,2,4,8,1,6,5]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,7,2,4,5,8,1,6]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,2,7,4,6,1,8,5]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,2,4,6,1,7,5]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,3,2,4,5,7,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[7,4,6,2,1,3,8,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,6,7,2,4,1,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,7,6,2,3,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,2,3,8,7,1,6,4]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,5,2,4,1,3,8,6]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,2,6,8,5,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[8,2,3,4,1,6,7,5]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,4,3,8,1,6,5,2]=>[[1,4],[2,6],[3,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,4,3,8,7,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,7,6,2,5,8,1,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,3,2,4,5,8,1,7]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[2,6,4,5,8,3,1,7]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,4,8,6,2,5,1]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,5,2,8,1,4,6]=>[[1,3,5],[2,7,8],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,5,8,7,4,2,3,6]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[1,7,2,4,5,8,6,3]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,8,7,2,5,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,2,7,5,3,4,8]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,3,7,2,6,4,5,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,3,2,8,5,6,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,5,2,4,8,3,7]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,7,3,8,4,2,5,6]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,2,4,7,5,8,3]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,2,7,4,3,8,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,8,2,3,6,4,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,9,1,2,3,4,5,7]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[5,8,9,1,2,3,4,6,7]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]=>[6,3]=>2
[2,5,3,6,7,1,4,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,4,1,5,7,2,3,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,4,1,5,7,3,8,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,7,3,8,5,6,4]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,1,6,3,8,2,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,7,4,3,8,6,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,1,4,5,8,6]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,3,4,5,6,7,1,9,8,10]=>[[1,2,3,4,5,6,8,10],[7,9]]=>[6,2,2]=>[6,2,2]=>3
[2,3,4,5,1,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[6,5,8,3,2,7,1,4]=>[[1,3],[2,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,3,1,7,6,5,2]=>[[1,5],[2,6],[3,7],[4],[8]]=>[5,3]=>[5,3]=>2
[1,2,6,7,5,3,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[3,4,5,6,7,9,1,8,2]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[3,4,5,6,8,2,7,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,5,6,7,8,10,1,9,2]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[3,4,5,6,7,9,2,8,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[7,2,1,4,5,6,3,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[1,5,6,7,3,4,2,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,6,8,5,2,1,7,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,6,7,8,2,4,5,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,8,3,2,4,6,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,8,2,3,1,6,4]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,2,7,8,6,1,3]=>[[1,2,4,5],[3,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[1,3,5,8,7,2,6,4]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,1,8,5,7,3,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,3,8,7,5,2,6]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,5,1,6,7,2,4,3]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,7,2,1,5,8,4]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,6,1,3,8,7,4]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,5,6,1,3,8,4]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,4,1,2,5,8,3,7]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[4,7,3,5,2,6,8,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,3,5,4,7,1,8,6]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,4,1,5,7,3,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,2,3,7,5,4]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,3,6,4,1,7,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,3,4,8,2,1,7]=>[[1,4,5],[2,8],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[5,4,8,7,3,6,2,1]=>[[1,3],[2,4],[5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,5,1,2,6,7,8,9]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]=>[6,3]=>2
[5,2,7,6,8,3,4,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,5,2,7,3,6,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,7,4,5,2,8,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,4,2,8,5,6,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,5,8,2,7,1]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,7,4,5,3,6,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,8,4,5,3,6,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,8,2,7,4,5,1]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,2,8,4,7,5,6,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,3,6,2,7,4,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,3,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[9,1]=>[9,1]=>2
[1,7,8,4,3,6,5,2]=>[[1,2,3],[4,6],[5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,3,6,5,4,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,8,1,7,2,4,3,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,7,3,8,1,4,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,3,5,2,1,6,7,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,6,4,7,1,8,5,3]=>[[1,2,4,6],[3,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,6,5,7,3,8,2,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,5,3,7,6,2,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,2,3,8,7,5,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[6,1,4,2,7,8,3,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,5,1,3,7,8,4,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[6,7,4,2,3,8,5,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,7,3,2,4,6,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,1,3,2,6,8,4,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,4,6,8,2,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,1,7,5,6,3,8]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,3,7,6,2,8,5]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,2,5,7,3,8,4]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,3,8,2,5,7,6]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,7,3,6,4,2,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,7,2,4,8,3,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,2,8,4,1,5,6]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,3,4,1,7,8,6,2]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[4,7,6,5,8,2,3,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,6,8,4,3,5,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[7,2,6,3,1,8,4,5]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,8,4,1,3,7,2,6]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,4,2,1,6,8,5,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,1,3,5,6,4,7,2]=>[[1,3,4,5,7],[2],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,7,1,5,6,2,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,2,6,5,3,7,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,7,2,5,6,1,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,6,4,7,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,5,2,3,1,6,7,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,8,6,3,5,1,7,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,3,2,6,4,1,7,5]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,5,3,6,7,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,5,1,4,6,7,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,5,1,3,4,6,7,2]=>[[1,4,5,6,7],[2],[3],[8]]=>[7,1]=>[7,1]=>2
[3,8,6,2,5,4,7,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,4,6,5,2,7,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,7,4,2,5,3,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,3,2,5,1,4,7,6]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,4,5,1,2,6,7,3]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,1,5,3,2,6,7,4]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,1,5,2,4,6,7,3]=>[[1,3,5,6,7],[2],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,2,6,4,1,3,8,7]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[8,6,4,7,1,3,5,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,1,8,5,4,3,7,6]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[6,4,8,5,3,2,7,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[9,10,6,7,4,5,2,3,1,8]=>[[1,2,10],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[8,5,4,6,2,7,1,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,8,5,4,7,2,3,1]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,7,3,4,8,1,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,7,8,1,3,6]=>[[1,3,4,5],[2,7,8],[6]]=>[5,3]=>[5,3]=>2
[8,5,9,3,6,1,2,4,7]=>[[1,3,8,9],[2,5],[4,7],[6]]=>[3,2,4]=>[4,3,2]=>3
[8,9,4,5,10,1,2,3,6,7]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>[2,3,5]=>[5,3,2]=>3
[8,4,3,9,10,1,2,5,6,7]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>[5,5]=>[5,5]=>2
[9,10,6,7,4,5,1,2,3,8]=>[[1,2,9,10],[3,4],[5,6],[7,8]]=>[2,2,2,4]=>[4,2,2,2]=>4
[9,6,4,10,3,7,1,2,5,8]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[4,2,4]=>[4,4,2]=>3
[10,1,8,9,6,7,4,5,2,3]=>[[1,3,4],[2,6],[5,8],[7,10],[9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[10,8,7,6,5,4,3,1,2,9]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[4,8,5,6,1,2,7,3]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,6,8,7,1,4,3]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,8,1,5,2,7,3]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,3,6,4,1,7,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,3,7,5,8,6,1,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[3,8,5,1,2,4,7,6]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[1,3,6,4,8,2,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,3,4,6,5,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]=>[5,5]=>2
[1,2,3,4,5,6,8,7,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]=>[7,3]=>2
[1,7,6,2,8,5,3,4]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,5,8,6,4,7,2,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,6,2,8,1,7,3,4]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,8,4,5,1,3,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,3,8,1,4,6,7]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[1,6,8,3,2,4,5,7]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[9,6,5,4,3,2,1,7,8]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[10,7,6,5,4,3,2,1,8,9]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[10]=>[10]=>1
[9,8,5,4,3,2,1,6,7]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[8,6,5,2,4,3,7,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,2,5,3,7,4,8,1]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,4,2,6,3,7,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,3,2,6,4,7,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,4,6,5,8,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,6,5,8,2,4,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,6,4,8,2,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,5,4,8,2,6,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,6,8,4,5,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,6,5,7,4,2,8,3]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,7,4,8,5,6,3]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,7,4,8,5,1,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[2,5,8,6,4,3,7,1]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,4,2,5,7,1,8,3]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[9,1,2,3,4,5,8,7,6]=>[[1,3,4,5,6,7],[2],[8],[9]]=>[7,2]=>[7,2]=>2
[8,1,4,7,3,5,6,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,3,7,2,4,5,6,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[10,1,2,3,4,5,6,9,8,7]=>[[1,3,4,5,6,7,8],[2],[9],[10]]=>[8,2]=>[8,2]=>2
[9,1,2,3,4,7,8,6,5]=>[[1,3,4,5,6,7],[2],[8],[9]]=>[7,2]=>[7,2]=>2
[9,1,2,3,6,8,5,7,4]=>[[1,3,4,5,6],[2,8],[7],[9]]=>[6,2,1]=>[6,2,1]=>3
[8,1,4,5,7,3,6,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[9,3,8,2,4,5,6,7,1]=>[[1,3,6,7,8],[2,5],[4],[9]]=>[3,5,1]=>[5,3,1]=>3
[5,6,3,4,2,8,7,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,5,7,4,6,8,1,3]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[2,5,6,4,1,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,6,1,3,5,7,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,2,7,5,8,1,6,4]=>[[1,3,5],[2,4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,6,8,5,2,1,7]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,5,3,2,1,8,6,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,6,5,8,1,7,4,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,1,6,8,5,2,3,7]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[4,5,2,8,6,7,1,3]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,5,2,8,6,7,3,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,8,6,2,4,7,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,1,6,4,8,3,7]=>[[1,2,4,6],[3,5,8],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,2,4,5,8,6,1,7]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,5,2,1,3,8,6,7]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,2,3,6,8,5,1,7]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[4,5,1,3,2,8,6,7]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,5,8,6,1,7,2]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,4,5,8,6,1,2,7]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[6,4,1,3,7,8,2,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[6,3,1,2,5,4,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[8,2,6,4,1,3,7,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,5,8,2,4,3,7,6]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,3,7,8,2,6,5,1]=>[[1,3,4],[2,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,8,5,1,2,6,7,4]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,4,7,8,3,6,5,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,7,8,3,6,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,8,1,3,2,5,7,4]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,8,5,7,2,3,6]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,8,7,3,2,4,5,6]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[8,6,2,7,3,4,1,5]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,2,7,3,4,5,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,3,2,8,7,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,1,6,7,8,3,2,4]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[1,5,6,3,7,2,4,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,5,6,7,4,2,3,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[5,1,6,7,3,4,2,8]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,6,1,7,3,4,5,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,5,1,7,4,2,3]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,4,2,3,5,7,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[4,8,5,2,3,1,6,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,4,8,3,1,2,6,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,4,7,3,2,5,6,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,5,1,7,3,4,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,2,7,3,8,1,4,5]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,2,6,7,1,5,3]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[1,7,8,3,6,5,2,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,5,1,8,2,3]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[3,5,2,6,8,7,4,1]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,3,6,8,4,1,2,5]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[6,4,2,3,7,5,8,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,7,5,1,2,8,4]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[7,2,5,4,8,6,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,2,3,8,7,4,5,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,1,2,8,4,6,5,3]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,5,8,1,2,7,6,4]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,3,6,8,5,2,7]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,6,2,8,5,3,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,8,3,5,4,7,2,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,7,6,4,1,3,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,3,7,5,1,6,2,4]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,7,1,4,2,6,3]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,1,5,6,3,2,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,5,7,1,6,3,8,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,5,7,2,3,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