Identifier
-
Mp00071:
Permutations
—descent composition⟶
Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000225: Integer partitions ⟶ ℤ
Values
=>
Cc0028;cc-rep-2
Cc0002;cc-rep
[1,3,2]=>[2,1]=>[[2,2],[1]]=>[1]=>0
[2,3,1]=>[2,1]=>[[2,2],[1]]=>[1]=>0
[1,2,4,3]=>[3,1]=>[[3,3],[2]]=>[2]=>0
[1,3,2,4]=>[2,2]=>[[3,2],[1]]=>[1]=>0
[1,3,4,2]=>[3,1]=>[[3,3],[2]]=>[2]=>0
[1,4,2,3]=>[2,2]=>[[3,2],[1]]=>[1]=>0
[1,4,3,2]=>[2,1,1]=>[[2,2,2],[1,1]]=>[1,1]=>0
[2,1,4,3]=>[1,2,1]=>[[2,2,1],[1]]=>[1]=>0
[2,3,1,4]=>[2,2]=>[[3,2],[1]]=>[1]=>0
[2,3,4,1]=>[3,1]=>[[3,3],[2]]=>[2]=>0
[2,4,1,3]=>[2,2]=>[[3,2],[1]]=>[1]=>0
[2,4,3,1]=>[2,1,1]=>[[2,2,2],[1,1]]=>[1,1]=>0
[3,1,4,2]=>[1,2,1]=>[[2,2,1],[1]]=>[1]=>0
[3,2,4,1]=>[1,2,1]=>[[2,2,1],[1]]=>[1]=>0
[3,4,1,2]=>[2,2]=>[[3,2],[1]]=>[1]=>0
[3,4,2,1]=>[2,1,1]=>[[2,2,2],[1,1]]=>[1,1]=>0
[4,1,3,2]=>[1,2,1]=>[[2,2,1],[1]]=>[1]=>0
[4,2,3,1]=>[1,2,1]=>[[2,2,1],[1]]=>[1]=>0
[1,2,3,5,4]=>[4,1]=>[[4,4],[3]]=>[3]=>0
[1,2,4,3,5]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[1,2,4,5,3]=>[4,1]=>[[4,4],[3]]=>[3]=>0
[1,2,5,3,4]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[1,2,5,4,3]=>[3,1,1]=>[[3,3,3],[2,2]]=>[2,2]=>0
[1,3,2,4,5]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[1,3,2,5,4]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[1,3,4,2,5]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[1,3,4,5,2]=>[4,1]=>[[4,4],[3]]=>[3]=>0
[1,3,5,2,4]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[1,3,5,4,2]=>[3,1,1]=>[[3,3,3],[2,2]]=>[2,2]=>0
[1,4,2,3,5]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[1,4,2,5,3]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[1,4,3,2,5]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[1,4,3,5,2]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[1,4,5,2,3]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[1,4,5,3,2]=>[3,1,1]=>[[3,3,3],[2,2]]=>[2,2]=>0
[1,5,2,3,4]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[1,5,2,4,3]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[1,5,3,2,4]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[1,5,3,4,2]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[1,5,4,2,3]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[1,5,4,3,2]=>[2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,1,3,5,4]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[2,1,4,3,5]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[2,1,4,5,3]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[2,1,5,3,4]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[2,1,5,4,3]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[2,3,1,4,5]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[2,3,1,5,4]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[2,3,4,1,5]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[2,3,4,5,1]=>[4,1]=>[[4,4],[3]]=>[3]=>0
[2,3,5,1,4]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[2,3,5,4,1]=>[3,1,1]=>[[3,3,3],[2,2]]=>[2,2]=>0
[2,4,1,3,5]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[2,4,1,5,3]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[2,4,3,1,5]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[2,4,3,5,1]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[2,4,5,1,3]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[2,4,5,3,1]=>[3,1,1]=>[[3,3,3],[2,2]]=>[2,2]=>0
[2,5,1,3,4]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[2,5,1,4,3]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[2,5,3,1,4]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[2,5,3,4,1]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[2,5,4,1,3]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[2,5,4,3,1]=>[2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,1,2,5,4]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[3,1,4,2,5]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[3,1,4,5,2]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[3,1,5,2,4]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[3,1,5,4,2]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[3,2,1,5,4]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[3,2,4,1,5]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[3,2,4,5,1]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[3,2,5,1,4]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[3,2,5,4,1]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[3,4,1,2,5]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[3,4,1,5,2]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[3,4,2,1,5]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[3,4,2,5,1]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[3,4,5,1,2]=>[3,2]=>[[4,3],[2]]=>[2]=>0
[3,4,5,2,1]=>[3,1,1]=>[[3,3,3],[2,2]]=>[2,2]=>0
[3,5,1,2,4]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[3,5,1,4,2]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[3,5,2,1,4]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[3,5,2,4,1]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[3,5,4,1,2]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[3,5,4,2,1]=>[2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,1,2,5,3]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[4,1,3,2,5]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[4,1,3,5,2]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[4,1,5,2,3]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[4,1,5,3,2]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[4,2,1,5,3]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[4,2,3,1,5]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[4,2,3,5,1]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[4,2,5,1,3]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[4,2,5,3,1]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[4,3,1,5,2]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[4,3,2,5,1]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[4,3,5,1,2]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[4,3,5,2,1]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[4,5,1,2,3]=>[2,3]=>[[4,2],[1]]=>[1]=>0
[4,5,1,3,2]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[4,5,2,1,3]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[4,5,2,3,1]=>[2,2,1]=>[[3,3,2],[2,1]]=>[2,1]=>1
[4,5,3,1,2]=>[2,1,2]=>[[3,2,2],[1,1]]=>[1,1]=>0
[4,5,3,2,1]=>[2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,1,2,4,3]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[5,1,3,2,4]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[5,1,3,4,2]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[5,1,4,2,3]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[5,1,4,3,2]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[5,2,1,4,3]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[5,2,3,1,4]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[5,2,3,4,1]=>[1,3,1]=>[[3,3,1],[2]]=>[2]=>0
[5,2,4,1,3]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[5,2,4,3,1]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[5,3,1,4,2]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[5,3,2,4,1]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[5,3,4,1,2]=>[1,2,2]=>[[3,2,1],[1]]=>[1]=>0
[5,3,4,2,1]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1]=>0
[5,4,1,3,2]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[5,4,2,3,1]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[1]=>0
[1,2,3,4,6,5]=>[5,1]=>[[5,5],[4]]=>[4]=>0
[1,2,3,5,4,6]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,2,3,5,6,4]=>[5,1]=>[[5,5],[4]]=>[4]=>0
[1,2,3,6,4,5]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,2,3,6,5,4]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[1,2,4,3,5,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,2,4,3,6,5]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,2,4,5,3,6]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,2,4,5,6,3]=>[5,1]=>[[5,5],[4]]=>[4]=>0
[1,2,4,6,3,5]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,2,4,6,5,3]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[1,2,5,3,4,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,2,5,3,6,4]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,2,5,4,3,6]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,2,5,4,6,3]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,2,5,6,3,4]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,2,5,6,4,3]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[1,2,6,3,4,5]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,2,6,3,5,4]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,2,6,4,3,5]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,2,6,4,5,3]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,2,6,5,3,4]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,2,6,5,4,3]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,2,4,5,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[1,3,2,4,6,5]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,3,2,5,4,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,3,2,5,6,4]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,3,2,6,4,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,3,2,6,5,4]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,4,2,5,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,3,4,2,6,5]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,3,4,5,2,6]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,3,4,5,6,2]=>[5,1]=>[[5,5],[4]]=>[4]=>0
[1,3,4,6,2,5]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,3,4,6,5,2]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[1,3,5,2,4,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,3,5,2,6,4]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,3,5,4,2,6]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,3,5,4,6,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,3,5,6,2,4]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,3,5,6,4,2]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[1,3,6,2,4,5]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,3,6,2,5,4]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,3,6,4,2,5]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,3,6,4,5,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,3,6,5,2,4]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,3,6,5,4,2]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,2,3,5,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[1,4,2,3,6,5]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,4,2,5,3,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,4,2,5,6,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,4,2,6,3,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,4,2,6,5,3]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,3,2,5,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[1,4,3,2,6,5]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,3,5,2,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,4,3,5,6,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,4,3,6,2,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,4,3,6,5,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,5,2,3,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,4,5,2,6,3]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,4,5,3,2,6]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,4,5,3,6,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,4,5,6,2,3]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[1,4,5,6,3,2]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[1,4,6,2,3,5]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,4,6,2,5,3]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,4,6,3,2,5]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,4,6,3,5,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,4,6,5,2,3]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,4,6,5,3,2]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,5,2,3,4,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[1,5,2,3,6,4]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,5,2,4,3,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,5,2,4,6,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,5,2,6,3,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,5,2,6,4,3]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,3,2,4,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[1,5,3,2,6,4]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,3,4,2,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,5,3,4,6,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,5,3,6,2,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,5,3,6,4,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,4,2,3,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[1,5,4,2,6,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,3,2,6]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,5,4,3,6,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,6,2,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,5,4,6,3,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,6,2,3,4]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[1,5,6,2,4,3]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,5,6,3,2,4]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,5,6,3,4,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[1,5,6,4,2,3]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[1,5,6,4,3,2]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,6,2,3,4,5]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[1,6,2,3,5,4]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,6,2,4,3,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,6,2,4,5,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,6,2,5,3,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,6,2,5,4,3]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,2,4,5]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[1,6,3,2,5,4]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,3,4,2,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,6,3,4,5,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[1,6,3,5,2,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,6,3,5,4,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,4,2,3,5]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[1,6,4,2,5,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,4,3,2,5]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,6,4,3,5,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,4,5,2,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[1,6,4,5,3,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,5,2,3,4]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[1,6,5,2,4,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,3,2,4]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,6,5,3,4,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,4,2,3]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,6,5,4,3,2]=>[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[2,1,3,4,6,5]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[2,1,3,5,4,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[2,1,3,5,6,4]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[2,1,3,6,4,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[2,1,3,6,5,4]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[2,1,4,3,5,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[2,1,4,3,6,5]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[2,1,4,5,3,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[2,1,4,5,6,3]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[2,1,4,6,3,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[2,1,4,6,5,3]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[2,1,5,3,4,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[2,1,5,3,6,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[2,1,5,4,3,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[2,1,5,4,6,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[2,1,5,6,3,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[2,1,5,6,4,3]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[2,1,6,3,4,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[2,1,6,3,5,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,4,3,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[2,1,6,4,5,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,5,3,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[2,1,6,5,4,3]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[2,3,1,4,5,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[2,3,1,4,6,5]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,3,1,5,4,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,3,1,5,6,4]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,3,1,6,4,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,3,1,6,5,4]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,4,1,5,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[2,3,4,1,6,5]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,3,4,5,1,6]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[2,3,4,5,6,1]=>[5,1]=>[[5,5],[4]]=>[4]=>0
[2,3,4,6,1,5]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[2,3,4,6,5,1]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[2,3,5,1,4,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[2,3,5,1,6,4]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,3,5,4,1,6]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[2,3,5,4,6,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,3,5,6,1,4]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[2,3,5,6,4,1]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[2,3,6,1,4,5]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[2,3,6,1,5,4]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,3,6,4,1,5]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[2,3,6,4,5,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,3,6,5,1,4]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[2,3,6,5,4,1]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,4,1,3,5,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[2,4,1,3,6,5]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,4,1,5,3,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,4,1,5,6,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,4,1,6,3,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,4,1,6,5,3]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,3,1,5,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[2,4,3,1,6,5]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,4,3,5,1,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,4,3,5,6,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,4,3,6,1,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,4,3,6,5,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,5,1,3,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[2,4,5,1,6,3]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,4,5,3,1,6]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[2,4,5,3,6,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,4,5,6,1,3]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[2,4,5,6,3,1]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[2,4,6,1,3,5]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[2,4,6,1,5,3]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,4,6,3,1,5]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[2,4,6,3,5,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,4,6,5,1,3]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[2,4,6,5,3,1]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,5,1,3,4,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[2,5,1,3,6,4]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,5,1,4,3,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,5,1,4,6,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,5,1,6,3,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,5,1,6,4,3]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,3,1,4,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[2,5,3,1,6,4]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,3,4,1,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,5,3,4,6,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,5,3,6,1,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,5,3,6,4,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,4,1,3,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[2,5,4,1,6,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,3,1,6]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,5,4,3,6,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,6,1,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,5,4,6,3,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,6,1,3,4]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[2,5,6,1,4,3]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,5,6,3,1,4]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[2,5,6,3,4,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[2,5,6,4,1,3]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[2,5,6,4,3,1]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,1,3,4,5]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[2,6,1,3,5,4]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,6,1,4,3,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,6,1,4,5,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,6,1,5,3,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,6,1,5,4,3]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,1,4,5]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[2,6,3,1,5,4]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,3,4,1,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,6,3,4,5,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[2,6,3,5,1,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,6,3,5,4,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,1,3,5]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[2,6,4,1,5,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,4,3,1,5]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,6,4,3,5,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,4,5,1,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[2,6,4,5,3,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,5,1,3,4]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[2,6,5,1,4,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,3,1,4]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,6,5,3,4,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,4,1,3]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,6,5,4,3,1]=>[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[3,1,2,4,6,5]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[3,1,2,5,4,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[3,1,2,5,6,4]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[3,1,2,6,4,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[3,1,2,6,5,4]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[3,1,4,2,5,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[3,1,4,2,6,5]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,1,4,5,2,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[3,1,4,5,6,2]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[3,1,4,6,2,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[3,1,4,6,5,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[3,1,5,2,4,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[3,1,5,2,6,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,1,5,4,2,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[3,1,5,4,6,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,1,5,6,2,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[3,1,5,6,4,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[3,1,6,2,4,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[3,1,6,2,5,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,4,2,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[3,1,6,4,5,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,5,2,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[3,1,6,5,4,2]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,2,1,4,6,5]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[3,2,1,5,4,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[3,2,1,5,6,4]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[3,2,1,6,4,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[3,2,1,6,5,4]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[3,2,4,1,5,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[3,2,4,1,6,5]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,2,4,5,1,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[3,2,4,5,6,1]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[3,2,4,6,1,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[3,2,4,6,5,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[3,2,5,1,4,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[3,2,5,1,6,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,2,5,4,1,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[3,2,5,4,6,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,2,5,6,1,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[3,2,5,6,4,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[3,2,6,1,4,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[3,2,6,1,5,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,4,1,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[3,2,6,4,5,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,5,1,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[3,2,6,5,4,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,4,1,2,5,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[3,4,1,2,6,5]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,4,1,5,2,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,4,1,5,6,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,4,1,6,2,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,4,1,6,5,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,1,5,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[3,4,2,1,6,5]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,4,2,5,1,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,4,2,5,6,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,4,2,6,1,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,4,2,6,5,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,5,1,2,6]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[3,4,5,1,6,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[3,4,5,2,1,6]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[3,4,5,2,6,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[3,4,5,6,1,2]=>[4,2]=>[[5,4],[3]]=>[3]=>0
[3,4,5,6,2,1]=>[4,1,1]=>[[4,4,4],[3,3]]=>[3,3]=>0
[3,4,6,1,2,5]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[3,4,6,1,5,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[3,4,6,2,1,5]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[3,4,6,2,5,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[3,4,6,5,1,2]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[3,4,6,5,2,1]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,1,2,4,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[3,5,1,2,6,4]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,5,1,4,2,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,5,1,4,6,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,5,1,6,2,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,5,1,6,4,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,2,1,4,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[3,5,2,1,6,4]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,2,4,1,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,5,2,4,6,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,5,2,6,1,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,5,2,6,4,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,4,1,2,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[3,5,4,1,6,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,2,1,6]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,5,4,2,6,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,6,1,2]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,5,4,6,2,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,6,1,2,4]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[3,5,6,1,4,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[3,5,6,2,1,4]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[3,5,6,2,4,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[3,5,6,4,1,2]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[3,5,6,4,2,1]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,6,1,2,4,5]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[3,6,1,2,5,4]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,6,1,4,2,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,6,1,4,5,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,6,1,5,2,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,6,1,5,4,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,2,1,4,5]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[3,6,2,1,5,4]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,2,4,1,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,6,2,4,5,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[3,6,2,5,1,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,6,2,5,4,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,4,1,2,5]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[3,6,4,1,5,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,4,2,1,5]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,6,4,2,5,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,4,5,1,2]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[3,6,4,5,2,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,5,1,2,4]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[3,6,5,1,4,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,2,1,4]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,6,5,2,4,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,4,1,2]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,6,5,4,2,1]=>[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[4,1,2,3,6,5]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[4,1,2,5,3,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,1,2,5,6,3]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[4,1,2,6,3,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,1,2,6,5,3]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[4,1,3,2,5,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[4,1,3,2,6,5]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,1,3,5,2,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,1,3,5,6,2]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[4,1,3,6,2,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,1,3,6,5,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[4,1,5,2,3,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[4,1,5,2,6,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,3,2,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,1,5,3,6,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,6,2,3]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,1,5,6,3,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[4,1,6,2,3,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[4,1,6,2,5,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,3,2,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,1,6,3,5,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,5,2,3]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,1,6,5,3,2]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,2,1,3,6,5]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[4,2,1,5,3,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[4,2,1,5,6,3]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[4,2,1,6,3,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[4,2,1,6,5,3]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[4,2,3,1,5,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[4,2,3,1,6,5]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,2,3,5,1,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,2,3,5,6,1]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[4,2,3,6,1,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,2,3,6,5,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[4,2,5,1,3,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[4,2,5,1,6,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,3,1,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,2,5,3,6,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,6,1,3]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,2,5,6,3,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[4,2,6,1,3,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[4,2,6,1,5,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,3,1,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,2,6,3,5,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,5,1,3]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,2,6,5,3,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,3,1,2,6,5]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[4,3,1,5,2,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[4,3,1,5,6,2]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[4,3,1,6,2,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[4,3,1,6,5,2]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[4,3,2,1,6,5]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[4,3,2,5,1,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[4,3,2,5,6,1]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[4,3,2,6,1,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[4,3,2,6,5,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[4,3,5,1,2,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[4,3,5,1,6,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,3,5,2,1,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,3,5,2,6,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,3,5,6,1,2]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[4,3,5,6,2,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[4,3,6,1,2,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[4,3,6,1,5,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,3,6,2,1,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,3,6,2,5,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[4,3,6,5,1,2]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[4,3,6,5,2,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,5,1,2,3,6]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[4,5,1,2,6,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[4,5,1,3,2,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,5,1,3,6,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[4,5,1,6,2,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,5,1,6,3,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,2,1,3,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[4,5,2,1,6,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,2,3,1,6]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,5,2,3,6,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[4,5,2,6,1,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,5,2,6,3,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,3,1,2,6]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[4,5,3,1,6,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,3,2,1,6]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,5,3,2,6,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,3,6,1,2]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,5,3,6,2,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,6,1,2,3]=>[3,3]=>[[5,3],[2]]=>[2]=>0
[4,5,6,1,3,2]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[4,5,6,2,1,3]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[4,5,6,2,3,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[3,2]=>1
[4,5,6,3,1,2]=>[3,1,2]=>[[4,3,3],[2,2]]=>[2,2]=>0
[4,5,6,3,2,1]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,6,1,2,3,5]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[4,6,1,2,5,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[4,6,1,3,2,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,6,1,3,5,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[4,6,1,5,2,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,6,1,5,3,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,2,1,3,5]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[4,6,2,1,5,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,2,3,1,5]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,6,2,3,5,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[4,6,2,5,1,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,6,2,5,3,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,3,1,2,5]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[4,6,3,1,5,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,3,2,1,5]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,6,3,2,5,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,3,5,1,2]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[4,6,3,5,2,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,5,1,2,3]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[4,6,5,1,3,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,5,2,1,3]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,6,5,2,3,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,5,3,1,2]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,6,5,3,2,1]=>[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[5,1,2,3,6,4]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[5,1,2,4,3,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,1,2,4,6,3]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[5,1,2,6,3,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,1,2,6,4,3]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[5,1,3,2,4,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,1,3,2,6,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,1,3,4,2,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,1,3,4,6,2]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[5,1,3,6,2,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,1,3,6,4,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[5,1,4,2,3,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,1,4,2,6,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,3,2,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,1,4,3,6,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,6,2,3]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,1,4,6,3,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[5,1,6,2,3,4]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,1,6,2,4,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,3,2,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,1,6,3,4,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,4,2,3]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,1,6,4,3,2]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,2,1,3,6,4]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[5,2,1,4,3,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,2,1,4,6,3]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[5,2,1,6,3,4]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,2,1,6,4,3]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[5,2,3,1,4,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,2,3,1,6,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,2,3,4,1,6]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,2,3,4,6,1]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[5,2,3,6,1,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,2,3,6,4,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[5,2,4,1,3,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,2,4,1,6,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,2,4,3,1,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,2,4,3,6,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,2,4,6,1,3]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,2,4,6,3,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[5,2,6,1,3,4]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,2,6,1,4,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,2,6,3,1,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,2,6,3,4,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,2,6,4,1,3]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,2,6,4,3,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,3,1,2,6,4]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[5,3,1,4,2,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,3,1,4,6,2]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[5,3,1,6,2,4]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,3,1,6,4,2]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[5,3,2,1,6,4]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[5,3,2,4,1,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,3,2,4,6,1]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[5,3,2,6,1,4]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,3,2,6,4,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[5,3,4,1,2,6]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,3,4,1,6,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,2,1,6]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,3,4,2,6,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,6,1,2]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[5,3,4,6,2,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[5,3,6,1,2,4]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,3,6,1,4,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,3,6,2,1,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,3,6,2,4,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,3,6,4,1,2]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,3,6,4,2,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,4,1,2,6,3]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[5,4,1,3,2,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,4,1,3,6,2]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[5,4,1,6,2,3]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,4,1,6,3,2]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,2,1,6,3]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[5,4,2,3,1,6]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,4,2,3,6,1]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[5,4,2,6,1,3]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,4,2,6,3,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,3,1,6,2]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[5,4,3,2,6,1]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[5,4,3,6,1,2]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[5,4,3,6,2,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,6,1,2,3]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[5,4,6,1,3,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,4,6,2,1,3]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,4,6,2,3,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[5,4,6,3,1,2]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[5,4,6,3,2,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,6,1,2,3,4]=>[2,4]=>[[5,2],[1]]=>[1]=>0
[5,6,1,2,4,3]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[5,6,1,3,2,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[5,6,1,3,4,2]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[5,6,1,4,2,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[5,6,1,4,3,2]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,2,1,3,4]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[5,6,2,1,4,3]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,2,3,1,4]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[5,6,2,3,4,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[3,1]=>2
[5,6,2,4,1,3]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[5,6,2,4,3,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,3,1,2,4]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[5,6,3,1,4,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,2,1,4]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,6,3,2,4,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,4,1,2]=>[2,2,2]=>[[4,3,2],[2,1]]=>[2,1]=>1
[5,6,3,4,2,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,4,1,2,3]=>[2,1,3]=>[[4,2,2],[1,1]]=>[1,1]=>0
[5,6,4,1,3,2]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,2,1,3]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,6,4,2,3,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,3,1,2]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,6,4,3,2,1]=>[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[6,1,2,3,5,4]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[6,1,2,4,3,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,1,2,4,5,3]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[6,1,2,5,3,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,1,2,5,4,3]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[6,1,3,2,4,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,1,3,2,5,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,1,3,4,2,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,1,3,4,5,2]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[6,1,3,5,2,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,1,3,5,4,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[6,1,4,2,3,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,1,4,2,5,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,3,2,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,1,4,3,5,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,5,2,3]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,1,4,5,3,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[6,1,5,2,3,4]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,1,5,2,4,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,3,2,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,1,5,3,4,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,4,2,3]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,1,5,4,3,2]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,2,1,3,5,4]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,2,1,4,3,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,2,1,4,5,3]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,2,1,5,3,4]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,2,1,5,4,3]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,2,3,1,4,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,2,3,1,5,4]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,2,3,4,1,5]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,2,3,4,5,1]=>[1,4,1]=>[[4,4,1],[3]]=>[3]=>0
[6,2,3,5,1,4]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,2,3,5,4,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[6,2,4,1,3,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,2,4,1,5,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,3,1,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,2,4,3,5,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,5,1,3]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,2,4,5,3,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[6,2,5,1,3,4]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,2,5,1,4,3]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,3,1,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,2,5,3,4,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,4,1,3]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,2,5,4,3,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,3,1,2,5,4]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,3,1,4,2,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,3,1,4,5,2]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,3,1,5,2,4]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,3,1,5,4,2]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,3,2,1,5,4]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[6,3,2,4,1,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,3,2,4,5,1]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,3,2,5,1,4]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,3,2,5,4,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,3,4,1,2,5]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,3,4,1,5,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,3,4,2,1,5]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,3,4,2,5,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,3,4,5,1,2]=>[1,3,2]=>[[4,3,1],[2]]=>[2]=>0
[6,3,4,5,2,1]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[2,2]=>0
[6,3,5,1,2,4]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,3,5,1,4,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,3,5,2,1,4]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,3,5,2,4,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,3,5,4,1,2]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,3,5,4,2,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,4,1,2,5,3]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,4,1,3,2,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,4,1,3,5,2]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,4,1,5,2,3]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,4,1,5,3,2]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,2,1,5,3]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[6,4,2,3,1,5]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,4,2,3,5,1]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,4,2,5,1,3]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,4,2,5,3,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,3,1,5,2]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[6,4,3,2,5,1]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[6,4,3,5,1,2]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,4,3,5,2,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,5,1,2,3]=>[1,2,3]=>[[4,2,1],[1]]=>[1]=>0
[6,4,5,1,3,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,2,1,3]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,4,5,2,3,1]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,3,1,2]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[1,1]=>0
[6,4,5,3,2,1]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,5,1,2,4,3]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,5,1,3,2,4]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,5,1,3,4,2]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,5,1,4,2,3]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,5,1,4,3,2]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,2,1,4,3]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[6,5,2,3,1,4]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,5,2,3,4,1]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[2]=>0
[6,5,2,4,1,3]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,5,2,4,3,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,3,1,4,2]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[6,5,3,2,4,1]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[6,5,3,4,1,2]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[1]=>0
[6,5,3,4,2,1]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,4,1,3,2]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[6,5,4,2,3,1]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1]=>0
[1,2,3,4,5,7,6]=>[6,1]=>[[6,6],[5]]=>[5]=>0
[1,2,3,4,6,5,7]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,3,4,6,7,5]=>[6,1]=>[[6,6],[5]]=>[5]=>0
[1,2,3,4,7,5,6]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,3,4,7,6,5]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,2,3,5,4,6,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,3,5,4,7,6]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,3,5,6,4,7]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,3,5,6,7,4]=>[6,1]=>[[6,6],[5]]=>[5]=>0
[1,2,3,5,7,4,6]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,3,5,7,6,4]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,2,3,6,4,5,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,3,6,4,7,5]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,3,6,5,4,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,3,6,5,7,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,3,6,7,4,5]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,3,6,7,5,4]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,2,3,7,4,5,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,3,7,4,6,5]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,3,7,5,4,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,3,7,5,6,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,3,7,6,4,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,3,7,6,5,4]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,4,3,5,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,2,4,3,5,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,4,3,6,5,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,4,3,6,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,4,3,7,5,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,4,3,7,6,5]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,4,5,3,6,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,4,5,3,7,6]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,4,5,6,3,7]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,4,5,6,7,3]=>[6,1]=>[[6,6],[5]]=>[5]=>0
[1,2,4,5,7,3,6]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,4,5,7,6,3]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,2,4,6,3,5,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,4,6,3,7,5]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,4,6,5,3,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,4,6,5,7,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,4,6,7,3,5]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,4,6,7,5,3]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,2,4,7,3,5,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,4,7,3,6,5]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,4,7,5,3,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,4,7,5,6,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,4,7,6,3,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,4,7,6,5,3]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,5,3,4,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,2,5,3,4,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,5,3,6,4,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,5,3,6,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,5,3,7,4,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,5,3,7,6,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,5,4,3,6,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,2,5,4,3,7,6]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,5,4,6,3,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,5,4,6,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,5,4,7,3,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,5,4,7,6,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,5,6,3,4,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,5,6,3,7,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,5,6,4,3,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,5,6,4,7,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,5,6,7,3,4]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,2,5,6,7,4,3]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,2,5,7,3,4,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,5,7,3,6,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,5,7,4,3,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,5,7,4,6,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,5,7,6,3,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,5,7,6,4,3]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,6,3,4,5,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,2,6,3,4,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,6,3,5,4,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,6,3,5,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,6,3,7,4,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,6,3,7,5,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,6,4,3,5,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,2,6,4,3,7,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,6,4,5,3,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,6,4,5,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,6,4,7,3,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,6,4,7,5,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,6,5,3,4,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,2,6,5,3,7,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,6,5,4,3,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,6,5,4,7,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,6,5,7,3,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,6,5,7,4,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,6,7,3,4,5]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,2,6,7,3,5,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,6,7,4,3,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,6,7,4,5,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,2,6,7,5,3,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,2,6,7,5,4,3]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,7,3,4,5,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,2,7,3,4,6,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,7,3,5,4,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,7,3,5,6,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,7,3,6,4,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,7,3,6,5,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,4,3,5,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,2,7,4,3,6,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,4,5,3,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,7,4,5,6,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,2,7,4,6,3,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,7,4,6,5,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,5,3,4,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,2,7,5,3,6,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,5,4,3,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,7,5,4,6,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,5,6,3,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,2,7,5,6,4,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,6,3,4,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,2,7,6,3,5,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,6,4,3,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,7,6,4,5,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,6,5,3,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,7,6,5,4,3]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[1,3,2,4,5,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[1,3,2,4,5,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,3,2,4,6,5,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,3,2,4,6,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,3,2,4,7,5,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,3,2,4,7,6,5]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,2,5,4,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,3,2,5,4,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,5,6,4,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,3,2,5,6,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,3,2,5,7,4,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,3,2,5,7,6,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,2,6,4,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,3,2,6,4,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,6,5,4,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,2,6,5,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,6,7,4,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,3,2,6,7,5,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,2,7,4,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,3,2,7,4,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,7,5,4,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,2,7,5,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,7,6,4,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,2,7,6,5,4]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,3,4,2,5,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,3,4,2,5,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,4,2,6,5,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,4,2,6,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,4,2,7,5,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,4,2,7,6,5]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,4,5,2,6,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,3,4,5,2,7,6]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,4,5,6,2,7]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,3,4,5,6,7,2]=>[6,1]=>[[6,6],[5]]=>[5]=>0
[1,3,4,5,7,2,6]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,3,4,5,7,6,2]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,3,4,6,2,5,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,3,4,6,2,7,5]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,4,6,5,2,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,3,4,6,5,7,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,4,6,7,2,5]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,3,4,6,7,5,2]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,3,4,7,2,5,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,3,4,7,2,6,5]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,4,7,5,2,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,3,4,7,5,6,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,4,7,6,2,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,3,4,7,6,5,2]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,3,5,2,4,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,3,5,2,4,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,5,2,6,4,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,5,2,6,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,5,2,7,4,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,5,2,7,6,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,4,2,6,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,3,5,4,2,7,6]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,5,4,6,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,5,4,6,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,5,4,7,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,5,4,7,6,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,6,2,4,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,3,5,6,2,7,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,5,6,4,2,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,3,5,6,4,7,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,5,6,7,2,4]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,3,5,6,7,4,2]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,3,5,7,2,4,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,3,5,7,2,6,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,5,7,4,2,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,3,5,7,4,6,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,5,7,6,2,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,3,5,7,6,4,2]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,3,6,2,4,5,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,3,6,2,4,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,6,2,5,4,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,6,2,5,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,6,2,7,4,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,6,2,7,5,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,6,4,2,5,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,3,6,4,2,7,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,6,4,5,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,6,4,5,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,6,4,7,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,6,4,7,5,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,6,5,2,4,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,3,6,5,2,7,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,6,5,4,2,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,6,5,4,7,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,6,5,7,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,6,5,7,4,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,6,7,2,4,5]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,3,6,7,2,5,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,6,7,4,2,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,3,6,7,4,5,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,3,6,7,5,2,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,3,6,7,5,4,2]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,3,7,2,4,5,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,3,7,2,4,6,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,7,2,5,4,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,7,2,5,6,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,7,2,6,4,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,7,2,6,5,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,7,4,2,5,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,3,7,4,2,6,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,4,5,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,7,4,5,6,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,3,7,4,6,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,7,4,6,5,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,7,5,2,4,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,3,7,5,2,6,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,5,4,2,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,7,5,4,6,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,5,6,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,3,7,5,6,4,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,7,6,2,4,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,3,7,6,2,5,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,6,4,2,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,7,6,4,5,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,6,5,2,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,7,6,5,4,2]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[1,4,2,3,5,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[1,4,2,3,5,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,4,2,3,6,5,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,4,2,3,6,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,4,2,3,7,5,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,4,2,3,7,6,5]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,2,5,3,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,4,2,5,3,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,5,6,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,4,2,5,6,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,4,2,5,7,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,4,2,5,7,6,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,2,6,3,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,4,2,6,3,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,6,5,3,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,2,6,5,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,6,7,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,4,2,6,7,5,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,2,7,3,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,4,2,7,3,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,7,5,3,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,2,7,5,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,7,6,3,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,2,7,6,5,3]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,3,2,5,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,4,3,2,5,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,3,2,6,5,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,3,2,6,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,3,2,7,5,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,3,2,7,6,5]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,3,5,2,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,4,3,5,2,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,5,6,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,4,3,5,6,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,4,3,5,7,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,4,3,5,7,6,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,3,6,2,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,4,3,6,2,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,6,5,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,3,6,5,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,6,7,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,4,3,6,7,5,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,3,7,2,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,4,3,7,2,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,7,5,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,3,7,5,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,7,6,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,3,7,6,5,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,5,2,3,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,4,5,2,3,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,5,2,6,3,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,5,2,6,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,5,2,7,3,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,5,2,7,6,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,5,3,2,6,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,4,5,3,2,7,6]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,5,3,6,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,5,3,6,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,5,3,7,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,5,3,7,6,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,5,6,2,3,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,4,5,6,2,7,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,4,5,6,3,2,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,4,5,6,3,7,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,4,5,6,7,2,3]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[1,4,5,6,7,3,2]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[1,4,5,7,2,3,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,4,5,7,2,6,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,4,5,7,3,2,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,4,5,7,3,6,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,4,5,7,6,2,3]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,4,5,7,6,3,2]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,4,6,2,3,5,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,4,6,2,3,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,6,2,5,3,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,6,2,5,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,6,2,7,3,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,6,2,7,5,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,6,3,2,5,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,4,6,3,2,7,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,6,3,5,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,6,3,5,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,6,3,7,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,6,3,7,5,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,6,5,2,3,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,4,6,5,2,7,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,6,5,3,2,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,6,5,3,7,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,6,5,7,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,6,5,7,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,6,7,2,3,5]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,4,6,7,2,5,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,4,6,7,3,2,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,4,6,7,3,5,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,4,6,7,5,2,3]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,4,6,7,5,3,2]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,4,7,2,3,5,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,4,7,2,3,6,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,7,2,5,3,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,7,2,5,6,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,7,2,6,3,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,7,2,6,5,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,7,3,2,5,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,4,7,3,2,6,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,7,3,5,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,7,3,5,6,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,4,7,3,6,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,7,3,6,5,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,7,5,2,3,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,4,7,5,2,6,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,7,5,3,2,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,7,5,3,6,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,7,5,6,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,4,7,5,6,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,7,6,2,3,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,4,7,6,2,5,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,7,6,3,2,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,7,6,3,5,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,7,6,5,2,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,7,6,5,3,2]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[1,5,2,3,4,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[1,5,2,3,4,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,5,2,3,6,4,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,2,3,6,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,5,2,3,7,4,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,2,3,7,6,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,2,4,3,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,5,2,4,3,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,4,6,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,2,4,6,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,5,2,4,7,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,2,4,7,6,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,2,6,3,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,5,2,6,3,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,6,4,3,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,2,6,4,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,6,7,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,2,6,7,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,2,7,3,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,5,2,7,3,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,7,4,3,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,2,7,4,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,7,6,3,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,2,7,6,4,3]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,3,2,4,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,5,3,2,4,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,3,2,6,4,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,3,2,6,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,3,2,7,4,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,3,2,7,6,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,3,4,2,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,5,3,4,2,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,4,6,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,3,4,6,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,5,3,4,7,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,3,4,7,6,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,3,6,2,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,5,3,6,2,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,6,4,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,3,6,4,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,6,7,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,3,6,7,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,3,7,2,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,5,3,7,2,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,7,4,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,3,7,4,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,7,6,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,3,7,6,4,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,4,2,3,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,5,4,2,3,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,4,2,6,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,2,6,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,4,2,7,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,2,7,6,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,4,3,2,6,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,5,4,3,2,7,6]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,4,3,6,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,3,6,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,4,3,7,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,3,7,6,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,4,6,2,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,5,4,6,2,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,6,3,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,4,6,3,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,6,7,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,5,4,6,7,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,4,7,2,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,5,4,7,2,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,7,3,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,4,7,3,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,7,6,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,4,7,6,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,6,2,3,4,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,5,6,2,3,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,5,6,2,4,3,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,6,2,4,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,5,6,2,7,3,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,6,2,7,4,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,6,3,2,4,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,5,6,3,2,7,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,6,3,4,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,6,3,4,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,5,6,3,7,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,6,3,7,4,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,6,4,2,3,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,5,6,4,2,7,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,6,4,3,2,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,5,6,4,3,7,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,6,4,7,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,6,4,7,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,6,7,2,3,4]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[1,5,6,7,2,4,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,5,6,7,3,2,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,5,6,7,3,4,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[1,5,6,7,4,2,3]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[1,5,6,7,4,3,2]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,5,7,2,3,4,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,5,7,2,3,6,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,5,7,2,4,3,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,7,2,4,6,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,5,7,2,6,3,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,7,2,6,4,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,7,3,2,4,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,5,7,3,2,6,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,7,3,4,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,7,3,4,6,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,5,7,3,6,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,7,3,6,4,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,7,4,2,3,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,5,7,4,2,6,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,7,4,3,2,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,5,7,4,3,6,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,7,4,6,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,5,7,4,6,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,7,6,2,3,4]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,5,7,6,2,4,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,7,6,3,2,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,5,7,6,3,4,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,7,6,4,2,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,5,7,6,4,3,2]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[1,6,2,3,4,5,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[1,6,2,3,4,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,6,2,3,5,4,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,2,3,5,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,6,2,3,7,4,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,2,3,7,5,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,2,4,3,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,2,4,3,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,4,5,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,2,4,5,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,6,2,4,7,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,2,4,7,5,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,2,5,3,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,2,5,3,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,5,4,3,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,2,5,4,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,5,7,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,2,5,7,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,2,7,3,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,2,7,3,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,7,4,3,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,2,7,4,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,7,5,3,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,2,7,5,4,3]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,3,2,4,5,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,6,3,2,4,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,3,2,5,4,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,3,2,5,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,3,2,7,4,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,3,2,7,5,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,3,4,2,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,3,4,2,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,4,5,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,3,4,5,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,6,3,4,7,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,3,4,7,5,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,3,5,2,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,3,5,2,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,5,4,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,5,4,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,5,7,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,3,5,7,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,3,7,2,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,3,7,2,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,7,4,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,7,4,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,7,5,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,7,5,4,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,4,2,3,5,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,6,4,2,3,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,4,2,5,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,4,2,5,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,4,2,7,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,4,2,7,5,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,4,3,2,5,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,6,4,3,2,7,5]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,4,3,5,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,4,3,5,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,4,3,7,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,4,3,7,5,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,4,5,2,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,4,5,2,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,4,5,3,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,4,5,3,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,4,5,7,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,6,4,5,7,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,4,7,2,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,4,7,2,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,4,7,3,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,4,7,3,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,4,7,5,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,4,7,5,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,5,2,3,4,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,6,5,2,3,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,5,2,4,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,2,4,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,5,2,7,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,2,7,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,5,3,2,4,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,6,5,3,2,7,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,5,3,4,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,3,4,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,5,3,7,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,3,7,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,5,4,2,3,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,6,5,4,2,7,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,5,4,3,2,7]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[1,6,5,4,3,7,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,5,4,7,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,4,7,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,5,7,2,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,6,5,7,2,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,5,7,3,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,5,7,3,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,5,7,4,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,5,7,4,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,7,2,3,4,5]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[1,6,7,2,3,5,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,6,7,2,4,3,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,6,7,2,4,5,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,6,7,2,5,3,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,6,7,2,5,4,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,7,3,2,4,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,6,7,3,2,5,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,7,3,4,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,6,7,3,4,5,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[1,6,7,3,5,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,6,7,3,5,4,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,7,4,2,3,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,6,7,4,2,5,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,7,4,3,2,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,6,7,4,3,5,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,7,4,5,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[1,6,7,4,5,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,7,5,2,3,4]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[1,6,7,5,2,4,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,7,5,3,2,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,6,7,5,3,4,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,7,5,4,2,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,6,7,5,4,3,2]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[1,7,2,3,4,5,6]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[1,7,2,3,4,6,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,7,2,3,5,4,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,2,3,5,6,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,7,2,3,6,4,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,2,3,6,5,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,2,4,3,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,2,4,3,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,4,5,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,2,4,5,6,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,7,2,4,6,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,2,4,6,5,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,2,5,3,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,2,5,3,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,5,4,3,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,2,5,4,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,5,6,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,2,5,6,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,2,6,3,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,2,6,3,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,6,4,3,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,2,6,4,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,6,5,3,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,2,6,5,4,3]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,3,2,4,5,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,7,3,2,4,6,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,3,2,5,4,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,3,2,5,6,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,3,2,6,4,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,3,2,6,5,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,3,4,2,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,3,4,2,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,4,5,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,3,4,5,6,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[1,7,3,4,6,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,3,4,6,5,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,3,5,2,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,3,5,2,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,5,4,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,3,5,4,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,5,6,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,3,5,6,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,3,6,2,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,3,6,2,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,6,4,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,3,6,4,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,6,5,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,3,6,5,4,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,4,2,3,5,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,7,4,2,3,6,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,4,2,5,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,4,2,5,6,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,4,2,6,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,4,2,6,5,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,4,3,2,5,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,7,4,3,2,6,5]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,4,3,5,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,4,3,5,6,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,4,3,6,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,4,3,6,5,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,4,5,2,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,4,5,2,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,5,3,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,4,5,3,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,5,6,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[1,7,4,5,6,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,4,6,2,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,4,6,2,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,6,3,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,4,6,3,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,6,5,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,4,6,5,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,5,2,3,4,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,7,5,2,3,6,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,5,2,4,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,5,2,4,6,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,5,2,6,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,5,2,6,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,3,2,4,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,7,5,3,2,6,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,5,3,4,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,5,3,4,6,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,5,3,6,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,5,3,6,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,4,2,3,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,7,5,4,2,6,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,5,4,3,2,6]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[1,7,5,4,3,6,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,5,4,6,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,5,4,6,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,6,2,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[1,7,5,6,2,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,5,6,3,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,5,6,3,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,5,6,4,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,5,6,4,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,6,2,3,4,5]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[1,7,6,2,3,5,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,6,2,4,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,6,2,4,5,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,6,2,5,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,6,2,5,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,6,3,2,4,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,7,6,3,2,5,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,3,4,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,6,3,4,5,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,6,3,5,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,6,3,5,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,6,4,2,3,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,7,6,4,2,5,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,4,3,2,5]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[1,7,6,4,3,5,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,4,5,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,6,4,5,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,6,5,2,3,4]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[1,7,6,5,2,4,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,5,3,2,4]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[1,7,6,5,3,4,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,5,4,2,3]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,1,3,4,5,7,6]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[2,1,3,4,6,5,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,3,4,6,7,5]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[2,1,3,4,7,5,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,3,4,7,6,5]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[2,1,3,5,4,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,3,5,4,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,3,5,6,4,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,3,5,6,7,4]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[2,1,3,5,7,4,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,3,5,7,6,4]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[2,1,3,6,4,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,3,6,4,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,3,6,5,4,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,3,6,5,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,3,6,7,4,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,3,6,7,5,4]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[2,1,3,7,4,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,3,7,4,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,3,7,5,4,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,3,7,5,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,3,7,6,4,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,3,7,6,5,4]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,4,3,5,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[2,1,4,3,5,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,4,3,6,5,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,4,3,6,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,4,3,7,5,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,4,3,7,6,5]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,4,5,3,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,4,5,3,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,4,5,6,3,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,4,5,6,7,3]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[2,1,4,5,7,3,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,4,5,7,6,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[2,1,4,6,3,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,4,6,3,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,4,6,5,3,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,4,6,5,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,4,6,7,3,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,4,6,7,5,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[2,1,4,7,3,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,4,7,3,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,4,7,5,3,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,4,7,5,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,4,7,6,3,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,4,7,6,5,3]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,5,3,4,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[2,1,5,3,4,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,5,3,6,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,5,3,6,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,5,3,7,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,5,3,7,6,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,5,4,3,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[2,1,5,4,3,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,5,4,6,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,5,4,6,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,5,4,7,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,5,4,7,6,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,5,6,3,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,5,6,3,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,5,6,4,3,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,5,6,4,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,5,6,7,3,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[2,1,5,6,7,4,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[2,1,5,7,3,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,5,7,3,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,5,7,4,3,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,5,7,4,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,5,7,6,3,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,5,7,6,4,3]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,6,3,4,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[2,1,6,3,4,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,6,3,5,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,3,5,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,6,3,7,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,3,7,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,6,4,3,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[2,1,6,4,3,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,6,4,5,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,4,5,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,6,4,7,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,4,7,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,6,5,3,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[2,1,6,5,3,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,6,5,4,3,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[2,1,6,5,4,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,6,5,7,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,5,7,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,6,7,3,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[2,1,6,7,3,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,6,7,4,3,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,6,7,4,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[2,1,6,7,5,3,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[2,1,6,7,5,4,3]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,7,3,4,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[2,1,7,3,4,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,7,3,5,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,3,5,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,7,3,6,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,3,6,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,7,4,3,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[2,1,7,4,3,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,4,5,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,4,5,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[2,1,7,4,6,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,4,6,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,7,5,3,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[2,1,7,5,3,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,5,4,3,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[2,1,7,5,4,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,5,6,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,5,6,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,7,6,3,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[2,1,7,6,3,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,6,4,3,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[2,1,7,6,4,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,6,5,3,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,3,1,4,5,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[2,3,1,4,5,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,3,1,4,6,5,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,3,1,4,6,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,3,1,4,7,5,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,3,1,4,7,6,5]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,1,5,4,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,3,1,5,4,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,5,6,4,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,3,1,5,6,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,3,1,5,7,4,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,3,1,5,7,6,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,1,6,4,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,3,1,6,4,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,6,5,4,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,1,6,5,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,6,7,4,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,3,1,6,7,5,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,1,7,4,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,3,1,7,4,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,7,5,4,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,1,7,5,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,7,6,4,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,1,7,6,5,4]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,3,4,1,5,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,3,4,1,5,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,4,1,6,5,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,4,1,6,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,4,1,7,5,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,4,1,7,6,5]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,4,5,1,6,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,3,4,5,1,7,6]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,4,5,6,1,7]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[2,3,4,5,6,7,1]=>[6,1]=>[[6,6],[5]]=>[5]=>0
[2,3,4,5,7,1,6]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[2,3,4,5,7,6,1]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[2,3,4,6,1,5,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,3,4,6,1,7,5]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,4,6,5,1,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,3,4,6,5,7,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,4,6,7,1,5]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[2,3,4,6,7,5,1]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[2,3,4,7,1,5,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,3,4,7,1,6,5]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,4,7,5,1,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,3,4,7,5,6,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,4,7,6,1,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,3,4,7,6,5,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,3,5,1,4,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,3,5,1,4,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,5,1,6,4,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,5,1,6,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,5,1,7,4,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,5,1,7,6,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,5,4,1,6,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,3,5,4,1,7,6]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,5,4,6,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,5,4,6,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,5,4,7,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,5,4,7,6,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,5,6,1,4,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,3,5,6,1,7,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,5,6,4,1,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,3,5,6,4,7,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,5,6,7,1,4]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[2,3,5,6,7,4,1]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[2,3,5,7,1,4,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,3,5,7,1,6,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,5,7,4,1,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,3,5,7,4,6,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,5,7,6,1,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,3,5,7,6,4,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,3,6,1,4,5,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,3,6,1,4,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,6,1,5,4,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,6,1,5,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,6,1,7,4,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,6,1,7,5,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,6,4,1,5,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,3,6,4,1,7,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,6,4,5,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,6,4,5,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,6,4,7,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,6,4,7,5,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,6,5,1,4,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,3,6,5,1,7,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,6,5,4,1,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,3,6,5,4,7,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,6,5,7,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,6,5,7,4,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,6,7,1,4,5]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,3,6,7,1,5,4]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,6,7,4,1,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,3,6,7,4,5,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,3,6,7,5,1,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,3,6,7,5,4,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,3,7,1,4,5,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,3,7,1,4,6,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,7,1,5,4,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,7,1,5,6,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,7,1,6,4,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,7,1,6,5,4]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,7,4,1,5,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,3,7,4,1,6,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,7,4,5,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,7,4,5,6,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,3,7,4,6,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,7,4,6,5,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,7,5,1,4,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,3,7,5,1,6,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,7,5,4,1,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,3,7,5,4,6,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,7,5,6,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,3,7,5,6,4,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,7,6,1,4,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,3,7,6,1,5,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,7,6,4,1,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,3,7,6,4,5,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,7,6,5,1,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,3,7,6,5,4,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[2,4,1,3,5,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[2,4,1,3,5,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,4,1,3,6,5,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,4,1,3,6,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,4,1,3,7,5,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,4,1,3,7,6,5]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,1,5,3,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,4,1,5,3,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,1,5,6,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,4,1,5,6,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,4,1,5,7,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,4,1,5,7,6,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,1,6,3,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,4,1,6,3,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,1,6,5,3,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,1,6,5,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,1,6,7,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,4,1,6,7,5,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,1,7,3,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,4,1,7,3,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,1,7,5,3,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,1,7,5,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,1,7,6,3,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,1,7,6,5,3]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,3,1,5,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,4,3,1,5,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,3,1,6,5,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,4,3,1,6,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,3,1,7,5,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,4,3,1,7,6,5]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,3,5,1,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,4,3,5,1,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,5,6,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,4,3,5,6,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,4,3,5,7,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,4,3,5,7,6,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,3,6,1,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,4,3,6,1,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,6,5,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,3,6,5,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,6,7,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,4,3,6,7,5,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,3,7,1,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,4,3,7,1,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,7,5,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,3,7,5,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,7,6,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,3,7,6,5,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,5,1,3,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,4,5,1,3,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,5,1,6,3,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,5,1,6,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,5,1,7,3,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,5,1,7,6,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,5,3,1,6,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,4,5,3,1,7,6]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,5,3,6,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,5,3,6,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,5,3,7,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,5,3,7,6,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,5,6,1,3,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,4,5,6,1,7,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,4,5,6,3,1,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,4,5,6,3,7,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,4,5,6,7,1,3]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[2,4,5,6,7,3,1]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[2,4,5,7,1,3,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,4,5,7,1,6,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,4,5,7,3,1,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,4,5,7,3,6,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,4,5,7,6,1,3]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,4,5,7,6,3,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,6,1,3,5,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,4,6,1,3,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,6,1,5,3,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,6,1,5,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,6,1,7,3,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,6,1,7,5,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,3,1,5,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,4,6,3,1,7,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,6,3,5,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,6,3,5,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,6,3,7,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,6,3,7,5,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,5,1,3,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,4,6,5,1,7,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,6,5,3,1,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,4,6,5,3,7,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,6,5,7,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,6,5,7,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,7,1,3,5]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,4,6,7,1,5,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,4,6,7,3,1,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,4,6,7,3,5,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,4,6,7,5,1,3]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,4,6,7,5,3,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,7,1,3,5,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,4,7,1,3,6,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,7,1,5,3,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,7,1,5,6,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,7,1,6,3,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,7,1,6,5,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,7,3,1,5,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,4,7,3,1,6,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,3,5,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,7,3,5,6,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,4,7,3,6,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,7,3,6,5,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,7,5,1,3,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,4,7,5,1,6,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,5,3,1,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,4,7,5,3,6,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,5,6,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,4,7,5,6,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,7,6,1,3,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,4,7,6,1,5,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,6,3,1,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,4,7,6,3,5,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,6,5,1,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,4,7,6,5,3,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[2,5,1,3,4,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[2,5,1,3,4,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,5,1,3,6,4,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,1,3,6,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,5,1,3,7,4,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,1,3,7,6,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,1,4,3,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,5,1,4,3,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,4,6,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,1,4,6,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,5,1,4,7,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,1,4,7,6,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,1,6,3,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,5,1,6,3,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,6,4,3,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,1,6,4,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,6,7,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,1,6,7,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,1,7,3,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,5,1,7,3,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,7,4,3,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,1,7,4,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,7,6,3,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,1,7,6,4,3]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,3,1,4,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,5,3,1,4,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,3,1,6,4,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,3,1,6,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,3,1,7,4,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,3,1,7,6,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,3,4,1,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,5,3,4,1,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,4,6,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,3,4,6,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,5,3,4,7,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,3,4,7,6,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,3,6,1,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,5,3,6,1,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,6,4,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,3,6,4,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,6,7,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,3,6,7,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,3,7,1,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,5,3,7,1,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,7,4,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,3,7,4,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,7,6,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,3,7,6,4,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,4,1,3,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,5,4,1,3,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,4,1,6,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,1,6,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,4,1,7,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,1,7,6,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,4,3,1,6,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,5,4,3,1,7,6]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,5,4,3,6,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,3,6,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,4,3,7,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,3,7,6,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,4,6,1,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,5,4,6,1,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,4,6,3,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,4,6,3,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,4,6,7,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,5,4,6,7,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,4,7,1,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,5,4,7,1,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,4,7,3,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,4,7,3,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,4,7,6,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,4,7,6,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,6,1,3,4,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,5,6,1,3,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,5,6,1,4,3,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,6,1,4,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,5,6,1,7,3,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,6,1,7,4,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,6,3,1,4,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,5,6,3,1,7,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,6,3,4,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,6,3,4,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,5,6,3,7,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,6,3,7,4,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,6,4,1,3,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,5,6,4,1,7,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,6,4,3,1,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,5,6,4,3,7,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,6,4,7,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,6,4,7,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,6,7,1,3,4]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[2,5,6,7,1,4,3]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,5,6,7,3,1,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,5,6,7,3,4,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[2,5,6,7,4,1,3]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[2,5,6,7,4,3,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,5,7,1,3,4,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,5,7,1,3,6,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,5,7,1,4,3,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,7,1,4,6,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,5,7,1,6,3,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,7,1,6,4,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,7,3,1,4,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,5,7,3,1,6,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,3,4,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,7,3,4,6,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,5,7,3,6,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,7,3,6,4,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,7,4,1,3,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,5,7,4,1,6,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,4,3,1,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,5,7,4,3,6,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,4,6,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,5,7,4,6,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,7,6,1,3,4]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,5,7,6,1,4,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,6,3,1,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,5,7,6,3,4,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,6,4,1,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,5,7,6,4,3,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[2,6,1,3,4,5,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[2,6,1,3,4,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,6,1,3,5,4,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,1,3,5,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,6,1,3,7,4,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,1,3,7,5,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,1,4,3,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,1,4,3,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,4,5,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,1,4,5,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,6,1,4,7,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,1,4,7,5,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,1,5,3,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,1,5,3,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,5,4,3,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,1,5,4,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,5,7,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,1,5,7,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,1,7,3,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,1,7,3,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,7,4,3,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,1,7,4,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,7,5,3,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,1,7,5,4,3]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,3,1,4,5,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,6,3,1,4,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,3,1,5,4,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,3,1,5,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,3,1,7,4,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,3,1,7,5,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,3,4,1,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,3,4,1,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,4,5,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,3,4,5,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,6,3,4,7,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,3,4,7,5,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,3,5,1,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,3,5,1,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,5,4,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,5,4,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,5,7,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,3,5,7,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,3,7,1,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,3,7,1,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,7,4,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,7,4,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,7,5,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,7,5,4,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,4,1,3,5,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,6,4,1,3,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,4,1,5,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,4,1,5,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,4,1,7,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,4,1,7,5,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,4,3,1,5,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,6,4,3,1,7,5]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,4,3,5,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,4,3,5,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,4,3,7,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,4,3,7,5,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,4,5,1,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,4,5,1,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,5,3,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,5,3,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,5,7,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,6,4,5,7,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,4,7,1,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,4,7,1,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,7,3,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,7,3,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,7,5,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,7,5,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,5,1,3,4,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,6,5,1,3,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,5,1,4,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,1,4,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,5,1,7,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,1,7,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,5,3,1,4,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,6,5,3,1,7,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,5,3,4,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,3,4,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,5,3,7,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,3,7,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,5,4,1,3,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,6,5,4,1,7,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,5,4,3,1,7]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[2,6,5,4,3,7,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,5,4,7,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,4,7,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,5,7,1,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,6,5,7,1,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,7,3,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,5,7,3,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,7,4,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,5,7,4,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,7,1,3,4,5]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[2,6,7,1,3,5,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,6,7,1,4,3,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,6,7,1,4,5,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,6,7,1,5,3,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,6,7,1,5,4,3]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,7,3,1,4,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,6,7,3,1,5,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,7,3,4,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,6,7,3,4,5,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[2,6,7,3,5,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,6,7,3,5,4,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,7,4,1,3,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,6,7,4,1,5,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,7,4,3,1,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,7,4,3,5,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,7,4,5,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[2,6,7,4,5,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,7,5,1,3,4]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[2,6,7,5,1,4,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,7,5,3,1,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,7,5,3,4,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,7,5,4,1,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,7,5,4,3,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[2,7,1,3,4,5,6]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[2,7,1,3,4,6,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,7,1,3,5,4,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,1,3,5,6,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,7,1,3,6,4,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,1,3,6,5,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,1,4,3,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,1,4,3,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,4,5,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,1,4,5,6,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,7,1,4,6,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,1,4,6,5,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,1,5,3,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,1,5,3,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,5,4,3,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,1,5,4,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,5,6,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,1,5,6,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,1,6,3,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,1,6,3,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,6,4,3,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,1,6,4,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,6,5,3,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,1,6,5,4,3]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,3,1,4,5,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,7,3,1,4,6,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,3,1,5,4,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,3,1,5,6,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,3,1,6,4,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,3,1,6,5,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,3,4,1,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,3,4,1,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,4,5,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,3,4,5,6,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[2,7,3,4,6,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,3,4,6,5,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,3,5,1,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,3,5,1,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,5,4,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,3,5,4,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,5,6,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,3,5,6,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,3,6,1,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,3,6,1,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,6,4,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,3,6,4,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,6,5,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,3,6,5,4,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,4,1,3,5,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,7,4,1,3,6,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,4,1,5,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,4,1,5,6,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,4,1,6,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,4,1,6,5,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,4,3,1,5,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,7,4,3,1,6,5]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,4,3,5,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,4,3,5,6,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,4,3,6,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,4,3,6,5,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,4,5,1,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,4,5,1,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,5,3,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,4,5,3,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,5,6,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[2,7,4,5,6,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,4,6,1,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,4,6,1,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,6,3,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,4,6,3,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,6,5,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,4,6,5,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,5,1,3,4,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,7,5,1,3,6,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,5,1,4,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,5,1,4,6,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,5,1,6,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,5,1,6,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,3,1,4,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,7,5,3,1,6,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,5,3,4,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,5,3,4,6,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,5,3,6,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,5,3,6,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,4,1,3,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,7,5,4,1,6,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,5,4,3,1,6]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[2,7,5,4,3,6,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,5,4,6,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,5,4,6,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,6,1,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[2,7,5,6,1,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,5,6,3,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,5,6,3,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,5,6,4,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,5,6,4,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,6,1,3,4,5]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[2,7,6,1,3,5,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,6,1,4,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,6,1,4,5,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,6,1,5,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,6,1,5,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,6,3,1,4,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,7,6,3,1,5,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,3,4,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,6,3,4,5,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,6,3,5,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,6,3,5,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,6,4,1,3,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,7,6,4,1,5,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,4,3,1,5]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[2,7,6,4,3,5,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,4,5,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,6,4,5,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,6,5,1,3,4]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[2,7,6,5,1,4,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,5,3,1,4]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[2,7,6,5,3,4,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,5,4,1,3]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[3,1,2,4,5,7,6]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[3,1,2,4,6,5,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,2,4,6,7,5]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[3,1,2,4,7,5,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,2,4,7,6,5]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,1,2,5,4,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,2,5,4,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,2,5,6,4,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,2,5,6,7,4]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[3,1,2,5,7,4,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,2,5,7,6,4]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,1,2,6,4,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,2,6,4,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,2,6,5,4,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,2,6,5,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,2,6,7,4,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,2,6,7,5,4]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,1,2,7,4,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,2,7,4,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,2,7,5,4,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,2,7,5,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,2,7,6,4,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,2,7,6,5,4]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,1,4,2,5,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[3,1,4,2,5,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,4,2,6,5,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,4,2,6,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,4,2,7,5,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,4,2,7,6,5]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,4,5,2,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,4,5,2,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,4,5,6,2,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,4,5,6,7,2]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[3,1,4,5,7,2,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,4,5,7,6,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,1,4,6,2,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,4,6,2,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,4,6,5,2,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,4,6,5,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,4,6,7,2,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,4,6,7,5,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,1,4,7,2,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,4,7,2,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,4,7,5,2,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,4,7,5,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,4,7,6,2,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,4,7,6,5,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,1,5,2,4,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[3,1,5,2,4,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,5,2,6,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,5,2,6,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,5,2,7,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,5,2,7,6,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,5,4,2,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,1,5,4,2,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,5,4,6,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,5,4,6,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,5,4,7,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,5,4,7,6,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,5,6,2,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,5,6,2,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,5,6,4,2,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,5,6,4,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,5,6,7,2,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,1,5,6,7,4,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,1,5,7,2,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,5,7,2,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,5,7,4,2,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,5,7,4,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,5,7,6,2,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,5,7,6,4,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,1,6,2,4,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[3,1,6,2,4,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,6,2,5,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,2,5,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,6,2,7,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,2,7,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,6,4,2,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,1,6,4,2,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,4,5,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,4,5,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,6,4,7,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,4,7,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,6,5,2,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,1,6,5,2,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,5,4,2,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,1,6,5,4,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,5,7,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,5,7,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,6,7,2,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,1,6,7,2,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,6,7,4,2,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,6,7,4,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,1,6,7,5,2,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,1,6,7,5,4,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,1,7,2,4,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[3,1,7,2,4,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,7,2,5,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,2,5,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,7,2,6,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,2,6,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,7,4,2,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,1,7,4,2,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,4,5,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,4,5,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,1,7,4,6,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,4,6,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,7,5,2,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,1,7,5,2,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,5,4,2,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,1,7,5,4,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,5,6,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,5,6,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,7,6,2,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,1,7,6,2,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,6,4,2,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,1,7,6,4,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,6,5,2,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,1,7,6,5,4,2]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,2,1,4,5,7,6]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[3,2,1,4,6,5,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[3,2,1,4,6,7,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[3,2,1,4,7,5,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[3,2,1,4,7,6,5]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,1,5,4,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[3,2,1,5,4,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,5,6,4,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[3,2,1,5,6,7,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[3,2,1,5,7,4,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[3,2,1,5,7,6,4]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,1,6,4,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[3,2,1,6,4,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,6,5,4,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[3,2,1,6,5,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,6,7,4,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[3,2,1,6,7,5,4]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,1,7,4,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[3,2,1,7,4,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,7,5,4,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[3,2,1,7,5,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,7,6,4,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,4,1,5,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[3,2,4,1,5,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,4,1,6,5,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,4,1,6,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,4,1,7,5,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,4,1,7,6,5]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,4,5,1,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,2,4,5,1,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,5,6,1,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,2,4,5,6,7,1]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[3,2,4,5,7,1,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,2,4,5,7,6,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,2,4,6,1,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,2,4,6,1,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,6,5,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,2,4,6,5,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,6,7,1,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,2,4,6,7,5,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,2,4,7,1,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,2,4,7,1,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,7,5,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,2,4,7,5,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,7,6,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,2,4,7,6,5,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,5,1,4,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[3,2,5,1,4,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,5,1,6,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,5,1,6,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,5,1,7,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,5,1,7,6,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,5,4,1,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,2,5,4,1,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,5,4,6,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,5,4,6,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,5,4,7,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,5,4,7,6,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,5,6,1,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,2,5,6,1,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,5,6,4,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,2,5,6,4,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,5,6,7,1,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[3,2,5,6,7,4,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[3,2,5,7,1,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,2,5,7,1,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,5,7,4,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,2,5,7,4,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,5,7,6,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,2,5,7,6,4,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,6,1,4,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[3,2,6,1,4,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,6,1,5,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,1,5,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,6,1,7,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,1,7,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,6,4,1,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,2,6,4,1,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,6,4,5,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,4,5,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,6,4,7,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,4,7,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,6,5,1,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,2,6,5,1,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,6,5,4,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,2,6,5,4,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,6,5,7,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,5,7,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,6,7,1,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[3,2,6,7,1,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,6,7,4,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,2,6,7,4,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[3,2,6,7,5,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[3,2,6,7,5,4,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,7,1,4,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[3,2,7,1,4,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,7,1,5,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,1,5,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,7,1,6,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,1,6,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,4,1,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,2,7,4,1,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,7,4,5,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,4,5,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[3,2,7,4,6,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,4,6,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,5,1,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,2,7,5,1,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,7,5,4,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,2,7,5,4,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,7,5,6,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,5,6,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,6,1,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[3,2,7,6,1,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,7,6,4,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,2,7,6,4,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,7,6,5,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[3,2,7,6,5,4,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,4,1,2,5,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[3,4,1,2,5,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,4,1,2,6,5,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,4,1,2,6,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,4,1,2,7,5,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,4,1,2,7,6,5]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,4,1,5,2,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,4,1,5,2,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,5,6,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,4,1,5,6,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,4,1,5,7,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,4,1,5,7,6,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,4,1,6,2,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,4,1,6,2,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,6,5,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,1,6,5,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,6,7,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,4,1,6,7,5,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,4,1,7,2,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,4,1,7,2,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,7,5,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,1,7,5,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,7,6,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,1,7,6,5,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,2,1,5,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,4,2,1,5,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,2,1,6,5,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,4,2,1,6,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,2,1,7,5,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,4,2,1,7,6,5]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,2,5,1,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,4,2,5,1,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,5,6,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,4,2,5,6,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,4,2,5,7,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,4,2,5,7,6,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,4,2,6,1,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,4,2,6,1,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,6,5,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,6,5,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,6,7,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,4,2,6,7,5,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,4,2,7,1,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,4,2,7,1,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,7,5,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,7,5,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,7,6,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,7,6,5,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,5,1,2,6,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[3,4,5,1,2,7,6]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,5,1,6,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,5,1,6,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,5,1,7,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,5,1,7,6,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,5,2,1,6,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,4,5,2,1,7,6]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,5,2,6,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,5,2,6,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,5,2,7,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,5,2,7,6,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,5,6,1,2,7]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[3,4,5,6,1,7,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[3,4,5,6,2,1,7]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[3,4,5,6,2,7,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[3,4,5,6,7,1,2]=>[5,2]=>[[6,5],[4]]=>[4]=>0
[3,4,5,6,7,2,1]=>[5,1,1]=>[[5,5,5],[4,4]]=>[4,4]=>0
[3,4,5,7,1,2,6]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[3,4,5,7,1,6,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[3,4,5,7,2,1,6]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[3,4,5,7,2,6,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[3,4,5,7,6,1,2]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[3,4,5,7,6,2,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,4,6,1,2,5,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[3,4,6,1,2,7,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,6,1,5,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,6,1,5,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,6,1,7,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,6,1,7,5,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,6,2,1,5,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,4,6,2,1,7,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,6,2,5,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,6,2,5,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,6,2,7,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,6,2,7,5,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,6,5,1,2,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,4,6,5,1,7,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,6,5,2,1,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,4,6,5,2,7,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,6,5,7,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,6,5,7,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,6,7,1,2,5]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[3,4,6,7,1,5,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[3,4,6,7,2,1,5]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[3,4,6,7,2,5,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[3,4,6,7,5,1,2]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[3,4,6,7,5,2,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,4,7,1,2,5,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[3,4,7,1,2,6,5]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,7,1,5,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,7,1,5,6,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,7,1,6,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,7,1,6,5,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,7,2,1,5,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,4,7,2,1,6,5]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,2,5,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,7,2,5,6,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,4,7,2,6,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,7,2,6,5,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,7,5,1,2,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,4,7,5,1,6,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,5,2,1,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,4,7,5,2,6,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,5,6,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,4,7,5,6,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,7,6,1,2,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,4,7,6,1,5,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,6,2,1,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,4,7,6,2,5,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,6,5,1,2]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,4,7,6,5,2,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[3,5,1,2,4,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[3,5,1,2,4,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,5,1,2,6,4,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,1,2,6,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,5,1,2,7,4,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,1,2,7,6,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,1,4,2,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,5,1,4,2,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,4,6,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,1,4,6,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,5,1,4,7,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,1,4,7,6,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,1,6,2,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,5,1,6,2,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,6,4,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,1,6,4,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,6,7,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,1,6,7,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,1,7,2,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,5,1,7,2,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,7,4,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,1,7,4,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,7,6,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,1,7,6,4,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,2,1,4,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,5,2,1,4,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,2,1,6,4,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,2,1,6,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,2,1,7,4,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,2,1,7,6,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,2,4,1,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,5,2,4,1,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,4,6,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,2,4,6,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,5,2,4,7,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,2,4,7,6,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,2,6,1,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,5,2,6,1,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,6,4,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,2,6,4,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,6,7,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,2,6,7,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,2,7,1,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,5,2,7,1,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,7,4,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,2,7,4,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,7,6,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,2,7,6,4,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,4,1,2,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,5,4,1,2,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,4,1,6,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,1,6,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,4,1,7,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,1,7,6,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,4,2,1,6,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,5,4,2,1,7,6]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,4,2,6,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,2,6,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,4,2,7,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,2,7,6,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,4,6,1,2,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,5,4,6,1,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,6,2,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,4,6,2,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,6,7,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,5,4,6,7,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,4,7,1,2,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,5,4,7,1,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,7,2,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,4,7,2,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,7,6,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,4,7,6,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,6,1,2,4,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[3,5,6,1,2,7,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,5,6,1,4,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,6,1,4,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,5,6,1,7,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,6,1,7,4,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,2,1,4,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,5,6,2,1,7,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,6,2,4,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,6,2,4,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,5,6,2,7,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,6,2,7,4,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,4,1,2,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,5,6,4,1,7,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,6,4,2,1,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,6,4,2,7,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,6,4,7,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,6,4,7,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,7,1,2,4]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[3,5,6,7,1,4,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[3,5,6,7,2,1,4]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[3,5,6,7,2,4,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[3,5,6,7,4,1,2]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[3,5,6,7,4,2,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,5,7,1,2,4,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[3,5,7,1,2,6,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,5,7,1,4,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,7,1,4,6,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,5,7,1,6,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,7,1,6,4,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,7,2,1,4,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,5,7,2,1,6,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,2,4,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,7,2,4,6,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,5,7,2,6,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,7,2,6,4,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,7,4,1,2,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,5,7,4,1,6,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,4,2,1,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,7,4,2,6,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,4,6,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,5,7,4,6,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,7,6,1,2,4]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,5,7,6,1,4,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,6,2,1,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,7,6,2,4,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,6,4,1,2]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,7,6,4,2,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[3,6,1,2,4,5,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[3,6,1,2,4,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,6,1,2,5,4,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,1,2,5,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,6,1,2,7,4,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,1,2,7,5,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,1,4,2,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,1,4,2,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,4,5,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,1,4,5,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,6,1,4,7,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,1,4,7,5,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,1,5,2,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,1,5,2,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,5,4,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,1,5,4,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,5,7,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,1,5,7,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,1,7,2,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,1,7,2,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,7,4,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,1,7,4,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,7,5,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,1,7,5,4,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,2,1,4,5,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,6,2,1,4,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,2,1,5,4,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,2,1,5,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,2,1,7,4,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,2,1,7,5,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,2,4,1,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,2,4,1,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,2,4,5,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,2,4,5,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,6,2,4,7,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,2,4,7,5,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,5,1,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,2,5,1,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,2,5,4,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,2,5,4,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,2,5,7,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,2,5,7,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,7,1,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,2,7,1,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,2,7,4,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,2,7,4,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,2,7,5,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,2,7,5,4,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,4,1,2,5,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,6,4,1,2,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,4,1,5,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,4,1,5,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,4,1,7,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,4,1,7,5,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,4,2,1,5,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,6,4,2,1,7,5]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,4,2,5,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,4,2,5,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,4,2,7,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,4,2,7,5,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,4,5,1,2,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,4,5,1,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,5,2,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,4,5,2,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,5,7,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,6,4,5,7,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,4,7,1,2,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,4,7,1,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,7,2,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,4,7,2,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,7,5,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,4,7,5,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,5,1,2,4,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,6,5,1,2,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,5,1,4,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,1,4,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,5,1,7,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,1,7,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,2,1,4,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,6,5,2,1,7,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,5,2,4,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,2,4,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,5,2,7,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,2,7,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,4,1,2,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,6,5,4,1,7,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,5,4,2,1,7]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[3,6,5,4,2,7,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,5,4,7,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,4,7,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,7,1,2,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,6,5,7,1,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,5,7,2,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,5,7,2,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,5,7,4,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,5,7,4,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,7,1,2,4,5]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[3,6,7,1,2,5,4]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,6,7,1,4,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,6,7,1,4,5,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,6,7,1,5,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,6,7,1,5,4,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,7,2,1,4,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,6,7,2,1,5,4]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,7,2,4,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,6,7,2,4,5,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[3,6,7,2,5,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,6,7,2,5,4,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,7,4,1,2,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,6,7,4,1,5,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,7,4,2,1,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,6,7,4,2,5,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,7,4,5,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[3,6,7,4,5,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,7,5,1,2,4]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[3,6,7,5,1,4,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,7,5,2,1,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,6,7,5,2,4,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,7,5,4,1,2]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,6,7,5,4,2,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[3,7,1,2,4,5,6]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[3,7,1,2,4,6,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,7,1,2,5,4,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,1,2,5,6,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,7,1,2,6,4,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,1,2,6,5,4]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,1,4,2,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,1,4,2,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,4,5,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,1,4,5,6,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,7,1,4,6,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,1,4,6,5,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,1,5,2,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,1,5,2,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,5,4,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,1,5,4,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,5,6,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,1,5,6,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,1,6,2,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,1,6,2,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,6,4,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,1,6,4,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,6,5,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,1,6,5,4,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,2,1,4,5,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,7,2,1,4,6,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,2,1,5,4,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,2,1,5,6,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,2,1,6,4,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,2,1,6,5,4]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,2,4,1,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,2,4,1,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,4,5,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,2,4,5,6,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[3,7,2,4,6,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,2,4,6,5,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,2,5,1,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,2,5,1,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,5,4,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,2,5,4,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,5,6,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,2,5,6,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,2,6,1,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,2,6,1,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,6,4,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,2,6,4,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,6,5,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,2,6,5,4,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,4,1,2,5,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,7,4,1,2,6,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,4,1,5,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,4,1,5,6,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,4,1,6,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,4,1,6,5,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,4,2,1,5,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,7,4,2,1,6,5]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,4,2,5,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,4,2,5,6,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,4,2,6,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,4,2,6,5,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,4,5,1,2,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,4,5,1,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,5,2,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,4,5,2,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,5,6,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[3,7,4,5,6,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,4,6,1,2,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,4,6,1,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,6,2,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,4,6,2,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,6,5,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,4,6,5,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,5,1,2,4,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,7,5,1,2,6,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,5,1,4,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,5,1,4,6,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,5,1,6,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,5,1,6,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,5,2,1,4,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,7,5,2,1,6,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,5,2,4,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,5,2,4,6,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,5,2,6,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,5,2,6,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,5,4,1,2,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,7,5,4,1,6,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,5,4,2,1,6]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[3,7,5,4,2,6,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,5,4,6,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,5,4,6,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,5,6,1,2,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[3,7,5,6,1,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,6,2,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,5,6,2,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,6,4,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,5,6,4,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,6,1,2,4,5]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[3,7,6,1,2,5,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,6,1,4,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,6,1,4,5,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,6,1,5,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,6,1,5,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,2,1,4,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,7,6,2,1,5,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,2,4,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,6,2,4,5,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,6,2,5,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,6,2,5,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,4,1,2,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,7,6,4,1,5,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,4,2,1,5]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[3,7,6,4,2,5,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,4,5,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,6,4,5,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,5,1,2,4]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[3,7,6,5,1,4,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,5,2,1,4]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[3,7,6,5,2,4,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,5,4,1,2]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,1,2,3,5,7,6]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[4,1,2,3,6,5,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,2,3,6,7,5]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[4,1,2,3,7,5,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,2,3,7,6,5]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,1,2,5,3,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,2,5,3,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,2,5,6,3,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,2,5,6,7,3]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[4,1,2,5,7,3,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,2,5,7,6,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,1,2,6,3,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,2,6,3,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,2,6,5,3,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,2,6,5,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,2,6,7,3,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,2,6,7,5,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,1,2,7,3,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,2,7,3,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,2,7,5,3,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,2,7,5,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,2,7,6,3,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,2,7,6,5,3]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,3,2,5,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,1,3,2,5,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,3,2,6,5,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,3,2,6,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,3,2,7,5,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,3,2,7,6,5]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,3,5,2,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,3,5,2,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,5,6,2,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,3,5,6,7,2]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[4,1,3,5,7,2,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,3,5,7,6,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,1,3,6,2,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,3,6,2,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,6,5,2,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,3,6,5,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,6,7,2,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,3,6,7,5,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,1,3,7,2,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,3,7,2,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,7,5,2,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,3,7,5,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,7,6,2,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,3,7,6,5,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,5,2,3,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,1,5,2,3,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,5,2,6,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,2,6,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,5,2,7,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,2,7,6,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,5,3,2,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,1,5,3,2,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,5,3,6,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,3,6,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,5,3,7,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,3,7,6,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,5,6,2,3,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,5,6,2,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,5,6,3,2,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,5,6,3,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,5,6,7,2,3]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,1,5,6,7,3,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,1,5,7,2,3,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,5,7,2,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,5,7,3,2,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,5,7,3,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,5,7,6,2,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,5,7,6,3,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,6,2,3,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,1,6,2,3,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,6,2,5,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,2,5,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,6,2,7,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,2,7,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,6,3,2,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,1,6,3,2,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,6,3,5,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,3,5,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,6,3,7,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,3,7,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,6,5,2,3,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,1,6,5,2,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,6,5,3,2,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,1,6,5,3,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,6,5,7,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,5,7,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,6,7,2,3,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,1,6,7,2,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,6,7,3,2,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,6,7,3,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,1,6,7,5,2,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,1,6,7,5,3,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,7,2,3,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,1,7,2,3,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,7,2,5,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,2,5,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,7,2,6,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,2,6,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,3,2,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,1,7,3,2,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,7,3,5,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,3,5,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,1,7,3,6,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,3,6,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,5,2,3,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,1,7,5,2,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,7,5,3,2,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,1,7,5,3,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,7,5,6,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,5,6,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,6,2,3,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,1,7,6,2,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,7,6,3,2,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,1,7,6,3,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,7,6,5,2,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,1,7,6,5,3,2]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,2,1,3,5,7,6]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[4,2,1,3,6,5,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,2,1,3,6,7,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[4,2,1,3,7,5,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,2,1,3,7,6,5]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,5,3,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,2,1,5,3,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,1,5,6,3,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,2,1,5,6,7,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[4,2,1,5,7,3,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,2,1,5,7,6,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,6,3,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,2,1,6,3,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,1,6,5,3,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,2,1,6,5,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,1,6,7,3,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,2,1,6,7,5,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,7,3,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,2,1,7,3,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,1,7,5,3,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,2,1,7,5,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,1,7,6,3,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,2,1,7,6,5,3]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,2,3,1,5,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,2,3,1,5,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,3,1,6,5,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,3,1,6,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,3,1,7,5,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,3,1,7,6,5]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,3,5,1,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,2,3,5,1,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,5,6,1,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,2,3,5,6,7,1]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[4,2,3,5,7,1,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,2,3,5,7,6,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,2,3,6,1,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,2,3,6,1,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,6,5,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,2,3,6,5,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,6,7,1,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,2,3,6,7,5,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,2,3,7,1,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,2,3,7,1,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,7,5,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,2,3,7,5,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,7,6,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,2,3,7,6,5,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,5,1,3,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,2,5,1,3,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,5,1,6,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,1,6,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,5,1,7,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,1,7,6,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,5,3,1,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,2,5,3,1,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,5,3,6,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,3,6,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,5,3,7,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,3,7,6,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,5,6,1,3,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,2,5,6,1,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,5,6,3,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,2,5,6,3,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,5,6,7,1,3]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,2,5,6,7,3,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,2,5,7,1,3,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,2,5,7,1,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,5,7,3,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,2,5,7,3,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,5,7,6,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,2,5,7,6,3,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,6,1,3,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,2,6,1,3,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,6,1,5,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,1,5,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,6,1,7,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,1,7,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,3,1,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,2,6,3,1,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,6,3,5,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,3,5,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,6,3,7,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,3,7,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,5,1,3,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,2,6,5,1,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,6,5,3,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,2,6,5,3,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,6,5,7,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,5,7,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,7,1,3,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,2,6,7,1,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,6,7,3,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,2,6,7,3,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,2,6,7,5,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,2,6,7,5,3,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,7,1,3,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,2,7,1,3,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,7,1,5,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,7,1,5,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,7,1,6,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,7,1,6,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,3,1,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,2,7,3,1,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,3,5,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,7,3,5,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,2,7,3,6,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,7,3,6,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,5,1,3,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,2,7,5,1,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,5,3,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,2,7,5,3,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,5,6,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,2,7,5,6,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,6,1,3,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,2,7,6,1,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,6,3,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,2,7,6,3,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,6,5,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,2,7,6,5,3,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,3,1,2,5,7,6]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[4,3,1,2,6,5,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,3,1,2,6,7,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[4,3,1,2,7,5,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,3,1,2,7,6,5]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,1,5,2,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,3,1,5,2,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,5,6,2,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,3,1,5,6,7,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[4,3,1,5,7,2,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,3,1,5,7,6,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,1,6,2,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,3,1,6,2,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,6,5,2,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,3,1,6,5,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,6,7,2,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,3,1,6,7,5,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,1,7,2,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,3,1,7,2,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,7,5,2,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,3,1,7,5,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,7,6,2,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,3,1,7,6,5,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,3,2,1,5,7,6]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[4,3,2,1,6,5,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[4,3,2,1,6,7,5]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[4,3,2,1,7,5,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,3,2,5,1,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,3,2,5,1,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,5,6,1,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,3,2,5,6,7,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[4,3,2,5,7,1,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,3,2,5,7,6,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,2,6,1,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,3,2,6,1,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,6,5,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,3,2,6,5,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,6,7,1,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[4,3,2,6,7,5,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,2,7,1,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[4,3,2,7,1,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,7,5,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,3,2,7,5,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,7,6,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[4,3,2,7,6,5,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,3,5,1,2,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,3,5,1,2,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,5,1,6,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,5,1,6,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,5,1,7,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,5,1,7,6,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,5,2,1,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,3,5,2,1,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,5,2,6,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,5,2,6,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,5,2,7,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,5,2,7,6,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,5,6,1,2,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,3,5,6,1,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,3,5,6,2,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,3,5,6,2,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,3,5,6,7,1,2]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[4,3,5,6,7,2,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[4,3,5,7,1,2,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,3,5,7,1,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,3,5,7,2,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,3,5,7,2,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,3,5,7,6,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,3,5,7,6,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,3,6,1,2,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,3,6,1,2,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,6,1,5,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,6,1,5,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,6,1,7,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,6,1,7,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,6,2,1,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,3,6,2,1,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,6,2,5,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,6,2,5,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,6,2,7,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,6,2,7,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,6,5,1,2,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,3,6,5,1,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,6,5,2,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,3,6,5,2,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,6,5,7,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,6,5,7,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,6,7,1,2,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[4,3,6,7,1,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,3,6,7,2,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,3,6,7,2,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[4,3,6,7,5,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[4,3,6,7,5,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,3,7,1,2,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[4,3,7,1,2,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,7,1,5,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,7,1,5,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,7,1,6,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,7,1,6,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,7,2,1,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,3,7,2,1,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,2,5,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,7,2,5,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[4,3,7,2,6,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,7,2,6,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,7,5,1,2,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,3,7,5,1,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,5,2,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,3,7,5,2,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,5,6,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[4,3,7,5,6,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,7,6,1,2,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[4,3,7,6,1,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,6,2,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,3,7,6,2,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,6,5,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[4,3,7,6,5,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,5,1,2,3,6,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[4,5,1,2,3,7,6]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,5,1,2,6,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,1,2,6,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,5,1,2,7,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,1,2,7,6,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,1,3,2,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,5,1,3,2,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,3,6,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,1,3,6,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,5,1,3,7,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,1,3,7,6,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,1,6,2,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,5,1,6,2,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,6,3,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,1,6,3,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,6,7,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,1,6,7,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,1,7,2,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,5,1,7,2,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,7,3,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,1,7,3,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,7,6,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,1,7,6,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,2,1,3,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,5,2,1,3,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,2,1,6,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,2,1,6,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,2,1,7,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,2,1,7,6,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,2,3,1,6,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,5,2,3,1,7,6]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,3,6,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,2,3,6,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,5,2,3,7,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,2,3,7,6,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,2,6,1,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,5,2,6,1,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,6,3,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,2,6,3,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,6,7,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,2,6,7,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,2,7,1,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,5,2,7,1,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,7,3,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,2,7,3,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,7,6,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,2,7,6,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,3,1,2,6,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,5,3,1,2,7,6]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,3,1,6,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,3,1,6,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,3,1,7,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,3,1,7,6,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,3,2,1,6,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,5,3,2,1,7,6]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,3,2,6,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,3,2,6,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,3,2,7,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,3,2,7,6,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,3,6,1,2,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,5,3,6,1,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,6,2,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,3,6,2,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,6,7,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,5,3,6,7,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,3,7,1,2,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,5,3,7,1,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,7,2,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,3,7,2,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,7,6,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,3,7,6,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,6,1,2,3,7]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[4,5,6,1,2,7,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,5,6,1,3,2,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,6,1,3,7,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,5,6,1,7,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,6,1,7,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,6,2,1,3,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[4,5,6,2,1,7,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,6,2,3,1,7]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,6,2,3,7,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,5,6,2,7,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,6,2,7,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,6,3,1,2,7]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[4,5,6,3,1,7,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,6,3,2,1,7]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,5,6,3,2,7,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,6,3,7,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,6,3,7,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,6,7,1,2,3]=>[4,3]=>[[6,4],[3]]=>[3]=>0
[4,5,6,7,1,3,2]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[4,5,6,7,2,1,3]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[4,5,6,7,2,3,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[4,3]=>1
[4,5,6,7,3,1,2]=>[4,1,2]=>[[5,4,4],[3,3]]=>[3,3]=>0
[4,5,6,7,3,2,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,5,7,1,2,3,6]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[4,5,7,1,2,6,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,5,7,1,3,2,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,7,1,3,6,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,5,7,1,6,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,7,1,6,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,7,2,1,3,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[4,5,7,2,1,6,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,2,3,1,6]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,7,2,3,6,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,5,7,2,6,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,7,2,6,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,7,3,1,2,6]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[4,5,7,3,1,6,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,3,2,1,6]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,5,7,3,2,6,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,3,6,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,5,7,3,6,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,7,6,1,2,3]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[4,5,7,6,1,3,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,6,2,1,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,5,7,6,2,3,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,6,3,1,2]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,5,7,6,3,2,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[4,6,1,2,3,5,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[4,6,1,2,3,7,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,6,1,2,5,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,1,2,5,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,6,1,2,7,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,1,2,7,5,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,1,3,2,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,1,3,2,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,1,3,5,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,1,3,5,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,6,1,3,7,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,1,3,7,5,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,1,5,2,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,1,5,2,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,1,5,3,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,1,5,3,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,1,5,7,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,1,5,7,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,1,7,2,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,1,7,2,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,1,7,3,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,1,7,3,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,1,7,5,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,1,7,5,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,2,1,3,5,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,6,2,1,3,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,2,1,5,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,2,1,5,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,2,1,7,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,2,1,7,5,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,2,3,1,5,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,2,3,1,7,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,3,5,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,2,3,5,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,6,2,3,7,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,2,3,7,5,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,2,5,1,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,2,5,1,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,5,3,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,2,5,3,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,5,7,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,2,5,7,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,2,7,1,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,2,7,1,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,7,3,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,2,7,3,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,7,5,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,2,7,5,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,3,1,2,5,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,6,3,1,2,7,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,3,1,5,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,3,1,5,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,3,1,7,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,3,1,7,5,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,3,2,1,5,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,6,3,2,1,7,5]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,3,2,5,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,3,2,5,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,3,2,7,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,3,2,7,5,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,3,5,1,2,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,3,5,1,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,5,2,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,3,5,2,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,5,7,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,6,3,5,7,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,3,7,1,2,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,3,7,1,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,7,2,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,3,7,2,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,7,5,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,3,7,5,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,5,1,2,3,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,6,5,1,2,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,5,1,3,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,5,1,3,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,5,1,7,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,5,1,7,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,5,2,1,3,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,6,5,2,1,7,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,5,2,3,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,5,2,3,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,5,2,7,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,5,2,7,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,5,3,1,2,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,6,5,3,1,7,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,5,3,2,1,7]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[4,6,5,3,2,7,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,5,3,7,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,5,3,7,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,5,7,1,2,3]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,6,5,7,1,3,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,7,2,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,5,7,2,3,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,7,3,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,5,7,3,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,7,1,2,3,5]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[4,6,7,1,2,5,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,6,7,1,3,2,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,6,7,1,3,5,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,6,7,1,5,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,6,7,1,5,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,2,1,3,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[4,6,7,2,1,5,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,2,3,1,5]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,6,7,2,3,5,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[4,6,7,2,5,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,6,7,2,5,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,3,1,2,5]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[4,6,7,3,1,5,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,3,2,1,5]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,6,7,3,2,5,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,3,5,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[4,6,7,3,5,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,5,1,2,3]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[4,6,7,5,1,3,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,5,2,1,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,6,7,5,2,3,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,5,3,1,2]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,6,7,5,3,2,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[4,7,1,2,3,5,6]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[4,7,1,2,3,6,5]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,7,1,2,5,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,1,2,5,6,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,7,1,2,6,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,1,2,6,5,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,1,3,2,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,1,3,2,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,3,5,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,1,3,5,6,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,7,1,3,6,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,1,3,6,5,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,1,5,2,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,1,5,2,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,5,3,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,1,5,3,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,5,6,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,1,5,6,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,1,6,2,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,1,6,2,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,6,3,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,1,6,3,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,6,5,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,1,6,5,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,2,1,3,5,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,7,2,1,3,6,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,2,1,5,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,2,1,5,6,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,2,1,6,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,2,1,6,5,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,2,3,1,5,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,2,3,1,6,5]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,3,5,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,2,3,5,6,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[4,7,2,3,6,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,2,3,6,5,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,2,5,1,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,2,5,1,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,5,3,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,2,5,3,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,5,6,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,2,5,6,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,2,6,1,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,2,6,1,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,6,3,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,2,6,3,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,6,5,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,2,6,5,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,3,1,2,5,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,7,3,1,2,6,5]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,3,1,5,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,3,1,5,6,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,3,1,6,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,3,1,6,5,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,3,2,1,5,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,7,3,2,1,6,5]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,3,2,5,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,3,2,5,6,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,3,2,6,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,3,2,6,5,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,3,5,1,2,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,3,5,1,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,5,2,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,3,5,2,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,5,6,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[4,7,3,5,6,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,3,6,1,2,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,3,6,1,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,6,2,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,3,6,2,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,6,5,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,3,6,5,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,5,1,2,3,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,7,5,1,2,6,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,5,1,3,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,5,1,3,6,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,5,1,6,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,5,1,6,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,5,2,1,3,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,7,5,2,1,6,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,5,2,3,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,5,2,3,6,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,5,2,6,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,5,2,6,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,5,3,1,2,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,7,5,3,1,6,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,5,3,2,1,6]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[4,7,5,3,2,6,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,5,3,6,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,5,3,6,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,5,6,1,2,3]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[4,7,5,6,1,3,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,6,2,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,5,6,2,3,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,6,3,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,5,6,3,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,6,1,2,3,5]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[4,7,6,1,2,5,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,6,1,3,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,6,1,3,5,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,6,1,5,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,6,1,5,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,2,1,3,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,7,6,2,1,5,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,2,3,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,6,2,3,5,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,6,2,5,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,6,2,5,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,3,1,2,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,7,6,3,1,5,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,3,2,1,5]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[4,7,6,3,2,5,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,3,5,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,6,3,5,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,5,1,2,3]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[4,7,6,5,1,3,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,5,2,1,3]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[4,7,6,5,2,3,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,5,3,1,2]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,1,2,3,4,7,6]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[5,1,2,3,6,4,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,2,3,6,7,4]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[5,1,2,3,7,4,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,2,3,7,6,4]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,4,3,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,2,4,3,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,2,4,6,3,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,2,4,6,7,3]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[5,1,2,4,7,3,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,2,4,7,6,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,6,3,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,2,6,3,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,2,6,4,3,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,2,6,4,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,2,6,7,3,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,2,6,7,4,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,7,3,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,2,7,3,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,2,7,4,3,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,2,7,4,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,2,7,6,3,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,2,7,6,4,3]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,3,2,4,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,1,3,2,4,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,3,2,6,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,3,2,6,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,3,2,7,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,3,2,7,6,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,3,4,2,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,3,4,2,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,4,6,2,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,3,4,6,7,2]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[5,1,3,4,7,2,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,3,4,7,6,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,1,3,6,2,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,3,6,2,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,6,4,2,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,3,6,4,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,6,7,2,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,3,6,7,4,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,1,3,7,2,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,3,7,2,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,7,4,2,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,3,7,4,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,7,6,2,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,3,7,6,4,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,4,2,3,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,1,4,2,3,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,4,2,6,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,2,6,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,4,2,7,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,2,7,6,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,4,3,2,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,1,4,3,2,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,4,3,6,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,3,6,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,4,3,7,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,3,7,6,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,4,6,2,3,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,4,6,2,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,6,3,2,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,4,6,3,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,6,7,2,3]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,1,4,6,7,3,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,1,4,7,2,3,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,4,7,2,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,7,3,2,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,4,7,3,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,7,6,2,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,4,7,6,3,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,6,2,3,4,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,1,6,2,3,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,6,2,4,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,2,4,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,6,2,7,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,2,7,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,6,3,2,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,1,6,3,2,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,6,3,4,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,3,4,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,6,3,7,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,3,7,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,6,4,2,3,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,1,6,4,2,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,6,4,3,2,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,1,6,4,3,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,6,4,7,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,4,7,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,6,7,2,3,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,1,6,7,2,4,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,6,7,3,2,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,6,7,3,4,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,1,6,7,4,2,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,1,6,7,4,3,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,7,2,3,4,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,1,7,2,3,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,7,2,4,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,2,4,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,7,2,6,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,2,6,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,3,2,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,1,7,3,2,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,3,4,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,3,4,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,1,7,3,6,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,3,6,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,4,2,3,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,1,7,4,2,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,4,3,2,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,1,7,4,3,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,4,6,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,4,6,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,6,2,3,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,1,7,6,2,4,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,6,3,2,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,1,7,6,3,4,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,6,4,2,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,1,7,6,4,3,2]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,2,1,3,4,7,6]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,2,1,3,6,4,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,2,1,3,6,7,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,2,1,3,7,4,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,2,1,3,7,6,4]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,1,4,3,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,2,1,4,3,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,4,6,3,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,2,1,4,6,7,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,2,1,4,7,3,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,2,1,4,7,6,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,1,6,3,4,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,2,1,6,3,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,6,4,3,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,2,1,6,4,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,6,7,3,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,2,1,6,7,4,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,1,7,3,4,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,2,1,7,3,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,7,4,3,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,2,1,7,4,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,7,6,3,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,2,1,7,6,4,3]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,2,3,1,4,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,2,3,1,4,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,3,1,6,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,3,1,6,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,3,1,7,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,3,1,7,6,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,3,4,1,6,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,2,3,4,1,7,6]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,4,6,1,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,2,3,4,6,7,1]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[5,2,3,4,7,1,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,2,3,4,7,6,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,2,3,6,1,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,2,3,6,1,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,6,4,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,2,3,6,4,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,6,7,1,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,2,3,6,7,4,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,2,3,7,1,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,2,3,7,1,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,7,4,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,2,3,7,4,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,7,6,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,2,3,7,6,4,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,2,4,1,3,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,2,4,1,3,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,1,6,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,4,1,6,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,1,7,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,4,1,7,6,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,4,3,1,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,2,4,3,1,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,4,3,6,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,4,3,6,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,3,7,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,4,3,7,6,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,4,6,1,3,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,2,4,6,1,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,4,6,3,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,2,4,6,3,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,4,6,7,1,3]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,2,4,6,7,3,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,2,4,7,1,3,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,2,4,7,1,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,4,7,3,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,2,4,7,3,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,4,7,6,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,2,4,7,6,3,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,2,6,1,3,4,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,2,6,1,3,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,6,1,4,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,6,1,4,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,6,1,7,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,6,1,7,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,3,1,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,2,6,3,1,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,3,4,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,6,3,4,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,6,3,7,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,6,3,7,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,4,1,3,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,2,6,4,1,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,4,3,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,2,6,4,3,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,4,7,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,6,4,7,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,7,1,3,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,2,6,7,1,4,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,6,7,3,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,2,6,7,3,4,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,2,6,7,4,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,2,6,7,4,3,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,2,7,1,3,4,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,2,7,1,3,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,7,1,4,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,7,1,4,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,7,1,6,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,7,1,6,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,3,1,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,2,7,3,1,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,3,4,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,7,3,4,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,2,7,3,6,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,7,3,6,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,4,1,3,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,2,7,4,1,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,4,3,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,2,7,4,3,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,4,6,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,2,7,4,6,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,6,1,3,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,2,7,6,1,4,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,6,3,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,2,7,6,3,4,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,6,4,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,2,7,6,4,3,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,3,1,2,4,7,6]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,3,1,2,6,4,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,3,1,2,6,7,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,3,1,2,7,4,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,3,1,2,7,6,4]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,1,4,2,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,3,1,4,2,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,4,6,2,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,3,1,4,6,7,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,3,1,4,7,2,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,3,1,4,7,6,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,1,6,2,4,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,3,1,6,2,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,6,4,2,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,3,1,6,4,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,6,7,2,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,3,1,6,7,4,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,1,7,2,4,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,3,1,7,2,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,7,4,2,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,3,1,7,4,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,7,6,2,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,3,1,7,6,4,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,3,2,1,4,7,6]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[5,3,2,1,6,4,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[5,3,2,1,6,7,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[5,3,2,1,7,4,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[5,3,2,1,7,6,4]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,3,2,4,1,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,3,2,4,1,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,4,6,1,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,3,2,4,6,7,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,3,2,4,7,1,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,3,2,4,7,6,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,2,6,1,4,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,3,2,6,1,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,6,4,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,3,2,6,4,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,6,7,1,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,3,2,6,7,4,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,2,7,1,4,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,3,2,7,1,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,7,4,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,3,2,7,4,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,7,6,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,3,2,7,6,4,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,3,4,1,2,6,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,3,4,1,2,7,6]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,1,6,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,1,6,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,1,7,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,1,7,6,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,4,2,1,6,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,3,4,2,1,7,6]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,4,2,6,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,2,6,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,2,7,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,2,7,6,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,4,6,1,2,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,3,4,6,1,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,3,4,6,2,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,3,4,6,2,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,3,4,6,7,1,2]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[5,3,4,6,7,2,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[5,3,4,7,1,2,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,3,4,7,1,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,3,4,7,2,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,3,4,7,2,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,3,4,7,6,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,3,4,7,6,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,6,1,2,4,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,3,6,1,2,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,1,4,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,6,1,4,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,1,7,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,6,1,7,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,6,2,1,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,3,6,2,1,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,6,2,4,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,6,2,4,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,2,7,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,6,2,7,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,6,4,1,2,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,3,6,4,1,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,6,4,2,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,3,6,4,2,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,6,4,7,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,6,4,7,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,6,7,1,2,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,3,6,7,1,4,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,3,6,7,2,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,3,6,7,2,4,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,3,6,7,4,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,3,6,7,4,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,7,1,2,4,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,3,7,1,2,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,7,1,4,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,1,4,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,7,1,6,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,1,6,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,2,1,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,3,7,2,1,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,7,2,4,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,2,4,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,3,7,2,6,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,2,6,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,4,1,2,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,3,7,4,1,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,7,4,2,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,3,7,4,2,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,7,4,6,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,4,6,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,6,1,2,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,3,7,6,1,4,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,7,6,2,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,3,7,6,2,4,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,7,6,4,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,3,7,6,4,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,1,2,3,7,6]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,4,1,2,6,3,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,1,2,6,7,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,4,1,2,7,3,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,1,2,7,6,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,3,2,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,4,1,3,2,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,1,3,6,2,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,1,3,6,7,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,4,1,3,7,2,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,1,3,7,6,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,6,2,3,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,4,1,6,2,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,1,6,3,2,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,1,6,3,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,1,6,7,2,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,1,6,7,3,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,7,2,3,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,4,1,7,2,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,1,7,3,2,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,1,7,3,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,1,7,6,2,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,1,7,6,3,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,2,1,3,7,6]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[5,4,2,1,6,3,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[5,4,2,1,6,7,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[5,4,2,1,7,3,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[5,4,2,1,7,6,3]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,4,2,3,1,6,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,4,2,3,1,7,6]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,3,6,1,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,2,3,6,7,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[5,4,2,3,7,1,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,2,3,7,6,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,2,6,1,3,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,4,2,6,1,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,6,3,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,2,6,3,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,6,7,1,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,2,6,7,3,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,2,7,1,3,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,4,2,7,1,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,7,3,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,2,7,3,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,7,6,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,2,7,6,3,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,3,1,2,7,6]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[5,4,3,1,6,2,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[5,4,3,1,6,7,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[5,4,3,1,7,2,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[5,4,3,1,7,6,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[5,4,3,2,6,1,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[5,4,3,2,6,7,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[5,4,3,2,7,1,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[5,4,3,2,7,6,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,4,3,6,1,2,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,4,3,6,1,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,6,2,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,3,6,2,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,6,7,1,2]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[5,4,3,6,7,2,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,3,7,1,2,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[5,4,3,7,1,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,7,2,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,3,7,2,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,7,6,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[5,4,3,7,6,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,6,1,2,3,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,4,6,1,2,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,4,6,1,3,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,6,1,3,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,4,6,1,7,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,6,1,7,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,6,2,1,3,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,4,6,2,1,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,2,3,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,6,2,3,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,4,6,2,7,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,6,2,7,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,6,3,1,2,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,4,6,3,1,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,3,2,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,4,6,3,2,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,3,7,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,6,3,7,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,6,7,1,2,3]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[5,4,6,7,1,3,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,4,6,7,2,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,4,6,7,2,3,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[5,4,6,7,3,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[5,4,6,7,3,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,4,7,1,2,3,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[5,4,7,1,2,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,4,7,1,3,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,7,1,3,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,4,7,1,6,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,7,1,6,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,7,2,1,3,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,4,7,2,1,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,7,2,3,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,7,2,3,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[5,4,7,2,6,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,7,2,6,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,7,3,1,2,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,4,7,3,1,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,7,3,2,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,4,7,3,2,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,7,3,6,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[5,4,7,3,6,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,7,6,1,2,3]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[5,4,7,6,1,3,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,7,6,2,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,4,7,6,2,3,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,7,6,3,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[5,4,7,6,3,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,6,1,2,3,4,7]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[5,6,1,2,3,7,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[5,6,1,2,4,3,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,1,2,4,7,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[5,6,1,2,7,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,1,2,7,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,1,3,2,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,1,3,2,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,3,4,2,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,1,3,4,7,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[5,6,1,3,7,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,1,3,7,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,1,4,2,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,1,4,2,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,4,3,2,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,1,4,3,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,4,7,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,1,4,7,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,1,7,2,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,1,7,2,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,7,3,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,1,7,3,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,7,4,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,1,7,4,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,2,1,3,4,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[5,6,2,1,3,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,2,1,4,3,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,2,1,4,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,2,1,7,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,2,1,7,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,2,3,1,4,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,2,3,1,7,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,3,4,1,7]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,2,3,4,7,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[5,6,2,3,7,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,2,3,7,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,2,4,1,3,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,2,4,1,7,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,4,3,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,2,4,3,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,4,7,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,2,4,7,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,2,7,1,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,2,7,1,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,7,3,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,2,7,3,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,7,4,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,2,7,4,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,3,1,2,4,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[5,6,3,1,2,7,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,3,1,4,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,1,4,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,3,1,7,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,1,7,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,3,2,1,4,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,6,3,2,1,7,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,3,2,4,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,2,4,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,3,2,7,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,2,7,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,3,4,1,2,7]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,3,4,1,7,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,4,2,1,7]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,3,4,2,7,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,4,7,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,6,3,4,7,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,3,7,1,2,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,3,7,1,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,7,2,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,3,7,2,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,7,4,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,3,7,4,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,4,1,2,3,7]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[5,6,4,1,2,7,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,4,1,3,2,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,1,3,7,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,4,1,7,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,1,7,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,4,2,1,3,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,6,4,2,1,7,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,4,2,3,1,7]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,2,3,7,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,4,2,7,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,2,7,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,4,3,1,2,7]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,6,4,3,1,7,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,4,3,2,1,7]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[5,6,4,3,2,7,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,4,3,7,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,3,7,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,4,7,1,2,3]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,6,4,7,1,3,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,7,2,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,4,7,2,3,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,7,3,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,4,7,3,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,7,1,2,3,4]=>[3,4]=>[[6,3],[2]]=>[2]=>0
[5,6,7,1,2,4,3]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[5,6,7,1,3,2,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[5,6,7,1,3,4,2]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[5,6,7,1,4,2,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[5,6,7,1,4,3,2]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,7,2,1,3,4]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[5,6,7,2,1,4,3]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,7,2,3,1,4]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[5,6,7,2,3,4,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[4,2]=>2
[5,6,7,2,4,1,3]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[5,6,7,2,4,3,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,7,3,1,2,4]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[5,6,7,3,1,4,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,7,3,2,1,4]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,6,7,3,2,4,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,7,3,4,1,2]=>[3,2,2]=>[[5,4,3],[3,2]]=>[3,2]=>1
[5,6,7,3,4,2,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,7,4,1,2,3]=>[3,1,3]=>[[5,3,3],[2,2]]=>[2,2]=>0
[5,6,7,4,1,3,2]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,7,4,2,1,3]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,6,7,4,2,3,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,7,4,3,1,2]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,6,7,4,3,2,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[2,2,2,2]=>0
[5,7,1,2,3,4,6]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[5,7,1,2,3,6,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[5,7,1,2,4,3,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,1,2,4,6,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[5,7,1,2,6,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,1,2,6,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,1,3,2,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,1,3,2,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,3,4,2,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,1,3,4,6,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[5,7,1,3,6,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,1,3,6,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,1,4,2,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,1,4,2,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,4,3,2,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,1,4,3,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,4,6,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,1,4,6,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,1,6,2,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,1,6,2,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,6,3,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,1,6,3,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,6,4,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,1,6,4,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,2,1,3,4,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[5,7,2,1,3,6,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,2,1,4,3,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,2,1,4,6,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,2,1,6,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,2,1,6,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,2,3,1,4,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,2,3,1,6,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,3,4,1,6]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,2,3,4,6,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[5,7,2,3,6,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,2,3,6,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,2,4,1,3,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,2,4,1,6,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,4,3,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,2,4,3,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,4,6,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,2,4,6,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,2,6,1,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,2,6,1,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,6,3,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,2,6,3,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,6,4,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,2,6,4,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,3,1,2,4,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[5,7,3,1,2,6,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,3,1,4,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,3,1,4,6,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,3,1,6,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,3,1,6,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,3,2,1,4,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,7,3,2,1,6,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,3,2,4,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,3,2,4,6,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,3,2,6,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,3,2,6,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,3,4,1,2,6]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,3,4,1,6,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,4,2,1,6]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,3,4,2,6,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,4,6,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[5,7,3,4,6,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,3,6,1,2,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,3,6,1,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,6,2,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,3,6,2,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,6,4,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,3,6,4,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,4,1,2,3,6]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[5,7,4,1,2,6,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,4,1,3,2,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,1,3,6,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,4,1,6,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,1,6,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,4,2,1,3,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,7,4,2,1,6,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,4,2,3,1,6]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,2,3,6,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,4,2,6,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,2,6,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,4,3,1,2,6]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,7,4,3,1,6,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,4,3,2,1,6]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[5,7,4,3,2,6,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,4,3,6,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,3,6,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,4,6,1,2,3]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[5,7,4,6,1,3,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,4,6,2,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,4,6,2,3,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,4,6,3,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,4,6,3,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,6,1,2,3,4]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[5,7,6,1,2,4,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,6,1,3,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,1,3,4,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,6,1,4,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,1,4,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,6,2,1,3,4]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,7,6,2,1,4,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,2,3,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,2,3,4,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,6,2,4,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,2,4,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,6,3,1,2,4]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,7,6,3,1,4,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,3,2,1,4]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[5,7,6,3,2,4,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,3,4,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,3,4,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,6,4,1,2,3]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[5,7,6,4,1,3,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,4,2,1,3]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[5,7,6,4,2,3,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,4,3,1,2]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[6,1,2,3,4,7,5]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[6,1,2,3,5,4,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,2,3,5,7,4]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[6,1,2,3,7,4,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,2,3,7,5,4]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,1,2,4,3,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,2,4,3,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,4,5,3,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,2,4,5,7,3]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[6,1,2,4,7,3,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,2,4,7,5,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,1,2,5,3,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,2,5,3,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,5,4,3,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,2,5,4,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,5,7,3,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,2,5,7,4,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,1,2,7,3,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,2,7,3,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,7,4,3,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,2,7,4,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,7,5,3,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,2,7,5,4,3]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,1,3,2,4,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,1,3,2,4,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,3,2,5,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,3,2,5,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,3,2,7,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,3,2,7,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,3,4,2,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,3,4,2,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,3,4,5,2,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,3,4,5,7,2]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[6,1,3,4,7,2,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,3,4,7,5,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,1,3,5,2,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,3,5,2,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,3,5,4,2,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,3,5,4,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,3,5,7,2,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,3,5,7,4,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,1,3,7,2,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,3,7,2,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,3,7,4,2,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,3,7,4,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,3,7,5,2,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,3,7,5,4,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,1,4,2,3,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,1,4,2,3,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,4,2,5,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,2,5,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,4,2,7,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,2,7,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,4,3,2,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,1,4,3,2,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,4,3,5,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,3,5,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,4,3,7,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,3,7,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,4,5,2,3,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,4,5,2,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,4,5,3,2,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,4,5,3,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,4,5,7,2,3]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,1,4,5,7,3,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,1,4,7,2,3,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,4,7,2,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,4,7,3,2,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,4,7,3,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,4,7,5,2,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,4,7,5,3,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,1,5,2,3,4,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,1,5,2,3,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,5,2,4,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,2,4,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,5,2,7,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,2,7,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,5,3,2,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,1,5,3,2,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,5,3,4,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,3,4,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,5,3,7,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,3,7,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,5,4,2,3,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,1,5,4,2,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,5,4,3,2,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,1,5,4,3,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,5,4,7,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,4,7,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,5,7,2,3,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,1,5,7,2,4,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,5,7,3,2,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,5,7,3,4,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,1,5,7,4,2,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,1,5,7,4,3,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,1,7,2,3,4,5]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,1,7,2,3,5,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,7,2,4,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,7,2,4,5,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,7,2,5,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,7,2,5,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,7,3,2,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,1,7,3,2,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,7,3,4,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,7,3,4,5,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,1,7,3,5,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,7,3,5,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,7,4,2,3,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,1,7,4,2,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,7,4,3,2,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,1,7,4,3,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,7,4,5,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,1,7,4,5,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,7,5,2,3,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,1,7,5,2,4,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,7,5,3,2,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,1,7,5,3,4,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,7,5,4,2,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,1,7,5,4,3,2]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,2,1,3,4,7,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,2,1,3,5,4,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,2,1,3,5,7,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,2,1,3,7,4,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,2,1,3,7,5,4]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,1,4,3,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,2,1,4,3,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,4,5,3,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,2,1,4,5,7,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,2,1,4,7,3,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,2,1,4,7,5,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,1,5,3,4,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,2,1,5,3,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,5,4,3,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,2,1,5,4,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,5,7,3,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,2,1,5,7,4,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,1,7,3,4,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,2,1,7,3,5,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,7,4,3,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,2,1,7,4,5,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,7,5,3,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,2,1,7,5,4,3]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,2,3,1,4,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,2,3,1,4,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,3,1,5,4,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,3,1,5,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,3,1,7,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,3,1,7,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,3,4,1,5,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,2,3,4,1,7,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,4,5,1,7]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,2,3,4,5,7,1]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[6,2,3,4,7,1,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,2,3,4,7,5,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,2,3,5,1,4,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,2,3,5,1,7,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,5,4,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,2,3,5,4,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,5,7,1,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,2,3,5,7,4,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,2,3,7,1,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,2,3,7,1,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,7,4,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,2,3,7,4,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,7,5,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,2,3,7,5,4,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,4,1,3,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,2,4,1,3,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,4,1,5,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,1,5,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,4,1,7,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,1,7,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,4,3,1,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,2,4,3,1,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,4,3,5,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,3,5,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,4,3,7,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,3,7,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,4,5,1,3,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,2,4,5,1,7,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,4,5,3,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,2,4,5,3,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,4,5,7,1,3]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,2,4,5,7,3,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,2,4,7,1,3,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,2,4,7,1,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,4,7,3,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,2,4,7,3,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,4,7,5,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,2,4,7,5,3,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,5,1,3,4,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,2,5,1,3,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,5,1,4,3,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,1,4,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,5,1,7,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,1,7,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,5,3,1,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,2,5,3,1,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,5,3,4,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,3,4,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,5,3,7,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,3,7,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,5,4,1,3,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,2,5,4,1,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,5,4,3,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,2,5,4,3,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,5,4,7,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,4,7,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,5,7,1,3,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,2,5,7,1,4,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,5,7,3,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,2,5,7,3,4,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,2,5,7,4,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,2,5,7,4,3,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,7,1,3,4,5]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,2,7,1,3,5,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,7,1,4,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,7,1,4,5,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,7,1,5,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,7,1,5,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,3,1,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,2,7,3,1,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,3,4,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,7,3,4,5,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,2,7,3,5,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,7,3,5,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,4,1,3,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,2,7,4,1,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,4,3,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,2,7,4,3,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,4,5,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,2,7,4,5,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,5,1,3,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,2,7,5,1,4,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,5,3,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,2,7,5,3,4,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,5,4,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,2,7,5,4,3,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,3,1,2,4,7,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,3,1,2,5,4,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,3,1,2,5,7,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,3,1,2,7,4,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,3,1,2,7,5,4]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,1,4,2,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,3,1,4,2,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,4,5,2,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,3,1,4,5,7,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,3,1,4,7,2,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,3,1,4,7,5,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,1,5,2,4,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,3,1,5,2,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,5,4,2,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,3,1,5,4,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,5,7,2,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,3,1,5,7,4,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,1,7,2,4,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,3,1,7,2,5,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,7,4,2,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,3,1,7,4,5,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,7,5,2,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,3,1,7,5,4,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,3,2,1,4,7,5]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,3,2,1,5,4,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,3,2,1,5,7,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,3,2,1,7,4,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,3,2,1,7,5,4]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,3,2,4,1,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,3,2,4,1,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,4,5,1,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,3,2,4,5,7,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,3,2,4,7,1,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,3,2,4,7,5,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,2,5,1,4,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,3,2,5,1,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,5,4,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,3,2,5,4,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,5,7,1,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,3,2,5,7,4,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,2,7,1,4,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,3,2,7,1,5,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,7,4,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,3,2,7,4,5,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,7,5,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,3,2,7,5,4,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,3,4,1,2,5,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,3,4,1,2,7,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,4,1,5,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,4,1,5,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,4,1,7,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,4,1,7,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,4,2,1,5,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,3,4,2,1,7,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,4,2,5,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,4,2,5,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,4,2,7,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,4,2,7,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,4,5,1,2,7]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,3,4,5,1,7,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,5,2,1,7]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,3,4,5,2,7,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,5,7,1,2]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[6,3,4,5,7,2,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[6,3,4,7,1,2,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,3,4,7,1,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,7,2,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,3,4,7,2,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,7,5,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,3,4,7,5,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,5,1,2,4,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,3,5,1,2,7,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,5,1,4,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,5,1,4,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,5,1,7,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,5,1,7,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,2,1,4,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,3,5,2,1,7,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,5,2,4,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,5,2,4,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,5,2,7,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,5,2,7,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,4,1,2,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,3,5,4,1,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,5,4,2,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,3,5,4,2,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,5,4,7,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,5,4,7,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,7,1,2,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,3,5,7,1,4,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,3,5,7,2,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,3,5,7,2,4,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,3,5,7,4,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,3,5,7,4,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,7,1,2,4,5]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,3,7,1,2,5,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,7,1,4,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,7,1,4,5,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,7,1,5,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,7,1,5,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,2,1,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,3,7,2,1,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,2,4,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,7,2,4,5,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,3,7,2,5,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,7,2,5,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,4,1,2,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,3,7,4,1,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,4,2,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,3,7,4,2,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,4,5,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,3,7,4,5,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,5,1,2,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,3,7,5,1,4,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,5,2,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,3,7,5,2,4,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,5,4,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,3,7,5,4,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,4,1,2,3,7,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,4,1,2,5,3,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,1,2,5,7,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,4,1,2,7,3,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,1,2,7,5,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,1,3,2,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,4,1,3,2,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,3,5,2,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,1,3,5,7,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,4,1,3,7,2,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,1,3,7,5,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,1,5,2,3,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,4,1,5,2,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,5,3,2,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,1,5,3,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,5,7,2,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,1,5,7,3,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,1,7,2,3,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,4,1,7,2,5,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,7,3,2,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,1,7,3,5,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,7,5,2,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,1,7,5,3,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,2,1,3,7,5]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,4,2,1,5,3,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,4,2,1,5,7,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,4,2,1,7,3,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,4,2,1,7,5,3]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,4,2,3,1,5,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,4,2,3,1,7,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,3,5,1,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,2,3,5,7,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,4,2,3,7,1,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,2,3,7,5,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,2,5,1,3,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,4,2,5,1,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,5,3,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,2,5,3,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,5,7,1,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,2,5,7,3,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,2,7,1,3,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,4,2,7,1,5,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,7,3,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,2,7,3,5,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,7,5,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,2,7,5,3,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,3,1,2,7,5]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,4,3,1,5,2,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,4,3,1,5,7,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,4,3,1,7,2,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,4,3,1,7,5,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,4,3,2,1,7,5]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[6,4,3,2,5,1,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,4,3,2,5,7,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,4,3,2,7,1,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,4,3,2,7,5,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,4,3,5,1,2,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,4,3,5,1,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,5,2,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,3,5,2,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,5,7,1,2]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,4,3,5,7,2,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,3,7,1,2,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,4,3,7,1,5,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,7,2,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,3,7,2,5,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,7,5,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,4,3,7,5,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,5,1,2,3,7]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,4,5,1,2,7,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,4,5,1,3,2,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,1,3,7,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,4,5,1,7,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,1,7,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,5,2,1,3,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,4,5,2,1,7,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,5,2,3,1,7]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,2,3,7,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,4,5,2,7,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,2,7,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,5,3,1,2,7]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,4,5,3,1,7,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,5,3,2,1,7]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,4,5,3,2,7,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,5,3,7,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,3,7,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,5,7,1,2,3]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[6,4,5,7,1,3,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,4,5,7,2,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,4,5,7,2,3,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[6,4,5,7,3,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[6,4,5,7,3,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,4,7,1,2,3,5]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,4,7,1,2,5,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,4,7,1,3,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,7,1,3,5,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,4,7,1,5,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,7,1,5,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,2,1,3,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,4,7,2,1,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,2,3,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,7,2,3,5,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,4,7,2,5,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,7,2,5,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,3,1,2,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,4,7,3,1,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,3,2,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,4,7,3,2,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,3,5,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,4,7,3,5,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,5,1,2,3]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,4,7,5,1,3,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,5,2,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,4,7,5,2,3,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,5,3,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,4,7,5,3,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,5,1,2,3,7,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,5,1,2,4,3,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,1,2,4,7,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,5,1,2,7,3,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,1,2,7,4,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,1,3,2,4,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,1,3,2,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,3,4,2,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,1,3,4,7,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,5,1,3,7,2,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,1,3,7,4,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,1,4,2,3,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,1,4,2,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,4,3,2,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,1,4,3,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,4,7,2,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,1,4,7,3,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,1,7,2,3,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,1,7,2,4,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,7,3,2,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,1,7,3,4,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,7,4,2,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,1,7,4,3,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,2,1,3,7,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,5,2,1,4,3,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,2,1,4,7,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,5,2,1,7,3,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,2,1,7,4,3]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,2,3,1,4,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,2,3,1,7,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,3,4,1,7]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,2,3,4,7,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[6,5,2,3,7,1,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,2,3,7,4,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,2,4,1,3,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,2,4,1,7,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,4,3,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,2,4,3,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,4,7,1,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,2,4,7,3,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,2,7,1,3,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,2,7,1,4,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,7,3,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,2,7,3,4,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,7,4,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,2,7,4,3,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,3,1,2,7,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,5,3,1,4,2,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,3,1,4,7,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,5,3,1,7,2,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,3,1,7,4,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,3,2,1,7,4]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[6,5,3,2,4,1,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,3,2,4,7,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,5,3,2,7,1,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,3,2,7,4,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,3,4,1,2,7]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,3,4,1,7,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,4,2,1,7]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,3,4,2,7,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,4,7,1,2]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[6,5,3,4,7,2,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,3,7,1,2,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,3,7,1,4,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,7,2,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,3,7,2,4,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,7,4,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,3,7,4,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,4,1,2,7,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,5,4,1,3,2,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,4,1,3,7,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,5,4,1,7,2,3]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,4,1,7,3,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,4,2,1,7,3]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[6,5,4,2,3,1,7]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,4,2,3,7,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[6,5,4,2,7,1,3]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,4,2,7,3,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,4,3,1,7,2]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[6,5,4,3,7,1,2]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,4,7,1,2,3]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[6,5,4,7,1,3,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,4,7,2,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,4,7,2,3,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,4,7,3,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,7,1,2,3,4]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[6,5,7,1,2,4,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,5,7,1,3,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,5,7,1,3,4,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,5,7,1,4,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,5,7,1,4,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,7,2,1,3,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,5,7,2,1,4,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,2,3,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,5,7,2,3,4,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[6,5,7,2,4,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,5,7,2,4,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,7,3,1,2,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,5,7,3,1,4,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,3,2,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,5,7,3,2,4,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,3,4,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[6,5,7,3,4,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,7,4,1,2,3]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[6,5,7,4,1,3,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,4,2,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,5,7,4,2,3,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,4,3,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,1,2,3,4,5]=>[2,5]=>[[6,2],[1]]=>[1]=>0
[6,7,1,2,3,5,4]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[6,7,1,2,4,3,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,1,2,4,5,3]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[6,7,1,2,5,3,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,1,2,5,4,3]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,1,3,2,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,1,3,2,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,3,4,2,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,1,3,4,5,2]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[6,7,1,3,5,2,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,1,3,5,4,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,1,4,2,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,1,4,2,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,4,3,2,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,1,4,3,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,4,5,2,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,1,4,5,3,2]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,1,5,2,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,1,5,2,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,5,3,2,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,1,5,3,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,5,4,2,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,1,5,4,3,2]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,2,1,3,4,5]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[6,7,2,1,3,5,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,2,1,4,3,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,2,1,4,5,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,2,1,5,3,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,2,1,5,4,3]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,2,3,1,4,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,2,3,1,5,4]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,3,4,1,5]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,2,3,4,5,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[4,1]=>3
[6,7,2,3,5,1,4]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,2,3,5,4,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,2,4,1,3,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,2,4,1,5,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,4,3,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,2,4,3,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,4,5,1,3]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,2,4,5,3,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,2,5,1,3,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,2,5,1,4,3]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,5,3,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,2,5,3,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,5,4,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,2,5,4,3,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,3,1,2,4,5]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[6,7,3,1,2,5,4]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,3,1,4,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,3,1,4,5,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,3,1,5,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,3,1,5,4,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,3,2,1,4,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[6,7,3,2,1,5,4]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,3,2,4,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,3,2,4,5,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,3,2,5,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,3,2,5,4,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,3,4,1,2,5]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,3,4,1,5,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,4,2,1,5]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,3,4,2,5,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,4,5,1,2]=>[2,3,2]=>[[5,4,2],[3,1]]=>[3,1]=>2
[6,7,3,4,5,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,3,5,1,2,4]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,3,5,1,4,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,5,2,1,4]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,3,5,2,4,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,5,4,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,3,5,4,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,4,1,2,3,5]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[6,7,4,1,2,5,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,4,1,3,2,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,4,1,3,5,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,4,1,5,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,4,1,5,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,4,2,1,3,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[6,7,4,2,1,5,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,4,2,3,1,5]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,4,2,3,5,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,4,2,5,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,4,2,5,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,4,3,1,2,5]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[6,7,4,3,1,5,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,4,3,2,1,5]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,4,3,2,5,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,4,3,5,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,4,3,5,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,4,5,1,2,3]=>[2,2,3]=>[[5,3,2],[2,1]]=>[2,1]=>1
[6,7,4,5,1,3,2]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,4,5,2,1,3]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,4,5,2,3,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,4,5,3,1,2]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,4,5,3,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,5,1,2,3,4]=>[2,1,4]=>[[5,2,2],[1,1]]=>[1,1]=>0
[6,7,5,1,2,4,3]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,5,1,3,2,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,5,1,3,4,2]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,5,1,4,2,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,5,1,4,3,2]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,5,2,1,3,4]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[6,7,5,2,1,4,3]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,5,2,3,1,4]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,5,2,3,4,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,5,2,4,1,3]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,5,2,4,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,5,3,1,2,4]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[6,7,5,3,1,4,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,5,3,2,1,4]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,5,3,2,4,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,5,3,4,1,2]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,5,3,4,2,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,5,4,1,2,3]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[1,1,1]=>0
[6,7,5,4,1,3,2]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,5,4,2,1,3]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,5,4,2,3,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,5,4,3,1,2]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,1,2,3,4,6,5]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[7,1,2,3,5,4,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,2,3,5,6,4]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[7,1,2,3,6,4,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,2,3,6,5,4]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,1,2,4,3,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,2,4,3,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,4,5,3,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,2,4,5,6,3]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[7,1,2,4,6,3,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,2,4,6,5,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,1,2,5,3,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,2,5,3,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,5,4,3,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,2,5,4,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,5,6,3,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,2,5,6,4,3]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,1,2,6,3,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,2,6,3,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,6,4,3,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,2,6,4,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,6,5,3,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,2,6,5,4,3]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,3,2,4,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,1,3,2,4,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,3,2,5,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,3,2,5,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,3,2,6,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,3,2,6,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,3,4,2,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,3,4,2,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,3,4,5,2,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,3,4,5,6,2]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[7,1,3,4,6,2,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,3,4,6,5,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,1,3,5,2,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,3,5,2,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,3,5,4,2,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,3,5,4,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,3,5,6,2,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,3,5,6,4,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,1,3,6,2,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,3,6,2,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,3,6,4,2,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,3,6,4,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,3,6,5,2,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,3,6,5,4,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,4,2,3,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,1,4,2,3,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,4,2,5,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,2,5,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,4,2,6,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,2,6,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,4,3,2,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,1,4,3,2,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,4,3,5,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,3,5,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,4,3,6,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,3,6,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,4,5,2,3,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,4,5,2,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,5,3,2,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,4,5,3,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,5,6,2,3]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,1,4,5,6,3,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,1,4,6,2,3,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,4,6,2,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,6,3,2,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,4,6,3,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,6,5,2,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,4,6,5,3,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,5,2,3,4,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,1,5,2,3,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,5,2,4,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,2,4,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,5,2,6,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,2,6,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,5,3,2,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,1,5,3,2,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,5,3,4,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,3,4,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,5,3,6,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,3,6,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,5,4,2,3,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,1,5,4,2,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,5,4,3,2,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,1,5,4,3,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,5,4,6,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,4,6,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,5,6,2,3,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,1,5,6,2,4,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,5,6,3,2,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,5,6,3,4,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,1,5,6,4,2,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,1,5,6,4,3,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,6,2,3,4,5]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,1,6,2,3,5,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,6,2,4,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,2,4,5,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,6,2,5,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,2,5,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,6,3,2,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,1,6,3,2,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,3,4,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,3,4,5,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,1,6,3,5,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,3,5,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,6,4,2,3,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,1,6,4,2,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,4,3,2,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,1,6,4,3,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,4,5,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,4,5,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,6,5,2,3,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,1,6,5,2,4,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,5,3,2,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,1,6,5,3,4,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,5,4,2,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,1,6,5,4,3,2]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,2,1,3,4,6,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,2,1,3,5,4,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,2,1,3,5,6,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,2,1,3,6,4,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,2,1,3,6,5,4]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,2,1,4,3,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,2,1,4,3,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,1,4,5,3,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,2,1,4,5,6,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,2,1,4,6,3,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,2,1,4,6,5,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,2,1,5,3,4,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,2,1,5,3,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,1,5,4,3,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,2,1,5,4,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,1,5,6,3,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,2,1,5,6,4,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,2,1,6,3,4,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,2,1,6,3,5,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,1,6,4,3,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,2,1,6,4,5,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,1,6,5,3,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,2,1,6,5,4,3]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,2,3,1,4,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,2,3,1,4,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,3,1,5,4,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,3,1,5,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,3,1,6,4,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,3,1,6,5,4]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,3,4,1,5,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,2,3,4,1,6,5]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,3,4,5,1,6]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,2,3,4,5,6,1]=>[1,5,1]=>[[5,5,1],[4]]=>[4]=>0
[7,2,3,4,6,1,5]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,2,3,4,6,5,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,2,3,5,1,4,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,2,3,5,1,6,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,3,5,4,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,2,3,5,4,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,3,5,6,1,4]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,2,3,5,6,4,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,2,3,6,1,4,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,2,3,6,1,5,4]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,3,6,4,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,2,3,6,4,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,3,6,5,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,2,3,6,5,4,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,4,1,3,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,2,4,1,3,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,4,1,5,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,4,1,5,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,4,1,6,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,4,1,6,5,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,3,1,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,2,4,3,1,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,4,3,5,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,4,3,5,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,4,3,6,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,4,3,6,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,5,1,3,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,2,4,5,1,6,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,4,5,3,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,2,4,5,3,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,4,5,6,1,3]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,2,4,5,6,3,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,2,4,6,1,3,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,2,4,6,1,5,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,4,6,3,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,2,4,6,3,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,4,6,5,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,2,4,6,5,3,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,5,1,3,4,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,2,5,1,3,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,5,1,4,3,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,5,1,4,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,5,1,6,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,5,1,6,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,3,1,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,2,5,3,1,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,5,3,4,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,5,3,4,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,5,3,6,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,5,3,6,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,4,1,3,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,2,5,4,1,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,5,4,3,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,2,5,4,3,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,5,4,6,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,5,4,6,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,6,1,3,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,2,5,6,1,4,3]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,5,6,3,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,2,5,6,3,4,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,2,5,6,4,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,2,5,6,4,3,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,6,1,3,4,5]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,2,6,1,3,5,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,1,4,3,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,6,1,4,5,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,1,5,3,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,6,1,5,4,3]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,3,1,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,2,6,3,1,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,6,3,4,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,6,3,4,5,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,3,5,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,6,3,5,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,4,1,3,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,2,6,4,1,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,6,4,3,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,2,6,4,3,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,6,4,5,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,2,6,4,5,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,5,1,3,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,2,6,5,1,4,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,6,5,3,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,2,6,5,3,4,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,6,5,4,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,2,6,5,4,3,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,3,1,2,4,6,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,3,1,2,5,4,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,3,1,2,5,6,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,3,1,2,6,4,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,3,1,2,6,5,4]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,1,4,2,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,3,1,4,2,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,1,4,5,2,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,3,1,4,5,6,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,3,1,4,6,2,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,3,1,4,6,5,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,1,5,2,4,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,3,1,5,2,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,1,5,4,2,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,3,1,5,4,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,1,5,6,2,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,3,1,5,6,4,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,1,6,2,4,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,3,1,6,2,5,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,1,6,4,2,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,3,1,6,4,5,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,1,6,5,2,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,3,1,6,5,4,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,3,2,1,4,6,5]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,3,2,1,5,4,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,3,2,1,5,6,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,3,2,1,6,4,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,3,2,1,6,5,4]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,3,2,4,1,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,3,2,4,1,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,2,4,5,1,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,3,2,4,5,6,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,3,2,4,6,1,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,3,2,4,6,5,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,2,5,1,4,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,3,2,5,1,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,2,5,4,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,3,2,5,4,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,2,5,6,1,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,3,2,5,6,4,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,2,6,1,4,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,3,2,6,1,5,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,2,6,4,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,3,2,6,4,5,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,2,6,5,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,3,2,6,5,4,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,3,4,1,2,5,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,3,4,1,2,6,5]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,4,1,5,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,4,1,5,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,4,1,6,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,4,1,6,5,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,4,2,1,5,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,3,4,2,1,6,5]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,4,2,5,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,4,2,5,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,4,2,6,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,4,2,6,5,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,4,5,1,2,6]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,3,4,5,1,6,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,3,4,5,2,1,6]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,3,4,5,2,6,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,3,4,5,6,1,2]=>[1,4,2]=>[[5,4,1],[3]]=>[3]=>0
[7,3,4,5,6,2,1]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[3,3]=>0
[7,3,4,6,1,2,5]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,3,4,6,1,5,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,3,4,6,2,1,5]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,3,4,6,2,5,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,3,4,6,5,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,3,4,6,5,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,3,5,1,2,4,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,3,5,1,2,6,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,5,1,4,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,5,1,4,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,5,1,6,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,5,1,6,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,5,2,1,4,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,3,5,2,1,6,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,2,4,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,5,2,4,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,5,2,6,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,5,2,6,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,5,4,1,2,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,3,5,4,1,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,4,2,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,3,5,4,2,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,4,6,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,5,4,6,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,5,6,1,2,4]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,3,5,6,1,4,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,3,5,6,2,1,4]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,3,5,6,2,4,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,3,5,6,4,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,3,5,6,4,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,3,6,1,2,4,5]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,3,6,1,2,5,4]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,6,1,4,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,6,1,4,5,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,6,1,5,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,6,1,5,4,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,2,1,4,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,3,6,2,1,5,4]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,2,4,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,6,2,4,5,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,3,6,2,5,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,6,2,5,4,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,4,1,2,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,3,6,4,1,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,4,2,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,3,6,4,2,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,4,5,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,3,6,4,5,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,5,1,2,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,3,6,5,1,4,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,5,2,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,3,6,5,2,4,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,5,4,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,3,6,5,4,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,4,1,2,3,6,5]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,4,1,2,5,3,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,1,2,5,6,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,4,1,2,6,3,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,1,2,6,5,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,1,3,2,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,4,1,3,2,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,1,3,5,2,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,1,3,5,6,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,4,1,3,6,2,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,1,3,6,5,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,1,5,2,3,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,4,1,5,2,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,1,5,3,2,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,1,5,3,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,1,5,6,2,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,1,5,6,3,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,1,6,2,3,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,4,1,6,2,5,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,1,6,3,2,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,1,6,3,5,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,1,6,5,2,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,1,6,5,3,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,2,1,3,6,5]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,4,2,1,5,3,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,4,2,1,5,6,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,4,2,1,6,3,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,4,2,1,6,5,3]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,4,2,3,1,5,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,4,2,3,1,6,5]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,3,5,1,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,2,3,5,6,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,4,2,3,6,1,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,2,3,6,5,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,2,5,1,3,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,4,2,5,1,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,5,3,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,2,5,3,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,5,6,1,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,2,5,6,3,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,2,6,1,3,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,4,2,6,1,5,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,6,3,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,2,6,3,5,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,6,5,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,2,6,5,3,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,3,1,2,6,5]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,4,3,1,5,2,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,4,3,1,5,6,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,4,3,1,6,2,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,4,3,1,6,5,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,4,3,2,1,6,5]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,4,3,2,5,1,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,4,3,2,5,6,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,4,3,2,6,1,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,4,3,2,6,5,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,4,3,5,1,2,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,4,3,5,1,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,5,2,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,3,5,2,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,5,6,1,2]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,4,3,5,6,2,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,3,6,1,2,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,4,3,6,1,5,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,6,2,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,3,6,2,5,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,6,5,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,4,3,6,5,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,5,1,2,3,6]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,4,5,1,2,6,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,4,5,1,3,2,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,5,1,3,6,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,4,5,1,6,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,5,1,6,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,5,2,1,3,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,4,5,2,1,6,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,2,3,1,6]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,5,2,3,6,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,4,5,2,6,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,5,2,6,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,5,3,1,2,6]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,4,5,3,1,6,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,3,2,1,6]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,4,5,3,2,6,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,3,6,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,5,3,6,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,5,6,1,2,3]=>[1,3,3]=>[[5,3,1],[2]]=>[2]=>0
[7,4,5,6,1,3,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,4,5,6,2,1,3]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,4,5,6,2,3,1]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[3,2]=>1
[7,4,5,6,3,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,2]=>0
[7,4,5,6,3,2,1]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,6,1,2,3,5]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,4,6,1,2,5,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,4,6,1,3,2,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,1,3,5,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,4,6,1,5,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,1,5,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,2,1,3,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,4,6,2,1,5,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,6,2,3,1,5]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,2,3,5,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,4,6,2,5,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,2,5,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,3,1,2,5]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,4,6,3,1,5,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,6,3,2,1,5]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,4,6,3,2,5,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,6,3,5,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,3,5,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,5,1,2,3]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,4,6,5,1,3,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,6,5,2,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,4,6,5,2,3,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,6,5,3,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,4,6,5,3,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,5,1,2,3,6,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,5,1,2,4,3,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,1,2,4,6,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,5,1,2,6,3,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,1,2,6,4,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,1,3,2,4,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,1,3,2,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,1,3,4,2,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,1,3,4,6,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,5,1,3,6,2,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,1,3,6,4,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,1,4,2,3,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,1,4,2,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,1,4,3,2,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,1,4,3,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,1,4,6,2,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,1,4,6,3,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,1,6,2,3,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,1,6,2,4,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,1,6,3,2,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,1,6,3,4,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,1,6,4,2,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,1,6,4,3,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,2,1,3,6,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,5,2,1,4,3,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,2,1,4,6,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,5,2,1,6,3,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,2,1,6,4,3]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,2,3,1,4,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,2,3,1,6,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,2,3,4,1,6]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,2,3,4,6,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,5,2,3,6,1,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,2,3,6,4,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,2,4,1,3,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,2,4,1,6,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,2,4,3,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,2,4,3,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,2,4,6,1,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,2,4,6,3,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,2,6,1,3,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,2,6,1,4,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,2,6,3,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,2,6,3,4,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,2,6,4,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,2,6,4,3,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,3,1,2,6,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,5,3,1,4,2,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,3,1,4,6,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,5,3,1,6,2,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,3,1,6,4,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,3,2,1,6,4]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,5,3,2,4,1,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,3,2,4,6,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,5,3,2,6,1,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,3,2,6,4,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,3,4,1,2,6]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,3,4,1,6,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,4,2,1,6]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,3,4,2,6,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,4,6,1,2]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,5,3,4,6,2,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,3,6,1,2,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,3,6,1,4,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,6,2,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,3,6,2,4,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,6,4,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,3,6,4,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,4,1,2,6,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,5,4,1,3,2,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,4,1,3,6,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,5,4,1,6,2,3]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,4,1,6,3,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,4,2,1,6,3]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,5,4,2,3,1,6]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,4,2,3,6,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,5,4,2,6,1,3]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,4,2,6,3,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,4,3,1,6,2]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,5,4,3,2,6,1]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,5,4,3,6,1,2]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,5,4,3,6,2,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,4,6,1,2,3]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,5,4,6,1,3,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,4,6,2,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,4,6,2,3,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,4,6,3,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,5,4,6,3,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,6,1,2,3,4]=>[1,2,4]=>[[5,2,1],[1]]=>[1]=>0
[7,5,6,1,2,4,3]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,5,6,1,3,2,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,5,6,1,3,4,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,5,6,1,4,2,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,5,6,1,4,3,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,6,2,1,3,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,5,6,2,1,4,3]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,6,2,3,1,4]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,5,6,2,3,4,1]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[3,1]=>2
[7,5,6,2,4,1,3]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,5,6,2,4,3,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,6,3,1,2,4]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,5,6,3,1,4,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,6,3,2,1,4]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,5,6,3,2,4,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,6,3,4,1,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,1]=>1
[7,5,6,3,4,2,1]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,6,4,1,2,3]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[1,1]=>0
[7,5,6,4,1,3,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,6,4,2,1,3]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,5,6,4,2,3,1]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,6,4,3,1,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[1,1,1]=>0
[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,1,2,3,5,4]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,6,1,2,4,3,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,1,2,4,5,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,6,1,2,5,3,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,1,2,5,4,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,1,3,2,4,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,1,3,2,5,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,3,4,2,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,1,3,4,5,2]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,6,1,3,5,2,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,1,3,5,4,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,1,4,2,3,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,1,4,2,5,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,4,3,2,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,1,4,3,5,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,4,5,2,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,1,4,5,3,2]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,1,5,2,3,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,1,5,2,4,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,5,3,2,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,1,5,3,4,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,5,4,2,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,1,5,4,3,2]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,2,1,3,5,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,2,1,4,3,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,2,1,4,5,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,2,1,5,3,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,2,1,5,4,3]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,2,3,1,4,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,2,3,1,5,4]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,3,4,1,5]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,2,3,4,5,1]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[3]=>0
[7,6,2,3,5,1,4]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,2,3,5,4,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,2,4,1,3,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,2,4,1,5,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,4,3,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,2,4,3,5,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,4,5,1,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,2,4,5,3,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,2,5,1,3,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,2,5,1,4,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,5,3,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,2,5,3,4,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,5,4,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,2,5,4,3,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,3,1,2,5,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,3,1,4,2,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,3,1,4,5,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,3,1,5,2,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,3,1,5,4,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,3,2,1,5,4]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,6,3,2,4,1,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,3,2,4,5,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,3,2,5,1,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,3,2,5,4,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,3,4,1,2,5]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,3,4,1,5,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,3,4,2,1,5]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,3,4,2,5,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,3,4,5,1,2]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[2]=>0
[7,6,3,4,5,2,1]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,3,5,1,2,4]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,3,5,1,4,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,3,5,2,1,4]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,3,5,2,4,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,3,5,4,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,3,5,4,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,4,1,2,5,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,4,1,3,2,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,4,1,3,5,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,4,1,5,2,3]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,4,1,5,3,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,4,2,1,5,3]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,6,4,2,3,1,5]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,4,2,3,5,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,4,2,5,1,3]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,4,2,5,3,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,4,3,1,5,2]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,6,4,3,2,5,1]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,6,4,3,5,1,2]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,4,3,5,2,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,4,5,1,2,3]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[1]=>0
[7,6,4,5,1,3,2]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,4,5,2,1,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,4,5,2,3,1]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,4,5,3,1,2]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[1,1]=>0
[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,5,1,2,4,3]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,5,1,3,2,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,5,1,3,4,2]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,5,1,4,2,3]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,5,1,4,3,2]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,5,2,1,4,3]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,6,5,2,3,1,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,5,2,3,4,1]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[2]=>0
[7,6,5,2,4,1,3]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,5,2,4,3,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,5,3,1,4,2]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,6,5,3,2,4,1]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,6,5,3,4,1,2]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[1]=>0
[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,5,4,1,3,2]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1]=>0
[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>[1,1,1,1,1,1]=>0
[8,6,7,5,4,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[8,7,5,6,4,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,6,5,7,4,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,7,6,4,5,3,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,6,4,5,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,6,7,4,5,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,8,4,5,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,8,4,5,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,7,5,4,6,3,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,5,4,6,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,8,4,5,6,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,6,5,4,7,3,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,6,4,7,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,5,6,7,3,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[6,7,5,4,8,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,5,6,4,8,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,7,4,8,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,7,4,8,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,7,4,5,8,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,4,5,6,8,3,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,6,4,7,8,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,4,5,7,8,3,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,4,6,7,8,3,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,7,6,5,3,4,2,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,8,6,5,3,4,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,6,7,5,3,4,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,8,5,3,4,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,8,5,3,4,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,5,7,3,4,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,6,7,3,4,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,6,5,8,3,4,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,7,5,8,3,4,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,5,7,8,3,4,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,6,7,8,3,4,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,7,6,4,3,5,2,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,8,6,4,3,5,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,6,7,4,3,5,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,8,4,3,5,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,8,4,3,5,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,8,6,3,4,5,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,6,7,3,4,5,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,6,8,3,4,5,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,7,8,3,4,5,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,7,5,4,3,6,2,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,8,5,4,3,6,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,7,4,5,3,6,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,8,5,3,4,6,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,4,3,5,6,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,3,4,5,6,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,6,5,4,3,7,2,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,5,6,4,3,7,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,4,5,3,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,4,6,3,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,6,3,4,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[6,7,5,4,3,8,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,5,6,4,3,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,7,4,3,8,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,6,4,5,3,8,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,7,4,5,3,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,4,6,3,8,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,5,6,3,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,5,4,7,3,8,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,6,4,7,3,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,4,5,7,3,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,6,7,3,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,5,6,7,3,8,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,7,5,3,4,8,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,5,7,3,4,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,7,3,4,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,6,4,3,7,8,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,4,6,3,7,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,6,3,7,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,3,6,7,8,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,4,5,6,7,8,2,1]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,8,6,5,4,2,3,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,8,5,4,2,3,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,5,6,4,2,3,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,5,7,4,2,3,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,7,4,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,6,5,8,4,2,3,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,7,5,8,4,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,6,8,4,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,5,7,8,4,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,7,8,4,2,3,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,7,6,4,5,2,3,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,8,6,4,5,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,7,4,5,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,8,4,5,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,8,4,5,2,3,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,7,5,4,6,2,3,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,4,5,6,2,3,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,8,4,5,6,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,5,4,7,2,3,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,6,4,7,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,4,5,7,2,3,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,5,6,7,2,3,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,6,5,4,8,2,3,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,7,5,4,8,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,5,6,4,8,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,4,8,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,7,4,8,2,3,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,6,4,5,8,2,3,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,4,5,8,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,4,6,8,2,3,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,4,5,6,8,2,3,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,4,7,8,2,3,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,6,4,7,8,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,5,7,8,2,3,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,4,6,7,8,2,3,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,8,6,5,3,2,4,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,6,7,5,3,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,8,5,3,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,8,5,3,2,4,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,7,5,6,3,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,8,5,6,3,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,6,5,7,3,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,7,3,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,6,5,8,3,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,7,5,8,3,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,6,8,3,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,5,7,8,3,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,7,8,3,2,4,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,6,7,5,2,3,4,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,6,8,5,2,3,4,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,8,5,2,3,4,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,7,5,6,2,3,4,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,8,5,6,2,3,4,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,6,5,7,2,3,4,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,6,7,2,3,4,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,6,5,8,2,3,4,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,5,8,2,3,4,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,7,8,2,3,4,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,7,8,2,3,4,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,8,6,4,3,2,5,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,6,7,4,3,2,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,8,4,3,2,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,8,4,3,2,5,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,7,6,3,4,2,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,8,6,3,4,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,7,3,4,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,8,3,4,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,8,3,4,2,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,8,6,4,2,3,5,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,6,7,4,2,3,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,6,8,4,2,3,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,8,4,2,3,5,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,8,6,3,2,4,5,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,6,7,3,2,4,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,8,3,2,4,5,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,8,2,3,4,5,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,8,5,4,3,2,6,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,7,5,3,4,2,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,8,5,3,4,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,4,3,5,2,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,8,4,3,5,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,3,4,5,2,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,5,4,2,3,6,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,4,5,2,3,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,4,3,2,5,6,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,7,3,4,2,5,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,8,3,4,2,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[8,5,6,4,3,2,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,4,5,3,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,4,6,3,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,5,3,4,2,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,6,3,4,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,4,3,5,2,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,3,4,5,2,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,4,3,6,2,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,4,5,3,6,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,3,4,6,2,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,3,5,6,2,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,3,4,5,6,2,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,5,6,4,2,3,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,4,5,2,3,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,4,6,2,3,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,5,3,2,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,3,4,2,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,3,5,2,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,4,5,2,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[6,7,5,4,3,2,8,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,5,6,4,3,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,7,4,3,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,7,4,3,2,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,6,4,5,3,2,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,7,4,5,3,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,4,6,3,2,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,6,3,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,5,4,7,3,2,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,6,4,7,3,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,5,7,3,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,6,7,3,2,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,6,5,3,4,2,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,6,3,4,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,3,4,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,7,3,4,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,6,4,3,5,2,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,7,4,3,5,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,3,4,5,2,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,4,3,6,2,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,5,3,6,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,3,4,6,2,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,4,5,6,2,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,4,3,7,2,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,6,4,3,7,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,5,3,7,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,6,3,7,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,5,3,4,7,2,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,6,3,4,7,2,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,3,5,7,2,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,4,5,7,2,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,4,3,6,7,2,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,5,3,6,7,2,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,4,6,7,2,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,3,5,6,7,2,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,7,5,4,2,3,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,6,4,2,3,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,5,7,4,2,3,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,7,4,2,3,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,6,4,5,2,3,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,4,5,2,3,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,4,6,2,3,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,5,6,2,3,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,4,7,2,3,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,4,7,2,3,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,5,7,2,3,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,4,6,7,2,3,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,6,7,2,3,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,7,5,3,2,4,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,6,3,2,4,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,5,7,3,2,4,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,7,2,3,4,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,7,4,3,2,5,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,6,3,4,2,5,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,5,3,2,6,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,3,4,2,6,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,3,5,2,6,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,4,5,2,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,5,3,2,7,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,6,3,2,7,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,5,6,3,2,7,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,5,3,4,2,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,3,4,2,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,3,5,2,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,4,5,2,7,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,4,3,6,2,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,5,3,6,2,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,5,6,2,7,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,5,6,2,7,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,5,6,2,3,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,4,5,2,6,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,4,5,6,7,8,1]=>[7,1]=>[[7,7],[6]]=>[6]=>0
[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,6,7,5,4,3,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,8,5,4,3,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,7,5,6,4,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,5,6,4,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,6,5,7,4,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,6,7,4,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,6,5,8,4,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,7,5,8,4,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,6,8,4,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,5,7,8,4,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,6,7,8,4,3,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,7,6,4,5,3,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,6,4,5,3,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,7,4,5,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,8,4,5,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,7,8,4,5,3,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,7,5,4,6,3,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,5,6,3,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,8,4,5,6,3,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,5,6,4,7,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,4,5,7,3,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,4,6,7,3,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,5,4,8,3,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,7,5,4,8,3,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,6,4,8,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,7,4,8,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,4,5,8,3,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,7,4,5,8,3,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,4,6,8,3,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,5,6,8,3,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,5,4,7,8,3,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,6,4,7,8,3,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,4,5,7,8,3,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,4,6,7,8,3,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,7,6,5,3,4,1,2]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,8,6,5,3,4,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,8,5,3,4,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,8,5,3,4,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,5,6,3,4,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,5,6,3,4,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,5,7,3,4,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,6,7,3,4,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,6,5,8,3,4,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,5,8,3,4,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,6,8,3,4,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,7,8,3,4,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,7,8,3,4,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,7,6,4,3,5,1,2]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,8,6,4,3,5,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,7,4,3,5,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,4,3,5,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,8,4,3,5,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,6,3,4,5,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,8,6,3,4,5,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,6,7,3,4,5,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,8,3,4,5,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,8,3,4,5,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,7,5,4,3,6,1,2]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,8,5,4,3,6,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,4,5,3,6,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,4,5,3,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,7,5,3,4,6,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,8,5,3,4,6,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,7,4,3,5,6,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,8,4,3,5,6,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,3,4,5,6,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,6,5,4,3,7,1,2]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,6,3,4,7,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,4,3,5,7,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,4,3,6,7,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,5,4,3,8,1,2]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[6,7,5,4,3,8,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,6,4,3,8,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,4,3,8,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,7,4,3,8,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,6,4,5,3,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,4,5,3,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,4,6,3,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,5,6,3,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,4,7,3,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,4,7,3,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,5,7,3,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,6,7,3,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,6,7,3,8,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,6,5,3,4,8,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,5,3,4,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,5,6,3,4,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,7,3,4,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,7,3,4,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,6,4,3,5,8,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,4,3,5,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,3,4,5,8,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,5,4,3,6,8,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,4,3,7,8,1,2]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,6,4,3,7,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,4,6,3,7,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,6,3,7,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,6,3,4,7,8,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,5,3,6,7,8,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,8,6,5,4,2,1,3]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,6,7,5,4,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,8,5,4,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,7,5,6,4,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,5,6,4,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,6,5,7,4,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,6,7,4,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,6,5,8,4,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,7,5,8,4,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,6,8,4,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,5,7,8,4,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,6,7,8,4,2,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,7,6,4,5,2,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,6,4,5,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,7,4,5,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,8,4,5,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,7,8,4,5,2,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,7,5,4,6,2,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,5,4,6,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,4,5,6,2,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,8,4,5,6,2,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,6,5,4,7,2,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,4,5,7,2,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,4,6,7,2,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,5,6,7,2,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,6,5,4,8,2,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,7,5,4,8,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,6,4,8,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,7,4,8,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,7,4,8,2,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,6,4,5,8,2,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,7,4,5,8,2,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,4,6,8,2,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,5,6,8,2,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,5,4,7,8,2,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,6,4,7,8,2,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,4,6,7,8,2,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,7,8,5,4,1,2,3]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,5,6,4,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,5,6,7,4,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,7,5,8,4,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,5,6,8,4,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,5,7,8,4,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,7,8,4,1,2,3]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[7,8,6,4,5,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,6,7,4,5,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,8,4,5,1,2,3]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,8,5,4,6,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,4,5,6,1,2,3]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,8,4,5,6,1,2,3]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,5,6,4,7,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,4,5,7,1,2,3]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,5,4,6,7,1,2,3]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,5,6,7,1,2,3]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,7,5,4,8,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,6,4,8,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,7,4,8,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,7,4,8,1,2,3]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,6,4,5,8,1,2,3]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,7,4,5,8,1,2,3]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,5,4,6,8,1,2,3]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,5,6,8,1,2,3]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,5,4,7,8,1,2,3]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,6,4,7,8,1,2,3]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,4,5,7,8,1,2,3]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,4,6,7,8,1,2,3]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,8,6,5,3,2,1,4]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,6,7,5,3,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,8,5,3,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,7,5,6,3,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,5,6,3,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,6,5,7,3,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,6,7,3,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,6,5,8,3,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,7,5,8,3,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,6,8,3,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,5,7,8,3,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,6,7,8,3,2,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,7,6,5,2,3,1,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,8,6,5,2,3,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,7,5,2,3,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,5,2,3,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,8,5,2,3,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,5,6,2,3,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,5,6,2,3,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,5,7,2,3,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,6,7,2,3,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,6,5,8,2,3,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,5,8,2,3,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,6,8,2,3,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,7,8,2,3,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,7,8,2,3,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,7,8,5,3,1,2,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,5,6,3,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,5,6,7,3,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,7,5,8,3,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,5,6,8,3,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,5,7,8,3,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,7,8,3,1,2,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[6,7,8,5,2,1,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,5,6,2,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,5,6,7,2,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,7,5,8,2,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,5,6,8,2,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,5,7,8,2,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,7,8,2,1,3,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,6,7,8,1,2,3,4]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[7,8,6,4,3,2,1,5]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,6,7,4,3,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,8,4,3,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,7,6,3,4,2,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,6,3,4,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,7,3,4,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,7,8,3,4,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,7,6,4,2,3,1,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,8,6,4,2,3,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,7,4,2,3,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,4,2,3,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,8,4,2,3,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,6,3,2,4,1,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,7,3,2,4,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,3,2,4,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,8,3,2,4,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,6,2,3,4,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,8,6,2,3,4,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,6,7,2,3,4,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,8,2,3,4,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,8,2,3,4,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,8,4,3,1,2,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,6,3,4,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,6,7,3,4,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,8,3,4,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,8,3,4,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,8,4,2,1,3,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,7,8,3,2,1,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,6,2,3,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,6,7,2,3,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,8,2,3,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,8,2,3,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,8,5,4,3,2,1,6]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,7,4,5,3,2,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,4,5,3,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,5,3,4,2,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,3,5,2,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,4,3,5,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,3,4,5,2,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,8,3,4,5,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,5,4,2,3,1,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,7,4,5,2,3,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,4,5,2,3,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,7,5,3,2,4,1,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,8,5,3,2,4,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,5,2,3,4,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,8,5,2,3,4,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,7,4,3,2,5,1,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,8,4,3,2,5,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,3,4,2,5,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,3,4,2,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,7,4,2,3,5,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,3,2,4,5,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,8,3,2,4,5,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,2,3,4,5,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,8,5,3,4,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,4,3,5,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,3,4,5,1,2,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,8,3,4,5,1,2,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,4,5,2,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,5,2,3,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,3,4,2,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,4,2,3,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,3,2,4,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,2,3,4,1,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,8,2,3,4,1,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,5,6,4,3,2,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,6,4,5,3,2,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,5,6,3,2,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,6,5,3,4,2,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,6,3,4,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,4,3,5,2,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,4,3,6,2,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,4,5,3,6,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,3,5,6,2,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,4,5,6,2,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,6,5,4,2,3,1,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,6,4,2,3,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,4,5,2,3,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,5,6,2,3,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,5,3,2,4,1,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,5,2,3,4,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,6,2,3,4,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,4,3,2,5,1,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,3,4,2,5,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,4,2,3,5,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,6,3,2,4,5,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,4,3,2,6,1,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,4,5,3,2,6,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,3,4,2,6,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,3,5,2,6,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,4,5,2,6,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,4,2,3,6,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,4,5,2,3,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,3,2,4,6,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,4,3,2,5,6,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,3,4,2,5,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,6,3,4,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,3,4,5,1,2,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,5,3,6,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,3,4,6,1,2,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,3,5,6,1,2,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,3,4,5,6,1,2,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,4,5,6,2,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,5,6,2,3,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,2,3,4,1,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,3,4,5,2,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,5,2,3,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,2,3,4,1,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,2,3,5,1,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,2,3,4,5,1,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,7,5,4,3,2,1,8]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,5,6,4,3,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,5,7,4,3,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,4,5,3,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,7,4,5,3,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,4,6,3,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,5,6,3,2,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,5,4,7,3,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,6,4,7,3,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,6,7,3,2,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,5,6,7,3,2,1,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[7,6,5,3,4,2,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,7,5,3,4,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,6,3,4,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,7,3,4,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,7,3,4,2,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,6,4,3,5,2,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,7,4,3,5,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,3,4,5,2,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,4,3,6,2,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,4,5,3,6,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,4,5,6,2,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,5,4,3,7,2,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,6,4,3,7,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,5,3,7,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,6,3,7,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,6,3,7,2,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,3,4,7,2,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,3,6,7,2,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,6,5,4,2,3,1,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[6,7,5,4,2,3,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,6,4,2,3,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,7,4,2,3,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,6,4,5,2,3,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,4,5,2,3,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,4,6,2,3,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,5,6,2,3,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,4,7,2,3,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,4,7,2,3,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,6,7,2,3,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,6,7,2,3,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,6,5,3,2,4,1,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,5,6,3,2,4,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,3,2,4,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,7,3,2,4,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,6,5,2,3,4,1,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,5,2,3,4,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,5,6,2,3,4,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,7,2,3,4,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,7,2,3,4,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,6,4,3,2,5,1,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[6,7,4,3,2,5,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,3,4,2,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,4,2,3,5,1,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,4,2,3,5,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,6,3,2,4,5,1,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,3,2,4,5,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,2,3,4,5,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,5,4,3,2,6,1,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,4,5,3,2,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,3,4,2,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,5,2,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,4,5,2,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,4,2,3,6,1,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,4,5,2,3,6,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,3,2,4,6,1,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,4,3,2,5,6,1,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,4,3,2,7,1,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[5,4,6,3,2,7,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,3,4,2,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,3,5,2,7,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,4,5,2,7,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,3,6,2,7,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,5,3,6,2,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,4,6,2,7,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,5,6,2,7,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,5,6,2,7,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,4,5,2,3,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,6,2,3,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,6,2,3,7,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,5,3,2,4,7,1,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,6,3,2,4,7,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,2,3,4,7,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,3,4,2,5,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,3,2,6,7,1,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,5,3,2,6,7,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,4,2,6,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,5,2,6,7,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,2,3,6,7,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,2,5,6,7,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,6,7,4,3,1,2,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,4,5,6,3,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,4,6,7,3,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,5,6,7,3,1,2,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[6,7,5,3,4,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,6,3,4,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,7,3,4,1,2,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,4,3,5,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,3,4,5,1,2,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,4,5,3,6,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,3,4,6,1,2,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,3,5,6,1,2,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,4,5,6,1,2,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,6,4,3,7,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,4,6,3,7,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,3,4,7,1,2,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,6,3,4,7,1,2,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,4,3,5,7,1,2,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,4,5,7,1,2,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,3,6,7,1,2,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,3,4,6,7,1,2,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,3,5,6,7,1,2,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,6,7,4,2,1,3,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,7,4,5,2,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,4,5,6,2,1,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,4,6,7,2,1,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,5,6,7,2,1,3,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,5,6,7,1,2,3,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[5,6,7,3,2,1,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,7,5,2,3,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,6,2,3,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,7,2,3,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,7,2,3,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,3,2,4,1,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,6,2,3,4,1,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,7,2,3,4,1,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,3,4,5,2,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,4,5,2,3,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,2,3,4,1,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,2,3,5,1,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,2,3,4,5,1,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,6,3,2,1,7,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,6,3,4,2,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,3,4,5,2,1,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,5,3,6,2,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,3,5,6,2,1,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,4,5,6,2,1,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,6,4,2,3,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,4,5,2,3,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,6,2,3,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,5,6,2,3,1,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,6,3,2,4,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,5,2,3,4,1,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,6,2,3,4,1,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,3,4,2,5,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,2,3,5,1,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,2,4,5,1,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,3,4,5,1,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,3,2,6,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,3,5,2,6,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,4,5,2,6,1,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,4,2,3,6,1,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,2,4,6,1,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,2,3,4,6,1,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,3,2,5,6,1,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,4,2,5,6,1,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,2,3,5,6,1,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,2,4,5,6,1,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,4,5,6,1,2,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,3,4,5,1,6,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>[1,1,1,1,1,1]=>0