,7,2,5,8,4,1]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,6,7,4,8,1,2]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,7,8,3,6,5,1]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,2,7,8,5,6,1,3]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[5,4,3,7,8,1,6,2]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,5,7,8,4,2,1,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,6,7,3,2,8,1,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,5,3,7,8,1,2]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,6,2,4,7,8,3,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,3,2,8,4,7,1]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,6,2,8,3,4,7,1]=>[[1,2,4,7],[3,5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,4,8,1,6,5,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,2,4,8,6,7,3,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,6,4,8,7,3,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,7,8,6,5,1,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,4,5,6,8,9,1,7,2]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[3,4,6,7,8,9,1,5,2]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[3,5,6,7,8,9,1,4,2]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[4,5,6,7,8,9,1,3,2]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[3,4,5,6,7,9,10,1,8,2]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[3,4,5,7,8,9,10,1,6,2]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[5,2,6,7,8,1,4,3]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[3,4,6,7,8,9,10,1,5,2]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[4,5,6,7,8,9,10,1,3,2]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[4,8,2,7,5,3,1,6]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,2,4,6,5,8,3,7]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,2,3,1,7,8,6]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,5,8,1,7,4,2,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,8,6,1,7,2,3,4]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[5,1,4,3,8,2,6,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,5,6,2,1,3]=>[[1,3,5],[2,8],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,8,6,7,5,2,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,5,4,7,3,6,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,2,8,7,3,6,5,1]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,6,1,4,5,2]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,7,8,2,1,5,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,7,6,3,8,1,5,2]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,1,4,6,2,5,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,4,5,3,8,7,1,6]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[4,7,5,6,2,8,1,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,7,5,1,6,3,2,4]=>[[1,5,8],[2,6],[3],[4],[7]]=>[5,3]=>[5,3]=>2
[7,8,6,2,3,5,1,4]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,4,6,7,3,5,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,1,6,7,8,2,5,3]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,6,3,4,1,2,7,5]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,5,8,4,6,1,3,7]=>[[1,2,3,8],[4,5],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,8,6,5,1,3,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,4,7,3,5,2,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,5,8,3,6,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,7,3,5,6,2,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,4,2,8,1,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,6,2,1,7,4,5]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,1,8,2,4,6,5,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,6,2,5,4,3]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,4,3,7,6,1,2]=>[[1,5],[2,6],[3,8],[4],[7]]=>[5,3]=>[5,3]=>2
[4,8,1,3,6,7,5,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,5,8,6,1,7,4,2]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,4,7,5,2,6,3]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,4,8,6,7,3,5,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,6,7,8,5,3,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,7,8,6,4,1,5,2]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,4,2,3,6,7,8,9,1]=>[[1,4,5,6,7,8],[2],[3],[9]]=>[8,1]=>[8,1]=>2
[6,5,4,2,3,7,8,9,1]=>[[1,5,6,7,8],[2],[3],[4],[9]]=>[8,1]=>[8,1]=>2
[7,6,5,4,2,3,8,9,1]=>[[1,6,7,8],[2],[3],[4],[5],[9]]=>[8,1]=>[8,1]=>2
[4,6,1,5,7,2,3,8]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,5,3,2,7,1,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,4,8,1,3,7,2,6]=>[[1,3,6],[2,5],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,5,3,1,7,2,6]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,4,5,3,1,8,6,2]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[5,6,8,7,2,4,3,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,6,4,2,3,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,8,7,5,1,3,2,4]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,8,2,6,7,5,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,6,3,8,2,5,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,7,4,1,8,2,5,3]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,6,8,3,2,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,6,4,2,8,1,5,3]=>[[1,5],[2,7],[3,8],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[6,3,4,8,7,1,2,5]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[2,7,4,8,1,6,3,5]=>[[1,2,4],[3,6,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,1,6,7,8,2,4]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[3,4,7,8,6,1,2,5]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[2,1,4,7,8,6,3,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[2,4,5,8,1,6,3,7]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,8,2,5,7,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,8,5,6,4,2,3,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,8,7,6,2,4,5,3]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,4,8,5,7,3,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,7,2,5,8,3]=>[[1,2,4,7],[3,6],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,7,5,1,8,6,3,4]=>[[1,2,5],[3,6,8],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,1,6,5,3,8,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,5,6,4,8,2,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,8,5,7,3,1,6]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,3,1,4,6,2,7,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[7,2,6,4,5,8,1,3]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,8,9,1,2,3,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[5,7,8,9,1,2,3,4,6]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]=>[5,4]=>2
[2,7,1,5,3,8,6,4]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,7,2,8,4,1,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,4,3,8,5,1,7,6]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,2,1,4,8,6,5]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[2,8,3,4,1,7,6,5]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,7,6,8,2,5,3,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,6,7,1,4,5,8,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,7,2,6,1,5,3,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,3,8,2,6,4,5]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,5,3,4,7,1,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,3,4,1,5,8,6]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,8,1,6,7,3,4]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,3,4,5,1,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,4,1,2,5,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,5,4,1,6,2,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,7,2,8,3,1,6]=>[[1,2,3,5],[4,6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,5,1,7,6,2,8,4]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,3,6,2,7,5,4,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,4,2,6,5,3,7,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,2,7,1,8,6,3]=>[[1,4,6],[2,7],[3,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[4,1,7,6,5,3,2,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[2,3,6,7,1,8,5,4]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,6,1,2,7,8,5,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,1,8,7,6,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[8,4,5,2,7,6,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,1,3,6,7,5,2,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[3,1,4,5,7,6,2,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,5,1,3,6,8,7,2]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,8,5,1,2,4,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[8,5,1,2,4,3,6,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[5,3]=>[5,3]=>2
[5,8,4,1,2,3,6,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[3,5,8,1,4,2,7,6]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,5,7,1,4,3,6]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,8,7,5,1,2,3,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,1,2,4,6,3,7,5]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,6,1,4,2,3,8,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[6,1,2,7,8,4,3,5]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[7,8,1,2,5,3,4,6]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,8,4,7,5,2,3,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,4,7,2,1,6,3,5]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,2,1,6,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[7,4,2,5,3,6,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,1,6,7,5,2,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[8,4,2,5,3,6,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,1,5,3,6,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,1,7,5,2,6,3,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,1,5,3,6,8,2,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,2,6,1,8,3,7]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,1,8,6,7,3,4,2]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,4,8,2,1,3,6,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[1,4,8,3,2,6,5,7]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,4,2,7,5,6]=>[[1,2,3,6,8],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,2,8,3,1,4,5,6]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[8,1,3,2,7,5,4,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,4,7,8,9,6,5,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[2,3,6,7,8,9,5,4,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[2,5,6,7,8,9,4,3,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[2,3,4,5,6,9,10,8,7,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[2,3,4,5,8,9,10,7,6,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[2,3,4,7,8,9,10,6,5,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[2,3,6,7,8,9,10,5,4,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[2,5,6,7,8,9,10,4,3,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[9,10,2,4,6,8,1,3,5,7]=>[[1,2,5,6],[3,4,9,10],[7,8]]=>[2,4,4]=>[4,4,2]=>3
[7,8,2,4,6,10,1,3,5,9]=>[[1,2,5,6],[3,4,9,10],[7,8]]=>[2,4,4]=>[4,4,2]=>3
[5,6,2,4,8,10,1,3,7,9]=>[[1,2,5,6],[3,4,9,10],[7,8]]=>[2,4,4]=>[4,4,2]=>3
[5,6,9,10,2,4,8,1,3,7]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[4,3,3]=>[4,3,3]=>3
[8,9,6,10,5,7,2,4,1,3]=>[[1,2,4],[3,6],[5,8],[7,10],[9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[3,4,2,6,8,10,1,5,7,9]=>[[1,2,4,5,6],[3,8,9,10],[7]]=>[2,4,4]=>[4,4,2]=>3
[3,4,9,10,2,6,8,1,5,7]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[4,3,3]=>[4,3,3]=>3
[9,3,4,7,10,2,6,8,1,5]=>[[1,3,4,5],[2,7,8],[6,10],[9]]=>[5,3,2]=>[5,3,2]=>3
[8,9,10,3,4,7,2,6,1,5]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[3,3,2,2]=>[3,3,2,2]=>4
[5,3,6,9,10,2,4,8,1,7]=>[[1,3,4,5],[2,7,8],[6,10],[9]]=>[5,3,2]=>[5,3,2]=>3
[4,8,5,9,10,3,7,2,6,1]=>[[1,2,4,5],[3,7],[6,9],[8],[10]]=>[2,3,2,2,1]=>[3,2,2,2,1]=>5
[3,10,11,12,4,7,9,2,6,8,1,5]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12]]=>[4,3,3,2]=>[4,3,3,2]=>4
[5,10,11,12,3,6,9,2,4,8,1,7]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12]]=>[4,3,3,2]=>[4,3,3,2]=>4
[7,6,1,8,2,5,4,3]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,4,1,6,7,3,5,2]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,8,4,2,1,6,3,7]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,6,4,1,2,5,3,8]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[5,4,2,8,1,6,3,7]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,7,2,6,4,5,3,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,8,4,3,6,1,5]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,5,4,8,6,2,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,6,3,5,2,1,7]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,6,3,2,7,1,4]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,3,2,4,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,7,3,2,8,6,4,1]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,5,1,6,8,2,7,3]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,2,3,5,7,8,10,6,9,4]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[1,2,4,5,7,8,10,3,9,6]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[7,2,1]=>3
[1,6,3,7,2,4,8,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,9,6,5,4,3,1,2]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[9,7,8,6,5,4,3,1,2]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[4,3,1,6,7,2,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[6,3,1,5,7,2,4,8]=>[[1,4,5,8],[2,6,7],[3]]=>[5,3]=>[5,3]=>2
[5,2,1,4,8,6,7,3]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[4,5,2,1,3,7,6,8]=>[[1,2,6,8],[3,5,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,2,7,4,1,6,5,3]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,2,8,4,1,6,5,7]=>[[1,3,6,8],[2,4],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,4,2,3,6,5]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[2,7,6,4,5,1,8,3]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,8,1,5,7,4,2]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,3,1,6,7,4,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,5,6,8,2,1,7,3]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,6,8,1,3,7,2]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,8,3,2,1,7,6]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,5,1,3,2,6,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,7,3,2,1,6,5,8]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,7,8,3,5,1,6,2]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,1,3,5,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,8,3,2,1,6,7,5]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,2,8,1,4,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,3,7,8,1,4,2]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,1,4,3,6,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,2,3,7,1,5,4,8]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,8,1,5,4,7,3]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,1,3,4,5,2,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[5,3]=>[5,3]=>2
[7,1,3,4,5,6,2,8]=>[[1,3,4,5,6,8],[2],[7]]=>[6,2]=>[6,2]=>2
[7,2,5,1,3,6,4,8]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[6,5,2,7,8,4,3,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[7,5,3,6,4,2,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[1,3,6,7,5,2,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[1,5,2,6,8,7,3,4]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,2,8,9,1,5,6,7]=>[[1,4,5,9],[2,7,8],[3],[6]]=>[5,4]=>[5,4]=>2
[6,9,4,7,2,5,1,3,8]=>[[1,2,9],[3,4],[5,6],[7,8]]=>[2,2,2,3]=>[3,2,2,2]=>4
[6,4,3,9,2,7,1,5,8]=>[[1,4,9],[2,6],[3,8],[5],[7]]=>[4,2,3]=>[4,3,2]=>3
[6,5,4,3,2,9,1,7,8]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[6,3]=>[6,3]=>2
[5,6,1,2,3,7,8,9,10,4]=>[[1,2,5,6,7,8,9],[3,4,10]]=>[2,7,1]=>[7,2,1]=>3
[2,5,1,3,6,7,8,9,10,4]=>[[1,2,5,6,7,8,9],[3,4,10]]=>[2,7,1]=>[7,2,1]=>3
[6,7,8,1,2,3,4,9,10,5]=>[[1,2,3,7,8,9],[4,5,6,10]]=>[3,6,1]=>[6,3,1]=>3
[2,6,7,1,3,4,8,9,10,5]=>[[1,2,3,7,8,9],[4,5,6,10]]=>[3,6,1]=>[6,3,1]=>3
[2,7,8,9,1,3,4,5,10,6]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[4,5,1]=>[5,4,1]=>3
[8,3,4,9,10,1,2,5,6,7]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[5,5]=>[5,5]=>2
[5,9,10,2,6,7,1,3,4,8]=>[[1,2,3,10],[4,5,6],[7,8,9]]=>[3,3,4]=>[4,3,3]=>3
[9,5,6,3,4,10,1,2,7,8]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[5,3,9,2,6,10,1,4,7,8]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[3,3,4]=>[4,3,3]=>3
[5,4,3,2,9,10,1,6,7,8]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[6,4]=>[6,4]=>2
[10,7,8,5,6,3,4,1,2,9]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[3,2,2,3]=>[3,3,2,2]=>4
[7,5,10,3,8,2,6,1,4,9]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[3,2,2,3]=>[3,3,2,2]=>4
[7,5,4,3,10,2,8,1,6,9]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[5,2,3]=>[5,3,2]=>3
[7,6,5,4,3,2,10,1,8,9]=>[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[7,3]=>[7,3]=>2
[5,3,4,7,2,1,6,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[4,8,5,7,1,2,3,6]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,2,3,7,6,1,8,5]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,2,6,3,1,5,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>[3,5]=>[5,3]=>2