[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>[1,1,1,1,1,1]=>0
[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[6,5,8,7,4,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[5,7,6,8,4,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>[1,1,1,1,1,1]=>0
[4,7,8,6,5,3,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[4,7,6,8,5,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[5,4,8,7,6,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[6,5,4,8,7,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,6,4,8,7,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,6,5,8,7,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[5,7,6,4,8,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,7,6,5,8,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,6,7,5,8,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,4,7,6,8,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,7,6,8,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,6,5,7,8,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>[1,1,1,1,1,1]=>0
[3,7,8,6,5,4,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[3,6,8,7,5,4,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[3,7,6,8,5,4,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[3,6,5,8,7,4,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,7,6,5,8,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,6,7,5,8,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,5,7,6,8,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,6,5,7,8,4,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,3,8,7,6,5,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,3,7,6,8,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,6,7,8,5,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[3,4,7,6,8,5,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,4,3,8,7,6,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,5,3,8,7,6,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,5,3,7,8,6,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,4,8,7,6,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,5,4,7,8,6,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,3,5,7,8,6,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,5,4,3,8,7,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[5,6,4,3,8,7,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,6,5,3,8,7,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,4,6,3,8,7,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,6,3,8,7,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,6,5,4,8,7,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,5,6,4,8,7,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,3,6,5,8,7,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,6,5,8,7,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,5,3,6,8,7,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,4,6,8,7,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,3,5,6,8,7,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,7,6,4,3,8,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,7,6,5,3,8,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,6,7,5,3,8,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,4,7,6,3,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,7,6,3,8,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,5,7,3,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,6,5,4,8,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,6,7,5,4,8,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,7,6,4,8,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,6,5,7,4,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,6,7,4,8,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,3,7,6,5,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,6,7,5,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,4,7,6,5,8,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,6,7,5,8,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,4,3,7,6,8,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,5,3,7,6,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,4,7,6,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,5,7,6,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,4,5,7,6,8,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,6,5,3,7,8,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,6,5,4,7,8,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,5,6,4,7,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,3,6,5,7,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,6,5,7,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,4,6,7,8,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>[1,1,1,1,1,1]=>0
[2,7,8,6,5,4,3,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[2,7,6,8,5,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,5,8,7,6,4,3,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[2,6,5,8,7,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,7,6,5,8,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,6,7,5,8,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,5,7,6,8,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,6,5,7,8,4,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[2,5,4,8,7,6,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,5,4,7,8,6,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,6,5,4,8,7,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,5,6,4,8,7,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,4,6,5,8,7,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,7,6,5,4,8,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,6,7,5,4,8,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,5,7,6,4,8,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,6,5,7,4,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,6,7,4,8,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,7,6,5,8,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,6,7,5,8,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,5,4,7,6,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,5,4,7,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,5,6,4,7,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,6,5,7,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,4,6,7,8,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,4,5,6,7,8,3,1]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[3,2,8,7,6,5,4,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[3,2,7,6,8,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,5,7,8,6,4,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,2,6,5,8,7,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,5,6,8,7,4,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,2,7,6,5,8,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,6,7,5,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,5,7,6,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,6,5,7,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[2,3,7,6,8,5,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,3,6,5,8,7,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,3,7,6,5,8,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,3,6,7,5,8,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,5,7,6,8,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,6,5,7,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,5,6,7,8,4,1]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[4,3,2,8,7,6,5,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,4,2,8,7,6,5,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,4,2,7,8,6,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,2,6,8,7,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,2,7,6,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,2,6,7,8,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,4,3,8,7,6,5,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,4,3,7,8,6,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,4,3,6,8,7,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,4,3,7,6,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,3,6,7,8,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,2,4,7,8,6,5,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,2,4,7,6,8,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,3,4,7,6,8,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,4,6,7,8,5,1]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[5,4,3,2,8,7,6,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[4,5,3,2,8,7,6,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,5,3,2,7,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,5,4,2,7,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,4,5,2,8,7,6,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,4,5,2,7,8,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,4,3,8,7,6,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,5,4,3,7,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,4,5,3,8,7,6,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,4,5,3,7,8,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,2,5,4,7,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,5,4,8,7,6,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,3,5,4,7,8,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,2,5,8,7,6,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,2,5,7,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,4,3,5,8,7,6,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,4,3,5,7,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,4,5,7,8,6,1]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[6,5,4,3,2,8,7,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[5,6,4,3,2,8,7,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,6,5,3,2,8,7,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,4,6,3,2,8,7,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,6,3,2,8,7,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,6,5,4,2,8,7,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,5,6,4,2,8,7,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,3,6,5,2,8,7,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,3,6,2,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,5,3,6,2,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,4,6,2,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,5,6,2,8,7,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,6,5,4,3,8,7,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,4,6,5,3,8,7,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,5,6,3,8,7,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,2,6,5,4,8,7,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,5,6,4,8,7,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,3,2,6,5,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,4,2,6,5,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,3,6,5,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,4,6,5,8,7,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,3,4,6,5,8,7,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,5,3,2,6,8,7,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,5,4,2,6,8,7,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,3,5,2,6,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,5,2,6,8,7,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,4,3,6,8,7,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,4,5,3,6,8,7,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,2,5,4,6,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,2,5,6,8,7,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,4,3,5,6,8,7,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,4,5,6,8,7,1]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[5,7,6,4,3,2,8,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,7,6,5,3,2,8,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,6,7,5,3,2,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,4,7,6,3,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,7,6,3,2,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,5,7,3,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,6,5,4,2,8,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,6,7,5,4,2,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,5,7,6,4,2,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,6,5,7,4,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,6,7,4,2,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,3,7,6,5,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,6,7,5,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,7,6,5,2,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,4,6,7,5,2,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,4,3,7,6,2,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,3,7,6,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,4,7,6,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,3,5,7,6,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,5,7,6,2,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,6,5,3,7,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,5,4,7,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,6,4,7,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,6,5,7,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,6,5,7,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,4,6,7,2,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,6,5,4,3,8,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,5,7,6,4,3,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,6,5,7,4,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,6,7,4,3,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,4,7,6,5,3,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,4,6,7,5,3,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,5,4,7,6,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,5,7,6,3,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,5,6,4,7,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,6,5,7,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,4,6,7,3,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,7,6,5,4,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,6,7,5,4,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,5,7,6,4,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,6,5,7,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,5,6,7,4,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,3,7,6,5,4,8,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,3,6,7,5,4,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,5,7,6,4,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,3,2,7,6,5,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,2,6,7,5,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,2,7,6,5,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,2,6,7,5,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,3,7,6,5,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,3,6,7,5,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,4,7,6,5,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,4,6,7,5,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,3,4,7,6,5,8,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,4,3,2,7,6,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,5,3,2,7,6,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,4,2,7,6,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,5,2,7,6,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,5,2,7,6,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,4,3,7,6,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,5,3,7,6,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,5,4,7,6,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,5,4,7,6,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,2,5,7,6,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,2,5,7,6,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,3,5,7,6,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,4,5,7,6,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,6,5,3,2,7,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,6,5,4,2,7,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,5,6,4,2,7,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,6,5,2,7,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,6,5,2,7,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,4,6,2,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,5,4,3,7,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,5,6,4,3,7,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,6,5,3,7,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,4,6,3,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,5,6,3,7,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,2,5,6,4,7,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,3,6,5,4,7,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,5,6,4,7,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,3,2,6,5,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,4,2,6,5,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,6,5,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,4,6,5,7,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,5,3,6,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,5,4,6,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>[1,1,1,1,1,1]=>0
[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[1,7,6,8,5,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[1,6,5,8,7,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,7,6,5,8,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,6,7,5,8,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,5,7,6,8,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,6,5,7,8,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[1,4,7,6,8,5,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,5,4,8,7,6,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,5,4,7,8,6,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,6,5,4,8,7,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,4,6,5,8,7,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,7,6,5,4,8,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,6,5,7,4,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,6,7,4,8,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,4,7,6,5,8,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,4,6,7,5,8,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,5,4,7,6,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,5,7,6,8,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,6,5,4,7,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,5,6,4,7,8,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,4,6,7,8,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,4,5,6,7,8,3,2]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[1,3,7,6,8,5,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,6,5,8,7,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,7,6,5,8,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,6,7,5,8,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,3,5,7,6,8,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,3,6,5,7,8,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,5,6,7,8,4,2]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,4,3,8,7,6,5,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,4,3,7,8,6,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,4,3,6,8,7,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,4,3,7,6,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,3,6,7,8,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,4,7,6,8,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,3,4,6,7,8,5,2]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,5,4,3,8,7,6,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,5,4,3,7,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,4,5,3,8,7,6,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,4,5,3,7,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,5,4,8,7,6,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,5,4,7,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,3,5,8,7,6,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,4,3,5,7,8,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,4,5,7,8,6,2]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,6,5,4,3,8,7,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,5,6,4,3,8,7,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,4,6,5,3,8,7,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,4,6,3,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,5,6,3,8,7,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,3,6,5,4,8,7,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,5,6,4,8,7,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,4,3,6,5,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,4,6,5,8,7,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,5,4,3,6,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,4,5,3,6,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,5,4,6,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,3,5,6,8,7,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,4,5,6,8,7,2]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,7,6,5,4,3,8,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,6,7,5,4,3,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,7,6,4,3,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,6,5,7,4,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,6,7,4,3,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,4,7,6,5,3,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,4,6,7,5,3,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,5,4,7,6,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,5,7,6,3,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,6,5,4,7,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,6,4,7,3,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,6,5,7,3,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,4,6,7,3,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,5,7,6,4,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,6,5,7,4,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,3,6,7,5,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,4,7,6,5,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,5,4,3,7,6,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,3,5,4,7,6,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,3,5,7,6,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,5,4,3,7,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,4,6,5,3,7,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,4,6,3,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,5,6,3,7,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,5,6,4,7,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,3,6,5,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,4,6,5,7,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,5,3,6,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,5,4,6,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,4,5,6,7,8,2]=>[7,1]=>[[7,7],[6]]=>[6]=>0
[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,1,7,6,8,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,6,7,8,5,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,5,7,8,6,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,6,5,8,7,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,5,6,8,7,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,7,6,5,8,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,6,7,5,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,5,7,6,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,6,5,7,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,4,7,8,6,5,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,4,6,8,7,5,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,4,7,6,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,5,4,8,7,6,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,5,4,7,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,4,5,8,7,6,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,6,5,4,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,5,6,4,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,4,6,5,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,5,4,6,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,7,6,5,4,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,6,7,5,4,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,5,7,6,4,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,6,5,7,4,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,5,6,7,4,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,4,7,6,5,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,4,6,7,5,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,5,4,7,6,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,4,5,7,6,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,6,5,4,7,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,1,5,6,4,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,4,6,5,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[2,2,2,2,2]=>0
[1,2,7,6,8,5,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,6,5,8,7,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,7,6,5,8,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,6,7,5,8,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,5,7,6,8,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,6,5,7,8,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,5,6,7,8,4,3]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,4,7,6,8,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,4,6,7,8,5,3]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,5,4,8,7,6,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,4,5,7,8,6,3]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,6,5,4,8,7,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,5,6,4,8,7,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,4,6,5,8,7,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,5,4,6,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,4,5,6,8,7,3]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,7,6,5,4,8,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,2,6,7,5,4,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,5,7,6,4,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,6,5,7,4,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,4,7,6,5,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,5,4,7,6,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,6,5,4,7,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,5,6,4,7,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,4,6,5,7,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,5,4,6,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,4,5,6,7,8,3]=>[7,1]=>[[7,7],[6]]=>[6]=>0
[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,2,1,7,6,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,1,6,5,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,1,7,6,5,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,2,1,6,7,5,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,1,5,7,6,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,1,6,5,7,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,3,1,8,7,6,5,4]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,3,1,7,8,6,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,3,1,6,8,7,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,3,1,7,6,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,3,1,6,7,8,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,1,5,8,7,6,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,3,1,5,7,8,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,1,6,5,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,3,1,5,6,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,1,7,6,5,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,1,6,7,5,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,1,5,7,6,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,1,6,5,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,2,8,7,6,5,4]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,3,2,7,8,6,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,3,2,6,8,7,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,3,2,7,6,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,2,6,7,8,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,2,5,8,7,6,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,3,2,5,7,8,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,2,6,5,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,2,5,6,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,2,7,6,5,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,2,6,7,5,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,2,5,7,6,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,2,6,5,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,3,7,8,6,5,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,3,6,8,7,5,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,3,7,6,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,3,5,8,7,6,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,3,6,5,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,3,7,6,5,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,3,6,7,5,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,3,5,7,6,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,3,6,5,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,3,7,6,8,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,3,6,7,8,5,4]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,3,5,7,8,6,4]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,3,6,5,8,7,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,3,5,6,8,7,4]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,3,7,6,5,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,3,6,5,7,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,3,5,6,7,8,4]=>[7,1]=>[[7,7],[6]]=>[6]=>0
[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[4,3,2,1,7,6,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,4,2,1,8,7,6,5]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,4,2,1,7,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,4,2,1,6,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,4,2,1,7,6,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,3,1,8,7,6,5]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,4,3,1,7,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,4,3,1,6,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,4,3,1,7,6,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,4,1,8,7,6,5]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,4,1,7,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,2,4,1,6,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,2,4,1,7,6,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,4,1,8,7,6,5]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,3,4,1,7,8,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,4,1,6,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,4,1,7,6,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,4,1,6,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,4,3,2,8,7,6,5]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,4,3,2,7,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,4,3,2,6,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,4,3,2,7,6,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,3,4,2,8,7,6,5]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,4,2,7,8,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,4,2,6,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,4,2,7,6,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,4,2,6,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,4,3,7,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,4,3,6,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,4,3,7,6,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,2,4,3,8,7,6,5]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,4,3,7,8,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,4,3,6,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,4,3,7,6,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,4,3,6,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,2,1,4,7,6,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,3,1,4,8,7,6,5]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,3,1,4,7,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,1,4,6,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,1,4,7,6,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,2,4,8,7,6,5]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,3,2,4,7,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,2,4,6,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,2,4,7,6,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,3,4,8,7,6,5]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,1,3,4,7,6,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,2,3,4,7,8,6,5]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,3,4,6,8,7,5]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,3,4,6,7,8,5]=>[7,1]=>[[7,7],[6]]=>[6]=>0
[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[4,5,3,2,1,8,7,6]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,5,3,2,1,7,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,5,4,2,1,8,7,6]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,5,4,2,1,7,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,3,5,2,1,8,7,6]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,5,2,1,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,5,2,1,8,7,6]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,5,2,1,7,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,4,3,1,8,7,6]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,5,4,3,1,7,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,4,5,3,1,8,7,6]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,5,3,1,7,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,2,5,4,1,8,7,6]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,5,4,1,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,3,5,4,1,8,7,6]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,3,5,4,1,7,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,2,5,1,8,7,6]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,2,5,1,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,4,2,5,1,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,2,5,1,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,5,1,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,3,5,1,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,2,4,5,1,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,4,5,1,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,3,4,5,1,8,7,6]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,4,5,1,7,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,4,3,2,8,7,6]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,5,4,3,2,7,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,4,5,3,2,8,7,6]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,4,5,3,2,7,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,5,4,2,8,7,6]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,5,4,2,7,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,3,5,2,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,3,5,2,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,4,5,2,8,7,6]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,3,4,5,2,7,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,1,5,4,3,8,7,6]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,5,4,3,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,1,4,5,3,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,4,5,3,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,5,4,3,8,7,6]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,5,4,3,7,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,4,5,3,8,7,6]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,4,5,3,7,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,2,1,5,4,8,7,6]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,1,5,4,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,3,1,5,4,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,2,5,4,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,2,5,4,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,3,5,4,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,3,5,4,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,3,5,4,8,7,6]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,3,5,4,7,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,4,2,1,5,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,4,3,1,5,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,2,4,1,5,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,4,1,5,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,4,1,5,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,4,3,2,5,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,3,4,2,5,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,4,2,5,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,4,3,5,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,4,3,5,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,4,3,5,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,1,4,5,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,2,4,5,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,2,3,4,5,8,7,6]=>[6,1,1]=>[[6,6,6],[5,5]]=>[5,5]=>0
[1,2,3,4,5,7,8,6]=>[7,1]=>[[7,7],[6]]=>[6]=>0
[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[5,6,4,3,2,1,8,7]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,6,5,3,2,1,8,7]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,4,6,3,2,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,6,3,2,1,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,6,5,4,2,1,8,7]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,5,6,4,2,1,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,3,6,5,2,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,4,6,5,2,1,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,4,3,6,2,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,3,6,2,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,4,6,2,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,3,5,6,2,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,5,6,2,1,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,6,5,4,3,1,8,7]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,5,6,4,3,1,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,4,6,5,3,1,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,5,4,6,3,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,5,6,3,1,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,2,6,5,4,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,5,6,4,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,6,5,4,1,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,3,5,6,4,1,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,3,2,6,5,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,4,2,6,5,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,3,6,5,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,4,6,5,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,4,6,5,1,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,4,3,2,6,1,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,5,3,2,6,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,4,2,6,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,5,2,6,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,5,2,6,1,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,4,3,6,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,5,3,6,1,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,5,4,6,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,2,5,6,1,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,2,5,6,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,3,5,6,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,5,4,3,2,8,7]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,5,6,4,3,2,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,4,6,3,2,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,5,6,3,2,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,6,5,4,2,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,3,5,6,4,2,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,4,6,5,2,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,1,6,5,4,3,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,5,6,4,3,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,4,6,5,3,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,5,4,6,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,4,5,6,3,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,2,6,5,4,3,8,7]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,2,5,6,4,3,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,4,6,5,3,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,5,4,6,3,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,1,6,5,4,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,2,1,5,6,4,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,3,1,6,5,4,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,2,6,5,4,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,2,5,6,4,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,3,5,6,4,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,2,3,6,5,4,8,7]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,4,2,1,6,5,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,3,1,6,5,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,4,1,6,5,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,4,1,6,5,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,3,2,6,5,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,3,4,2,6,5,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,2,4,3,6,5,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,1,4,6,5,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,3,1,4,6,5,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,2,4,6,5,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,3,4,6,5,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,5,3,2,1,6,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,5,4,2,1,6,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,3,5,2,1,6,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,5,2,1,6,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,4,3,1,6,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,4,5,3,1,6,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,2,5,4,1,6,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,3,5,4,1,6,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,2,5,1,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,4,2,5,1,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,5,1,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,2,4,5,1,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,3,4,5,1,6,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,4,3,2,6,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,4,5,3,2,6,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,5,4,2,6,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,3,5,2,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,4,5,2,6,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,1,5,4,3,6,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,1,4,5,3,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,5,4,3,6,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,4,5,3,6,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,2,1,5,4,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,3,2,5,4,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,3,5,4,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,3,5,4,6,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,4,1,5,6,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,4,2,5,6,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,4,3,5,6,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,3,4,5,6,8,7]=>[7,1]=>[[7,7],[6]]=>[6]=>0
[5,7,6,4,3,2,1,8]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,7,6,5,3,2,1,8]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,4,7,6,3,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,6,5,7,3,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,6,5,4,2,1,8]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[3,5,6,7,4,2,1,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,3,7,6,5,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,3,7,6,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,5,3,7,6,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,4,7,6,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,5,7,6,2,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,6,5,3,7,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,4,7,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,6,4,7,2,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,3,6,5,7,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,6,5,4,3,1,8]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,6,5,7,4,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,6,7,4,3,1,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,6,7,5,3,1,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,5,4,7,6,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,5,7,6,3,1,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,5,6,4,7,3,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,4,6,7,3,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,2,7,6,5,4,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,2,6,7,5,4,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,5,7,6,4,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,6,5,7,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,5,6,7,4,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,3,6,7,5,4,1,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,3,5,7,6,4,1,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,3,6,5,7,4,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,3,2,7,6,5,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,3,2,6,7,5,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,4,2,7,6,5,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,2,6,7,5,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,3,7,6,5,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,4,7,6,5,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,4,6,7,5,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,3,4,7,6,5,1,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,4,3,2,7,6,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,5,3,2,7,6,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,4,2,7,6,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,5,2,7,6,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,5,2,7,6,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,4,3,7,6,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,5,4,7,6,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,3,5,4,7,6,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,3,2,5,7,6,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,4,2,5,7,6,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,3,5,7,6,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,2,4,5,7,6,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,6,5,4,2,7,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,6,4,2,7,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,3,6,5,2,7,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,4,6,5,2,7,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,4,6,2,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,4,3,7,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,4,6,5,3,7,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,4,6,3,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,5,6,3,7,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,2,6,5,4,7,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,3,5,6,4,7,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,3,2,6,5,7,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,4,2,6,5,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,6,5,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,4,6,5,7,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,4,6,5,7,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,5,4,2,6,7,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,4,3,6,7,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,5,3,6,7,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,2,5,4,6,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,3,5,4,6,7,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,3,5,6,7,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,7,6,5,4,3,2,8]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[1,6,5,7,4,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,6,7,4,3,2,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,4,6,7,5,3,2,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,5,4,7,6,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,5,7,6,3,2,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,5,6,4,7,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,6,5,7,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,4,6,7,3,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,6,7,5,4,2,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,3,5,7,6,4,2,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,3,6,5,7,4,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,3,7,6,5,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,5,3,7,6,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,4,7,6,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,3,5,7,6,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,5,4,3,7,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,6,4,3,7,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,6,5,3,7,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,4,6,3,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,5,6,3,7,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,6,5,4,7,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,5,6,4,7,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,4,3,6,5,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,4,6,5,7,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,4,3,6,7,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,5,3,6,7,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,5,4,6,7,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,7,6,5,4,3,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,1,6,7,5,4,3,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,5,6,7,4,3,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,4,7,6,5,3,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,4,6,7,5,3,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,5,4,7,6,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,4,5,7,6,3,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,5,4,6,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,2,6,7,5,4,3,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,5,7,6,4,3,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,4,7,6,5,3,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,5,4,7,6,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,5,6,4,7,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,4,6,5,7,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,5,4,6,7,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,2,1,7,6,5,4,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,1,6,7,5,4,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,1,5,7,6,4,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,1,6,5,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,3,1,7,6,5,4,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,3,1,6,7,5,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,1,6,5,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,5,6,7,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,2,7,6,5,4,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,3,2,6,7,5,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,2,5,7,6,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,2,6,5,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,5,6,7,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,3,7,6,5,4,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,3,6,7,5,4,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,3,6,5,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,2,3,7,6,5,4,8]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,3,6,5,7,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,3,2,1,7,6,5,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,3,2,1,6,7,5,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,2,4,1,7,6,5,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,4,1,6,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,3,4,1,7,6,5,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,4,1,6,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,3,2,7,6,5,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,3,2,6,7,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,4,2,7,6,5,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,4,2,6,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,4,3,7,6,5,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,4,3,6,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,2,1,4,7,6,5,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,3,1,4,6,7,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,2,4,7,6,5,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,4,3,2,1,7,6,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[4,5,3,2,1,7,6,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,4,2,1,7,6,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,5,2,1,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,4,5,2,1,7,6,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,4,3,1,7,6,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,4,5,3,1,7,6,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,5,4,1,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,3,5,4,1,7,6,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,3,2,5,1,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,4,2,5,1,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,5,1,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,4,5,1,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,4,5,1,7,6,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,4,3,2,7,6,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,5,3,2,7,6,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,5,4,2,7,6,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,3,5,2,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,4,5,2,7,6,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,5,4,3,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,5,4,3,7,6,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,4,5,3,7,6,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,2,1,5,4,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,3,1,5,4,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,5,4,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,3,5,4,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,2,3,5,4,7,6,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,3,2,1,5,7,6,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,4,2,1,5,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,3,1,5,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,4,1,5,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,3,4,1,5,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,3,2,5,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,4,2,5,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,4,3,5,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,1,4,5,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,2,4,5,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,5,6,4,2,1,7,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,4,6,2,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,6,5,3,1,7,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,5,4,6,3,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,5,6,3,1,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,3,6,5,4,1,7,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,3,5,6,4,1,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,4,2,6,5,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,3,6,5,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,4,6,5,1,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,5,4,2,6,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,3,6,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,5,4,6,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,3,5,4,6,1,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,3,5,6,1,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,6,4,3,2,7,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,6,5,3,2,7,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,5,4,6,3,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,5,6,3,2,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,3,6,5,4,2,7,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,5,6,4,2,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,4,3,6,5,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,4,6,5,2,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,4,3,6,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,5,3,6,2,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,5,4,6,2,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,3,5,6,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,5,6,4,3,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,4,6,5,3,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,5,4,6,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,4,5,6,3,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,2,6,5,4,3,7,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,5,6,4,3,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,4,6,5,3,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,5,4,6,3,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,1,5,6,4,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,3,1,6,5,4,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,1,5,6,4,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,2,6,5,4,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,2,5,6,4,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,3,6,5,4,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,3,5,6,4,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,2,3,6,5,4,7,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,4,2,1,6,5,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,4,3,1,6,5,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,4,1,6,5,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,3,4,1,6,5,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,3,2,6,5,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,1,4,3,6,5,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,2,4,3,6,5,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,1,4,6,5,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,3,1,4,6,5,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,2,4,6,5,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,3,4,6,5,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,4,5,2,6,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,2,4,5,3,6,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,2,3,5,4,6,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,2,3,7,5,6,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,3,7,5,6,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,3,8,5,6,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,3,8,5,7,6,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,3,8,6,5,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,3,8,6,7,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,4,3,8,6,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,4,7,5,6,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,4,8,5,6,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,4,8,5,7,6,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,4,8,6,5,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,4,8,6,7,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,5,4,8,6,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,6,4,5,3,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,6,4,5,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,6,4,5,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,7,4,5,6,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,7,4,5,6,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,8,4,5,6,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,8,4,5,7,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,7,4,6,5,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,4,6,5,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,8,4,6,7,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,8,4,7,6,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,7,5,4,6,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,5,4,6,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,8,5,4,6,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,8,5,4,7,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,7,5,6,4,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,5,6,4,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,8,5,6,4,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,8,5,6,7,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,8,5,7,6,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,8,6,5,4,7,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,2,8,6,5,7,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,8,7,5,6,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,2,4,8,6,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,2,5,8,6,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,2,7,5,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,7,5,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,2,8,5,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,2,8,5,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,2,8,6,5,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,2,8,6,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,4,2,8,6,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,4,7,5,6,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,4,8,5,6,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,4,8,6,5,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,4,8,6,7,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,3,6,4,5,2,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,6,4,5,7,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,6,4,5,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,6,4,5,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,7,4,5,6,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,7,4,5,6,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,8,4,5,6,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,7,4,6,5,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,8,4,6,5,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,8,4,6,7,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,8,4,7,6,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,7,5,4,6,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,8,5,4,6,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,8,5,4,7,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,7,5,6,4,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,8,5,6,4,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,8,5,6,7,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,8,5,7,6,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,8,6,5,7,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,8,7,5,6,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,4,3,2,8,6,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,4,3,5,8,6,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,3,7,5,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,8,5,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,3,8,5,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,3,8,6,5,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,3,8,6,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,4,2,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,4,2,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,3,4,2,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,4,6,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,3,4,6,2,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,3,4,6,7,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,5,3,4,7,6,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,3,4,7,6,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,3,4,8,6,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,3,4,8,7,6,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,6,3,4,5,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,3,4,5,7,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,6,3,4,5,8,7,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,7,3,4,5,6,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,3,4,5,7,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,7,3,4,6,5,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,3,4,6,5,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,3,4,6,5,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,3,4,6,7,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,8,3,4,7,6,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,6,3,5,4,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,5,4,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,5,4,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,3,5,4,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,3,5,4,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,5,4,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,3,5,4,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,3,5,6,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,3,5,6,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,3,5,6,7,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,8,3,5,7,6,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,7,3,6,5,4,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,3,6,5,4,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,3,6,5,4,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,3,6,5,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,3,7,5,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,3,7,6,5,4,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,6,4,3,5,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,4,3,5,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,4,3,5,7,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,4,3,6,5,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,4,3,6,5,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,4,3,6,5,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,4,3,6,7,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,6,4,5,3,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,4,5,3,2,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,4,5,3,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,4,5,3,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,4,5,3,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,4,5,3,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,4,5,6,3,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,4,5,6,3,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,4,5,6,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,4,5,6,7,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,8,4,5,7,6,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,7,4,6,5,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,4,6,5,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,4,6,5,3,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,4,6,5,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,4,7,5,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,4,7,6,5,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,7,5,4,3,6,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,5,4,3,6,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,5,4,3,6,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,5,4,3,7,6,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,7,5,4,6,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,4,6,3,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,4,6,7,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,5,4,7,6,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,7,6,4,5,3,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,6,4,5,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,6,4,5,3,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,6,4,5,7,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,7,4,5,6,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,7,4,6,5,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,8,6,5,4,3,7,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,8,6,5,4,7,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,7,5,4,6,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,7,5,6,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,1,3,4,8,6,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,3,5,8,6,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,3,7,5,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,3,8,5,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,3,8,5,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,3,8,6,5,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,3,8,6,7,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,4,3,8,6,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,4,5,8,6,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,4,7,5,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,4,8,5,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,4,8,5,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,4,8,6,5,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,4,8,6,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,5,4,8,6,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,4,5,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,4,5,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,4,5,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,1,6,4,5,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,8,4,5,7,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,7,4,6,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,4,6,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,4,6,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,8,4,7,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,7,5,4,6,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,1,8,5,4,6,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,1,8,5,4,7,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,7,5,6,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,7,5,6,4,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,5,6,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,5,6,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,8,5,7,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,8,6,5,4,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,8,6,5,7,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,8,7,5,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,1,4,8,6,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,1,5,8,6,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,1,7,5,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,7,5,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,1,8,5,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,1,8,5,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,3,1,8,6,5,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,1,8,6,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,3,4,1,8,6,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,4,7,5,6,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,4,7,5,6,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,4,8,5,6,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,4,8,5,7,6,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,4,8,6,5,7,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,4,8,6,7,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,5,4,8,6,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,6,4,5,1,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,6,4,5,1,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,6,4,5,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,6,4,5,8,7,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,7,4,5,6,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,7,4,5,6,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,8,4,5,6,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,8,4,5,7,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,7,4,6,5,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,7,4,6,5,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,4,6,5,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,4,6,7,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,8,4,7,6,5,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,3,7,5,4,6,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,7,5,4,6,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,8,5,4,6,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,8,5,4,7,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,3,7,5,6,4,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,7,5,6,4,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,5,6,4,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,5,6,7,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,8,5,7,6,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,3,8,6,5,4,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,3,8,6,5,7,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,3,8,7,5,6,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,3,1,8,6,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,3,5,8,6,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,3,7,5,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,7,5,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,8,5,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,8,5,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,3,8,6,5,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,3,8,6,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,3,4,1,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,4,1,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,3,4,1,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,3,4,6,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,3,4,6,7,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,5,3,4,6,8,7,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,5,3,4,7,6,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,3,4,7,6,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,3,4,8,6,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,3,4,8,7,6,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,6,3,4,5,1,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,6,3,4,5,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,3,4,5,8,7,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,7,3,4,5,6,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,8,3,4,5,7,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,8,3,4,6,7,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,6,3,5,4,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,5,4,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,5,4,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,3,5,4,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,3,5,4,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,5,4,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,3,5,4,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,3,5,4,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,3,5,6,4,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,3,5,6,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,3,5,6,7,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,8,3,5,7,6,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,7,3,6,5,4,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,3,6,5,4,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,3,6,5,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,3,7,5,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,3,7,6,5,4,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,5,4,3,8,6,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,4,3,5,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,4,3,5,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,4,3,5,8,7,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,4,3,5,7,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,4,3,6,5,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,4,3,6,5,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,4,3,6,5,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,4,3,6,7,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,4,3,7,6,5,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,6,4,5,3,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,5,3,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,4,5,3,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,4,5,3,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,4,5,3,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,4,5,3,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,4,5,6,3,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,4,5,6,3,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,4,5,6,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,4,5,6,7,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,7,4,6,5,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,4,6,5,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,4,6,5,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,4,6,5,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,4,7,5,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,4,7,6,5,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,7,5,4,3,6,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,5,4,3,6,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,8,5,4,3,6,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,8,5,4,3,7,6,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,7,5,4,6,3,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,4,6,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,4,6,7,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,5,4,7,6,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,7,6,4,5,3,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,4,5,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,4,5,7,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,7,4,5,6,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,7,4,6,5,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,8,6,5,4,3,7,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,8,6,5,4,7,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,7,5,4,6,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,7,5,6,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,2,1,4,8,6,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,1,5,8,6,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,1,7,5,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,7,5,6,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,1,8,5,6,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,1,8,5,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,1,8,6,5,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,2,1,8,6,7,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,4,1,8,6,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,4,5,8,6,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,2,4,7,5,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,7,5,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,4,8,5,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,4,8,5,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,4,8,6,5,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,4,8,6,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,5,4,8,6,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,4,5,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,4,5,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,7,4,5,6,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,7,4,6,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,4,6,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,4,6,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,7,5,4,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,8,5,4,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,8,5,4,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,7,5,6,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,5,6,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,5,6,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,5,6,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,2,8,5,7,6,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,8,6,5,4,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,8,6,5,7,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,8,7,5,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,3,1,5,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,3,1,5,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,3,1,6,5,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,3,1,6,5,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,3,1,6,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,3,1,6,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,3,1,7,6,5,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,3,1,7,6,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,3,1,8,6,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,3,1,8,7,6,5]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,2,3,5,1,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,3,5,1,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,5,1,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,3,5,1,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,3,5,6,1,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,2,3,5,7,6,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,3,5,7,6,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,2,3,5,8,7,6,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,2,3,6,5,1,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,3,6,5,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,3,6,5,8,7,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,3,7,5,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,7,5,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,3,8,5,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,3,8,5,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,3,7,6,5,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,3,7,6,5,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,3,8,6,5,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,3,8,6,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,3,4,1,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,3,4,1,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,4,1,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,3,4,1,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,3,4,6,1,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,3,4,7,6,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,2,3,4,7,6,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,3,4,8,6,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,3,4,8,7,6,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,2,3,4,5,1,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,3,4,6,5,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,3,4,6,5,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,3,4,6,5,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,3,4,7,6,5,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,2,3,5,4,1,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,3,5,4,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,3,5,4,7,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,5,4,7,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,3,5,4,8,7,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,3,5,4,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,3,5,4,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,3,5,4,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,3,5,6,4,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,3,5,6,4,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,3,5,6,4,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,3,5,7,6,4,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,2,3,6,5,4,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,3,6,5,4,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,3,6,5,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,3,7,5,6,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,4,3,1,6,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,4,3,1,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,4,3,1,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,4,3,1,8,7,6]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,4,3,6,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,4,3,6,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,4,3,6,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,3,7,6,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,4,3,7,6,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,4,3,8,7,6,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,4,3,5,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,4,3,5,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,4,3,5,7,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,2,4,3,6,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,3,6,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,4,3,6,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,4,3,6,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,4,3,7,6,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,4,5,3,1,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,4,5,3,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,4,5,3,7,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,4,5,3,7,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,4,5,3,8,7,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,4,5,3,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,4,5,3,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,4,5,3,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,4,5,3,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,4,5,6,3,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,4,5,6,3,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,4,5,6,3,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,4,5,7,6,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,2,4,6,5,3,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,4,6,5,3,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,4,6,5,3,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,4,6,5,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,4,7,5,6,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,5,4,3,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,5,4,3,7,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,5,4,3,7,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,5,4,3,8,7,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,5,4,3,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,5,4,3,6,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,5,4,3,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,5,4,3,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,5,4,6,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,4,6,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,5,4,6,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,5,4,6,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,5,4,7,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,6,4,5,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,4,5,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,4,5,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,4,5,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,7,4,5,6,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,7,4,6,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,6,5,4,3,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,2,6,5,4,3,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,6,5,4,3,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,6,5,4,7,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,7,5,4,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,7,5,6,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,7,6,5,4,3,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,3,2,1,8,6,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,3,2,7,5,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,7,5,6,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,2,8,5,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,2,8,5,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,2,8,6,5,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,2,8,6,7,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,4,1,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,2,4,1,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,4,1,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,2,4,1,8,7,6]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,4,6,1,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,2,4,7,6,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,2,4,7,6,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,2,4,8,6,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,2,4,5,1,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,3,2,4,6,5,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,2,5,4,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,3,2,5,4,7,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,5,4,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,2,5,4,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,2,5,4,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,2,5,4,6,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,2,5,4,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,2,5,4,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,2,5,6,4,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,3,2,5,6,4,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,2,6,5,4,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,2,6,5,4,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,2,6,5,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,3,2,7,5,6,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,3,2,7,6,5,4,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,3,4,2,1,6,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,4,2,1,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,4,2,1,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,4,2,1,8,7,6]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,4,2,6,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,4,2,7,6,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,4,2,7,6,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,4,2,8,6,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,4,2,5,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,4,2,5,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,4,2,5,7,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,4,2,6,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,4,2,6,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,2,6,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,2,6,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,4,2,7,6,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,4,5,2,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,4,5,2,8,7,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,4,5,2,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,4,5,7,6,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,3,4,6,5,2,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,3,4,6,5,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,4,6,5,2,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,4,6,5,7,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,4,7,5,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,5,4,2,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,5,4,2,7,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,5,4,2,7,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,5,4,2,8,7,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,5,4,2,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,4,2,6,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,3,5,4,2,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,3,5,4,2,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,5,4,6,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,5,4,6,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,4,6,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,4,6,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,5,4,7,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,6,4,5,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,4,5,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,6,4,5,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,6,4,5,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,7,4,5,6,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,7,4,6,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,6,5,4,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,3,6,5,4,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,6,5,4,2,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,6,5,4,7,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,7,5,4,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,7,5,6,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,3,7,6,5,4,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,4,3,2,8,6,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,3,2,5,1,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,3,2,6,5,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,4,3,2,6,5,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,4,3,2,6,5,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,4,3,2,7,6,5,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,3,5,2,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,3,5,2,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,4,3,5,2,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,3,6,5,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,3,6,5,2,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,3,6,5,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,3,6,5,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,4,3,7,5,6,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,4,3,7,6,5,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,5,3,4,2,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,5,3,4,2,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,3,4,2,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,3,5,4,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,3,5,4,2,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,3,5,4,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,3,5,4,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,7,3,5,4,6,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,7,3,6,5,4,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,5,4,3,2,7,6,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,5,4,3,7,6,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,4,3,6,5,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,4,6,5,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,4,1,3,6,5,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,4,6,3,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,4,1,6,3,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,6,1,3,5,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,4,3,6,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,1,3,6,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,4,6,3,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,1,6,3,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,6,1,3,8,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,4,6,8,3,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,4,1,6,8,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,6,1,8,3,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,6,8,1,3,5,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,4,1,3,6,5,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,1,3,6,7,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,4,6,3,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,1,6,3,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,6,1,3,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,1,6,7,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,6,7,1,3,5,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,4,6,3,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,4,1,6,3,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,6,1,3,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,4,6,7,3,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,1,6,7,3,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,6,1,7,3,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,6,7,1,3,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,1,6,7,8,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,6,1,7,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,6,7,1,8,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,4,3,7,5,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,1,3,7,5,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,4,7,3,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,4,1,7,3,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,7,1,3,5,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,4,3,7,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,1,3,7,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,4,7,3,8,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,1,7,3,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,7,1,3,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,4,7,8,3,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,4,1,7,8,3,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,7,1,8,3,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,7,8,1,3,5,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,4,1,3,7,5,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,1,3,5,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,1,5,3,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,5,1,3,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,5,1,7,3,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,1,5,3,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,5,1,3,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,4,5,7,3,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,1,5,7,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,5,1,7,3,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,5,7,1,3,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,1,5,7,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,5,1,7,8,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,5,7,1,8,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,4,3,8,5,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,4,1,3,8,5,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,4,3,5,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,1,3,5,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,1,5,3,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,4,5,8,3,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,4,1,5,8,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,5,1,8,3,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,5,8,1,3,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,4,1,5,3,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,1,5,6,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,5,1,6,3,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,5,6,1,3,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,1,5,6,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,5,1,6,8,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,5,6,1,8,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,1,5,6,3,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,5,1,6,3,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,5,6,1,3,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,4,1,5,6,7,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,5,1,6,7,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,5,6,1,7,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,5,1,6,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,4,5,6,1,7,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,1,5,3,6,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,1,3,6,4,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,5,6,3,4,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,1,6,3,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,6,1,3,4,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,5,3,6,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,1,3,6,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,5,1,6,3,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,6,1,3,8,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,5,6,8,3,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,5,1,6,8,3,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,6,1,8,3,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,6,8,1,3,4,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,5,3,6,4,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,5,1,3,6,4,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,5,3,6,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,1,3,6,7,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,5,6,3,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,1,6,3,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,6,1,3,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,5,6,7,3,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,5,1,6,7,3,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,6,1,7,3,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,6,7,1,3,4,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,5,6,3,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,1,6,3,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,6,1,3,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,5,6,7,3,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,5,1,6,7,3,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,6,1,7,3,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,6,7,1,3,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,5,1,6,7,8,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,5,6,1,7,8,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,5,6,7,1,8,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,5,3,7,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,1,3,7,4,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,5,7,3,4,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,1,7,3,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,7,1,3,4,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,5,3,7,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,1,3,7,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,5,7,3,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,1,7,3,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,7,1,3,8,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,5,7,8,3,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,5,1,7,8,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,7,1,8,3,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,7,8,1,3,4,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,5,3,7,4,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,5,1,3,7,4,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,1,3,4,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,5,1,4,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,1,5,7,4,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,5,7,1,4,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,3,5,1,4,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,5,1,7,4,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,5,7,1,4,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,1,5,7,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,5,1,7,8,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,5,7,1,8,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,5,3,8,4,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,5,1,3,8,4,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,1,3,4,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,3,5,4,8,6,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,5,1,4,8,6,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,3,5,8,4,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,3,1,5,8,4,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,5,1,8,4,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,5,8,1,4,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,3,5,1,6,4,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,5,6,1,4,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,1,5,6,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,5,1,6,8,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,5,6,1,8,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,5,1,6,4,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,5,6,1,4,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,3,5,1,6,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,5,6,1,7,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,5,1,6,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,5,6,1,7,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,1,6,3,7,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,1,3,7,4,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,6,7,3,4,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,1,7,3,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,7,1,3,4,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,6,3,7,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,1,3,7,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,6,7,3,8,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,6,1,7,3,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,7,1,3,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,6,7,8,3,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,6,1,7,8,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,6,7,1,8,3,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,7,8,1,3,4,5]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,6,3,7,4,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,1,3,7,4,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,6,3,4,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,1,3,4,7,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,1,6,4,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,6,1,4,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,1,6,7,4,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,6,1,7,4,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,6,7,1,4,5,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,3,6,4,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,3,1,6,4,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,6,1,4,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,3,6,7,4,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,3,1,6,7,4,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,6,1,7,4,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,6,7,1,4,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,1,6,7,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,6,1,7,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,6,7,1,8,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,6,3,8,4,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,1,3,8,4,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,6,3,4,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,1,3,4,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,3,6,4,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,1,6,4,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,6,1,4,8,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,1,6,8,4,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,6,1,8,4,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,6,8,1,4,5,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,3,6,4,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,3,1,6,4,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,6,1,4,5,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,4,6,1,5,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,1,4,6,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,4,1,6,8,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,4,6,1,8,5,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,4,6,1,5,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,3,4,6,1,7,5,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,4,6,1,7,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,1,7,3,8,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,7,1,3,8,4,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,7,3,4,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,1,3,4,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,3,7,4,8,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,1,7,4,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,7,1,4,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,3,7,8,4,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,3,1,7,8,4,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,7,1,8,4,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,7,8,1,4,5,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,3,7,4,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,3,1,7,4,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,7,1,4,5,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,3,4,7,5,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,3,4,1,7,5,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,4,7,1,5,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,1,4,7,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,4,1,7,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,4,7,1,8,5,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,3,4,7,5,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,3,1,4,7,5,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,4,1,7,5,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,4,7,1,5,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,1,3,4,8,5,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,3,1,4,8,5,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,4,1,8,5,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,4,8,1,5,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[2,3,1,4,5,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,4,1,5,8,6,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,4,5,1,8,6,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,4,2,6,5,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,1,2,6,5,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,4,6,2,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,1,6,2,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,6,1,2,5,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,4,2,6,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,1,2,6,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,4,6,2,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,1,6,2,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,4,6,8,2,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,4,1,6,8,2,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,4,6,1,8,2,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,6,8,1,2,5,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,4,2,6,5,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,4,1,2,6,5,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,4,2,6,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,1,2,6,7,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,4,6,2,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,1,6,2,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,6,1,2,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,4,6,7,2,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,4,1,6,7,2,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,4,6,1,7,2,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,6,7,1,2,5,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,4,6,2,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,1,6,2,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,6,1,2,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,4,6,7,2,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,4,1,6,7,2,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,6,1,7,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,6,7,1,2,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,4,1,6,7,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,6,1,7,8,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,6,7,1,8,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,4,2,7,5,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,1,2,7,5,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,4,7,2,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,1,7,2,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,7,1,2,5,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,4,2,7,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,1,2,7,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,4,7,2,8,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,7,1,2,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,1,7,8,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,4,7,1,8,2,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,7,8,1,2,5,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,4,2,7,5,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,4,1,2,7,5,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,4,2,5,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,1,2,5,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,4,5,2,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,1,5,2,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,5,1,2,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,4,5,7,2,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,4,1,5,7,2,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,4,5,1,7,2,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,5,7,1,2,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,4,5,2,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,1,5,2,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,5,1,2,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,4,5,7,2,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,4,1,5,7,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,5,1,7,2,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,5,7,1,2,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,4,1,5,7,8,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,5,1,7,8,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,5,7,1,8,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,4,2,8,5,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,4,1,2,8,5,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,4,2,5,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,1,2,5,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,1,5,2,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,5,1,2,8,6,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,4,5,8,2,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,4,1,5,8,2,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,4,5,1,8,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,5,8,1,2,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,4,1,5,2,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,5,1,2,6,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,4,5,6,2,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,4,1,5,6,2,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,5,1,6,2,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,5,6,1,2,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,4,1,5,6,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,5,1,6,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,5,6,1,8,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,4,5,6,2,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,4,1,5,6,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,4,5,1,6,2,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,1,5,6,7,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,5,1,6,7,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,5,6,1,7,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,4,5,1,6,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,4,5,6,1,7,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,1,5,2,6,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,1,2,6,4,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,5,6,2,4,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,5,1,6,2,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,6,1,2,4,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,5,2,6,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,1,2,6,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,5,6,2,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,1,6,2,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,6,1,2,8,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,5,6,8,2,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,5,1,6,8,2,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,6,1,8,2,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,6,8,1,2,4,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,5,2,6,4,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,1,2,6,4,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,5,2,6,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,1,2,6,7,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,5,6,2,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,1,6,2,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,6,1,2,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,5,6,7,2,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,5,1,6,7,2,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,6,1,7,2,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,6,7,1,2,4,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,5,6,2,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,5,1,6,2,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,6,1,2,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,5,6,7,2,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,5,1,6,7,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,6,1,7,2,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,6,7,1,2,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,1,6,7,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,5,6,1,7,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,6,7,1,8,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,5,2,7,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,1,2,7,4,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,5,7,2,4,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,5,1,7,2,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,7,1,2,4,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,5,2,7,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,1,2,7,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,5,7,2,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,1,7,2,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,7,1,2,8,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,5,7,8,2,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,5,1,7,8,2,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,7,1,8,2,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,7,8,1,2,4,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,5,2,7,4,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,1,2,7,4,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,5,2,4,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,1,2,4,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,2,5,4,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,3,5,2,4,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,2,5,7,4,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,2,5,7,4,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,5,2,7,4,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,5,7,2,4,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,3,5,2,4,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,2,5,7,4,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,3,2,5,7,4,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,5,2,7,4,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,5,7,2,4,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,2,5,7,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,5,2,7,8,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,5,7,2,8,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,5,2,8,4,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,1,2,8,4,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,5,2,4,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,1,2,4,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,2,5,4,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,5,2,4,8,6,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,2,5,8,4,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,2,5,8,4,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,5,2,8,4,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,5,8,2,4,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,2,5,4,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,5,2,4,6,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,5,2,6,4,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,5,6,2,4,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,2,5,6,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,5,2,6,8,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,5,6,2,8,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,2,5,6,4,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,5,2,6,4,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,5,6,2,4,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,3,5,2,6,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,5,6,2,7,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,5,2,6,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,5,6,2,7,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,1,6,2,7,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,6,1,2,7,4,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,1,7,2,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,7,1,2,4,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,6,2,7,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,1,2,7,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,6,7,2,8,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,1,7,2,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,7,1,2,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,6,7,8,2,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,6,1,7,8,2,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,7,1,8,2,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,7,8,1,2,4,5]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,6,2,7,4,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,1,2,7,4,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,6,2,4,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,1,2,4,7,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,2,6,4,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,3,2,6,4,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,6,2,4,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,2,6,7,4,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,2,6,7,4,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,6,2,7,4,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,6,7,2,4,5,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,2,6,4,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,2,6,4,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,6,2,4,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,2,6,7,4,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,3,2,6,7,4,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,6,2,7,4,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,6,7,2,4,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,2,6,7,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,6,2,7,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,6,7,2,8,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,6,2,8,4,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,1,2,8,4,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,6,2,4,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,1,2,4,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,2,6,4,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,3,2,6,4,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,6,2,4,8,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,2,6,8,4,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,2,6,8,4,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,6,2,8,4,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,6,8,2,4,5,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,2,6,4,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,6,2,4,5,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,2,4,6,5,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,3,4,6,2,5,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,2,4,6,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,4,2,6,8,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,4,6,2,8,5,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,4,6,2,5,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,3,4,6,2,7,5,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,4,6,2,7,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,1,7,2,8,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,7,1,2,8,4,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,7,2,4,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,1,2,4,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,2,7,4,8,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,3,2,7,4,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,7,2,4,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,1,2,7,8,4,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,2,7,8,4,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,7,2,8,4,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,7,8,2,4,5,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,2,7,4,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,2,7,4,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,7,2,4,5,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,2,4,7,5,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,3,2,4,7,5,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,4,2,7,5,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,4,7,2,5,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,2,4,7,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,4,2,7,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,4,7,2,8,5,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,2,4,7,5,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,2,4,7,5,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,4,2,7,5,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,4,7,2,5,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[3,1,2,4,8,5,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,2,4,8,5,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,4,2,8,5,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,4,8,2,5,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,3,2,4,5,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,4,2,5,8,6,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,4,5,2,8,6,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,5,2,6,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,1,2,6,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,5,6,2,3,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,1,6,2,3,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,6,1,2,3,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,5,2,6,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,1,2,6,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,5,6,2,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,1,6,2,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,6,1,2,8,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,5,6,8,2,3,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,1,6,8,2,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,5,6,1,8,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,6,8,1,2,3,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[4,1,5,2,6,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,2,6,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,1,2,6,7,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,5,6,2,7,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,1,6,2,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,6,1,2,7,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,5,6,7,2,3,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,1,6,7,2,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,5,6,1,7,2,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,1,6,2,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,6,1,2,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,5,6,7,2,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,5,1,6,7,2,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,6,1,7,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,6,7,1,2,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,5,1,6,7,8,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,5,6,1,7,8,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,6,7,1,8,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,5,2,7,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,1,2,7,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,5,7,2,3,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,1,7,2,3,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,7,1,2,3,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,5,2,7,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,1,2,7,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,5,7,2,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,1,7,2,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,7,1,2,8,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,5,7,8,2,3,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,1,7,8,2,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,5,7,1,8,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,7,8,1,2,3,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[4,1,5,2,7,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,5,1,2,7,3,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,1,5,2,3,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,1,2,3,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,2,5,3,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,2,5,3,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,5,2,3,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,2,5,7,3,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,5,7,3,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,5,2,7,3,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,5,7,2,3,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[4,1,2,5,3,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,2,5,3,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,5,2,3,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,2,5,7,3,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,2,5,7,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,5,2,7,3,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,5,7,2,3,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,2,5,7,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,5,2,7,8,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,5,7,2,8,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,5,2,8,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,5,1,2,8,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,1,5,2,3,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,1,2,3,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,2,5,3,8,6,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,2,5,3,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,5,2,3,8,6,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,2,5,8,3,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,5,8,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,5,2,8,3,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,5,8,2,3,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,4,2,5,3,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,2,5,6,3,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,2,5,6,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,5,2,6,3,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,5,6,2,3,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,2,5,6,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,5,2,6,8,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,5,6,2,8,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,2,5,6,3,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,5,6,3,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,5,2,6,3,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,5,6,2,3,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,4,2,5,6,7,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,5,2,6,7,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,5,6,2,7,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,4,5,2,6,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,4,5,6,2,7,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,1,6,2,7,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,1,2,7,3,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,6,7,2,3,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,6,1,7,2,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,7,1,2,3,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,6,2,7,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,1,2,7,8,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,6,7,2,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,1,7,2,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,7,1,2,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,6,7,8,2,3,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,6,1,7,8,2,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,7,1,8,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,7,8,1,2,3,5]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[4,1,6,2,7,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,1,2,7,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,1,6,2,3,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,1,2,3,7,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,2,6,3,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,2,6,3,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,6,2,3,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,2,6,7,3,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,6,7,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,6,2,7,3,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,6,7,2,3,5,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[4,1,2,6,3,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,2,6,3,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,6,2,3,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,2,6,7,3,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,2,6,7,3,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,6,2,7,3,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,6,7,2,3,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,2,6,7,8,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,6,2,7,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,6,7,2,8,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,6,2,8,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,1,2,8,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,1,6,2,3,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,1,2,3,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,2,6,3,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,2,6,3,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,6,2,3,8,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,2,6,8,3,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,6,8,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,6,2,8,3,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,6,8,2,3,5,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[4,1,2,6,3,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,2,6,3,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,6,2,3,5,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,2,3,6,5,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,2,3,6,5,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,4,6,3,5,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,2,3,6,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,4,3,6,8,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,4,6,3,8,5,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,2,3,6,5,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,3,6,5,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,4,6,3,5,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,4,2,3,6,7,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,4,6,3,7,5,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,4,6,3,7,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,1,7,2,8,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,1,2,8,3,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,1,7,2,3,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,1,2,3,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,2,7,3,8,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,2,7,3,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,7,2,3,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,2,7,8,3,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,7,8,3,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,7,2,8,3,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,7,8,2,3,5,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[4,1,2,7,3,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,2,7,3,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,7,2,3,5,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,2,3,7,5,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,2,3,7,5,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,4,3,7,5,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,4,7,3,5,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,2,3,7,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,4,3,7,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,4,7,3,8,5,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,2,3,7,5,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,3,7,5,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,4,3,7,5,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,4,7,3,5,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,4,2,3,5,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,2,3,8,5,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,2,3,8,5,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,4,3,8,5,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,4,8,3,5,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,4,2,3,5,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,4,3,5,8,6,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,4,5,3,8,6,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,1,6,2,7,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,1,2,7,3,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,6,7,2,3,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,1,7,2,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,7,1,2,3,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,1,6,2,7,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,1,2,7,8,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,1,6,7,2,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,1,7,2,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,7,1,2,8,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,6,7,8,2,3,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,6,1,7,8,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,7,1,8,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,1,6,2,7,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,1,2,7,3,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,1,6,2,3,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,1,2,3,7,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,1,2,6,3,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,2,6,3,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,6,2,3,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,2,6,7,3,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,2,6,7,3,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,6,2,7,3,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,6,7,2,3,4,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[5,1,2,6,3,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,2,6,3,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,6,2,3,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,1,2,6,7,3,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,5,2,6,7,3,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,6,2,7,3,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,6,7,2,3,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,2,6,7,8,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,5,6,2,7,8,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,6,7,2,8,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,1,6,2,8,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,1,2,8,3,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,1,6,2,3,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,1,2,3,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,1,2,6,3,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,2,6,3,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,6,2,3,8,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,2,6,8,3,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,2,6,8,3,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,6,2,8,3,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,6,8,2,3,4,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[5,1,2,6,3,4,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,2,6,3,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,6,2,3,4,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,1,2,3,6,4,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,5,2,3,6,4,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,5,3,6,4,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,5,6,3,4,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,2,3,6,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,5,3,6,8,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,5,6,3,8,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,1,2,3,6,4,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,2,3,6,4,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,5,3,6,4,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,5,6,3,4,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,5,2,3,6,7,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,5,3,6,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,5,6,3,7,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,5,3,6,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,5,6,3,7,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,1,7,2,8,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,1,2,8,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,1,7,2,3,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,1,2,3,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,1,2,7,3,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,2,7,3,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,7,2,3,8,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,2,7,8,3,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,2,7,8,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,7,2,8,3,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,7,8,2,3,4,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[5,1,2,7,3,4,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,2,7,3,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,7,2,3,4,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,1,2,3,7,4,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,5,2,3,7,4,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,5,3,7,4,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,5,7,3,4,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,2,3,7,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,5,3,7,8,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,5,7,3,8,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,1,2,3,7,4,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,2,3,7,4,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,5,3,7,4,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,5,7,3,4,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,5,2,3,4,7,6,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,5,3,4,7,6,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,5,3,4,7,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,1,2,3,8,4,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,2,3,8,4,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,5,3,8,4,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,5,8,3,4,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,5,2,3,4,8,6,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,5,3,4,8,6,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,3,5,4,8,6,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,5,3,4,6,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,1,7,2,8,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,1,2,8,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,1,7,2,3,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,1,2,3,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,1,2,7,3,8,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,2,7,3,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,7,2,3,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,1,2,7,8,3,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,6,2,7,8,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,7,2,8,3,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,7,8,2,3,4,5]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[6,1,2,7,3,4,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,2,7,3,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,7,2,3,4,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,1,2,3,7,4,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,6,2,3,7,4,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,6,3,7,4,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,6,7,3,4,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,6,2,3,7,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,6,3,7,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,6,7,3,8,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,1,2,3,7,4,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,6,2,3,7,4,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,6,3,7,4,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,6,7,3,4,5,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,6,2,3,4,7,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,6,3,4,7,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,3,6,4,7,5,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,6,3,4,7,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,3,6,4,7,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,1,2,3,8,4,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,6,2,3,8,4,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,6,3,8,4,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,6,8,3,4,5,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,6,2,3,4,8,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,6,3,4,8,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,3,6,4,8,5,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,6,3,4,5,8,7]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,3,6,4,5,8,7]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,3,6,4,5,7,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[7,1,2,3,8,4,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,7,2,3,8,4,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,7,3,8,4,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,7,8,3,4,5,6]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,7,2,3,4,8,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,7,3,4,8,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,3,7,4,8,5,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,7,3,4,5,8,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,3,7,4,5,8,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,3,7,4,5,6,8]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[1,2,3,8,4,5,6,7]=>[4,4]=>[[7,4],[3]]=>[3]=>0
[5,3,2,6,1,4,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,2,5,4,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,5,2,3,7,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,4,5,2,3,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,5,2,3,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,2,1,3,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,1,5,4,2,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,5,1,3,2,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,4,3,1,2,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,4,3,2,8,1,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,4,3,7,2,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,4,3,8,2,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,7,4,3,8,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,3,1,8,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,5,1,3,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,1,5,4,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,7,5,4,8,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,1,5,4,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,5,1,3,7,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,4,3,1,7,6,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,8,4,3,7,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,4,3,6,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,5,7,3,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,6,7,1,3,4,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,6,1,7,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,1,6,7,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,8,6,7,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,7,6,8,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,1,6,8,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,6,1,8,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,6,8,1,3,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,7,2,1,8,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,2,8,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,2,8,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,6,2,7,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,2,6,7,4,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,2,6,8,4,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,2,7,8,1,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,2,7,1,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,1,7,8,5,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,4,1,2,8,7,6,5]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,3,2,8,1,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,2,8,7,1,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,2,8,6,5,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,7,2,6,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,8,2,6,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,8,2,7,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,2,1,7,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,8,1,2,7,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,1,8,2,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,5,8,3,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,6,8,7,3,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,6,1,8,7,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,8,1,7,2,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,8,7,1,2,4,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,5,8,7,2,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,8,6,2,4,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,7,6,2,4,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,8,6,1,4,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,8,1,6,5,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,1,8,6,5,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,7,8,6,5,3,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,8,1,7,6,5,4,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,8,7,1,6,5,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,8,7,6,1,4,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,8,7,5,4,1,3,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,6,2,5,8,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,2,5,8,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,3,5,8,1,2,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,2,4,8,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,3,4,8,1,2,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,7,2,5,8,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,2,5,8,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,3,5,8,1,2,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,2,4,8,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,3,4,8,1,2,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,7,2,6,8,1,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,2,6,8,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,3,6,8,1,2,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,2,6,8,1,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,3,6,8,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,4,6,8,1,2,3]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,7,2,4,8,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,7,3,4,8,1,2,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,7,3,5,8,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,8,2,5,7,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,8,2,5,7,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,8,3,5,7,1,2,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,2,4,7,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,8,2,6,7,1,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,8,2,6,7,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,8,3,6,7,1,2,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,2,6,7,1,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,3,6,7,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,2,4,7,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,2,5,7,1,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,3,5,7,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,4,5,7,1,2,3]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,2,4,6,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,3,4,6,1,2,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,2,5,6,1,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,3,5,6,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,3,2,6,8,1,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,2,6,8,1,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,2,6,8,1,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,3,6,8,1,2,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,2,5,8,1,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,2,5,8,1,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,3,5,8,1,2,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,2,4,8,1,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,3,4,8,1,2,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,2,7,8,1,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,2,7,8,1,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,2,7,8,1,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,3,7,8,1,2,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,2,7,8,1,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,3,7,8,1,2,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,2,7,8,1,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,3,7,8,1,2,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,2,5,8,1,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,2,5,8,1,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,3,5,8,1,2,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,2,4,8,1,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,3,4,8,1,2,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,2,6,8,1,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,2,6,8,1,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,3,6,8,1,2,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,2,6,8,1,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,3,6,8,1,2,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,2,4,8,1,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,3,4,8,1,2,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,2,5,8,1,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,3,5,8,1,2,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,3,2,5,7,1,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,2,5,7,1,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,3,5,7,1,2,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,5,2,4,7,1,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,5,3,4,7,1,2,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,3,2,6,7,1,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,2,6,7,1,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,3,6,7,1,2,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,5,2,6,7,1,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,5,3,6,7,1,2,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,6,2,4,7,1,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,6,3,4,7,1,2,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,6,2,5,7,1,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,6,3,5,7,1,2,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,7,2,4,6,1,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,7,3,4,6,1,2,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,7,2,5,6,1,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,7,3,5,6,1,2,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,7,2,6,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,2,6,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,7,2,6,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,7,3,6,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,7,2,5,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,7,2,5,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,7,3,5,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,7,2,4,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,6,2,5,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,2,5,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,3,5,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,6,2,4,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,8,2,6,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,8,2,6,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,8,2,6,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,8,3,6,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,8,2,5,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,8,2,5,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,8,3,5,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,8,2,4,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,8,3,4,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,8,2,7,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,8,2,7,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,8,2,7,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,8,3,7,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,8,2,7,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,8,2,7,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,8,3,7,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,8,2,7,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,8,3,7,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,8,4,7,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,8,2,5,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,8,2,5,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,8,3,5,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,8,2,4,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,8,3,4,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,8,2,6,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,8,2,6,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,8,3,6,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,8,2,6,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,8,3,6,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,8,4,6,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,8,2,4,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,8,2,5,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,8,3,5,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,6,2,5,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,6,2,5,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,6,3,5,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,6,2,4,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,7,2,5,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,7,3,5,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,7,2,4,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,7,2,6,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,7,2,6,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,7,3,6,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,7,2,6,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,7,2,4,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,7,2,5,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,7,3,5,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,3,7,2,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,7,2,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,7,2,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,7,3,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,7,2,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,7,2,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,7,3,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,5,7,2,4,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,5,7,3,4,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,6,2,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,4,6,2,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,4,6,3,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,5,6,2,4,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,3,8,2,7,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,8,2,7,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,8,2,7,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,4,8,2,7,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,4,8,3,7,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,8,2,6,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,8,2,6,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,4,8,2,6,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,4,8,3,6,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,3,8,2,5,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,4,8,2,5,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,4,8,3,5,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,5,8,2,4,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,3,7,2,6,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,3,7,2,6,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,4,7,2,6,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,4,7,3,6,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,3,7,2,5,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,4,7,2,5,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,4,7,3,5,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,5,7,2,4,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,3,6,2,5,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,4,6,2,5,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,4,6,3,5,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,5,6,2,4,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,4,3,2,8,1,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,6,4,3,2,8,1,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,6,5,3,2,8,1,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,6,5,4,2,8,1,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,4,3,2,7,1,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,4,3,2,7,1,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,5,3,2,7,1,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,5,4,2,7,1,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,7,4,3,2,6,1,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,7,5,3,2,6,1,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,7,5,4,2,6,1,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,7,6,3,2,5,1,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,7,6,4,2,5,1,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,7,6,5,2,4,1,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,1,2,3,6,4,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,2,3,7,4,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,1,2,3,6,4,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,2,3,8,7,4,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,2,8,3,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,5,3,4,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,2,6,3,4,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,2,5,3,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,2,5,3,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,2,6,3,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,5,3,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,1,2,8,6,3,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,2,8,7,3,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,2,7,6,3,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,2,5,6,3,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,2,5,7,3,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,2,7,6,3,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,2,5,6,3,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,2,5,8,7,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,2,8,6,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,8,2,4,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,8,2,6,4,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,8,2,7,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,2,6,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,5,2,8,7,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,8,2,6,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,4,2,3,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,4,2,3,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,5,2,3,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,2,3,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,8,2,3,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,4,2,8,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,2,7,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,2,6,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,4,2,7,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,2,6,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,2,6,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,5,2,7,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,8,2,6,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,2,6,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,4,2,6,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,4,2,8,7,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,4,2,6,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,2,6,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,4,8,2,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,7,5,2,4,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,7,6,2,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,6,5,2,8,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,8,5,2,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,8,6,2,7,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,5,2,7,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,4,5,2,3,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,4,6,2,3,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,6,5,2,3,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,4,5,2,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,5,2,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,6,2,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,6,5,2,7,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,4,5,2,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,1,4,8,6,2,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,4,8,7,2,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,4,7,6,2,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,8,5,6,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,8,5,7,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,5,6,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,5,6,2,3,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,4,5,7,2,3,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,4,7,6,2,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,7,5,6,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,5,6,2,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,1,4,5,8,7,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,4,8,6,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,8,5,6,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,1,3,4,7,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,8,1,3,6,4,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,8,1,3,7,4,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,1,3,6,4,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,1,3,8,7,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,8,1,3,6,7,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,1,8,3,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,5,3,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,1,6,3,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,1,5,3,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,5,3,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,6,3,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,5,3,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,1,8,6,3,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,1,8,7,3,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,1,7,6,3,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,1,5,6,3,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,8,1,5,7,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,8,1,7,6,3,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,1,5,6,3,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,1,5,8,7,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,1,8,6,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,5,6,7,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,3,1,2,8,4,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,1,2,7,4,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,3,1,2,6,4,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,3,1,2,7,4,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,1,2,6,4,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,1,2,8,7,4,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,8,1,2,3,7,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,4,1,2,8,3,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,1,2,7,3,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,1,2,6,3,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,1,2,7,3,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,1,2,6,3,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,8,1,2,6,3,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,1,2,7,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,7,1,2,6,3,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,7,1,2,6,3,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,4,1,2,8,7,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,8,1,2,6,7,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,3,1,7,2,5,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,1,6,2,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,8,2,7,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,6,2,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,1,5,2,4,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,1,6,2,4,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,1,5,2,8,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,1,5,2,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,1,6,2,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,5,2,7,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,1,5,2,3,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,1,6,2,3,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,1,5,2,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,1,5,2,8,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,1,5,2,7,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,1,6,2,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,8,1,5,2,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,1,5,2,7,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,1,5,8,2,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,1,5,7,2,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,1,7,6,2,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,1,5,6,2,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,3,1,5,7,2,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,1,5,6,2,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,1,5,6,2,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,1,5,7,2,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,8,1,5,6,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,4,1,5,6,2,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,1,5,8,7,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,1,8,6,7,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,3,8,1,4,7,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,8,1,6,4,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,8,1,7,4,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,7,1,6,4,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,5,1,8,7,4,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,8,1,6,7,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,4,1,3,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,4,1,3,7,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,5,1,3,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,5,1,3,7,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,8,1,3,7,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,5,4,1,8,3,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,1,7,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,4,1,6,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,4,1,7,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,4,1,6,3,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,1,6,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,5,1,7,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,8,1,6,3,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,7,5,1,6,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,4,1,6,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,4,1,8,7,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,1,6,7,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,5,1,6,7,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,3,4,1,2,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,4,1,2,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,5,1,2,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,5,1,2,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,8,1,2,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,4,1,2,8,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,4,1,2,7,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,8,4,1,2,7,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,5,1,2,7,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,4,1,8,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,1,7,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,1,6,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,4,1,7,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,4,1,6,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,1,6,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,5,1,7,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,8,1,6,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,5,1,6,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,4,1,6,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,5,1,6,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,4,1,6,2,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,3,4,1,6,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,1,8,7,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,4,1,6,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,5,1,6,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,4,1,6,7,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,3,4,8,1,7,5,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,7,5,1,4,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,7,6,1,4,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,6,5,1,8,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,8,5,1,7,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,8,6,1,7,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,6,5,1,7,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,7,4,5,1,3,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,4,6,1,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,6,5,1,3,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,6,4,5,1,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,4,5,1,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,4,6,1,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,5,1,7,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,4,5,1,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,4,5,1,2,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,4,6,1,2,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,6,5,1,2,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,6,4,5,1,2,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,4,5,1,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,4,5,1,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,4,6,1,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,6,5,1,7,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,4,5,1,7,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,4,5,1,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,3,4,8,6,1,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,3,4,8,7,1,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,3,4,7,6,1,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,8,5,6,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,8,5,7,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,8,7,6,1,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,3,7,5,6,1,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,4,5,6,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,8,4,5,7,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,8,4,7,6,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,7,5,6,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,4,5,6,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,4,5,7,1,2,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,3,4,7,6,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,3,7,5,6,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,4,5,6,1,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,3,4,8,6,7,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,8,5,6,7,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,8,4,5,6,7,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,4,5,6,7,8,9,1]=>[8,1]=>[[8,8],[7]]=>[7]=>0