[4,6,3,2,5,8,7,1]=>[[1,2,6],[3,5,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,4,3,2,6,1,7]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,5,7,4,8,6,2,3]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,7,3,8,2,4]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,8,6,4,3,5]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[3,5,1,7,8,6,2,4]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,2,4,1,7,6,8,3]=>[[1,3,5,7],[2,6],[4,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,1,3,4,5,7,8,9,10,6]=>[[1,3,4,5,6,7,8,9],[2,10]]=>[9,1]=>[9,1]=>2
[9,3,4,5,6,7,8,2,1]=>[[1,3,4,5,6,7],[2],[8],[9]]=>[7,2]=>[7,2]=>2
[10,3,4,5,6,7,8,9,2,1]=>[[1,3,4,5,6,7,8],[2],[9],[10]]=>[8,2]=>[8,2]=>2
[5,4,3,8,1,7,2,6]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,3,1,5,6,8,4,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[2,9,1,3,4,5,6,7,10,8]=>[[1,2,5,6,7,8,9],[3,4,10]]=>[2,7,1]=>[7,2,1]=>3
[7,2,3,1,6,8,4,5]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,1,6,2,3,4]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,2,7,3,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,2,5,8,6,3,7]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,1,5,7,3,6]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,7,1,6,3,4,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[4,8,2,5,1,6,3,7]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,1,2,4,6,3,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,1,7,3,6,4,2,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,5,6,1,4,8]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[3,2,7,1,6,4,5,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[6,3,1,7,5,4,2,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[6,2,8,7,3,4,5,1]=>[[1,3,6,7],[2,4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,4,8,5,6,2,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,3,6,8,4,5,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,2,8,3,1,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,7,5,6,2,8,3]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,4,8,3,5,6,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,3,1,4,8,6,2,7]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[5,2,4,8,3,1,6,7]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,4,5,1,8,6,2,3]=>[[1,3,5],[2,6,8],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[8,1,5,7,6,3,2,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[1,8,6,7,5,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,4,8,3,1,6,5,2]=>[[1,3],[2,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,3,7,6,2,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,7,3,5,1,2]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,2,3,5,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[3,5]=>[5,3]=>2
[7,1,4,3,8,6,5,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,7,2,8,3,4]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,8,2,6,7,4,3,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,2,4,1,8,5,3,6]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,2,1,4,6,8,5]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[4,7,2,6,1,8,3,5]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,3,2,1,6,8,4]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[6,8,1,3,4,2,5,7]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,6,1,4,7,8,2,5]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,5,7,1,3,6,4,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,4,7,2,5,3,6,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,5,3,1,2,6,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,5,1,3,8,2,6,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,1,5,3,2,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,1,4,2,6,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,2,1,7,4,3,8,5]=>[[1,4,7],[2,5,8],[3,6]]=>[4,3,1]=>[4,3,1]=>3
[2,4,3,6,7,1,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,3,5,2,1,6,4,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,6,5,2,1,3,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[2,5,6,1,4,3,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,3,7,2,4,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,5,4,1,7,2,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,5,4,2,1,3]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,6]=>[6,2]=>2
[1,6,8,7,3,2,4,5]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[8,7,5,4,6,1,3,2]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,7,8,2,4,6,3,5]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,4,8,1,3,6,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,1,8,4,3,7,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,2,6,7,5,4,3]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,7,5,1,6,8,3,4]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[8,5,4,2,7,3,6,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,8,6,1,2,4,5,7]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[1,8,5,3,2,7,4,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,8,4,7,2,3,5,6]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[3,2,8,1,7,5,4,6]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,5,6,2,3,4,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[6,5,1,7,2,3,4,8]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[1,6,8,2,7,3,4,5]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,8,7,3,4,2,5]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,1,3,6,7,8,5,2]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[7,4,1,5,6,8,3,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[4,1,2,6,7,8,5,3]=>[[1,3,4,5,6],[2,7],[8]]=>[6,2]=>[6,2]=>2
[3,4,5,8,9,1,2,6,7]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[3,4,7,8,9,1,2,5,6]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[3,6,7,8,9,1,2,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[3,4,5,6,7,10,1,2,8,9]=>[[1,2,3,4,5,6,10],[7,8,9]]=>[6,4]=>[6,4]=>2
[3,4,5,6,9,10,1,2,7,8]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[6,4]=>2
[3,4,5,8,9,10,1,2,6,7]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[6,4]=>2
[1,3,7,8,9,2,4,5,6]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[3,4,7,8,9,10,1,2,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[6,4]=>2
[2,6,7,8,9,1,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[3,6,7,8,9,10,1,2,4,5]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[6,4]=>2
[6,3,7,1,8,2,4,5]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[1,5,4,7,8,3,6,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,1,4,7,8,3,6,2]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,8,1,5,6,2,3,7]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,4,1,7,3,8,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,7,8,2,5,1,6]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,7,8,5,4,2,1,6]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[1,7,4,5,6,8,3,2]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,2,4,5,6,8,3,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[2,7,4,5,6,8,3,1]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,4,7,8,3,1,6,5]=>[[1,2,3,4],[5,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,3,6,8,1,7,2]=>[[1,4,5],[2,7],[3,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,7,4,5,8,1,6,2]=>[[1,2,4,5],[3,7],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,4,3,5,6,8,2,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,4,6,5,8,2,7,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,1,7,3,2,8,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,7,3,6,4,2,8,5]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,3,5,1,2,8,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,4,2,3,5,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,8,3,5,2,1,6,7]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,8,4,7,5,3,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,7,1,6,8,2,3,5]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,5,8,2,3,7,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,8,2,4,5,3,6]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,8,2,3,4,1,6]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,3,8,7,1,4,6]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[8,7,1,3,2,6,4,5]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,7,6,4,8,3,1,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,6,3,7,5,8,4,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,1,2,3,8,4,6]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[3,2,4,1,5,6,7,8,9,10]=>[[1,3,5,6,7,8,9,10],[2],[4]]=>[3,7]=>[7,3]=>2
[8,6,2,1,3,7,4,5]=>[[1,5,6,8],[2,7],[3],[4]]=>[6,2]=>[6,2]=>2
[4,2,3,6,8,5,7,1]=>[[1,3,4,5],[2,6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,7,3,2,6,5,1,8]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,3,7,8,2,1,6,5]=>[[1,3,4],[2,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,8,7,2,1,5,6,3]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,3,8,2,5,1,6,4]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,3,8,6,1,2,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[6,3,5,8,4,1,2,7]=>[[1,3,4],[2,7,8],[5],[6]]=>[4,4]=>[4,4]=>2
[7,3,8,4,5,1,2,6]=>[[1,3,5,8],[2,4],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,7,5,1,2,6,3]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[7,8,4,6,1,3,5,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,8,7,5,1,3,6,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,5,3,6,8,1,2,7]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[7,8,6,2,1,4,3,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[7,8,6,3,1,2,5,4]=>[[1,2,7],[3,6],[4,8],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,2,8,4,7,1,3,6]=>[[1,3,5],[2,4,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,3,1,2,8,6,5,4]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[8,7,1,3,2,4,5,6]=>[[1,4,6,7,8],[2],[3],[5]]=>[4,4]=>[4,4]=>2
[6,8,2,1,4,5,3,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[1,5,4,8,7,3,2,6]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,1,2,6,5,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[7,5,8,1,2,4,6,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,1,5,2,8,7,4,3]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,6,3,5,7,1,2,8]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,7,2,6,5,8,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,5,7,2,6,4,8,3]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,4,6,1,8,3,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,2,7,8,3,5,4,6]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,6,2,8,5,4,3]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,2,7,8,3,4,6,5]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,7,6,8,3,4,2,5]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,1,7,8,6,5,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[2,4,8,6,5,7,1,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,3,4,8,2,7,6]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[8,7,3,6,1,4,2,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,5,1,8,3,4,7,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,1,5,6,4,7,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,5,6,1,3,4,8,2]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,7,2,4,6,1,8,3]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,1,5,6,3,8,7,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[3,2,7,5,8,6,4,1]=>[[1,3,5],[2,4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,4,5,3,8,1,7,6]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,5,4,3,8,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,5,3,1,2,6,7,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[7,2,5,1,3,6,8,4]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[8,4,7,3,1,2,6,5]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,8,7,3,5,2,6,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,4,8,3,6,5,7,1]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,2,6,5,7,4]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,7,8,5,2,1,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[4,7,2,1,8,6,5,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,6,2,8,4,1,7,3]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,2,4,8,6,1,3]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,2,4,8,5,1,3]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,7,3,2,8,5,1,4]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,2,3,1,8,6,5,4]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[7,2,8,3,5,6,1,4]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,3,8,4,6,1,5]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[1,7,3,4,8,5,2,6]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,8,5,4,2,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,2,8,4,5,3,1,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,6,4,3,1,7,5]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,7,3,4,8,2,5,6]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,5,8,3,4,6,2,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,4,2,5,7,6]=>[[1,2,3,6,7],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,4,7,6,2,3,8,5]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,8,4,6,7,2,3,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,4,2,3,7,8,6,5]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,7,1,6,4,8,3,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,4,5,8,1,3,6,2]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,3,6,2,5,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,6,5,8,2,4,7]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,4,6,3,2,8,5,7]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,8,4,1,5,7,2,3]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[5,2,6,7,4,1,8,3]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[8,5,6,4,1,7,3,2]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,3,1,6,4,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,2,6,3,1,7,4]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,8,1,6,3,7,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,1,4,6,2,5,7,3]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,8,1,6,2,7,3]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,6,8,1,4,3,7]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,7,3,8,2,1,4,5]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,7,3,5,4,1,8,6]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,7,4,1,8,5]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,1,4,8,5,3,7,6]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,7,3,8,4,1,6,5]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,1,5,4,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,8,3,4,7,2,6]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[5,3,8,1,4,6,2,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[4,5,8,1,3,6,2,7]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,6,5,2,8,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,3,8,5,7,6,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,3,7,2,8,6,5]=>[[1,3,4,6],[2,7],[5,8]]=>[4,2,2]=>[4,2,2]=>3
[4,6,3,1,7,2,8,5]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,6,3,1,8,5,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,2,5,3,1,6]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,3,2,8,7,4,5]=>[[1,2,5,8],[3,6],[4,7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,1,7,5,4,6,3]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,3,1,5,7,2,4]=>[[1,2,6],[3,5,8],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,3,1,2,5,6,4]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[3,5,7,1,2,4,6,9,8]=>[[1,2,3,7,8],[4,5,6,9]]=>[3,5,1]=>[5,3,1]=>3
[1,3,5,7,2,8,4,9,6,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[1,3,5,6,2,7,4,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[1,3,4,5,2,7,6,9,8,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[5,4,3,6,1,7,8,2]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,2,7,8,5,6,1,4]=>[[1,3,4],[2,5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,3,2,1,7,5,6]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,9,8,7,6,4,3,2,5]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,9,8,7,5,4,3,2,6]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,9,8,6,5,4,3,2,7]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,9,7,6,5,4,3,2,8]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,9,8,7,6,5,2,3,4]=>[[1,2,8,9],[3],[4],[5],[6],[7]]=>[2,7]=>[7,2]=>2
[1,10,9,8,7,6,5,3,2,4]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[1,10,9,8,7,6,4,3,2,5]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[1,10,9,8,7,5,4,3,2,6]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[1,10,9,8,6,5,4,3,2,7]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[1,8,4,5,6,3,2,7]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,10,9,7,6,5,4,3,2,8]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[1,7,8,6,5,4,3,2,9]=>[[1,2,3,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[1,10,8,7,6,5,4,3,2,9]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[8,5,1,7,4,6,3,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,7,8,4,6,2,5]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,7,3,6,1,2,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,8,4,3,7,1,2,6]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[5,6,4,8,7,2,1,3]=>[[1,2,4],[3,5],[6,8],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,8,3,7,6,1,2,5]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[2,8,4,7,1,3,6,5]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,8,9,10,2,3,4,5,1,6]=>[[1,2,3,4,10],[5,6,7,8],[9]]=>[4,4,2]=>[4,4,2]=>3