[3,5,2,6,1,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,2,6,4,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,2,7,4,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,7,4,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,7,2,3,8,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,7,2,3,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,6,2,3,1,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,6,2,1,3,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,1,6,4,2,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,6,1,3,2,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,6,3,1,2,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,7,3,2,8,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,3,2,8,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,7,3,8,2,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,3,8,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,3,8,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,7,3,1,8,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,1,3,8,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,1,7,4,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,5,7,4,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,5,7,4,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,1,7,4,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,7,1,3,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,7,3,1,8,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,7,3,8,1,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,3,8,5,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,3,8,5,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,6,7,8,3,1,4,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,6,7,8,1,3,4,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,6,7,1,8,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,1,7,8,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,6,7,8,4,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,6,7,8,4,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,6,1,7,8,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,7,1,8,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,7,8,1,3,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,7,2,1,8,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,2,8,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,7,2,8,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,2,8,3,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,2,7,8,4,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,2,7,8,4,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,7,8,1,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,2,7,1,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,1,7,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,1,2,7,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,5,2,7,1,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,2,7,8,1,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,2,7,8,5,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,7,8,5,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,6,7,2,8,5,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,6,7,2,8,5,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,2,8,1,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,7,2,1,8,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,5,7,1,2,8,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,1,7,2,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,5,7,3,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,6,7,8,3,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,1,7,8,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,7,1,8,2,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,7,8,1,2,4,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,6,7,8,2,1,4,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,6,7,8,2,4,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,6,7,8,2,4,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,6,7,8,1,4,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,6,7,1,8,5,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,1,7,8,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,1,6,7,8,5,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,6,1,7,8,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,6,7,1,8,5,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,6,7,8,1,4,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,6,7,8,4,1,3,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,5,8,7,3,4,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,7,4,5,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,7,4,5,1,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,7,4,5,2,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,4,7,6,2,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,4,7,6,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,4,7,6,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,7,8,6,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,4,3,8,7,6,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,8,3,7,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,8,4,5,7,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,8,6,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,5,6,8,7,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,2,5,6,1,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,5,6,8,1,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,4,8,6,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,8,4,5,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,2,4,5,1,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,1,4,5,2,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,1,8,4,5,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,8,6,2,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,3,2,8,6,5,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,3,8,2,6,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,8,3,2,5,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,8,1,3,2,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,3,1,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,8,3,1,5,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,3,8,1,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,3,8,2,1,7,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,3,2,1,6,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,8,4,2,6,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,2,8,7,1,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,2,7,8,1,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,3,7,1,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,3,7,2,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,7,3,2,5,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,7,3,1,5,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,6,7,2,1,8,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,8,5,6,2,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,8,1,7,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,3,1,2,6,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,1,8,2,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,2,8,7,5,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,3,8,5,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,1,8,3,4,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,1,2,6,5,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,1,6,2,4,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,1,5,2,4,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,1,5,2,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,5,1,2,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,5,1,2,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,1,6,5,3,4,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,1,5,2,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,4,1,2,8,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,4,1,8,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,1,2,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,5,1,2,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,1,5,2,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,7,5,3,8,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,8,5,3,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,1,5,2,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,5,1,2,7,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,4,1,2,7,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,4,1,7,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,6,1,7,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,1,6,7,2,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,8,6,7,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,6,8,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,7,1,6,8,2,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,6,1,8,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,4,7,1,2,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,7,1,8,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,1,8,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,6,1,7,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,1,6,7,2,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,1,6,8,2,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,1,7,8,2,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,1,7,2,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,4,3,8,7,5,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,1,2,8,7,5,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,4,7,1,6,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,8,1,6,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,8,1,2,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,8,1,2,7,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,1,8,2,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,5,8,3,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,6,8,7,3,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,6,1,8,7,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,8,1,7,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,8,1,6,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,7,1,8,6,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,1,7,8,6,3,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,8,1,7,6,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,7,1,6,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,4,7,3,8,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,3,5,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,7,2,5,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,2,7,6,1,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,3,7,6,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,7,8,6,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,8,3,5,7,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,3,8,6,7,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,6,8,7,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,2,6,7,1,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,2,6,7,1,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,2,6,1,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,6,1,7,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,2,6,1,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,4,2,6,8,1,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,2,8,6,1,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,8,2,5,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,4,2,5,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,4,2,5,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,2,6,1,8,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,1,6,8,5,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,3,2,1,8,6,5,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,3,2,8,1,6,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,8,2,1,5,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,8,3,2,1,5,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,3,2,1,5,6,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,3,8,2,1,5,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,2,8,1,6,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,2,7,8,1,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,2,7,1,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,7,1,6,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,2,7,1,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,7,2,1,5,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,2,1,5,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,7,2,1,8,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,7,2,8,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,8,2,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,7,2,1,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,2,1,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,2,7,1,4,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,8,4,2,6,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,3,2,1,6,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,8,2,1,7,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,2,8,1,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,1,8,7,5,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,3,2,1,7,5,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,3,2,1,8,5,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,3,2,8,1,4,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,8,2,1,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,3,2,1,4,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,3,2,1,5,8,6,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,8,5,6,1,2,4,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,4,1,6,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,1,4,6,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,8,4,7,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,8,4,7,2,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,8,3,2,7,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,1,8,3,2,7,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,1,3,2,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,3,1,2,6,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,3,4,6,5,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,2,4,6,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,2,3,1,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,2,1,3,6,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,1,2,3,6,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,1,8,2,3,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,8,2,3,7,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,2,8,3,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,2,8,3,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,1,8,3,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,2,8,1,3,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,8,3,1,7,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,8,4,7,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,8,4,7,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,8,4,7,5,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,8,4,7,1,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,8,3,1,7,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,6,8,1,3,7,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,1,8,3,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,5,8,3,7,6,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,1,3,8,7,6,5]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,5,3,8,1,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,4,8,7,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,4,8,7,6,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,4,8,7,6,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,2,4,8,7,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,3,8,1,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,2,3,8,7,6,5]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,4,2,3,8,7,6,5]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,1,3,2,8,7,6,5]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,8,1,2,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,1,8,2,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,1,3,8,2,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,5,3,8,2,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,4,8,7,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,4,8,7,2,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,4,1,8,7,2,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,8,1,7,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,7,1,2,4,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,8,7,3,4,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,8,7,2,1,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,5,1,8,7,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,5,8,7,2,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,4,5,8,7,2,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,5,8,2,7,6,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,1,5,8,2,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,6,8,1,2,7,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,8,2,1,7,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,8,2,7,1,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,8,3,7,5,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,3,8,7,6,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,2,8,7,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,2,8,1,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,4,2,8,7,6,5]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,2,4,8,7,6,5]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,2,5,8,1,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,5,8,7,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,5,8,7,6,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,4,5,8,7,6,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,5,8,7,1,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,5,8,1,7,6,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,1,3,2,6,5,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,3,2,6,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,3,2,5,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,3,2,5,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,3,2,5,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,2,5,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,4,2,5,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,4,2,5,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,4,2,6,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,3,5,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,2,5,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,2,5,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,1,4,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,1,4,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,7,1,4,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,8,1,4,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,8,1,4,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,1,4,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,6,1,4,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,5,1,4,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,2,5,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,7,2,5,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,7,3,5,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,3,5,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,2,5,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,2,5,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,5,1,4,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,1,4,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,4,3,8,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,3,7,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,3,7,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,5,3,8,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,1,5,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,2,6,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,2,6,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,2,6,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,3,6,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,7,3,6,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,2,6,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,2,6,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,6,1,5,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,1,5,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,8,1,5,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,2,6,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,2,7,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,4,2,7,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,2,6,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,3,2,6,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,3,2,6,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,3,2,7,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,3,2,7,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,3,2,7,5,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,4,3,8,5,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,4,2,8,5,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,3,2,8,5,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,3,2,8,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,3,2,8,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,1,3,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,8,1,3,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,1,4,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,1,4,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,4,2,8,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,4,2,8,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,5,2,8,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,5,2,8,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,5,3,8,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,3,8,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,2,8,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,2,8,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,2,8,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,2,8,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,1,5,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,1,5,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,3,8,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,8,3,7,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,2,6,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,3,7,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,3,7,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,4,7,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,4,7,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,7,4,8,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,7,4,8,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,3,8,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,3,8,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,2,6,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,3,7,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,6,3,8,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,2,6,8,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,3,6,2,8,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,6,2,4,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,3,8,2,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,8,2,4,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,2,5,8,3,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,4,2,5,8,3,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,2,6,3,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,1,6,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,1,6,8,2,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,5,6,1,4,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,5,6,3,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,1,6,3,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,6,3,2,8,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,4,5,3,8,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,5,3,8,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,4,8,3,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,8,3,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,4,1,8,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,5,3,1,8,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,1,5,8,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,3,7,8,1,4,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,8,2,4,6,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,5,8,1,4,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,1,7,8,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,4,1,5,8,3,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,4,3,8,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,4,8,3,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,8,3,5,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,7,3,8,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,6,7,3,1,8,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,6,1,7,3,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,6,7,3,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,4,7,1,8,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,8,3,1,4,5,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,2,8,4,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,8,4,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,7,4,8,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,6,7,3,2,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,1,7,3,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,7,3,2,1,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,6,7,3,2,8,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,6,2,7,3,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,2,7,3,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,2,1,7,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,7,4,2,8,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,2,1,8,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,3,1,8,2,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,1,5,2,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,4,2,5,1,8,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,4,2,1,8,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,4,2,8,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,4,2,8,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,7,2,8,4,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,7,2,8,4,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,7,2,1,8,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,3,8,2,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,7,8,2,1,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,7,8,1,4,6,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,7,8,2,6,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,7,3,8,2,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,7,2,8,5,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,7,8,5,2,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,6,7,8,5,2,4,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,4,7,8,2,5,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,4,7,8,2,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,5,7,8,2,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,3,7,8,1,6,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,2,8,5,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,4,1,7,8,2,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,6,2,7,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,2,1,7,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,2,7,1,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,2,7,8,4,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,6,7,2,8,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,6,7,2,1,8,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,6,1,7,2,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,6,7,2,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,4,7,1,8,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,6,7,1,8,5,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,7,8,5,2,4,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,7,8,3,5,1,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,8,1,5,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,1,6,7,8,4,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,6,1,7,8,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,6,7,1,8,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,6,1,3,4,2,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,3,2,5,1,6,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,3,6,2,4,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,7,4,1,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,3,8,2,4,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,4,5,8,3,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,5,3,7,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,2,4,5,6,3,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,2,4,5,6,1,3,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,2,5,1,3,6,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,6,2,1,4,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,1,5,6,3,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,4,5,6,3,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,5,3,7,2,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,5,8,3,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,6,7,2,8,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,6,7,2,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,3,6,7,2,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,3,7,1,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,5,3,7,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,4,7,1,2,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,5,8,2,1,4,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,3,8,4,1,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,8,3,6,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,6,7,8,1,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,6,4,7,8,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,7,8,3,5,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,6,1,7,8,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,7,1,4,8,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,2,4,1,7,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,7,1,4,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,3,6,7,8,1,2,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,3,6,7,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,2,7,1,3,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,1,7,8,2,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,5,2,7,8,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,2,6,7,8,3,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,6,7,8,3,5,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,2,7,4,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,2,7,4,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,1,6,4,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,7,4,2,1,5,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,3,4,2,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,4,2,1,3,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,1,3,4,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,3,4,2,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,2,7,1,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,6,2,7,1,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,3,8,2,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,4,7,8,5,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,4,7,8,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,2,7,8,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,4,5,8,6,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,1,5,8,6,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,8,2,1,6,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,1,3,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,3,1,7,8,2,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,6,1,7,8,5,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,2,6,7,8,4,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,2,6,7,8,4,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,5,2,6,7,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,6,4,7,8,5,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,7,1,3,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,7,8,2,1,5,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,7,3,8,5,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,7,8,5,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,5,2,3,7,6,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,4,3,7,2,5,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,5,6,3,4,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,6,2,7,3,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,6,7,4,5,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,2,6,5,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,6,2,4,3,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,4,8,3,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,5,4,1,3,2,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[5,8,6,2,4,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,2,6,5,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,2,6,5,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,6,2,4,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,5,4,2,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,5,4,8,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,4,7,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,8,6,7,4,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,1,6,7,4,5,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,6,8,4,2,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,7,8,2,4,5,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,7,2,8,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,2,7,8,5,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,2,1,7,8,5,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,8,7,1,5,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,2,7,1,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,7,2,1,4,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,7,1,2,4,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,6,1,4,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,6,1,4,3,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,7,6,8,4,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,7,8,3,4,5,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,6,7,1,3,4,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,8,1,3,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,8,4,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,6,2,8,3,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,8,2,3,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,5,7,3,1,4,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,7,3,8,4,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,3,7,8,5,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,3,7,1,5,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,5,2,3,8,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,2,5,4,8,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,5,2,3,1,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,3,1,8,2,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,4,3,1,7,6,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,5,8,3,7,6,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,5,1,3,7,6,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,1,3,8,2,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,1,3,2,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,6,1,2,3,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,2,1,3,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,2,6,1,4,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,2,7,1,8,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,2,1,8,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,2,8,3,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,1,8,2,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,1,8,3,2,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,1,7,3,5,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,6,8,7,3,5,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,7,8,6,5,3,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,7,1,6,5,3,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,1,6,5,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,1,7,2,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,2,7,6,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,8,2,1,7,6,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,8,1,7,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,8,2,7,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,8,7,2,5,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,8,6,5,2,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,7,6,5,4,2,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,1,2,6,5,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,6,2,4,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,5,2,4,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,1,2,3,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,1,2,3,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,6,5,3,4,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,1,5,2,4,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,1,2,7,3,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,1,2,8,3,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,1,2,8,3,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,5,2,8,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,5,3,8,4,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,3,7,4,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,1,5,2,7,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,1,2,7,3,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,1,2,7,3,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,1,7,2,3,5,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,6,7,2,4,5,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,6,7,3,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,6,8,3,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,6,8,2,4,5,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,6,1,8,2,3,5,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,7,1,2,8,3,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,7,2,8,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,2,7,8,5,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,3,8,7,5,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,2,8,7,5,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,2,8,7,5,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,8,2,7,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,1,2,7,3,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,2,7,3,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,8,2,7,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,8,3,7,4,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,8,7,3,4,5,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,1,8,7,2,4,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,1,7,2,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,1,6,2,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,8,6,2,4,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,8,6,3,4,5,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,8,7,6,3,4,5,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,1,7,6,2,4,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,1,6,2,3,5,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,5,1,6,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,5,4,7,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,5,3,7,6,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,5,3,7,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,5,3,6,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,5,1,6,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,5,4,6,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,5,3,6,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,5,1,6,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,5,2,7,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,2,7,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,2,7,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,1,7,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,5,1,7,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,5,4,7,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,5,4,7,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,5,4,7,6,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,5,3,7,6,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,5,1,7,6,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,1,7,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,5,7,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,4,7,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,4,7,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,1,7,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,3,7,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,3,7,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,4,7,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,4,7,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,4,7,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,4,7,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,3,7,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,3,7,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,1,7,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,2,7,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,2,7,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,3,7,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,3,7,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,1,7,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,5,1,7,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,1,7,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,3,7,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,3,7,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,4,7,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,4,7,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,1,7,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,5,1,7,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,4,1,7,5,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,4,2,7,6,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,5,1,7,6,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,1,7,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,5,7,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,5,7,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,5,7,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,1,7,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,5,1,7,6,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,5,2,7,6,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,5,2,7,6,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,5,3,7,6,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,3,7,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,2,7,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,2,7,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,2,7,4,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,1,7,4,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,4,7,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,4,7,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,2,7,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,2,7,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,1,7,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,4,7,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,5,7,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,5,7,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,5,7,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,5,7,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,5,7,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,4,7,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,1,7,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,3,7,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,2,1,6,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,3,5,2,4,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,5,2,4,1,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,7,5,2,4,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,4,5,7,3,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,5,7,3,1,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,2,4,6,5,3,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,5,4,6,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,3,5,1,4,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,1,4,5,3,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,5,6,4,3,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,7,4,3,2,1,8,6]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,5,7,4,3,2,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,8,3,2,7,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,7,6,3,2,8,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,6,7,3,2,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,4,7,3,1,8,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,4,5,3,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,5,1,4,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,4,2,1,3,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,5,7,4,2,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,7,5,1,4,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,1,7,5,3,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,3,8,7,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,4,8,6,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,7,6,3,5,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,8,7,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,5,8,6,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,8,1,6,7,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,4,1,8,7,5,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,2,6,1,4,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,7,6,8,1,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,6,4,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,5,6,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,6,7,5,8,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,7,6,5,8,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,8,5,7,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,5,7,6,8,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,6,5,7,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,7,6,8,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,8,7,3,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,2,4,6,7,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,7,2,6,4,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,7,2,1,8,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,3,2,1,5,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,7,6,1,3,4,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,7,3,2,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,6,7,2,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,7,8,6,2,1,5,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,7,6,3,5,2,4,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,7,4,8,1,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,8,2,1,7,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,4,1,5,7,2,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,3,7,1,6,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,7,2,1,3,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,6,7,1,3,5,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,6,1,7,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,1,8,7,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,6,5,7,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,7,8,5,6,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,7,6,8,5,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,2,5,8,6,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,7,4,8,2,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,8,1,6,5,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,7,8,6,1,3,5,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,7,6,3,5,1,4,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,4,7,6,5,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,3,5,1,2,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,1,4,5,7,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,7,2,4,5,1,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,6,2,4,5,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,1,4,5,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,2,4,5,3,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,6,3,2,1,4,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,4,3,6,1,2,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,1,4,5,2,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,1,6,4,5,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,4,5,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,8,7,4,2,6,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,7,4,1,6,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,7,4,2,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,8,4,5,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,1,6,8,5,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,3,8,1,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,6,4,5,8,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,5,7,4,1,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,8,4,7,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,8,4,7,6,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,8,3,5,6,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,5,8,4,3,6,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,3,8,4,1,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,1,5,8,4,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,4,8,3,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,3,8,2,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,8,4,2,6,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,3,8,1,5,6,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,8,2,4,3,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,2,4,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,1,7,8,5,4,3,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,7,3,8,1,4,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,8,4,5,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,8,4,5,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,7,1,4,3,6,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,7,4,2,6,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,8,4,3,6,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,6,3,8,4,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,3,6,2,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,6,3,1,4,2,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,3,8,2,4,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,4,3,1,8,5,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,1,3,2,6,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,3,6,2,8,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,3,5,1,2,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,3,2,6,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,3,8,6,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,8,4,7,6,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,8,2,4,7,6,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,5,4,1,6,2,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[2,7,6,4,5,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,1,6,4,5,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,3,6,1,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,7,6,5,8,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,8,5,3,6,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,3,5,2,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,5,4,2,6,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,4,8,1,5,6,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,4,2,8,5,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,1,8,5,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,2,8,5,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,5,2,4,8,6,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,3,2,8,1,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,1,5,3,8,6,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,3,5,8,1,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,5,4,8,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,1,8,5,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,1,4,8,5,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,3,7,2,8,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,4,5,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,7,2,4,5,8,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,1,7,4,8,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,7,4,8,6,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,6,3,7,1,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,7,4,5,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,5,4,8,6,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,7,1,4,8,6,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,3,1,8,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,3,5,8,2,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,3,8,1,2,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,8,4,1,6,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,5,1,6,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,2,5,4,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,4,7,1,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,8,2,4,7,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,2,5,8,3,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,6,5,3,8,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,2,1,6,8,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,3,5,1,4,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,1,5,3,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,1,6,4,3,8,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,3,2,7,1,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,4,3,8,2,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,6,2,8,7,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,7,6,2,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,3,1,7,2,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,4,3,1,8,2,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[1,4,7,5,8,3,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,1,3,5,8,4,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,5,8,4,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,8,5,7,4,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,8,7,1,4,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,5,8,7,3,6,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,5,4,8,7,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,3,8,1,7,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,7,1,8,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,3,7,6,5,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[5,3,8,7,6,4,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,5,3,1,8,6,4,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,6,5,3,7,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,5,8,6,3,7,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,1,8,7,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,7,3,1,4,5,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,2,8,7,4,5,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,1,6,8,4,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,7,6,4,8,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,1,6,3,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,7,5,3,2,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,5,3,2,1,8,4]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[6,5,3,2,8,7,4,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[5,2,6,3,8,7,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,7,6,3,1,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,2,1,7,3,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,2,7,4,1,8,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,2,6,3,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,8,6,3,7,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,8,6,2,4,7,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,3,6,2,4,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,6,7,2,1,4,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,7,8,2,1,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,3,7,1,4,6,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,2,5,7,1,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,6,2,7,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,3,6,2,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,3,6,2,5,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,7,8,2,1,6,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,2,6,8,1,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,8,2,7,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,1,5,7,2,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,3,7,1,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,7,2,6,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,8,1,7,5,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,6,8,2,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,5,2,8,1,7,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,1,8,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,2,7,6,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,2,8,7,5,4,3,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,6,2,1,8,5,4,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[6,1,7,2,8,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,1,8,2,6,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,7,1,8,6,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,3,1,6,5,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,4,6,1,5,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,1,6,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,1,7,5,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[7,1,8,6,5,4,3,2]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,4,2,3,7,6,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,2,7,3,5,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,6,3,5,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,7,6,4,5,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,2,6,3,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,6,2,3,4,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,5,2,3,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,5,2,8,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,5,2,3,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,6,2,3,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,2,6,3,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,2,1,6,4,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,5,2,8,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,5,2,7,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,1,7,8,4,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,8,2,3,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,2,3,8,1,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,5,4,1,8,6,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,2,3,1,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,2,3,1,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,1,3,8,5,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,4,2,8,7,3,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,8,2,7,3,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,5,1,2,7,3,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,1,2,8,3,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,6,2,1,3,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,6,1,4,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,7,1,8,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,2,1,8,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,2,1,7,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,8,1,7,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,8,2,7,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,5,6,1,2,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,3,7,5,1,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,2,7,1,8,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,1,5,4,3,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,3,5,1,2,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,1,4,6,2,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,1,4,6,5,2,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,7,4,6,2,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,1,4,7,2,6,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,7,8,5,2,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,1,8,5,7,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,3,5,1,7,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,8,2,4,6,7,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,4,8,6,5,7,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,5,4,8,1,6,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,1,4,6,8,2,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,5,4,6,7,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,6,3,7,5,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,6,3,8,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,4,2,8,6,5,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,5,8,4,1,7,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,5,3,7,4,1,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,1,4,8,3,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,4,3,8,2,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,4,1,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,8,2,7,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,3,8,1,6,7,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,3,7,2,6,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,7,2,3,8,5,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,2,1,7,5,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,1,3,6,5,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,7,1,6,3,4,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,6,7,2,4,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,8,7,4,2,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,8,7,2,1,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,6,1,4,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,5,8,2,4,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,4,1,8,5,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,5,6,2,7,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,6,1,8,7,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,2,8,7,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,5,6,1,4,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,5,4,7,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,6,4,5,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,3,6,1,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,8,6,5,7,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,5,3,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,3,5,2,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,4,1,6,5,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,1,2,8,7,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,1,5,8,7,6,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,1,2,5,8,6,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,5,2,4,6,1,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,3,2,6,8,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,1,5,3,6,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,5,4,6,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,1,5,7,6,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,5,2,6,3,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,2,1,4,3,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,2,7,4,8,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,2,7,4,1,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,7,5,2,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,7,5,2,8,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,1,6,5,4,2,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,3,2,4,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,2,4,1,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,1,3,5,4,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,2,3,4,8,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,7,2,3,4,1,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,7,3,8,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,7,3,8,6,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,6,7,4,1,8,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,6,3,7,4,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,6,7,4,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,8,7,4,3,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,3,7,4,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,7,4,1,2,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,1,3,5,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,7,3,2,6,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,6,3,1,5,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,1,6,3,2,5,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,4,1,6,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,1,2,7,6,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,8,4,2,5,7,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,3,5,2,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,5,3,8,7,6,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,3,2,8,7,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,2,4,8,1,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,2,8,5,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,1,8,7,6,5,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,4,2,1,7,5,3,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,3,1,8,6,7,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,1,4,8,6,5,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,6,5,4,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,5,6,8,4,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,7,1,6,8,2,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,2,5,1,7,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,6,2,1,8,7,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,2,5,8,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,2,6,3,8,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,4,3,1,8,5,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,2,8,3,4,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,2,8,4,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,2,8,1,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,8,7,1,5,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,7,8,6,3,4,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,1,8,5,4,3,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,8,4,5,3,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,3,8,1,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,7,8,5,4,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,5,8,4,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,8,4,3,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,8,3,5,6,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,8,3,6,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,8,1,7,2,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,4,1,3,7,2,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,1,8,2,4,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,8,1,4,6,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,3,8,2,5,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,8,4,2,5,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,3,8,2,5,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,4,8,3,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,8,2,4,3,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,3,5,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,8,2,1,4,6,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,4,1,6,5,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,1,6,5,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,7,6,1,4,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,5,6,7,4,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,5,8,6,1,4,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,5,7,6,1,4,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,2,4,1,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,5,8,2,4,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,5,3,4,7,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,5,3,4,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,3,4,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,7,6,1,4,5,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,8,5,3,6,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,6,7,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,8,5,3,4,7,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,5,3,4,6,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,7,2,4,6,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,5,2,8,3,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,8,2,4,6,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,8,6,1,4,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,8,2,1,3,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,5,6,2,1,8,7,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,7,6,1,4,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,7,2,4,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,2,4,6,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,5,2,7,3,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,2,6,3,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,2,3,7,6,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,2,7,3,4,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,6,7,4,3,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,2,6,4,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,2,8,6,4,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,6,8,7,3,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,5,2,8,3,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,2,3,8,7,5,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,2,3,8,6,5,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,2,3,8,6,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,2,3,7,6,5,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,2,3,8,5,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,6,8,4,3,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,2,8,4,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,8,2,3,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,5,8,2,4,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,8,2,4,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,2,8,3,4,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,8,3,7,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,7,3,4,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,6,7,4,3,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,6,8,7,3,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,6,8,4,3,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,7,8,6,3,4,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,1,8,3,6,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,3,6,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,4,8,6,2,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,4,8,6,5,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,6,5,8,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,6,7,8,3,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,6,5,7,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,2,6,3,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,7,3,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,6,2,4,8,7,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,6,2,4,8,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,5,6,8,4,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,5,2,8,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,2,5,8,4,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,6,5,8,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,2,6,3,8,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,5,2,7,3,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,6,7,8,3,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,2,6,8,5,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,5,2,6,3,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,5,6,1,4,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,4,2,1,5,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,2,1,6,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,8,1,5,7,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,3,8,1,7,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,1,4,7,2,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,8,3,4,5,1,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,3,5,4,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,3,6,5,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,2,1,5,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,2,6,4,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,2,5,6,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,1,6,5,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,2,1,7,5,4,3,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,1,8,7,5,4,3,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,3,8,2,6,4,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,7,1,6,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,2,7,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,2,5,8,7,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,3,1,8,4,2,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,2,1,5,3,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,3,7,5,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,8,7,5,6,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,4,7,1,5,3,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,7,6,4,2,8,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,1,7,5,6,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,7,2,8,6,4,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,1,7,6,4,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,5,7,3,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,5,8,3,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,6,8,2,4,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,6,8,5,3,1,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,1,4,7,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,7,3,8,4,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,2,8,1,4,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,7,5,2,1,3,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,5,6,7,2,8,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,7,6,1,8,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,8,6,2,7,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,5,8,3,2,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,5,7,1,2,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,5,6,3,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,6,3,4,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,1,4,2,3,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,6,4,3,8,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,4,5,8,7,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,2,4,1,8,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,3,5,4,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,2,7,6,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,2,4,7,8,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,7,2,4,1,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,4,2,8,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,7,5,8,1,4,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,7,6,3,4,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,7,6,2,3,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,1,7,2,6,5,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,2,1,5,6,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,7,8,1,6,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,8,7,6,5,3,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,1,4,7,8,2,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,2,7,1,6,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,5,6,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,8,6,3,5,7,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,1,2,5,3,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,6,5,2,4,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,5,6,1,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,7,8,2,1,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,8,7,1,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,8,7,5,2,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,6,7,8,5,1,4,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,7,6,8,5,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,1,6,4,2,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,8,6,3,5,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,8,7,6,5,4,1,2]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,8,1,6,4,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,7,5,1,4,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,6,7,5,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,3,1,2,7,4,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,2,7,1,3,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,2,5,1,3,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,3,6,1,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,3,6,1,7,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,6,2,4,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,2,7,1,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,6,7,1,2,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,3,7,4,1,2,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,7,1,5,2,3,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,4,2,3,8,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,6,4,2,3,7,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,7,6,3,8,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,2,3,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,6,1,4,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,2,6,1,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,7,5,2,8,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,8,5,2,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,2,6,3,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,6,1,2,7,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,6,2,4,7,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,4,3,7,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,5,3,7,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,6,2,7,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,3,7,5,8,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,7,6,4,8,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,7,4,8,1,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,4,6,7,2,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,3,7,1,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,7,1,4,8,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,3,7,2,4,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,7,3,8,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,3,8,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,6,3,7,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,1,6,7,2,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,1,6,8,2,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,1,7,8,2,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,3,7,1,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,6,4,7,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,7,4,8,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,1,5,8,6,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,1,2,8,6,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,3,8,1,6,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,2,8,1,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,7,8,2,5,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,7,8,5,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,6,8,2,7,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,8,2,7,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,1,8,6,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,4,7,5,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,7,1,6,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,1,4,2,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,5,3,8,2,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,7,4,5,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,1,4,5,8,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,7,8,5,3,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,7,3,8,1,2,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,1,4,5,3,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,7,8,4,1,6,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,1,8,4,2,6,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,3,1,8,4,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,3,8,1,5,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,1,4,2,6,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,4,1,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,4,5,6,7,8,9,10,1]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[3,6,4,5,7,2,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,2,7,4,6,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,3,6,2,4,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,2,5,1,8,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,3,6,2,7,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,6,3,4,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,2,7,4,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,5,7,3,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,4,7,6,2,3,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,3,5,2,4,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,3,1,2,8,4,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,6,5,2,3,7,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,6,3,2,8,4,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,2,3,1,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,2,6,5,1,8,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,8,6,2,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,3,5,2,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,5,2,3,6,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,2,1,7,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,6,3,7,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,6,1,7,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,1,5,7,2,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,2,8,3,7,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,5,8,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,2,7,1,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,7,1,2,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,1,8,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,6,1,7,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,1,5,8,2,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,1,5,8,4,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,5,3,4,6,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,3,5,1,6,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,6,3,8,7,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,4,5,8,7,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,5,3,4,8,7,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,1,8,3,7,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,8,1,7,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,8,2,3,5,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,8,2,4,6,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,3,8,2,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,7,8,2,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,5,8,7,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,6,2,8,7,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,8,1,6,2,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,8,3,6,2,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,1,5,8,7,2,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,8,3,7,5,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,6,2,5,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,1,6,7,3,2,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,6,7,3,2,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,5,3,7,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,5,3,6,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,1,3,6,2,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,8,3,6,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,8,3,2,6,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,1,3,2,6,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,4,3,2,6,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,4,3,2,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,4,3,2,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,5,4,6,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,3,6,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,3,2,6,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,1,4,3,2,5,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,8,3,2,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,3,8,2,5,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,1,3,2,5,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,1,3,2,6,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,1,3,6,2,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,8,3,6,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,8,3,2,6,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,8,3,2,5,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,3,8,2,5,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,7,2,5,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,3,2,8,6,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,4,3,2,8,7,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,3,8,7,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,4,1,7,8,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,3,1,7,2,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,4,3,2,1,8,6,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[6,5,3,1,8,2,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,4,1,8,7,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,1,4,8,6,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,1,3,2,8,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,1,3,2,8,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,1,2,8,5,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,4,3,1,2,7,5,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,4,3,8,2,7,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,3,8,7,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,1,3,8,2,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,1,8,4,5,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,8,1,4,5,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,8,1,3,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,3,7,8,2,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,3,7,2,8,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,8,3,2,1,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,8,3,1,2,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,8,4,1,6,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,4,8,1,7,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,8,1,2,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,3,2,8,1,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,3,7,2,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,5,3,7,1,2,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,4,7,1,8,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,7,8,2,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,3,7,2,8,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,2,7,8,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,4,3,2,6,8,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,8,2,7,4,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,3,7,8,2,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,7,8,4,3,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,3,7,4,1,5,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,1,2,5,4,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,8,3,1,4,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,4,1,3,7,6,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,8,7,4,2,1,6,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,5,1,6,8,3,4,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,2,1,8,7,4,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[4,7,2,8,1,3,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,8,6,1,2,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,7,1,8,2,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,2,7,3,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,8,3,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,8,3,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,8,3,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,8,3,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,8,4,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,3,8,4,6,5,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,3,7,4,6,5,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,2,7,4,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,7,3,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,7,3,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,7,3,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,6,3,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,6,3,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,5,3,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,5,3,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,5,3,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,4,3,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,4,3,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,4,3,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,4,3,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,3,4,6,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,7,2,3,4,6,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,2,3,4,7,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,2,4,3,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,4,3,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,4,3,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,4,3,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,5,3,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,5,3,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,5,3,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,6,3,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,6,3,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,3,8,4,7,5,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,2,8,4,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,8,3,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,8,3,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,8,3,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,8,3,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,7,3,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,7,2,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,7,5,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,3,8,5,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,3,8,5,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,8,3,4,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,6,8,3,4,1,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,2,7,5,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,7,2,4,3,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,8,4,3,1,7,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,6,8,4,3,1,2,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,7,8,4,1,6,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,8,4,1,6,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,7,8,4,1,3,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,6,8,4,2,1,7,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,6,8,2,4,1,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,2,8,5,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,6,8,5,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,6,8,5,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,6,2,8,5,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,8,2,4,1,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,6,8,4,2,1,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,7,8,4,1,3,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,8,4,1,2,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,8,1,5,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,8,1,5,2,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,8,1,5,3,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,7,8,1,3,5,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,7,8,2,1,6,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,2,8,1,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,7,8,1,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,7,8,1,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,2,8,1,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,8,2,1,6,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,7,8,1,3,5,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,7,8,1,5,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,8,1,5,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,7,8,1,5,4,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,7,8,1,4,5,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,8,1,4,5,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,7,8,1,4,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,8,1,3,4,5,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,7,8,2,1,4,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,7,2,8,1,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,2,7,8,1,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,6,8,4,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,2,8,3,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,8,3,2,1,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,7,8,3,1,4,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,7,8,3,1,6,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,7,8,3,1,6,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,3,8,1,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,8,1,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,3,8,1,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,3,8,2,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,3,2,8,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,2,3,8,1,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,5,4,8,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,3,2,8,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,3,8,2,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,3,8,1,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,8,1,2,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,8,3,1,2,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,7,8,3,1,4,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,8,3,2,1,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,2,7,8,1,5,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,8,2,1,4,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,7,8,1,3,4,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,8,1,4,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,7,8,1,4,2,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,8,1,4,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,8,1,2,5,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,8,1,2,5,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,7,8,1,2,4,5,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,7,8,1,3,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,8,2,1,3,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,2,7,8,1,4,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,7,8,1,3,2,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,8,1,2,4,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,8,1,2,3,5,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,2,8,5,1,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,7,5,2,6,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,5,4,2,6,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,2,8,5,4,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,5,4,3,1,7,6]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,8,4,5,6,1,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,6,5,7,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,5,3,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,4,3,5,6,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,8,4,5,6,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,3,7,5,2,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,3,8,5,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,8,2,5,6,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,8,5,1,3,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,7,5,2,1,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,7,5,1,2,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,1,7,5,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,1,2,7,6,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,2,1,7,5,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,5,7,1,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,2,7,4,1,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,5,2,6,4,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,1,8,6,4,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,6,1,8,7,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,5,8,2,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,5,8,4,2,3,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,5,8,3,7,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,5,7,3,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,7,4,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,1,8,7,6,3,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,1,3,8,4,6,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,4,8,6,1,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,4,8,6,5,1,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,7,3,5,8,6,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,2,4,7,8,6,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,5,4,6,2,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,4,7,1,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,6,4,1,8,7,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,6,1,4,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,5,6,8,4,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,3,5,1,8,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,1,5,8,4,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,6,5,8,3,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,6,3,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,4,1,7,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,4,2,7,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,1,4,7,2,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,6,4,7,8,2,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,4,6,8,5,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,3,4,5,7,1,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,5,4,6,1,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,1,4,3,6,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,4,1,2,6,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,3,2,1,6,5,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,6,3,2,5,4,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,7,3,2,5,4,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,3,2,5,4,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,4,5,2,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,5,1,6,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,1,5,6,3,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,2,1,6,5,4,3,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,3,6,1,5,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,5,1,3,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,5,4,3,2,7,6]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,8,6,4,3,7,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,7,4,3,1,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,7,5,1,3,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,7,1,5,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,1,7,5,4,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,2,1,8,5,4,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,3,8,1,5,4,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,8,5,1,3,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,8,4,3,1,7,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,6,8,4,3,7,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,7,8,4,3,6,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,8,7,4,3,6,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,7,5,6,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,8,5,6,3,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,8,5,7,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,8,6,7,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,8,6,1,7,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,1,8,6,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,7,6,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,1,6,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,7,6,1,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,7,6,8,1,3,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,5,8,3,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,6,5,7,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,6,7,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,5,6,8,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,5,7,8,2,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,4,6,7,1,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,6,1,7,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,1,5,7,3,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,5,1,7,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,5,7,1,2,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,4,7,2,1,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,6,4,7,2,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,6,2,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,2,6,7,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,3,2,6,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,3,2,7,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,5,3,2,7,1,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,2,1,4,3,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,2,1,4,3,8,7,6]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,4,1,2,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,6,3,2,8,7,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,3,2,8,6,5,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,8,3,2,7,6,5,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,8,4,7,2,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,4,8,2,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,4,8,2,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,8,2,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,5,8,1,2,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,3,5,1,8,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,1,5,8,3,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,2,1,6,8,7,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,6,1,8,7,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,6,8,1,7,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,5,6,8,7,1,2,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,6,5,8,7,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,5,8,6,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,5,7,6,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,6,7,5,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,7,8,5,4,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,5,7,8,6,1,4,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,4,7,8,1,6,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,8,1,7,6,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,4,8,7,1,6,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,5,8,7,6,1,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,4,6,1,8,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,1,7,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,1,7,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,3,1,7,5,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,2,1,7,5,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,4,6,2,7,5,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,5,2,6,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,4,3,1,7,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,6,8,4,1,7,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,6,7,5,1,8,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,5,6,1,8,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,6,5,7,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,5,6,1,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,5,1,8,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,4,1,7,5,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,7,5,3,1,8,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,4,2,6,7,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,5,3,2,7,6,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,2,1,7,6,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,5,3,1,7,6,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,4,1,6,7,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,5,1,6,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,4,6,1,7,5,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,1,6,5,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,6,5,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,1,2,7,5,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,1,2,7,6,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,2,5,3,7,6,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,1,2,7,6,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,5,1,2,7,6,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,1,5,8,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,6,1,5,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,3,5,1,7,6,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,6,1,5,8,3,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,6,7,1,5,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,1,6,5,8,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,1,6,8,4,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,1,6,7,5,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,3,1,7,6,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,2,1,7,6,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,3,5,2,7,6,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,6,2,5,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,6,2,1,5,8,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,3,1,5,7,6,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,4,1,7,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,1,7,4,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,4,8,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,4,7,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,2,7,4,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,2,5,8,3,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,5,7,6,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,8,3,5,7,6,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,2,3,7,6,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,1,3,7,6,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,2,6,8,4,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,2,6,7,5,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,1,4,2,7,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,5,7,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,6,8,2,5,7,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,3,2,5,7,6,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,1,3,2,7,6,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,3,2,7,6,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,1,3,7,6,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,4,2,3,7,6,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,1,3,7,6,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,1,3,7,6,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,3,5,7,6,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,2,3,5,7,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,7,1,3,5,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,3,5,7,6,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,2,3,7,6,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,1,2,4,7,6,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,2,4,3,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,3,5,6,2,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,3,4,2,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,7,8,3,4,5,6,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,6,3,8,4,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,1,4,2,6,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,7,8,5,6,1,2,3]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,7,8,5,6,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,8,4,2,6,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,8,2,4,5,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,2,8,4,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,6,7,4,5,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,2,4,8,6,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,4,2,8,7,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,5,8,7,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,4,5,1,7,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,4,1,3,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,4,8,3,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,5,8,7,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,5,1,7,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,4,6,7,3,8,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,2,6,7,3,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,7,8,2,3,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,8,3,2,1,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,6,4,8,1,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,8,1,2,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,5,3,7,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,6,7,2,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,6,7,2,8,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,4,5,2,7,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,2,5,6,8,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,2,7,8,6,4,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,2,7,8,6,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,7,1,8,6,5,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,1,2,8,6,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,6,8,1,2,7,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,8,7,1,5,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,7,3,5,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,1,6,3,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,3,6,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,3,6,5,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,2,8,6,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,3,4,8,6,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,2,7,1,8,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,2,3,6,5,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,5,7,1,6,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,7,1,2,6,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,2,7,1,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,7,2,5,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,4,8,7,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,8,3,7,4,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,8,3,4,7,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,2,4,8,1,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,7,2,3,5,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,2,1,7,3,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,7,2,1,6,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,6,2,1,4,3,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,7,2,3,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,4,2,7,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,7,5,3,4,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,7,3,5,4,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,5,4,7,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,2,7,3,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,6,2,4,3,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,6,1,2,4,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,6,4,1,3,2,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[5,8,4,7,2,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,7,5,4,3,6,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,6,8,4,3,7,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,8,7,3,2,5,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,1,7,3,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,5,7,3,1,6,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,7,1,3,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,3,1,2,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,8,4,7,1,2,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,4,1,7,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,4,7,1,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,2,6,5,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,5,6,7,4,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,8,5,7,1,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,5,7,1,2,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,5,1,7,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,3,1,7,2,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,3,7,1,2,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,8,1,3,7,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,2,8,1,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,4,8,3,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,7,4,5,3,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,5,7,2,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,5,3,7,2,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,6,3,1,4,2,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,3,2,7,1,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,8,5,2,7,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,7,4,3,5,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,2,4,5,7,1,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,5,2,3,7,1,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,1,5,4,2,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,1,5,2,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,4,2,1,7,3,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,4,2,1,7,6,3]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[6,5,4,2,3,1,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,3,2,5,1,4,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,4,1,3,2,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,4,1,6,3,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,1,6,3,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,4,1,6,5,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,4,3,1,7,6,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,3,2,5,1,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,1,8,5,3,7,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,2,5,1,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,4,3,1,7,2,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,4,1,3,7,2,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,4,1,6,5,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,1,6,2,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[8,7,4,3,6,2,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,3,2,7,6,4,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,1,8,7,6,4,3,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,1,8,7,6,4,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,2,7,6,4,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,4,3,6,2,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,6,5,2,4,3,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,2,6,5,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,4,2,6,3,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,4,2,6,3,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,3,1,7,6,4,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,1,7,6,4,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,1,7,6,5,4,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,3,1,5,4,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,3,1,5,4,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,1,7,6,5,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,1,7,6,2,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,4,2,6,1,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,4,2,6,5,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,4,2,3,7,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,3,2,5,4,7,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,8,5,4,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,2,7,6,5,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,4,3,6,5,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[8,7,6,5,1,3,2,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[8,7,4,3,6,1,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,3,2,7,6,1,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,1,8,7,6,3,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,6,5,1,4,2,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,3,5,1,8,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,4,1,8,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,6,2,1,8,7,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,6,5,2,7,4,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,3,1,8,6,5,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,5,1,8,4,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,4,1,8,5,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,2,1,8,7,5,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[1,6,4,2,7,5,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,3,2,7,6,4,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,2,1,8,7,6,4]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[2,5,3,1,7,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,4,1,7,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,5,1,7,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,5,7,1,6,8,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,5,1,2,8,4,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,1,2,8,5,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,1,2,8,6,4,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,1,2,8,6,5,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,1,2,5,8,3,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,1,3,4,8,2,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,1,5,6,8,2,3,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,6,1,5,7,8,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,4,1,6,8,5,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,3,1,8,6,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,2,1,6,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,6,2,5,7,3,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,2,1,5,8,7,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,1,5,8,6,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,4,1,8,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,1,8,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,1,4,8,6,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,1,4,8,7,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,6,2,4,7,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,2,1,3,8,7,4,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,1,3,8,5,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,1,3,8,4,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,6,7,1,4,8,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,6,1,4,8,3,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,3,8,7,5,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,6,1,4,7,8,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,1,4,6,8,2,3,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,1,3,5,8,2,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,1,2,4,8,3,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,2,3,1,6,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,5,2,3,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,3,5,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,5,2,4,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,5,2,4,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,4,1,6,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,3,5,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,4,1,5,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,3,4,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,7,3,4,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,8,6,7,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,8,5,7,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,3,4,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,4,1,5,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,3,5,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,7,4,5,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,7,4,5,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,6,7,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,6,7,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,3,4,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,3,4,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,6,2,7,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,3,5,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,4,7,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,5,7,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,5,7,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,5,7,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,7,4,6,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,7,4,6,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,3,6,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,3,6,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,3,5,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,8,4,7,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,3,6,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,6,2,5,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,1,7,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,4,1,7,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,4,1,7,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,3,6,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,4,6,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,6,2,3,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,3,1,7,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,3,1,7,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,3,1,7,5,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,4,2,8,6,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,3,1,8,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,6,2,3,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,8,5,6,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,5,6,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,6,2,4,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,4,1,8,6,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,5,2,8,6,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,5,2,8,6,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,3,8,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,2,8,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,2,8,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,2,8,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,6,2,5,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,4,6,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,3,8,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,5,1,6,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,4,6,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,5,6,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,5,6,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,5,6,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,7,4,8,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,7,4,8,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,3,8,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,4,5,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,5,1,7,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,6,2,8,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,5,6,1,3,4,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,1,3,6,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,8,4,7,2,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,1,4,7,2,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,1,2,5,7,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,8,2,5,7,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,8,2,4,5,6,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,8,1,5,4,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,2,1,6,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,3,5,6,4,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,1,4,2,3,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,5,1,4,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,4,5,3,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,8,4,3,2,7,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,6,1,4,3,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,8,3,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,6,8,3,7,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,8,5,3,1,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,5,8,1,4,7,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,8,4,7,6,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,2,4,7,3,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,2,5,3,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,3,6,2,4,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,3,6,1,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,6,7,2,1,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,7,5,2,4,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,4,7,2,5,3,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,8,3,5,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,6,1,8,4,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,7,5,8,2,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,5,7,8,2,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,2,7,6,1,4,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,7,6,8,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,7,5,6,8,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,1,6,8,4,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,1,8,5,3,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,6,8,5,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,8,5,6,7,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,8,1,6,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,5,4,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,8,4,5,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,2,8,6,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,7,1,5,2,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,3,7,8,1,2,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,7,3,8,5,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,8,3,6,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,8,6,1,3,4,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,6,5,8,1,3,4,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,6,4,3,8,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,1,3,4,8,2,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,5,1,7,8,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,6,3,4,5,8,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,6,4,1,8,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,6,4,8,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,1,4,8,3,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,1,6,5,3,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,5,6,3,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,2,7,1,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,6,2,7,3,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,7,4,2,8,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,6,4,1,8,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,7,1,5,2,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,5,2,4,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,1,5,2,8,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,5,3,8,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,5,4,2,3,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,1,5,3,4,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,1,5,3,2,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,6,4,1,2,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,5,4,3,1,8,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,4,6,1,2,5,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,4,2,5,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,1,4,2,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,4,2,5,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,3,7,5,4,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,1,3,7,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,1,3,5,6,4,2,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,3,1,6,4,5,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,6,3,1,5,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,4,1,5,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,3,5,4,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,5,7,2,3,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,8,2,3,7,6,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,2,8,1,3,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,2,3,5,4,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,2,4,1,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,4,1,5,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,3,5,7,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,1,7,8,3,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,3,6,8,4,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,4,7,8,5,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,7,6,8,5,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,3,7,6,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,7,8,1,4,6,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,7,4,1,6,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,3,4,1,8,6,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,8,4,6,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,1,8,6,3,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,2,8,6,5,3,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,8,5,7,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,2,7,5,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,8,6,7,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,8,7,6,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,4,7,6,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,7,4,3,6,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,8,3,1,7,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,8,7,2,5,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,3,7,1,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,3,8,6,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,3,7,8,6,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,7,6,4,2,8,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,8,7,4,1,6,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,8,1,2,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,5,2,4,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,5,3,1,2,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,5,1,2,7,6,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,1,2,6,8,7,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,5,6,1,8,4,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,1,2,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,2,7,5,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,6,1,7,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,3,1,2,7,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,3,1,7,6,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,5,7,1,6,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,2,7,8,1,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,4,7,5,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,6,5,8,7,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,1,4,5,8,6,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,4,6,8,5,2,7,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,5,6,2,8,4,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,5,6,1,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,5,3,1,6,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,1,7,5,8,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,2,7,5,3,8,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,1,2,7,3,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,3,7,5,2,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,2,6,8,5,4,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,7,1,2,5,4,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,7,2,4,8,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,1,7,8,6,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,7,5,1,8,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,7,4,1,5,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,7,1,5,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,2,8,1,3,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,1,6,8,3,4,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,8,3,1,5,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,8,6,4,1,5,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,6,4,8,5,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,7,4,5,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,3,7,5,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,1,7,8,3,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,7,2,3,6,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,2,7,3,6,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,4,6,2,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,4,6,1,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,8,4,6,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,2,4,1,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,3,5,1,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,8,3,6,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,8,1,7,3,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,4,1,3,6,2,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,8,3,1,7,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,2,8,4,7,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,4,7,3,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,8,3,1,7,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,3,8,2,7,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,1,8,2,4,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,8,1,2,6,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,4,1,6,2,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,5,4,1,2,6,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,1,8,4,2,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,2,8,5,3,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,5,3,1,7,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,4,5,1,2,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,3,7,2,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,2,7,8,5,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,7,8,3,1,6,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,7,2,5,8,1,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,3,4,6,2,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,8,2,4,6,7,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,5,6,8,2,7,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,8,3,5,6,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,2,3,7,8,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,8,7,3,4,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,7,3,4,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,4,7,1,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,4,7,2,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,8,7,2,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,8,7,1,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,3,7,5,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,4,6,5,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,8,4,7,5,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,8,7,6,1,2,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,8,7,6,1,2,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,5,8,7,6,1,2,3]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,5,8,7,1,6,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,5,8,7,2,6,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,8,2,7,6,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,5,8,1,7,6,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,5,8,1,7,6,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,5,8,7,1,6,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,8,7,1,6,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,4,7,1,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,2,4,6,1,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,6,2,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,8,4,7,2,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,8,7,2,6,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,8,7,2,6,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,8,2,7,6,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,5,8,3,7,6,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,4,2,8,7,6,5,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,3,8,2,7,6,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,3,2,7,5,4,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,3,2,6,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,3,1,6,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,3,1,7,5,4,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,8,1,7,6,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,1,8,7,6,5,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,3,1,8,7,6,5,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,2,1,8,7,6,5,3]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,8,2,1,7,5,4,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,2,1,6,5,4,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,4,2,6,1,5,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,8,7,1,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,8,7,1,6,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,8,1,7,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,8,1,7,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,8,2,7,6,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,3,2,7,5,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,3,1,7,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,2,1,7,5,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,2,7,1,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,7,2,1,4,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,6,1,2,4,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,7,1,2,4,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,1,2,7,5,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,8,2,3,7,5,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,2,8,3,7,6,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,8,3,7,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,8,7,2,6,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,8,7,2,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,1,7,2,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,1,6,2,5,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,1,2,6,5,4,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,8,1,2,7,5,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,1,8,2,7,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,8,3,7,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,1,3,7,5,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,1,3,6,5,4,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,2,3,6,5,4,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,2,3,7,5,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,8,3,7,6,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,3,6,8,2,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,6,2,5,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,1,8,2,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,5,2,8,3,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,2,6,5,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,2,6,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,1,6,5,8,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,6,4,2,5,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,2,6,4,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,6,5,4,8,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,5,4,7,3,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,2,6,3,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,5,4,2,8,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,7,5,2,8,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,1,3,5,2,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,5,1,8,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,5,2,8,7,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,4,2,8,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,4,2,8,3,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,5,3,8,7,6,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,8,6,5,3,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,2,8,6,3,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,4,2,8,7,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,1,6,2,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,7,6,4,2,8,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,5,2,6,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,2,7,5,3,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,2,7,6,5,3,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,2,6,5,3,8,7,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,2,6,3,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,2,7,6,3,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,5,2,7,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,7,4,2,8,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,1,2,8,6,3,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,8,6,2,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,7,1,8,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,1,6,2,4,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,8,3,2,4,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,8,7,3,2,4,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,4,2,8,7,3,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,4,2,8,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,1,5,4,2,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,8,5,2,7,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,6,4,2,7,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,5,2,6,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,2,7,3,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,8,5,3,7,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,6,3,8,7,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,7,6,3,8,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,6,2,7,3,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,2,8,5,3,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,4,2,8,6,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,8,3,2,6,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,7,3,2,6,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,2,8,7,6,3,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,2,8,7,5,3,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,2,8,6,3,7,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,7,3,8,6,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,1,7,3,6,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,7,6,2,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,7,6,3,4,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,8,6,2,4,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,1,6,2,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,1,5,2,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,4,5,3,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,4,5,3,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,4,5,3,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,7,8,6,2,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,4,8,3,5,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,8,6,3,4,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,4,5,3,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,4,5,3,6,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,4,5,3,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,4,1,5,2,6,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,5,7,2,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,3,5,8,2,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,5,7,2,1,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,5,7,3,6,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,5,8,3,7,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,8,7,6,2,4,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,8,6,3,1,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,1,8,2,3,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,1,6,2,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,1,5,2,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,5,8,2,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,3,4,1,8,6,5,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,3,5,6,2,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,3,8,5,1,4,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,8,6,1,5,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,8,6,7,1,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,3,5,7,2,1,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,8,5,6,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,4,5,6,3,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,5,6,3,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,5,6,2,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,5,8,2,1,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,5,6,2,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,6,8,1,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,6,5,8,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,5,6,1,4,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,4,1,8,5,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,1,3,8,5,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,1,3,6,5,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,6,8,4,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,6,1,8,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,6,1,4,3,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,5,1,2,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,1,5,2,3,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,8,1,6,3,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,1,8,3,2,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,3,8,6,4,1,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,8,6,7,4,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,3,5,7,2,4,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,4,1,8,7,5,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,8,6,1,7,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,3,8,1,6,4,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,1,4,5,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,8,6,1,4,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,2,3,4,5,6,7,9,8]=>[8,1]=>[[8,8],[7]]=>[7]=>0
[1,2,3,4,5,6,7,8,10,9]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[8,4,3,6,5,1,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,3,4,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[1,8,6,5,2,7,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,5,4,1,6,3,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,8,5,4,1,3,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,8,5,4,2,1,7,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,6,2,4,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,2,6,5,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,8,6,5,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,1,3,7,6,2,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,7,3,6,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,5,2,4,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,6,5,2,3,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,2,8,3,7,4,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,1,7,2,6,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,2,6,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,8,2,4,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,8,3,2,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,3,8,2,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,1,8,4,7,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,8,7,1,6,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,2,7,1,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,7,2,1,6,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,8,7,1,3,5,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,6,1,5,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,6,1,5,4,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,7,2,6,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,8,2,5,6,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,6,7,1,4,5,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,6,8,1,4,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,3,2,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,8,3,1,4,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,7,3,1,6,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,8,4,2,7,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,4,8,2,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,3,7,1,6,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,3,8,1,5,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,3,1,2,6,5,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,1,4,2,3,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,1,4,2,6,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,1,3,4,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,2,1,5,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,6,1,5,4,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,1,4,6,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,2,1,3,6,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,1,3,2,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,2,4,5,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,6,1,2,5,4,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,1,2,5,3,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,7,2,3,6,4,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,1,2,4,3,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,3,2,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,2,3,5,4,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,7,3,8,5,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,4,5,1,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,7,6,8,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,8,6,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,8,4,5,7,1,2,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,4,8,6,7,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,6,7,1,8,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,5,6,2,7,4,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,6,1,7,8,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,6,1,8,7,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,5,6,8,1,7,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,2,4,5,1,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,8,6,2,3,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,6,8,2,3,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,6,2,8,4,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,6,3,4,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,4,2,6,8,5,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,3,2,5,4,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,3,1,5,6,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,3,1,5,7,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,1,6,8,7,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,1,6,7,8,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,3,1,7,6,8,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,8,1,6,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,2,6,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,3,1,5,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,7,2,1,8,5,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,7,2,8,1,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,8,2,1,4,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,7,1,2,8,4,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,1,3,4,8,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,1,7,3,4,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,1,7,8,2,3,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,1,8,7,2,3,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,1,2,7,4,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,1,3,7,5,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,8,3,4,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,8,3,4,6,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,2,1,6,5,8,7,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,1,4,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,2,6,4,1,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,7,4,8,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,7,4,8,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,2,3,8,6,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,2,3,8,1,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,2,3,1,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,2,1,3,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,1,6,4,2,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,1,3,2,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,3,1,2,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,3,2,1,8,7,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,7,3,2,8,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,3,2,8,6,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,3,8,2,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,3,8,1,2,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,3,1,8,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,3,8,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,7,4,8,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,7,4,8,3,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,7,4,8,6,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,1,7,4,8,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,1,3,8,6,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,3,1,8,6,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,3,8,1,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,8,5,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,8,3,1,4,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,7,1,8,3,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,7,8,4,5,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,7,8,4,5,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,6,7,8,4,3,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,1,7,8,4,2,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,7,1,8,3,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,2,1,8,3,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,2,8,1,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,2,8,3,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,2,8,3,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,7,8,4,5,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,7,8,4,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,7,8,1,4,5,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,7,1,8,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,1,7,8,5,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,2,7,8,6,5,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,2,7,8,1,5,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,7,8,5,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,7,8,5,4,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,7,2,8,5,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,2,1,8,6,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,1,2,8,6,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,7,2,8,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,7,3,8,6,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,6,7,8,3,5,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,1,7,8,2,5,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,7,1,8,2,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,8,2,4,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,8,2,4,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,7,1,8,5,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,7,8,5,2,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,7,8,5,3,4,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,1,7,8,5,4,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,7,1,8,5,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,8,4,1,3,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,3,8,5,2,7,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,2,8,4,7,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,4,5,8,7,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,8,4,7,5,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,1,4,7,2,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,1,4,8,7,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,6,4,8,5,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,1,4,8,6,3,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,7,1,8,6,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,3,8,4,2,7,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,8,7,1,4,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,3,7,1,6,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,8,5,6,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,8,1,7,6,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,1,2,7,8,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,6,4,2,8,7,5,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,3,7,5,2,8,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,2,7,4,8,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,1,4,8,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,3,5,1,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,1,4,6,7,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,5,8,4,3,7,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,7,4,2,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,1,6,2,4,5,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,6,7,1,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,8,7,1,5,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,1,8,7,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,2,7,3,6,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,3,6,4,2,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,1,5,3,8,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,6,3,4,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,2,6,3,5,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,4,3,5,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,3,6,4,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,6,4,5,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,6,5,3,4,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,5,4,3,1,8,2,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,5,4,2,7,3,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,5,4,1,7,2,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,4,1,8,3,2,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,6,5,2,8,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,3,4,8,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,4,6,3,1,8,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,8,4,2,7,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,2,6,4,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,6,2,5,7,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,5,3,2,6,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,8,3,1,7,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,6,3,7,5,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,5,2,6,4,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,1,6,2,5,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,8,1,6,3,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,1,7,3,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,6,1,7,4,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,1,3,7,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,8,5,7,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,6,8,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,1,5,8,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,3,1,8,4,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,3,8,4,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,8,5,3,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,1,8,4,3,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,1,7,4,2,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,1,2,7,3,4,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,2,8,3,5,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,6,1,8,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,6,1,7,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,1,4,7,5,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,1,5,8,4,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,5,8,3,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,2,7,1,8,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,1,6,8,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,7,5,6,8,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,5,4,8,2,7,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,1,8,7,4,2,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,4,7,5,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,1,8,3,7,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,8,1,7,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,8,3,2,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,8,2,4,7,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,7,3,8,2,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,6,8,2,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,6,8,7,3,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,7,2,8,6,3,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,8,1,7,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,7,4,5,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,8,6,4,3,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,8,7,5,6,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,7,6,3,5,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,7,6,5,2,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,8,6,5,3,2,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,2,8,7,6,3,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,8,7,4,6,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,8,3,7,6,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,6,8,7,4,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,8,4,7,5,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,8,7,2,5,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,8,7,6,4,5,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,7,6,5,3,4,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,8,7,6,5,4,2,3]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,8,6,7,3,4,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,6,7,3,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,6,7,4,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,7,4,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,6,7,4,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,7,4,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,5,7,4,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,5,7,3,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,6,4,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,7,4,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,7,4,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,8,5,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,8,5,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,8,5,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,8,5,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,8,5,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,8,5,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,8,5,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,8,5,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,7,4,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,2,7,4,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,6,4,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,6,4,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,1,7,4,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,7,4,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,8,5,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,8,5,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,5,6,1,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,6,2,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,8,4,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,1,7,3,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,7,3,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,1,7,3,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,6,3,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,2,7,3,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,7,3,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,7,3,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,8,4,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,8,4,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,8,4,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,7,3,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,4,7,3,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,7,2,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,5,7,2,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,5,7,2,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,5,7,3,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,7,3,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,6,7,3,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,7,3,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,6,7,2,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,6,7,2,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,6,7,2,4,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,5,7,1,4,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,6,7,1,4,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,6,7,1,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,6,7,1,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,8,6,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,8,6,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,8,5,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,8,5,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,5,7,1,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,7,1,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,4,6,1,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,6,1,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,7,1,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,7,1,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,7,1,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,8,4,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,8,4,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,6,1,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,6,2,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,1,6,2,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,6,2,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,5,2,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,5,1,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,2,5,1,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,6,1,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,6,1,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,6,2,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,6,1,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,3,4,5,6,8,9,7]=>[8,1]=>[[8,8],[7]]=>[7]=>0
[1,2,3,4,5,7,8,9,6]=>[8,1]=>[[8,8],[7]]=>[7]=>0
[1,2,3,4,6,7,8,9,5]=>[8,1]=>[[8,8],[7]]=>[7]=>0
[1,2,3,5,6,7,8,9,4]=>[8,1]=>[[8,8],[7]]=>[7]=>0
[1,2,4,5,6,7,8,9,3]=>[8,1]=>[[8,8],[7]]=>[7]=>0
[1,3,4,5,6,7,8,9,2]=>[8,1]=>[[8,8],[7]]=>[7]=>0
[1,2,3,4,5,6,7,9,10,8]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[1,2,3,4,5,6,8,9,10,7]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[1,2,3,4,5,7,8,9,10,6]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[1,2,3,4,6,7,8,9,10,5]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[1,2,3,5,6,7,8,9,10,4]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[1,2,4,5,6,7,8,9,10,3]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[1,3,4,5,6,7,8,9,10,2]=>[9,1]=>[[9,9],[8]]=>[8]=>0
[6,7,4,8,3,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,4,5,2,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,4,6,2,3,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,4,6,3,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,4,8,3,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,5,3,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,6,3,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,8,3,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,7,2,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,7,2,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,8,2,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,8,2,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,6,2,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,5,2,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,4,5,2,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,5,2,3,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,6,2,3,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,8,2,3,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,8,2,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,4,2,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,5,2,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,5,2,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,8,2,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,6,2,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,6,2,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,5,2,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,5,2,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,5,2,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,6,2,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,6,2,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,8,2,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,7,2,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,6,2,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,6,2,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,8,2,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,4,8,2,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,6,2,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,6,2,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,5,2,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,5,2,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,4,8,2,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,5,8,2,4,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,5,7,2,3,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,4,8,2,3,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,8,2,4,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,4,2,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,4,2,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,4,2,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,4,8,2,3,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,7,2,3,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,7,2,3,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,4,6,2,3,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,6,2,4,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,7,2,4,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,7,2,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,7,2,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,8,2,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,5,2,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,5,2,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,7,2,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,7,2,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,8,2,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,5,2,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,4,2,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,4,2,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,4,2,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,4,2,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,4,2,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,5,2,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,8,2,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,6,2,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,2,1,8,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,5,2,1,7,6,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,6,5,2,1,3,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,6,4,2,3,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,5,3,1,2,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,6,1,3,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,8,1,7,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,8,1,6,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,4,8,1,6,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,8,1,3,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,4,5,3,1,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,7,1,3,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,8,1,7,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,8,7,2,1,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[8,5,7,6,4,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,4,6,3,7,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,2,8,7,4,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,1,6,8,7,4,3,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,7,8,6,4,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,2,8,6,4,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,5,2,4,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,8,6,2,3,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,8,7,6,3,2,1,4]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[6,8,7,5,3,2,4,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,4,2,3,7,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,4,2,6,5,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,7,2,6,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,2,7,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,1,8,7,4,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,1,8,6,4,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,1,6,7,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,1,6,8,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,6,2,8,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,4,2,8,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,4,2,7,5,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,8,6,7,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,2,6,7,5,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,4,3,7,5,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,8,6,7,3,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,5,8,1,3,4,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,5,8,1,4,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,6,5,7,4,1,3,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,4,3,8,1,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,3,2,6,8,1,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,1,7,6,8,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,8,1,4,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,7,8,1,2,4,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,3,7,4,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,8,7,4,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,2,5,4,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,7,5,4,8,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,3,5,4,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,5,4,3,8,7,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,5,3,4,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,7,2,4,5,6,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,3,2,7,5,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,2,5,6,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,8,2,4,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,2,1,4,3,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,6,2,1,4,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,1,8,5,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,2,6,3,5,4,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,1,2,8,6,5,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,1,6,3,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,1,5,2,4,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,2,6,1,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,6,7,2,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,5,6,4,2,1,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,5,8,3,1,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,7,5,6,3,2,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,2,3,8,5,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,2,3,6,5,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,1,3,8,6,4,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,7,3,1,8,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,2,4,1,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,2,6,3,4,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,1,6,3,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,8,6,4,2,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,6,7,4,3,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,5,8,7,2,4,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,1,3,8,7,5,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,8,3,1,7,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,6,1,3,7,2,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,8,1,3,6,4,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,2,3,4,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1]=>0
[9,10,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[1,4,2,7,8,6,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,2,4,8,5,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,2,4,7,5,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,3,8,5,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,3,2,8,6,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,5,7,8,6,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,3,1,8,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,5,1,7,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,1,8,3,4,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,8,3,5,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,4,8,5,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,3,6,4,8,5,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,6,4,7,5,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,2,4,7,5,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,8,2,1,4,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,6,4,2,3,1,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,7,2,3,1,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,4,2,6,8,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,2,5,4,6,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,6,3,1,8,7,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,6,4,3,1,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,4,1,3,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,3,8,2,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,8,1,2,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,8,3,2,6,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,1,2,6,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,5,4,2,6,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,8,2,4,6,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,8,4,2,7,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,6,2,8,3,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,1,6,7,2,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,6,1,2,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,3,2,7,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,4,5,3,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,3,1,4,2,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,3,2,4,1,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,3,2,6,7,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,5,2,6,8,1,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,3,6,7,1,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,2,3,4,1,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,7,5,1,8,2,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,1,5,2,8,7,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,2,4,6,5,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,1,2,5,4,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,1,6,2,5,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,2,6,4,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,2,5,6,4,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,1,2,6,5,4,3,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,7,5,4,2,8,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,1,4,8,2,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,6,8,2,7,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,4,7,6,2,8,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,1,4,7,2,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,4,5,2,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,1,2,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,1,5,8,2,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,6,2,8,7,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,2,8,6,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,2,6,4,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,7,6,3,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,2,7,4,6,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,7,2,6,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,4,2,7,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,2,7,6,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,6,8,7,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,1,2,8,4,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,1,2,7,6,4,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,3,7,1,8,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,4,3,2,5,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,7,3,4,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,1,7,8,2,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,2,7,8,3,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,8,6,3,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,4,2,6,8,3,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,3,7,5,8,6,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,4,2,7,3,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,7,2,8,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,7,8,3,4,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,3,8,7,5,6,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,7,8,5,6,2,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,8,4,2,6,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,7,8,4,2,5,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,6,3,7,2,1,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,3,8,2,1,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,7,8,3,2,1,5,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,7,8,3,2,1,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,7,8,4,3,5,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,7,8,4,2,5,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,8,3,2,1,5,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,7,8,3,2,1,4,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,6,3,8,2,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,4,8,2,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,8,3,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,4,7,3,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,4,7,2,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,7,2,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,3,7,2,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,4,3,2,1,6,5,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[6,4,3,2,1,7,5,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[4,5,3,2,7,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,2,8,6,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,3,2,1,8,5,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,4,3,2,1,8,5,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,4,3,2,1,7,5,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,4,3,2,1,7,6,5]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,4,3,2,1,8,6,5]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[6,4,3,2,1,8,7,5]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[5,6,3,8,2,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,3,2,8,1,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,4,2,7,6,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,4,2,8,6,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,4,2,8,7,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,6,5,8,7,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,5,7,8,3,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,5,4,2,7,8,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,4,2,6,7,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,3,2,6,1,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,3,2,6,1,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,6,3,7,2,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,3,7,2,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,4,7,2,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,7,3,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,4,2,7,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,3,2,7,1,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,4,2,6,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,3,4,1,2,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,3,7,2,6,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,4,2,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,8,4,2,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,8,5,6,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,3,7,5,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,3,8,1,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,6,4,8,5,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,5,8,4,6,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,2,4,1,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,2,1,5,7,3,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,2,5,3,8,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,8,3,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,5,4,2,8,6,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,5,3,8,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,8,3,2,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,7,3,5,2,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,3,6,2,5,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,3,2,5,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,1,7,3,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,1,4,2,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,4,3,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,1,4,3,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,1,4,2,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,5,7,2,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,6,1,5,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,3,1,5,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,3,6,1,7,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,4,1,2,7,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,3,1,7,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,2,7,3,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,7,2,3,1,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,2,1,7,3,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,6,1,4,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,2,7,4,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,4,8,5,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,1,4,6,3,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,6,1,5,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,2,1,5,7,4,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,2,6,1,5,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,1,5,6,2,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,1,5,2,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,1,5,3,6,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,5,1,2,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,5,1,7,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,5,1,2,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,5,3,1,4,7,2,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,3,1,8,5,4,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,1,5,8,3,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,1,5,3,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,5,1,2,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,5,1,8,2,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,4,5,3,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,8,5,3,1,7,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,4,5,8,2,1,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,4,5,2,8,1,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,6,2,1,7,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,4,6,2,1,7,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,6,2,7,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,6,2,7,1,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,6,2,7,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,6,2,8,7,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,6,8,2,7,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,8,6,3,7,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,4,6,3,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,6,3,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,6,8,2,7,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,4,6,2,8,7,5,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,5,6,2,7,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,6,2,7,4,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,6,7,2,8,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,5,6,8,7,2,4,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,5,8,6,7,3,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,5,6,7,3,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,5,6,7,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,8,6,7,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,8,7,2,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,5,6,7,2,1,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,4,6,1,8,7,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,1,6,8,7,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,1,8,6,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,2,6,7,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,5,1,6,7,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,5,1,6,7,4,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,1,6,7,4,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,6,1,7,4,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,1,7,4,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,6,1,8,7,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,4,6,8,1,7,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,8,6,1,7,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,8,4,6,2,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,5,6,7,2,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,8,6,7,1,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,6,8,7,1,4,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,5,6,7,1,3,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,5,6,7,1,3,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,6,7,3,1,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,5,6,8,7,4,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,5,8,6,7,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,5,6,7,4,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,5,6,7,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,5,8,6,7,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,2,5,3,7,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,4,3,7,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,2,4,3,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,2,5,6,1,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,5,6,1,7,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,5,7,3,2,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,5,8,3,2,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,8,2,4,7,1,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,8,2,4,7,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,3,5,6,7,1,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,7,1,5,6,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,7,1,5,8,2,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,3,2,4,6,1,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,2,4,6,1,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,5,1,7,4,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,5,1,8,4,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,5,1,7,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,3,2,4,6,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,1,5,7,8,3,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,5,6,1,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,6,1,8,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,6,1,7,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,5,8,7,3,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,7,3,2,4,6,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,2,5,1,8,7,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,5,1,6,4,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,4,1,8,7,5,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,5,1,6,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,6,5,1,7,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,7,6,5,1,8,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,5,1,7,8,4,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,4,1,8,5,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,4,1,7,5,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,4,1,6,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,4,1,8,5,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,2,4,7,6,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,5,1,8,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,5,1,6,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,2,3,7,5,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,6,1,8,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,1,8,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,6,1,7,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,1,8,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,2,3,8,5,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,5,1,7,6,4,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,5,1,8,6,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,2,4,8,6,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,1,5,7,3,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,6,1,8,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,6,1,7,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,6,8,5,1,7,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,5,1,6,7,4,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,5,1,8,6,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,4,1,8,6,5,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,4,1,5,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,5,1,7,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,5,1,6,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,5,1,7,6,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,7,5,1,8,6,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,7,5,1,6,4,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,2,5,1,8,7,6,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,7,3,1,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,3,7,1,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,3,7,5,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,6,1,7,5,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,7,4,1,6,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,4,1,6,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,4,7,3,6,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,7,8,3,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,7,5,1,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,3,8,5,1,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,3,6,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,8,3,6,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,3,6,7,1,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,5,4,6,1,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,5,8,1,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,4,6,8,1,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,8,4,1,6,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,6,2,1,8,5,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,1,7,5,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,1,7,5,3,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,4,1,8,5,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,8,2,1,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,8,4,1,6,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,5,6,1,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,3,2,6,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,2,8,1,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,1,6,8,5,4,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,7,1,5,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,7,1,5,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,2,5,1,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,3,2,6,7,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,8,2,6,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,2,6,7,1,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,7,2,6,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,7,8,2,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,7,4,8,1,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,5,7,8,1,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,2,5,7,1,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,5,7,1,6,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,2,7,1,5,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,7,1,5,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,2,7,8,1,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,2,6,1,7,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,7,5,3,8,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,1,8,5,3,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,3,2,7,1,4,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,2,1,4,7,5,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,5,2,1,7,4,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,2,1,7,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,4,2,1,7,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,2,1,8,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,1,7,3,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,7,1,4,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,8,2,1,7,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,3,7,2,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,3,7,2,8,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,3,2,7,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,2,8,1,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,2,8,1,4,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,1,4,7,5,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1]=>0
[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[6,2,3,1,5,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,5,2,3,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,2,5,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,5,3,4,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,3,4,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,2,4,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,5,1,3,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,3,4,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,5,1,4,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,2,4,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,5,6,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,2,4,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,1,4,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,3,4,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,5,1,3,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,4,5,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,4,5,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,1,5,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,3,5,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,5,6,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,3,6,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,4,6,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,4,6,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,1,6,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,3,6,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,5,6,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,5,6,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,4,7,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,3,4,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,3,6,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,1,6,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,2,6,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,3,6,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,3,6,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,1,6,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,2,4,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,3,2,7,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,3,7,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,2,4,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,1,4,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,3,4,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,5,6,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,5,6,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,2,3,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,3,1,7,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,3,1,5,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,3,1,8,5,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,3,2,8,6,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,2,3,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,3,1,7,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,2,6,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,2,6,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,5,6,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,2,5,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,1,5,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,1,3,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,6,7,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,3,7,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,3,2,7,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,5,6,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,2,6,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,1,6,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,4,6,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,4,6,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,2,6,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,2,6,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,1,6,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,4,6,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,1,6,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,5,7,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,4,6,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,1,6,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,4,6,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,1,6,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,3,6,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,8,3,6,1,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,5,8,1,3,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,8,6,3,2,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,8,7,3,6,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,2,8,4,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,2,8,4,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,2,8,4,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,1,8,4,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,4,6,1,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,1,8,4,5,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,1,6,8,4,5,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,3,6,8,4,5,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,3,7,8,4,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,3,7,8,4,6,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,5,7,8,2,4,6,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,1,7,8,2,4,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,6,7,8,4,2,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,6,1,8,4,2,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,8,3,7,1,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,8,7,3,6,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,1,8,4,6,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,8,4,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,7,8,1,4,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,7,8,5,4,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,2,1,3,8,5,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,2,5,8,3,4,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,8,5,4,3,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,8,3,5,4,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,4,5,3,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,4,8,5,2,3,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,8,2,4,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,1,2,8,5,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,4,2,1,8,5,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,6,8,4,3,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,1,8,3,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,5,8,1,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,5,8,3,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,8,5,1,3,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,8,1,4,3,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,5,8,6,3,4,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,8,3,6,5,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,8,4,1,5,6,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,1,8,3,5,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,8,4,1,3,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,1,5,3,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,8,4,5,3,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,3,8,5,4,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,1,8,5,4,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,3,8,4,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,1,3,8,4,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,7,8,4,3,6,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,7,4,1,6,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,5,8,4,2,3,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,3,2,8,5,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,3,2,8,5,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,2,8,5,4,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,8,2,5,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,4,3,5,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,3,4,5,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,2,8,4,5,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,3,8,5,4,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,3,1,8,5,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,1,4,8,5,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,1,3,2,4,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,1,5,3,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,2,8,4,5,3,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,2,8,5,3,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,4,2,5,3,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,1,4,8,2,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,2,8,4,3,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,2,8,5,4,3,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,5,4,3,8,6,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,4,8,5,3,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,7,4,8,5,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,2,7,8,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,2,7,4,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,5,1,4,7,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,1,5,4,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,8,5,7,4,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,4,8,7,5,3,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,8,1,4,3,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,1,2,8,7,4,3,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,4,1,2,8,7,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,6,4,8,1,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,1,4,2,8,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,6,2,8,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,7,2,8,4,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,7,1,4,2,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,7,1,4,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,8,1,5,2,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,1,2,8,5,3,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,7,2,8,4,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,7,8,5,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,2,8,4,3,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,4,1,2,8,3,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,1,3,2,4,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,1,3,2,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,2,7,3,5,8,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,7,5,8,3,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,8,1,3,7,2,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,5,8,7,3,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,5,8,3,7,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,8,1,7,3,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,1,3,2,4,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,2,8,1,7,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,1,7,4,3,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,2,8,4,3,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,2,8,4,7,5,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,8,7,4,5,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,1,7,5,3,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,7,1,5,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,6,1,4,7,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,6,1,4,2,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,6,2,7,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,2,8,6,4,3,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,1,2,8,6,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,7,4,8,1,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,8,7,1,6,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,8,1,7,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,1,7,6,4,3,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,3,4,1,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,4,1,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,4,1,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,4,1,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,4,1,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,4,1,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,4,1,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,4,1,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,4,1,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,4,1,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,8,3,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,7,3,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,8,3,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,5,1,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,5,1,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,5,1,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,5,1,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,3,1,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,4,1,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,4,1,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,5,1,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,5,1,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,8,3,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,7,3,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,7,3,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,7,3,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,7,4,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,8,4,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,8,4,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,8,3,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,8,3,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,7,3,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,8,3,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,5,2,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,3,5,2,4,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,8,2,4,5,7,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,7,2,4,5,3,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,6,1,4,5,2,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,7,4,5,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,8,4,5,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,8,7,4,3,6,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,7,4,3,6,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,7,4,3,6,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,3,5,1,4,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,6,8,5,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,3,5,1,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,8,4,7,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,8,4,7,6,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,8,7,4,1,6,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,3,6,1,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,3,6,1,2,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,7,4,1,6,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,1,4,2,6,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,7,4,5,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,8,7,4,5,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,2,4,1,6,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,8,3,6,2,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,3,6,2,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,7,4,2,6,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,8,4,5,7,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,1,8,4,5,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,3,5,1,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,5,8,3,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,8,3,6,1,2,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,8,1,5,6,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,4,8,2,5,6,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,8,1,4,7,6,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,3,1,6,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,3,8,6,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,1,8,5,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,7,6,2,3,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,7,2,6,4,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,7,3,6,4,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,7,3,6,8,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,4,3,7,6,1,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,7,2,3,5,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,7,3,6,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,7,6,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,4,7,1,6,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,4,7,6,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,3,7,6,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,7,3,6,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,7,1,3,5,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,8,7,3,6,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,3,7,6,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,4,7,6,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,4,7,1,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,1,4,7,2,6,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,3,2,7,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,3,1,7,6,5,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,8,2,1,7,6,5,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,7,1,2,8,5,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,2,3,1,7,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,3,2,1,7,6,5,4]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[3,4,1,7,6,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,2,7,8,6,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,4,2,7,1,6,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,2,1,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,7,2,8,6,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,5,7,1,8,6,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,5,7,1,6,8,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,7,4,5,8,1,3,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,4,7,6,8,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,7,8,1,6,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,5,7,8,2,6,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,5,7,1,2,6,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,4,1,7,2,6,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,4,8,7,2,6,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,8,7,6,1,5,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,3,8,7,6,1,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,7,8,6,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,7,2,8,1,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,7,8,1,6,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,8,7,1,6,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,8,1,7,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,3,8,2,7,6,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,8,3,7,6,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,1,8,3,7,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,8,7,2,6,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,7,8,2,6,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,7,1,8,2,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,7,1,2,6,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,1,7,2,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,1,2,7,6,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,8,1,3,7,6,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,8,2,3,7,6,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,1,2,3,7,6,5,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,7,1,8,4,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,5,8,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,1,5,8,3,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,5,1,8,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,5,1,8,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,5,1,8,7,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,4,1,8,7,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,4,5,7,6,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,4,5,1,8,7,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,6,1,8,7,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,6,1,8,7,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,1,8,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,6,1,8,3,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,6,1,3,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,6,1,2,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,3,6,1,2,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,6,1,8,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,1,5,8,2,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,3,5,7,2,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,2,5,7,3,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,1,5,8,3,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,2,5,1,8,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,1,3,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,6,1,4,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,2,5,3,1,8,7,6]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,4,1,3,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,2,1,4,3,8,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,2,4,3,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,3,4,2,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,1,4,2,8,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,4,1,2,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,6,3,1,2,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,6,4,1,2,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,4,1,3,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,1,4,3,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,1,4,2,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,1,3,2,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,1,6,7,2,3,5,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,7,1,2,3,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,7,1,2,4,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,7,1,3,4,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,6,3,1,4,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,6,2,1,4,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,2,1,8,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,5,2,1,8,3,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,1,5,2,7,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,2,3,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,2,3,1,8,7,6]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,5,2,4,1,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,1,3,2,4,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,3,1,4,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,4,3,6,1,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,6,5,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,6,3,5,8,7,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,6,3,5,8,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,6,3,5,1,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,6,3,1,5,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,1,6,5,3,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,6,1,5,3,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,6,5,3,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,6,5,1,3,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,6,5,1,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,6,5,8,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,5,8,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,5,8,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,4,6,1,5,8,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,1,6,5,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,4,6,5,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,1,6,5,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,6,1,5,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,2,6,5,3,8,7,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,6,5,8,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,4,3,8,7,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,4,3,8,7,5,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,2,6,8,5,3,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,6,8,1,5,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,6,1,8,5,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,1,6,8,5,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,4,6,8,5,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,4,6,8,5,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,4,1,6,8,5,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,6,1,8,5,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,8,1,5,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,2,6,8,5,3,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,6,8,5,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,6,8,5,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,6,8,3,5,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,6,8,3,5,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,6,8,3,1,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,4,6,3,1,8,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,6,3,8,1,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,6,3,8,5,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,3,8,5,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,3,6,8,5,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,3,6,8,5,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,3,6,8,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,3,6,1,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,1,6,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,1,3,6,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,4,3,6,1,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,3,6,8,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,5,2,8,7,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,6,5,2,8,7,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,2,5,8,7,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,2,5,8,7,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,4,6,3,8,1,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,6,3,1,8,7,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,1,6,3,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,4,6,3,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,4,6,8,3,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,1,6,8,3,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,6,1,8,3,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,6,8,1,3,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,6,8,3,1,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,6,2,8,5,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,2,8,5,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,4,8,7,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,4,2,8,7,5,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,6,4,8,1,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,4,1,8,7,5,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,6,1,4,8,7,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,1,6,4,8,7,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,6,4,8,7,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,1,4,8,7,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,4,1,8,7,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,4,8,1,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,2,8,7,5,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,2,4,8,7,3,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,4,8,7,3,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,6,4,7,3,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,7,4,5,8,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,2,4,7,3,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,7,6,3,4,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,6,3,7,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,3,8,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,2,7,4,8,3,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,1,7,3,4,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,1,7,4,5,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,4,7,3,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,1,7,5,8,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,8,6,3,7,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,1,3,7,2,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,2,1,7,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,2,1,8,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,1,3,8,2,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,1,2,4,8,3,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,3,6,1,5,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,1,4,5,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,6,2,4,8,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,5,1,3,7,2,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,5,3,2,8,4,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,4,2,1,5,8,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,5,3,4,1,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,5,2,1,8,6,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,4,8,7,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,4,8,7,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,8,3,6,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,2,4,8,7,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,8,3,7,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,8,7,2,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,8,2,5,1,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,2,5,1,3,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,2,1,5,4,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,2,1,5,4,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,2,5,1,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,2,1,5,6,4,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,3,2,1,4,6,5,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,2,8,1,4,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,2,1,4,7,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,2,1,5,7,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,2,5,1,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,5,1,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,1,5,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,2,1,4,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,1,7,5,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,1,6,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,7,6,1,8,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,6,8,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,8,6,7,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,8,6,1,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,8,1,6,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,1,8,7,5,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,2,1,7,4,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,8,1,7,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,1,6,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,7,1,6,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,7,6,1,3,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,8,6,1,3,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,8,7,1,3,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,8,3,4,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,2,7,8,1,3,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,6,8,1,3,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,6,7,1,3,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,6,1,8,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,2,1,8,4,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,2,1,8,5,4,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,3,8,5,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,3,7,8,6,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,2,7,1,8,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,1,6,8,5,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,6,1,8,7,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,8,1,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,6,8,7,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,6,7,1,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,6,1,7,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,6,8,7,5,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,3,6,4,8,7,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,6,2,7,8,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,7,5,4,8,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,3,7,5,4,8,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,8,5,4,6,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,7,5,4,6,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,6,7,8,5,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,5,6,3,8,7,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,8,5,4,7,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,3,5,4,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,3,5,4,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,6,2,5,4,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,1,2,5,8,3,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,8,2,5,7,3,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,2,1,5,4,8,7,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,6,2,8,7,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,1,2,4,6,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,8,3,1,4,2,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,6,1,8,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,8,5,4,1,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,8,1,5,2,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,1,6,4,3,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,8,1,6,4,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,5,7,4,3,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,4,6,1,5,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,8,4,1,5,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,5,1,6,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,1,5,7,3,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,1,7,4,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,1,7,4,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,7,6,4,3,2,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,1,7,8,4,3,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,8,6,4,3,2,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,8,7,6,4,3,2,5]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,1,7,5,6,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,7,5,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,8,1,6,5,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,1,5,4,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,1,5,4,6,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,2,8,5,6,3,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,2,5,7,3,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,2,1,5,6,3,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,6,1,5,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,6,3,7,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,3,6,8,5,7,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,6,3,7,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,6,4,8,7,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,1,6,7,3,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,6,1,3,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,1,7,5,2,3,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,3,5,4,1,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,8,3,5,4,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,6,3,8,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,2,3,4,1,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,1,4,6,3,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,1,6,4,7,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,5,7,4,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,5,8,4,3,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,8,7,4,3,2,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,5,1,8,4,3,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,7,1,4,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,8,1,4,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,7,1,4,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,7,8,4,3,2,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,7,5,1,3,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,8,4,6,1,3,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,5,4,1,3,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,6,4,1,8,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,4,5,1,3,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,5,8,4,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,5,1,4,3,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,5,1,4,3,2,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,4,6,2,7,1,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,2,5,4,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,3,6,2,8,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,2,5,4,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,8,5,1,3,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,6,8,1,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,6,4,1,7,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,1,5,8,3,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,6,7,4,8,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,6,3,7,5,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,2,5,8,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,6,1,7,5,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,7,5,4,1,6,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,4,6,2,8,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,7,5,4,3,8,6,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,4,6,3,5,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,8,4,3,6,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,4,6,2,7,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,4,1,6,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,3,2,7,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,2,7,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,6,3,2,7,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,2,8,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,1,7,8,5,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,4,1,6,3,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,3,2,1,8,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,2,1,6,4,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,8,2,1,6,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,5,8,2,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,3,2,8,5,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,6,3,2,1,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,6,4,3,2,1,8,5]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,8,4,3,2,1,6,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,4,7,2,1,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,8,3,2,6,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,2,1,6,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,3,2,1,6,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,7,2,5,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,8,3,5,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,2,5,7,8,4,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,5,7,8,6,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,6,7,2,8,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,3,7,2,8,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,6,1,7,4,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,2,1,4,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,3,5,2,1,8,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,8,4,1,3,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,1,7,8,3,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,2,8,6,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,8,2,1,7,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,3,8,2,1,4,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,3,5,2,1,4,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,3,5,4,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,3,7,5,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,1,6,3,2,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,1,6,2,3,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,7,1,6,2,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,6,2,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,6,5,1,8,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,5,1,8,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,3,6,5,1,4,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,6,4,1,5,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,6,1,5,4,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,7,6,1,4,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,6,1,4,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,3,5,1,8,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,5,1,8,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,6,1,5,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,6,4,1,8,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,1,7,6,3,8,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,7,6,3,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,6,2,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,6,4,1,8,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,5,1,8,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,1,8,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,3,4,8,7,6,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,3,4,8,5,7,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,3,5,4,8,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,4,5,8,7,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,4,3,5,8,7,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,5,4,8,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,4,8,7,5,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,4,8,7,5,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,7,6,5,4,8,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,5,6,8,4,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,3,5,6,8,1,4,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,3,5,6,8,1,2,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,4,1,5,8,7,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,1,5,8,3,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,7,1,6,3,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,1,5,8,3,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,1,5,8,2,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,1,5,8,2,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,5,7,8,2,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,3,5,7,8,2,4,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,7,6,4,5,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,3,6,1,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,4,5,8,6,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,3,5,4,8,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,3,4,8,5,6,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,4,8,7,1,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,4,8,1,7,6,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,4,8,1,6,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,4,8,5,1,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,3,5,4,8,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,3,5,8,2,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,1,4,5,8,3,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,4,3,5,8,2,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,5,4,8,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,3,4,8,5,1,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,3,4,8,1,6,5,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,4,8,1,5,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[7,8,2,6,1,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,6,2,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,6,7,2,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,7,2,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,7,2,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,7,1,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,7,1,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,5,7,1,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,7,5,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,7,5,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,7,4,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,7,4,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,4,7,1,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,7,1,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,1,7,2,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,7,2,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,1,7,5,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,7,5,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,7,5,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,1,7,5,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,1,7,4,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,7,4,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,7,2,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,1,7,2,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,2,7,1,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,2,7,4,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,2,7,5,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,7,5,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,7,5,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,7,5,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,4,7,5,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,7,5,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,7,4,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,7,1,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,7,3,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,2,8,6,4,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,8,6,1,5,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,8,4,5,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,8,1,7,4,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,7,4,2,8,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,6,7,3,8,5,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,1,8,3,5,6,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,8,6,2,5,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,8,4,1,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,8,3,5,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,8,3,4,6,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,7,8,2,6,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,2,3,8,5,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,4,8,5,3,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,1,4,8,5,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,6,3,7,8,5,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,6,3,7,8,4,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,7,3,5,6,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,4,7,3,6,8,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,3,7,8,1,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,5,4,7,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,1,4,8,2,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,2,4,8,6,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,2,3,8,4,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,2,3,6,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,2,3,5,7,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,7,8,3,6,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,8,1,3,6,7,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,3,8,2,4,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,3,8,1,2,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,4,2,8,1,3,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,8,2,5,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,8,1,4,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,1,3,6,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,7,4,2,6,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,8,1,4,2,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,1,2,7,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,5,1,2,8,7,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,3,1,4,2,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,2,6,4,1,7,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,1,7,5,2,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,1,7,2,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,6,1,2,8,7,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,7,1,8,6,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,2,7,5,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,5,7,1,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,4,7,2,8,6,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,5,8,2,7,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,4,6,2,8,1,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,2,6,8,1,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,5,6,1,3,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,3,6,8,4,7,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,7,2,5,4,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,4,2,5,7,3,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,7,2,5,8,3,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,6,8,4,3,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,6,5,4,8,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,6,5,8,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,6,8,4,3,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,5,4,7,6,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,7,1,8,4,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,1,5,4,3,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,1,5,4,3,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,1,5,7,3,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,6,7,1,3,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,6,1,7,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,6,1,4,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,6,1,4,3,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,8,5,1,3,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,6,8,2,3,4,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,2,8,4,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,8,2,4,3,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,6,2,8,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,6,2,4,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,7,6,2,4,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,3,8,4,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,3,5,8,6,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,7,2,1,4,3,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,3,1,4,6,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,6,3,2,5,4,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,7,3,5,1,6,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,2,5,1,3,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,6,5,1,3,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,6,5,7,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,6,8,4,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,6,5,8,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,6,5,1,8,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,4,8,7,5,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,4,3,8,7,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,2,4,7,8,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,6,2,4,8,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,4,7,2,8,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,7,2,5,8,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,3,8,4,5,6,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,6,4,8,7,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,8,5,3,7,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,5,3,4,7,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,5,4,2,8,7,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,5,2,7,3,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,2,7,5,1,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,1,4,2,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,6,4,8,2,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,5,1,3,4,2,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,8,5,3,1,7,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,5,3,2,8,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,3,6,1,4,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,8,6,4,1,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,6,2,5,8,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,2,5,8,1,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,8,7,4,2,3,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,1,7,8,2,4,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,8,6,3,4,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,8,3,6,5,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,3,2,7,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,3,8,5,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,1,7,5,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,5,8,1,4,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,8,6,7,3,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,4,3,7,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,3,4,8,7,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,3,4,5,2,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,8,3,5,4,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,6,3,8,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,2,4,6,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,2,6,4,7,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,5,7,4,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,5,8,3,4,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,8,7,1,2,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,5,3,8,2,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,7,4,1,3,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,7,8,4,1,2,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,4,7,5,3,8,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,6,7,3,1,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,8,4,6,3,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,5,3,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,5,8,4,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,8,4,2,3,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,4,2,8,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,6,5,3,2,7,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,7,5,8,2,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,5,8,2,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,8,5,7,6,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,3,8,5,7,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,1,5,6,2,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,5,2,1,4,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,2,5,6,1,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,1,5,6,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,2,5,6,3,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,8,2,5,7,6,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,8,6,2,7,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,8,6,1,7,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,6,1,5,7,2,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,8,6,5,7,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,6,5,8,1,2,4,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,7,6,8,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,3,7,8,6,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,5,8,1,6,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,8,5,7,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,1,5,7,6,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,8,6,1,7,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,8,6,5,7,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,2,5,6,3,7,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,6,5,4,1,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,1,3,5,4,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,5,6,2,4,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,2,6,3,7,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,6,5,7,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,5,8,6,2,7,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,8,1,6,3,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,6,3,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,6,5,4,2,8,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,7,6,1,4,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,4,2,6,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,6,4,1,2,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,7,6,1,5,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,6,4,5,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,3,6,5,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,1,6,5,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,3,5,7,6,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,8,5,4,1,6,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,1,5,4,3,7,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,6,4,2,1,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,2,6,5,7,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,6,2,5,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,6,4,5,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,3,6,5,7,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,7,3,6,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,7,8,5,6,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,4,7,2,5,1,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,7,2,5,8,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,2,4,7,1,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,3,4,5,7,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,3,6,7,5,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,7,5,8,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,6,4,5,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,7,6,5,8,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,2,6,1,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,8,6,4,1,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,3,6,2,5,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,3,2,5,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,1,2,5,6,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,6,2,5,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,2,5,8,7,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,8,6,4,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,3,6,8,4,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,3,6,7,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,1,5,8,3,6,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,8,7,2,3,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,5,7,4,2,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,6,4,7,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,4,7,5,1,8,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,5,7,1,4,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,8,1,3,2,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,8,5,1,3,4,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,3,4,5,1,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,8,3,1,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,7,4,8,2,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,3,7,4,1,6,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,4,7,3,6,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,5,6,8,1,4,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,4,7,1,6,5,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,8,5,4,3,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[6,3,1,2,8,4,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,2,1,3,6,5,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,1,4,5,6,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,2,1,5,4,6,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,6,1,8,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,8,2,1,4,5,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,4,1,5,3,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,6,1,5,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,5,1,6,4,3,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,1,6,3,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,1,8,2,7,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,8,1,7,5,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,1,8,5,3,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,6,1,7,4,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,5,7,4,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,6,1,7,4,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,7,5,6,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,6,4,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,7,8,5,3,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,8,6,5,4,2,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,6,5,7,3,4,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,4,7,5,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,5,3,6,2,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,3,7,4,6,8,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,7,5,6,3,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,6,5,4,8,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,6,5,7,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,2,7,6,8,3,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,1,7,5,3,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,5,6,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,1,7,6,8,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,5,6,2,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,6,4,2,7,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,8,5,2,4,6,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,6,3,7,4,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,1,6,2,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,1,4,7,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,4,1,7,2,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,7,1,8,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,4,1,8,5,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,1,4,8,3,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,1,8,4,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,2,8,4,3,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,5,1,4,3,8,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,6,2,5,8,3,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,5,1,3,7,2,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,2,1,7,3,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,2,1,8,5,3,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,5,4,2,8,3,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,4,3,1,5,8,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,7,6,8,4,5,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,6,8,5,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,6,8,5,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,8,6,7,5,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,8,6,7,3,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,3,8,5,4,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,8,5,6,7,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,3,5,8,4,7,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,3,8,6,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,4,2,8,7,3,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,2,5,8,7,3,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,8,5,7,4,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,3,8,7,5,6,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,1,8,7,4,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,8,5,7,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,5,8,7,4,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,4,1,8,7,6,2,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,8,6,7,4,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,8,7,5,6,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,2,1,6,3,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,1,4,3,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,1,4,3,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,1,4,3,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,4,1,3,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,4,1,3,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,1,6,4,3,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,6,1,4,3,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,4,2,1,3,6,5,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,6,2,1,8,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,1,4,3,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,6,4,3,8,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,8,4,3,6,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,1,4,3,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,4,1,3,6,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,2,1,3,6,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,2,1,6,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,2,1,4,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,1,4,6,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,8,4,6,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,4,8,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,1,4,8,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,6,4,1,8,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,2,6,1,3,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,6,1,8,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,1,8,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,4,1,6,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,1,4,6,3,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,1,4,8,3,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,2,1,6,8,3,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,2,1,6,3,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,4,3,8,6,5,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,4,1,3,8,6,5,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,2,1,3,8,6,5,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,8,3,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,6,1,4,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,8,1,4,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,8,1,6,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,8,1,3,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,8,1,3,6,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,1,8,3,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,4,8,3,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,4,8,6,3,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,4,8,1,6,3,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,8,1,4,3,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,1,8,4,3,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,1,6,8,4,3,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,8,1,6,4,3,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,2,6,1,5,4,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,4,3,8,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,4,1,5,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,1,5,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,5,2,8,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,2,6,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,8,2,6,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,8,1,7,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,8,1,5,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,3,4,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,1,3,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,5,4,8,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,6,8,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,6,8,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,1,8,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,5,8,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,5,4,7,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,5,4,8,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,3,8,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,6,5,8,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,8,4,6,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,6,1,3,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,6,3,4,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,6,3,7,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,1,7,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,2,6,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,5,2,6,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,3,5,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,1,5,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,4,1,5,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,4,1,7,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,4,3,6,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,4,6,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,1,5,4,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,7,6,8,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,7,1,8,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,5,8,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,2,4,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,2,4,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,4,1,8,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,8,2,4,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,8,1,5,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,7,3,8,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,3,2,8,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,5,6,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,2,6,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,8,1,5,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,4,5,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,7,2,6,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,2,6,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,1,7,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,5,8,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,4,8,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,1,8,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,7,4,8,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,7,1,8,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,3,8,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,3,1,5,4,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,3,4,7,1,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,8,3,5,7,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,2,5,3,1,8,6,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,1,3,8,2,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,1,4,8,3,2,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,5,8,4,3,2,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,7,4,3,8,5,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,7,3,8,4,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,4,7,8,3,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,8,1,5,7,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,5,3,7,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,4,7,6,5,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,6,8,5,3,7,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,8,1,7,4,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,8,1,7,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,8,7,1,5,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,4,1,3,8,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,7,5,6,3,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,1,7,8,5,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,7,4,6,3,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,8,4,3,7,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,2,4,8,3,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,6,3,4,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,7,3,1,4,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,7,1,8,3,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,7,3,5,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,7,1,3,6,2,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,2,1,7,3,5,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,8,2,6,3,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,2,6,3,5,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,2,8,7,4,5,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,3,7,1,5,6,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,1,2,7,5,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,6,2,7,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,5,2,6,7,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,2,1,8,6,7,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,8,5,7,6,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,7,8,5,2,6,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,8,1,6,4,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,6,1,5,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,8,6,1,5,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,6,1,5,3,4,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,1,6,4,5,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,5,6,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,6,7,5,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,3,5,2,1,4,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,5,7,2,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,5,2,7,4,3,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,5,3,6,1,2,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,1,4,6,2,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,4,5,7,2,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,7,4,6,3,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,4,6,3,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,4,7,3,6,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,4,7,5,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,5,1,4,7,3,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,3,7,1,4,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,8,5,7,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,3,7,1,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,4,7,5,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,6,8,3,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,7,1,3,5,8,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,8,3,7,1,2,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,6,4,1,7,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,1,2,5,7,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,6,7,4,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,6,8,4,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,3,7,8,2,4,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,6,2,1,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,7,6,2,1,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,6,2,8,7,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,7,5,4,8,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,7,4,5,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,3,5,1,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,1,6,7,5,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,5,7,3,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,3,6,1,2,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,7,1,6,5,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,2,1,8,7,5,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,4,6,2,7,8,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,6,1,2,5,8,7,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,6,1,4,8,2,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,3,1,8,7,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,6,4,7,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,6,1,5,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,4,1,5,7,6,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,2,7,1,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,2,7,6,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,2,7,6,5,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,2,7,6,5,4,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,8,7,2,6,5,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,7,2,6,5,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,7,2,6,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,7,2,1,6,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,7,3,1,6,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,7,3,2,1,6,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,8,7,3,2,6,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,7,3,2,6,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,7,3,6,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,7,3,6,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,7,3,6,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,7,3,6,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,7,3,6,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,8,7,6,3,4,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,7,6,3,1,4,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,7,6,3,2,4,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,7,6,2,4,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,7,6,2,1,4,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,7,6,4,2,3,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,7,6,4,2,1,3]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,8,7,6,4,1,3,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,7,6,4,3,1,2]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,3,4,2,1,6,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,2,6,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,5,2,6,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,2,7,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,1,5,6,4,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,5,1,6,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,5,6,1,3,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,5,7,3,2,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,4,6,7,3,8,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,4,5,7,3,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,4,5,7,1,3,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,3,5,1,7,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,1,5,7,4,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,1,5,7,4,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,4,6,7,3,8,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,4,6,7,3,8,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,3,6,1,7,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,6,7,1,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,4,5,7,2,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,4,6,7,2,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,6,2,7,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,6,2,7,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,5,2,7,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,4,2,1,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,6,2,7,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,6,2,7,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,3,6,2,7,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,6,7,2,8,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,4,6,7,2,8,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,4,5,7,2,1,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,2,1,5,7,3,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,6,1,7,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,6,7,1,8,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,3,6,1,7,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,6,1,7,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,6,7,1,8,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,4,3,7,6,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,7,5,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,7,2,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,7,4,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,6,5,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,8,2,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,8,3,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,3,6,5,8,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,8,2,4,5,7,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,7,8,4,5,2,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,8,1,4,5,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,7,4,1,6,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,3,6,1,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,3,1,6,4,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,1,4,7,6,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,5,1,8,6,2,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,1,8,2,6,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,8,4,2,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,3,8,5,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,3,8,5,2,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,8,3,6,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,1,8,4,2,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,2,8,4,1,6,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,8,3,6,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,8,3,6,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,2,3,6,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,2,8,3,5,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,2,3,8,4,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,2,3,8,4,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,3,8,1,4,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,8,1,3,5,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,4,1,8,7,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,1,4,2,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,1,6,4,2,8,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,3,8,7,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,8,5,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,1,8,3,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,1,3,8,4,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,5,3,8,4,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,4,8,3,7,6,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,8,1,3,7,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,8,3,7,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,8,3,7,6,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,3,8,1,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,4,1,3,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,1,5,4,8,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,1,4,8,2,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,3,8,4,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,2,3,7,6,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,8,2,3,7,1,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,1,2,3,7,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,4,8,2,3,7,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,8,3,7,2,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,8,1,5,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,3,8,2,4,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,3,8,2,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,4,8,2,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,4,8,2,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,8,1,2,7,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,1,6,4,2,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,1,6,2,8,7,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,5,8,2,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,2,5,8,7,6,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,4,2,5,8,7,6,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,3,5,2,8,7,4,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,1,2,8,7,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,8,7,5,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,2,6,1,8,7,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,1,5,8,2,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,5,2,8,7,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,8,7,2,6,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,8,7,1,2,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,4,8,1,7,2,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,4,8,7,2,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,4,8,2,7,6,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,4,8,1,2,7,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,8,2,7,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,8,2,7,6,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,5,8,1,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,4,2,5,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,5,1,8,7,6,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,8,2,1,5,3,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,1,2,7,3,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,3,7,5,4,1,8,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,8,1,5,4,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,3,5,4,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,2,5,4,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,2,5,4,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,1,5,4,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,6,2,4,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,2,1,7,3,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,3,7,5,8,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,1,8,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,7,4,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,6,7,4,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,7,6,5,3,8,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,7,6,5,3,8,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,5,2,4,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,7,1,4,8,3,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,7,6,4,8,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,6,3,8,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,6,2,4,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,6,5,2,8,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,5,1,8,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,7,6,5,2,8,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,5,3,2,8,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,7,6,5,1,2,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,7,6,5,3,1,8,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,1,3,5,4,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,6,3,4,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,2,6,3,4,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,7,2,4,8,3,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,4,2,8,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,8,2,6,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,2,1,5,3,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,1,6,2,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,2,6,8,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,6,7,4,8,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,1,6,7,4,2,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,8,5,4,6,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,6,3,5,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,1,2,5,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,6,5,2,4,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,5,1,4,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,6,5,2,1,8,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,7,6,5,8,2,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,6,5,8,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,1,6,8,4,2,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,7,6,8,3,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,6,5,1,4,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,5,8,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,6,5,8,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,2,1,7,4,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,2,1,7,3,5,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,1,5,4,2,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,1,5,2,7,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,5,1,3,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,7,2,1,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,7,4,2,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,2,5,3,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,5,4,1,3,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,4,3,2,1,8,6]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[8,5,3,2,1,7,6,4]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[6,5,2,1,8,4,3,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,6,3,2,8,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,3,2,8,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,2,4,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,3,6,4,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,7,5,3,8,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,8,5,3,6,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,1,6,2,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,6,2,3,7,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,6,3,2,7,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,3,2,7,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,3,1,6,5,4,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,2,6,1,5,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,8,5,7,4,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,5,7,2,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,6,1,7,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,8,5,6,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,7,5,8,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,2,6,8,4,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,5,8,1,4,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,8,4,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,5,4,8,3,2,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,3,7,2,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,4,7,1,3,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,5,8,1,4,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,6,8,2,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,3,5,1,8,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,1,5,7,3,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,2,5,8,3,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,6,8,2,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,2,1,7,8,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,3,7,4,8,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,2,5,8,6,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,3,1,8,4,7,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,2,8,7,3,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,5,3,8,7,4,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,8,1,7,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,1,7,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,8,2,1,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,8,1,4,7,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,7,3,8,1,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,4,7,8,1,5,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,8,7,1,3,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,3,8,7,2,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,7,6,1,5,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,7,6,5,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,8,7,6,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,4,8,7,6,1,3,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,8,7,2,6,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,3,8,6,5,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,8,6,4,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,8,7,3,6,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,7,6,2,5,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,8,7,6,5,1,4,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,8,7,6,5,4,1,3]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[3,7,5,8,2,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,5,7,2,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,1,7,8,4,3,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,2,6,4,3,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,2,5,4,3,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,2,4,6,3,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,2,6,5,3,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,5,7,8,3,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,5,8,7,3,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,7,1,8,3,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,7,8,5,2,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,7,4,8,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,3,8,1,4,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,5,8,7,3,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,8,4,7,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,1,6,3,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,2,3,7,5,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,2,3,8,6,5,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,8,1,4,3,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,7,3,2,4,1,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,1,7,3,4,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,3,2,4,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,1,4,3,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,2,3,8,5,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,2,3,7,5,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,2,3,6,5,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,8,5,4,3,2,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,8,2,6,3,4,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,2,7,3,4,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,8,3,4,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,7,1,4,2,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,8,1,4,2,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,8,1,4,2,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,8,2,4,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,6,7,1,4,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,1,7,5,4,3,2,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,1,7,4,5,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,3,7,1,4,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,2,4,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,2,4,3,6,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,2,3,8,7,4,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,3,8,7,6,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,1,2,3,8,6,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,6,2,4,3,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,3,2,4,8,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,1,6,3,4,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,6,3,2,4,7,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,2,4,3,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,8,1,2,6,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,8,2,7,3,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,8,5,4,7,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,8,5,4,2,7,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,3,6,8,4,7,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,6,8,4,7,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,8,1,7,3,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,8,5,7,6,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,6,8,4,5,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[7,5,1,2,4,3,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,6,1,5,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,2,6,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,1,4,7,2,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,4,2,8,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,3,8,5,4,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,1,7,3,5,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,1,3,6,5,4,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,3,1,6,5,4,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,2,1,4,6,3,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,2,3,6,5,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,2,3,6,5,4,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,8,1,2,7,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,2,3,8,5,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,8,2,7,6,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,8,2,7,6,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,2,7,6,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,8,1,7,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,8,2,1,7,4,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,4,1,2,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,1,6,3,8,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,1,8,7,6,3,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,3,8,7,4,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,2,5,3,8,7,4,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,3,8,7,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,8,4,1,7,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,8,7,1,4,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,3,8,4,1,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,8,7,6,3,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,8,7,6,5,3,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,1,8,7,6,5,3,2]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,3,8,7,6,5,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,3,1,8,7,2,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,3,7,6,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,3,8,7,6,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,5,3,8,7,6,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,8,4,7,2,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,1,8,4,7,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,7,4,6,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,2,4,3,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,1,2,4,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,8,1,7,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,8,1,7,2,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,2,5,8,7,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,1,8,7,4,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,1,8,7,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,3,6,1,2,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,8,3,1,7,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,2,8,7,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,2,5,8,7,1,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,4,8,7,6,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,3,4,8,7,6,2,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,4,8,7,6,2,5,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,2,5,8,7,4,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,8,3,1,7,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,1,3,5,8,7,4,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,2,7,5,8,6,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,1,4,8,2,6,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,1,3,7,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,8,1,2,6,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,7,8,2,6,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,7,8,1,6,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,7,8,1,3,6,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,1,2,6,7,3,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,2,6,7,5,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,2,5,7,1,3,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,8,1,6,7,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,8,3,7,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,6,4,7,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,3,4,1,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,3,7,4,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,8,3,7,5,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,8,1,6,7,5,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,5,7,1,6,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,7,2,3,6,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,7,4,2,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,5,7,4,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,2,4,7,1,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,3,5,7,1,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,4,7,3,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,7,1,4,6,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,7,1,4,6,2,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,7,1,3,6,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,8,3,7,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,5,7,1,2,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,8,7,1,3,6,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,5,4,7,1,6,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,4,7,1,2,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,1,4,7,2,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,4,6,8,2,7,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,6,5,8,2,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,5,6,3,1,7,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,2,8,1,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,4,5,7,2,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,7,3,6,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,3,5,7,1,6,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,8,3,7,5,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,3,8,2,7,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,4,2,7,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,4,7,3,1,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,5,7,3,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,2,5,7,1,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,3,4,7,2,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,7,2,4,6,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,4,5,7,1,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,7,3,4,5,1,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,7,4,5,2,6,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,8,7,2,3,6,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,7,2,3,6,1,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,3,2,8,5,4,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,8,5,3,7,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,1,8,4,3,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,2,8,4,3,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,8,4,3,1,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,4,8,2,1,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,4,8,2,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,4,1,8,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,5,2,3,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,5,4,3,2,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,4,2,8,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,3,2,8,7,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,3,2,8,7,5,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[5,6,3,2,7,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,1,6,3,2,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,4,2,7,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,6,4,3,7,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,7,4,3,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,4,1,3,6,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,4,2,6,1,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,1,7,3,2,6,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,2,6,4,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,3,2,5,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,3,2,1,5,4,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[4,7,5,6,2,3,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,7,5,6,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,5,7,1,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,5,7,2,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,7,2,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,5,4,1,7,2,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,4,6,2,1,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,5,7,1,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,6,1,7,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,6,7,2,3,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,1,4,6,8,7,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,4,6,8,7,1,2,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,3,1,6,8,7,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,6,8,7,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,5,1,8,7,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,5,8,6,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,8,5,6,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,8,5,1,7,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,1,8,6,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,3,2,8,6,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,8,6,7,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,1,3,2,6,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,3,8,7,1,6,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,2,8,7,6,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,2,8,7,6,4,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,2,1,8,6,5,4,3]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,3,6,1,8,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,7,8,6,4,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,4,7,8,6,1,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,1,5,7,6,2,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,7,6,8,1,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,7,6,8,3,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,4,1,7,6,8,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,5,8,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,6,5,1,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,6,4,3,1,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,1,7,4,3,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,7,5,3,8,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,7,5,1,4,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,1,6,7,5,4,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,7,6,1,5,4,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,5,1,4,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,4,1,5,2,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,5,1,3,2,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,1,6,4,2,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,1,3,6,4,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,1,5,3,4,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,1,5,2,4,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,1,2,7,4,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,1,2,5,4,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,1,4,2,3,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,4,2,7,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,8,2,6,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,8,1,2,4,6,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,7,8,1,3,4,6,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,8,1,7,3,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,5,7,2,4,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,4,1,2,7,6,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,4,2,3,8,7,5,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,2,7,6,3,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,2,8,7,5,3,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,1,2,4,8,7,5,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,1,8,4,6,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,7,6,4,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,2,6,8,5,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,1,2,7,8,5,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,1,2,7,4,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,6,4,7,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,1,3,8,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,1,8,4,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,5,3,2,8,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,4,5,2,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,3,1,5,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,7,3,1,5,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,1,7,4,5,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,5,3,2,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,7,1,2,6,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,2,8,4,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,2,8,6,4,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,7,2,6,4,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,2,3,8,6,5,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,2,3,8,5,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,7,2,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,1,3,4,7,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,1,8,6,4,7,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,2,6,7,4,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,1,2,8,7,3,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,2,8,3,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,2,8,6,4,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,7,8,4,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,8,7,6,4,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,2,7,4,6,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,2,7,3,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,5,6,3,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,5,3,6,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,6,3,1,4,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,8,3,1,4,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,8,5,3,1,4,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,5,3,1,6,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,5,3,1,6,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,8,5,3,6,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,5,3,6,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,5,3,4,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,5,3,1,4,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,5,3,1,2,6,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,3,8,1,2,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,8,3,4,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,8,3,4,6,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,6,3,4,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,3,1,4,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,6,3,1,2,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,3,6,1,2,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,3,4,1,2,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,3,1,4,2,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,3,1,6,2,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,3,1,6,4,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,3,6,1,4,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,3,6,4,1,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,3,6,4,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,8,4,6,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,8,1,4,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,3,1,8,4,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,3,1,8,2,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,3,1,6,4,2,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,3,1,8,4,2,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,3,1,8,6,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,3,8,1,6,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,5,3,8,6,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,3,8,6,4,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,8,3,6,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,8,3,6,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,8,3,1,6,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,8,3,1,6,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,3,6,1,4,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,8,6,3,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,8,6,3,4,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,6,8,3,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,6,3,8,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,3,4,1,6,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,4,1,8,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,6,3,1,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,6,3,1,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,6,3,8,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,3,8,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,3,6,8,4,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,3,6,8,1,4,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,3,6,1,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,5,3,1,6,8,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,5,3,1,4,8,2,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,5,3,1,4,6,2,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,5,3,1,2,6,4,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,5,3,1,2,8,4,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,5,3,4,1,8,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,5,3,4,8,1,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,3,4,8,6,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,3,4,6,1,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,3,4,1,6,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,2,5,4,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,2,8,4,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,7,3,2,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,8,3,2,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,5,3,2,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,2,6,4,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,8,3,2,7,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,7,6,3,8,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,6,3,7,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,5,3,2,7,6,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,4,3,2,7,6,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,3,2,8,4,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,1,5,8,4,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,2,7,4,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,7,4,3,2,8,6,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,7,5,3,2,8,6,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,7,8,3,6,5,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,6,8,3,7,5,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,6,4,3,8,5,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[2,1,8,6,7,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,6,4,3,7,5,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,7,6,4,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,4,5,3,2,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,7,3,6,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,6,3,7,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,6,3,8,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,2,6,8,5,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,8,2,6,7,5,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,8,2,5,4,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,2,8,6,5,4,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,6,2,8,7,5,4,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,4,7,3,8,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,8,3,7,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,8,3,6,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,5,3,2,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,4,3,2,8,6,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,3,2,5,4,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,1,7,5,4,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,2,8,6,5,4,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,8,4,3,6,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,5,7,4,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,8,4,3,7,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,3,2,8,7,5,4,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,4,3,8,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,6,8,3,5,7,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,8,2,4,7,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,3,5,2,4,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,7,3,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,2,8,3,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,5,8,3,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,6,8,4,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,2,5,8,3,6,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,3,6,8,4,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,5,8,2,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,2,6,8,5,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,3,8,2,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,3,7,2,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,6,2,7,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,3,2,1,8,5,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,1,7,3,2,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,1,7,8,2,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,5,1,2,7,8,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,5,1,4,8,2,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,7,3,8,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,4,7,6,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,7,1,4,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,5,1,2,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,8,3,1,7,2,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,4,3,5,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,3,1,5,2,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,3,6,5,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,7,6,4,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,6,3,4,2,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,3,6,2,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,8,7,4,2,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,4,8,7,5,3,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,4,3,8,5,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,7,6,2,8,4,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,3,2,6,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,5,3,2,7,4,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,2,1,8,5,4,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,3,2,7,4,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,2,6,3,7,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,5,3,1,6,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,7,3,8,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,2,3,7,8,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,6,7,2,8,4,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,1,8,2,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,2,7,8,3,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,1,7,8,6,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,2,1,7,3,8,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,3,2,5,6,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,6,3,5,2,4,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,6,2,5,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,4,1,6,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,8,1,7,5,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,4,1,7,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,7,1,5,6,2,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,7,3,6,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,3,7,5,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,6,7,5,2,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,2,6,4,3,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,8,1,7,5,4,3,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,1,8,6,4,3,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,2,6,4,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,7,5,4,3,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,1,8,6,5,4,3,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,2,7,5,4,3,8,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,7,2,4,3,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,2,8,3,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,8,6,5,2,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,3,8,6,5,4,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,8,7,6,5,2,4,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,1,7,3,2,6,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,4,3,2,8,7,6]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[8,6,3,2,1,7,4,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,5,4,1,7,2,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,5,1,7,3,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,1,7,4,3,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,6,3,2,7,5,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,3,7,2,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,8,3,1,6,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,5,8,3,2,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,7,4,1,8,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,4,3,1,8,6,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,7,2,5,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,3,7,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,1,8,7,5,2,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,4,8,6,3,5,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,4,6,3,5,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,5,4,8,7,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,1,4,6,8,7,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,6,3,8,7,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,2,4,8,7,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,1,6,4,8,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,8,5,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,3,7,2,6,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,5,2,8,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,7,2,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,2,6,3,8,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,7,3,5,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,2,4,7,5,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,4,1,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,8,2,1,6,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,2,1,8,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[8,7,6,4,1,5,2,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[3,8,7,2,1,4,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,2,7,1,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,8,2,1,5,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,8,1,6,5,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,8,1,5,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,7,6,1,4,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,1,7,3,5,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,6,1,7,5,4,2,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,6,2,8,7,3,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,2,4,6,7,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,8,5,4,7,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,1,5,8,6,4,3,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,5,6,4,3,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,2,7,4,8,6,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,8,3,6,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[7,1,8,6,3,5,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,7,6,3,5,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,7,4,6,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,5,8,3,4,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,6,2,4,7,3,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,7,1,4,5,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,1,6,4,5,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,6,5,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,2,3,8,5,4,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,1,5,4,3,8,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,3,4,2,6,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,5,4,6,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,5,6,4,3,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,6,5,4,3,2,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,6,2,5,4,3,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,5,1,7,4,3,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,1,4,7,8,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,5,1,4,8,6,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,4,7,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,6,2,4,8,7,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,8,2,4,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,8,7,2,3,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,8,2,4,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,2,8,5,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,7,2,5,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,6,8,1,3,5,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,3,8,1,2,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,4,1,7,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,3,1,5,6,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,7,1,5,4,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,1,7,6,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,4,1,7,5,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,1,5,7,6,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,4,1,6,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,7,2,5,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,8,1,2,3,6,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,8,6,1,5,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,5,1,3,8,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,2,6,4,1,3,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,5,2,1,3,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,4,5,3,7,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,5,2,8,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,8,4,1,5,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,3,4,1,6,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,8,3,6,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,5,7,2,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,5,2,7,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,3,5,2,1,7,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,5,3,1,4,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,5,4,2,8,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,4,7,2,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,4,8,2,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,5,8,2,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,8,2,4,3,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,2,4,3,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,6,2,4,7,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,6,2,4,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,5,8,2,4,7,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,7,2,4,8,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,5,7,2,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,7,2,4,3,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,6,7,2,4,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,8,2,4,6,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,5,7,2,4,6,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,5,7,8,3,2,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,6,2,4,8,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,6,2,8,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,3,4,2,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,2,4,3,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,6,2,4,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,8,7,3,2,4,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,2,3,5,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,5,2,3,4,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,6,5,2,3,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,4,2,8,6,5,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,7,6,5,2,8,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,6,7,5,2,3,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,7,5,2,8,4,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,6,2,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,7,6,2,4,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,8,3,2,4,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,5,2,3,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,8,4,2,3,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,7,4,6,2,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,5,2,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,8,5,2,3,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,4,2,3,7,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,8,6,2,4,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,7,3,2,4,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,7,3,4,2,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,2,8,5,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,7,4,2,3,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,4,2,3,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,6,4,2,8,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,7,5,2,8,6,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,6,4,2,3,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,3,5,6,1,4,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,7,5,6,1,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,2,4,1,6,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,6,1,4,2,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,6,1,4,2,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,7,4,3,5,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,1,4,3,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,1,4,3,5,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,7,1,6,3,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,4,7,6,5,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,7,4,3,5,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,6,4,3,5,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,6,4,3,5,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,1,6,4,2,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,1,3,7,2,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,7,1,3,8,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,4,1,3,8,2,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,3,6,4,2,8,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,3,1,2,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,8,1,2,6,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,8,1,4,2,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,6,4,2,7,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,1,3,7,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,7,1,3,6,2,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,5,7,3,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,4,3,7,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,3,4,7,6,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,8,4,6,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,4,6,8,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,3,7,8,6,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,7,3,8,2,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,7,6,8,3,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,3,4,8,6,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,5,4,8,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,3,4,2,8,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,4,3,8,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,3,8,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,4,3,7,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,3,4,7,6,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,3,7,8,6,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,2,3,4,8,6,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,7,5,6,3,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,6,3,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,6,8,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,5,6,8,4,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,3,8,5,6,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,8,7,6,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,3,7,5,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,8,3,7,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,8,4,2,6,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,7,1,8,2,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,4,8,5,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,3,8,5,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,8,3,6,2,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,5,8,6,3,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,5,8,7,3,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,5,7,6,3,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,5,3,8,7,6,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,5,8,6,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,7,3,6,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,7,5,3,2,1,4]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,7,6,8,3,4,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,6,8,4,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,7,6,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,6,5,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,6,5,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,8,6,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,6,5,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,7,5,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,7,5,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,4,8,5,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,6,5,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,8,6,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,5,4,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,5,2,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,6,5,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,8,5,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,6,5,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,7,6,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,6,8,2,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,6,8,4,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,6,8,1,4,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,5,6,1,3,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,6,7,1,3,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,7,6,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,6,8,2,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,3,2,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,6,2,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,6,7,2,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,4,2,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,4,2,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,1,4,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,1,2,4,3,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,3,6,5,8,7,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,6,5,7,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,2,3,8,7,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,4,3,2,8,6,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,4,7,6,2,5,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,6,5,3,7,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,6,5,3,7,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,7,5,2,6,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,7,4,2,6,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,6,4,3,7,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,6,4,3,7,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,7,3,2,5,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,3,2,5,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,3,2,4,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,5,3,2,8,6,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,5,3,2,4,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,6,5,4,3,1,8,2]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[6,8,5,4,3,2,1,7]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,1,5,4,3,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,4,8,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,1,4,3,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,5,4,3,7,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,1,4,3,8,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,5,8,3,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,5,1,3,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,2,4,3,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,5,4,7,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,3,4,8,7,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,4,5,8,3,7,6,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,8,5,4,1,2,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,5,2,3,7,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,2,4,3,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,4,7,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,8,4,3,2,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,8,5,7,3,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,7,6,8,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,8,5,2,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,8,6,7,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,7,5,2,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,8,2,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,4,5,8,1,2,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,4,6,5,2,1,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,6,5,2,1,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,7,5,6,1,3,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,1,8,4,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,6,7,4,3,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,5,2,4,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,3,6,4,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,4,5,3,2,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,7,1,4,6,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,1,2,4,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,7,6,8,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,8,1,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,6,8,5,7,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,7,2,4,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,4,8,6,5,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,1,8,2,5,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,3,7,4,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,4,7,5,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,7,6,2,3,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,8,7,3,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,1,7,4,2,5,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,3,8,2,5,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,4,1,5,8,2,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,5,8,7,3,6,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,1,5,8,7,4,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,5,6,7,4,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,4,3,2,8,5,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,2,7,1,8,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,2,8,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,8,7,3,5,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,7,8,3,1,5,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,4,7,2,8,5,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,1,4,8,5,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,3,4,8,5,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,1,8,5,2,7,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,7,4,5,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,8,3,6,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,1,6,4,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,8,2,6,4,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,5,8,7,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,2,7,6,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,6,8,4,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,8,6,5,2,3,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,6,4,7,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,4,8,5,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,3,5,8,4,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,5,8,4,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,7,1,5,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,7,5,6,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,1,4,8,7,3,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,2,8,4,3,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,7,8,1,3,5,6,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[8,7,3,4,1,5,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,8,2,7,3,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,8,7,2,5,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,1,7,2,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,2,3,7,1,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,8,7,1,3,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,4,6,7,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,3,8,2,7,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,4,2,1,3,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,2,4,3,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,3,7,1,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,2,7,3,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,1,3,2,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,5,2,8,3,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,7,5,1,8,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,5,2,7,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,2,5,4,3,8,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,8,1,4,5,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,8,1,2,4,5,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,1,6,2,4,5,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,6,1,2,5,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,1,6,5,8,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,8,6,2,5,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,6,1,4,5,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,3,6,8,4,5,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,7,5,4,3,8,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,8,7,4,2,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,4,3,7,6,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,4,3,1,6,2,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[1,7,4,3,8,6,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,5,3,4,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,6,1,7,4,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,5,7,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,8,2,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,8,7,4,3,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,8,6,3,4,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,8,6,3,4,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,1,3,8,5,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,8,4,3,1,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,5,2,8,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,8,1,3,6,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,8,2,3,6,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,1,2,7,8,6,4,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,5,1,8,2,4,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,5,8,1,2,4,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,5,8,1,2,3,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,2,7,1,8,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,3,6,7,4,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,1,6,8,4,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,3,7,1,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,7,3,2,8,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,7,1,4,3,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,1,8,6,3,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,1,3,6,2,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,5,1,7,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,6,5,8,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,3,5,8,2,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,8,7,3,6,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,2,8,6,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,5,6,1,4,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,1,8,3,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,1,6,2,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,1,5,3,8,7,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,6,3,7,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,1,5,8,2,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,6,8,5,1,2,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,5,2,4,8,1,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,4,8,2,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,2,5,1,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,8,5,2,6,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,2,1,8,5,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,5,4,8,2,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,1,5,8,6,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,8,4,5,1,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,8,3,7,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,5,8,6,2,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,4,8,5,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,3,4,8,1,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,6,1,2,8,3,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,8,4,1,2,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,8,4,6,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,4,8,7,1,3,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,5,4,8,1,2,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,1,6,2,3,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,1,6,8,2,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,4,1,8,2,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,4,7,1,2,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,4,7,8,1,3,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,3,7,1,4,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,1,8,4,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,1,4,8,3,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,6,4,7,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,1,4,8,3,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,3,7,1,4,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,1,5,3,8,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,5,4,3,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,5,4,3,7,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,1,5,3,8,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,6,4,2,5,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,3,1,2,7,4,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,3,8,1,4,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,8,1,4,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,2,5,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,2,5,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,1,2,5,4,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,3,8,1,4,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,1,4,2,6,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,6,4,2,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,1,5,3,2,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,3,1,5,2,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,3,1,5,7,2,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,4,1,5,3,6,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,5,4,3,6,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,5,4,3,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,1,5,3,6,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,3,8,4,5,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,4,5,1,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,6,2,3,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,6,1,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,6,3,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,8,4,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,8,6,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,6,5,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,7,1,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,7,3,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,8,2,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,8,4,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,1,6,5,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,8,6,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,4,5,1,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,3,1,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,8,1,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,4,1,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,5,2,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,5,1,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,8,1,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,6,1,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,4,1,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,5,3,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,5,3,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,8,6,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,6,2,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,4,8,2,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,7,3,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,6,4,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,6,4,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,8,4,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,5,8,4,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,5,8,2,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,5,6,3,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,5,6,3,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,5,3,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,5,3,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,5,8,1,4,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,6,7,2,3,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,3,1,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,8,1,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,7,5,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,7,5,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,5,8,1,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,7,5,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,8,4,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,3,1,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,6,1,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,7,1,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,4,3,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,5,4,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,7,3,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,8,2,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,8,2,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,8,6,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,5,1,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,8,1,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,2,5,1,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,8,1,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,6,1,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,5,8,4,6,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,7,1,4,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,1,8,3,5,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,3,8,5,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,8,2,4,5,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,2,8,3,5,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,3,8,5,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,1,5,2,6,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,1,5,2,3,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,2,3,1,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,6,2,3,7,1,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,2,7,3,1,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,7,2,4,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,7,2,5,1,6,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,2,1,7,6,3,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,2,7,1,6,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,7,2,1,4,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,7,3,1,4,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,7,3,1,4,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,5,7,2,1,4,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,2,7,1,3,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,4,1,2,6,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,4,3,1,7,2,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,1,3,7,2,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,1,3,2,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,4,1,6,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,6,4,7,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,8,4,2,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,3,6,4,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,4,7,5,1,6,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,5,1,2,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,3,5,1,2,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,8,6,3,5,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,7,3,1,5,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,7,2,1,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,2,7,1,5,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,2,1,7,6,4,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,3,1,4,2,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,3,1,2,6,4,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,3,2,1,7,4,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,3,2,7,1,5,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,7,2,1,5,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,2,1,3,6,4,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,6,5,4,1,2,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,5,6,7,4,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,5,8,6,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,7,8,6,3,4,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,8,5,7,6,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,3,2,1,5,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,2,1,5,3,4,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,1,3,7,6,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,7,2,3,6,1,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,4,2,8,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,2,6,8,5,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,4,2,7,3,8,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,6,7,5,3,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,5,8,7,6,3,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,4,7,6,3,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,3,7,6,2,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,1,6,3,2,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,1,5,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,8,4,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,4,6,1,3,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,8,6,7,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,5,8,1,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,4,3,2,7,8,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,4,8,5,7,1,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,7,1,4,6,8,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,8,2,5,6,1,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,3,8,7,5,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,7,3,5,1,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,6,8,4,2,5,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,5,7,1,6,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,7,2,8,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,8,2,1,7,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,3,5,1,6,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,1,6,3,5,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,5,8,4,3,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,6,7,1,5,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,6,5,8,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,8,5,4,3,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,8,5,6,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,4,8,7,3,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,8,4,3,5,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,2,7,6,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,1,8,2,7,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,1,2,6,7,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,8,4,3,2,7,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,8,6,3,2,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,4,7,2,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,1,8,4,3,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,2,3,6,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,2,4,3,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,3,1,6,4,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,8,2,6,3,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,7,3,5,4,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,3,8,4,5,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,8,3,4,5,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,8,2,6,4,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,7,2,3,6,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,2,3,5,4,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,8,2,4,5,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,3,8,4,6,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,8,2,3,5,4,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,7,8,2,3,6,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,7,8,2,3,5,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,7,8,2,5,3,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,8,2,4,5,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,8,3,6,4,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,8,2,3,6,4,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,8,3,5,4,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,7,8,3,6,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,2,7,8,3,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,2,8,4,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,8,2,4,3,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,3,1,5,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,3,1,5,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,4,5,1,2,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,4,5,1,2,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,6,1,5,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,5,4,1,2,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,6,4,1,7,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,4,1,8,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,7,4,1,8,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,5,7,4,1,2,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,7,5,1,2,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,1,7,5,3,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,3,8,1,5,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,8,5,1,2,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,5,8,4,1,2,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,8,4,1,7,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,5,7,1,2,3]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,8,6,7,1,2,3]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,4,8,6,1,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,8,1,6,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,1,8,6,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,7,6,8,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,7,6,1,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,7,6,8,1,2,3]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,7,5,8,1,2,3]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,8,6,5,7,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,5,6,7,1,2,3]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,5,6,8,1,2,3]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,5,7,8,1,2,3]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,4,6,1,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,6,1,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,1,6,7,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,3,1,6,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,3,1,7,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,2,1,4,3,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,8,3,1,7,6,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,4,8,1,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,1,6,8,7,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,6,8,1,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,6,8,7,1,2,3]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,7,5,8,6,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,5,7,6,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,6,7,5,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,6,8,5,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,7,8,5,1,2,3]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,5,7,8,6,1,2,3]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,4,7,8,1,6,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,1,8,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,1,7,8,6,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,8,1,7,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,8,7,1,6,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,8,7,5,1,2,3]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,7,8,6,5,1,2,3]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,5,4,7,3,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,6,3,7,5,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,7,3,6,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,3,1,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,5,3,1,6,4,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,3,7,6,4,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,5,3,7,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,7,6,3,5,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,5,3,6,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,3,7,5,4,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,5,2,3,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,1,3,7,5,4,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,1,8,6,5,4,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,3,1,8,6,4,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,8,3,1,6,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,2,8,3,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,2,6,3,8,7,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,8,3,6,4,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,7,6,3,4,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,1,3,8,7,5,4,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,2,3,8,6,4,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,3,7,4,8,6,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,7,6,3,8,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,3,6,4,8,7,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,3,7,6,4,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,6,3,1,8,5,4,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,3,8,5,4,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,8,4,3,5,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,6,3,1,8,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,5,8,2,4,1,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,4,8,3,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,1,8,3,5,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,5,2,8,7,3,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,2,7,3,6,4,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,8,6,3,7,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,3,8,6,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,3,8,4,7,6,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,7,3,4,8,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,6,3,8,4,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,2,3,8,7,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,2,1,8,3,7,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,8,4,2,7,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,2,8,6,3,4,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,7,3,8,4,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,3,8,7,4,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,3,8,7,6,4,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,5,3,8,1,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,7,1,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,7,1,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,5,7,1,2,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,5,7,2,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,8,6,2,5,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,7,1,4,8,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,8,1,5,7,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,3,8,1,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,7,5,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,3,8,1,6,5,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,8,1,3,5,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,5,7,6,2,4,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,8,6,7,2,3,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,6,7,1,3,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,8,6,1,5,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,8,5,7,1,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,8,5,6,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,5,7,2,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,8,6,2,1,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,7,6,2,1,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,8,6,7,2,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,6,7,3,5,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,6,7,3,4,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,6,7,2,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,6,7,2,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,6,7,2,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,3,1,7,5,2,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,2,8,5,1,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,8,5,1,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,6,7,1,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,6,7,1,4,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,6,7,2,3,4,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,6,7,2,4,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,6,7,1,2,4,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,3,8,5,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,8,5,1,7,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,2,8,5,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,4,8,6,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,2,5,7,6,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,8,6,7,1,3,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,6,7,1,2,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,6,7,2,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,8,5,2,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,6,7,5,1,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,8,5,7,1,4,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,7,1,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,8,4,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,7,4,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,7,2,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,3,8,5,2,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,2,6,7,5,3,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,6,7,5,3,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,8,6,7,3,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,6,7,3,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,1,5,7,6,2,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,4,1,7,5,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,7,5,2,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,6,7,5,2,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,8,6,7,2,3,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,6,7,3,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,6,7,4,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,6,7,4,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,6,7,4,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,6,7,3,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,6,7,3,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,6,7,5,3,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,7,5,3,2,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,8,5,3,1,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,1,6,7,5,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,8,6,7,3,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,6,7,4,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,6,7,4,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,5,8,1,4,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,7,6,1,4,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,1,8,3,6,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,7,8,5,6,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,4,7,1,5,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,1,4,7,8,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,6,8,4,7,5,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,1,3,5,7,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,6,1,4,3,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,1,6,5,4,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,3,7,5,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,7,3,8,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,8,6,3,5,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,6,5,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,7,6,5,3,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,1,6,7,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,4,1,6,8,2,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,3,8,6,2,7,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,1,3,2,7,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,6,2,5,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,2,6,8,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,7,3,6,4,5,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,7,8,6,2,1,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,7,4,1,6,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,2,4,5,1,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,8,6,4,5,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,4,6,5,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,1,7,5,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,5,8,6,1,2,4,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,8,7,3,1,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,5,4,3,6,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,5,4,6,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,2,1,3,7,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,1,2,7,5,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,8,3,6,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,7,4,5,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,8,5,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,4,8,2,7,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,2,7,3,6,5,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,7,6,3,4,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,2,6,3,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,7,5,8,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,8,4,3,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,7,5,4,3,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,8,1,4,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,4,5,6,1,2,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,3,5,7,8,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,5,8,7,1,3,4,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,7,2,4,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,2,7,4,3,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,5,6,4,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,6,5,4,3,2,7]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[6,1,5,2,8,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,1,8,5,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,2,8,5,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,7,2,8,5,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,3,5,8,6,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,5,8,6,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,6,8,1,5,7,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,6,5,8,1,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,8,1,5,7,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,1,2,5,8,6,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,7,2,5,8,6,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,6,8,2,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,1,5,8,6,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,7,1,8,5,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,5,8,3,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,2,1,8,5,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,8,2,1,3,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,2,7,6,8,3,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,6,8,2,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,1,8,5,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,7,4,3,1,8,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,7,4,1,6,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,7,6,8,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,4,2,6,8,5,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,2,5,8,6,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,1,7,6,8,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,6,8,1,2,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,7,6,8,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,4,2,6,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,1,4,2,8,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,2,5,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,4,6,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,8,1,6,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,8,5,4,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,2,6,8,5,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,7,2,6,8,5,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,7,6,8,3,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,6,8,3,1,2,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,5,8,6,3,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,5,8,6,3,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,6,7,1,8,5,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,2,6,8,5,4,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,6,8,2,3,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,6,8,3,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,1,6,8,5,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,7,3,1,8,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,7,1,8,5,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[7,6,8,3,2,1,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,8,5,6,1,3,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,5,8,7,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,4,8,1,2,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,5,6,7,2,4,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,4,5,1,8,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,7,1,2,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,6,7,2,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,6,7,1,4,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,6,7,3,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,1,3,6,7,4,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,1,6,8,4,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,6,7,1,4,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,6,7,3,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,4,1,5,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,2,1,5,4,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,4,5,3,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,1,5,4,8,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,4,1,5,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,2,1,8,6,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,5,2,7,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,3,8,1,4,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,8,2,3,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,2,8,1,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,1,3,2,6,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,6,3,2,5,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,1,3,5,2,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,2,3,1,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,4,3,5,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,4,2,1,6,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,8,4,2,1,5,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,2,3,4,8,7,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,8,3,4,6,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,3,6,4,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,3,5,6,2,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,3,8,7,5,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,3,7,8,5,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,2,6,3,8,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,2,5,8,7,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,2,8,4,7,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,8,7,5,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,3,7,8,5,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,4,1,7,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,2,7,4,8,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,2,3,6,1,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,2,3,6,1,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,5,8,3,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,6,8,3,2,1,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,6,8,4,3,7,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,1,4,2,3,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,8,3,4,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,5,8,3,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,5,6,3,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,4,3,6,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,4,3,7,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,4,3,8,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,2,4,1,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,2,4,1,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,2,4,1,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,1,4,2,8,7,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,4,2,7,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,8,2,4,1,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,7,4,1,6,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,1,3,7,2,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,1,4,3,6,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,8,6,4,3,7,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,1,4,2,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,6,3,4,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,6,5,3,2,1,7]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,8,5,6,3,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,7,8,3,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,4,8,7,3,2,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,6,7,8,3,2,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,7,6,8,3,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,1,3,4,2,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,1,3,4,2,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,8,7,5,3,2,1,6]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,8,7,6,3,2,1,5]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,8,2,6,3,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,2,3,6,7,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,8,3,1,6,7,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,3,8,1,6,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,8,7,3,5,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,3,8,7,2,5,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,3,7,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,1,4,7,2,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,7,4,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,1,2,4,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,7,1,3,4,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,4,7,3,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,3,8,2,7,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,8,3,7,5,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,3,8,2,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,2,8,1,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,1,3,8,2,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,8,3,7,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,7,3,5,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,8,1,5,4,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,3,8,1,5,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,8,1,6,2,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,8,7,2,5,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,8,2,7,5,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,4,8,3,6,5,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,4,3,8,6,5,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,2,1,8,6,5,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,1,8,2,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,7,8,4,1,2,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,1,7,8,5,3,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,2,8,3,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,3,2,8,6,5,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,3,1,8,6,5,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,6,8,4,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,1,8,5,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,8,6,2,4,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,8,2,6,4,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,3,8,1,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,1,8,2,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,4,7,8,5,3,2,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,3,7,8,5,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,7,2,8,4,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,8,4,7,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,8,6,3,1,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,3,6,8,4,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,6,2,8,3,5,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,7,3,8,4,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,4,8,2,6,5,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,2,4,8,1,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,8,6,2,4,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,8,2,6,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,8,3,6,1,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,2,8,7,4,3,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,1,8,5,2,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,2,8,4,6,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,4,3,1,8,6,5,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,4,2,8,6,5,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,2,4,8,6,5,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,2,1,4,8,6,5,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,1,2,4,8,6,5,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,4,2,8,6,5,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,4,8,2,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,4,8,5,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,7,4,8,5,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,2,8,3,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,3,1,4,8,6,5,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,1,3,4,8,6,5,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,8,3,6,2,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,8,2,6,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,5,8,2,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,8,7,2,4,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,8,4,5,7,3,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,5,7,3,8,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,2,4,5,8,3,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,8,1,2,5,6,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,1,3,5,2,6,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,1,6,3,8,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,5,1,8,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,1,5,8,4,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,4,5,8,3,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,6,4,8,1,3,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,5,4,3,8,2,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,4,3,7,2,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,8,4,3,7,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,8,3,7,2,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,4,6,3,2,8,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,3,6,2,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,4,3,7,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,8,5,3,1,2,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,7,3,4,1,2,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,4,7,6,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,7,4,3,6,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,8,1,6,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,7,8,3,6,1,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,8,6,7,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,8,6,4,7,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,6,2,7,4,1,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,2,1,4,3,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,1,3,4,2,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,7,3,2,6,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,7,3,2,5,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,2,6,8,5,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,8,2,3,6,7,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,5,2,3,1,6,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,6,4,7,2,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,7,5,2,8,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,7,4,1,8,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,6,1,7,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,7,6,3,8,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,8,7,2,3,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,6,8,7,4,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,7,4,1,6,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,2,1,7,8,4,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,7,1,8,4,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,1,3,7,5,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,3,7,4,2,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,3,7,6,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,5,2,7,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,2,8,7,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,3,2,8,1,6,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,7,2,6,5,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,2,7,8,6,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,8,2,4,7,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,1,8,7,3,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,1,6,3,7,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,8,3,1,7,5,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,1,6,7,2,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,2,8,1,5,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,8,2,6,1,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,6,7,5,2,4,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,6,8,1,5,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,2,7,8,5,6,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[7,4,8,1,6,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,1,8,2,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,7,3,8,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,1,7,6,5,4,3]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,6,7,5,1,4,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,6,5,4,1,3,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,4,7,3,2,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,3,6,2,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,3,7,8,2,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,8,4,2,6,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,7,2,5,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,3,2,6,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,3,2,5,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,7,2,5,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,7,2,5,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,2,6,7,1,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,8,2,6,5,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,7,8,5,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,2,7,6,8,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,7,3,1,5,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,7,3,1,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,3,7,1,5,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,3,6,1,8,7,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,8,1,4,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,3,7,6,1,4,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,7,6,1,5,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,7,6,1,4,5,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,5,4,2,1,7,3,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[6,4,7,2,1,5,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,7,2,1,5,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,3,2,1,4,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,8,3,2,1,5,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,3,7,2,1,4,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,5,2,7,1,4,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,8,2,6,1,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,2,7,1,5,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,6,1,8,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,2,6,1,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,7,8,1,4,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,7,6,1,5,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,4,1,8,7,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[5,8,4,1,6,7,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,4,7,1,5,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,7,1,6,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,8,7,1,5,6,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,8,7,1,5,4,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,2,1,6,4,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,2,1,5,4,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,3,2,1,6,4,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,8,2,1,5,4,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,2,7,1,5,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,1,6,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,1,5,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,7,1,5,4,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,8,7,1,5,4,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,1,6,7,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,4,1,7,5,8,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,8,1,6,5,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,3,1,7,5,4,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,3,1,6,7,4,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,1,6,5,7,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,1,6,5,4,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,2,1,6,7,4,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,6,5,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,8,1,6,5,4,3,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,7,6,5,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,1,7,6,5,4,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,8,1,2,6,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,5,7,2,6,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,3,5,6,2,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,1,3,5,7,2,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,6,8,1,7,2,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,8,2,6,7,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,2,3,5,4,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,1,2,3,5,4,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,7,8,1,3,5,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,8,3,5,6,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,8,1,7,6,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,5,8,7,2,1,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,7,3,5,6,2,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,2,1,3,5,4,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,6,8,7,2,1,5,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,6,4,1,7,5,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,4,3,1,8,5,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[3,6,8,1,2,5,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,6,7,2,5,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,1,4,2,8,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,2,5,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,2,6,5,4,3,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,6,3,2,5,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,3,1,2,5,4,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,2,5,7,6,3,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,6,8,1,7,5,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,2,6,7,5,4,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,7,8,6,3,1,5,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,7,8,1,6,5,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,3,1,8,6,5,4,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,7,2,1,6,5,4,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[2,1,8,6,3,7,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,1,5,2,7,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,1,7,4,2,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,5,4,3,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,8,4,5,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,8,3,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,4,8,5,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,5,4,6,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,1,5,2,3,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,7,5,2,6,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,7,4,6,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,3,7,6,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,4,8,6,3,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,6,3,8,5,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,3,2,7,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,2,4,7,5,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,5,2,7,4,6,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,8,2,1,7,6,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,3,2,4,1,7,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,4,3,1,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,3,1,5,4,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,8,1,4,6,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,1,4,3,2,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,1,4,5,3,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,1,5,4,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,5,1,3,4,2,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,2,6,1,4,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,1,6,3,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,5,6,1,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,6,5,4,1,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,6,4,5,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,5,4,1,2,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,6,3,5,1,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,8,5,1,6,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,7,3,6,5,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,8,3,4,6,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,4,3,6,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,7,2,8,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,2,3,5,8,1,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,2,8,4,7,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,4,7,1,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,4,6,1,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,4,5,7,6,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,3,8,4,6,7,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,6,8,1,4,2,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,7,8,4,6,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,5,7,8,6,1,2,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,5,1,6,8,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,5,6,8,2,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,6,4,8,2,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,6,3,8,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,1,6,8,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,2,6,8,3,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,7,1,8,6,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,2,7,8,6,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,7,5,2,8,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,7,5,2,8,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,7,5,1,8,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,2,8,6,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,7,8,6,2,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,1,7,8,6,3,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,3,7,8,6,4,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,2,7,8,4,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,5,7,8,6,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,2,7,5,1,8,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,6,7,5,8,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,2,7,5,4,1,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,5,2,4,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,2,5,3,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,4,5,2,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,7,8,6,3,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,1,7,8,6,3,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,7,5,1,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,7,5,3,8,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,7,5,4,2,8,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,7,5,1,4,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,8,6,4,1,2,3]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,1,7,2,6,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,7,1,5,6,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,7,4,1,5,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,7,4,5,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,3,7,5,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,1,7,5,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,5,3,7,8,6,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,5,4,2,1,8,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,3,2,7,5,8,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,4,2,5,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,7,4,5,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,3,7,5,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,1,6,3,2,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,1,6,3,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,1,6,3,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,7,6,1,3,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,6,1,3,8,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,3,5,1,8,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,5,1,8,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,7,5,1,8,6,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,7,1,5,8,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,7,4,1,8,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,1,6,7,3,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,7,4,1,8,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,6,7,1,5,8,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,5,1,8,4,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,5,1,8,4,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,5,4,8,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,5,4,8,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,1,5,8,7,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,6,1,5,8,7,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,1,5,8,2,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,1,6,2,8,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,1,6,2,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,1,5,8,2,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,1,5,8,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,5,4,3,2,7,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,8,5,4,3,7,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,4,3,2,1,7,6]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,5,4,3,1,8,7,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[8,3,4,6,2,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,5,6,2,1,8,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,2,6,8,4,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,3,2,8,4,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,3,2,8,4,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,4,5,7,3,8,6,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,2,5,6,8,3,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,8,1,5,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,6,1,8,4,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,3,6,8,1,4,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,6,8,1,3,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,6,3,8,2,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,3,7,2,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,4,7,3,2,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,4,7,3,2,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,7,8,4,5,3,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,7,3,8,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,1,7,4,3,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,7,4,1,8,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,3,7,1,4,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,1,7,3,8,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,6,3,7,8,4,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,1,6,3,7,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,1,3,7,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,6,1,7,8,3,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,3,7,4,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,2,4,1,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,2,1,4,3,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,7,3,1,2,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,1,3,2,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,3,2,1,7,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,5,6,3,7,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,6,3,1,7,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,4,7,3,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,7,2,8,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,7,2,8,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,2,7,1,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,3,2,1,8,4,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[4,7,2,1,3,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,3,7,8,6,4,2,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[7,3,8,4,6,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,3,8,2,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,7,8,5,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,6,2,7,8,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,6,2,1,7,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,4,5,8,1,2,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,1,7,3,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,2,1,3,8,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,1,6,7,8,2,4,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,3,7,1,8,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,1,7,3,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,1,8,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,3,6,8,2,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,2,3,6,8,1,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,3,2,1,8,4,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,6,5,8,2,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,2,1,3,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,2,6,4,5,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,6,5,8,1,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,2,4,5,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,3,2,1,6,8,4,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,2,4,5,8,1,3,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,4,6,5,8,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,6,3,4,5,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,1,8,5,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,4,1,7,6,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,4,2,7,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,3,2,8,7,4,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,6,4,5,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,7,4,1,2,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,7,4,6,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,2,5,8,6,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,8,6,7,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,3,6,2,8,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,4,8,2,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,5,8,6,7,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,2,5,6,8,7,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,8,5,6,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,2,8,3,5,6,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,2,3,7,1,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,6,4,8,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,1,6,7,3,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,7,8,5,4,1,3,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,7,5,3,8,4,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,5,3,1,2,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,2,4,8,5,3,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,8,3,1,2,7,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,5,2,7,4,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,2,3,7,1,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,2,4,6,7,1,3,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,8,2,3,6,7,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,5,2,7,6,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,3,2,5,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,3,2,1,6,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,7,3,4,6,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,2,7,4,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,4,2,8,7,6,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,6,5,8,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,7,1,6,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,8,7,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,3,2,1,8,5,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,7,5,4,1,8,6,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,2,5,6,8,7,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,8,5,6,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,7,1,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,4,7,1,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,3,6,5,2,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,4,3,6,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,5,2,1,8,7,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,3,2,4,6,5,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,2,1,6,5,3,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,4,1,2,6,5,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,4,2,1,5,3,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,3,6,4,1,5,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,6,3,4,5,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,3,4,8,5,7,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,8,4,7,6,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,4,7,5,8,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,5,2,4,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,6,5,1,3,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,7,1,6,5,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,8,7,6,3,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,8,5,1,4,7,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,3,1,5,8,6,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,3,5,8,6,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,3,8,4,7,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,8,4,3,2,7,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,4,7,8,2,1,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,1,3,2,8,6,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,1,2,8,6,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,3,1,6,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,2,1,8,6,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,4,7,3,8,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,8,2,7,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,1,3,6,4,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,5,1,7,8,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,4,5,8,3,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,4,3,7,2,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,8,7,2,1,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,4,7,8,3,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,4,3,8,7,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,5,7,2,4,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,4,7,2,3,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,7,1,3,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,4,1,3,2,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,4,2,3,1,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,5,7,2,6,1,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,3,8,5,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,3,2,6,7,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,5,3,6,2,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,1,5,4,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,8,7,4,6,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,1,7,6,4,5,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,2,4,6,5,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,1,7,6,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,6,1,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,5,8,7,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,5,7,8,4,1,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,1,5,2,6,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,5,1,6,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,2,8,5,1,6,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,8,5,2,6,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,7,1,8,5,4,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,6,2,1,3,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,6,3,5,8,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,8,3,5,4,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,5,1,8,6,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,5,7,1,8,6,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,4,6,2,8,5,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,6,8,1,5,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,4,7,2,1,8,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,7,8,1,5,6,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,2,6,7,8,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,5,2,7,8,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,2,8,4,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,6,2,8,4,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,8,4,1,2,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,5,7,2,4,8,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,7,2,8,4,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,8,4,1,6,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,6,2,1,7,8,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,6,2,1,8,5,4,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,7,2,4,8,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,7,2,8,5,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,6,7,8,4,5,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,6,8,2,4,5,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,2,1,4,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,7,2,1,8,5,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,2,8,4,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,8,2,4,5,6,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,5,7,3,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,6,3,7,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,6,3,8,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,6,7,3,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,6,7,8,5,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,6,8,3,5,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,7,3,2,8,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,7,8,3,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,2,6,7,8,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,5,2,6,8,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,5,6,3,8,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,6,8,3,1,2,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,5,7,3,8,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,8,3,2,1,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,6,2,3,7,8,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,2,3,8,5,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,2,7,3,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,2,7,8,5,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,7,3,2,8,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,8,3,2,5,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,2,3,1,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,2,8,3,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,8,3,2,5,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,1,2,6,8,4,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,7,4,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,2,7,8,4,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,2,8,4,3,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,6,3,8,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,6,7,4,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,6,7,8,4,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,8,3,4,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,2,3,8,4,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,2,7,8,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,8,3,4,2,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,2,3,4,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,7,2,3,8,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,8,3,4,2,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,8,2,3,4,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,1,2,3,8,5,4,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,1,2,7,8,5,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,1,2,8,4,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,7,3,4,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,7,3,8,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,7,8,4,5,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,8,3,4,5,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,2,3,8,5,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,7,2,8,4,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,2,3,4,5,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,1,2,8,4,5,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,1,8,2,3,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,1,2,4,3,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,5,7,2,6,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,6,8,2,4,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,6,2,8,1,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,1,3,8,4,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,5,1,3,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,2,5,7,4,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,1,3,7,6,4,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,2,5,1,3,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,7,5,3,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,6,5,4,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,5,2,4,8,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,8,2,5,3,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,1,5,3,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,7,5,3,2,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,1,6,4,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,3,6,5,2,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,3,7,2,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,2,6,5,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,8,4,2,5,6,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,2,7,4,5,6,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,3,6,5,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,9,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1]=>0