[6,8,3,4,5,2,1,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[3,7,1,4,5,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,1,4,5,2,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,8,2,4,5,1,7,6]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,2,1,5,6,4,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[3,6,8,1,5,4,7,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,4,6,3,5,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,3,6,5,7,2,4,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,7,2,5,6,4,3,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,8,5,4,3,7,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,7,8,4,3,1,6]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[6,8,5,3,2,4,1,7]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,6,8,5,3,2,7,4]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,6,1,8,7,5,3,2]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[1,3,7,6,8,5,2,4]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,7,8,6,5,2,3]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[5,4,3,7,6,1,2,8]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[4,7,6,1,2,3,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,5,2,6,7,8,1,3]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,8,7,6,5,4,3,1,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[1,7,6,2,3,8,5,4]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,1,3,7,6,2,8]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,2,3,8,6,4,5,1]=>[[1,3,4,7],[2,5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,5,4,3,8,6,2,7]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,3,7,5,8,4,6,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,8,1,2,7,6,4,3]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,4,5,3,2,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,2,6,7,5,3,8]=>[[1,2,4,5,8],[3,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,4,6,5,3,7]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,2,1,6,4,3,8,5]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,4,8,7,2,3,6,5]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,3,6,5,8,2,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,7,1,5,8,2,6]=>[[1,3,6],[2,5,8],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,6,5,2,7,4,3]=>[[1,2,6],[3,7],[4],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,8,6,2,7,4,3,5]=>[[1,2,5,8],[3,6],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,1,8,3,7,5,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,7,3,6,2,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,5,4,1,7,8,6,2]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,2,1,5,4,3]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,3,7,5,4,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,1,3,7,6,4,2]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,3,6,5,4,2,1,7]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,1,3,5,7,2,8,4]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,8,1,5,6,4,3,7]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,7,5,8,4,2,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,4,1,6,5,2,8,3]=>[[1,4,7],[2,5,8],[3],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,2,8,6,5,3,1]=>[[1,4],[2,5],[3,6],[7],[8]]=>[4,4]=>[4,4]=>2
[6,8,4,7,3,2,5,1]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,7,3,2,1,6,4]=>[[1,2],[3,7],[4,8],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,8,7,2,6,4,3,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,3,5,1,4,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,5,6,8,3,4,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,6,5,7,8,3,2,4]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,6,7,2,3,5,4,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,4,8,6,7,3,1,2]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,3,1,6,8,5]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[7,3,6,4,2,1,8,5]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,5,2,7,3,1,6]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,4,3,1,8,5,2,7]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,4,3,1,5,8,6,2]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,4,8,6,5,3,1,2]=>[[1,3],[2,4],[5,8],[6],[7]]=>[3,5]=>[5,3]=>2
[4,8,5,2,6,7,3,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,3,2,1,8,5,6,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[1,5,7,2,4,3,8,6]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,2,7,5,8,4,3,6]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,1,3,8,2,7,4,6]=>[[1,3,4,8],[2,6],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,1,3,2,8,4,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,1,6,3,2,8,4,5]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,2,3,6,5,4]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,1,2,6,4,3,8,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,4,7,8,3,2,5,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[8,7,1,3,2,4,6,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,1,6,3,2,4,7,5]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,8,2,7,6,3,5,4]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,6,3,2,7,4,5]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,2,1,7,6,3,4,5]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[8,7,2,4,3,1,5,6]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[4,7,6,2,3,1,5,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,7,6,1,3,2,8,5]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,1,3,5,6,4,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[2,6,3,4,7,8,5,1]=>[[1,2,4,5,6],[3,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[7,6,3,1,8,5,2,4]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[7,2,1,3,6,8,5,4]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[7,6,3,8,1,5,2,4]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[1,6,4,7,8,5,3,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,2,5,8,6,1,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>[4,4]=>[4,4]=>2
[4,1,3,6,2,5,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[7,1,4,6,3,2,5,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[7,4,5,8,6,2,3,1]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,7,2,3,8,4,1,5]=>[[1,2,5,8],[3,4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,7,8,1,5,4,3,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,5,2,6,8,7,4,3]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,2,3,4,5,6,8,9,7,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]=>[8,2]=>2
[1,8,3,7,5,2,6,4]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,3,6,5,2,7,4]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,1,3,8,5,2,6,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,7,1,5,2,6,8,3]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,4,1,5,2,6,8,3]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[3,1,6,7,5,2,8,4]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,6,2,4,5,1,7,3]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,6,7,5,2,1,4,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[7,1,4,5,2,6,8,3]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,1,6,2,3,8,7,5]=>[[1,3,5,6],[2,4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,7,6,5,2,8,3]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[8,4,1,5,6,2,7,3]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[8,4,5,3,6,1,7,2]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,8,4,7,3,5,6,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,4,8,3,2,6,7]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,5,7,6,3,8,2,4]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,3,1,7,8,4,5]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[2,1,7,8,3,5,4,6]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,5,8,6,7,4,2,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,1,3,5,2,6,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,7,8,2,5,4,1,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,7,6,5,8,1,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,7,8,6,2,1,5,3]=>[[1,2,3],[4,7],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,8,6,3,2,1,7,5]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[5,1,4,7,6,8,3,2]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,6,4,7,1,8,3,2]=>[[1,2,4,6],[3,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,7,4,6,1,8,2]=>[[1,3,5,7],[2,4],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,5,7,8,6,3,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[3,6,7,1,5,4,8,2]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,6,4,7,5,8,2,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,8,1,2,4,5,6,9,7]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[8,1,7,3,2,4,5,6]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[3,9,1,2,4,5,6,7,10,8]=>[[1,2,5,6,7,8,9],[3,4,10]]=>[2,7,1]=>[7,2,1]=>3
[6,4,7,1,5,2,8,3]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,5,2,8,7,4,3]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,2,3,4,5,7,8,6,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]=>[7,3]=>2
[2,3,4,5,7,9,1,6,8]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[1,2,3,4,5,7,8,9,6,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]=>[8,2]=>2
[2,1,4,5,3,6,7,8,9]=>[[1,3,4,6,7,8,9],[2,5]]=>[4,5]=>[5,4]=>2
[4,1,7,2,5,8,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,2,5,8,6,1,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,1,7,2,8,6,3]=>[[1,2,4,6],[3,5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,4,7,2,5,3,1,8]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,3,6,8,2,5]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,8,7,3,5,1,6,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,8,7,1,6,2,4]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,6,7,4,3,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,5,1,6,4,3,2,7]=>[[1,4,8],[2,5],[3],[6],[7]]=>[4,4]=>[4,4]=>2
[8,6,3,5,2,7,1,4]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,4,6,2,1,5,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,5,2,1,6,4,7,3]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[1,7,2,8,5,4,6,3]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,7,1,4,8,5,3,2]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,3,2,8,5,1,4,6]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[4,1,7,3,2,8,5,6]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,3,5,2,4,7,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,3,7,8,6,1,5,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,2,6,3,7,8,5,4]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,3,7,8,5,4,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,6,4,7,5,3,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,5,1,8,6,2,7,3]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,6,1,8,7,2,3,4]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,5,1,6,8,7,3,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,9,2,4,5,6,7,8,1]=>[[1,2,5,6,7,8],[3,4],[9]]=>[2,6,1]=>[6,2,1]=>3
[3,8,6,1,5,2,4,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[3,2,8,1,5,6,4,7]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,3,2,1,4,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,6]=>[6,2]=>2
[3,4,7,6,8,2,1,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,8,1,3,7,5,6,4]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,7,2,5,6,4,3]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,4,7,1,5,8,2,6]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,5,2,4,6,7,8,9]=>[[1,2,3,6,7,8,9],[4,5]]=>[3,6]=>[6,3]=>2
[1,2,4,7,3,5,6,8,9]=>[[1,2,3,4,7,8,9],[5,6]]=>[4,5]=>[5,4]=>2
[1,4,7,5,2,3,6,8]=>[[1,2,3,7,8],[4,6],[5]]=>[3,5]=>[5,3]=>2
[2,5,7,6,8,3,4,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,6,7,2,8,5,4]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,5,3,6,8,4,7,2]=>[[1,2,4,5],[3,6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,1,3,8,4,7,2]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,7,4,8,5,3,2,6]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,3,1,6,8,4,5,2]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,5,1,4,6,7,3,2]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[3,4,7,5,6,8,2,1]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,4,7,8,5,2,6,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,1,7,5,6,3,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,8,7,5,2,6,3,4]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,7,6,3,4,5,8,2]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,7,4,5,6,2,3]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,8,7,3,6,4,2,5]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,4,7,5,8,2,6,3]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,4,7,2,3,6,5,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,7,2,5,6,3,4,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,6,5,8,3,4,7]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,5,8,2,6,3,4,7]=>[[1,2,3,7,8],[4,5],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,8,3,2,7,5,1,4]=>[[1,2],[3,5],[4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[7,3,6,8,1,2,5,4]=>[[1,3,4],[2,6,7],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,1,5,7,2,6,3,8]=>[[1,3,4,8],[2,5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,2,1,3,6,4,8]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,7,9,1,2,3,4,5,10,8]=>[[1,2,3,7,8,9],[4,5,6,10]]=>[3,6,1]=>[6,3,1]=>3
[3,5,6,7,2,4,1,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,4,7,5,2,3,1,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,6,4,8,3,2,7]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,1,5,6,4,8,3,7]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,1,4,7,8,6,2,3]=>[[1,3,4,5],[2,6],[7,8]]=>[5,3]=>[5,3]=>2
[1,6,7,2,8,5,4,3]=>[[1,2,3,5],[4,6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[5,3,2,1,7,8,6,4]=>[[1,5,6],[2,7],[3,8],[4]]=>[6,2]=>[6,2]=>2
[7,4,3,8,6,1,5,2]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,7,1,5,8,6,2]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[8,2,4,5,3,1,7,6]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[1,4,3,2,7,5,8,6]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,2,8,6,3,10,9,7,4]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[4,8,7,2,6,1,3,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,5,8,2,1,7,3,6]=>[[1,2,3],[4,6,8],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,4,1,7,3,2,5]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,4,3,2,1,7,8,9]=>[[1,2,7,8,9],[3],[4],[5],[6]]=>[2,7]=>[7,2]=>2
[5,6,4,3,2,1,7,8,9,10]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[2,8]=>[8,2]=>2
[4,5,3,2,1,6,7,8,9]=>[[1,2,6,7,8,9],[3],[4],[5]]=>[2,7]=>[7,2]=>2
[6,7,5,4,3,2,1,8,9,10]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[2,8]=>[8,2]=>2
[7,5,4,3,1,2,6,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[6,5,4,3,7,1,2,8,9]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[5,4]=>[5,4]=>2
[6,7,9,8,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[7,6,8,9,5,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[7,8,10,9,6,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[5,7,9,8,6,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[8,7,9,10,6,5,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[4,6]=>[6,4]=>2
[6,3,1,8,2,7,5,4]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,7,8,3,2,5,6]=>[[1,3,4,8],[2,5,7],[6]]=>[4,4]=>[4,4]=>2
[7,6,2,8,4,5,3,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,8,2,1,3,6,4,7]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[8,5,1,7,3,4,6,2]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,6,3,4,1,8,2]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,9,10,1,5,6,3,4,2]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[4,3,2,1]=>[4,3,2,1]=>4
[1,8,3,5,2,6,4,7]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,4,6,1,8,5,7,2]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,8,7,4,5,1,6]=>[[1,2,3,6,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,3,5,7,4,2,6]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,8,4,6,7,1,3]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[9,8,6,1,2,3,4,5,7]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[9]=>[9]=>1
[9,8,7,5,1,2,3,4,6]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[9]=>[9]=>1
[9,8,7,6,4,1,2,3,5]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[9]=>[9]=>1
[9,8,7,6,5,3,1,2,4]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[7,1,2,6,4,3,5,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[7,1,2,6,5,3,4,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[4,7,8,6,2,3,5,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,1,2,4,8,6,5,3]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