[6,9,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1]=>0
[5,9,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1]=>0
[4,9,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1]=>0
[3,9,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1]=>0
[2,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1]=>0
[8,10,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[7,10,9,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[4,8,6,5,7,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,10,9,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[3,8,7,5,4,6,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,5,6,7,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,10,9,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[2,8,7,6,4,3,5,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,8,7,4,5,6,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,10,9,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[1,8,7,6,5,3,2,4]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,8,7,6,3,4,5,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,10,9,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[2,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[1,1,1,1,1,1,1,1]=>0
[7,2,8,6,5,4,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,2,8,5,4,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,2,8,5,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,2,5,6,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,5,4,3,1,7,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,6,4,1,3,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,8,6,1,5,3,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,1,8,5,2,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,1,2,8,6,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,3,5,4,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,2,5,8,3,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,5,6,3,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,6,8,5,3,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,6,3,8,5,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,2,6,4,8,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,7,4,2,6,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,3,1,7,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,8,4,1,7,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,3,4,7,2,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,3,4,5,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,3,2,5,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,3,2,1,5,4,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,3,7,1,5,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,5,1,8,4,3,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,5,4,8,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,1,6,5,8,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,3,5,4,6,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,3,4,1,5,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,4,1,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,8,4,5,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,1,8,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,7,3,2,5,4,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,1,5,8,7,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,3,6,4,5,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,8,1,2,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,7,8,6,2,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,5,1,8,4,7,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,1,8,4,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,7,4,6,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,3,2,8,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,1,4,7,2,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,7,3,6,1,5,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,6,8,2,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,4,7,3,8,5,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,6,1,5,7,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,2,5,4,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,3,4,2,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,5,3,7,4,2,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,2,4,1,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,3,4,7,1,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,7,6,3,2,5,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,1,5,6,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,2,5,6,1,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,5,2,8,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,4,8,7,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,6,4,5,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,3,6,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,2,1,7,5,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,4,1,8,7,6,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,7,2,6,5,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,1,4,2,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,4,7,1,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,7,8,2,5,6,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,2,4,1,6,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,2,5,7,6,1,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,5,6,1,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,4,1,7,6,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,4,6,5,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,7,3,5,6,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,1,3,6,4,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,3,2,7,5,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,2,5,8,3,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,2,7,8,5,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,2,6,8,4,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,2,6,8,5,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,5,2,4,8,7,6,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,2,6,4,8,7,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,2,7,4,8,6,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,2,7,5,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,8,5,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,5,8,7,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,2,4,8,7,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,6,4,8,7,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,8,5,6,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,6,8,5,7,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,6,8,2,7,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,8,2,6,7,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,7,2,8,6,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,7,8,2,5,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,7,8,2,3,6,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,2,7,8,4,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,7,2,8,3,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,6,2,4,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,6,7,3,4,8,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,3,7,4,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,4,1,5,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,1,5,7,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,6,4,2,8,7,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,7,4,2,8,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,8,4,2,7,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,8,4,7,3,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,7,4,8,3,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,6,4,8,3,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,2,4,8,3,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,4,5,7,2,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,8,3,5,2,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,5,1,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,8,6,2,7,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,8,6,7,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,6,8,7,2,3,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,6,8,5,3,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,5,8,7,3,6,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,6,8,7,3,5,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,7,8,6,3,5,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,6,7,8,5,2,3,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,7,8,6,2,3,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,4,7,6,8,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,7,6,2,8,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,8,7,4,1,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,2,8,4,7,6,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,5,8,7,6,3,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,6,8,7,5,3,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,7,8,6,5,3,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,2,6,7,3,4,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,4,7,6,3,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,2,1,7,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,2,1,4,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,1,4,5,8,7,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,4,2,7,6,3,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,3,7,6,4,5,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,1,7,5,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,7,4,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,2,7,8,4,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,6,1,7,4,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,1,7,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,4,6,1,3,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,6,4,1,5,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,1,5,4,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,1,4,7,8,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,1,2,4,8,6,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,2,4,8,7,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,4,8,7,6,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,2,3,8,5,4,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,3,1,2,8,5,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,1,5,3,8,6,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,2,3,8,5,6,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,3,8,6,4,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,3,8,6,5,4,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,3,8,5,4,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,6,1,5,4,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,1,2,4,8,6,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,4,8,3,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,6,3,1,4,8,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,4,3,1,8,6,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,6,3,1,8,7,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,4,5,1,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,5,4,1,8,7,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,2,6,1,7,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,1,6,2,8,7,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,3,7,8,6,4,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,3,7,8,5,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,4,1,7,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,1,2,8,6,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,4,2,8,6,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,3,6,8,5,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,2,3,8,6,7,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,3,8,7,5,4,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,3,8,7,4,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,3,8,5,7,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,3,6,8,7,4,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,6,2,8,7,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,2,8,4,5,3,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,4,7,6,5,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,4,7,5,6,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,7,4,6,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,6,3,5,4,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,7,3,5,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,7,3,6,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,7,4,6,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,7,3,6,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,7,3,6,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,3,7,2,6,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,7,2,6,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,6,7,2,5,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,6,2,5,4,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,7,1,6,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,3,7,1,6,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,7,1,6,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,7,2,6,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,6,2,5,3,4,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,1,7,6,5,3,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,7,6,5,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,7,6,5,2,3,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,7,6,4,2,3,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,7,5,4,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,7,6,4,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,7,6,5,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,6,4,5,1,3,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,6,2,5,1,4,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,6,1,5,2,4,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,8,1,3,2,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,1,4,2,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,6,1,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,5,3,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,5,1,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,1,4,3,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,4,3,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,2,5,1,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,2,5,3,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,2,5,4,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,4,7,6,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,7,6,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,4,3,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,4,3,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,8,1,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,5,3,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,7,4,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,7,5,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,6,4,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,6,4,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,6,3,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,1,5,3,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,1,5,2,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,3,7,1,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,7,1,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,3,2,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,7,1,3,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,7,1,3,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,5,7,1,3,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,6,8,2,4,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,6,8,1,3,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,8,1,3,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,3,2,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,4,2,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,8,1,4,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,6,8,1,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,6,8,2,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,6,8,2,5,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,8,3,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,8,2,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,8,2,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,8,2,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,8,1,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,5,2,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,6,1,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,6,5,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,6,5,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,5,8,4,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,8,4,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,8,3,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,7,1,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,4,2,8,5,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,4,3,8,2,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,4,8,5,2,3,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,8,4,3,7,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,4,3,5,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,3,5,4,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,3,7,5,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,6,8,3,5,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,3,5,8,2,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,3,5,2,4,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,6,4,2,5,1,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,2,8,4,1,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,3,8,2,4,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,3,4,8,2,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,3,7,4,5,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,3,5,8,4,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,7,8,3,6,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,8,3,6,7,2,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,4,8,7,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,8,4,7,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,8,4,1,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,7,4,1,5,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,4,7,5,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,5,7,8,4,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,7,3,6,8,2,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,8,3,7,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,7,3,4,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,8,3,5,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,6,8,3,5,7,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,7,3,5,6,8,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,7,3,5,8,2,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,4,7,8,2,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,3,8,2,4,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,8,2,6,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,3,6,2,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,3,5,7,2,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,3,5,6,7,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,7,8,3,5,6,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,7,8,3,6,2,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,3,6,7,2,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,3,7,2,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,4,8,2,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,8,2,4,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,8,4,1,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,2,5,1,8,7,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,3,5,8,2,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,5,8,7,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,3,7,2,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,3,4,8,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,4,2,3,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,4,2,3,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,5,3,8,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,8,5,3,7,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,3,8,5,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,2,8,5,3,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,2,7,3,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,5,3,7,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,4,2,3,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,3,7,1,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,4,7,1,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,3,4,8,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,5,7,4,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,5,4,7,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,3,5,7,1,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,2,5,1,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,7,2,4,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,7,2,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,3,6,2,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,3,6,8,2,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,7,3,5,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,7,8,3,6,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,5,8,3,6,7,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,8,3,7,2,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,4,6,8,2,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,3,6,8,2,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,6,7,1,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,4,6,7,1,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,6,3,5,7,8,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,5,7,3,6,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,6,8,3,7,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,7,4,8,6,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,2,6,5,1,8,7,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,6,7,2,8,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,6,2,5,3,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,8,2,4,6,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,2,3,6,4,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,8,2,5,3,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,2,5,3,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,2,3,6,4,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,5,2,8,4,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,7,3,5,4,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,8,2,7,3,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,8,2,3,7,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,8,2,3,5,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,1,5,8,4,2,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,5,7,4,2,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,4,5,8,2,3,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,4,1,6,2,8,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,1,7,2,6,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,4,7,5,2,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,5,4,7,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,5,8,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,4,8,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,8,5,2,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,4,1,7,2,3,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,1,8,4,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,1,7,4,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,1,8,4,5,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,8,5,3,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,2,3,8,7,5,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,8,1,4,2,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,3,1,2,7,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,3,1,2,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,1,4,2,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,6,8,5,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,5,4,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,8,5,4,1,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,2,1,4,6,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,1,5,8,3,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,5,6,1,8,4,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,6,8,7,4,2,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,8,5,7,3,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,1,5,8,3,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,1,6,8,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,8,1,2,5,7,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,4,6,2,5,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,6,4,7,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,1,4,7,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,7,8,4,6,2,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,4,8,5,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,1,6,5,4,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,3,1,5,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,4,6,8,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,5,8,6,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,7,1,6,4,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,8,2,7,4,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,2,8,7,4,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,2,7,8,1,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,3,7,5,6,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,3,8,1,7,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,8,7,1,4,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,7,3,8,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,1,4,5,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,6,7,4,5,3,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,7,3,5,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,7,2,8,5,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,8,7,2,4,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,5,7,1,2,4,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,4,1,7,5,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,4,3,7,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,8,2,1,5,7,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,8,4,1,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,4,8,6,5,3,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[7,1,5,6,8,4,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,7,8,1,4,6,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,8,2,5,7,1,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,6,8,5,3,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,6,4,8,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,7,3,2,4,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,6,5,2,8,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,1,6,5,3,4,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,4,2,8,7,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,8,7,5,2,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,7,4,2,3,5,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,6,4,5,2,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,1,3,5,4,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,5,6,3,4,8,7,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,3,6,8,7,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,8,7,3,5,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,7,2,6,4,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,5,4,8,7,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,8,6,1,5,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,6,2,5,3,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,5,2,6,8,1,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,2,7,1,4,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,8,5,3,6,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,1,7,2,4,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,3,4,8,6,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,4,1,3,8,6,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,1,8,6,3,4,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,2,8,3,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,2,3,7,6,4,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,2,4,7,6,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,8,2,5,3,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,5,6,4,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,7,4,8,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,1,3,5,8,2,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,3,1,4,7,5,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,3,8,2,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,8,3,6,7,5,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,1,7,2,8,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,1,4,7,2,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,8,4,7,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,1,3,6,2,8,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,7,4,5,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,1,8,4,5,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,5,7,3,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,4,1,5,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,4,8,6,2,3,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,1,4,6,3,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,5,6,8,1,3,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,1,3,2,8,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,4,2,3,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,6,5,1,4,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,3,4,8,6,5,2,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,1,8,6,5,3,2,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,8,5,2,7,3,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,8,5,3,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,8,4,3,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,7,5,2,3,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,2,8,4,6,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,4,3,6,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,5,1,2,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,6,8,3,4,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,6,8,4,7,2,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,6,3,8,4,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,3,8,4,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,2,3,6,5,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,7,5,8,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,3,6,4,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,5,6,8,3,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,8,1,2,6,4,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,8,3,2,7,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,5,7,2,8,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,1,2,8,4,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,8,3,6,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,2,7,4,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,5,8,2,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,7,3,6,4,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,6,4,8,2,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,5,6,4,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,3,6,2,5,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,4,6,3,5,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,5,1,6,4,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,1,4,2,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,6,3,1,7,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,6,5,2,7,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,6,4,3,8,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,6,3,5,8,7,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,5,1,8,4,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,6,1,8,5,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,4,6,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,7,5,1,8,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,2,5,3,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,7,5,4,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,2,7,6,4,8,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,7,3,6,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,6,1,8,5,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,5,4,8,7,6,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,2,5,8,4,7,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,6,8,5,4,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,6,8,5,2,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,5,7,4,8,2,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,7,6,8,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,6,8,3,5,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,6,8,5,2,4,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,6,8,5,4,3,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,5,8,4,3,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,5,8,2,4,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,6,8,2,5,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,4,6,8,3,2,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,5,7,4,8,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,1,7,5,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,6,7,5,8,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,7,5,6,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,6,5,8,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,6,2,8,1,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,4,6,8,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,4,6,8,1,2,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,4,7,5,8,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,6,7,4,8,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,6,4,7,1,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,6,7,3,8,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,5,7,3,8,6,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,1,5,7,6,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,4,6,8,2,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,6,1,8,7,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,6,5,8,7,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,3,6,5,8,7,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,4,6,8,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,7,5,6,8,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,1,6,7,5,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,6,2,7,5,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,7,4,8,2,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,6,8,3,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,6,8,3,5,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,6,8,2,5,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,5,8,2,7,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,5,8,4,7,6,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,4,8,7,3,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,5,8,7,4,3,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,3,5,8,7,2,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,3,7,6,8,5,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,1,2,8,6,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,1,7,6,8,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,2,6,8,5,7,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,5,8,7,4,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,4,8,7,6,3,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[6,4,5,7,2,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,4,7,2,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,7,4,6,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,2,7,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,3,4,7,1,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,3,4,5,8,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,7,4,5,6,8,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,5,7,3,6,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,7,6,2,3,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,3,5,2,4,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,1,2,8,4,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,2,3,7,1,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,2,8,4,5,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,1,2,8,4,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,1,3,8,5,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,2,3,1,8,4,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,2,7,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,2,4,7,1,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,2,3,6,1,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,6,3,7,2,4,5,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,1,7,2,4,5,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,5,7,2,3,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,7,5,8,2,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,8,3,4,5,6,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,4,5,8,3,6,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,5,7,1,8,3,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,2,7,1,8,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,1,3,8,5,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,2,8,4,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,3,6,8,2,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,3,4,6,8,2,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,6,3,8,7,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,4,5,8,7,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,4,8,7,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,2,8,7,1,4,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,8,7,2,4,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,2,3,5,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,8,2,6,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,2,8,7,1,4,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,3,6,2,4,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,8,7,2,3,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,6,2,4,7,1,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,7,2,5,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,1,6,4,8,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,8,5,3,2,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,2,5,7,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,8,3,7,5,4,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,1,3,2,8,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,1,2,8,4,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,3,8,7,4,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,8,7,1,2,5,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,2,8,5,4,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,2,4,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,1,6,5,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,1,2,4,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,5,2,7,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,8,4,7,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,5,1,2,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,4,6,2,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,4,6,5,2,8,7,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,5,6,1,8,7,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,4,5,8,7,2,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,4,7,2,6,3,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,4,7,5,2,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,4,7,2,3,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,5,7,3,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,5,1,7,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,4,8,7,3,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,4,8,5,7,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,8,1,6,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,8,6,3,7,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,4,7,6,3,8,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,3,7,5,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,3,5,8,6,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,7,4,3,8,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,8,3,7,6,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,3,8,2,1,6,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,4,2,7,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,1,2,5,7,6,4,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,2,7,6,5,4,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,8,1,6,7,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,2,6,8,5,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,3,8,5,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,1,7,5,6,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,3,6,5,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,4,3,6,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,8,5,4,3,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,8,4,5,3,2,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,5,4,3,1,6,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,1,6,3,4,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,7,1,4,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,1,4,2,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,8,5,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,5,1,2,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,5,6,7,2,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,1,7,6,2,4,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,1,4,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,5,4,7,1,3,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,6,4,5,7,2,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,3,6,1,7,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,6,5,7,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,5,3,6,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,4,1,6,5,8,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,2,5,8,6,7,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,2,1,5,8,7,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,4,6,1,7,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,3,6,8,7,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,4,6,1,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,5,7,6,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,6,3,7,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,3,6,5,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,6,2,5,4,1,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,7,2,6,5,4,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,2,5,4,3,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,7,5,2,6,3,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,6,4,7,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,3,7,5,4,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,3,4,7,6,2,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,8,3,6,1,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,7,2,5,1,6,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,2,6,5,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,2,5,4,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,5,2,6,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,1,3,7,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,3,7,5,2,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,3,6,2,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,3,6,2,7,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,2,4,7,3,8,6,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[7,1,8,2,6,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,8,6,2,7,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,7,8,2,6,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,6,1,8,2,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,2,7,8,1,6,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,8,6,1,7,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,8,1,6,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,7,2,6,5,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,8,7,1,6,5,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,8,7,1,6,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,7,5,1,6,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,7,8,5,1,4,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,6,3,8,4,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,3,8,5,4,1,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,4,8,6,5,1,7,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,3,7,5,1,6,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,8,6,2,7,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,4,6,7,1,5,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,6,4,7,8,1,3,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,6,5,1,2,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,3,5,1,2,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,4,6,2,3,8,7,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,2,7,4,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,2,1,6,3,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,3,1,7,6,4,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,2,1,7,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,7,1,2,8,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,7,5,1,2,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,7,1,6,2,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,1,3,8,6,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,7,2,3,8,6,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,8,1,2,6,5,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,8,1,6,2,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,5,1,2,7,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,8,1,2,7,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,1,3,7,4,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,7,3,6,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,4,2,8,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,5,3,8,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,4,7,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,3,4,7,5,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,3,5,4,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,3,5,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,3,6,4,2,8,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,4,5,2,8,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,1,8,2,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,4,2,7,3,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,4,1,7,2,6,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,8,3,4,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,2,1,8,3,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,3,4,8,2,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,5,3,8,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,3,1,8,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,4,2,7,3,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,6,4,7,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,2,5,7,4,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,3,2,6,4,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,3,1,7,2,5,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,2,6,4,3,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,1,6,2,5,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,3,5,6,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,6,1,7,4,5,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,3,7,2,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,7,6,8,3,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,1,5,8,4,2,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,8,4,5,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,8,5,3,4,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,7,4,2,5,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,7,3,4,6,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,8,4,3,5,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,2,8,3,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,1,7,3,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,5,8,4,2,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,3,1,6,8,2,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,7,4,8,3,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,8,2,7,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,7,3,4,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,5,3,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,8,3,7,6,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,3,2,6,4,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,2,4,7,5,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,8,2,6,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,8,2,7,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,8,7,3,4,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,2,8,6,3,5,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,1,7,2,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,7,4,5,6,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,6,4,3,5,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,3,5,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,6,5,2,4,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,7,4,6,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,3,7,6,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,7,5,3,2,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,7,2,5,4,3,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,8,3,2,5,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,4,5,2,3,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,7,8,4,3,6,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,3,8,1,5,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,1,8,5,4,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,3,1,7,5,4,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,5,7,4,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,6,8,4,3,7,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,4,7,5,8,1,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,4,7,1,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,1,8,7,6,4,3]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,8,5,7,6,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,6,7,5,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,7,5,6,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,5,4,8,2,1,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,7,2,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,7,4,8,2,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,7,3,2,8,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,8,3,2,7,6,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,5,7,4,2,6,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,1,5,7,6,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,5,1,7,6,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,5,4,7,1,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,7,5,6,1,2,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,5,8,6,7,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,5,4,6,1,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,5,1,6,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,7,3,8,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,2,7,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,2,8,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,3,2,8,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,2,4,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,7,2,5,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,5,2,8,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,2,8,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,2,7,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,2,4,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,6,2,4,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,8,2,4,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,8,2,5,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,6,2,5,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,6,2,7,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,8,2,7,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,7,2,8,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,7,2,5,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,7,2,4,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,2,4,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,5,2,4,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,2,4,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,2,5,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,2,8,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,2,6,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,2,7,5,4,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,2,7,4,3,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,6,4,7,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,4,2,6,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,4,8,1,5,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,2,6,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,4,3,6,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,8,3,2,4,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,5,4,3,6,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,5,4,3,7,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,5,4,7,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,4,2,5,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,4,2,6,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,4,8,2,3,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,8,1,5,6,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,7,2,6,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,7,4,2,6,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,6,3,2,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,3,7,1,2,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,4,3,7,1,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,4,2,7,1,6,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,1,7,3,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,8,5,7,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,4,2,8,3,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,4,3,8,2,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,4,3,8,7,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,4,8,6,1,3,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,3,8,5,4,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,3,8,1,7,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,8,3,1,7,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,8,2,1,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,3,8,1,6,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,3,7,1,6,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,8,6,1,5,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,8,3,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,1,7,8,2,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,2,1,6,7,3,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,1,5,2,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,7,3,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,1,5,3,2,8,6,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,2,8,7,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,1,7,8,5,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,7,8,2,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,3,1,6,7,2,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,4,2,6,3,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,1,5,2,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,7,1,2,5,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,8,1,3,2,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,2,1,3,5,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,3,7,1,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,3,6,1,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,7,3,1,8,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,7,1,3,5,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,2,8,3,1,7,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,5,7,1,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,2,7,3,6,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,7,8,2,3,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,3,4,7,8,6,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,5,4,6,8,7,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,4,6,8,2,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,7,3,2,4,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,3,6,2,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,3,7,2,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,4,7,8,1,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,2,5,7,6,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,2,8,6,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,3,1,8,2,6,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,1,8,3,2,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,5,7,6,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,5,7,6,2,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,5,1,8,6,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,2,1,8,3,6,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,4,2,1,8,7,5,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,5,4,2,1,8,3]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,6,5,4,8,1,3,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,5,8,2,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,6,5,4,1,8,3,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,6,5,2,8,1,4,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,5,8,4,1,3,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,5,2,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,6,3,2,1,5,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,8,2,4,5,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,7,2,5,1,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,8,4,1,5,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,7,1,5,2,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,7,3,5,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,4,7,1,5,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,6,7,2,3,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,5,4,6,7,8,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,5,4,6,7,2,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,2,4,6,7,1,3,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,5,4,6,7,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,6,7,4,5,1,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,2,7,4,5,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,6,7,1,3,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,2,6,7,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,1,7,4,5,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,7,4,5,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,1,6,7,2,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,5,2,4,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,5,2,1,4,3,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[1,3,6,7,5,2,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,3,4,1,6,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,4,1,6,5,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,4,1,5,6,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,2,5,1,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,5,4,1,3,2,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,3,4,1,5,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,3,6,7,2,5,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,7,4,6,2,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,1,7,2,6,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,1,4,7,3,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,2,1,7,4,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,3,4,5,8,1,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,5,1,6,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,7,5,4,6,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,1,4,6,5,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,4,6,5,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,7,5,4,6,8,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,1,4,7,2,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,1,7,5,6,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,1,7,6,5,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,4,5,2,6,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,7,5,2,6,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,5,2,6,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,1,2,7,4,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,1,4,2,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,5,2,6,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,1,5,2,6,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,4,6,5,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,4,6,1,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,6,1,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,3,6,7,1,5,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,6,7,5,1,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,3,2,6,7,1,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,5,4,6,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,4,6,5,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,4,5,8,6,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,3,4,5,8,1,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,3,4,5,8,1,2,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,3,4,5,8,2,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,3,4,5,8,2,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,3,4,5,8,6,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,7,4,6,5,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,1,5,4,6,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,4,6,1,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,3,4,5,8,1,2,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,3,4,5,8,2,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,3,4,5,8,2,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,7,6,1,8,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,1,7,5,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,8,2,6,1,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,6,4,2,8,3,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,4,2,7,5,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,7,3,6,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,6,1,7,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,7,1,8,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,8,3,6,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,4,3,6,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,1,7,3,5,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,8,6,3,5,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,3,5,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,3,1,4,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,1,8,3,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,1,8,6,3,5,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,1,7,3,5,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,7,3,1,4,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,1,7,3,6,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,7,5,6,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,8,5,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,1,8,3,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,6,8,3,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,8,3,5,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,1,5,7,4,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,2,4,1,7,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,4,7,5,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,3,6,1,7,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,1,7,3,5,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,8,6,3,1,7,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,4,7,1,8,5,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,8,5,1,6,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,2,1,7,3,4,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,1,7,8,3,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,1,8,3,6,4,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,1,6,7,4,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,1,6,8,4,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,1,8,3,7,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,8,3,6,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,8,5,1,6,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,8,5,6,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,8,3,7,2,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,8,1,5,7,2,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,6,8,4,7,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,1,5,8,2,4,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,4,8,3,6,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,1,2,7,8,3,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,5,7,4,8,6,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,3,8,4,7,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,7,1,2,5,4,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,8,1,2,3,7,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,2,8,4,3,5,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,5,3,7,6,4,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,1,2,8,7,4,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,6,2,8,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,2,6,3,8,5,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,8,5,3,6,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,3,8,5,4,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,1,2,7,8,6,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,6,2,8,4,3,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,4,2,7,3,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,3,2,8,4,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,1,7,8,6,2,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,8,7,3,5,6,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,2,8,7,4,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,3,2,6,4,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,2,8,4,3,7,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,5,1,7,2,4,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,8,7,4,6,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,6,4,7,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,8,2,7,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,2,5,3,8,6,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,7,5,3,6,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,6,3,7,5,4,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,3,7,5,4,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,7,4,8,6,5,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,2,7,6,4,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,7,6,5,1,4,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,1,6,3,2,5,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,6,3,1,5,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,4,3,6,5,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,4,6,5,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,2,1,6,5,3,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,1,4,3,5,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,1,3,5,2,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,8,6,3,4,5,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,6,7,4,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,2,1,4,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,7,1,5,2,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,7,4,1,5,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,2,7,1,5,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,1,2,8,6,5,4,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,8,2,7,4,3,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,8,2,3,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,8,5,3,1,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,8,6,1,3,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,8,1,6,3,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,2,8,6,4,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,3,2,6,4,8,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,1,6,3,5,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,5,3,8,6,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,5,3,2,7,6,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,4,5,2,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,2,7,6,5,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,1,6,7,8,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,8,4,3,6,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,7,3,2,8,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,3,6,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,3,2,1,4,8,6,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,3,1,4,2,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,4,7,8,1,2,6,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,6,7,8,1,4,5,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,6,2,8,1,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,6,8,5,1,4,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,1,6,4,8,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,2,6,8,5,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,5,8,4,6,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,2,8,4,1,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,8,2,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,8,5,2,4,6,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,2,8,3,5,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,4,8,2,5,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,5,4,8,3,6,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,7,4,8,5,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,5,4,8,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,2,5,8,4,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,6,3,7,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,6,3,8,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,6,8,3,4,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,4,6,2,7,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,6,7,2,4,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,6,8,4,3,1,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,5,7,8,4,1,3,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[6,5,7,8,4,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,6,8,2,4,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,6,2,8,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,2,6,8,5,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,5,6,8,2,4,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,5,6,8,4,2,1,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,6,7,8,1,4,5,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,6,7,8,1,4,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,5,7,8,2,1,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,6,7,8,1,4,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,5,7,8,3,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,7,8,3,1,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,4,7,3,8,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,4,7,3,8,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,7,3,8,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,3,8,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,2,5,4,8,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,5,2,3,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,5,3,2,8,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,3,8,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,7,3,8,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,7,8,3,1,6,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,5,7,8,3,1,2,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,5,6,8,2,3,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,4,6,2,8,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,6,8,4,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,7,2,8,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,5,7,8,2,1,3,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,6,7,8,1,3,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,6,7,8,1,3,5,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,6,7,8,1,3,5,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,6,7,8,1,5,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,6,7,8,1,5,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,6,7,8,1,2,5,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,5,7,8,2,1,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,4,7,2,8,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,2,7,8,1,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,2,7,8,1,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,5,7,8,2,1,6,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,6,7,8,1,2,5,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,6,7,8,1,5,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,6,7,8,1,5,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,6,7,8,1,5,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,2,7,1,5,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,8,6,1,5,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,6,7,5,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,1,3,5,4,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,2,1,5,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,6,4,7,1,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,4,8,2,7,5,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,4,8,2,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,1,6,2,5,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,8,6,2,1,5,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,8,3,6,5,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,7,3,5,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,7,5,1,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,1,7,5,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,5,1,6,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,3,5,6,1,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,6,8,5,1,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,6,8,2,1,5,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,8,2,3,5,7,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,6,1,3,5,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,3,2,5,6,1,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,7,5,2,6,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,2,8,1,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,1,2,7,5,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,6,2,7,1,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,5,1,2,6,3,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,6,2,7,4,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,1,7,8,5,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,7,3,8,4,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,8,4,1,5,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,7,1,8,5,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,2,5,1,6,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,4,5,1,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,8,4,5,6,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,8,3,6,7,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,8,3,7,6,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,8,3,7,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,3,4,8,1,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,3,4,8,1,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,6,3,4,8,5,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,3,5,8,4,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,3,8,4,5,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,3,8,5,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,3,8,5,1,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,4,8,1,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,3,8,4,1,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,3,5,8,1,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,8,2,3,6,1,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,2,3,6,1,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,6,3,7,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,3,5,8,1,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,3,8,4,1,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,4,8,1,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,4,8,1,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,6,5,1,4,2,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,6,4,5,1,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,5,4,1,2,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,5,6,4,1,2,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,6,5,1,2,4,3,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,5,1,3,2,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,5,1,3,4,2,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,2,3,4,5,1,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,6,4,3,1,5,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,6,4,3,1,8,5,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,4,3,1,8,7,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,5,8,4,1,2,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,8,4,1,6,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,8,3,6,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,8,4,1,6,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,8,4,1,7,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,4,2,1,7,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,6,4,2,1,7,5,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,6,4,1,8,7,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,6,5,1,4,3,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,5,1,2,8,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,5,1,8,2,4,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,5,1,8,3,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,5,1,4,8,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,6,4,5,1,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,6,4,1,7,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,8,5,4,1,6,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,5,6,4,1,7,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,4,5,1,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,5,1,8,3,4,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,5,1,8,4,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,1,7,6,2,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,6,2,1,3,5,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,6,1,2,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,5,3,1,4,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,6,1,5,3,2,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,1,4,2,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,4,5,7,8,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,7,1,6,5,2,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,2,5,6,8,1,3,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,1,3,4,2,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,4,5,6,1,8,7,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,4,1,6,5,7,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,8,3,4,7,5,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,2,7,4,3,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,8,5,1,6,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,2,6,4,7,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,6,1,7,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,3,2,1,5,4,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[3,8,5,1,7,2,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,7,1,3,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,1,8,7,4,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,1,8,4,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,3,8,4,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,6,4,3,1,7,2,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,3,7,4,6,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,3,8,6,4,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,5,8,6,7,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[7,4,2,1,8,6,5,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[4,6,7,2,5,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,6,2,5,3,8,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,4,2,8,3,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,4,3,1,8,7,2,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,1,4,3,8,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,6,2,8,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,5,1,7,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,3,1,7,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,2,1,8,6,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,6,8,1,5,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,5,8,3,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,6,8,1,5,2,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,8,7,4,5,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,8,5,7,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,6,8,5,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,4,8,7,5,3,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,6,8,3,7,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,6,8,2,4,1,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,2,8,1,7,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,5,4,8,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,5,3,4,8,1,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,3,2,5,1,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,2,8,1,5,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,8,2,6,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,2,8,3,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,5,8,3,6,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,5,3,6,7,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,5,6,4,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,4,1,6,3,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,1,3,5,7,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,1,4,5,6,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,6,8,3,5,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,6,3,5,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,8,7,6,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,8,4,7,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,4,2,5,3,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,4,8,3,1,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,8,5,6,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,2,5,6,3,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,7,5,6,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,7,5,6,2,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,3,5,6,2,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,2,5,6,4,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,3,5,6,1,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,8,5,2,7,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,2,8,5,1,7,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,4,8,2,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,7,8,6,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,8,5,6,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,8,2,5,6,4,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,8,5,3,7,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,1,5,2,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,2,1,5,3,7,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,6,5,3,7,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,4,6,3,2,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,6,4,1,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,3,5,1,7,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,6,5,1,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,4,6,1,2,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,5,6,1,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,8,4,7,2,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,8,7,5,6,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,7,5,6,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,6,5,1,7,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,7,4,6,2,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,4,6,1,3,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,4,3,7,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,4,2,7,1,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,4,1,3,5,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,4,1,5,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,2,5,3,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,1,5,4,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,2,1,5,6,4,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,8,1,5,6,4,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,4,1,2,5,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,8,1,6,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,4,1,5,2,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,1,5,4,7,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,1,5,3,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,4,1,3,2,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,1,4,3,5,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,3,5,4,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,8,2,5,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,2,6,1,4,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,8,1,6,4,3,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,1,3,8,7,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,5,7,1,3,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,6,8,1,5,7,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,7,1,5,8,4,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,1,6,4,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,6,5,3,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,1,7,6,5,4,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,3,2,7,1,6,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,8,7,3,2,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,1,7,2,8,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,1,8,6,5,4,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,7,6,1,4,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,8,5,1,4,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,3,5,8,2,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,6,2,1,5,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,2,8,1,6,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[7,4,6,2,1,8,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,4,5,2,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,8,5,1,7,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,7,5,1,3,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,7,6,1,5,3,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,7,6,3,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,6,4,2,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,1,8,7,6,4,3,2]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,5,2,1,7,6,4,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,2,1,6,3,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,1,8,6,3,2,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,1,7,4,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,8,6,3,7,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,2,5,7,3,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,4,6,8,5,7,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,4,8,2,7,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,7,3,6,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,4,7,3,6,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,2,4,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,8,4,2,7,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,7,4,2,8,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,5,2,7,1,3,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[6,4,7,3,1,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,4,3,8,6,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,8,4,6,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,4,8,3,5,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,5,3,8,2,4,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,6,3,7,4,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,3,8,5,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,8,1,3,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,8,6,3,1,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,7,6,5,3,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,7,2,4,6,5,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,1,3,4,5,2,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,6,8,4,2,5,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,2,8,4,1,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,4,8,5,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,2,7,8,5,1,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,8,1,5,4,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,8,5,3,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,4,8,5,2,6,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,1,8,4,3,7,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,1,4,2,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,5,3,6,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,8,5,3,2,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,4,6,3,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,6,4,1,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,4,3,1,8,2,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[3,5,2,1,8,7,6,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,5,3,2,8,6,4,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,2,7,1,4,5,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,7,3,6,2,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,6,3,2,1,8,5,4]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[5,2,3,4,7,1,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,7,3,1,5,4,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,1,7,2,3,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,1,6,5,4,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,1,5,6,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,8,1,6,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,1,5,4,7,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,5,1,4,6,7,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,2,1,4,7,6,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,8,2,1,3,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,4,1,3,6,2,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,4,1,3,6,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,1,3,5,4,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,4,6,2,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,1,3,2,5,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,2,4,5,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,7,2,5,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,7,3,1,5,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,8,1,2,4,7,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,8,1,3,5,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,1,8,2,3,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,8,4,2,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,1,8,4,6,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,3,5,7,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,7,2,6,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,7,3,2,6,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,7,2,3,6,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,6,3,4,7,5,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,4,2,7,5,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,2,7,1,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,1,6,5,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,2,8,5,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,1,4,8,5,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,6,3,1,7,4,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,4,1,8,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,2,8,7,1,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,2,4,8,1,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,3,8,5,2,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,2,6,7,1,8,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,3,1,7,8,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,1,6,2,7,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,3,4,8,7,5,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,8,3,7,6,5,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,8,7,5,4,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,3,8,7,6,4,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,8,7,6,1,5,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,2,8,7,6,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,8,7,5,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,2,6,5,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,8,7,5,4,3,2]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[3,1,8,7,6,5,4,2]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,8,2,6,1,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,2,8,7,1,5,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,8,1,7,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,2,7,6,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,7,2,1,6,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,5,8,7,1,4,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,1,7,6,5,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[5,4,1,8,7,6,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,4,8,1,7,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,4,1,6,5,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,8,3,1,6,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,3,8,1,7,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,1,8,7,6,4,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,8,2,1,6,5,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,5,3,1,8,7,4,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,3,1,8,7,5,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,3,1,8,7,6,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,2,1,8,6,4,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,2,1,8,7,6,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,3,2,1,8,6,5,4]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[6,3,2,1,8,7,5,4]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,1,4,2,3,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,1,8,2,3,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,2,3,8,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,8,2,3,6,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,2,3,6,4,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,3,8,4,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,2,3,6,1,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,2,3,8,1,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,6,4,3,8,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,4,3,6,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,3,8,4,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,3,6,4,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,6,2,4,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,1,3,8,4,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,2,1,3,6,4,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,8,2,4,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,3,8,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,4,7,8,5,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,4,2,7,5,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,4,2,7,1,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,7,2,5,6,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,4,8,5,3,7,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,5,4,2,7,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,2,5,3,6,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,3,6,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,5,2,4,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,4,6,2,8,5,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,8,1,4,2,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,8,5,2,1,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,8,5,3,1,6,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,1,3,5,8,2,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,2,8,5,7,3,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,6,8,7,5,2,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,8,2,5,4,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,7,3,5,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,6,2,1,7,5,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,3,7,8,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,2,3,7,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,6,3,7,1,2,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,2,4,5,1,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,8,2,5,4,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,4,2,6,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,6,3,8,7,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,2,7,4,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,8,5,1,7,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,6,8,1,2,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,3,5,2,8,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,8,4,2,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,8,1,7,5,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,2,5,7,3,6,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,8,6,7,5,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,6,7,5,3,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,5,8,7,2,6,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,4,8,6,2,3,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,7,6,1,3,5,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,1,8,2,5,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,8,6,1,3,5,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,1,3,6,5,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,6,3,5,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,4,1,3,8,5,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,1,3,5,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,6,1,3,5,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,1,3,5,8,7,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,1,4,3,5,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,1,3,6,5,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,1,8,3,5,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,1,3,8,5,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,4,3,8,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,4,3,8,5,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,1,4,3,6,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,1,3,6,5,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,1,3,6,5,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,1,6,3,5,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,1,4,3,5,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,1,6,3,5,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,4,6,3,5,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,4,6,3,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,4,8,3,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,1,8,3,5,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,6,8,1,3,5,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,6,8,1,3,5,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,6,1,8,3,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,6,8,3,5,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,6,3,8,5,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,1,3,8,5,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,1,8,3,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,6,8,3,5,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,1,3,6,8,5,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,3,6,8,5,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,3,8,6,5,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,8,3,6,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,1,4,3,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,1,6,3,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,1,3,6,5,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,8,3,6,5,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,8,6,3,5,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,1,8,6,3,5,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,1,6,3,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,1,4,3,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,8,4,3,5,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,6,8,4,3,5,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,8,6,4,3,5,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,1,6,4,3,5,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,1,4,3,5,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,8,6,5,2,1,4,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,7,4,1,8,6,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,6,4,2,8,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,4,2,7,3,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,1,4,6,3,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,1,4,6,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,7,4,5,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,7,4,6,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,8,4,1,7,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,6,1,7,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,4,1,8,7,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,5,8,4,6,7,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,8,4,5,7,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,7,8,4,5,6,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,8,1,4,5,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,1,4,5,3,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,1,5,4,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,1,5,4,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,1,5,4,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,1,4,5,3,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,1,4,6,3,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,4,2,7,3,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,7,2,8,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,7,2,8,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,4,2,8,3,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,1,4,6,3,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,8,1,5,4,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,5,4,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,1,5,4,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,1,4,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,8,1,4,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,3,1,4,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,1,5,4,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,1,2,7,6,5,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,4,1,2,6,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,8,3,1,4,7,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,7,2,8,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,1,4,7,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,1,4,5,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,8,1,5,4,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,5,4,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,1,5,4,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,1,4,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,3,1,4,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,3,1,4,6,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,4,2,6,5,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,8,7,3,4,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,3,1,4,6,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,7,3,1,4,5,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,1,5,4,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,8,1,5,4,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,1,4,7,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,4,2,7,5,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,4,7,2,8,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,7,1,4,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,3,1,4,7,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,7,1,5,4,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,1,2,8,5,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,1,2,5,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,7,1,5,4,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,3,8,1,4,5,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,3,1,4,5,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,1,5,4,2,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,7,6,3,5,2,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,6,3,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,7,4,3,2,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,7,6,2,5,4,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,4,7,3,2,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,3,6,5,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,8,4,3,2,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,4,7,6,3,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,8,7,4,3,2,1,6]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,5,2,7,3,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,2,6,3,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,7,8,6,5,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,7,2,5,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,2,1,5,6,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,6,2,5,8,4,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,1,8,7,4,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,1,6,8,5,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,5,8,6,2,3,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,8,3,1,6,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,2,7,1,8,6,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,1,3,8,7,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,5,2,8,1,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,8,3,5,1,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,3,8,7,1,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,4,3,7,2,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,3,7,4,2,6,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,6,5,1,7,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,3,2,8,4,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,8,3,4,1,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,2,8,3,1,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,8,4,3,1,7,6,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,5,3,1,7,6,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,6,4,1,7,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,8,7,5,1,6,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,3,7,5,2,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,7,6,2,5,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,7,6,1,5,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,4,8,6,2,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,8,5,2,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,8,4,2,1,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,4,3,8,2,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,7,8,4,1,2,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,7,8,5,1,2,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,7,8,6,1,2,5,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,7,4,6,3,5,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,7,8,6,1,2,4,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,4,7,8,3,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,4,8,2,1,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,6,4,8,3,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,8,6,2,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,8,7,3,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,4,8,3,1,5,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,3,2,4,8,1,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,3,8,4,1,6,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,8,5,1,6,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,4,8,7,3,1,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,4,7,3,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,4,7,2,5,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,8,7,1,5,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,8,6,1,5,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,8,6,1,4,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,3,5,7,2,4,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,4,6,7,2,3,5,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,6,8,7,1,3,5,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,8,5,1,3,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,8,4,1,3,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,8,3,1,4,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,6,8,7,1,3,4,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,4,6,8,2,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,3,5,4,1,8,6,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,6,4,8,1,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,8,4,6,3,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,6,8,1,5,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,5,6,1,4,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,5,6,1,4,7,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,3,5,1,6,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,7,6,1,8,5,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,7,6,8,1,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,7,6,3,2,5,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,7,8,6,2,3,4,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,7,6,1,8,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,5,1,7,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,3,4,7,6,1,5,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[7,3,5,8,4,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,8,4,5,2,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,5,2,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,3,5,8,4,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,7,6,4,8,5,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,5,4,6,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,5,4,7,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,5,4,7,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,4,1,5,6,8,7,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,7,1,6,8,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,1,8,6,4,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,4,3,6,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,3,1,8,6,4,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,1,6,8,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,3,5,4,7,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,5,4,6,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,7,6,4,8,5,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,8,4,5,2,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,5,8,4,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,3,4,6,5,8,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,4,7,5,1,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,4,7,5,1,6,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,3,4,7,1,6,5,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,4,7,1,6,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,4,6,1,8,7,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,3,5,8,4,2,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,8,5,3,2,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,4,8,5,3,2,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,5,8,4,2,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,2,4,6,8,3,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,5,7,4,6,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,2,8,4,6,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,5,4,6,7,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,3,4,5,7,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,5,7,4,6,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,1,7,8,3,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,2,7,8,3,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,4,6,8,3,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,8,4,6,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,6,4,5,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,3,5,4,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,6,2,4,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,7,1,2,4,3,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,7,6,2,4,3,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,6,3,4,5,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,2,5,4,3,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,7,2,4,5,3,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,8,2,4,7,3,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,3,2,4,7,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,1,6,3,4,5,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,2,5,4,3,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,4,8,7,5,2,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,2,8,6,1,5,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,1,2,4,3,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,7,3,6,4,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,7,2,5,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,6,2,4,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,2,8,6,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,2,5,1,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,4,1,8,6,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,1,8,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,3,6,1,4,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,2,6,3,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,3,6,4,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,3,6,4,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,6,3,1,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,4,1,3,8,2,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,7,5,8,3,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,3,6,1,4,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,7,2,5,8,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,2,3,5,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,4,8,1,3,6,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,1,4,7,3,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,6,3,7,1,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,3,8,1,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,4,8,1,3,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,4,7,1,3,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,3,1,8,5,4,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,6,5,1,3,4,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,1,7,6,3,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,4,7,6,1,8,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,2,6,7,1,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,8,4,7,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,7,5,1,3,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,1,6,5,2,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,2,8,3,4,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,8,3,1,7,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,2,5,6,1,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,4,2,5,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,3,8,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,1,4,7,2,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,3,2,1,5,7,4,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,8,3,6,4,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,6,4,8,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,6,4,7,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,2,8,3,5,7,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,8,3,2,5,7,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,5,1,7,4,2,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,4,8,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,1,7,3,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,7,3,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,7,3,4,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,1,6,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,7,1,6,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,4,2,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,1,7,6,5,3,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,2,8,6,5,1,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,2,8,5,1,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,4,7,1,5,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,4,8,1,5,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,6,4,2,3,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,3,8,7,5,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,8,7,1,6,5,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,3,8,1,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,7,1,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,3,7,8,5,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,4,7,8,1,5,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,7,4,6,1,5,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,7,8,1,4,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,8,6,1,5,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,4,7,8,1,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,2,4,8,7,1,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,8,7,6,1,5,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,7,6,1,4,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,5,7,1,4,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,6,7,4,2,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,7,4,8,1,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,7,6,1,5,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,2,4,7,1,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,2,4,8,1,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,5,3,7,1,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,6,7,1,5,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,6,8,1,5,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,6,8,4,2,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,3,7,5,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,5,8,1,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,7,1,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,7,1,5,8,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,2,4,7,6,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,7,6,8,1,5,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,5,6,7,1,4,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,7,5,1,4,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,5,1,4,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,7,5,1,4,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,8,7,1,4,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,7,1,5,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,6,7,1,5,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,7,8,5,1,4,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,8,6,5,1,4,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,7,5,4,2,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,8,5,4,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,1,2,6,3,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,7,1,5,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,1,5,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,7,1,5,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,1,5,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,5,3,8,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,1,3,6,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,6,8,1,5,4,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,3,1,5,4,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,3,1,5,4,2,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,6,2,1,5,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,2,1,7,5,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,8,1,5,7,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,1,3,2,8,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,6,2,8,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,1,2,6,3,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,8,1,5,3,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,2,1,5,3,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,2,1,8,5,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,2,1,4,5,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,5,6,1,4,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,7,8,6,1,4,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,7,4,1,6,5,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,6,4,5,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,1,4,7,6,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,4,1,7,5,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,8,7,1,4,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,8,5,7,1,4,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,5,7,1,4,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,6,1,4,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,7,8,1,4,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,3,1,5,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,8,1,6,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,4,1,8,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,1,4,8,6,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,1,6,3,4,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,5,8,4,3,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,1,6,4,3,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,3,1,8,4,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,1,5,4,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,6,1,4,5,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,8,1,4,5,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,1,5,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,8,6,1,5,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,2,1,5,6,3,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,2,5,8,3,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,5,6,7,1,4,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,6,8,5,1,4,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,7,5,1,4,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,6,7,1,4,5,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,1,7,4,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,5,6,4,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,6,5,4,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,6,1,4,5,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,6,8,1,4,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,6,5,1,4,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,3,1,6,5,8,7,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,6,2,1,8,7,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,7,2,8,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,5,8,3,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,2,4,5,1,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,4,5,2,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,6,4,5,2,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,4,5,8,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,4,2,6,3,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,4,5,2,1,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,1,8,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,4,1,6,3,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,4,8,6,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,4,8,6,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,3,5,6,7,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,3,5,6,7,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,8,1,5,6,7,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,8,4,3,6,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,8,4,1,7,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,8,4,6,7,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,8,3,6,7,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,3,8,2,1,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,4,2,6,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,2,5,6,7,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,1,5,6,7,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,2,5,6,7,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,1,4,3,6,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,4,3,6,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,1,8,5,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,1,8,2,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,5,8,2,7,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,4,8,6,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,1,4,8,6,2,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,6,4,5,8,1,3,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,6,4,5,8,2,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,3,6,1,8,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,6,5,8,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,3,6,7,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,3,5,2,1,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,8,5,6,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,8,5,6,7,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,3,8,6,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,5,8,6,7,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,3,5,8,1,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,4,8,6,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,8,5,6,7,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,8,5,6,7,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,1,5,6,3,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,1,4,3,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,4,2,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,1,5,6,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,1,5,6,8,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,5,2,6,7,3,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,2,6,3,7,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,7,3,2,5,6,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,4,6,2,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,4,2,8,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,2,3,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,7,2,8,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,2,4,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,5,1,8,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,6,1,4,5,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,6,1,3,2,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,2,4,3,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,4,5,1,6,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,6,4,1,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,3,1,2,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,6,2,3,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,4,2,1,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,3,4,2,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,2,3,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,5,3,1,2,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,7,5,4,1,8,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,4,3,8,7,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,5,4,1,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,5,7,3,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,5,7,3,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,1,8,4,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,2,4,7,5,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,2,4,7,5,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,6,3,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,1,6,3,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,3,5,8,6,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,7,6,8,3,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,1,7,3,8,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,8,1,7,4,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,1,7,4,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,8,6,2,1,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,2,1,3,7,5,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,2,1,6,3,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,6,7,5,2,1,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,6,7,5,2,1,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,3,4,2,6,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,8,6,2,7,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,4,2,6,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,7,5,2,4,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,6,7,5,2,4,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,1,7,3,6,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,1,7,3,6,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,7,6,8,4,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,1,7,4,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,8,6,2,4,5,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,2,1,3,8,6,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,2,1,3,7,6,5,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,8,1,7,3,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,8,6,3,5,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,2,1,8,3,7,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,8,2,4,1,3,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,1,5,4,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,3,5,8,7,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,6,1,4,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,6,8,4,1,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,7,5,1,8,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,6,2,4,1,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,6,1,4,8,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,8,4,1,5,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,1,6,8,4,5,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,4,6,5,2,8,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,5,6,4,2,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,7,4,6,8,1,3,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,8,1,4,6,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,1,5,7,4,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,8,4,6,7,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,1,8,4,7,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,8,6,1,7,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,8,5,1,6,7,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,7,1,4,2,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,4,2,6,1,5,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,8,5,2,1,6,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,1,8,4,2,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,4,6,2,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,3,1,4,6,2,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,1,8,2,5,6,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,1,8,2,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,2,8,4,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,5,8,6,1,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,2,4,3,6,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,8,5,7,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,6,2,8,5,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,1,8,4,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,8,7,1,4,6,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,2,7,1,5,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,5,3,6,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,1,5,6,2,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,7,5,1,6,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,3,6,5,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,7,2,4,1,6,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,8,7,2,3,6,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,8,2,6,4,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,3,8,2,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,7,3,6,4,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,1,5,8,3,2,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,6,2,8,4,3,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,8,7,2,4,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,8,3,7,2,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,4,7,3,2,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,7,8,1,3,2,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,2,1,4,7,3,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,1,3,8,4,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,4,7,5,6,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,8,7,5,6,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,5,3,8,4,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,5,7,3,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,8,5,2,7,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,8,3,4,5,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,5,7,3,4,8,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,7,8,5,3,6,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,7,6,3,4,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,1,8,7,2,6,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,7,6,1,4,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,1,7,2,3,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,7,2,3,6,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,1,8,2,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,7,8,2,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,1,6,5,8,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,5,1,6,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,6,1,4,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,3,6,1,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,6,1,2,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,1,2,8,5,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,8,1,5,2,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,2,5,3,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,6,8,7,5,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,4,1,8,2,7,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,4,1,8,2,7,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,7,4,1,2,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,8,1,2,5,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,3,1,4,8,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,3,8,7,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,1,6,8,2,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,7,1,2,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,7,4,1,2,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,4,1,2,5,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,6,3,5,7,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,6,3,7,2,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,6,2,5,3,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,3,4,5,1,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,8,3,4,2,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,4,1,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,2,3,1,6,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,2,4,6,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,2,4,3,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,8,2,3,1,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,1,4,3,7,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,3,5,7,2,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,1,4,7,5,3,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,3,6,2,5,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,3,6,2,4,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,8,3,7,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,8,2,5,6,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,5,8,2,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,2,8,1,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,5,8,1,4,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,8,5,1,6,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,7,1,4,6,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,3,8,2,5,7,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,8,7,1,6,4,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,7,1,5,6,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,4,8,5,6,1,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,7,4,1,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,8,6,2,7,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,4,5,7,1,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,6,8,4,1,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,2,3,1,5,4,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,3,1,4,6,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,1,3,2,4,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,1,3,2,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,1,4,5,3,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,4,1,5,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,6,1,3,2,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,7,1,2,6,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,4,1,2,6,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,1,4,2,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,3,5,6,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,6,1,2,4,3,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,8,1,2,5,3,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,6,7,5,3,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,7,5,3,2,8,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,7,5,3,8,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,6,5,7,2,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,8,2,6,5,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,5,7,6,3,4,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,3,4,8,2,5,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,3,8,2,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,8,3,2,5,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,8,3,5,7,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,4,8,3,5,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,8,4,2,6,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,8,2,3,5,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,5,7,3,8,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,7,5,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,7,5,2,1,8,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,7,5,2,8,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,8,3,1,7,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,4,8,3,2,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,7,1,8,6,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,6,8,2,1,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,8,2,5,6,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,2,8,6,4,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,2,5,7,3,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,4,2,5,3,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,1,2,8,5,6,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,1,6,8,3,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,2,6,8,4,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,5,6,8,3,4,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,8,1,6,3,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,1,6,8,3,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,7,3,8,2,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,4,3,7,8,2,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,3,1,7,8,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,5,3,1,7,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,1,3,5,4,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,2,8,1,4,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,3,8,4,6,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,5,7,3,8,6,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,6,3,7,8,5,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,3,6,7,8,4,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,5,3,6,7,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,1,7,3,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,3,7,1,8,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,2,4,8,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,1,4,7,3,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,1,3,2,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,1,7,3,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,7,1,8,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,6,3,7,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,6,3,7,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,7,3,8,2,4,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,2,7,4,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,3,2,1,4,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,1,8,3,4,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,4,1,8,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,4,8,6,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,4,8,6,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,5,7,2,1,8,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,7,8,3,2,5,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,3,7,8,2,5,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,7,4,8,5,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,2,4,7,1,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,6,2,7,1,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,4,8,5,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,7,8,5,2,6,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,5,7,8,1,6,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,3,7,1,8,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,4,7,8,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,6,1,7,8,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,6,1,2,7,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,7,2,1,8,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,2,8,5,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,7,4,8,5,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,8,2,4,6,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,7,4,3,6,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,4,5,3,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,3,4,7,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,2,4,6,3,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,2,5,4,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,7,4,6,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,7,5,2,6,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,2,3,6,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,5,3,7,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,2,3,8,6,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,4,8,5,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,4,8,1,3,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,5,4,8,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,3,5,8,2,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,3,4,8,1,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,5,2,4,7,1,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,3,4,8,1,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,3,7,1,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,4,8,5,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,4,3,7,8,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,2,6,7,3,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,7,4,2,8,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,7,2,8,6,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,3,7,8,6,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,3,6,8,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,2,7,1,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,6,5,7,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,6,4,7,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,6,7,3,8,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,5,6,8,1,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,4,5,2,3,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,4,6,7,5,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,5,2,3,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,2,5,3,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,2,5,3,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,6,4,7,5,2,3,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,2,7,4,5,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,2,5,3,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,5,2,3,8,7,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,7,4,5,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,7,5,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,4,7,5,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,2,7,4,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,4,7,2,5,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,8,2,4,7,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,8,2,6,7,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,8,4,6,7,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,8,6,7,4,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,7,2,4,5,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,4,5,8,7,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,6,4,8,7,5,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,6,2,8,7,5,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,2,4,6,7,5,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,2,6,5,8,7,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,4,5,8,7,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,2,6,7,4,5,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,6,7,2,4,5,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,5,2,8,7,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,2,3,6,8,7,5,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,4,5,8,7,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,6,7,4,2,5,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,6,7,2,5,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,4,8,7,2,5,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,8,7,4,5,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,8,7,5,2,3,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,8,7,5,2,3,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,5,8,7,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,6,8,7,4,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,8,7,4,5,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,8,6,7,5,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,2,8,6,7,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,8,4,7,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,6,4,7,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,8,2,7,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,8,2,7,5,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,6,8,4,7,5,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,6,8,7,2,5,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,5,8,2,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,6,8,4,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,8,6,4,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,7,4,2,5,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,6,4,7,5,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,6,2,7,5,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,2,5,6,3,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,5,7,4,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,7,3,2,5,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,2,6,4,8,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,3,6,4,7,8,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,5,1,8,3,4,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,7,8,2,6,3,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,1,6,3,5,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,3,1,7,8,4,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,6,7,4,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,3,5,2,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,8,2,7,5,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,3,2,8,5,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,4,7,2,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,8,1,5,3,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,8,1,6,2,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,4,6,7,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,6,8,3,4,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,1,6,5,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,8,2,5,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,2,3,7,6,1,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,3,7,4,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,6,8,4,3,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,8,1,5,4,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,2,4,8,5,3,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,7,5,1,8,4,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,8,5,4,6,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,4,3,8,6,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,1,6,3,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,3,7,6,2,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,3,6,8,7,1,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,3,2,8,5,7,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,6,4,2,8,5,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,3,2,5,1,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,4,7,5,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,3,8,6,5,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,4,3,5,1,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,8,1,4,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,8,5,6,1,2,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,1,8,4,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,6,8,4,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,6,8,3,2,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,1,8,3,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,8,1,3,2,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,8,3,1,2,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,7,8,3,4,6,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,7,8,2,1,3,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,1,8,2,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,6,8,2,3,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,1,2,8,3,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,2,1,8,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,2,8,1,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,2,8,4,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,6,8,4,7,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,2,6,8,4,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,6,8,3,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,5,1,8,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,2,5,8,3,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,2,4,3,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,4,1,3,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,5,3,8,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,5,4,8,7,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,5,2,4,8,7,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,4,2,3,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,1,3,2,8,7,6]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,5,3,1,8,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,1,3,8,2,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,5,4,8,7,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,5,1,4,8,7,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,4,1,8,7,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,8,7,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,6,8,7,3,4,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,4,5,1,8,7,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,1,5,8,7,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,3,5,8,2,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,3,6,8,2,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,6,8,3,7,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,4,5,2,8,7,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,3,1,4,2,8,7,6]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,1,3,4,2,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,3,2,4,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,2,5,8,1,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,2,5,8,7,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,2,4,5,8,7,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,3,5,8,1,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,3,1,4,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,5,7,4,2,8,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,5,3,8,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,5,6,2,4,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,2,1,3,5,4,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,2,3,7,8,4,5,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,5,8,2,6,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,1,6,5,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,5,6,7,3,4,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,7,8,2,1,4,5,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,3,8,4,7,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,3,7,6,4,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,1,7,8,6,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,5,8,2,7,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,2,8,5,3,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,6,4,7,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,4,2,8,5,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,6,5,2,1,7,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,3,7,4,2,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,5,7,2,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,1,8,2,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,4,6,3,7,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,8,3,4,1,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,7,6,2,8,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,2,5,7,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,8,5,6,7,1,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,7,6,3,1,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,5,7,3,8,4,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,7,1,8,5,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,1,8,7,5,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,6,7,1,5,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,3,7,5,8,6,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,7,8,4,3,1,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,7,4,5,8,3,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,7,1,4,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,2,8,5,1,4,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,6,5,3,8,4,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,4,8,3,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,6,1,3,5,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,3,2,4,7,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,4,3,2,5,7,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,6,4,8,2,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,7,2,5,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,4,7,8,5,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,6,4,3,8,5,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,2,1,6,4,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,8,3,2,1,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,2,6,8,5,4,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,3,8,2,5,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,5,3,8,7,6,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,2,6,5,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,8,5,4,1,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,1,8,6,5,4,2,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,8,7,3,2,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,8,3,7,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,3,6,2,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,3,7,1,8,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,8,5,1,4,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,8,7,6,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,8,1,5,7,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,5,7,3,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,4,8,3,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,3,6,7,1,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,8,3,1,6,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,7,5,3,6,4,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[4,6,1,3,8,7,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,8,2,1,7,4,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,1,6,4,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,2,7,5,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,6,1,2,7,5,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,6,2,5,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,2,5,8,7,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,7,2,6,3,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,4,6,1,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,7,2,8,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,2,8,7,5,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,3,8,2,6,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,8,7,2,5,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,4,8,1,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,8,1,7,6,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,1,8,7,5,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,1,2,8,7,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,5,2,8,1,6,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,7,6,8,1,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,5,1,6,2,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,4,8,6,1,2,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,1,8,3,6,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,8,7,1,6,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,5,4,3,7,2,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,4,8,3,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,4,3,2,8,5,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,3,1,4,8,2,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,7,4,2,5,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,2,4,6,8,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,7,5,1,6,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,4,6,3,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,1,4,3,2,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,1,3,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,1,2,7,6,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,4,6,8,3,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,4,8,1,3,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,1,3,8,5,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,8,4,5,7,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,7,4,5,3,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,8,4,3,5,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,4,2,8,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,1,3,7,2,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,8,1,3,6,5,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,8,7,3,5,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,2,6,8,7,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,4,2,3,6,1,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,2,3,6,5,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,8,4,1,2,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,3,2,7,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,6,3,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,4,2,5,8,1,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,7,8,3,4,5,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,1,2,4,6,5,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,5,6,8,2,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,6,5,2,7,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,6,5,3,4,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,4,6,2,8,5,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,1,7,5,8,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,7,2,6,5,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,1,6,5,2,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,3,6,5,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,3,7,1,6,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,1,7,5,6,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,4,8,6,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,6,8,7,3,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,4,6,1,8,5,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,1,6,7,5,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,6,7,5,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,3,7,1,6,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,7,5,6,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,7,3,6,5,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,7,4,5,3,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,7,4,3,5,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,1,4,2,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,7,3,6,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,8,7,6,1,2,4,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,1,7,2,6,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,7,3,6,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,7,3,6,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,2,4,1,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,5,6,2,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,5,3,7,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,6,5,1,4,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,2,5,4,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,7,5,6,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,7,5,6,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,7,5,3,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,8,7,3,4,5,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,1,2,4,6,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,8,7,6,1,3,4,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,7,6,2,3,4,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,1,7,5,6,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,1,5,2,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,7,5,3,4,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,7,5,4,3,1,6]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,1,7,5,6,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,7,6,1,3,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,2,3,7,6,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,4,3,5,2,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,3,7,5,1,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,2,5,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,7,1,2,6,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,4,1,7,3,6,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,4,7,5,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,7,6,2,5,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,7,5,6,1,3,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,6,4,3,1,8,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,7,6,3,1,4,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,7,5,3,4,1,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,7,1,3,8,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,5,2,7,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,8,6,7,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,3,6,5,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,7,2,3,5,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,7,2,5,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,5,1,8,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,2,8,3,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,7,8,2,5,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,5,2,8,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,4,5,8,6,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,7,6,4,2,8,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,6,1,2,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,3,7,8,6,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,4,3,6,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,7,6,8,2,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,6,8,4,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,6,8,4,2,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,8,2,3,6,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,8,4,7,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,4,7,8,5,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,6,4,8,5,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,4,3,8,2,6,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,8,3,2,5,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,1,3,5,4,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,8,3,4,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,8,3,1,4,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,4,8,2,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,8,2,6,3,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,2,3,7,4,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,2,3,4,6,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,1,7,2,4,5,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,3,6,2,5,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,1,6,3,5,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,7,1,6,3,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,5,4,3,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,3,5,4,2,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,5,3,4,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,5,6,2,3,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,4,5,3,2,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,4,3,5,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,1,4,5,3,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,7,1,4,5,3,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,6,3,1,5,4,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,1,4,5,2,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,1,6,2,5,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,1,6,2,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,4,5,2,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,2,1,5,4,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,3,6,1,5,4,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,3,4,1,5,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,1,5,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,4,1,5,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,1,3,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,2,5,1,3,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,2,1,3,7,4,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,1,2,8,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,1,2,5,4,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,2,1,3,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,6,1,3,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,6,1,5,3,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,1,3,5,2,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,1,5,3,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,1,4,2,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,6,2,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,3,1,2,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,6,1,2,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,6,1,5,2,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,5,1,8,7,3,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,8,5,2,3,4,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,8,7,1,5,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,5,6,2,7,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,6,1,5,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,6,4,1,3,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,6,2,4,5,3,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,7,5,3,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,7,5,3,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,2,7,1,6,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,1,5,3,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,6,2,4,7,8,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,6,1,7,8,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,8,6,7,1,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,5,6,7,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,6,4,1,2,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,6,1,7,2,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,7,3,2,6,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,1,7,2,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,1,5,7,2,6,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,7,2,5,6,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,7,2,5,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,7,2,1,6,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,1,5,2,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,8,5,1,6,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,5,2,7,8,1,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,2,8,5,6,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,7,2,1,5,6,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,6,7,1,5,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,7,8,5,2,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,5,6,2,1,8,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,5,2,1,6,4,3]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,1,3,5,8,6,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,5,3,6,8,2,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,3,4,8,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,7,8,5,1,3,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,5,1,6,3,4,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,8,6,3,4,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,6,8,1,5,3,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,4,5,8,3,2,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,6,4,8,7,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,8,3,1,2,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,1,8,3,5,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,8,3,5,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,1,3,5,2,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,8,3,5,1,2,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,8,1,2,6,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,8,2,4,3,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,2,3,1,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,2,3,5,1,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,2,3,5,6,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,6,5,1,4,3,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,4,8,6,1,3,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,1,8,4,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,8,6,1,4,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,7,3,8,1,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,1,8,2,4,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,7,8,4,1,6,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,5,4,1,3,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,1,7,6,3,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,2,5,7,6,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,6,5,1,8,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,5,3,4,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,1,5,2,3,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,3,5,1,4,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,7,5,1,8,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,6,1,2,5,3,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,5,1,8,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,5,2,8,3,4,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,6,3,5,1,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,7,6,5,8,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,1,4,8,7,6,3,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,1,3,5,7,4,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,2,8,7,5,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,5,1,6,7,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,5,1,6,7,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,6,1,3,5,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,7,2,8,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,1,8,6,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,1,8,6,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,3,8,6,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,5,4,6,7,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,3,8,6,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,5,8,6,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,1,5,3,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,6,3,2,8,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,1,6,3,5,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,7,6,2,5,3,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,7,6,8,3,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,6,2,8,5,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,1,3,7,5,2,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,8,7,5,1,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,3,8,1,4,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,8,5,7,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,8,5,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,4,8,7,5,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,5,8,2,6,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,6,8,2,4,1,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,8,2,6,7,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,2,8,1,6,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,8,4,6,7,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,8,3,4,6,7,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,4,3,2,6,7,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,2,8,1,6,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,8,1,6,7,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,8,2,6,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,8,7,2,1,5,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,5,3,6,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,8,5,7,4,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,4,1,6,7,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,1,4,6,7,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,2,7,3,8,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,3,2,8,5,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,3,2,8,4,6,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,2,6,5,3,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,6,2,5,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,8,3,2,6,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,5,8,2,4,6,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,4,7,8,2,3,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,6,2,5,3,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,4,3,2,8,7,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,5,3,2,8,4,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,7,3,5,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,1,2,7,3,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,7,4,3,8,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,3,2,8,7,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,8,4,2,7,6,5,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,8,3,7,2,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,4,8,3,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,6,8,5,4,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,5,7,8,2,4,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,3,1,6,7,2,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,4,8,6,1,3,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,6,1,5,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,8,3,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,3,6,1,2,5,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,7,1,3,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,8,2,5,1,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,6,3,8,5,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,2,6,8,4,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,2,3,8,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,4,7,5,8,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,8,5,1,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,3,6,1,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,4,2,1,7,5,3]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,6,4,1,8,5,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,6,4,8,7,5,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,3,1,2,8,4,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,1,3,2,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,7,1,2,5,8,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,8,4,1,2,7,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,4,8,1,6,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,2,1,7,3,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,1,8,2,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,8,7,6,2,5,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,4,1,8,7,3,2,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,5,1,8,7,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,1,8,3,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,2,8,6,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,4,1,7,6,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,8,1,5,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,1,7,5,4,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,1,8,7,3,6,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,8,7,6,2,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,8,7,6,5,2,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,8,6,7,3,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,7,3,4,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,4,2,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,8,4,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,8,5,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,5,2,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,7,3,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,6,2,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,6,2,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,2,8,5,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,8,5,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,8,4,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,8,4,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,2,4,5,3,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,6,4,7,2,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,6,2,3,5,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,8,2,3,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,6,2,4,5,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,6,2,3,5,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,6,4,8,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,5,3,4,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,3,7,2,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,5,1,6,3,7,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,3,7,4,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,7,3,5,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,6,4,8,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,3,8,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,7,8,2,3,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,7,4,8,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,6,2,3,8,1,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,8,5,1,6,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,2,3,1,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,4,1,2,7,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,7,2,8,6,3,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,1,3,8,2,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,8,1,3,6,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,1,3,8,2,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,6,8,1,5,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,8,6,2,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,8,2,7,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,7,6,4,5,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,7,3,6,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,1,5,8,3,4,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,2,3,8,5,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,2,7,5,8,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,4,1,7,5,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,4,6,5,2,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,4,6,5,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,6,3,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,3,2,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,4,6,5,2,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,4,6,5,3,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,4,6,5,3,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,4,2,7,5,3,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,4,7,2,6,8,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,7,1,6,8,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,7,1,6,8,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,1,7,5,3,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,1,7,8,6,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,4,2,3,8,5,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,2,7,5,8,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,7,5,3,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,4,7,2,6,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,4,7,3,6,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,7,2,6,5,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,8,3,2,5,6,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,7,3,5,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,7,1,3,5,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,3,1,2,6,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,7,1,6,2,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,7,1,6,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,7,2,6,5,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,8,1,6,3,4,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,5,1,3,7,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,3,4,2,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,7,3,6,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,7,2,6,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,3,7,5,1,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,2,4,3,1,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,7,4,1,5,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,4,7,3,6,1,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,8,3,2,1,6,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,7,3,6,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,2,1,6,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,3,8,5,2,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,2,8,4,3,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,3,2,8,6,5,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,3,8,7,5,1,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,5,8,6,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,3,7,5,2,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,8,5,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,7,8,4,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,5,8,3,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,4,8,3,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,2,3,8,4,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,8,7,4,1,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,2,8,6,4,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,3,8,4,2,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,5,3,6,2,4,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,5,3,7,2,4,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,4,3,8,2,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,5,3,8,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,6,3,8,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,3,8,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,6,3,7,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,6,3,5,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,6,3,5,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,3,5,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,3,4,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,8,4,3,2,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,8,4,3,2,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,8,3,4,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,8,3,4,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,8,4,6,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,8,3,6,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,8,3,5,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,8,3,5,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,7,3,5,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,3,7,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,3,7,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,4,7,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,4,7,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,7,3,8,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,7,3,8,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,3,8,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,1,4,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,1,5,8,6,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,1,5,8,6,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,1,7,5,8,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,7,3,1,4,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,7,1,4,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,1,8,5,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,8,7,5,4,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,2,7,1,8,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,7,2,1,8,4,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,2,1,8,4,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,1,8,5,6,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,8,6,5,4,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,2,1,6,8,5,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,2,1,6,8,5,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,6,1,8,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,1,8,7,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,6,1,8,7,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,1,8,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,1,6,8,3,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,3,1,5,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,1,7,8,6,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,1,8,7,6,4,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,1,8,6,4,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,2,1,8,4,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,8,4,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,1,8,4,7,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,1,8,7,4,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,2,1,7,8,3,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,7,1,8,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,2,1,8,3,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,7,1,8,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,1,7,8,3,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,1,8,4,5,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,2,8,6,3,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,8,6,2,5,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,8,6,2,4,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,2,8,5,6,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,8,5,2,4,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,8,4,5,6,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,3,8,2,4,5,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,8,2,5,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,3,8,1,5,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,7,8,2,4,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,7,3,8,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,7,2,6,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,8,2,4,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,4,2,6,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,8,2,7,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,4,2,6,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,2,3,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,3,7,8,2,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,3,8,2,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,7,2,4,5,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,7,2,5,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,6,8,2,4,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,4,6,2,3,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,7,8,2,4,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,4,2,1,5,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,6,3,4,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,3,4,2,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,4,2,1,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,4,2,1,3,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,5,4,1,7,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,8,5,4,1,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,8,5,4,1,6,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,3,8,5,4,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,6,3,5,4,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,8,6,3,5,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,3,8,5,7,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,2,1,8,4,3,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,1,8,5,6,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,1,8,5,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,2,1,5,6,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,5,6,3,8,4,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,3,4,2,1,8,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,8,5,6,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,8,5,6,4,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,4,2,1,8,5,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,3,7,6,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,2,4,1,8,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,4,1,7,6,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,1,7,8,6,4,3,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,6,4,3,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,7,8,4,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,8,4,2,1,6,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,2,3,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,1,8,4,3,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,1,7,5,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,4,2,3,7,5,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,7,6,2,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,5,7,6,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,6,2,1,3,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,6,1,8,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,5,8,4,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,4,3,6,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,7,8,3,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,4,3,7,5,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,3,2,8,4,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,2,7,8,4,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,3,2,5,8,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,3,7,2,5,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,2,7,5,4,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,2,6,3,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,5,3,7,4,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,7,3,4,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,6,5,2,3,1,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,7,6,3,4,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,6,3,2,5,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,5,2,1,4,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,8,5,2,3,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,6,2,3,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,2,6,3,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,8,6,4,1,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,1,7,5,4,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,1,3,7,5,2,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,7,3,4,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,3,2,5,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,2,7,4,3,6,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,1,8,3,2,6,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,8,7,1,5,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,2,7,1,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,7,2,1,4,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,8,2,4,5,6,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,5,8,2,3,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,8,3,2,5,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,3,8,2,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,4,2,7,1,5,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,2,8,1,5,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,4,2,8,3,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,2,3,8,1,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,5,2,3,1,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,1,3,2,6,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,1,3,4,2,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,2,1,5,3,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,3,2,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,1,3,2,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,2,4,3,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,7,6,3,2,5,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,8,3,2,7,6,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,8,2,7,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,7,3,6,2,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,3,2,8,1,7,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,8,3,7,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,8,1,2,5,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,7,6,2,1,8,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,4,2,7,1,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,6,7,4,1,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,6,3,4,7,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,6,7,8,3,4,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,7,8,4,2,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,3,2,8,7,5,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,8,2,6,4,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,3,8,1,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,1,8,2,5,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,3,6,7,4,2,5,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,2,7,8,4,1,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,8,6,3,1,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,2,4,8,6,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,2,7,4,8,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,3,6,4,7,2,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,4,7,1,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,7,4,2,6,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,4,6,2,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,5,8,2,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,7,6,4,8,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,1,7,4,8,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,7,3,8,4,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,6,4,7,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,7,5,2,6,3,4,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,5,2,7,3,4,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,8,5,6,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,2,6,4,7,5,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,8,5,4,7,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,2,5,4,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,2,5,6,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,6,4,8,5,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,8,3,1,4,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,1,8,4,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,8,6,4,3,2,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,1,6,3,8,7,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,2,5,8,3,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,1,8,7,4,3,2,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,1,2,5,4,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,2,7,5,8,3,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,6,3,7,5,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,2,6,4,7,8,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,1,6,3,7,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,6,4,8,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,4,1,6,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,6,3,8,7,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,1,8,4,3,2,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,1,7,4,3,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,1,8,5,2,3,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,6,8,3,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,6,1,3,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,8,1,4,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,5,7,6,8,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,5,7,6,2,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,5,7,2,6,