[2,7,5,6,4,8,1,3]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,8,3,6,5,7,1,4]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[9,3,8,7,6,5,4,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[9,2,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[3,6]=>[6,3]=>2
[10,3,9,8,7,6,5,4,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[10,2,9,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[7,4,3,1,6,5,2,8]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[3,5,1,2,6,8,7,4]=>[[1,2,5,6],[3,4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,1,2,4,8,7,5,6]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[5,4,1,2,3,7,8,6]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[1,6,7,2,5,8,3,4]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,8,5,6,2,4,3,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,8,6,2,4,1,7]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,7,4,6,3,8,1,5]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,4,7,8,6,2,1,3]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[2,7,4,8,3,1,5,6]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[8,2,1,3,7,4,6,5]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,5,8,2,3,4,7,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,8,2,3,6,4,5,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,2,7,5,3,4,6]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[4,2,8,1,3,7,5,6]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,1,8,2,3,4,6]=>[[1,4,6,7,8],[2,5],[3]]=>[4,4]=>[4,4]=>2
[8,2,4,1,3,7,5,6]=>[[1,3,6,8],[2,5,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,1,6,2,3,7,4,5]=>[[1,3,5,6,8],[2,7],[4]]=>[3,3,2]=>[3,3,2]=>3
[7,1,8,2,3,6,4,5]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,7,5,1,8,3]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,7,2,5,3,8,1,6]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,7,4,2,8,1,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,7,6,3,8,1,5]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,8,5,1,2,3,7]=>[[1,2,3,8],[4,6,7],[5]]=>[3,5]=>[5,3]=>2
[4,6,5,7,1,2,3,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[4,6,5,7,1,3,8,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,7,6,1,8,2,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,5,2,1,6,3,4,7]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[7,1,8,5,3,2,4,6]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[8,2,7,5,4,1,6,3]=>[[1,3,7],[2,8],[4],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,2,8,5,7,1,6,3]=>[[1,3,5],[2,4],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,8,7,4,5,3,2,1]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[5,2,6,7,4,8,3,1]=>[[1,3,4,6],[2,5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,5,8,1,7,3,2,4]=>[[1,3,8],[2,5],[4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,1,5,2,3,7]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[7,2,4,1,6,3,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[2,6,1,5,3,4,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,7,5,4,2,6,1]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,5,1]=>[5,2,1]=>3
[5,7,8,2,3,6,4,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,7,3,1,4,5,6]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,6]=>[6,2]=>2
[5,6,1,2,4,7,8,3]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[10,2,3,1,4,5,6,7,8,9]=>[[1,3,5,6,7,8,9,10],[2],[4]]=>[3,7]=>[7,3]=>2
[3,8,6,7,5,4,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[7,8,5,1,4,6,2,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,2,7,5,4,6,1,3]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,6,3,1,2,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,6,7,1,3,2,8,5]=>[[1,2,3,7],[4,5,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,5,3,2,8,1]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,4,6,3,1,5,7,2]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,3,1,4,5,6,8,2]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[6,7,3,4,2,1,8,5]=>[[1,2,7],[3,4,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,4,8,3,1,5,7,2]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,4,2,3,5,1,8,6]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[3,1,6,5,2,4,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,5,3,8,6,4,1,7]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,8,4,1,3,2,7,6]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,3,4,7,6,1,8,2]=>[[1,3,4,7],[2,5],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,2,1,6,3,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,5,2,1,6,7,3,8]=>[[1,2,5,6,8],[3,7],[4]]=>[2,4,2]=>[4,2,2]=>3
[5,3,8,6,2,4,7,1]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,5,1,6,4,3,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,6,2,8,5,7,1,4]=>[[1,2,4],[3,5,6],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,6,8,1,5,7,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[4,1,2,5,7,6,3,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[4,6,5,8,1,7,3,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,1,3,6,4,8,7,5]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,1,2,7,5,6,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,6,4,3,8,7,5,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[4,5,1,6,8,7,2,3]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,5,1,8,6,4,7,3]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,8,7,3,1,4,6]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[9,8,7,4,3,2,1,5,6]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[9,8,7,6,3,2,1,4,5]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[9]=>[9]=>1
[3,8,7,2,6,1,4,5]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,4,5,1,6,7,2,3]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[8,4,7,3,1,5,2,6]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,5,1,8,3,6,4,7]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,4,7,3,2,1,6]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[4,3,8,6,1,2,5,7]=>[[1,3,7,8],[2,4],[5,6]]=>[3,5]=>[5,3]=>2
[4,8,6,5,7,1,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,2,3,5,6,8,4,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[6,2]=>[6,2]=>2
[5,8,1,3,4,7,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[8,3,4,2,7,6,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,5,6,4,1,3,2]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,7,4,2,3,6,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[8,4,2,3,7,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[7,2,4,5,3,1,6,8]=>[[1,3,4,7,8],[2],[5],[6]]=>[4,4]=>[4,4]=>2
[7,6,3,1,4,5,8,2]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[5,4,1,7,8,6,2,3]=>[[1,4,5],[2,6,8],[3,7]]=>[5,3]=>[5,3]=>2
[5,3,4,7,8,1,6,2]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[4,3,7,6,5,1,8,2]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,1,4,8,2,3,7,6]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[3,2,8,5,4,1,6,7]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[7,8,9,1,3,4,5,6,2]=>[[1,2,3,7,8],[4,5,6],[9]]=>[3,5,1]=>[5,3,1]=>3
[6,1,2,9,3,4,5,7,8]=>[[1,3,4,6,7,8,9],[2,5]]=>[4,5]=>[5,4]=>2
[1,2,8,3,4,6,5,7]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,2,7,3,5,4,6]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,1,2,6,3,4,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,2,7,5,6,3,4,8]=>[[1,2,3,5,8],[4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,1,4,7,2,3,6,8]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[4,8,1,2,3,6,5,7]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[1,2,3,5,6,7,8,4,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]=>[7,2]=>2
[2,1,5,3,6,7,4,8,9]=>[[1,3,5,6,8,9],[2,4,7]]=>[3,3,3]=>[3,3,3]=>3
[1,3,5,7,8,6,4,2,9]=>[[1,2,3,4,5,9],[6],[7],[8]]=>[5,4]=>[5,4]=>2
[1,3,4,2,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[3,7]=>[7,3]=>2
[1,2,4,5,6,3,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]=>[5,5]=>2
[1,2,3,5,6,7,8,4,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]=>[7,3]=>2
[2,1,5,3,6,7,4,8,9,10]=>[[1,3,5,6,8,9,10],[2,4,7]]=>[3,3,4]=>[4,3,3]=>3
[1,3,4,6,7,2,8,5,9,10]=>[[1,2,3,4,5,7,9,10],[6,8]]=>[5,2,3]=>[5,3,2]=>3
[1,2,4,5,7,8,9,6,3,10]=>[[1,2,3,4,5,6,7,10],[8],[9]]=>[7,3]=>[7,3]=>2
[6,2,3,8,7,1,4,5]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[8,2,3,6,4,7,5,1]=>[[1,3,4,6],[2,7],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,2,3,6,4,8,1,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,4,1,6,2,7,8,3]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,1,3,5,4,2,8,6]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,6,8,2,4,5,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,2,8,6,5,1,3,7]=>[[1,3,8],[2,4],[5,7],[6]]=>[3,5]=>[5,3]=>2
[3,8,5,4,7,1,2,6]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,4,8,3,6,2,7,5]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,3,2,4,8,7,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>[5,3]=>[5,3]=>2
[8,3,2,7,4,1,5,6]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[7,3,2,6,5,8,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,6,2,5,7,4,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,1,5,8,6,4,3]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,2,4,1,6,8,5,3]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,2,3,8,5,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,5,7,4,2,3]=>[[1,3,5],[2,4],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,3,6,5,8,2]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,5,6,3,4,8,2]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,1,8,5,4,7,3,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,1,5,4,2,8,3]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,1,6,8,7,2,4,3]=>[[1,3,4],[2,5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,6,7,5,3,1,8,2]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,3,2,6,8,7,4,1]=>[[1,4,5],[2,6],[3,7],[8]]=>[5,3]=>[5,3]=>2
[5,4,6,2,8,7,3,1]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[4,5,8,6,7,2,3,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,7,6,1,2,8,3]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,6,5,7,2,1,8,3]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,4,6,7,8,9,10,5,3,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[3,5,6,7,8,9,4,2,1,10]=>[[1,2,3,4,5,6,10],[7],[8],[9]]=>[6,4]=>[6,4]=>2
[7,4,8,6,3,5,1,2]=>[[1,3],[2,4],[5,6],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[7,2,4,3,6,1,8,5]=>[[1,3,5,7],[2,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,4,7,8,6,1,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,3]=>[5,3]=>2
[6,3,7,1,4,2,8,5]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,6,3,5,1,8,2,7]=>[[1,2,6],[3,4,8],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,5,7,6,2,3,4,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[3,5,6,7,8,9,2,4,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[3,4,6,7,8,2,5,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,6,7,8,9,1,3,5]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[2,5,6,7,3,8,1,4]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,8,4,6,2,1,7,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,6,8,3,4,2,7,5]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,7,6,2,8,3,5]=>[[1,3,6,8],[2,4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,1,8,2,7,5,3,6]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,1,7,2,8,5,3,6]=>[[1,3,5,8],[2,4,6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,6,3,7,4,8,1]=>[[1,2,3,5,7],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,5,3,8,4,7,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,6,5,3,7,4,8,1]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,1,6,3,5,4,8,2]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,7,3,2,8,4,1,6]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,6,1,7,5,3,4]=>[[1,2,5],[3,6,8],[4],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,1,5,2,7,4,3,6]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[7,1,4,2,8,5,3,6]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[2,6,8,1,7,5,3,4]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,4,6,5,3,8,2,7]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,4,5,8,7,1,3,6]=>[[1,2,3,4],[5,7,8],[6]]=>[4,4]=>[4,4]=>2
[3,1,6,8,7,5,4,2]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[3,1,8,7,5,6,4,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,1,8,7,6,3,4,2]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[8,2,7,5,3,6,4,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,7,2,3,1,5,6,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[2,8,5,7,6,1,3,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,8,7,2,6,4,5,3]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,7,2,1,6,4,5,3]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,8,4,7,6,2,5,3]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,1,6,4,3,5,2]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,1,7,3,6,5,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,3,6,7,8,9,2,4,5]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[6,3]=>2
[4,5,1,8,7,3,6,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,8,5,2,6,7,4,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,6,4,7,5,2,1,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,4,1,2,6,8,3]=>[[1,2,6,7],[3,5],[4,8]]=>[2,5,1]=>[5,2,1]=>3
[2,8,6,7,5,3,1,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[7,4,5,2,6,3,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,6,3,4,5,1,7,2]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[8,6,3,5,4,1,7,2]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[8,7,4,5,1,3,6,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,2,5,3,1,4,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[8,4,7,3,1,2,5,6]=>[[1,3,7,8],[2,6],[4],[5]]=>[3,5]=>[5,3]=>2
[8,7,3,5,1,6,4,2]=>[[1,4,6],[2,7],[3],[5],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,8,3,2,6,1,7,5]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,7,6,1,5,2,8]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,5,4,3,6,1,8,2]=>[[1,5,7],[2,8],[3],[4],[6]]=>[5,2,1]=>[5,2,1]=>3
[4,6,8,5,3,1,2,7]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,5]=>[5,3]=>2
[5,6,8,4,3,7,2,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,5,8,4,2,1,6,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,4,8,7,6,2,5,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,2,4,1,5,3,8,6]=>[[1,3,5,7],[2,6,8],[4]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,3,4,1,7,2,6]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[2,8,5,4,3,6,1,7]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,6,5,3,1,2,7,4]=>[[1,6,7],[2,8],[3],[4],[5]]=>[7,1]=>[7,1]=>2
[7,4,6,5,3,2,8,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,7,2,3,8,4,1]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,4,2,6,5,7,3,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,7,4,2,8,5,6,3]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,2,1,7,4,6,8,5]=>[[1,4,6,7],[2,5],[3,8]]=>[4,3,1]=>[4,3,1]=>3
[6,2,5,7,1,4,3,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,8,5,3,1,2,6,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[8,5,2,4,6,1,3,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[1,5,3,4,7,2,6,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[8,4,6,1,5,7,3,2]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,2,1,3,8,5]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[6,7,3,1,2,4,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[3,1,8,7,6,2,5,4]=>[[1,3,7],[2,4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[1,3,8,6,7,2,5,4]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,2,3,6,1,8,4,7]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,2,6,4,7,1,5,8]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[3,6,2,5,7,8,4,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,7,4,6,8,3,5,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,6,8,1,5,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,7,6,8,4,2,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,7,4,6,8,5,3,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[3,7,6,8,5,1,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,1,3,8,6,2,4,5]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[2,7,1,8,6,5,3,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[2,3,4,5,7,9,8,6,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[8,1,5,2,6,4,7,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,4,7,6,2,1,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[4,1,8,5,7,2,6,3]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,1,8,2,7,5,6,3]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,6,8,2,4,3,5,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,5,3,8,1,6,2]=>[[1,3,5],[2,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,6,1,4,2,8,5]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,7,2,6,4,5,1,3]=>[[1,4,6],[2,8],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,2,3,4,7,9,5,6,8]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[1,2,3,4,6,7,9,5,8]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[7,2]=>2
[7,1,4,6,8,5,3,2]=>[[1,3,4,5],[2],[6],[7],[8]]=>[5,3]=>[5,3]=>2