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,5,2,7,6,4,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,7,6,2,4,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,3,5,7,4,6,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,5,7,4,6,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,5,7,4,2,6,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,3,5,4,7,2,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,5,4,7,8,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,5,4,7,2,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,5,7,4,2,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,5,7,4,8,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,5,7,4,8,6,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,3,5,2,7,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,5,7,2,8,6,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,6,3,2,7,4,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,1,6,2,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,7,2,5,4,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,1,7,4,3,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,7,3,5,2,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,7,5,2,4,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,7,4,3,8,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,3,7,4,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,7,2,3,8,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,4,7,3,1,8,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,4,6,3,8,2,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,7,3,8,2,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,1,7,8,4,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,6,7,8,1,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,3,6,7,8,2,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,5,2,7,8,4,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,7,4,8,3,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,1,6,8,4,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,2,1,7,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,6,4,7,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,2,6,8,4,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,4,6,8,7,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,6,2,8,7,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,4,6,3,8,7,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,7,4,3,8,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,7,2,4,8,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,6,3,7,2,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,7,3,8,6,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,2,6,7,8,5,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,3,7,2,8,6,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,1,6,8,2,4,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,8,2,4,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,3,7,2,4,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,4,7,3,1,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,4,7,8,3,1,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[6,3,1,5,8,2,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,3,4,2,8,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,4,3,8,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,4,6,8,1,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,5,7,3,2,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,6,7,2,3,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,7,8,2,3,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,4,6,8,2,3,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,4,8,3,1,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,8,7,2,4,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,4,8,7,3,1,5,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,6,8,7,2,3,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,4,6,2,3,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,8,7,2,3,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,4,8,7,2,3,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,4,2,8,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,8,4,1,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,4,8,2,3,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,6,8,2,3,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,6,8,2,3,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,4,7,2,3,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,3,7,4,1,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,7,8,4,1,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,7,4,8,2,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,7,4,1,6,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,1,6,4,2,3,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,7,8,6,2,3,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,3,1,5,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,3,1,7,4,2,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,7,6,2,3,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,8,6,2,3,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,4,2,3,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,7,6,4,2,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,7,6,2,3,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,7,5,2,3,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,6,1,5,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,6,5,1,8,7,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,3,5,1,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,3,1,5,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,1,6,5,3,8,7,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,1,5,3,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,5,3,1,8,7,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,6,5,1,8,7,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,5,8,1,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,8,1,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,5,8,3,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,5,3,8,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,1,5,8,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,6,5,8,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,6,5,8,3,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,6,5,8,7,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,5,3,8,7,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,3,8,7,1,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,8,3,7,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,8,5,3,7,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,1,5,7,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,6,1,8,5,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,6,8,5,7,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,4,6,8,5,7,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,4,6,8,5,3,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,6,1,8,5,3,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,8,5,3,1,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,6,8,5,1,7,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,3,5,1,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,8,3,1,5,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,3,1,8,5,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,3,8,1,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,3,8,5,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,6,8,1,5,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,6,1,8,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,1,6,8,5,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,3,6,8,7,5,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,3,6,1,8,7,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,6,8,1,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,5,2,8,7,3,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,2,5,8,7,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,5,8,7,3,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,6,3,8,1,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,3,1,8,7,5,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,1,6,3,8,7,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,6,3,8,7,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,1,6,8,3,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,6,1,8,3,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,8,1,3,7,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,2,8,5,7,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,8,5,7,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,4,8,7,1,5,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,8,7,5,3,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,4,1,8,7,5,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,6,4,8,7,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,1,8,7,3,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,4,8,7,3,5,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,4,7,1,8,6,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,6,7,4,8,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,5,6,3,7,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,7,1,4,8,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,6,1,3,7,8,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,5,6,7,4,8,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,7,8,4,5,6,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,6,7,3,4,8,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,3,2,6,4,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,3,2,6,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,3,2,8,5,4,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,3,2,5,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,2,7,5,4,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,2,4,3,7,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,5,3,7,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,7,6,2,3,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,4,8,2,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,2,8,5,3,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,2,3,7,5,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,2,3,6,5,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,2,3,5,6,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,3,2,7,4,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,2,6,4,7,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,2,3,5,7,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,5,2,1,6,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,2,6,8,4,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,7,2,8,4,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,2,1,8,6,4,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,8,4,2,1,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,3,2,6,1,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,5,8,2,7,4,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,2,3,4,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,8,2,3,4,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,1,8,4,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,1,4,3,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,3,4,7,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,8,1,3,5,4,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,7,1,4,3,5,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,2,1,5,6,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,2,1,6,5,4,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,8,3,5,4,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,4,1,8,3,5,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,1,7,3,5,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,4,6,2,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,3,2,5,1,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,5,2,4,1,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,7,8,1,5,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,8,7,3,5,4,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,8,2,7,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,2,8,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,2,8,5,3,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,2,8,4,5,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,7,8,4,3,5,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,1,8,3,5,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,8,2,3,4,6,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,7,1,3,4,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,8,1,3,4,7,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,6,2,3,4,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,6,2,3,4,1,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,2,3,4,1,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,7,3,5,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,2,7,4,5,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,2,3,4,1,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,4,8,7,5,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,8,7,3,5,6,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,7,5,3,6,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,7,3,4,6,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,4,2,1,6,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,3,7,2,6,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,8,1,6,3,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,2,1,4,7,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,2,5,1,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,4,1,2,6,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,1,5,2,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,1,2,4,7,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,2,8,3,6,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,7,6,2,4,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,2,6,5,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,7,6,2,4,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,7,6,3,4,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,7,3,6,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,7,2,6,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,7,1,6,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,2,8,5,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,1,8,5,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,8,5,7,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,1,7,5,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,1,3,8,5,2,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,7,1,6,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,7,2,6,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,8,2,6,5,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,6,7,5,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,2,7,5,6,3,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,7,6,4,3,1,5]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[3,8,7,6,1,2,5,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,7,6,2,1,5,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,8,7,6,1,3,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,3,6,5,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,7,5,6,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,8,7,6,4,2,1,5]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,1,4,6,8,2,3,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,7,6,3,5,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,7,2,6,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,6,1,5,7,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,8,5,7,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,1,5,8,6,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,1,2,5,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,6,7,2,1,4,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,8,6,5,1,2,4,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,3,6,5,7,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,4,8,5,3,1,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,5,2,4,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,3,1,6,8,5,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,3,2,5,1,4,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,5,8,3,4,6,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,8,1,6,5,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,1,4,7,2,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,2,4,1,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,7,8,6,2,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,4,8,6,2,7,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,8,2,1,6,7,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,2,8,6,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,1,2,7,5,3,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,2,8,6,4,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,7,8,4,6,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,5,7,2,6,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[7,3,5,2,6,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,2,3,6,1,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,6,3,5,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,6,4,3,7,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,2,6,4,7,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,2,8,7,3,6,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,2,8,7,3,6,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,8,7,1,2,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,8,7,3,2,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,6,8,1,7,5,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,6,8,4,7,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,8,3,7,6,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,2,8,4,7,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,8,3,7,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,8,4,7,2,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,8,2,3,7,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,8,4,2,7,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,8,4,2,7,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,8,2,3,7,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,1,8,4,3,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,8,4,3,7,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,8,4,1,2,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,6,8,1,3,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,8,4,3,2,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,1,4,8,6,2,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,1,8,6,2,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,2,4,8,3,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,8,3,2,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,5,8,3,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,6,2,8,7,5,4,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,6,4,8,7,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,4,8,7,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,5,8,7,6,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,4,8,7,6,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,1,5,8,7,2,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,4,8,7,2,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,4,8,2,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,5,8,2,7,6,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,5,8,3,7,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,6,5,8,1,2,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,4,8,3,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,5,8,3,2,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,6,1,4,8,2,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,1,3,8,2,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,3,4,8,2,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,2,5,1,8,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,5,3,8,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,3,4,8,6,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,3,5,4,8,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,5,1,8,7,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,3,5,4,8,7,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,5,4,8,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,5,3,8,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,3,4,8,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,5,4,8,2,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,5,4,8,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,5,2,3,8,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,1,4,2,8,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,2,4,3,8,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,5,4,2,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,5,2,3,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,1,2,4,3,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,5,4,3,8,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,1,4,3,2,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,1,5,4,3,2,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,4,2,6,7,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,4,2,6,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,4,2,6,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,7,3,5,4,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,7,8,3,5,4,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,8,3,5,4,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,1,2,8,5,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,8,1,2,7,5,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,1,6,3,7,5,4,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,1,3,6,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,7,3,2,8,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,4,2,6,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,1,2,8,5,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,4,2,1,5,3,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,4,1,2,6,5,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,7,4,1,5,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,7,5,1,6,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,5,3,1,7,6,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,1,2,7,5,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,1,3,6,5,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,8,2,6,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,1,2,8,5,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,3,1,8,6,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,5,6,3,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,3,4,8,6,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,4,3,8,1,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,3,4,1,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,4,8,2,1,5,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,3,2,5,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,3,2,5,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,1,4,6,8,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,1,3,4,7,6,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,1,4,2,7,5,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,3,7,1,6,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,5,4,1,8,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,6,4,2,1,5,3,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,2,7,6,5,4,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,2,8,6,5,4,3,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,7,2,6,5,4,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,8,7,6,5,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,8,7,6,5,3,1,2]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,8,6,1,5,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,3,8,6,5,4,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,8,5,7,6,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,8,7,4,6,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,5,6,1,3,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,1,5,3,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,6,1,4,5,2,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,6,1,5,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,2,1,5,4,3,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,2,6,1,4,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,2,1,7,4,3,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,2,1,5,4,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,3,1,5,2,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,7,1,5,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,6,1,7,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,4,3,2,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,5,7,3,2,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,7,8,1,3,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,2,6,1,5,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,1,6,7,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,6,1,8,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,2,5,1,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,1,6,8,2,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,7,1,8,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,1,4,8,2,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,1,6,4,7,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,8,1,3,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,4,1,3,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,1,7,3,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,1,8,4,3,6,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,1,8,6,4,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,1,7,4,6,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,5,1,7,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,8,1,7,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,5,8,1,2,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,1,8,5,6,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,7,8,3,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,1,7,3,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,1,7,3,2,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,4,7,1,2,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,7,4,1,3,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,8,2,1,3,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,3,8,1,2,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,3,6,7,1,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,6,8,7,1,5,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,8,5,2,3,6,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,7,5,2,3,1,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,5,2,6,8,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,2,4,6,8,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,5,7,3,6,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,5,3,6,8,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,2,4,6,8,1,3,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,3,5,2,6,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,5,7,2,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,5,7,2,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,6,3,7,2,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,3,1,7,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,5,1,7,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,1,3,4,8,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,5,7,1,3,6,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,3,6,7,1,5,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,6,3,5,1,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,3,5,7,2,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,6,4,1,7,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,1,5,6,7,4,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,6,7,3,4,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,7,3,4,5,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,6,7,4,5,8,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,7,4,8,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,2,6,1,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,2,6,7,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,3,6,7,4,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,3,6,1,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,6,7,3,5,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,5,7,2,8,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,7,2,4,8,1,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,2,4,6,8,1,3,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,7,2,4,6,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,5,7,2,6,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,3,7,2,5,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,5,7,2,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,5,7,2,4,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,4,5,7,3,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,2,4,5,1,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,7,5,8,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,7,1,2,5,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,6,2,4,7,3,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,4,2,6,7,3,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,2,6,1,7,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,5,4,6,2,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,5,1,7,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,7,2,8,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,4,7,1,3,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,6,3,1,7,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,3,2,4,8,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,4,5,2,6,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,4,2,1,6,3,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,3,4,1,6,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,5,3,1,6,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,4,2,1,8,3,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,4,5,3,1,6,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,3,5,6,1,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,6,3,7,4,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,7,3,1,4,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,3,4,1,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,4,2,1,5,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,6,7,3,1,8,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,3,7,8,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,3,7,2,4,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,7,2,3,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,4,5,2,8,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,3,2,4,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,6,3,4,1,2,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,6,3,2,4,1,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,7,3,2,5,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,5,3,2,7,8,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,3,2,7,4,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,5,2,7,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,5,2,7,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,5,2,6,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,5,6,1,2,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,5,6,2,1,3,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,3,5,1,2,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,7,4,1,2,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,6,7,2,4,1,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,4,2,7,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,5,7,2,1,8,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,2,1,4,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,6,7,3,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,7,8,3,6,4,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,8,5,6,4,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,8,5,6,1,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,8,5,6,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,5,8,6,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,5,8,6,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,5,8,6,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,3,8,6,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,8,5,6,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,5,8,6,4,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,5,7,8,6,4,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,5,7,8,6,3,4,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,5,7,8,3,6,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,5,7,8,1,6,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,3,7,8,1,6,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,5,8,6,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,8,5,6,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,1,5,6,3,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,1,8,5,6,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,5,8,6,3,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,7,8,3,6,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,7,8,5,6,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,3,7,8,5,6,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,1,7,5,8,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,7,3,8,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,5,3,8,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,5,8,3,6,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,1,5,3,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,3,5,1,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,3,5,8,1,6,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,7,1,8,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,7,1,8,6,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,7,5,3,8,6,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,7,3,1,8,6,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,7,3,8,6,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,5,8,1,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,5,8,3,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,8,5,3,6,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,7,8,5,1,6,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,7,8,3,6,1,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,8,6,3,1,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,5,8,6,1,3,4,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,8,1,6,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,8,1,3,6,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,7,8,1,5,6,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,7,8,3,5,6,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,7,3,8,5,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,1,8,5,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,1,8,3,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,1,8,6,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,1,8,6,3,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,8,1,6,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,5,1,6,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,5,1,3,6,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,5,8,1,3,6,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,1,8,3,6,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,7,1,3,8,6,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,1,5,8,6,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,7,3,5,8,6,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,5,3,7,8,6,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,1,7,8,6,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,3,1,8,5,6,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,1,5,6,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,3,1,5,6,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,1,3,5,6,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,1,8,3,5,6,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,1,3,8,5,6,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,3,5,8,6,4,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,1,5,7,8,6,4,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,7,3,4,6,8,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,7,3,4,8,6,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,3,4,8,1,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,3,4,1,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,3,4,1,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,3,4,6,1,2,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,3,5,6,1,2,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,3,1,4,6,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,3,1,4,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,3,1,4,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,7,4,1,2,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,7,1,4,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,1,4,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,5,1,2,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,3,5,1,2,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,8,5,1,2,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,5,8,1,2,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,7,5,1,2,6,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,1,4,3,5,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,7,3,8,4,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,4,7,8,6,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,6,2,8,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,2,5,8,3,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,4,5,1,3,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,4,6,3,2,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,6,2,4,1,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,8,6,7,5,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,7,8,3,4,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,3,4,8,1,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,7,1,2,5,3,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,7,6,2,8,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,8,1,5,4,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,6,5,7,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,7,1,4,6,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,6,1,8,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,2,6,3,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,8,4,6,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,8,6,3,1,2,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,8,1,5,6,7,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,7,2,4,8,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,8,3,6,7,5,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,1,7,6,3,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,2,4,5,8,1,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,4,6,3,2,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,3,2,1,8,6,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,4,7,5,2,3,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,8,1,7,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,7,2,3,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,2,3,1,8,7,5,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,8,1,3,5,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,5,2,3,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,2,6,5,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,2,1,8,5,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,2,6,4,1,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,7,8,2,5,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,1,7,3,6,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,5,7,8,4,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,5,7,8,3,6,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,4,1,5,7,2,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,2,7,8,6,3,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,7,4,3,2,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,3,4,2,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,6,7,3,5,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,5,8,3,7,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,4,8,3,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,8,7,5,3,4,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,6,3,1,5,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,4,8,2,5,7,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,7,2,8,6,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,7,4,8,6,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,3,7,5,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,7,5,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,4,8,7,5,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,7,2,8,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,2,5,8,7,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,2,8,4,7,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,8,6,5,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,4,8,7,5,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,4,5,8,7,6,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,3,4,6,2,8,7,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,2,3,6,1,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,7,3,8,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,1,4,7,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,3,8,7,2,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,5,6,2,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,2,4,6,3,8,7,5]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,1,5,2,8,7,6,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,4,2,8,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,3,7,2,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,5,3,2,8,7,6]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,1,4,3,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,2,3,5,1,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,4,1,8,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,5,1,8,7,6,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,4,5,2,8,7,6,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,6,4,2,8,7,5,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,6,3,1,8,7,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,4,2,5,1,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,6,2,8,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,2,7,5,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,2,6,1,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,6,2,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,8,3,2,7,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,5,8,3,1,7,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,5,8,2,1,7,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,6,2,5,1,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,8,4,1,3,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,4,8,7,1,3,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,8,1,3,7,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,8,1,4,7,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,8,2,4,7,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,2,1,7,4,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,1,7,2,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,1,2,8,7,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,6,2,3,8,7,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,5,2,3,8,7,6,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,5,1,2,8,7,6,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,3,1,7,2,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,1,3,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,2,8,3,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,5,6,8,3,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,6,4,7,5,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,6,3,7,5,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,7,4,5,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,2,6,3,4,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,7,4,6,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,4,7,5,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,7,5,6,3,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,7,6,4,5,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,5,2,8,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,5,2,1,4,3,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[2,7,6,4,5,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,2,6,4,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,3,7,5,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,7,3,6,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,6,4,3,7,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,7,4,8,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,8,6,3,7,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,8,2,7,3,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,3,8,4,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,2,7,4,3,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,3,1,6,8,4,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,2,8,7,1,4,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,2,1,5,4,3,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,2,3,1,4,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,3,8,2,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,7,2,1,5,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,7,2,8,4,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,2,5,8,6,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,4,5,7,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,4,6,2,7,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,3,1,8,4,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,7,5,8,6,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,5,1,2,8,3,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,1,4,3,7,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,8,4,1,3,7,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,5,7,1,3,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,8,3,1,7,4,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,1,7,5,4,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,3,8,7,4,6,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,8,7,6,3,5,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,3,1,8,7,4,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,1,8,5,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,1,7,6,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,7,1,8,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,7,1,6,5,4,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,1,8,3,6,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,8,7,5,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,7,8,4,6,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,8,7,2,6,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,8,2,7,1,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,6,4,5,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,3,7,5,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,6,3,8,5,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,3,7,5,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,7,8,2,6,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,6,2,4,1,3,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,3,8,5,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,3,4,6,1,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,2,3,4,6,1,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,3,4,7,5,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,3,6,1,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,3,7,5,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,3,4,7,1,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,3,4,8,7,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,8,5,7,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,6,4,5,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,6,4,5,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,3,6,5,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,3,7,5,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,7,5,1,6,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,5,8,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,1,7,3,6,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,7,8,4,6,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,8,3,7,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,7,3,1,6,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,3,2,5,7,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,2,3,4,7,5,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,2,3,4,8,5,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,2,3,4,1,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,4,1,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,4,8,7,5,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,8,3,1,5,7,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,2,3,4,1,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,3,4,1,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,6,7,4,1,5,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,6,7,5,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,8,4,6,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,7,1,5,4,6,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,7,1,4,6,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,8,5,1,7,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,5,7,1,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,4,7,1,5,6,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,4,5,6,1,3,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,7,5,1,4,6,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,2,5,1,4,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,8,7,2,5,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,4,8,5,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,1,4,2,5,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,8,5,6,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,8,7,1,2,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,8,5,7,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,8,7,1,5,6,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,8,7,1,6,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,8,6,7,5,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,2,8,6,7,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,8,6,2,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,8,6,7,5,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,1,8,2,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,7,1,5,6,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,7,1,5,2,4,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,8,2,4,6,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,2,8,4,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,8,5,7,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,3,7,2,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,1,8,2,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,6,3,7,4,1,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,2,8,6,7,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,2,7,5,6,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,3,6,1,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,4,7,5,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,7,4,5,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,7,4,2,5,6,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,2,4,1,5,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,8,6,1,7,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,1,8,2,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,2,8,6,7,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,1,6,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,7,1,3,6,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,3,6,7,1,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,7,2,3,6,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,7,2,6,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,7,3,6,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,7,3,6,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,2,7,6,3,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,2,7,4,1,5,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,1,7,5,6,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,3,1,5,6,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,8,7,3,5,6,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,3,1,6,7,5,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,5,2,8,6,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,8,6,7,5,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,3,6,7,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,3,6,7,5,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,3,7,2,5,6,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,3,7,5,6,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,1,2,7,5,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,4,2,6,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,8,6,7,3,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,1,2,7,3,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,7,3,6,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,7,2,6,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,7,2,3,6,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,3,7,2,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,3,6,7,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,8,2,3,6,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,8,5,7,4,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,8,5,7,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,5,7,4,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,8,6,4,3,5,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,6,8,3,5,4,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,7,5,8,4,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,1,7,6,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,1,8,6,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,7,6,4,5,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,5,8,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,6,8,7,5,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,8,7,5,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,5,8,4,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,6,4,2,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,3,6,2,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,8,2,1,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,4,6,3,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,8,5,2,1,4,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,2,3,1,4,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,6,2,3,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,2,5,8,3,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,6,5,8,1,3,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,5,3,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,8,1,3,6,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,7,1,3,4,6,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,8,6,1,3,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,6,2,1,3,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,8,7,2,3,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,3,7,2,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,6,8,2,3,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,4,2,8,3,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,7,2,1,8,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,3,4,1,2,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,8,5,4,1,3,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,3,7,1,5,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,6,1,5,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,5,6,1,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,2,8,1,5,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,7,8,2,5,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,5,6,4,2,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,3,1,5,6,2,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,4,5,2,6,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,7,2,8,6,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,8,2,6,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,3,8,2,5,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,8,2,1,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,3,1,8,2,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,3,7,8,2,6,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,8,5,6,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,3,7,6,8,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,8,4,6,2,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,8,4,3,6,7,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,6,4,7,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,8,6,2,7,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,5,8,6,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,8,6,7,5,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,3,8,7,2,4,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,8,7,2,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,8,6,7,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,7,8,6,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,7,6,4,8,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,4,6,7,2,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,4,2,8,1,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,4,3,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,6,2,8,7,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,3,8,7,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,3,1,8,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,4,3,6,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,3,8,6,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,8,6,7,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,6,8,5,7,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,6,8,3,7,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,6,8,2,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,7,8,2,5,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,7,8,2,6,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,4,8,6,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,2,5,7,8,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,2,7,4,6,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,7,1,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,5,6,7,1,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,6,3,5,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,3,6,7,2,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,4,2,5,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,4,2,7,5,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,3,8,2,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,2,4,1,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,7,3,1,5,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,4,1,8,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,4,1,5,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,7,5,2,8,6,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,4,1,8,5,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,3,1,7,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,6,4,8,1,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,8,4,2,6,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,4,1,6,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,7,1,2,6,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,1,8,2,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,1,8,2,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,1,8,4,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,4,1,2,7,3,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,8,4,5,1,3,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,3,2,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,4,3,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,3,1,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,4,3,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,4,1,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,6,5,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,4,2,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,4,1,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,4,3,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,3,1,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,5,4,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,1,6,5,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,6,4,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,6,4,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,5,7,4,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,4,3,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,6,1,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,6,3,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,6,1,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,4,1,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,4,3,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,3,2,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,7,1,3,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,4,5,1,3,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,5,8,1,3,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,3,2,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,7,1,3,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,1,3,2,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,3,6,2,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,6,5,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,3,1,7,6,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,7,6,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,7,3,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,7,2,3,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,6,1,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,6,4,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,6,4,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,6,2,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,6,1,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,6,4,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,6,1,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,3,1,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,6,1,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,6,4,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,6,1,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,7,3,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,2,7,5,4,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,1,7,3,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,6,7,4,3,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,2,7,6,4,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,7,4,3,8,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,3,1,8,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,7,2,8,3,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,7,3,1,8,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,7,3,4,8,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,2,6,7,1,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,3,7,2,8,5,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,1,5,8,4,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,5,6,8,4,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,3,1,5,8,6,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,7,3,1,8,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,2,8,5,4,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,1,6,8,5,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,2,7,1,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,3,6,8,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,4,5,7,8,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,5,1,7,8,6,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,6,2,8,7,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,1,5,6,8,4,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,1,7,8,5,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,6,2,8,4,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,1,5,6,8,7,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,6,5,2,7,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,2,4,7,5,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,5,7,8,4,2,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,7,4,1,8,6,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,6,8,5,7,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,2,5,7,3,1,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,6,2,8,7,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,5,6,8,1,7,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,5,6,1,8,7,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,5,6,3,1,8,7,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,3,6,2,1,7,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,3,2,1,7,5,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,3,1,7,5,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,3,7,6,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,1,7,3,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,7,1,4,3,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,5,7,6,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,6,1,7,5,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,2,6,1,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,6,2,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,6,3,2,7,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,1,4,7,5,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,1,7,4,2,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,1,7,5,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,6,3,7,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,1,6,3,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,6,3,1,7,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,6,3,1,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,2,1,7,4,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,2,7,4,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,7,2,8,6,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,4,7,1,3,6,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,1,3,7,5,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,1,7,5,2,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,1,6,2,7,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,1,6,2,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,6,4,2,7,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,1,7,5,4,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,1,5,4,3,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,1,6,2,5,4,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,1,6,5,4,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,2,8,1,5,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,6,5,8,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,2,6,5,4,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,8,6,1,4,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,6,8,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,7,2,5,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,2,1,5,6,3,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,3,2,6,7,4,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,7,2,5,6,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,1,4,3,2,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,6,7,1,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,7,1,6,5,2,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,6,2,4,7,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,8,7,2,4,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,7,8,2,5,4,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,7,2,5,4,3,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,5,6,4,7,1,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,1,6,3,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,8,7,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,5,3,7,8,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,8,2,7,6,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,3,5,1,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,7,3,6,1,5,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,5,8,7,4,6,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,4,2,1,7,8,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,7,8,3,5,2,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,6,2,1,8,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,6,7,3,5,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,3,6,2,1,7,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,7,6,4,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,3,1,8,4,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,4,8,6,5,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,4,1,7,3,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,3,7,2,8,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,3,8,2,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,5,3,8,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,7,4,1,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,3,2,7,5,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,7,5,1,3,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,6,4,3,8,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,2,4,8,6,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,2,8,7,6,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,4,3,2,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,7,8,5,2,4,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,6,2,4,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,8,2,5,7,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,7,2,5,8,4,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,2,7,8,4,3,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,1,7,8,4,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,7,6,4,1,3,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,1,7,6,3,2,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,2,7,6,3,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,3,1,7,5,2,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,5,3,1,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,8,2,7,4,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,2,8,4,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,3,1,8,4,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,7,3,1,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,8,5,7,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,5,2,1,7,4,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,7,4,6,2,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,4,8,3,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,1,8,3,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,3,5,1,4,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,7,1,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,4,3,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,8,6,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,7,4,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,4,8,3,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,8,5,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,5,6,4,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,6,4,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,3,1,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,2,4,3,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,7,1,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,6,2,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,5,3,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,3,5,1,7,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,5,1,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,3,7,1,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,6,3,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,6,3,4,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,6,4,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,6,4,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,8,1,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,4,2,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,4,2,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,8,3,7,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,8,2,3,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,6,5,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,6,2,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,5,4,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,2,7,1,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,3,1,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,8,1,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,3,8,4,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,8,1,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,8,3,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,8,7,4,6,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,1,8,7,6,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,2,8,7,6,3,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,2,8,7,6,3,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,5,8,7,6,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,3,6,8,7,4,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,7,8,6,4,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,5,7,8,2,6,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,5,6,8,2,7,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,2,6,8,3,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,6,8,7,4,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,4,8,7,2,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,8,4,7,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,7,8,6,4,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,7,8,2,5,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[7,4,5,2,8,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,8,4,2,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,4,5,2,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,2,5,3,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,3,8,4,2,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,5,3,8,6,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,7,5,8,6,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,6,7,4,8,5,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,7,4,2,8,5,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,7,5,2,8,6,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,7,5,3,8,6,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,6,2,8,3,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,8,3,2,7,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,6,8,4,2,7,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,8,2,7,3,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,8,4,7,2,3,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,4,8,1,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,2,8,3,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,4,8,6,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,5,3,7,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,5,2,3,7,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,5,3,8,2,6,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,7,4,5,8,6,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,7,3,4,8,5,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,6,4,7,8,5,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,1,8,3,4,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,4,2,5,7,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,5,8,3,4,6,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,4,5,8,1,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,4,7,8,5,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,7,2,3,4,1,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,1,8,4,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,8,3,4,5,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,1,2,7,4,5,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,7,2,3,1,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,1,3,8,5,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,7,8,4,5,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,5,8,3,4,1,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,6,2,7,4,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,7,3,2,5,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,7,3,8,5,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,6,1,8,4,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,7,8,4,3,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,6,8,4,5,7,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,8,4,7,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,5,7,6,8,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,6,7,4,8,5,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,5,8,7,2,3,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,5,8,3,6,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,4,5,8,6,2,3,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[7,8,1,4,6,2,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,7,4,8,2,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,5,8,6,2,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,5,8,3,4,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,6,7,2,3,5,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,8,1,2,3,5,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,6,7,2,3,5,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,5,7,6,2,3,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,5,7,3,6,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,5,7,3,6,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,6,8,2,3,5,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,6,8,4,5,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,8,4,5,2,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,8,2,3,4,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,6,8,2,3,7,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,5,7,6,2,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,8,1,4,5,2,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,1,2,3,6,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,6,7,2,3,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,5,6,3,8,7,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,2,1,6,5,3,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,4,3,1,6,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,4,3,1,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,6,3,5,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,2,1,5,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,6,5,2,1,8,7,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,1,6,4,3,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,2,1,6,7,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,2,1,4,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,2,4,3,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,7,2,4,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,8,4,6,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,6,4,8,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,5,2,8,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,4,5,8,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,2,8,3,5,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,2,6,3,5,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,4,8,5,3,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,6,3,5,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,6,3,8,7,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,4,3,8,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,4,3,6,5,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,1,4,6,5,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,1,4,8,5,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,2,1,8,7,4,3,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,2,1,8,4,3,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,8,5,2,1,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,8,5,7,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,4,8,6,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,6,8,7,4,5,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,8,6,7,5,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,8,6,5,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,6,4,5,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,6,2,1,5,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,8,7,2,1,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,5,8,2,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,6,8,4,3,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,8,6,4,7,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,6,2,1,7,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,4,8,3,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,8,3,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,8,4,3,5,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,3,8,4,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,3,8,4,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,8,4,3,5,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,8,4,3,5,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,1,4,8,3,5,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,8,1,5,6,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,8,4,3,5,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,3,1,8,4,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,3,8,4,5,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,1,4,8,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,4,1,3,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,7,8,4,3,2,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[7,2,1,8,4,5,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,7,1,8,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,8,4,3,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,7,8,4,3,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,7,4,8,3,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,7,4,8,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,8,1,3,6,2,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,7,8,6,3,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,6,7,1,8,5,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,7,8,5,3,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,6,7,8,5,3,4,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,2,7,8,4,5,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,1,8,4,5,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,7,2,8,4,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,8,1,5,6,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,3,7,8,1,5,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,1,2,8,5,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,7,8,4,2,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,1,2,7,6,5,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,2,4,7,3,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,7,5,3,6,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,2,6,7,4,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,5,7,3,2,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,6,1,7,3,2,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,1,8,3,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,1,8,3,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,7,8,6,2,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,6,5,7,8,3,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,5,8,7,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,1,7,3,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,1,6,3,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,1,6,3,2,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,2,3,7,5,4,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,8,1,5,3,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,7,5,2,4,1,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,5,7,3,4,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,8,3,4,7,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,8,5,2,4,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,1,2,3,5,4,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,8,4,6,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,2,4,3,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,2,4,3,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,1,8,6,4,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,4,3,7,5,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,1,2,6,7,5,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,8,1,7,6,4,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,2,4,3,5,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,7,4,6,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,6,5,3,2,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,5,7,3,4,6,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[8,7,2,5,3,6,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,2,3,5,4,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,2,3,7,6,4,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,3,8,6,4,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,5,6,3,4,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[8,6,5,2,4,7,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,2,5,3,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,2,3,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,3,7,4,5,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,7,3,2,5,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,3,1,2,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,6,2,3,1,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,4,6,8,5,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,7,3,2,8,6,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,4,5,1,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,2,6,7,4,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,1,5,6,7,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,8,2,4,6,7,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,8,1,3,4,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,2,4,3,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,7,6,8,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,6,1,8,5,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,2,3,8,5,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,3,6,4,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,6,1,4,8,5,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,3,7,8,5,4,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,2,3,8,4,5,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,3,6,8,4,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,2,3,5,7,1,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,4,8,3,5,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,3,6,7,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,1,8,4,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,1,8,4,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,8,3,5,2,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,8,3,2,4,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,2,3,5,6,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,2,7,4,8,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,8,2,1,4,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,7,5,2,8,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,2,4,1,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,2,3,4,8,5,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,7,3,1,4,2,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,4,1,8,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,3,7,4,8,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,7,4,2,6,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,4,1,5,6,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,4,1,6,3,7,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,7,4,2,1,6,3,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,3,5,2,7,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,3,8,7,6,4,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[7,2,4,8,1,3,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,8,7,5,6,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,1,8,6,7,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,8,6,5,7,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,5,4,8,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,1,6,8,3,4,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,5,1,7,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,1,8,7,4,3,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,2,6,3,8,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,8,3,4,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,8,4,3,1,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,8,1,3,6,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,8,1,4,6,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,8,5,4,6,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,8,4,6,3,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,8,4,1,2,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,8,4,3,6,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,3,6,5,2,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,2,4,7,6,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,8,1,4,6,7,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,2,5,1,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,8,2,5,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,4,3,5,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,1,4,6,5,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,8,5,2,7,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,5,1,3,6,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,1,5,7,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,1,2,8,5,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,8,2,3,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,3,5,1,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,7,5,8,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,8,4,2,6,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,7,4,1,6,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,4,5,7,1,3,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,4,6,1,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,1,4,7,8,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,6,7,2,4,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,6,3,7,4,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,6,7,4,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,2,8,6,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,4,8,2,6,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,8,6,2,7,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,8,5,6,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,3,8,4,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,3,2,8,7,5,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,6,3,8,2,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,5,8,7,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,3,6,8,2,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,7,2,8,6,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,7,2,6,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,7,3,8,5,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,2,7,5,4,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,2,5,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,5,1,4,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,7,8,5,3,6,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,3,7,8,4,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,7,8,4,6,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,3,7,8,4,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,7,8,2,4,6,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,8,4,3,7,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,6,8,4,7,3,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,4,8,6,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,4,8,7,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,4,8,2,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,7,5,8,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,7,3,8,6,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,5,6,8,4,7,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,3,1,8,7,5,4,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,8,1,7,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,4,1,7,6,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,5,4,1,8,6,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,4,1,7,6,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,2,5,6,3,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,2,8,4,5,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,3,7,5,6,2,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,7,4,3,5,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,5,2,3,7,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,2,5,3,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,8,4,3,5,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,5,8,3,2,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,8,4,1,5,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,8,1,2,6,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,7,4,3,2,8,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,2,6,4,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,5,7,1,4,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,4,3,8,1,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,3,6,8,5,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,7,8,3,6,5,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,7,8,5,4,6,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,6,5,8,3,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,7,3,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,5,7,4,1,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,5,8,4,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,8,4,6,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,1,2,8,3,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,8,5,4,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,5,7,8,1,3,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,5,4,2,6,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,5,7,3,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,7,5,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,2,7,8,5,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,2,4,8,7,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,5,2,1,8,7,3,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,6,5,3,7,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,2,5,3,8,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,2,3,8,7,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,5,4,2,6,3,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,6,3,8,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,7,6,2,5,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,2,7,4,1,6,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,3,1,5,6,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,3,4,1,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,8,4,5,6,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,8,4,2,6,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,3,8,5,2,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,3,7,5,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,7,3,4,8,6,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,3,4,8,1,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,7,3,2,1,6,5,4]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,7,6,3,1,5,2,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[2,4,8,5,3,7,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,1,8,5,3,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,8,6,3,1,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,4,6,8,2,1,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,4,1,5,8,2,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,4,5,3,2,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,1,5,2,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,6,2,1,8,7,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,6,2,1,7,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,4,6,2,7,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,1,4,6,3,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,6,3,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,6,2,1,7,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,1,5,6,7,3,4,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,5,6,7,3,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,4,1,6,8,7,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,6,1,8,7,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,1,3,8,6,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,3,2,6,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,8,6,7,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,1,8,6,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,8,6,1,7,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,6,1,8,7,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,4,1,6,8,7,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,6,8,7,1,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,1,4,6,2,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,1,6,7,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,5,6,1,7,8,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,6,1,7,3,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,1,6,7,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,5,6,7,4,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,1,5,6,7,4,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,5,1,6,7,4,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,6,1,7,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,5,8,7,4,3,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,4,2,7,8,5,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,1,4,8,7,5,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,6,4,8,7,5,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,6,2,4,7,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,6,2,4,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,2,1,4,8,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,4,1,7,8,5,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,6,3,4,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,6,3,4,7,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,2,5,4,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,2,5,4,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,1,5,4,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,3,4,7,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,6,1,4,7,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,1,5,4,8,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,2,7,5,4,8,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,7,5,4,8,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,8,4,7,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,7,5,4,8,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,3,2,4,7,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,2,5,4,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,7,5,4,8,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,7,5,4,8,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,8,4,7,3,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,8,4,7,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,2,4,7,3,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,4,3,7,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,5,6,2,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,2,4,7,3,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,5,4,7,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,8,5,4,7,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,3,5,4,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,3,1,4,7,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,6,4,2,7,5,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,4,1,7,2,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,3,7,4,6,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,3,2,7,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,3,2,7,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,3,1,7,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,3,5,4,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,5,4,7,3,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,3,4,6,8,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,2,5,4,7,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,3,5,4,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,7,6,4,3,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,4,5,2,7,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,8,6,4,3,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,2,5,1,6,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,6,5,2,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,6,5,2,1,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,8,6,4,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,2,8,1,3,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,2,6,4,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,4,2,5,1,8,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,5,8,6,3,1,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,3,5,8,1,4,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,6,8,1,5,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,3,8,5,2,7,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,7,6,3,1,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,8,7,6,3,1,5,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,4,8,1,6,5,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,7,3,6,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,2,5,1,3,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,3,6,8,1,4,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,7,8,6,3,1,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,3,6,1,8,4,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,8,1,3,7,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,5,8,1,7,3,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,1,5,7,3,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,6,1,4,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,6,1,4,7,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,1,5,8,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,6,1,8,5,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,5,8,1,2,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,6,1,2,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,8,1,6,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,1,8,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,5,8,6,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,8,4,5,1,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,1,7,6,2,3,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,1,6,2,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,1,8,7,5,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,6,1,7,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,5,1,7,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,1,8,7,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,6,4,7,1,2,5,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,4,8,7,1,2,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,5,1,2,7,3,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,1,8,2,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,5,1,2,7,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,1,7,2,8,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,7,2,3,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,7,4,1,8,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,8,7,4,1,2,3]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,8,5,7,4,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,3,8,1,5,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,5,3,6,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,8,3,4,6,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,5,2,3,1,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,2,6,7,4,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,2,7,1,4,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,3,8,1,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,6,8,3,4,7,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,6,2,7,5,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,1,8,4,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,4,3,7,8,1,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,3,2,7,4,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,2,7,6,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,3,1,8,7,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,6,4,7,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,3,6,4,2,8,7,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,8,2,5,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,8,4,7,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,3,8,4,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,4,1,5,3,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,7,6,4,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,5,4,1,7,6,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,5,1,7,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,5,2,1,6,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,3,7,8,1,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,8,3,1,7,2,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,3,1,5,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,2,7,1,6,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,4,2,6,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,2,1,4,7,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,3,2,5,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,4,3,1,5,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,8,4,2,1,5,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,2,1,8,3,6,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,8,1,6,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,7,2,1,6,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,1,7,3,4,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,4,3,1,7,5,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,3,1,7,2,6,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,1,7,6,4,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,2,1,6,5,8,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,1,8,5,7,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,1,8,5,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,2,1,7,5,3,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,2,1,8,6,3,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,1,8,4,2,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,1,8,3,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,7,3,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,8,1,7,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,5,8,4,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,2,5,8,1,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,2,5,7,1,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,3,1,6,2,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,7,2,8,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,1,7,2,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,2,1,7,8,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,3,2,1,6,7,4,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,3,2,6,8,1,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,1,4,8,7,5,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,2,6,1,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,6,4,5,7,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,8,3,7,4,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,8,5,4,7,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,6,3,7,4,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,6,5,7,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,2,8,4,3,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,2,7,3,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,8,3,6,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,3,8,4,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,4,3,7,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,8,3,7,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,2,7,3,1,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,3,7,1,2,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,4,3,8,1,2,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,6,3,8,4,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,2,8,5,1,6,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,3,8,4,2,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,4,8,2,3,5,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,6,8,1,2,5,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,1,7,8,4,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,2,7,8,4,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,1,6,3,8,7,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,1,7,8,2,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,1,7,8,4,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,7,3,8,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,7,8,4,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,1,5,4,3,2,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,6,1,3,5,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,1,6,5,7,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,1,5,7,6,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,8,6,2,5,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,3,5,2,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,3,7,4,2,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,3,8,7,5,2,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,1,8,5,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,6,4,8,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,5,2,7,1,4,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,6,1,3,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,2,1,3,8,4,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,4,7,6,3,1,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,1,5,6,3,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,7,5,6,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,5,6,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,1,7,6,2,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,5,6,7,1,4,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,7,2,1,6,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,2,5,6,3,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,2,5,7,1,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,7,4,5,3,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,7,1,3,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,5,7,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,4,3,2,6,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,5,6,2,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,5,6,2,4,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,8,1,3,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,5,2,8,6,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,1,7,8,6,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,7,6,2,8,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,6,1,2,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,4,1,2,8,6,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,5,2,1,6,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,2,6,8,4,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,3,2,7,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,4,2,7,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,7,8,3,1,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,6,2,8,4,3,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,2,8,6,3,4,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,8,4,3,2,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,3,8,1,7,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,7,8,4,2,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[6,5,1,8,4,3,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,3,8,4,2,1,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,5,8,3,1,6,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,8,1,2,6,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,5,8,3,2,6,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,8,6,2,4,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,2,7,8,4,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,7,2,1,6,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,1,6,3,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,3,4,2,1,6,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,2,5,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,5,2,6,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,4,5,8,3,6,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,5,8,1,2,6,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,6,1,3,5,2,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,5,1,2,6,4,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,8,6,1,3,4,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,4,6,1,3,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,4,5,2,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,4,3,6,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,4,3,7,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,2,1,7,8,4,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,3,1,5,4,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,4,6,5,1,7,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,7,5,6,8,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,7,6,5,8,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,1,7,4,2,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,4,8,1,2,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,5,7,8,1,4,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,5,7,1,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,4,7,8,2,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,7,3,8,4,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,8,3,4,6,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,5,8,4,1,3,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,5,8,3,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,7,4,8,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,7,3,1,6,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,3,1,8,6,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,3,1,5,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,6,8,1,2,4,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,8,5,1,3,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,5,4,6,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,5,2,7,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,7,1,3,5,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,2,3,6,8,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,5,3,2,7,6,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,4,6,7,5,8,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,4,5,7,6,1,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,6,4,5,7,8,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,5,1,6,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,1,3,6,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,3,5,7,1,4,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,4,6,8,1,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,7,6,4,1,8,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,8,4,1,5,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[3,5,8,6,7,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,8,1,6,7,3,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,2,5,1,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,2,1,6,7,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,5,2,8,6,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,1,2,5,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,5,8,2,3,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,6,4,5,8,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,2,4,6,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,6,1,5,8,2,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,6,5,1,4,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,6,1,4,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,1,8,4,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,1,4,3,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,7,5,8,2,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,2,1,5,7,3,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,5,4,8,1,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,1,3,8,6,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,3,7,1,2,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,7,3,5,8,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,4,2,6,7,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,1,6,8,7,2,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,1,6,8,3,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,1,7,6,8,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,2,6,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,1,6,3,5,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,6,1,7,3,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,2,5,3,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,3,4,7,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,8,1,2,7,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,8,1,2,4,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,1,3,8,7,2,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,3,7,4,8,2,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,6,8,2,3,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,8,1,7,2,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,8,1,7,3,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,1,5,8,2,3,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,3,2,7,5,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,1,7,2,8,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,7,3,8,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,4,1,7,3,6,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,2,8,6,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,3,8,7,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,7,8,4,2,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,8,7,4,2,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,2,8,3,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,7,8,5,3,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,7,4,8,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,7,5,3,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,2,7,3,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,2,6,3,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,2,4,3,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,2,4,3,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,2,7,3,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,7,2,4,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,8,2,4,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,8,2,4,5,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,6,7,2,4,5,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,5,1,4,2,3,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,1,7,2,5,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,4,3,1,6,2,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,3,4,7,1,6,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,1,8,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,5,2,7,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,7,5,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,8,7,3,6,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,5,8,2,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,2,7,4,3,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,5,2,7,3,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,7,1,8,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,5,4,8,3,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,3,2,7,1,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,1,6,2,3,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,8,1,3,2,7,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,1,4,7,5,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,8,7,4,5,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,4,8,5,2,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,5,7,4,6,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,7,8,2,3,5,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,7,4,6,2,1,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,1,3,5,2,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,8,3,2,4,6,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,2,6,5,3,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,7,6,5,2,3,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,1,8,6,4,3,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,7,6,5,3,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,5,4,6,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,1,7,6,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,1,7,8,5,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,4,3,1,8,6,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,5,6,2,7,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,2,5,6,1,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,5,4,1,7,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,3,6,7,5,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,7,5,3,8,2,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,2,4,5,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,2,5,3,1,6,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,4,5,8,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,4,7,8,3,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,4,7,8,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,6,4,7,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,4,5,8,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,5,3,1,8,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,1,4,7,8,3,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,4,7,8,1,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,6,7,1,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,6,7,1,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,4,7,8,1,2,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,6,4,1,7,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,7,2,1,5,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,4,5,2,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,6,4,7,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,4,7,2,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,3,4,2,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,7,3,8,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,7,3,8,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,4,7,8,5,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,2,7,3,1,8,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,4,7,8,1,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,6,7,3,1,8,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,4,7,8,3,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,6,1,2,5,4,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,8,6,1,5,3,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,6,4,1,3,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,6,4,5,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,5,7,4,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,8,7,1,6,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,3,7,8,1,6,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,8,7,4,1,2,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,8,1,2,7,3,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,1,2,7,4,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,8,4,1,3,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,5,4,7,1,6,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,5,8,7,3,6,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,8,7,5,6,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,4,8,5,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,1,8,4,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,7,8,5,6,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,7,6,8,5,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,7,8,5,1,3,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,4,7,8,1,6,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,4,7,8,2,6,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,8,3,4,1,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,3,4,1,2,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,7,1,5,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,3,2,7,6,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,3,1,8,6,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,3,2,8,6,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,8,6,1,4,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,8,5,6,1,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,6,1,5,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,2,3,7,6,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,8,5,3,2,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,6,4,8,5,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,6,4,8,5,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,4,8,6,5,2,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,4,8,7,5,6,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,5,3,2,8,6,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,5,1,3,8,6,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,1,2,8,6,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,5,4,1,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,4,8,5,6,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,5,7,2,4,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,4,3,1,2,8,5,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,4,7,6,2,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,6,5,7,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,1,6,3,5,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,5,7,6,4,1,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,7,5,2,1,3,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,2,3,6,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,2,3,7,1,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,7,2,4,8,3,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,2,4,8,6,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,6,1,5,4,8,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,7,3,2,1,8,5,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,7,2,5,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,8,7,6,1,2,5,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,6,1,3,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,7,4,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,6,4,2,3,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,3,1,6,5,4,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,1,2,5,7,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,8,5,4,2,7,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,6,8,7,3,1,5,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,5,3,7,8,4,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,1,3,8,7,5,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,7,4,8,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,5,2,1,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,2,6,8,1,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,5,6,3,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,4,2,8,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,1,3,8,4,2,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,8,7,3,5,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,8,4,3,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,8,7,4,1,2,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,6,8,1,7,3,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,1,6,8,7,4,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,6,8,2,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,8,3,6,7,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,5,1,3,7,4,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,8,3,7,4,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,8,2,7,1,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,2,3,6,4,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,2,3,4,7,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,5,8,7,4,2,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,5,1,8,4,2,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,6,8,5,2,7,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,1,6,5,4,8,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,8,4,6,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,7,4,3,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,5,7,8,4,6,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,5,2,8,4,6,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,8,2,4,3,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,3,8,1,5,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,1,8,2,3,5,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,4,1,6,3,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,3,1,7,5,2,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,3,8,5,2,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,8,7,1,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,1,8,5,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,2,4,3,6,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,5,6,3,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,5,7,2,3,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,2,7,5,8,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,2,7,3,4,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,2,5,4,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,2,4,5,3,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,2,8,3,6,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,3,4,7,5,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,3,2,1,4,8,5,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,2,1,3,6,4,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,8,3,5,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,2,4,8,5,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,7,3,5,4,2,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,6,5,3,2,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,1,6,4,3,2,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,7,1,4,6,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,3,6,4,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,2,1,7,5,8,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,8,7,5,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,7,2,1,5,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,6,8,1,5,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,8,7,6,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,1,8,5,4,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,5,8,1,7,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,8,7,4,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,4,8,3,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,3,5,6,2,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,8,5,6,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,8,5,3,7,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,2,5,6,1,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,8,2,5,4,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,2,5,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,4,2,1,3,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,4,3,8,5,7,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,5,3,4,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,7,4,5,6,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,4,2,3,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,5,2,4,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,1,3,2,8,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,7,4,8,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,8,2,3,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,2,4,7,1,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,7,4,1,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,4,5,1,8,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,4,1,3,7,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,4,1,2,8,3,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,8,1,3,5,7,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,8,4,1,3,6,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,5,8,1,3,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,1,8,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,8,5,4,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,5,8,3,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,5,3,8,7,6,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,1,8,2,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,5,3,1,7,6,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,5,2,8,1,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,2,1,8,7,6,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,6,2,7,8,1,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,2,8,7,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,6,3,7,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,3,7,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,8,2,7,5,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,2,8,7,5,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,2,7,4,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,7,2,3,1,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,7,2,8,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,7,2,1,8,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,7,2,1,3,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,6,1,7,8,2,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,1,7,2,4,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,6,7,8,3,4,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,6,8,7,3,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,8,6,7,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,6,7,4,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,6,1,7,8,4,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,8,1,7,5,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,8,6,1,7,5,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,6,7,1,8,3,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,7,1,3,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,6,7,1,3,2,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,7,3,1,2,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,6,7,3,8,1,2,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,6,7,3,8,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,4,6,2,3,5,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,8,6,3,2,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,4,1,6,3,8,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,2,5,7,3,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,5,7,6,3,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,5,6,1,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,5,8,6,3,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,2,7,6,1,8,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,5,1,6,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,5,1,4,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,4,1,3,2,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,4,2,3,6,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,4,8,3,7,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,1,8,2,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,1,8,5,3,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,6,1,3,5,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,5,4,7,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,3,7,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,6,7,2,5,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,7,6,5,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,7,5,6,8,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,1,4,7,2,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,1,7,6,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,8,6,4,7,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,8,4,6,3,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,6,5,3,7,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,5,3,6,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,5,2,7,6,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,5,3,1,8,6,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,5,3,6,8,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,2,6,1,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,3,5,7,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,4,6,7,8,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,4,6,5,7,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,5,2,6,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,2,6,8,7,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,8,4,3,1,2,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,5,1,4,3,2,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,5,1,4,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,4,5,2,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,4,1,3,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,5,4,2,3,8,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,2,6,7,3,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,4,3,8,6,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,1,3,5,6,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,8,3,1,5,6,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,1,3,8,5,6,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,8,3,5,6,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,7,8,3,4,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,7,8,3,4,6,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,7,1,5,8,6,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,7,8,2,5,6,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,1,7,8,5,2,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,3,7,5,8,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,7,5,8,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,7,1,8,4,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,8,1,4,6,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,3,7,8,4,6,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,8,4,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,3,7,8,1,4,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,3,7,1,8,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,3,7,8,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,3,7,8,4,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,6,2,5,1,3,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,2,5,1,3,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,5,8,1,7,3,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,8,2,7,3,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,2,3,7,1,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,6,2,7,4,5,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,8,1,7,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,8,3,7,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,8,4,6,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,5,8,4,3,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,8,3,2,7,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,8,2,7,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,8,2,6,1,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,8,3,7,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,1,8,3,7,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,8,4,6,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,8,4,1,6,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,8,1,6,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,4,8,1,6,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,5,1,6,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,1,5,4,8,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,5,2,7,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,5,2,6,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,1,4,8,5,3,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,7,5,6,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,4,3,8,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,4,3,8,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,2,6,7,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,8,4,1,6,7,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,1,7,5,2,8,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,4,3,2,8,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,7,5,3,8,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,7,4,8,2,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,6,7,5,3,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,4,2,1,6,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,4,3,8,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,4,8,1,2,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,5,8,1,2,4,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,4,8,3,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,8,1,2,5,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,1,3,4,8,2,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,2,3,4,8,1,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,4,8,2,1,5,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,5,8,2,4,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,5,8,3,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,8,1,5,7,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,7,6,1,4,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,4,8,2,3,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,4,8,1,3,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,7,5,1,3,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,3,1,4,8,2,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,7,4,8,1,3,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,5,8,4,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,8,2,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,6,3,4,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,3,6,5,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,3,4,7,2,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,7,3,4,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,8,2,3,5,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,8,6,2,3,7,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,3,4,7,5,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,3,4,7,6,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,8,1,7,5,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,1,6,7,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,3,8,4,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,1,7,4,3,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,3,2,8,5,4,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,1,5,7,2,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,5,1,7,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,6,8,7,4,2,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,4,8,5,7,6,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,8,5,7,3,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,8,6,5,7,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,2,8,5,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,2,7,8,6,3,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,8,6,7,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,7,5,4,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,8,7,5,6,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,8,6,7,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,8,6,4,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,7,1,8,5,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,3,2,6,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,4,8,2,6,1,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,8,4,1,5,6,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,1,4,5,6,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,8,1,2,6,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,5,1,4,6,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,4,5,1,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,8,4,1,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,4,8,1,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,8,5,1,6,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,8,1,4,6,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,4,8,2,6,3,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,6,8,1,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,2,8,1,5,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,7,5,8,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,1,8,4,5,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,2,7,8,5,3,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[6,3,7,8,5,4,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,1,5,7,8,4,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,7,5,6,8,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,1,4,8,6,5,3,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,4,1,8,6,5,3,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,2,1,8,6,5,3,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,7,8,5,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,3,7,8,5,1,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,7,3,8,5,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,2,8,5,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,2,8,7,5,3,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,4,2,8,7,5,3,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,6,8,5,4,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,2,6,8,4,5,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,1,6,5,8,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,7,1,8,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,6,1,8,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,7,1,5,8,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,7,3,8,5,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,2,8,4,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,6,1,8,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,7,4,2,5,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,4,2,5,3,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,1,6,4,2,5,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,5,4,7,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,1,5,3,6,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,1,6,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,6,4,2,7,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,3,8,7,4,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,2,8,6,3,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,3,6,1,8,7,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,5,3,8,7,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,7,5,4,6,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,3,1,8,7,5,4,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,8,7,4,2,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,4,2,1,8,6,3,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,8,6,3,5,7,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,3,8,5,2,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,3,7,4,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,8,6,4,7,5,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,8,6,3,7,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,7,4,1,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,5,2,6,3,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,1,8,7,4,2,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,3,7,4,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,8,6,3,2,4,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,1,8,6,3,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,1,8,7,5,3,2,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,3,2,8,7,6,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,4,5,1,3,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,5,8,6,3,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,5,8,6,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,4,2,5,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,6,3,1,7,4,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,2,5,3,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,3,1,8,7,4,2,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,1,8,7,5,3,2,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,8,6,4,1,3,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,1,8,6,3,2,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,2,8,6,3,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,3,1,8,5,2,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,2,6,3,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,8,5,2,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,2,7,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,2,7,4,6,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,3,1,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,1,7,4,8,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,5,8,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,3,1,7,5,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,8,5,2,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,2,1,7,4,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,7,4,6,3,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,5,2,1,4,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,5,6,2,1,4,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,7,8,1,4,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,8,5,7,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,5,8,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,5,8,7,4,3,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,1,5,7,8,4,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,7,4,8,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,2,8,3,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,7,3,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,8,2,4,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,8,7,2,4,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,6,2,4,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,8,4,1,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,4,8,1,6,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,8,1,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,4,8,1,2,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,5,8,1,2,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,5,4,2,3,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,5,4,8,1,2,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,3,8,1,2,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,3,8,1,7,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,3,8,1,6,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,3,8,7,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,3,8,1,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,8,4,1,7,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,7,4,2,6,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,3,8,6,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,5,8,6,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,8,5,6,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,8,7,5,6,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,8,5,7,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,3,6,8,7,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,3,5,8,7,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,8,5,6,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,8,6,7,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,3,2,7,6,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,7,8,1,6,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,8,5,7,6,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,8,7,6,1,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,4,6,5,8,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,7,8,5,1,2,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,6,8,7,5,1,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,8,6,7,5,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,8,6,5,1,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,7,6,4,8,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,4,8,7,1,3,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,6,1,3,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,4,2,7,6,8,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,8,7,1,4,5,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,1,6,3,2,8,7,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,1,8,7,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,2,3,5,4,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,1,4,8,7,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,5,2,8,7,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,2,8,6,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,6,8,1,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,1,8,6,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,6,1,7,3,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,6,3,5,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,5,1,6,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,5,8,1,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,5,6,4,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,7,4,1,8,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,4,6,8,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,8,2,6,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,1,6,5,4,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,3,2,6,1,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,2,3,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,1,8,4,6,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,1,6,7,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,4,3,6,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,4,6,1,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,8,5,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,7,4,8,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,1,6,3,2,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,6,2,7,4,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,1,4,5,2,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,4,8,5,3,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,1,3,6,7,5,4,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,5,2,3,8,6,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,2,4,1,3,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,7,5,1,8,6,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,7,3,2,8,5,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,5,7,6,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,8,4,2,3,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,4,6,1,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,4,6,5,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,7,6,1,5,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,5,1,6,8,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,5,7,3,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,8,4,7,3,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,2,6,5,8,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,2,5,1,6,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,6,8,3,7,4,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,1,5,6,4,7,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,8,1,6,4,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,4,1,8,3,2,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,7,4,2,1,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,2,6,8,3,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,6,5,8,4,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,3,6,1,8,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,3,4,6,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,8,2,5,6,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,3,1,6,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,3,2,4,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,4,2,3,6,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,7,1,5,2,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,8,7,1,4,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,8,6,2,4,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,6,2,7,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,6,2,8,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,4,1,7,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,4,3,5,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,2,3,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,3,5,1,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,6,3,1,4,8,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,1,8,2,7,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,8,1,6,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,4,3,8,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,4,3,8,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,1,7,4,8,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,8,2,1,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,4,1,6,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,5,1,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,7,3,2,8,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,2,1,6,3,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,1,5,3,8,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,6,2,8,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,5,2,8,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,3,8,1,5,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,8,1,5,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,5,3,2,8,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,4,2,8,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,6,3,4,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,1,3,7,4,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,8,6,1,5,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,1,3,7,5,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,8,5,6,1,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,1,3,8,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,7,1,5,2,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,1,3,8,4,2,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,2,7,1,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,2,8,1,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,8,3,7,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,2,1,5,8,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,4,1,5,8,3,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,2,6,4,8,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,7,3,8,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,8,3,7,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,8,3,1,5,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,1,7,4,8,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,8,4,5,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,4,5,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,2,7,1,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,7,3,1,6,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,7,2,8,6,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,1,7,2,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,7,2,8,1,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,7,2,1,5,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,7,1,3,8,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,1,5,7,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,7,1,5,8,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,1,3,7,4,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,1,7,4,8,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,1,5,2,7,6,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,1,3,7,6,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,1,4,3,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,2,1,5,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,2,7,1,4,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,7,4,2,1,8,5,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,5,3,1,8,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,1,4,2,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,1,7,6,4,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,3,2,8,1,5,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,3,2,8,1,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,2,4,8,3,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,6,4,8,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,5,3,8,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,5,3,6,4,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,3,2,7,5,4,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,2,7,1,6,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,6,1,5,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,4,3,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,5,7,2,4,6,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,4,6,7,1,3,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,5,6,1,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,6,8,4,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,6,4,8,3,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,5,8,1,4,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,4,1,3,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,8,3,2,1,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,7,2,1,6,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,8,1,4,3,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,8,2,1,5,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,7,4,8,1,3,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,1,4,8,2,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,4,1,8,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,1,8,4,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,5,7,3,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,5,8,3,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,2,7,8,3,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,3,1,8,6,4,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,1,8,4,7,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,8,7,3,5,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,1,7,6,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,1,4,7,5,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,8,1,6,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,8,1,5,3,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,1,8,6,2,5,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,7,1,3,6,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,8,7,2,1,6,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,7,1,6,3,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,6,1,5,4,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,7,6,1,3,5,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,7,2,6,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,1,7,5,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,8,4,3,1,2,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,8,6,4,3,2,1,7]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,7,3,6,4,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,1,4,2,5,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,3,7,5,4,2,8,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,1,3,5,4,2,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,2,5,4,7,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,6,3,4,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,7,5,8,6,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,7,1,5,3,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,6,7,4,8,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,6,7,4,8,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,7,6,5,3,1,8,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,7,6,5,2,1,8,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,3,6,2,4,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,1,5,4,7,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,6,1,4,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,4,2,6,3,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,1,2,5,3,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,7,6,3,8,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,5,2,8,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,5,1,2,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,7,2,6,1,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,1,6,8,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,6,5,8,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,8,7,6,4,3,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,2,7,6,1,5,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,1,7,6,5,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,5,6,2,3,8,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,3,2,7,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,5,7,3,8,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,7,2,4,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,7,4,5,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,1,5,2,4,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,3,4,6,1,5,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,4,7,5,8,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,3,4,7,8,2,5,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,3,7,4,8,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,6,4,1,7,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,7,4,8,6,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,8,5,4,1,2,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,4,3,1,7,8,2,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,7,6,2,8,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,7,5,8,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,4,1,3,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,5,6,8,4,7,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,1,3,7,6,5,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,1,7,5,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,5,7,4,3,1,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,5,1,7,2,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,4,1,3,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,3,6,2,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,7,4,2,3,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,8,3,1,6,7,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,2,3,1,5,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,4,1,2,7,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,3,2,1,8,4,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,3,7,4,1,8,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,4,1,3,2,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,7,8,5,1,3,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,2,5,6,7,1,3,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,8,5,4,7,6,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,1,5,8,2,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,7,6,2,3,5,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,1,5,3,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,7,3,8,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,4,7,2,5,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,4,6,1,5,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,4,5,7,1,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,2,6,8,3,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,6,2,4,5,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,3,6,5,8,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,5,8,6,1,4,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,2,3,8,6,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,4,1,2,8,3,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,2,3,7,4,6,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,1,5,3,8,7,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,3,2,4,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,2,7,1,8,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,8,2,7,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,2,7,5,3,8,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,7,1,4,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,2,3,7,6,8,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,2,8,3,7,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,8,3,7,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,4,8,6,5,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,4,8,7,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,5,8,7,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,3,8,5,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,3,8,6,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,8,3,7,4,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,4,3,7,5,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,8,3,7,4,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,4,3,8,6,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,5,4,8,7,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,3,8,6,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,7,8,4,5,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,6,8,5,4,7,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,8,5,6,4,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,8,6,4,7,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,4,6,5,8,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,7,8,4,5,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,7,8,5,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,8,6,4,7,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,8,6,5,7,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,8,6,7,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,8,7,5,4,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,8,2,7,4,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,8,6,3,4,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,8,4,5,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,2,8,4,6,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,8,5,6,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,6,8,5,7,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,4,6,8,7,2,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,3,5,8,6,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,8,3,5,7,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,8,4,5,6,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,7,5,8,4,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,4,6,8,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,6,5,8,4,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,8,4,5,7,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,2,7,1,3,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,5,1,3,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,6,1,7,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,7,1,2,5,8,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,7,4,1,2,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,2,3,7,1,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,3,8,1,2,5,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,2,3,8,1,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,7,5,2,8,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,6,3,7,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,1,2,7,4,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,2,7,1,3,5,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,6,4,8,1,3,5,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,8,1,2,5,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,7,2,4,8,1,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,7,8,2,3,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,2,8,6,3,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,8,1,6,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,1,3,7,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,8,1,6,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,8,2,5,1,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,8,2,7,1,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,8,6,2,3,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,4,1,2,5,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,1,2,6,5,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,8,2,7,5,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,1,3,4,7,2,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,8,2,1,6,3,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,2,7,5,4,3,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,7,3,6,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,1,5,7,4,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,3,7,4,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,4,8,7,5,6,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,8,7,4,1,5,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,7,3,8,6,4,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,3,7,6,4,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,7,5,2,1,8,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,3,1,4,6,2,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,1,2,4,7,6,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,7,4,1,2,6,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,1,2,6,7,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,7,8,2,6,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,8,4,5,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,2,8,5,4,7,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,8,1,5,3,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,8,5,7,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,2,1,6,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,6,5,2,7,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,5,6,1,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,7,8,1,2,6,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,7,8,5,2,1,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,7,2,8,4,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,1,7,4,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,7,5,1,6,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,6,7,5,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,4,8,7,5,2,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,2,4,1,7,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,1,4,2,3,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,1,4,2,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,8,4,3,7,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,1,4,7,8,5,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,1,7,4,3,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,7,4,3,6,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,1,3,8,2,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,8,2,3,1,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,6,2,1,3,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,7,4,1,8,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,8,4,2,3,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,7,1,3,8,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,7,1,3,4,2,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,7,4,3,6,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,6,4,5,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,4,6,5,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,3,7,5,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,7,3,6,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,3,4,2,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,1,3,7,2,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,4,3,6,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,3,8,5,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,5,7,3,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,6,4,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,5,8,4,3,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,3,5,8,7,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,2,3,5,4,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,8,3,4,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,6,4,2,3,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,4,5,6,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,3,5,7,8,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,8,6,5,4,2,1,7]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[6,3,1,4,2,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,1,2,6,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,4,5,3,2,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,8,4,2,6,5,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,4,8,6,3,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,1,8,4,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,8,1,5,7,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,4,2,6,5,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,4,1,6,5,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,3,6,4,8,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,4,5,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,2,4,5,1,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,5,4,8,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,5,4,8,6,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,1,8,7,5,3,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,3,7,4,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,7,4,2,6,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,3,1,8,4,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,4,8,6,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,7,4,8,6,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,6,7,4,5,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,1,7,4,5,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,7,4,8,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,3,6,1,4,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,3,6,8,2,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,3,7,4,8,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,5,8,4,1,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,8,4,5,1,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,3,8,4,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,3,8,1,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,8,4,1,6,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,5,1,7,2,6,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,7,1,4,5,2,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,1,8,2,6,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,3,1,5,4,2,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,6,2,1,5,4,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,2,6,1,3,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,6,5,1,4,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,5,8,1,7,4,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,2,7,4,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,2,3,7,5,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,6,2,5,4,8,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,5,1,8,4,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,7,3,1,8,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,3,7,1,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,7,3,8,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,1,5,8,4,3,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,4,2,6,7,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,4,8,1,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,4,8,3,1,7,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,3,2,1,7,6,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,1,3,7,2,6,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,8,2,1,6,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,3,7,2,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,8,1,7,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,1,7,4,6,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,6,4,8,1,5,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,1,8,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,6,3,8,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,1,7,6,4,8,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,5,4,8,7,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,8,7,2,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,4,3,8,7,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,1,8,6,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,5,4,2,1,7,6]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,8,6,5,2,7,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,8,7,5,4,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,8,6,5,4,3,1,7]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,4,2,6,3,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,5,2,8,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,5,3,1,4,2,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,1,5,3,8,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,2,3,5,8,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,7,6,4,2,8,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,1,7,6,4,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,3,7,2,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,2,3,5,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,8,6,3,1,4,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,1,4,8,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,7,5,4,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,7,5,8,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,1,5,8,3,4,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,7,5,1,3,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,2,6,1,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,6,8,3,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,2,8,1,4,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,8,1,3,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,7,8,4,5,1,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,7,3,8,4,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,8,1,5,6,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,8,1,5,2,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,8,4,1,2,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,8,1,2,5,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,7,4,6,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,7,6,3,5,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,8,7,6,5,2,4,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,4,7,6,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,8,5,4,7,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,8,7,6,2,5,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,7,6,3,2,5,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,8,7,6,5,2,1,4]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,5,8,4,6,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,8,2,5,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,2,4,7,6,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,4,7,2,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,4,7,6,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,4,7,6,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,7,4,6,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,4,6,1,2,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,7,4,6,2,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,2,5,7,4,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,2,7,6,4,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,7,2,6,4,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,3,7,6,2,4,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,7,6,1,2,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,7,6,1,4,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,5,7,2,6,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,2,7,6,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,3,7,6,4,1,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,5,4,1,8,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,5,4,1,8,6,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,7,5,1,4,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,7,5,1,4,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,7,1,2,6,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,5,7,2,1,6,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,2,7,1,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,7,2,1,6,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,3,7,1,6,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,7,1,4,6,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,5,7,1,4,6,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,7,1,4,2,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,5,7,4,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,5,2,7,4,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,7,4,2,1,6,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,4,7,1,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,4,7,2,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,4,2,7,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,5,4,7,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,4,7,2,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,4,7,1,2,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,6,3,1,8,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,7,6,3,1,8,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,7,4,1,2,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,7,4,2,1,8,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,2,5,7,4,1,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,5,7,1,4,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,5,2,7,1,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,7,2,1,4,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,7,1,4,2,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,5,2,1,8,6,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,7,2,5,1,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,7,5,1,8,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,7,5,1,8,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,2,5,1,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,2,1,8,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,1,2,5,7,4,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,3,2,7,4,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,5,8,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,3,6,8,4,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,1,8,3,4,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,7,2,4,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,2,6,7,1,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,8,7,2,1,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,8,3,4,1,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,7,2,4,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,6,4,1,7,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,3,5,6,8,1,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,7,6,4,1,8,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,7,4,1,8,6,5,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,8,4,1,7,6,5,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,2,7,6,1,5,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,8,7,6,1,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,8,2,4,1,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,5,8,1,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,5,8,1,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,2,4,1,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,6,8,1,5,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,2,5,6,1,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,8,6,7,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,8,7,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,6,7,1,5,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,7,3,2,5,6,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,2,8,1,5,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,4,1,8,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,5,7,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,5,7,1,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,1,8,7,4,3,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,4,6,3,5,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,5,4,1,6,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,3,4,1,5,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,7,6,8,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,2,3,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,8,5,3,4,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,4,6,8,7,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,6,8,3,4,5,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,7,4,8,6,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,2,7,3,5,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,1,8,3,5,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,4,8,7,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,1,3,2,5,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,8,2,3,1,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,4,3,8,5,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,7,2,1,5,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,8,2,4,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,4,7,3,2,6,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,1,6,7,4,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,5,7,4,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,7,3,4,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,3,5,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,5,6,7,1,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,2,7,8,6,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,6,8,5,1,4,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,2,8,6,5,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,1,6,8,7,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,6,2,1,3,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,5,8,7,4,1,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,1,7,5,2,6,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,6,2,4,5,1,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,4,2,5,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,4,2,5,1,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,1,4,5,2,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,4,8,6,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,6,2,1,3,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,6,5,1,7,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,3,5,2,4,6,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,7,2,4,6,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,5,2,4,6,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,3,2,4,6,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,3,2,4,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,3,2,7,4,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,3,2,4,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,2,5,4,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,1,3,2,4,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,3,2,7,4,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,3,2,5,4,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,3,2,5,4,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,2,4,7,1,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,2,1,4,7,6,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,3,2,7,5,4,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,7,2,5,4,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,3,1,2,5,4,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,1,2,7,4,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,5,1,4,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,1,2,5,4,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,7,2,1,5,4,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,1,2,7,5,4,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,7,2,5,4,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,7,4,2,6,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,5,1,7,6,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,5,1,2,7,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,1,4,7,6,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,8,7,4,3,2,6,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,8,5,4,2,7,6,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,5,3,4,2,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,3,6,2,4,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,6,3,7,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,6,2,7,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,6,3,4,1,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,7,2,3,6,8,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,5,6,4,8,2,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,1,4,8,2,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,5,4,8,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,5,1,6,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,4,8,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,5,4,8,6,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,4,8,6,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,5,1,4,8,7,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,4,2,8,7,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,2,4,8,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,6,4,8,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,6,4,8,7,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,4,1,8,7,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,4,5,8,7,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,6,4,3,8,5,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,1,4,5,3,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,1,3,5,4,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,3,2,5,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,4,2,8,5,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,5,8,2,4,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,5,8,3,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,4,3,8,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,4,3,8,5,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,3,1,5,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,1,5,6,3,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,6,5,1,4,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,6,5,3,8,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,3,1,4,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,2,3,5,4,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,4,5,8,1,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,6,4,8,3,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,6,4,8,3,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,1,4,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,1,3,2,4,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,1,5,3,4,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,6,1,5,4,3,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,6,4,5,8,3,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,6,5,8,1,3,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,4,6,8,7,2,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,5,6,8,2,1,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,2,1,5,3,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,2,5,6,3,1,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,6,8,1,7,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,5,6,3,2,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,3,1,7,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,1,3,5,2,7,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,4,7,3,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,7,1,8,4,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,1,5,3,2,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,5,3,7,1,2,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,6,1,2,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,1,7,4,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,3,7,1,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,6,1,3,7,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,2,1,3,7,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,2,1,7,4,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,1,4,7,6,5,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,6,2,7,1,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,7,1,8,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,1,7,2,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,1,7,5,4,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,2,5,3,8,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,2,3,5,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,2,4,5,1,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,6,7,1,4,5,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,6,7,4,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,2,3,5,8,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,6,4,1,5,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,1,6,7,4,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,4,5,7,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,6,1,4,7,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,1,6,4,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,1,4,8,5,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,4,5,2,8,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,3,6,1,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,1,6,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,3,8,6,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,4,5,8,2,3,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,6,7,2,4,5,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,8,5,2,3,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,8,3,1,6,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,4,8,1,3,6,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,4,1,8,3,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,4,8,6,3,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,4,8,2,5,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,2,4,7,5,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,6,8,2,3,5,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,6,8,4,1,5,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,8,1,4,5,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,1,6,8,4,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,8,1,4,6,7,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,8,6,2,3,7,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,4,2,6,7,3,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,4,5,1,3,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,6,7,5,3,4,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,6,2,3,8,4,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,6,7,5,8,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,2,5,8,3,4,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,3,8,7,4,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,4,7,3,5,8,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,3,7,1,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,3,6,5,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,3,6,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,4,3,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,1,3,7,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,4,5,3,8,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,5,3,7,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,1,3,6,2,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,6,5,1,7,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,5,7,2,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,4,7,6,8,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,6,2,5,8,7,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,2,4,6,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,5,1,6,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,2,3,6,5,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,8,3,5,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,8,6,5,7,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,7,2,6,5,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,6,4,2,5,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,4,7,3,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,3,8,4,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,3,4,8,2,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,2,8,3,4,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,3,8,5,2,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,2,7,3,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,3,8,2,4,5,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,5,3,7,6,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,3,7,8,2,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,3,7,8,5,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,2,6,5,7,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,6,7,5,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,7,8,5,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,2,6,7,8,1,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,1,8,3,6,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,6,8,5,7,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,8,5,6,1,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,8,1,7,6,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,6,8,5,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,8,5,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,3,6,8,7,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,8,4,6,7,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,8,3,7,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,5,8,6,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,6,8,7,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,4,8,3,1,7,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,8,7,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,4,8,2,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,4,8,2,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,3,8,2,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,8,1,7,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,3,8,2,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,8,1,3,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,8,3,4,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,5,4,3,7,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,4,2,5,3,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,7,8,5,3,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,5,3,1,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,8,7,6,3,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,3,1,8,7,5,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,3,1,7,5,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,2,7,6,3,