[7,2,5,1,6,4,8,3]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,7,1,5,6,4,8,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,5,7,8,4,6,3,2]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[1,4,8,5,7,6,3,2]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[2,8,1,5,6,4,7,3]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,2,8,1,5,6,4]=>[[1,2,4],[3,6,7],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,2,5,1,6,8,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,7,2,1,3,6,5,4]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[7,3,2,8,1,4,6,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[3,6,2,1,8,4,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,5,1,7,6,4,8,2]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,7,4,2,1,6,5,3]=>[[1,6],[2,7],[3,8],[4],[5]]=>[6,2]=>[6,2]=>2
[5,4,7,6,2,1,8,3]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,5,2,8,7,1,6,4]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,6,5,4,1,8,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[4,6,5,3,1,8,7,2]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[4,5,2,6,7,3,8,1]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[9,3,10,1,2,4,5,6,7,8]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[3,7]=>[7,3]=>2
[8,6,7,4,3,1,5,2]=>[[1,3],[2,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[4,7,1,8,5,3,2,6]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[8,6,7,1,4,3,5,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,7,2,1,3,5,4]=>[[1,3,7],[2,6],[4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[8,5,6,1,7,4,2,3]=>[[1,3,5],[2,6,8],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,1,2,5,7,8,3]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[6,1,5,4,2,7,3,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,4,2,3,1,7,5,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,4,6,1,8,2,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,1,4,7,6,2,8]=>[[1,4,5,8],[2,6],[3,7]]=>[5,3]=>[5,3]=>2
[6,4,5,2,7,1,3,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,3,5,1,6,2,8]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,5,3,6,2,1,4,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[4,4]=>[4,4]=>2
[6,4,3,7,1,8,2,5]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,1,2,7,6,4,5,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[5,1,2,7,6,3,4,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[5,6,1,7,2,4,3,8]=>[[1,2,4,8],[3,5,6],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,5,6,8,1,2,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,6,5,7,1,3,4,8]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,3,7,1,5,6,4,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,5,3,4,1,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,6,1,3,5,4,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,6,1,5,2,8,7,3]=>[[1,2,6],[3,4,7],[5,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[6,1,5,4,2,7,8,3]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,6,1,5,2,7,8,3]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,6,5,1,3,7,4]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[5,1,8,6,2,7,4,3]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,6,8,2,7,5,1,4]=>[[1,2,3],[4,5],[6,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,6,4,1,7,2,8,3]=>[[1,2,5,7],[3,6,8],[4]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,6,1,5,7,4,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,3,4,2,5,7]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,4,2,3,1,6,8,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[9,8,10,7,6,5,4,3,1,2]=>[[1,3],[2,10],[4],[5],[6],[7],[8],[9]]=>[3,7]=>[7,3]=>2
[8,7,9,6,5,4,2,1,3]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[8,9,7,6,5,4,2,3,1]=>[[1,2],[3,8],[4],[5],[6],[7],[9]]=>[2,6,1]=>[6,2,1]=>3
[1,6,4,5,7,3,2,8]=>[[1,2,4,5,8],[3],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,6,4,5,7,2,8,3]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,5,6,4,8,3,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,5,6,7,3,2,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,4]=>[4,4]=>2
[8,2,4,3,1,7,5,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,2,1,4,3,7,5,6]=>[[1,4,6,8],[2,5,7],[3]]=>[4,2,2]=>[4,2,2]=>3
[7,6,8,2,1,5,3,4]=>[[1,3,8],[2,6],[4,7],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,6,2,5,1,3,7,4]=>[[1,4,7],[2,6,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,7,2,6,4,1,8,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,6,1,3,8,2,7]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,5,7,4,2,8,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,4,8,5,3,1,2]=>[[1,4],[2,5],[3,8],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,1,6,4,7,3,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,3,8,6,5,2,7,4]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[2,7,3,8,5,6,4,1]=>[[1,2,4,6],[3,5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,2,8,5,7,4,6,3]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,8,5,4,7,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,8,3,2,6,4]=>[[1,2,4],[3,5,7],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,2,5,4,3,7,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,4,3,7,6,2,1]=>[[1,2],[3,5],[4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,1,5,3,4,7,2,6]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,8,7,4,5,3,2]=>[[1,3,6],[2,4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,5,8,6,4,3,7,2]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,8,6,4,2,1,7,3]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[2,6,1,8,4,7,5,3]=>[[1,2,4],[3,5,6],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,3,8,6,1,2,7,4]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[5,8,1,4,6,2,7,3]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,6,2,1,4,8,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,6,2,3,7,1,8,5]=>[[1,2,5,7],[3,4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,7,5,1,3,4,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[6,4,3,2,7,8,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[2,7,6,1,5,3,8,4]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,6,4,2,5,3,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,4,5,8,7,1,3,2]=>[[1,3,4],[2,5],[6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,4,1,7,8,3,2,5]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[6,2,3,4,5,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[9,1]=>[9,1]=>2
[2,6,3,4,5,7,8,9,10,1]=>[[1,2,4,5,6,7,8,9],[3],[10]]=>[2,7,1]=>[7,2,1]=>3
[6,4,3,8,7,2,5,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,4,7,2,1,3,8,6]=>[[1,3,7],[2,6,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[2,6,4,5,7,1,8,3]=>[[1,2,4,5,7],[3,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,7,4,6,1,5,8,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,4,6,5,2,8,1,7]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,6,7,5,8,2,1,3]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[2,5,7,6,4,1,8,3]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[5,1,4,6,2,7,8,3]=>[[1,3,4,6,7],[2,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[1,2,5,3,7,8,6,4]=>[[1,2,3,5,6],[4,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,8,3,5,1,2,7,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,3,7,2,8,4,5]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,8,5,4,1,7,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[3,1,5,8,2,6,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,8,5,3,1,7,4,6]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,5,2,3,7,1,8,4]=>[[1,4,5,7],[2,8],[3],[6]]=>[5,2,1]=>[5,2,1]=>3
[7,2,1,6,4,8,3,5]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[2,1,3,7,5,8,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,4,5,7,1,8,3]=>[[1,3,4,5,7],[2,8],[6]]=>[5,2,1]=>[5,2,1]=>3
[2,3,8,7,1,4,6,5]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,2,7,5,6,8,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,2,5,4,7,3,1]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,2,3,4,5,6,9,1,8]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[3,2,9,1,4,5,6,7,8]=>[[1,3,6,7,8,9],[2,5],[4]]=>[3,6]=>[6,3]=>2
[5,3,2,7,6,1,8,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[5,6,4,2,8,7,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,4,2,6,1,8,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,4,7,1,6,2,8,3]=>[[1,3,7],[2,5,8],[4,6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,8,7,6,2,1,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[6,4,7,1,2,3,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[10,4,5,6,9,3,8,2,7,1]=>[[1,3,4,5],[2,7],[6,9],[8],[10]]=>[5,2,2,1]=>[5,2,2,1]=>4
[1,8,7,2,3,4,6,5]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[1,8,3,7,6,2,5,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,8,2,5,6,4,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,3,2,7,4,6,8,5]=>[[1,2,4,6,7],[3,5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,3,8,4,6,2,7,5]=>[[1,2,3,5,7],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,3,6,7,4,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,6,4,2,1,7,3,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[2,5,7,6,3,8,4,1]=>[[1,2,3,6],[4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,4,7,1,2,5,3,8]=>[[1,3,6,8],[2,5],[4,7]]=>[3,3,2]=>[3,3,2]=>3
[1,2,7,5,8,6,3,4]=>[[1,2,3,5],[4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[7,4,5,1,6,8,2,3]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[1,7,8,4,2,6,3,5]=>[[1,2,3,8],[4,6],[5,7]]=>[3,3,2]=>[3,3,2]=>3
[6,3,2,5,7,4,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[6,2,1,5,3,7,8,4]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[6,2,5,1,3,8,7,4]=>[[1,3,6],[2,5,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,2,8,5,1,3,7,4]=>[[1,3,7],[2,4,8],[5,6]]=>[3,4,1]=>[4,3,1]=>3
[4,1,7,8,3,6,5,2]=>[[1,3,4],[2,5,6],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,4,2,1,7,3,5,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[5,8,4,2,1,3,6,7]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[4,5,3,6,7,8,9,1,2]=>[[1,2,4,5,6,7],[3,9],[8]]=>[2,5,2]=>[5,2,2]=>3
[5,3,4,6,7,8,9,1,2]=>[[1,3,4,5,6,7],[2,9],[8]]=>[7,2]=>[7,2]=>2
[1,7,5,8,4,3,6,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,8,1,6,4,7,2,3]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,4,7,5,1,8,6,3]=>[[1,2,3,6],[4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[2,3,7,1,8,5,6,4]=>[[1,2,3,5],[4,6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,1,2,7,4,8,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[3,6,5,7,8,2,4,1]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,6,5,1,8,7,4,2]=>[[1,2,5],[3,6],[4,7],[8]]=>[2,3,3]=>[3,3,2]=>3
[7,8,1,2,5,4,3,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,3,5,1,7,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,2,4,7,6,8,1,3]=>[[1,3,4,6],[2,5],[7,8]]=>[4,2,2]=>[4,2,2]=>3
[3,1,5,7,4,8,6,2]=>[[1,3,4,6],[2,5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,1,7,6,8,2,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,2,6,4,1,5,3,8]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[1,2,6,5,8,3,7,4]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,5,6,1,4,2,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,8,3,1,6,7,4,2]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,5,8,1,7,3,6,2]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,7,1,6,8,5,2,3]=>[[1,2,5],[3,4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,1,6,4,2,3]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,7,3,8,2,5,4,6]=>[[1,2,4,8],[3,6],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,4,1,3,6,7,5,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[5,3,1,8,6,7,4,2]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[6,2,7,1,4,3,5,8]=>[[1,3,7,8],[2,5],[4,6]]=>[3,2,3]=>[3,3,2]=>3
[9,5,4,3,2,1,6,7,8]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[9]=>[9]=>1
[10,3,4,1,2,5,6,7,8,9]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[3,7]=>[7,3]=>2
[8,3,2,6,5,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[2,6,8,4,7,1,3,5]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]=>[3,3,2]=>3
[7,8,6,3,2,5,4,1]=>[[1,2],[3,6],[4,7],[5],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,4,8,2,3,5,7]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]=>[4,2,2]=>3
[2,8,5,6,4,1,7,3]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,4,7,3,5,8,6,2]=>[[1,2,3,6],[4,5,7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,8,2,5,1,6,4]=>[[1,2,3],[4,5,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,6,1,4,3,2,7,5]=>[[1,4,7],[2,8],[3],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,3,8,2,4,1,5,6]=>[[1,3,7,8],[2,5],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[6,3,7,8,1,2,5,4]=>[[1,3,4],[2,6,7],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,1,5,2,3,8,4]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[5,1,8,6,7,2,3,4]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[5,7,1,6,8,2,3,4]=>[[1,2,5,8],[3,4,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[6,8,4,2,1,7,3,5]=>[[1,2,8],[3,6],[4,7],[5]]=>[2,4,2]=>[4,2,2]=>3
[6,3,2,8,1,7,4,5]=>[[1,4,8],[2,6],[3,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[6,4,1,3,7,8,5,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[6,8,5,4,3,7,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,7,4,8,3,1,2,6]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[6,1,2,4,8,3,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>[5,2,1]=>[5,2,1]=>3
[2,5,6,8,1,4,7,3]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,1,6,5,2,3,8]=>[[1,4,7,8],[2,5],[3],[6]]=>[4,4]=>[4,4]=>2
[4,1,6,5,2,3,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[4,5,1,7,8,6,2,3]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,5,7,3,4,6,2,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,7,4,3,5,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,8,7,5,3,4,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,6,2,4,7,3,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[4,8,6,2,5,7,3,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,6,4,7,5,3,2,8]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[1,6,5,3,2,7,4,8]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[1,6,8,7,4,5,3,2]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,7,5,3,2,6,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,7,5,4,3,2,8,6]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[1,4,7,5,3,2,8,6]=>[[1,2,3,7],[4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,7,4,6,8,5,3,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,2,3,5,4,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,1,8,2,4,3]=>[[1,2,5],[3,6,7],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,6,5,7,2,3,1]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,7,8,5,1,4,3,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,5,6,2,4,7,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,1,3,6,4,5,2,7]=>[[1,3,4,6,8],[2],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,3,1,6,2,5,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>[4,3,1]=>[4,3,1]=>3
[7,5,2,1,8,4,3,6]=>[[1,5,8],[2,6],[3,7],[4]]=>[5,3]=>[5,3]=>2
[5,3,1,4,7,8,2,6]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[7,1,2,4,8,3,5,6]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[8,6,1,3,5,7,4,2]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[7,1,5,8,2,3,4,6]=>[[1,3,4,7,8],[2,6],[5]]=>[4,4]=>[4,4]=>2
[3,6,8,5,1,4,2,7]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,2,4,1,6,8,3,7]=>[[1,3,5,6],[2,7,8],[4]]=>[3,3,2]=>[3,3,2]=>3
[2,5,3,4,6,8,1,7]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,7,1,2,5,6,3,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]=>[4,2,2]=>3
[6,7,3,1,8,2,4,5]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[7,3,1,4,6,2,8,5]=>[[1,4,5,7],[2,6,8],[3]]=>[5,2,1]=>[5,2,1]=>3
[7,4,1,2,5,6,3,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[5,4,1,3,6,8,7,2]=>[[1,4,5,6],[2,7],[3],[8]]=>[6,2]=>[6,2]=>2
[5,7,4,8,1,6,3,2]=>[[1,2,4],[3,6],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[4,3,1,2,5,7,6,8]=>[[1,4,5,6,8],[2,7],[3]]=>[6,2]=>[6,2]=>2
[1,2,3,4,5,8,9,7,6]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,2]=>[7,2]=>2
[1,2,3,4,8,9,6,7,5]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[1,2,4,7,8,5,6,3]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,2,8,9,4,5,6,7,3]=>[[1,2,3,4,7,8],[5,6],[9]]=>[4,4,1]=>[4,4,1]=>3
[8,3,6,5,7,4,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,6,5,7,4,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,4,7,1,5,2,6,3]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,2,6,3,7,5,4,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,2,5,3,7,6,4,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,5,7,1,4,3,6,2]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,1,8,4,2,6,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[2,1,6,5,8,7,3,4]=>[[1,3,5],[2,4,6],[7,8]]=>[3,2,3]=>[3,3,2]=>3
[6,1,5,4,7,3,8,2]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,1,8,4,2,7,6,5]=>[[1,3,6],[2,4,7],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,8,7,4,1,3,6,5]=>[[1,2,7],[3,6,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[8,2,3,1,7,6,4,5]=>[[1,3,5,8],[2,6],[4],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,7,2,3,1,6,4,5]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[7,2,5,8,3,1,4,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[6,8,2,3,1,7,4,5]=>[[1,2,6,8],[3,4],[5,7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,5,7,3,1,4,6]=>[[1,3,4,8],[2,7],[5],[6]]=>[4,4]=>[4,4]=>2
[8,2,7,3,1,4,5,6]=>[[1,3,6,7,8],[2],[4],[5]]=>[3,5]=>[5,3]=>2
[5,3,2,8,7,1,6,4]=>[[1,4],[2,5],[3,7],[6,8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,7,4,1,3,5,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,1,3,6,5,2,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[4,6,3,2,5,1,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,2,6,5,7,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,6,5,2,7,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[8,1,6,2,5,4,7,3]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,4,3,8,6,1,7,5]=>[[1,2,4,7],[3,5],[6,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,6,3,8,5,4,7,1]=>[[1,2,4,7],[3,5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,1,3,2,5,8,7,4]=>[[1,3,5,6],[2,7],[4,8]]=>[3,3,2]=>[3,3,2]=>3
[6,8,4,2,5,3,7,1]=>[[1,2,7],[3,5],[4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,4,3,5,2,7,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,4,6,5,3,7,2]=>[[1,3,4,7],[2],[5],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,5,4,6,1,2,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[7,3,5,6,1,8,2,4]=>[[1,3,4,6],[2,7,8],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,7,6,3,4,2,8,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,6,7,2,3,5,8,1]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[6,5,4,8,7,2,3,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,7,6,5,3,2,1,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,7]=>[7,2]=>2
[5,9,8,7,6,4,3,2,1,10]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,8]=>[8,2]=>2
[5,7,4,3,6,2,1,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[1,8,2,9,4,3,5,6,7]=>[[1,2,4,7,8,9],[3,5],[6]]=>[2,2,5]=>[5,2,2]=>3
[1,5,2,9,3,10,4,6,7,8]=>[[1,2,4,6,8,9,10],[3,5,7]]=>[2,2,2,4]=>[4,2,2,2]=>4
[1,8,5,6,2,3,7,4]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,3,9,4,2,5,6,7]=>[[1,2,4,7,8,9],[3,5],[6]]=>[2,2,5]=>[5,2,2]=>3
[8,5,6,1,3,2,7,4]=>[[1,3,7],[2,5,8],[4],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[5,3,7,8,2,6,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,3,6,1,7,2]=>[[1,2,3,7],[4,5],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[4,5,8,7,2,3,1,6]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,6,4,3,7,5,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[6,3,1,8,7,4,5,2]=>[[1,4,7],[2,5],[3,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,3,2,7,4,5,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,3,6,8,7,4,5,2]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,7,1,3,6,2,4,8]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]=>[3,3,2]=>3
[4,7,5,2,3,6,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,6,4,1,2,5,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,6]=>[6,2]=>2
[4,7,1,3,2,5,8,6]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,7,1,3,2,6,8,5]=>[[1,2,6,7],[3,4],[5,8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,7,1,3,6,2,8,4]=>[[1,2,5,7],[3,4],[6,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,8,2,5,7,3,1,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,8,5,2,3,6,1,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,8,6,3,4,7,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[3,7,5,4,2,8,1,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,6,5,1,7,8,2,3]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[4,7,1,3,2,8,5,6]=>[[1,2,6,8],[3,4,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[3,6,5,1,8,2,4,7]=>[[1,2,5,8],[3,6,7],[4]]=>[2,3,3]=>[3,3,2]=>3
[5,8,7,3,4,2,6,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,5,2,3,7,4,6,1]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,1,5,4,8,2,7]=>[[1,4,6],[2,5,8],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[4,7,6,3,5,2,8,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,5,3,4,8,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,8,2,3,4,7,6,1]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[8,7,3,2,6,4,5,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>[5,2,1]=>[5,2,1]=>3
[8,3,1,4,7,5,2,6]=>[[1,4,5,8],[2,6],[3],[7]]=>[5,3]=>[5,3]=>2
[5,3,1,6,4,8,7,2]=>[[1,4,6],[2,5,7],[3,8]]=>[4,2,2]=>[4,2,2]=>3
[3,4,8,5,7,2,6,1]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,5,1,2,7,6,4,3]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[10,7,8,1,2,3,4,5,6,9]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[3,7]=>[7,3]=>2
[6,7,10,1,2,3,4,5,8,9]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]=>[7,3]=>2
[3,7,8,5,6,2,4,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,4,3,6,2,5,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,3,8,7,1,6,2,5]=>[[1,3,8],[2,4],[5,6],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,5,3,8,4,7,2,6]=>[[1,2,4,6],[3,5],[7,8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,2,3,1,6,5,7,4]=>[[1,3,5,7],[2,6],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[8,4,2,7,1,3,6,5]=>[[1,4,7],[2,6],[3,8],[5]]=>[4,3,1]=>[4,3,1]=>3
[8,4,2,3,1,6,7,5]=>[[1,4,6,7],[2,8],[3],[5]]=>[4,3,1]=>[4,3,1]=>3
[4,7,2,3,6,5,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,2,6,4,7,1,5]=>[[1,2,6],[3,4,8],[5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,5,8,6,2,4,3]=>[[1,2,4],[3,5],[6,7],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,5,1,7,4,8,3,2]=>[[1,4,6],[2,5],[3],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,6,3,5,1,4,8,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[6,5,4,1,7,2,3,8]=>[[1,5,7,8],[2,6],[3],[4]]=>[5,3]=>[5,3]=>2
[8,3,6,1,7,4,5,2]=>[[1,3,5],[2,6,7],[4],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,1,2,6,4,8,3,5]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,1,8,6,2,4,7]=>[[1,2,4,8],[3,5,7],[6]]=>[2,2,4]=>[4,2,2]=>3
[9,8,7,6,4,3,2,5,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[8,1]=>[8,1]=>2
[7,6,5,3,2,1,4,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[9]=>[9]=>1
[9,8,7,6,4,3,5,1,2]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[9,8,7,6,4,3,2,5,1,10]=>[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[8,2]=>[8,2]=>2
[9,8,7,6,4,5,2,3,1]=>[[1,6],[2,8],[3],[4],[5],[7],[9]]=>[6,2,1]=>[6,2,1]=>3
[1,8,7,5,4,6,2,3]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,7,4,5,3,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[8,1,6,4,7,5,3,2]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[6,4,8,1,5,3,7,2]=>[[1,3,7],[2,5],[4,6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,4,3,5,8,2,7]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[5,1,4,3,7,8,6,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[5,7,1,8,6,3,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,6,3,4,2,1,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,3,7,6,5,2,8]=>[[1,3,4,8],[2,5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,7,6,5,4,2,3,1,9]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[7,2]=>[7,2]=>2
[4,3,6,1,2,7,8,5]=>[[1,3,6,7],[2,5,8],[4]]=>[3,4,1]=>[4,3,1]=>3
[5,8,3,6,7,2,4,1]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,1,6,2,5,7,4,3]=>[[1,3,5,6],[2],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[2,7,1,5,3,6,8,4]=>[[1,2,6,7],[3,4,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,7,3,4,2,5,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,6,2,4,7,5,3]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[5,7,3,6,4,2,1,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,3,6,4,1,8,2]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[3,7,5,6,4,1,8,2]=>[[1,2,4,7],[3,8],[5],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,1,2,3,4,5,9,7]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[2,8,5,7,3,4,6,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,2,6,3,1,7,8,9]=>[[1,2,4,7,8,9],[3,5],[6]]=>[2,2,5]=>[5,2,2]=>3
[2,8,4,1,6,3,7,5,9]=>[[1,2,5,7,9],[3,6,8],[4]]=>[2,3,2,2]=>[3,2,2,2]=>4
[2,4,3,1,5,6,7,8,9,10]=>[[1,2,5,6,7,8,9,10],[3],[4]]=>[2,8]=>[8,2]=>2
[4,5,2,6,3,1,7,8,9,10]=>[[1,2,4,7,8,9,10],[3,5],[6]]=>[2,2,6]=>[6,2,2]=>3
[2,8,4,1,6,3,7,5,9,10]=>[[1,2,5,7,9,10],[3,6,8],[4]]=>[2,3,2,3]=>[3,3,2,2]=>4
[2,7,4,9,6,3,10,8,5,1]=>[[1,2,4,7],[3,5,8],[6,9],[10]]=>[2,2,3,3]=>[3,3,2,2]=>4
[2,1,3,8,5,4,6,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[5,3,6,8,2,4,1,7]=>[[1,3,4],[2,6,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[1,7,8,6,3,2,4,5]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,1,2,5,3,8,4,6]=>[[1,3,4,6,8],[2,7],[5]]=>[4,2,2]=>[4,2,2]=>3
[3,7,4,2,5,1,8,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,8,3,4,5,7,2,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,5,7,6,2,1,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>[3,5]=>[5,3]=>2
[7,8,2,6,5,4,3,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[5,3,7,8,4,2,1,6]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,3,6,8,1,5,4,2]=>[[1,3,4],[2,6],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,5,8,2,4,3,6,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,5,8,2,3,4,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,1,5,3,4,6,2,7]=>[[1,3,5,6,8],[2],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,8,7,2,4,3,6,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,2,4,8,5,6,3]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,8,2,3,7,4,6,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[7,8,2,3,5,4,6,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,4,1,3,2,6,5,7]=>[[1,4,6,8],[2,7],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[8,7,2,3,5,4,6,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[1,7,6,8,4,5,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[2,7,3,1,8,5,6,4]=>[[1,2,5,7],[3,6],[4,8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,5,2,1,6,7,4]=>[[1,2,6,7],[3,8],[4],[5]]=>[2,5,1]=>[5,2,1]=>3
[4,8,7,1,2,5,3,6]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,7,2,6,1,4,3,5]=>[[1,4,8],[2,6],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,1,7,3,8,2,4,5]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,6,4,2,3,5]=>[[1,3,7,8],[2,4],[5],[6]]=>[3,5]=>[5,3]=>2
[4,1,3,5,8,2,6,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[1,8,5,7,4,6,3,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,4,7,6,8,3,5,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,7,2,8,6,5,3,4]=>[[1,2,4,8],[3,5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,7,1,6,4,2,3,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[4,8,2,7,5,1,6,3]=>[[1,2,7],[3,4],[5,8],[6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,8,4,6,7,1,5,3]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,8,5,1,4,2,6,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,7,6,2,5,3,8,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[1,7,5,2,4,3,8,6]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,8,5,1,4,3,6,7]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,3,3]=>[3,3,2]=>3
[9,7,6,5,4,3,2,8,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[8,1]=>[8,1]=>2
[3,1,2,5,7,6,8,4]=>[[1,3,4,5,7],[2,6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,1,7,3,2,6,8,4]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[4,7,2,3,5,1,6,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[4,8,2,3,7,5,1,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[8,7,2,4,3,5,6,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,6,2,4,3,5,1,7]=>[[1,4,6,8],[2],[3],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[8,1,2,4,7,3,5,6]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[7,6,2,8,4,5,1,3]=>[[1,4,6],[2,5],[3,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,8,1,5,7,3,2,4]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[4,1,7,5,6,8,2,3]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,7,6,2,1,4,5,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,6]=>[6,2]=>2
[1,6,8,7,2,5,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,4,8,7,6,3,5,2]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,6,7,5,2,3,1,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,2,5,3,1,8,7,4]=>[[1,3,6],[2,7],[4,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[6,2,5,3,8,7,1,4]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[6,4,5,3,8,7,1,2]=>[[1,3,5],[2,6],[4,8],[7]]=>[3,2,3]=>[3,3,2]=>3
[1,6,4,5,8,7,3,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,4,7,5,2,3,1,6]=>[[1,3,8],[2,6],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,2,7,4,5,3,1,6]=>[[1,3,5,8],[2],[4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[8,2,4,7,5,3,1,6]=>[[1,3,4,8],[2],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,2,6,7,5,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[8,4,6,7,5,3,1,2]=>[[1,3,4],[2,8],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[6,4,5,8,7,3,1,2]=>[[1,3,4],[2,5],[6,8],[7]]=>[4,4]=>[4,4]=>2
[6,2,8,7,5,3,1,4]=>[[1,3,8],[2,4],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[4,6,5,3,8,7,1,2]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,7,2,4,5,3,1,8]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,7,4,5,3,1,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[2,8,4,7,5,3,1,6]=>[[1,2,4,8],[3],[5],[6],[7]]=>[2,2,4]=>[4,2,2]=>3
[5,8,7,4,6,3,1,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,5,8,4,7,2,1,3]=>[[1,3],[2,5],[4,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,8,6,2,5,7,1,3]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[8,1,6,2,5,7,3,4]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,8,1,2,4,7,3,5]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[8,1,5,3,2,7,4,6]=>[[1,3,6,8],[2,7],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,3,7,6,2,5,4,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[1,2,3,4,7,8,5,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[1,2,3,4,8,9,5,6,7]=>[[1,2,3,4,5,6,9],[7,8]]=>[6,3]=>[6,3]=>2
[4,6,1,3,5,8,2,7]=>[[1,2,5,6],[3,4,8],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,5,1,3,8,7,2,6]=>[[1,2,5],[3,4,6],[7,8]]=>[2,3,3]=>[3,3,2]=>3
[6,2,7,1,8,3,4,5]=>[[1,3,5,8],[2,6,7],[4]]=>[3,2,3]=>[3,3,2]=>3
[6,4,5,8,1,7,2,3]=>[[1,3,4],[2,6,8],[5,7]]=>[4,2,2]=>[4,2,2]=>3
[6,2,8,5,1,4,7,3]=>[[1,3,7],[2,4],[5,6],[8]]=>[3,4,1]=>[4,3,1]=>3
[2,4,7,6,1,8,3,5]=>[[1,2,3,6],[4,7,8],[5]]=>[3,3,2]=>[3,3,2]=>3
[2,6,7,8,9,10,1,3,4,5]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[6,4]=>2
[10,8,9,7,6,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[3,7]=>[7,3]=>2
[7,4,5,8,6,3,2,1]=>[[1,3,4],[2,5],[6],[7],[8]]=>[4,4]=>[4,4]=>2
[9,6,7,8,5,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[4,5]=>[5,4]=>2
[10,8,9,6,5,4,3,2,1,7]=>[[1,3],[2,10],[4],[5],[6],[7],[8],[9]]=>[3,7]=>[7,3]=>2
[2,5,1,6,3,7,4,8,9,10]=>[[1,2,4,6,8,9,10],[3,5,7]]=>[2,2,2,4]=>[4,2,2,2]=>4
[3,4,5,1,6,2,7,8,9,10]=>[[1,2,3,5,7,8,9,10],[4,6]]=>[3,2,5]=>[5,3,2]=>3
[2,6,1,7,3,8,4,9,5,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>[2,2,2,2,2]=>[2,2,2,2,2]=>5
[3,4,6,1,7,2,8,5,9,10]=>[[1,2,3,5,7,9,10],[4,6,8]]=>[3,2,2,3]=>[3,3,2,2]=>4
[4,5,6,7,1,8,2,9,3,10]=>[[1,2,3,4,6,8,10],[5,7,9]]=>[4,2,2,2]=>[4,2,2,2]=>4
[9,8,7,6,5,2,3,4,1]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[8,1]=>[8,1]=>2
[3,5,6,7,9,1,2,4,8]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[5,4]=>2
[4,1,6,7,8,9,2,3,5]=>[[1,3,4,5,6],[2,7,8,9]]=>[6,3]=>[6,3]=>2
[5,1,6,7,8,9,10,2,3,4]=>[[1,3,4,5,6,7],[2,8,9,10]]=>[7,3]=>[7,3]=>2
[7,4,1,3,6,8,2,5]=>[[1,4,5,6],[2,8],[3],[7]]=>[6,2]=>[6,2]=>2
[6,8,1,2,7,3,4,5]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]=>[3,3,2]=>3
[1,6,2,8,7,3,4,5]=>[[1,2,4,7,8],[3,5],[6]]=>[2,2,4]=>[4,2,2]=>3
[1,6,8,5,7,4,3,2]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[3,8,1,2,4,7,6,5]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,2]=>[4,2,2]=>3
[1,4,5,7,3,6,8,2]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[2,3,8,1,4,6,5,7]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,6,2,4,7,5,8,1]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,8,4,6,2,5,7]=>[[1,3,5,8],[2,4,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[4,2,7,3,5,8,1,6]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[3,1,8,4,5,6,2,7]=>[[1,3,5,6,8],[2,4],[7]]=>[3,3,2]=>[3,3,2]=>3
[4,2,7,8,6,3,1,5]=>[[1,3,4],[2,5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,1,4,2,8,6,3,5]=>[[1,3,5,8],[2,6],[4,7]]=>[3,2,3]=>[3,3,2]=>3
[2,3,7,4,8,1,6,5]=>[[1,2,3,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,6,3,5,8,7,4,2]=>[[1,2,4,5],[3,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,4,6,3,5,1,7,2]=>[[1,3,7],[2,5],[4,8],[6]]=>[3,2,2,1]=>[3,2,2,1]=>4
[7,3,2,6,8,4,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,4,5,7,1,6,8,3]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,4,2,6,7,3,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[4,1,5,7,8,6,2,3]=>[[1,3,4,5],[2,6,8],[7]]=>[5,3]=>[5,3]=>2
[6,1,4,8,2,3,7,5]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[7,6,2,3,5,8,4,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[2,8,5,7,6,3,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[2,5,7,8,6,4,1,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,4]=>[4,4]=>2
[7,4,1,6,2,5,8,3]=>[[1,4,6,7],[2,5],[3],[8]]=>[4,3,1]=>[4,3,1]=>3
[5,6,2,4,8,7,3,1]=>[[1,2,5],[3,4,6],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[8,5,6,2,3,7,4,1]=>[[1,3,6],[2,5,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,8,1,4,5,6,2,3]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]=>[4,2,2]=>3
[5,6,7,8,9,1,3,4,2]=>[[1,2,3,4,5],[6,7,8],[9]]=>[5,3,1]=>[5,3,1]=>3
[6,7,8,9,1,3,4,5,2]=>[[1,2,3,4],[5,6,7,8],[9]]=>[4,4,1]=>[4,4,1]=>3
[6,7,8,9,1,4,5,2,3]=>[[1,2,3,4],[5,6,7],[8,9]]=>[4,3,2]=>[4,3,2]=>3
[6,7,8,9,1,4,5,3,2]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[4,3,2]=>[4,3,2]=>3
[6,7,8,9,1,5,4,3,2]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[4,2,3]=>[4,3,2]=>3
[7,8,9,1,5,6,3,4,2]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[3,3,2,1]=>[3,3,2,1]=>4
[7,8,9,1,5,6,4,3,2]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[3,3,3]=>[3,3,3]=>3
[7,8,9,1,6,5,4,3,2]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[3,2,4]=>[4,3,2]=>3
[9,1,7,8,5,6,3,4,2]=>[[1,3,4],[2,6],[5,8],[7],[9]]=>[4,2,2,1]=>[4,2,2,1]=>4
[9,1,7,8,5,6,4,3,2]=>[[1,3,4],[2,6],[5],[7],[8],[9]]=>[4,2,3]=>[4,3,2]=>3
[5,6,7,8,9,10,1,3,4,2]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[6,3,1]=>[6,3,1]=>3
[5,6,7,8,9,10,1,4,3,2]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[6,2,2]=>[6,2,2]=>3
[7,8,9,10,1,4,5,6,2,3]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[4,4,2]=>[4,4,2]=>3
[7,8,9,10,1,4,5,6,3,2]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[4,4,2]=>[4,4,2]=>3
[7,8,9,10,1,5,6,4,3,2]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[4,3,3]=>[4,3,3]=>3
[7,8,9,10,1,6,5,4,3,2]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[4,2,4]=>[4,4,2]=>3
[8,9,10,1,6,7,4,5,2,3]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[3,3,2,2]=>[3,3,2,2]=>4
[8,9,10,1,6,7,4,5,3,2]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[3,3,2,2]=>[3,3,2,2]=>4
[8,9,10,1,6,7,5,4,3,2]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[3,3,4]=>[4,3,3]=>3
[8,9,10,1,7,6,5,4,3,2]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[3,2,5]=>[5,3,2]=>3
[10,1,8,9,6,7,4,5,3,2]=>[[1,3,4],[2,6],[5,8],[7],[9],[10]]=>[4,2,2,2]=>[4,2,2,2]=>4
[10,1,8,9,6,7,5,4,3,2]=>[[1,3,4],[2,6],[5],[7],[8],[9],[10]]=>[4,2,4]=>[4,4,2]=>3
[10,1,8,9,7,6,5,4,3,2]=>[[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[4,6]=>[6,4]=>2
[2,6,1,4,7,5,8,3]=>[[1,2,5,7],[3,4,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[3,1,5,7,2,6,8,4]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[3,1,7,5,2,6,8,4]=>[[1,3,6,7],[2,4,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[3,2,7,5,1,6,8,4]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[5,2,7,3,1,6,8,4]=>[[1,3,6,7],[2,4],[5,8]]=>[3,4,1]=>[4,3,1]=>3
[6,7,2,1,3,4,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[4,6,3,1,2,7,8,5]=>[[1,2,6,7],[3,5,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,3,4,5,7,9,6,8,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[6,2,1]=>3
[2,3,5,6,8,4,7,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[5,2,1]=>3
[2,3,5,9,4,6,7,8,1]=>[[1,2,3,4,7,8],[5,6],[9]]=>[4,4,1]=>[4,4,1]=>3
[2,4,5,8,3,6,7,1]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,5,8,7,6,3,1,2]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,5]=>[5,3]=>2
[8,7,4,6,5,3,1,2]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[4,4]=>[4,4]=>2
[9,5,8,7,6,4,3,1,2]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[3,6]=>[6,3]=>2
[8,1,4,3,6,2,5,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[1,6,3,7,8,4,2,5]=>[[1,2,4,5],[3,6,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[7,4,2,8,5,6,3,1]=>[[1,4,6],[2,5],[3,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[5,2,1,3,8,4,6,7]=>[[1,4,5,7,8],[2,6],[3]]=>[5,3]=>[5,3]=>2
[1,4,3,5,8,2,6,7]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]=>[3,3,2]=>3
[2,1,3,8,6,4,5,7]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[1,3,6,4,5,8,2,7]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,1,4,3,5,8,2,7]=>[[1,3,5,6],[2,8],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[6,5,1,3,8,2,4,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[5,3]=>[5,3]=>2
[1,4,3,8,6,2,5,7]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[4,1,3,8,6,2,5,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[7,1,5,4,6,3,8,2]=>[[1,3,5,7],[2],[4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[6,4,7,8,3,5,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[3,5,6,7,1,8,4,2]=>[[1,2,3,4,6],[5,7],[8]]=>[4,2,2]=>[4,2,2]=>3
[4,5,8,1,7,3,2,6]=>[[1,2,3],[4,5,8],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[4,6,7,1,3,8,2,5]=>[[1,2,3,6],[4,5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[2,6,3,1,4,7,8,5]=>[[1,2,5,6,7],[3,8],[4]]=>[2,5,1]=>[5,2,1]=>3
[2,7,3,4,1,8,5,6]=>[[1,2,4,6,8],[3,7],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,6,4,5,1,3,7,2]=>[[1,4,7],[2,6],[3],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[7,4,8,5,3,6,1,2]=>[[1,3,6],[2,4],[5,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[8,4,6,5,1,3,7,2]=>[[1,3,7],[2,6],[4],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[4,5,3,8,7,1,2,6]=>[[1,2,4],[3,5,8],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[8,5,4,7,6,1,2,3]=>[[1,4,8],[2,5],[3,7],[6]]=>[4,4]=>[4,4]=>2
[2,3,7,8,1,4,6,5]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[8,2,3,5,4,1,7,6]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,1,3,8,2,4,6,5]=>[[1,3,4,7],[2,6],[5,8]]=>[4,3,1]=>[4,3,1]=>3
[7,2,3,6,4,1,8,5]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[6,5,2,4,1,8,3,7]=>[[1,4,6],[2,7,8],[3],[5]]=>[4,2,2]=>[4,2,2]=>3
[5,7,2,4,1,3,8,6]=>[[1,2,7],[3,4,8],[5,6]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,2,5,4,1,8,3,7]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[4,2,6,3,5,8,1,7]=>[[1,3,5,6],[2,4,8],[7]]=>[3,3,2]=>[3,3,2]=>3
[7,4,2,6,8,5,3,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[8,5,2,4,6,3,1,7]=>[[1,4,5,8],[2],[3],[6],[7]]=>[5,3]=>[5,3]=>2
[7,4,1,2,8,5,6,3]=>[[1,4,5,7],[2,6],[3,8]]=>[5,2,1]=>[5,2,1]=>3
[6,4,1,8,5,2,3,7]=>[[1,4,7,8],[2,5],[3,6]]=>[4,4]=>[4,4]=>2
[8,4,1,6,3,5,2,7]=>[[1,4,6,8],[2,5],[3],[7]]=>[4,2,2]=>[4,2,2]=>3
[7,3,4,1,6,8,5,2]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[8,6,2,3,5,7,4,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[6,2]=>[6,2]=>2
[8,6,2,5,7,3,4,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[6,3,4,8,5,1,2,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[8,5,1,2,7,4,6,3]=>[[1,4,5,7],[2,6],[3],[8]]=>[5,2,1]=>[5,2,1]=>3
[7,2,6,8,3,4,5,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,6,7,5,4,8,2,3]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,8,5,4,2,6,3,7]=>[[1,2,6,8],[3,7],[4],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,2,6,7,8,9,1,4,3]=>[[1,3,4,5,6],[2,8],[7,9]]=>[6,2,1]=>[6,2,1]=>3
[3,7,2,4,8,9,1,5,6]=>[[1,2,5,6],[3,4,8,9],[7]]=>[2,4,3]=>[4,3,2]=>3
[6,2,3,7,8,9,1,5,4]=>[[1,3,4,5,6],[2,8],[7,9]]=>[6,2,1]=>[6,2,1]=>3
[5,2,6,7,8,9,10,1,3,4]=>[[1,3,4,5,6,7],[2,9,10],[8]]=>[7,3]=>[7,3]=>2
[8,9,7,6,5,4,1,3,2]=>[[1,2],[3,8],[4],[5],[6],[7],[9]]=>[2,6,1]=>[6,2,1]=>3
[9,10,8,7,6,5,4,1,3,2]=>[[1,2],[3,9],[4],[5],[6],[7],[8],[10]]=>[2,7,1]=>[7,2,1]=>3
[10,8,7,6,5,4,3,2,9,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[9,1]=>[9,1]=>2
[5,8,6,1,2,4,3,7]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,4,2]=>[4,2,2]=>3
[4,1,5,7,3,6,8,2]=>[[1,3,4,7],[2,5,6],[8]]=>[4,3,1]=>[4,3,1]=>3
[1,4,5,7,6,8,2,3]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]=>[4,2,2]=>3
[5,7,2,1,6,8,4,3]=>[[1,2,6],[3,5],[4,7],[8]]=>[2,4,2]=>[4,2,2]=>3
[2,6,3,1,7,8,5,4]=>[[1,2,5,6],[3,7],[4,8]]=>[2,4,2]=>[4,2,2]=>3
[6,2,5,7,4,1,8,3]=>[[1,3,4,7],[2,8],[5],[6]]=>[4,3,1]=>[4,3,1]=>3
[3,6,1,8,7,4,5,2]=>[[1,2,4],[3,5,7],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[6,8,4,5,1,3,7,9,2]=>[[1,2,7,8],[3,4],[5,6],[9]]=>[2,2,4,1]=>[4,2,2,1]=>4
[4,7,1,3,5,6,8,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]=>[5,2,1]=>3
[4,3,5,7,8,2,6,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[5,2,1]=>[5,2,1]=>3
[5,3,2,7,6,4,1,8]=>[[1,4,8],[2,5],[3,6],[7]]=>[4,4]=>[4,4]=>2
[5,3,7,4,6,2,1,8]=>[[1,3,5,8],[2,4],[6],[7]]=>[3,2,3]=>[3,3,2]=>3
[5,7,3,2,1,8,6,4]=>[[1,2,6],[3,7],[4,8],[5]]=>[2,4,2]=>[4,2,2]=>3
[5,7,6,3,2,1,8,4]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[3,2,7,5,4,1,8,6]=>[[1,3,7],[2,4,8],[5],[6]]=>[3,4,1]=>[4,3,1]=>3
[1,7,3,5,4,2,6,8]=>[[1,2,4,7,8],[3],[5],[6]]=>[2,2,4]=>[4,2,2]=>3
[5,3,7,4,1,8,6,2]=>[[1,3,6],[2,4,7],[5,8]]=>[3,3,2]=>[3,3,2]=>3
[7,3,5,4,1,6,8,2]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,5,1,6,8,3,2,4]=>[[1,4,5],[2,6,8],[3],[7]]=>[5,3]=>[5,3]=>2
[5,3,1,7,6,8,2,4]=>[[1,4,6],[2,5,8],[3,7]]=>[4,2,2]=>[4,2,2]=>3
[7,1,5,3,2,4,8,6]=>[[1,3,6,7],[2,8],[4],[5]]=>[3,4,1]=>[4,3,1]=>3
[7,1,5,2,4,3,6,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,8,9,3,4,5,1,2,6]=>[[1,2,3,9],[4,5,6],[7,8]]=>[3,3,3]=>[3,3,3]=>3
[7,8,9,3,4,5,2,1,6]=>[[1,2,3,9],[4,5,6],[7],[8]]=>[3,3,3]=>[3,3,3]=>3
[8,9,5,6,3,4,1,2,7]=>[[1,2,9],[3,4],[5,6],[7,8]]=>[2,2,2,3]=>[3,2,2,2]=>4
[8,9,5,6,3,4,2,1,7]=>[[1,2,9],[3,4],[5,6],[7],[8]]=>[2,2,2,3]=>[3,2,2,2]=>4
[8,9,5,6,4,3,2,1,7]=>[[1,2,9],[3,4],[5],[6],[7],[8]]=>[2,2,5]=>[5,2,2]=>3
[8,9,10,4,5,6,1,2,3,7]=>[[1,2,3,10],[4,5,6],[7,8,9]]=>[3,3,4]=>[4,3,3]=>3
[8,9,10,4,5,6,3,2,1,7]=>[[1,2,3,10],[4,5,6],[7],[8],[9]]=>[3,3,4]=>[4,3,3]=>3
[9,10,6,7,4,5,3,2,1,8]=>[[1,2,10],[3,4],[5,6],[7],[8],[9]]=>[2,2,2,4]=>[4,2,2,2]=>4
[9,10,6,7,5,4,3,2,1,8]=>[[1,2,10],[3,4],[5],[6],[7],[8],[9]]=>[2,2,6]=>[6,2,2]=>3
[1,8,3,6,2,4,7,5]=>[[1,2,4,7],[3,6,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,8,7,5,6,4,2,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,3,3]=>[3,3,2]=>3
[6,8,2,1,5,4,3,7]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,7,1,2,3,4,8,9,10,6]=>[[1,2,5,6,7,8,9],[3,4,10]]=>[2,7,1]=>[7,2,1]=>3
[6,3,2,1,5,8,4,7]=>[[1,5,6],[2,7,8],[3],[4]]=>[6,2]=>[6,2]=>2
[4,3,5,6,2,8,1,7]=>[[1,3,4,6],[2,8],[5],[7]]=>[4,2,2]=>[4,2,2]=>3
[6,3,5,2,7,8,4,1]=>[[1,3,5,6],[2,7],[4],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,5,3,1,6,8,2,7]=>[[1,2,5,6],[3,7,8],[4]]=>[2,4,2]=>[4,2,2]=>3
[3,4,6,7,5,1,8,2]=>[[1,2,3,4,7],[5,8],[6]]=>[4,3,1]=>[4,3,1]=>3
[7,4,1,2,5,6,8,3]=>[[1,4,5,6,7],[2,8],[3]]=>[7,1]=>[7,1]=>2
[4,8,2,6,7,1,5,3]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[6,5,8,3,7,1,4,2]=>[[1,3],[2,5],[4,7],[6,8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,3,4,5,6,10,1,9,7,8]=>[[1,2,3,4,5,6,10],[7,8],[9]]=>[6,2,2]=>[6,2,2]=>3
[1,5,2,4,7,6,8,3]=>[[1,2,4,5,7],[3,6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[2,5,4,7,1,8,3,6]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[8,1,2,4,6,3,5,7]=>[[1,3,4,5,8],[2,7],[6]]=>[5,3]=>[5,3]=>2
[4,5,6,7,9,8,3,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[5,4,6,7,8,9,3,2,1]=>[[1,3,4,5,6],[2],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[5,6,7,8,10,9,4,3,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,5]=>[5,5]=>2
[6,5,7,8,9,4,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[6,5,7,8,9,10,4,3,2,1]=>[[1,3,4,5,6],[2],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[4,5,6,7,8,10,9,3,2,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,4]=>[6,4]=>2
[3,5,6,7,9,8,4,2,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,4]=>[5,4]=>2
[5,4,6,7,8,9,10,3,2,1]=>[[1,3,4,5,6,7],[2],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[3,4,5,8,9,6,7,1,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[5,2,2]=>[5,2,2]=>3
[3,4,5,9,1,6,7,8,2]=>[[1,2,3,4,7,8],[5,6],[9]]=>[4,4,1]=>[4,4,1]=>3
[3,7,8,4,5,6,1,2]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]=>[3,3,2]=>3
[1,3,8,6,7,4,5,2]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[2,6,5,3,7,1,8,4]=>[[1,2,5,7],[3,8],[4],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,1,3,6,4,8,2]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[8,2,5,4,1,7,3,6]=>[[1,3,6],[2,7,8],[4],[5]]=>[3,3,2]=>[3,3,2]=>3
[8,1,7,6,4,2,3,5]=>[[1,3,7,8],[2],[4],[5],[6]]=>[3,5]=>[5,3]=>2
[1,8,6,3,7,4,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[5,7,3,4,2,8,6,1]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,3,4,2,7,6,1]=>[[1,2,6],[3,4],[5,7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,6,4,2,3,8,5,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>[6,2]=>[6,2]=>2
[3,5,6,8,2,4,7,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[4,3,1]=>3
[4,8,7,3,2,5,6,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,5,1]=>[5,2,1]=>3
[3,7,4,2,6,8,5,1]=>[[1,2,5,6],[3,7],[4],[8]]=>[2,4,2]=>[4,2,2]=>3
[6,4,8,7,3,2,5,1]=>[[1,3],[2,4],[5,7],[6],[8]]=>[3,4,1]=>[4,3,1]=>3
[5,6,2,8,7,4,3,1]=>[[1,2,4],[3,5],[6],[7],[8]]=>[2,2,4]=>[4,2,2]=>3
[6,2,8,3,7,4,5,1]=>[[1,3,5,7],[2,4],[6],[8]]=>[3,2,2,1]=>[3,2,2,1]=>4
[3,7,5,6,4,2,8,1]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[5,2,3,8,6,1,4,7]=>[[1,3,4,8],[2,5],[6,7]]=>[4,4]=>[4,4]=>2
[1,4,3,8,5,6,2,7]=>[[1,2,4,6,8],[3,5],[7]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,8,2,6,4,3,5,1]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[4,5,8,7,2,3,6,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,4,1]=>[4,3,1]=>3
[7,8,6,1,4,2,5,3]=>[[1,2,7],[3,5],[4,8],[6]]=>[2,3,2,1]=>[3,2,2,1]=>4
[10,5,4,1,2,3,6,7,8,9]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[10]=>[10]=>1
[8,3,6,5,2,7,1,4]=>[[1,3,6],[2,8],[4],[5],[7]]=>[3,3,2]=>[3,3,2]=>3
[5,1,3,6,4,2,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>[4,4]=>[4,4]=>2
[6,1,2,4,7,5,3,8]=>[[1,3,4,5,8],[2,6],[7]]=>[5,3]=>[5,3]=>2
[8,3,1,4,6,7,2,5]=>[[1,4,5,6],[2,7,8],[3]]=>[6,2]=>[6,2]=>2
[7,8,5,1,2,6,3,4]=>[[1,2,6,8],[3,5],[4,7]]=>[2,4,2]=>[4,2,2]=>3
[6,4,5,1,8,7,3,2]=>[[1,3,5],[2,6],[4,7],[8]]=>[3,2,3]=>[3,3,2]=>3
[8,6,2,1,7,3,5,4]=>[[1,5,7],[2,6],[3,8],[4]]=>[5,2,1]=>[5,2,1]=>3
[9,3,4,5,6,8,7,2,1]=>[[1,3,4,5,6],[2],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[10,3,4,5,6,7,9,8,2,1]=>[[1,3,4,5,6,7],[2],[8],[9],[10]]=>[7,3]=>[7,3]=>2
[9,2,4,5,6,8,7,3,1]=>[[1,3,4,5,6],[2],[7],[8],[9]]=>[6,3]=>[6,3]=>2
[7,8,6,1,4,3,5,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,3,6,2,5,7,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[3,3,2]=>[3,3,2]=>3
[1,6,5,7,3,4,8,2]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,2,3,4,5,8,6,9,7,10]=>[[1,2,3,4,5,6,8,10],[7,9]]=>[6,2,2]=>[6,2,2]=>3
[1,2,3,4,5,9,6,10,7,8]=>[[1,2,3,4,5,6,8,10],[7,9]]=>[6,2,2]=>[6,2,2]=>3
[8,2,6,5,1,7,4,3]=>[[1,3,6],[2,7],[4],[5],[8]]=>[3,3,2]=>[3,3,2]=>3
[7,6,4,1,2,5,8,3]=>[[1,5,6,7],[2,8],[3],[4]]=>[7,1]=>[7,1]=>2
[2,6,5,4,8,7,1,3]=>[[1,2,5],[3,6],[4,8],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,7,1,3,2,4,8]=>[[1,2,3,8],[4,5,7],[6]]=>[3,2,3]=>[3,3,2]=>3
[7,1,8,4,3,2,6,5]=>[[1,3,7],[2,4],[5,8],[6]]=>[3,4,1]=>[4,3,1]=>3
[3,7,1,2,4,5,6,9,8]=>[[1,2,5,6,7,8],[3,4,9]]=>[2,6,1]=>[6,2,1]=>3
[1,8,5,2,7,6,4,3]=>[[1,2,5],[3,6],[4],[7],[8]]=>[2,3,3]=>[3,3,2]=>3
[1,7,6,8,2,5,4,3]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[1,7,8,6,2,5,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[4,6,5,7,1,8,2,3]=>[[1,2,4,6],[3,7,8],[5]]=>[2,2,2,2]=>[2,2,2,2]=>4
[7,5,3,6,8,4,2,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>[5,3]=>[5,3]=>2
[7,2,5,6,4,8,3,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[4,2,2]=>[4,2,2]=>3
[7,4,6,2,8,5,3,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>[3,2,3]=>[3,3,2]=>3
[1,6,3,4,2,5,8,7]=>[[1,2,4,6,7],[3,8],[5]]=>[2,2,3,1]=>[3,2,2,1]=>4
[1,5,7,6,2,3,8,4]=>[[1,2,3,7],[4,6,8],[5]]=>[3,4,1]=>[4,3,1]=>3
[1,4,3,7,6,2,5,8]=>[[1,2,4,8],[3,5],[6,7]]=>[2,2,4]=>[4,2,2]=>3
[1,3,7,4,6,8,5,2]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,2]=>[3,3,2]=>3
[3,7,4,6,8,1,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]=>[3,2,2,1]=>4
[4,8,3,1,7,6,2,5]=>[[1,2,8],[3,5],[4,6],[7]]=>[2,3,3]=>[3,3,2]=>3
[5,6,1,4,3,8,7,2]=>[[1,2,6],[3,4,7],[5],[8]]=>[2,2,2,2]=>[2,2,2,2]=>4
[5,8,6,4,3,1,7,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>[2,5,1]=>[5,2,1]=>3
[4,1,3,7,8,6,5,2]=>[[1,3,4,5],[2,6],[7],[8]]=>[5,3]=>[5,3]=>2
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searching the database for statistics with the same generating function
Description
The length of the partition.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
Map
peak composition
Description
The composition corresponding to the peak set of a standard tableau.
Let T be a standard tableau of size n.
An entry i of T is a descent if i+1 is in a lower row (in English notation), otherwise i is an ascent.
An entry 2≤i≤n−1 is a peak, if i−1 is an ascent and i is a descent.
This map returns the composition c1,…,ck of n such that {c1,c1+c2,…,c1+⋯+ck} is the peak set of T.
Let T be a standard tableau of size n.
An entry i of T is a descent if i+1 is in a lower row (in English notation), otherwise i is an ascent.
An entry 2≤i≤n−1 is a peak, if i−1 is an ascent and i is a descent.
This map returns the composition c1,…,ck of n such that {c1,c1+c2,…,c1+⋯+ck} is the peak set of T.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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