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,3,1,8,4,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,4,2,1,8,3,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[1,8,2,7,6,4,3,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,2,4,6,3,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,8,6,3,7,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,7,5,2,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,6,4,7,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,2,7,5,3,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,2,1,8,3,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,2,6,3,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,4,1,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,8,7,4,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,4,1,5,2,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,1,5,2,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,3,1,4,2,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,2,8,6,3,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,5,2,6,3,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,2,1,3,6,4,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,3,7,6,5,8,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,6,4,7,5,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,8,7,5,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,3,1,4,7,5,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,7,6,3,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,2,5,7,6,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,8,2,6,4,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,2,1,6,4,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,3,8,7,4,1,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,7,4,1,5,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,1,6,3,5,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,1,8,6,3,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,6,3,1,7,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,7,5,2,1,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,4,7,5,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,6,3,5,2,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,2,8,7,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,5,2,7,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,7,3,5,2,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,7,4,2,6,3,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,6,3,5,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,5,8,2,7,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,5,8,1,6,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,3,4,7,1,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,5,7,8,1,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,3,4,6,5,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,3,7,4,2,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,6,8,2,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,2,3,1,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,2,6,8,1,5,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,6,1,5,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,2,7,1,5,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,8,3,1,5,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,7,2,8,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,2,8,6,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,7,3,8,1,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,8,5,2,4,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,2,8,1,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,6,8,3,1,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,4,6,5,3,1,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,4,8,3,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,1,6,2,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,3,1,7,2,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,3,1,2,6,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,7,1,3,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,1,2,4,3,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,1,6,2,3,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,1,3,6,5,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,3,4,2,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,2,5,7,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,4,3,5,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,5,3,1,7,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,4,3,6,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,6,3,1,8,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,4,6,3,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,5,7,4,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,6,5,7,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,2,7,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,5,3,8,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,5,8,3,4,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,5,3,8,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,5,4,7,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,4,7,5,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,5,8,7,4,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,7,2,8,5,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,8,7,3,5,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,1,7,6,3,5,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,8,5,7,4,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,6,8,5,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,2,8,6,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,7,5,6,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,8,7,6,4,5,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,7,6,5,3,4,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,6,7,2,5,3,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,8,5,7,6,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,7,8,2,6,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,7,8,1,6,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,2,6,8,7,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,7,8,2,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,3,8,2,7,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,8,4,2,7,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,3,7,1,5,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,3,8,1,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,3,8,2,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,8,4,1,7,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,7,1,2,8,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,1,8,2,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,4,1,2,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,3,7,1,2,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,1,8,3,7,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,5,6,3,2,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,7,8,3,5,2,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,5,3,7,2,4,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,7,2,4,8,5,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,8,7,4,3,5,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,7,5,8,4,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,1,7,8,4,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,7,8,2,1,5,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,5,1,4,7,3,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,7,5,3,6,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,4,6,7,3,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,5,8,6,7,4,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,8,4,7,1,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,1,3,6,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,7,6,4,8,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,1,7,5,6,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,3,6,5,7,1,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,5,4,2,1,8,6]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,3,6,7,4,2,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,6,4,8,2,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,6,3,2,7,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,7,1,5,6,3,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,6,7,5,3,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,7,8,2,6,4,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,7,2,5,4,6,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,2,5,3,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,6,7,3,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,7,2,8,5,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,1,8,4,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,8,2,1,6,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,8,1,2,3,7,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,2,3,6,5,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,8,4,7,2,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,5,4,6,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,5,4,6,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,5,1,6,4,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,5,4,6,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,5,4,6,3,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,4,6,3,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,8,4,7,3,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,4,2,7,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,5,4,1,6,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,8,1,7,6,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,8,4,7,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,8,4,7,3,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,4,1,7,8,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,6,4,8,7,5,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,6,4,3,7,8,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,1,3,4,8,6,5,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,6,1,3,8,4,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,6,4,2,7,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,4,3,7,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,4,1,7,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,3,4,8,6,5,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,2,3,1,8,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,3,4,1,6,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,4,3,8,5,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,3,8,6,1,4,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,8,6,3,4,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,3,8,1,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,3,8,5,6,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,4,8,7,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,8,4,7,6,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,8,1,6,7,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,1,3,8,2,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,6,1,8,5,4,2,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,1,6,5,8,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,5,8,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,5,8,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,1,6,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,6,4,8,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,4,8,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,6,4,8,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,5,8,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,7,4,8,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,7,4,8,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,1,6,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,2,6,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,1,5,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,1,6,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,2,6,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,1,6,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,2,7,6,3,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,7,2,6,3,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,2,7,3,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,8,7,6,3,2,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,1,8,6,7,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,8,6,3,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,7,2,8,3,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,6,8,3,7,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,8,3,2,1,4,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,7,5,2,1,8,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,4,1,6,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,3,1,6,5,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,8,4,3,1,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,5,2,8,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,2,4,1,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,4,6,5,7,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,6,7,3,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,7,6,3,8,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,7,6,3,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,2,7,5,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,4,7,5,1,6,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,1,2,6,5,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,4,6,5,7,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,5,7,3,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,4,6,2,8,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,7,3,8,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,2,6,8,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,3,2,5,7,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,8,5,3,4,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,4,3,8,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,8,5,3,4,7,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,4,7,6,1,5,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,2,6,7,5,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,7,5,8,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,4,5,7,6,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,4,7,6,2,3,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,4,1,5,3,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,3,4,7,2,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,4,7,6,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,7,6,2,5,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,3,5,2,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,3,5,1,4,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,3,5,1,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,5,8,4,3,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,8,4,7,2,3,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,2,6,5,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,1,6,5,8,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,3,4,8,2,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,8,2,4,7,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,7,2,8,5,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,7,4,6,2,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,2,3,8,5,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,5,4,2,3,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,8,4,7,1,3,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,2,4,3,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,5,8,2,7,6,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,8,3,4,5,2,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,1,5,3,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,6,3,2,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,1,3,5,4,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,3,4,2,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,3,4,2,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,3,2,5,6,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,2,4,5,3,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,2,4,3,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,3,8,4,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,1,6,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,3,5,6,2,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,8,4,1,3,5,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,1,6,8,4,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,6,1,5,7,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,7,3,5,8,6,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,2,7,5,8,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,4,7,5,8,6,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,4,7,8,1,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,7,6,1,8,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,6,8,1,7,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[7,3,6,8,2,5,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,3,8,6,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,3,8,6,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,4,7,8,3,5,6,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,4,7,2,8,5,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,2,7,8,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,2,7,6,1,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,6,8,1,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,2,8,1,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,6,2,1,8,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,4,2,5,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,2,3,5,8,7,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,2,3,7,5,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,4,2,7,5,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,6,2,7,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,5,2,1,7,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,5,3,2,1,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,3,4,2,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,4,2,3,7,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,6,4,2,1,8,7,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,4,8,3,2,7,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,8,3,2,7,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,8,3,7,2,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,5,7,4,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,6,5,4,1,7,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,5,6,4,1,8,7,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,8,6,4,5,7,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,6,2,5,7,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,6,5,3,7,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,5,6,4,7,1,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,5,4,1,7,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,5,4,8,1,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,6,3,2,8,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,7,3,2,8,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,3,8,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,4,2,7,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,4,3,2,1,8,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,4,3,6,2,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,2,6,5,8,7,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,2,8,4,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,2,7,4,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,2,7,3,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,2,8,3,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,3,4,8,7,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,1,2,8,3,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,1,2,7,3,6,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,2,8,3,6,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,3,8,4,6,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,3,7,4,6,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,2,7,3,6,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,7,2,3,5,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,7,2,4,5,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,8,2,4,5,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,1,8,2,3,5,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,2,8,3,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,7,2,4,5,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,6,8,2,4,5,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,3,8,7,5,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,2,7,4,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,3,7,4,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,7,3,4,5,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,7,2,4,5,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,7,2,3,5,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,6,2,3,5,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,6,2,4,5,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,6,2,4,5,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,1,6,2,3,5,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,7,4,6,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,2,6,1,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,2,5,1,4,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,7,5,1,4,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,5,8,7,3,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,2,4,7,3,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,8,3,5,7,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,4,8,7,5,6,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,5,7,4,8,6,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,6,3,7,8,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,7,1,8,6,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,6,8,3,7,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,1,3,5,2,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,4,5,1,3,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,7,8,3,5,6,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,6,7,1,8,4,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,6,1,3,7,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,4,1,8,5,2,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,8,1,5,3,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,8,3,1,4,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,4,1,5,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,4,2,6,7,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,1,8,5,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,2,7,8,5,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,2,6,7,8,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,5,1,6,7,3,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,4,1,7,5,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,5,3,1,7,4,2,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,2,8,7,1,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,8,1,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,7,1,6,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,3,2,6,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,4,7,3,1,6,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,1,2,8,4,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,7,2,3,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,6,7,8,4,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,4,8,5,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,8,2,3,6,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,2,3,5,1,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,2,4,5,7,3,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,6,3,8,7,5,4,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,2,3,7,5,4,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,6,3,5,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,1,5,2,4,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,2,4,1,5,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,1,6,5,3,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,6,1,5,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,2,6,5,4,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,2,5,7,4,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,1,7,5,4,2,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,2,7,4,1,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,1,8,7,5,4,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,8,1,5,7,6,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,2,8,7,6,4,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,4,8,2,7,6,5,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,4,8,7,1,6,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,1,3,5,7,6,4,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,1,8,5,7,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,7,3,4,6,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,1,7,2,6,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,2,4,7,6,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,8,3,7,4,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,2,3,7,1,6,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,7,1,3,6,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,7,2,6,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,5,2,4,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,3,7,4,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,8,5,7,6,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,2,4,3,7,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,7,3,5,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,7,3,1,5,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,1,8,7,5,4,3]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,1,8,2,7,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,7,3,5,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,2,7,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,7,2,4,6,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,4,1,7,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,2,8,3,7,6,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,2,1,7,6,5,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,1,8,7,2,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,1,3,7,6,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,5,4,1,7,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,4,3,7,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,1,3,7,6,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,3,8,1,7,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,6,3,2,1,7,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,7,6,3,2,4,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,7,2,4,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,1,3,2,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,1,3,2,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,5,1,3,7,2,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,1,3,2,4,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,8,2,1,4,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,1,2,5,4,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,8,1,4,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,3,1,2,7,5,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,8,1,2,5,7,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,1,2,3,8,6,4,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,1,3,8,2,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,8,5,3,4,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,4,8,2,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,6,5,2,3,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,5,7,4,1,3,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,8,2,3,5,6,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,6,8,1,3,4,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,8,2,3,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,3,8,2,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,8,1,5,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,5,4,1,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,5,4,2,1,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,5,2,1,6,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,3,2,6,1,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,3,2,8,5,6,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,5,4,1,6,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,2,4,7,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,5,1,2,8,6,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,3,4,7,8,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,7,4,3,6,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,4,3,6,8,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,7,1,8,2,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,6,3,2,5,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,7,6,5,2,3,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,7,6,5,1,3,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,6,5,2,3,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,6,5,8,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,5,1,3,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,5,3,8,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,3,2,8,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,4,6,8,7,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,4,2,8,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,4,2,1,8,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,7,3,2,1,8,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,7,6,2,1,4,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,6,3,2,8,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,8,1,7,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,2,3,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,5,8,3,4,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,3,6,8,1,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,2,6,3,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,2,8,5,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,2,8,5,3,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,6,3,7,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,7,1,6,8,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,4,1,6,5,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,8,2,6,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,7,8,3,5,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,1,7,3,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,6,2,8,4,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,1,5,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,6,5,8,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,6,2,5,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,6,5,8,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,5,8,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,6,2,8,4,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,6,8,5,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,6,1,5,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,2,6,8,5,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,1,5,8,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,6,1,8,4,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,2,6,3,5,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,7,5,8,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,5,1,4,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,5,4,3,6,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,6,3,4,5,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,8,4,2,5,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,7,8,6,2,5,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,1,4,8,7,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,1,2,7,8,5,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,7,3,1,6,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,4,5,8,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,6,1,5,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,6,5,4,1,8,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,7,1,8,5,3,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,5,4,6,7,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,5,6,4,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,2,6,4,3,5,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,2,6,4,7,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,7,5,8,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,1,3,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,8,1,6,2,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,5,1,3,2,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,3,1,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,8,4,2,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,2,3,8,4,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,2,7,3,4,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,3,8,5,4,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,7,6,8,5,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,8,6,1,5,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,7,6,8,5,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,6,8,2,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,8,6,1,3,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,8,6,5,2,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,7,4,6,3,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,6,1,8,3,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,4,1,5,7,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,8,6,4,2,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,8,5,7,4,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,6,4,5,3,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,6,3,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,6,5,1,4,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,8,4,3,1,6,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,2,8,7,4,3,5,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,6,2,5,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,4,8,6,3,5,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,8,1,3,2,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,8,6,4,1,7,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,4,6,1,5,7,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,5,6,8,7,4,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,7,2,3,6,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,2,7,4,1,8,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,2,3,5,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,7,2,3,6,5,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,2,3,1,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,3,1,5,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,4,6,2,8,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,5,1,4,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,5,1,4,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,7,4,5,8,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,3,6,8,4,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,4,3,8,6,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[6,7,5,1,3,4,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,8,2,6,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,8,2,5,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,4,3,6,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,3,8,7,6,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,6,2,5,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,8,6,4,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,8,5,6,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,6,1,5,3,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,2,3,1,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,2,3,8,6,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,2,3,8,1,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,2,3,5,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,2,7,8,6,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,7,8,6,3,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,5,2,3,8,1,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,2,3,8,4,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,1,7,6,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,2,4,1,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,5,4,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,7,5,2,3,6,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,5,1,6,2,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,1,3,8,7,6,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,8,3,6,1,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,7,8,3,4,5,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,5,6,1,7,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,7,5,8,6,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,3,8,6,5,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,8,7,4,6,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,8,4,6,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,3,6,5,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,5,8,7,2,6,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,8,6,7,5,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,7,6,5,8,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,7,8,5,2,3,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,5,3,8,2,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,5,4,1,7,6,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,4,7,2,5,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,3,8,7,5,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,6,4,1,2,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,4,3,5,7,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,4,8,7,6,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,8,3,5,4,2,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,2,5,4,3,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,2,4,5,1,8,6,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,8,5,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,4,1,7,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,5,1,7,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,4,1,3,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,1,4,8,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,5,3,8,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,1,8,2,4,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,2,1,5,3,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,1,4,7,8,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,8,3,1,6,7,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,8,2,6,5,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,8,2,7,3,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,7,2,5,3,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,4,6,5,3,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,2,4,8,7,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,3,2,6,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,3,4,6,8,1,2,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,6,7,2,5,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,6,8,3,7,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,6,5,8,3,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,2,7,1,4,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,4,6,3,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,5,8,3,4,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,8,1,3,4,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,8,5,6,3,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,1,3,5,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,6,3,5,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,7,3,6,4,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,4,2,8,3,6,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,1,2,5,8,4,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,8,1,4,7,3,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,8,6,1,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,4,8,1,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,7,8,5,4,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,2,7,4,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,1,8,4,3,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,1,8,3,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,4,7,3,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,6,7,4,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,8,2,3,7,1,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,8,3,7,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,8,3,6,7,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,6,3,5,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,5,6,8,1,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,5,7,4,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,2,8,1,5,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,6,8,7,2,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,5,7,6,8,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,6,1,4,2,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,8,2,4,6,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,4,6,8,5,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,4,6,7,3,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,7,8,1,5,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,5,7,8,3,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,7,8,1,5,6,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,6,3,5,7,8,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,2,5,7,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,6,7,3,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,6,7,5,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,5,8,6,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,1,8,3,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,8,3,2,5,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,5,4,7,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,5,2,3,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,2,1,3,6,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,5,1,3,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,7,5,4,3,2,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,1,6,8,2,3,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,8,1,5,4,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,4,7,6,2,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,7,6,5,1,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,5,2,1,6,4,3,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,7,2,4,3,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,1,3,4,2,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,5,8,6,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,5,8,3,2,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,2,4,8,5,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,5,8,4,6,3,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,2,5,8,4,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,4,5,8,7,3,2,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[7,1,5,4,8,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,1,7,5,3,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,2,7,4,6,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,1,5,3,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,6,4,8,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,5,4,8,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,2,5,3,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,2,1,4,3,8,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,1,3,8,6,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,1,4,2,3,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,1,6,5,3,2,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,3,8,6,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,2,3,8,6,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,4,8,1,3,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,2,8,4,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,8,3,2,6,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,4,8,1,5,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,8,1,5,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,4,8,3,7,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,2,8,4,1,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,5,2,1,8,3,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,6,5,2,1,8,4,3]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[2,7,5,1,8,3,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,8,7,4,3,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,7,2,4,6,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,1,3,2,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,7,6,3,5,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,7,6,3,5,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,8,3,2,5,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,8,5,3,7,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,6,8,3,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,6,5,1,7,4,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[5,6,2,7,4,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,7,6,2,5,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,5,2,6,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,2,5,6,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,8,2,6,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,7,8,5,2,1,4,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,8,4,7,3,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,2,7,8,4,1,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,8,4,7,3,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,8,2,6,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,6,2,1,7,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,7,6,2,1,5,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,7,6,2,1,5,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,6,5,1,2,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,5,4,6,1,8,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,5,4,6,1,8,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,4,5,1,8,6,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,5,1,7,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,5,1,7,6,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,4,6,7,1,2,5,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,2,6,1,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,2,6,1,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,2,6,1,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,6,8,1,3,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,6,8,1,3,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,8,7,5,6,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,4,7,2,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,5,6,1,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,6,5,1,7,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,5,1,7,6,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,4,6,5,1,3,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,4,6,1,3,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,5,6,1,4,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,5,4,6,1,3,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,7,3,4,5,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,2,5,4,3,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,7,3,4,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,1,5,7,4,3,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,8,7,5,6,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,8,7,4,3,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,1,7,4,6,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,2,4,6,8,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,6,4,2,7,3,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,8,6,2,7,3,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,8,6,2,3,5,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,1,8,3,5,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,8,1,7,6,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,8,1,3,6,7,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,2,4,8,6,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,7,5,8,3,6,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,3,2,8,1,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,2,4,3,8,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,4,3,1,6,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,4,3,1,6,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,2,8,1,5,7,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,3,5,4,2,6,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,2,5,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,7,3,2,6,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,7,6,4,2,5,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,2,6,3,4,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,5,4,6,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,4,6,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,2,5,4,6,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,5,4,2,8,6,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,7,2,3,6,8,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,7,2,6,5,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,2,7,6,8,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,8,1,7,3,4,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,3,2,1,7,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,5,1,7,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,1,7,5,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,8,2,6,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,6,2,8,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,5,2,8,1,3,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,3,7,2,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,7,6,2,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,5,2,8,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,2,6,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,3,2,6,5,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,6,5,2,8,7,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,6,5,7,2,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,5,3,8,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,5,8,7,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,5,8,4,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,8,4,1,7,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,8,1,6,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,8,7,6,4,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,2,8,7,3,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,6,8,5,1,7,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,2,6,4,3,5,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,2,8,5,4,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,2,8,6,3,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,5,6,3,1,4,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,7,8,5,3,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,3,7,8,5,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,4,5,1,2,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,3,2,4,1,8,7]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,8,7,3,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,2,4,1,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,1,4,7,8,5,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,3,6,4,7,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,1,6,5,7,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,6,7,3,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,7,5,3,2,6,4,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[4,8,7,5,3,2,6,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,7,8,5,3,1,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,3,4,6,5,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,3,6,4,7,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,1,6,4,3,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,1,4,3,7,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,4,7,8,1,2,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,3,6,5,8,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,5,7,1,6,8,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,1,2,7,5,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,1,7,3,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,6,1,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,3,1,6,5,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,6,7,3,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,8,5,3,1,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,2,4,6,1,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,8,1,6,2,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,5,6,7,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,5,1,2,8,4,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,2,4,8,5,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,5,8,1,4,6,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,4,5,8,7,3,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,1,4,2,6,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,1,8,5,2,4,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,1,8,7,5,4,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,1,7,5,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,7,5,3,4,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,1,4,3,6,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,3,4,1,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,7,3,4,2,6,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,4,5,2,3,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,2,8,6,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,5,2,3,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,7,5,2,8,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,1,3,6,4,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,2,6,3,1,5,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,6,3,8,7,5,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,4,1,5,7,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,4,2,5,7,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,5,4,1,7,6,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,5,8,3,7,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,5,2,4,7,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,4,6,2,8,7,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,8,2,4,1,6,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,6,1,8,7,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,8,4,5,1,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,8,2,7,6,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,1,6,8,7,5,3,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,8,2,4,5,7,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,2,8,3,5,7,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,8,2,5,7,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,8,1,5,7,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,6,1,8,7,5,3,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,2,8,7,5,3,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,3,8,7,5,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,3,8,7,5,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,8,1,5,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,8,2,5,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,1,4,5,7,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,8,2,1,4,6,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,6,8,7,5,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,1,6,8,7,2,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,4,5,1,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,4,5,7,2,3,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,4,7,6,3,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,3,1,6,4,7,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,8,6,2,7,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,6,1,5,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,5,3,7,2,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,1,4,5,2,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,8,4,6,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,1,6,5,3,8,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,6,8,5,2,3,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,6,8,1,4,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,4,7,2,3,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,5,1,8,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,1,5,3,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,7,8,1,2,6,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,7,1,5,6,2,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,6,5,8,7,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,2,1,3,6,4,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,7,1,6,2,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,2,7,6,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,7,2,5,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,6,5,8,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,8,5,7,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,1,5,2,7,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,3,8,7,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,1,4,2,5,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,1,8,3,2,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,2,7,8,4,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,8,1,2,7,6,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,4,8,2,6,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,2,6,8,7,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,6,2,5,7,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,8,1,2,6,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,1,5,7,6,2,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,6,8,5,2,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,1,2,8,4,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,1,8,3,4,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,1,2,7,6,4,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,5,8,7,6,2,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,6,1,5,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,6,3,1,5,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,1,3,4,5,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,7,4,8,2,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,6,1,4,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,8,2,4,6,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,8,4,1,5,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,2,8,1,5,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,5,4,1,7,2,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,4,7,3,2,5,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,5,3,8,4,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,4,5,7,8,1,3,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,7,4,1,6,8,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,1,2,7,6,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,2,8,4,5,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,8,3,5,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,5,2,4,6,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,4,8,3,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,8,6,3,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,2,5,3,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,5,2,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,8,6,5,3,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,8,4,6,3,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,3,2,8,6,4,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,8,1,2,7,4,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,7,3,6,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,5,4,2,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,1,3,7,8,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,3,7,2,1,8,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,4,2,5,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,1,6,4,7,5,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,2,7,5,4,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,7,5,3,6,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,3,4,1,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,5,8,6,4,7,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,4,7,3,8,6,5,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,4,2,7,5,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,5,4,7,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,7,2,3,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,8,1,4,6,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,5,8,7,4,1,3,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,4,7,5,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,4,7,1,3,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,5,1,4,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,7,1,3,2,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,4,7,5,3,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,7,1,4,3,5,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,1,8,4,7,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,3,6,1,2,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,1,7,4,3,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,7,6,2,3,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,8,2,5,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,6,1,8,7,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,4,1,7,5,2,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,7,8,2,3,6,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,8,7,4,1,5,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,6,7,5,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,3,7,5,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,3,1,8,5,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,7,5,3,4,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,4,5,7,3,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,4,5,8,3,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,1,8,5,3,4,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,5,6,8,3,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,4,7,1,8,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,1,8,7,2,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,7,2,6,8,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,8,5,4,1,7,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,8,5,1,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,8,5,2,7,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,8,6,7,2,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,8,3,6,7,1,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,8,5,6,1,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,3,7,6,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,7,4,6,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,8,4,6,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,3,8,6,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,7,8,6,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,8,6,5,1,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,3,8,5,2,4,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,8,6,5,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,3,8,7,6,2,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,7,8,6,2,3,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,7,5,6,8,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,4,6,8,5,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,5,8,2,6,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,6,5,8,1,3,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,6,4,8,1,3,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,5,3,6,8,2,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,6,7,8,1,3,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,7,8,1,6,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,6,8,1,2,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,8,6,1,2,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,6,8,7,5,1,2,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,6,8,4,7,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,2,6,8,7,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,4,6,8,7,2,3,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,5,3,8,1,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,8,4,1,7,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,8,1,5,7,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,3,8,4,2,7,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,4,8,1,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,8,7,2,6,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,8,6,2,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,5,7,8,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,7,3,5,8,2,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,4,8,5,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,4,8,2,3,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,4,8,1,3,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,6,4,8,5,1,3,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,5,8,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,6,5,8,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,3,4,6,2,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,3,6,5,2,4,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,5,2,4,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,1,2,7,4,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,7,4,6,1,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,8,3,1,2,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,1,7,4,5,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,3,1,5,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,1,7,4,5,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,4,8,3,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,3,7,5,6,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,8,2,6,1,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,4,7,5,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,8,5,7,3,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,5,3,8,6,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,5,7,8,1,2,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,1,6,5,7,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,1,2,6,4,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,3,7,4,2,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,7,2,4,1,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,1,3,5,4,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,8,4,6,3,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,1,4,6,2,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,8,4,2,6,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,5,3,4,2,7,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,3,4,5,2,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,4,3,5,1,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,5,2,1,3,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,2,6,1,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,1,6,8,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,8,2,5,6,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,7,8,2,5,6,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,1,7,5,2,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,6,7,2,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,6,8,3,5,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,7,3,8,5,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,3,4,8,1,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,4,6,2,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,6,2,3,1,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,2,4,6,1,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,6,7,1,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,6,5,2,4,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,6,7,5,2,8,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,4,6,7,8,1,3,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,3,6,7,8,1,4,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,3,7,6,8,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,5,4,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,7,6,4,8,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,3,2,8,6,4,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,8,6,7,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,8,4,6,3,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,4,3,7,5,2,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,7,3,6,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,6,3,8,2,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,4,7,1,3,5,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,4,7,8,1,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,1,6,3,5,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,4,3,6,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,4,8,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,7,4,6,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,3,7,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,4,7,3,5,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,6,5,7,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,5,7,2,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,5,6,2,7,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,1,7,6,2,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,1,6,4,2,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,6,1,5,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,2,8,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,6,1,7,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,1,6,2,7,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,1,6,3,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,5,6,3,7,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,2,8,5,4,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,7,4,1,5,3,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,4,2,5,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,3,1,5,2,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,4,1,5,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,3,8,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,7,4,3,1,6,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,3,4,2,7,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,5,3,1,2,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,5,1,3,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,5,1,2,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,1,7,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,3,5,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,3,2,6,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,1,8,6,3,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,3,5,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,2,5,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,2,4,1,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,1,6,4,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,3,2,7,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,6,1,7,4,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,2,6,1,5,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,7,3,6,1,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,7,6,1,5,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,4,1,7,3,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,4,1,7,2,5,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,8,5,7,1,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,2,6,1,3,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,5,6,3,2,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,2,5,4,6,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,1,6,5,3,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,2,7,5,6,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,6,5,4,3,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,5,1,4,6,2,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,1,3,5,6,2,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,2,1,5,6,3,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,5,1,6,4,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,4,5,3,2,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,4,6,5,2,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,4,1,5,3,2,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,1,5,2,3,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,7,3,1,8,4,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,8,6,3,7,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,2,3,7,6,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,8,3,1,7,6,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,8,5,1,2,6,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,5,7,2,4,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,6,3,1,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,1,6,8,3,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,3,2,8,5,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,1,8,4,6,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,4,1,3,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,8,5,2,6,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,8,4,7,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,3,8,7,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,6,8,7,4,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,7,3,8,1,5,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,3,8,4,1,5,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,8,1,5,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,8,1,4,5,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,8,5,7,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,8,5,1,4,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,8,4,5,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,3,4,8,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,1,8,7,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[5,2,3,1,4,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,1,3,2,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,4,2,8,5,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,4,3,2,8,6,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,3,4,2,8,6,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,1,4,3,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,2,4,3,8,6,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,1,8,3,5,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,6,1,8,4,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,7,3,8,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,3,2,8,5,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,7,4,8,5,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,6,8,2,4,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,7,2,8,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,7,1,8,5,4,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,4,3,1,2,8,6,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,2,4,1,3,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,3,1,8,6,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,4,2,7,8,5,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,1,6,8,2,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,4,1,2,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,2,4,1,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,3,4,1,8,6,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,6,1,7,4,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,7,4,3,1,6,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,8,7,1,4,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,6,3,7,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,2,8,1,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,6,2,8,1,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,1,4,8,5,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,8,4,2,5,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,5,1,6,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,3,2,8,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,8,2,5,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,8,3,5,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,3,7,4,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,2,6,8,4,3,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,7,2,8,6,5,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,7,3,6,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,5,8,1,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,5,1,8,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,1,8,2,3,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,3,1,8,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,4,8,3,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,8,1,7,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,1,6,7,3,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,7,8,4,3,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,8,1,4,3,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,1,3,5,6,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,3,7,8,4,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,7,8,2,4,5,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,5,2,4,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,2,4,3,1,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,4,2,3,1,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,6,5,3,1,8,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,4,1,3,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,2,5,1,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,6,1,8,4,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,5,6,2,8,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,6,4,8,1,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,4,2,5,3,7,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,5,4,6,7,1,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,2,6,5,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,2,6,4,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,2,5,3,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,2,6,3,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,2,6,4,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,6,4,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,2,5,3,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,1,4,3,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,2,5,4,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,3,5,4,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,2,6,3,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,3,6,4,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,3,6,4,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,2,6,4,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,2,6,3,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,2,7,4,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,3,7,5,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,2,8,5,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,2,8,4,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,1,3,2,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,8,4,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,8,4,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,3,8,4,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,2,8,3,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,3,8,1,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,7,1,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,7,3,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,4,8,3,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,2,6,1,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,8,1,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,3,1,4,2,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,7,3,5,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,7,3,5,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,5,1,2,6,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,3,1,5,4,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,4,1,5,3,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,5,4,1,3,2,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[5,3,8,7,4,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,8,7,4,6,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,3,5,7,4,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,8,5,3,1,2,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,8,7,3,1,5,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,8,5,4,1,3,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,5,8,7,4,6,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,8,7,6,5,1,3,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,8,7,5,1,6,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,3,8,7,5,6,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,7,1,3,6,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,7,3,5,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,8,6,4,2,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,8,4,1,5,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,2,1,7,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,4,6,1,2,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,8,6,5,1,7,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,8,7,6,5,2,1,3]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[4,8,7,5,1,6,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,2,1,8,6,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,8,3,1,6,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,7,2,8,4,6,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,3,2,4,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,2,8,6,4,5,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,8,4,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,8,6,4,1,3,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,6,3,5,2,8,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,4,8,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,6,5,1,7,2,4,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,8,5,1,7,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,8,3,7,4,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,6,3,4,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,2,6,4,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,4,8,1,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,8,2,4,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,3,8,7,5,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,3,8,7,5,4,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[6,8,4,2,1,7,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,2,6,4,3,8,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,3,1,4,8,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,1,7,8,6,4,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,8,1,7,6,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,7,6,4,2,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,6,3,8,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,8,6,4,1,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,5,8,2,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,5,2,4,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,6,3,8,2,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,7,1,3,6,5,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,6,7,4,3,8,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,2,4,7,3,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,5,8,7,2,4,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,8,7,3,6,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,3,7,2,5,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,2,8,1,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,6,1,5,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,1,5,8,4,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,2,8,1,4,3,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,8,3,2,6,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,7,4,8,3,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,5,4,8,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,5,4,3,8,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,4,5,6,8,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,2,7,6,4,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,2,3,7,6,4,5,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,4,2,3,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,2,3,7,4,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,4,2,3,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,2,8,6,4,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,4,2,8,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,1,5,8,6,3,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,8,4,6,1,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,3,8,6,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,5,8,1,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,2,5,8,1,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,2,8,6,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,6,1,3,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,8,6,1,4,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,6,5,4,8,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,5,7,2,6,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,4,6,8,5,3,7,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,4,8,1,7,6,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,3,8,1,5,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,4,1,5,7,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,3,6,8,5,2,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,4,7,2,6,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,6,8,5,4,2,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,6,4,8,5,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,4,1,8,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,4,1,5,2,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,5,1,3,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,8,3,5,6,7,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,6,2,4,7,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,5,4,6,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,3,7,4,6,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,7,4,1,3,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,5,7,4,1,3,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,4,6,3,5,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,6,1,5,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,4,1,6,5,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,6,5,3,1,7,4,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[6,4,7,3,1,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,7,5,3,1,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,2,7,5,1,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,4,2,6,3,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,5,4,2,6,1,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,4,6,3,1,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,7,3,1,8,6,5,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,6,5,3,1,7,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,6,4,7,3,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,4,2,7,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,6,8,2,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,7,5,3,1,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,8,6,5,3,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,2,8,6,3,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,6,3,2,8,4,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,6,4,8,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,4,3,2,5,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,3,2,6,5,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,2,5,4,1,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,2,5,1,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,3,8,7,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,6,3,2,5,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,3,8,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,3,8,6,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,8,7,2,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,4,8,2,1,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,2,6,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,3,2,6,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,2,7,1,8,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,5,1,8,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,1,8,6,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,7,5,3,1,8,6,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,6,5,3,1,7,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,7,5,4,2,6,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,2,8,4,3,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,2,8,7,4,3,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,2,7,3,1,8,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,2,4,1,8,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,8,7,4,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,3,2,7,5,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,3,7,5,8,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,7,5,2,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,7,3,2,6,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,3,8,2,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,4,5,3,7,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,5,8,7,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,5,4,8,7,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,4,8,2,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,2,7,1,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,2,7,5,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,2,8,6,5,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,5,2,8,6,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,3,6,8,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,8,6,4,5,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,8,4,1,6,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,5,6,1,3,4,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,6,4,1,8,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,8,6,2,3,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,7,5,2,3,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,2,4,7,6,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,3,7,6,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,2,8,6,5,3,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,5,1,3,2,6,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,1,8,5,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,8,7,5,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,7,6,3,2,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,1,8,7,3,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,5,4,2,7,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,1,2,8,5,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,4,6,8,3,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,7,6,1,5,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,6,5,8,2,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,2,7,4,6,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,7,6,4,8,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,5,8,4,1,3,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,6,2,3,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,7,1,3,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,3,8,7,2,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,7,1,6,2,5,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,5,2,4,7,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,7,3,5,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,5,2,3,6,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,1,7,4,8,6,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,5,2,4,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,5,1,4,7,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,5,4,1,3,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,2,5,8,4,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,7,2,3,8,1,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,2,3,1,6,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,8,1,6,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,2,5,6,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,2,4,1,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,7,5,1,6,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,8,1,6,2,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,2,8,4,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,3,7,4,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,4,8,5,6,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,6,8,4,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,5,8,2,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,6,3,8,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,6,4,3,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,8,1,4,6,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,4,6,1,3,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,5,8,6,3,2,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,4,5,7,2,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,1,5,6,3,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,7,4,5,6,2,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,2,6,7,3,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,2,5,6,3,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,7,5,3,6,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,6,3,5,7,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,6,3,1,7,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,6,3,5,7,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,7,8,3,2,6,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,2,8,3,6,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,5,8,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,6,3,1,7,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,5,7,3,4,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,2,5,6,3,1,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,3,1,5,2,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,8,6,5,1,7,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,7,5,1,2,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,7,6,8,5,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,6,8,1,2,4,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,2,7,5,4,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,4,2,8,6,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[3,4,6,1,5,2,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,3,7,1,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,2,5,8,6,4,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,3,2,1,8,6,4,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,8,7,4,5,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,1,4,2,3,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,6,3,4,1,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,3,4,2,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,6,4,5,7,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,6,1,4,5,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,5,1,4,6,2,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,8,1,4,6,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,3,1,7,8,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,8,4,1,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,5,4,7,6,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,4,6,7,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,3,7,8,2,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,8,3,7,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,3,7,2,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,8,5,3,6,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,5,3,6,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,8,3,2,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,4,3,2,6,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,4,3,2,6,5,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,4,3,2,6,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,4,3,2,6,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,3,8,2,1,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,8,3,2,1,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,4,3,2,7,6,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,5,8,3,1,2,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,8,1,3,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,1,3,2,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,8,6,7,3,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,6,7,3,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,1,3,2,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,6,1,3,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,4,3,2,7,5,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,3,8,2,6,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,8,3,2,5,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,4,3,2,5,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,4,8,3,2,5,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,3,8,2,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,4,2,3,5,1,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,3,6,1,4,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,3,8,6,4,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,3,7,4,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,3,2,5,4,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,2,8,1,5,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,6,4,7,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,1,8,6,4,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,2,5,7,3,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,2,3,4,7,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,3,4,7,8,2,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,8,5,1,4,7,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,6,8,5,2,7,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,7,8,5,2,6,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,8,6,2,7,4,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,4,7,1,3,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,6,2,8,1,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,5,2,3,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,8,3,7,2,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,2,8,4,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,8,4,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,2,6,5,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,8,3,2,6,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,7,5,8,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,2,7,8,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,1,3,8,2,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,3,6,2,1,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,4,5,1,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,5,8,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,4,5,2,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,4,5,1,6,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,4,1,6,3,2,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,5,4,8,6,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,4,8,6,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,7,5,3,6,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,3,7,4,1,6,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,4,1,6,3,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,7,4,2,6,5,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,1,8,4,7,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,4,8,6,3,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,8,5,6,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,4,8,6,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,6,8,2,7,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,7,4,8,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,6,1,4,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,6,8,2,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,4,8,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,8,4,1,6,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,8,1,4,7,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,4,1,6,3,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,8,4,1,6,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,8,3,6,7,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,8,2,5,6,7,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,8,4,1,6,5,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,8,1,5,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,4,2,6,5,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,3,7,4,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,8,7,4,3,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,4,1,8,3,2,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,1,4,3,8,7,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,8,3,4,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,1,3,8,2,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,5,4,8,3,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,1,4,8,3,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,8,1,2,3,6,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,6,8,2,3,4,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,5,7,4,6,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,5,2,3,8,6,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,2,8,3,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,4,5,8,1,2,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,7,8,1,4,5,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,8,7,1,5,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,2,1,6,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,1,8,5,4,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,1,3,7,5,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,3,8,4,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,7,8,5,3,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,8,3,1,5,7,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,1,4,7,2,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,1,7,4,2,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,8,5,1,2,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,4,7,5,8,3,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,5,8,2,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,8,5,3,7,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,5,7,3,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,7,5,1,3,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,8,4,1,5,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,5,8,2,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,5,7,2,8,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,6,8,7,2,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,4,8,7,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,8,2,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,7,2,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,6,8,5,4,2,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,6,3,8,4,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,6,4,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,2,7,4,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,8,2,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,2,7,5,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,3,6,7,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,6,8,2,7,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,6,5,4,3,8,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,3,4,5,6,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,3,6,2,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,8,3,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,5,8,3,6,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,6,8,4,5,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,7,8,4,5,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,2,8,4,3,6,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,8,5,6,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,3,8,5,4,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,2,8,7,5,4,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,2,8,4,3,7,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,8,4,3,1,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,7,3,2,6,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,7,3,6,2,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,2,7,1,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,5,4,8,3,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,3,6,8,7,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,3,7,6,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,2,6,5,7,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,5,7,6,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,2,7,4,8,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,6,8,4,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,8,7,5,2,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,8,6,4,7,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,8,5,4,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,2,8,7,6,4,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,4,8,1,7,6,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,8,1,7,6,5,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,1,5,3,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,6,4,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,2,6,7,3,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,2,7,6,3,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,3,8,2,7,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,4,8,3,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,7,2,4,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,5,1,3,7,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,8,7,2,6,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,6,8,2,5,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,5,8,1,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,5,1,8,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,6,2,1,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,5,2,1,6,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,7,3,2,8,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,4,8,1,2,5,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,4,8,3,2,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,8,4,3,1,6,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,5,3,6,2,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,4,7,3,2,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,8,5,6,2,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,5,8,7,3,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,5,8,6,7,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,3,1,5,6,2,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,5,8,6,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,7,6,1,2,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,7,5,6,1,2,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,7,5,6,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,1,8,6,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,5,8,6,7,2,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,1,5,8,6,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,4,5,8,7,1,2,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,7,1,5,6,2,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,4,7,1,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,8,6,4,7,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,4,7,2,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,4,6,1,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,5,6,4,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,4,5,6,7,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,6,5,2,7,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,8,6,5,1,7,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,1,7,3,2,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,1,4,6,7,2,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,4,7,1,3,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,1,6,5,3,7,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,4,7,2,3,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,2,5,4,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,2,7,5,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,3,5,8,2,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,6,4,3,1,8,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,3,5,8,1,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,7,2,3,8,4,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,2,1,3,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,4,1,8,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,7,5,8,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,1,3,8,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,7,4,3,8,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,1,7,4,2,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,6,7,4,3,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,7,3,2,1,8,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,5,7,3,1,4,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,3,2,8,4,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,2,6,7,4,3,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,7,1,8,4,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,5,8,1,6,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,8,4,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,7,6,1,2,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,3,4,6,2,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,5,7,1,4,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,4,7,1,5,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,3,4,7,1,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,7,3,5,6,2,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,7,4,6,5,2,3,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,6,7,5,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,6,7,5,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,5,7,6,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,7,3,6,2,1,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,3,4,6,2,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,4,6,5,2,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,5,2,7,4,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,3,7,6,5,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,6,7,4,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,2,7,5,1,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,4,2,7,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,5,2,7,4,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,2,6,7,4,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,3,7,6,4,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,2,5,7,3,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,2,4,7,3,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,2,3,7,4,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,3,2,7,6,4,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,1,7,3,6,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,1,5,4,3,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,4,5,8,3,1,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,7,4,6,1,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,3,7,1,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,3,4,8,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,4,3,8,5,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,8,4,5,1,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,8,2,4,5,3,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,3,1,5,4,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,8,3,2,5,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,8,3,5,4,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,4,8,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,7,3,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,7,6,3,1,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,6,7,3,8,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,6,5,4,8,3,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,4,8,5,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,3,5,8,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,1,7,4,5,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,1,6,4,8,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,2,3,5,8,4,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,4,8,2,3,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,8,3,2,4,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,8,3,4,6,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,5,3,8,6,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,7,2,4,6,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,6,5,1,8,3,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,7,1,3,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,3,6,4,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,1,5,8,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,7,6,4,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,1,6,7,4,5,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,7,6,4,8,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,7,5,8,4,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,8,7,6,4,2,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,1,8,7,5,4,2,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,1,7,6,5,4,2,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,7,1,6,5,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,1,6,5,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,1,7,6,3,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,1,8,6,3,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,1,7,6,3,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,4,1,8,5,3,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,1,7,5,3,2,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,1,6,5,3,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,6,1,4,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,5,6,1,4,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,1,4,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,6,1,4,3,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,6,1,4,3,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,5,1,4,3,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,5,1,4,3,2,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,5,1,4,3,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,1,5,2,7,6,4,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,6,7,8,5,4,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,6,1,7,2,5,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,8,6,3,4,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,1,6,4,5,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,6,4,5,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,7,8,5,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,6,4,5,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,6,4,5,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,6,3,4,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,8,6,3,4,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,7,3,2,1,8,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,8,7,2,5,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,3,5,2,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,3,7,4,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,3,7,5,1,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,3,1,7,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,7,3,5,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,3,4,5,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,3,1,4,5,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,3,8,4,5,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,8,1,7,4,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,1,4,7,6,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,1,4,7,3,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,2,5,1,7,6,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,7,6,1,4,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,8,1,4,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,7,6,8,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,3,8,4,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,7,3,5,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,3,5,1,2,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,6,3,1,2,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,2,3,6,1,5,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,7,6,1,4,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,3,4,7,1,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,2,3,4,8,1,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,3,7,1,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,7,5,3,1,6,4,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[3,7,4,2,5,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,7,8,5,2,3,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,2,6,7,4,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,7,3,5,1,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,3,2,5,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,8,7,4,1,3,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,8,3,7,6,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,1,7,2,4,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,7,1,4,2,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,5,8,2,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,5,2,7,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,2,7,5,4,3,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,5,1,8,3,7,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,5,3,2,6,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,3,6,5,4,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,1,5,4,3,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,6,5,2,8,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,1,7,4,6,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,8,7,5,3,2,6,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,1,7,6,3,2,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,6,2,5,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,1,5,4,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,1,8,4,5,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,5,1,4,6,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,1,4,5,3,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,6,8,1,5,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,7,6,1,4,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,1,7,5,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,7,1,4,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,5,7,1,4,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,6,7,4,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,5,2,4,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,6,4,8,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,5,2,6,4,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,3,6,8,2,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,1,2,7,5,4,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,7,4,1,3,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,2,8,4,3,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,5,7,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,6,1,7,5,2,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,4,1,8,3,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,4,1,6,5,2,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,5,3,4,7,8,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,5,3,7,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,4,6,5,2,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,5,4,6,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,2,4,7,6,3,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,7,4,1,8,5,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,4,3,7,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,5,4,8,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,2,8,7,4,3,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,2,1,7,5,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,3,6,4,7,8,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,1,3,7,8,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,2,3,1,7,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,4,3,7,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,6,4,3,1,5,2,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,5,4,6,1,3,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,6,5,1,2,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,5,6,3,7,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,8,3,5,7,2,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,2,4,3,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,5,7,2,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,1,4,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,3,8,4,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,4,2,6,3,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,1,4,3,2,8,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,8,4,7,5,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,2,8,6,4,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,2,4,8,5,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,4,6,2,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,7,3,1,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,5,8,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,8,6,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,1,7,5,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,2,3,4,7,5,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,7,8,6,1,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,6,7,3,8,5,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,8,5,1,7,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,3,5,1,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,2,4,6,3,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,4,6,3,5,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,6,2,5,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,5,2,6,1,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,5,7,8,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,5,3,8,2,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,3,2,5,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,4,8,3,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,1,7,4,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,8,6,1,3,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,5,2,6,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,4,2,8,6,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,6,2,3,8,5,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,7,1,3,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,7,8,2,5,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,5,3,4,7,2,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,4,7,1,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,5,8,2,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,8,2,5,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,1,2,4,7,5,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,6,2,7,5,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,2,7,5,1,4,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,4,6,8,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,4,1,5,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,2,1,5,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,4,2,8,6,5,3,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,8,5,2,6,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,2,4,6,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,5,3,2,6,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,1,3,2,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,2,3,7,8,1,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,8,6,3,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,3,5,1,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,6,3,4,2,8,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,3,2,5,7,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,2,5,3,7,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,3,6,7,2,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,7,8,6,2,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,8,4,3,6,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,7,4,5,3,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,3,2,6,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,2,7,1,4,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,1,7,8,3,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,6,5,2,7,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,2,5,3,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,2,5,4,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,2,6,3,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,4,7,5,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,7,6,5,1,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,4,7,6,2,8,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,7,8,2,6,5,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,7,8,1,6,5,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,6,7,1,5,4,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,8,6,1,4,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,4,7,2,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,7,5,2,8,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,7,6,3,8,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,7,8,2,6,5,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,6,2,7,5,4,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,2,6,5,4,3,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,3,8,2,7,5,4,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,4,2,7,6,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,1,7,5,4,3,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,1,6,5,4,3,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,2,6,5,4,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,2,1,6,5,4,3,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,2,8,1,6,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,8,6,1,4,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,7,1,5,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,1,6,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,8,2,6,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,5,3,1,7,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,6,1,2,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,4,1,2,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,6,5,1,2,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,1,2,7,5,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,2,3,8,7,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,2,7,4,8,6,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,6,2,7,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,1,7,3,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,1,2,8,5,4,3,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,3,7,4,8,6,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,4,1,8,7,3,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,5,1,7,3,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,1,7,2,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,5,4,3,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,6,1,5,4,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,1,5,8,4,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,8,1,5,4,3,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,4,6,1,5,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,6,1,5,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,6,1,5,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,1,6,8,4,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,1,7,8,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,8,6,1,5,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,8,4,6,1,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,1,5,3,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,4,7,8,2,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,4,6,8,3,2,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,4,5,8,3,2,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,5,8,2,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,6,8,1,5,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,6,1,8,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,8,7,1,5,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,4,7,1,5,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,1,5,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,7,2,1,6,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,5,7,2,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,4,7,2,1,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,4,6,2,1,8,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,2,1,6,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,1,5,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,4,8,3,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,4,8,2,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,6,8,1,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,5,8,2,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,1,7,2,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,4,2,6,3,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,4,1,6,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,3,1,5,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,4,1,7,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,7,3,1,4,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,6,1,7,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,1,6,7,8,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,8,2,6,7,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,8,2,1,7,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,2,6,1,3,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,6,8,2,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,6,5,7,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,3,7,1,5,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,6,7,3,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,4,6,7,2,5,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,6,7,2,5,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[7,1,4,6,8,3,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,8,2,6,1,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,8,2,1,3,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,7,1,5,6,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,7,1,2,4,8,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,6,3,4,7,8,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,6,4,7,5,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,3,7,4,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,2,6,7,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,3,2,8,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,1,4,6,2,3,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,4,5,2,3,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,2,6,3,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,4,1,2,6,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,2,6,3,7,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,2,7,6,3,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,8,6,3,1,2,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,8,7,3,1,6,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,8,3,1,6,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,4,3,1,6,2,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,4,3,1,6,2,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,3,1,8,6,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,7,6,2,4,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,3,5,7,4,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,3,7,2,8,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,2,8,6,3,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,2,7,4,3,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,2,6,3,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,2,7,3,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,2,7,3,5,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,6,2,1,7,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,2,1,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,2,8,3,5,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,5,3,2,1,8,6,4]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[6,2,5,4,1,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,3,2,1,8,7,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,5,3,2,1,8,7,4]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,4,3,2,7,6,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,5,8,4,7,6,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,2,7,4,8,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,3,2,8,6,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,8,3,7,5,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,3,8,5,2,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,2,5,4,7,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,4,8,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,3,2,8,6,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,5,4,8,6,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,8,6,5,4,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,4,3,6,5,2,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,4,3,7,5,2,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,7,8,5,4,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,8,7,4,3,2,1,5]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,3,1,8,5,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,1,4,8,7,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,1,3,7,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,5,1,8,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,2,1,8,7,4,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,2,3,1,8,7,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,7,1,8,5,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,8,1,7,5,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,5,1,8,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,1,5,8,4,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,4,6,8,2,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,5,1,7,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,8,1,7,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,6,1,2,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,6,1,5,3,7,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,3,6,4,1,7,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,8,6,1,7,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,1,5,2,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,1,6,4,2,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,4,1,5,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,6,1,2,7,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,1,4,3,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,1,4,3,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,1,5,3,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,1,2,4,7,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,1,6,4,8,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,6,3,4,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,3,6,1,7,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,1,5,3,6,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,6,1,2,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,4,5,6,1,7,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,6,2,5,4,7,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,6,3,5,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,3,2,4,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,1,4,5,8,7,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,1,3,8,7,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,8,2,1,7,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,1,3,8,4,2,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,8,3,5,7,4,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,4,5,8,6,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,7,2,8,6,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,4,8,5,1,3,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,7,8,5,2,4,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,2,4,7,5,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,2,5,4,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,7,3,5,6,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,3,4,2,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,4,3,2,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,5,2,3,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,5,3,1,6,2,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,6,3,2,1,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,3,6,7,2,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,8,3,7,4,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,1,3,7,4,5,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,1,3,7,5,4,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,2,7,4,3,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,6,5,4,3,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,2,7,6,4,5,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,3,5,4,2,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,3,5,4,2,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,7,2,1,8,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,8,1,3,6,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,7,1,8,2,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,8,6,1,3,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,8,6,2,7,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,7,1,5,3,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,2,1,8,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,7,8,4,5,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,8,3,2,7,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,2,3,7,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,8,1,7,4,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,8,3,7,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,7,1,5,8,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,8,4,6,2,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,1,5,7,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,8,2,5,4,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,6,2,5,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,8,6,2,1,7,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,5,8,6,1,2,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,8,5,2,7,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,8,5,2,6,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,8,5,4,1,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,8,5,3,1,7,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,8,2,3,5,4,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,8,1,5,7,4,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,3,2,6,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,2,4,8,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,4,5,2,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,6,8,3,7,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,7,4,6,3,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,8,5,7,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,6,5,3,7,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,3,7,8,4,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,3,7,6,4,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,5,2,7,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,5,1,7,3,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,5,3,4,2,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,5,1,7,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,2,5,1,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,2,4,8,5,3,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,7,1,4,8,5,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,3,7,4,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,1,7,2,5,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,4,8,5,1,2,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,8,1,6,7,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,7,6,3,8,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,2,8,5,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,5,3,7,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,5,2,4,7,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,6,5,1,4,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,8,1,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,5,3,7,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,5,8,4,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,5,1,8,6,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,3,8,4,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,7,3,4,6,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,5,2,8,6,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,8,6,4,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,5,8,6,7,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,1,7,4,8,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,3,1,6,5,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,1,7,5,3,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,1,4,6,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,8,6,1,4,5,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,8,6,4,1,3,5,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,2,7,3,8,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,3,4,8,1,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,7,5,3,4,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,8,3,6,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,8,3,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,3,5,1,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,8,2,5,3,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,7,8,1,2,5,6,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,8,7,3,4,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,7,6,2,4,3,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,2,7,4,5,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,1,5,7,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,1,8,6,4,5,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,5,1,4,3,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,5,7,8,3,4,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,8,4,3,1,7,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,1,3,7,5,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,8,1,3,7,5,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,2,5,4,8,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,5,7,4,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,1,6,8,5,3,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,4,1,3,8,6,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,5,1,3,8,6,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,6,8,5,3,4,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,6,8,7,3,1,2,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,7,5,3,8,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,2,3,4,7,1,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,8,5,7,3,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,8,6,3,1,2,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,1,4,2,6,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,3,2,4,7,1,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,6,8,4,2,3,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,7,8,3,6,1,2,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,8,1,2,5,7,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,5,8,6,2,4,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,3,7,2,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,8,6,2,4,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,3,7,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,8,6,3,7,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,2,4,8,6,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,4,2,6,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,6,3,8,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,8,3,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,5,7,3,8,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,5,6,3,7,1,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,5,3,6,8,7,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,1,4,6,2,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,7,2,1,5,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,6,1,4,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,1,6,5,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,3,5,1,7,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,7,5,1,8,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,6,1,7,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,4,2,6,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,6,8,4,2,7,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,5,4,1,6,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,2,6,4,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,6,3,4,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,6,2,8,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,8,2,1,3,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,8,1,5,3,2,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,2,3,5,8,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,2,3,5,1,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,2,8,7,5,3,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,3,7,5,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,8,6,5,2,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,8,7,2,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,5,4,1,6,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,5,7,3,2,1,6,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,2,8,1,6,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,8,2,3,7,5,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,4,6,3,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,3,1,4,7,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,4,3,6,7,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,7,2,8,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,1,6,4,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,2,5,6,1,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,6,7,8,2,4,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,2,8,5,3,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,4,2,5,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,2,7,5,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,6,3,7,4,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,5,6,4,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,3,5,6,4,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,5,7,6,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,6,8,3,2,5,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,1,7,5,2,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,1,7,2,6,5,4,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,4,7,2,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,7,1,3,6,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,2,8,3,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,8,1,6,4,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,8,1,3,4,6,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,7,1,4,5,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,2,7,4,3,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,1,3,8,4,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,8,7,1,3,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,3,5,1,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,6,8,2,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,6,5,2,7,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,2,5,6,8,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,7,2,4,8,3,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,2,4,5,3,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,8,2,3,7,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,2,8,4,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,8,2,4,3,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,7,2,5,3,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,8,2,6,7,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,8,2,3,6,7,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,8,3,6,7,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,4,8,2,6,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,7,2,5,3,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,2,3,5,4,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,1,5,6,2,3,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,1,3,7,2,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,7,5,1,3,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,5,6,2,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,4,3,8,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,1,5,3,4,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,7,5,2,8,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,8,4,1,5,6,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,1,3,6,7,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,8,4,3,7,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,4,6,7,1,2,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,3,8,4,7,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,2,5,4,8,3,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,4,7,8,1,2,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,3,1,4,7,2,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,6,4,7,8,2,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,2,7,3,8,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,7,8,5,6,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,2,6,7,5,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,7,4,6,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,5,8,4,7,1,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,1,8,5,7,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,7,4,6,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,4,1,8,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,5,1,4,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,4,1,3,8,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,3,5,4,2,8,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,8,7,4,2,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,7,4,3,1,5,2,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[3,8,4,5,1,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,3,1,7,5,6,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,4,7,6,5,3,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,1,4,5,7,6,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,4,1,8,5,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,2,1,4,7,6,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,1,7,4,2,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,7,3,1,6,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,4,2,3,7,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,1,2,8,7,4,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,1,2,4,3,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,3,7,4,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,5,7,6,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,1,8,7,6,4,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,3,4,8,7,2,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,4,8,2,6,7,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,8,2,5,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,8,2,5,7,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,2,1,7,5,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,2,7,5,6,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,8,5,4,1,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,5,4,1,7,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,1,5,7,6,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,1,8,2,7,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,1,6,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,4,7,3,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,4,7,2,1,6,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,4,7,6,5,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,8,1,7,4,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,4,7,1,3,6,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,4,7,6,8,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,7,1,2,8,6,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,8,1,2,5,6,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,7,1,2,5,6,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,8,1,6,5,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,1,8,5,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,2,6,3,8,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,3,1,6,5,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,2,4,6,5,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,5,2,6,7,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,1,2,6,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,8,2,6,4,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,3,4,1,6,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,7,4,3,8,6,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,6,3,1,5,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,4,1,6,3,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,4,2,8,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,3,4,2,1,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,3,5,2,1,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,5,4,2,7,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,6,4,7,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,7,8,6,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,4,6,8,1,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,3,8,4,6,1,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,8,6,5,2,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,1,5,2,6,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,2,4,1,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,3,2,4,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,6,8,4,3,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,3,8,4,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,3,2,4,8,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,2,5,3,4,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,2,4,6,1,3,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,4,6,7,5,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,8,3,4,7,5,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,8,1,5,7,6,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,4,6,8,2,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,1,6,8,3,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,2,8,1,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,2,8,6,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,5,2,6,7,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,4,8,6,1,2,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,6,5,2,7,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,6,4,7,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,6,4,8,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,2,3,5,1,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,5,7,4,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,3,5,6,2,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,5,8,4,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,8,4,7,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,4,3,2,8,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,6,1,4,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,2,1,4,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,8,3,5,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,4,8,1,5,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,8,4,2,5,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,2,5,8,1,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,1,7,5,8,3,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,8,5,6,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,4,8,1,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,8,3,1,5,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,5,8,3,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,3,5,8,7,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,6,5,3,7,2,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,8,5,3,7,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,8,6,5,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[7,4,8,5,6,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,8,3,4,1,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,1,8,2,5,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,3,8,1,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,8,7,3,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,7,4,8,6,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,8,2,3,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,1,8,3,5,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,6,2,3,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,1,6,3,8,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,5,1,4,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,6,1,3,8,4,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,1,5,8,3,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,4,1,8,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,6,2,8,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,6,7,3,8,4,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,3,6,2,8,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,1,8,6,4,2,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,1,8,4,7,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,8,4,2,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,4,8,6,1,7,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,8,5,7,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,5,4,8,1,6,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,5,8,7,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,5,4,8,1,2,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,4,8,6,7,5,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,8,1,4,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,1,5,8,7,2,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,6,2,8,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,1,8,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,5,8,6,3,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,5,4,8,6,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,8,1,7,6,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,4,8,1,6,7,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,8,5,1,7,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,4,8,2,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,5,8,2,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,3,5,8,2,6,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,8,1,6,5,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,4,7,2,3,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,7,1,5,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,1,5,4,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,6,3,1,4,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,6,3,5,1,2,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,2,8,5,4,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,8,4,7,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,7,5,4,3,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,4,3,7,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,5,3,7,2,4,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,3,8,1,7,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,4,2,3,8,6,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,6,4,3,8,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,6,8,4,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,8,7,5,3,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,2,8,5,4,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,6,2,8,7,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,2,8,4,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,8,3,2,5,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,7,8,3,2,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,2,6,8,3,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,3,6,2,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,6,2,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,6,2,5,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,7,4,8,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,2,7,8,5,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,1,3,6,5,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,7,4,6,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,4,3,6,8,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,1,4,3,6,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,3,6,2,8,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,2,7,8,3,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,3,5,2,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,3,4,8,2,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,6,4,1,7,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,6,4,1,7,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,1,7,6,3,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,6,3,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,3,8,6,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,7,8,2,4,3,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,2,4,8,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,7,8,2,3,5,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,7,5,2,4,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,5,2,3,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,4,7,3,2,5,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,3,2,8,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,7,2,8,4,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,2,5,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,7,3,2,5,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,3,5,1,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,3,2,6,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,5,3,2,6,4,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,2,6,7,3,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,2,6,3,7,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,2,3,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,6,2,8,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,6,2,8,3,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,6,2,3,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,6,3,2,5,8,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,3,8,5,4,7,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,2,5,1,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,6,3,8,7,5,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,4,6,1,8,7,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,3,6,8,7,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,6,3,8,7,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,5,8,7,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,8,5,7,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,4,6,8,5,7,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,6,8,3,7,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,6,8,1,7,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,6,5,1,8,7,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,6,5,8,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,6,5,8,1,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,6,8,5,1,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,4,6,8,7,3,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,4,6,8,7,1,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,4,6,8,7,1,3,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,4,6,8,5,1,3,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,4,6,5,1,8,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,6,5,1,3,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,6,5,3,8,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,6,5,8,3,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,8,5,3,1,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,6,8,7,3,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,4,6,8,7,5,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[6,1,4,7,5,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,8,6,5,3,2,7,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,6,3,5,8,2,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,1,7,8,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,1,2,7,8,4,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,1,3,2,7,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,3,1,7,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,3,7,1,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,7,2,6,5,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,3,2,1,7,6,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,4,3,8,1,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,3,8,7,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,8,2,7,6,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,2,7,6,5,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[7,8,2,6,5,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,7,6,2,5,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,3,7,2,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,6,3,1,7,5,4,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,3,7,1,5,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,8,3,7,6,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,2,7,6,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,2,1,7,6,5,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[1,6,4,2,5,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,6,2,7,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,2,6,4,3,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,2,4,6,3,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,8,6,2,3,7,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,2,8,6,3,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,6,8,2,7,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,2,3,8,5,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,2,8,5,4,3,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,2,3,8,6,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,3,8,2,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,6,5,2,8,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,6,4,2,8,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,8,2,5,6,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,7,3,2,8,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,3,6,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,2,3,6,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,7,2,5,8,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,2,3,5,8,1,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,2,4,8,1,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,4,5,7,3,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,6,3,4,7,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,7,5,6,8,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,3,6,7,4,5,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,5,6,3,4,2,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,6,3,4,7,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,3,6,4,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,5,6,8,3,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,5,6,3,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,3,7,5,2,8,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,7,2,5,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,3,7,4,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,3,7,6,4,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,3,6,7,4,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,6,3,7,4,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,7,6,3,4,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,7,3,6,4,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,7,2,5,6,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,7,5,6,2,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,8,3,1,7,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,4,1,3,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,3,1,8,5,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,3,6,1,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,1,5,8,7,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,5,1,7,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,4,7,2,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,3,6,8,7,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,6,3,5,8,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,5,8,4,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,4,8,6,3,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,3,5,7,4,1,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,6,4,1,8,7,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,2,5,3,1,7,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,4,8,3,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,6,4,3,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,3,5,2,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,3,4,6,2,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,5,2,1,7,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,5,2,1,8,6,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,6,3,1,8,7,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,7,5,2,1,8,6,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,5,3,6,2,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,6,4,3,8,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,7,3,1,2,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,1,8,3,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,4,6,3,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,1,2,4,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,5,3,8,4,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,2,8,3,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,3,2,8,5,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,2,8,3,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,2,3,1,7,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,7,2,3,1,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,2,3,1,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,3,4,1,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,3,4,1,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,2,3,1,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,3,4,1,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,3,4,1,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,5,2,3,6,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,8,4,5,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,2,3,7,6,4,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,7,3,5,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,5,3,4,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,8,4,5,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,3,1,7,8,5,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,8,5,1,4,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,7,1,4,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,7,1,4,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,2,5,3,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,8,5,1,4,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,6,2,3,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,3,8,2,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,4,1,8,2,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,1,7,6,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,2,1,8,4,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,1,2,7,6,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,8,2,1,7,6,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,7,8,2,4,6,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[7,8,2,5,4,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,3,7,8,2,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,4,7,3,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,3,6,8,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,8,2,7,3,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,6,3,5,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,3,6,1,5,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,7,8,4,6,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,7,5,6,2,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,1,7,4,5,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,2,6,4,7,5,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,5,6,3,8,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,8,4,7,5,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,7,5,1,4,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,4,1,6,5,3,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,2,7,3,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,5,7,3,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,6,8,4,2,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,5,4,1,8,2,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,1,8,2,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,8,5,3,2,6,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,5,1,7,6,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,4,3,8,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,2,7,8,6,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,6,1,4,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,7,8,6,1,3,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,7,8,6,5,2,4,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,5,2,7,8,6,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,6,2,5,3,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,5,6,3,2,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,6,7,5,4,1,3,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,1,6,7,5,3,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,7,4,3,1,5,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,5,6,4,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,5,3,1,8,4,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,8,6,4,3,1,5,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,5,7,3,8,6,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,5,3,7,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,7,8,5,3,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,4,7,5,6,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,7,1,5,8,2,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,6,1,2,8,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,7,6,2,1,8,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,5,8,3,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,8,2,6,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,4,8,2,6,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,8,1,6,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,3,6,5,7,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,3,4,8,5,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,3,8,4,1,5,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,4,5,1,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,7,5,1,4,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,8,7,1,5,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,1,2,8,5,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,8,2,3,5,7,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,5,2,3,8,6,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,4,8,5,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,7,6,1,4,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,5,6,1,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,5,2,6,4,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,7,2,4,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,1,8,7,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,2,8,5,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,5,6,4,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,1,4,6,7,5,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,6,4,5,8,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,2,3,6,4,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,1,7,2,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,7,5,8,1,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,1,8,7,3,4,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,7,4,1,3,5,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,1,6,4,8,7,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,1,4,5,8,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,5,6,3,8,7,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,8,7,4,1,3,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,4,7,5,1,3,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,1,5,3,4,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,6,4,8,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,7,6,2,1,5,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,5,4,2,7,6,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[2,7,4,3,1,6,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,8,4,6,7,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,8,3,4,6,7,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,2,3,6,1,5,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,3,1,6,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,5,1,6,4,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,8,4,2,6,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,5,1,4,2,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,5,1,8,6,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,8,7,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,2,4,8,5,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,3,8,4,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,8,1,4,3,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,7,8,3,5,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,6,7,8,2,1,5,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,6,7,2,8,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,7,1,3,5,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,6,7,1,2,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,6,7,1,8,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,1,8,7,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,1,7,3,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,5,7,2,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,5,7,8,2,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,8,1,4,7,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,1,3,2,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,8,3,2,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,3,8,2,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,4,2,3,7,6,5,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,3,1,8,2,7,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,8,1,2,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,8,2,1,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,2,8,7,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,4,2,7,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,4,3,7,6,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,3,8,7,6,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,5,7,6,1,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,4,5,7,6,8,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,8,4,7,6,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,8,2,4,7,1,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,4,8,7,1,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,5,7,1,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,3,5,7,1,6,8,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,2,3,8,1,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,8,3,1,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,2,3,1,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,2,1,3,7,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,2,8,1,3,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,4,7,2,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,7,8,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,3,4,6,1,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,7,8,6,1,3,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,4,7,6,8,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,5,1,7,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,4,7,1,2,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,7,5,8,2,3,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,1,7,6,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,7,1,6,8,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,2,7,6,8,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,5,1,7,6,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,5,7,1,3,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,6,1,5,2,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,8,3,5,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,2,3,1,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,8,3,1,6,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,2,8,3,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,1,7,6,2,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,3,1,2,8,4,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,2,7,8,4,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,6,8,3,4,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,4,1,6,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,6,7,2,4,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,8,3,6,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,7,8,4,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,8,5,2,4,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,2,3,7,8,4,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,6,2,3,1,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,3,7,8,4,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,8,5,3,4,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,5,2,3,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,1,4,2,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,1,7,8,5,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,3,7,8,5,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,4,8,5,2,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,1,8,5,2,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,5,3,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,8,4,7,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,3,1,4,2,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,1,8,5,4,2,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,1,3,2,7,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,4,2,3,1,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,3,7,8,5,4,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,3,5,6,1,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,8,1,2,6,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,3,6,7,8,2,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,3,4,8,6,2,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,3,7,4,6,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,3,5,7,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,4,8,7,3,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,2,7,8,3,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,4,1,3,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,2,5,4,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,4,5,2,6,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,6,2,7,8,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,7,3,8,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,8,6,3,1,7,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,1,4,2,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,8,1,3,2,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,1,2,6,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,8,2,3,7,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,7,2,3,6,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,5,7,3,4,6,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,8,2,1,3,7,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,5,2,3,1,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,8,2,3,1,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,2,3,4,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,2,3,7,4,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,3,4,8,5,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,7,5,8,4,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,5,8,4,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,8,5,6,2,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,8,5,6,1,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,5,8,4,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,7,4,5,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,7,4,5,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,3,8,5,2,6,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,8,4,5,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,8,4,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,8,5,2,6,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,2,8,5,3,6,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,1,3,5,2,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,4,1,3,2,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,8,2,1,6,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,3,2,1,5,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,2,4,1,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,3,5,1,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,6,2,4,1,5,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,7,3,5,2,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,4,3,2,7,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,6,4,3,1,7,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,8,1,5,3,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,1,5,2,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,1,5,6,2,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,4,1,5,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,1,5,2,6,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,2,5,3,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,4,1,6,3,7,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,5,8,1,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,5,3,8,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,7,4,2,8,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,8,3,7,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,5,8,6,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,6,3,4,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,4,1,5,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,6,1,7,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,4,1,8,6,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,7,2,4,1,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,2,4,1,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,2,7,5,3,4,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,4,7,8,5,1,3,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[7,8,3,4,1,2,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,3,8,4,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,2,1,7,4,6,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,7,6,5,3,8,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,7,6,8,1,3,4,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,5,1,7,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,5,3,7,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,6,8,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,7,4,5,6,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,7,1,2,5,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,3,4,8,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,5,7,4,2,3,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,5,4,8,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,8,3,5,7,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,1,7,2,4,3,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,3,8,2,4,7,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,7,2,4,6,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,3,2,4,6,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,3,7,4,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,4,3,5,7,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,1,7,4,6,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,6,5,1,7,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,2,6,7,1,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,8,6,7,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,6,2,7,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,8,6,7,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,6,2,8,7,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,4,7,6,5,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,4,2,6,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,7,8,6,4,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,7,5,6,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,8,6,3,2,4,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,4,2,1,7,6,3,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,1,6,5,2,7,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,1,6,7,2,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,5,3,1,7,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,2,6,3,8,7,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,1,7,3,4,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,8,3,6,7,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,3,5,2,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,7,3,2,6,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,1,3,7,2,6,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,6,7,2,4,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,4,8,2,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,4,8,3,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,7,2,6,3,5,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,5,6,8,2,4,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,7,1,5,2,4,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,1,5,2,4,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,6,3,5,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,7,3,5,4,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,3,5,6,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,7,8,3,6,4,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,7,6,4,5,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,7,4,6,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,5,7,6,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,5,1,6,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,7,5,6,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,7,4,3,1,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,7,8,5,3,1,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,4,6,2,5,3,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,3,2,5,4,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,8,2,5,4,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,4,2,6,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,8,2,7,5,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,7,4,3,2,6,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,5,4,7,2,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,7,6,2,8,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,7,6,2,8,4,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,2,8,4,3,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,2,8,4,3,6,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,8,5,6,3,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,3,5,2,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,7,2,5,8,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,8,3,2,7,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,5,8,2,6,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,6,4,8,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,4,8,6,5,2,7,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,3,8,2,6,5,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,6,3,8,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,2,7,6,4,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,2,4,3,8,7,5,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,3,8,7,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,8,5,4,2,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,7,2,4,8,6,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,6,5,3,2,8,7,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,3,2,8,7,5,4,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,3,4,6,5,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,3,1,4,6,5,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,8,3,1,2,6,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,1,7,5,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,1,7,5,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,5,1,4,2,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,3,2,1,6,4,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,1,5,4,2,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,2,4,1,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,7,1,5,2,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,7,1,5,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,6,8,4,1,3,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,4,1,3,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,2,7,5,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,8,4,1,5,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,4,8,6,3,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,6,5,3,4,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,2,5,3,4,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,5,1,3,6,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,1,5,3,6,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,1,3,5,4,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,4,8,3,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,5,2,4,3,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,8,2,5,4,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,2,5,3,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,8,1,5,3,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,8,2,6,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,8,2,6,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,7,3,1,6,4,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,3,1,6,4,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,4,3,2,7,5,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,3,4,1,8,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,7,3,1,6,2,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,8,6,4,2,5,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,2,4,6,5,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,1,7,3,5,6,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,7,5,2,4,6,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,1,7,5,4,6,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,3,2,6,1,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,3,1,7,6,4,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,5,3,2,1,6,4,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,6,5,3,1,4,2,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[1,8,6,4,3,2,7,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,8,7,6,4,2,5,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,4,8,6,7,5,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,3,8,5,6,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,2,5,6,4,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,7,3,6,8,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,1,3,6,8,5,4,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,8,3,6,7,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,8,2,7,5,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,1,6,4,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,6,1,8,4,5,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,6,1,7,4,5,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,2,8,6,4,5,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,7,6,4,5,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,8,6,4,5,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,2,5,4,3,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,2,7,4,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,6,4,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,8,4,3,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,2,6,4,3,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,2,6,4,3,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,2,7,4,3,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,2,5,4,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,5,4,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,8,3,4,7,5,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,1,2,3,7,6,4,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,5,7,2,3,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,2,8,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,2,8,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,5,8,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,2,5,8,1,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,3,5,8,1,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,3,6,8,2,4,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,3,5,8,2,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,7,2,4,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,7,5,8,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,3,8,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,7,4,8,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,7,4,8,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,4,8,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,4,8,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,7,6,4,2,5,3,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,6,2,3,5,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,8,4,5,7,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,8,7,1,6,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,4,2,1,7,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,7,5,1,4,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,5,1,4,3,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,4,2,1,8,7,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,8,5,1,4,3,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,6,8,3,5,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,7,8,4,3,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,7,8,6,4,5,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,8,5,6,2,3,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,8,1,3,5,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,2,3,1,8,7,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,1,5,3,8,6,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,1,6,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,8,2,7,6,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,8,7,4,5,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,6,7,1,3,5,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,1,8,6,3,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,2,4,8,1,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,7,1,4,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,6,8,7,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,3,1,7,5,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,8,7,3,4,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,8,1,4,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,3,6,7,1,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,2,3,1,4,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,3,1,5,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,8,7,5,3,4,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,6,5,1,4,3,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,5,1,2,4,3,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,6,5,3,1,2,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,8,7,5,3,1,4,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,7,5,6,3,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,3,4,6,5,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,1,4,8,7,3,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,8,7,3,1,2,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,7,3,4,1,2,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,3,1,6,5,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,3,2,6,5,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,8,7,3,4,6,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,7,3,6,5,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,7,1,6,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,1,2,6,5,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,1,2,4,3,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,1,8,7,3,4,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,5,1,2,4,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,8,7,1,4,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,7,3,4,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,7,5,6,3,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,8,7,3,1,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,8,7,3,1,4,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,4,3,1,8,7,5,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,7,5,6,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,7,5,3,1,6,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,8,7,5,3,6,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,7,5,6,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,8,7,5,1,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,8,7,5,1,2,4,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,7,5,6,1,2,4,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,4,8,7,3,6,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,7,2,4,3,6,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,8,7,1,2,6,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,7,5,3,6,4,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,1,4,3,6,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,7,3,4,1,6,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,1,2,3,5,4,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,1,2,6,4,5,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,3,6,5,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,2,6,3,7,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,4,2,8,3,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,5,8,6,1,4,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,3,6,1,5,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,8,5,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,1,8,2,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,6,1,8,4,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,5,1,8,4,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,2,1,8,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,2,7,1,5,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,8,6,4,3,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,3,8,7,4,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,3,2,8,4,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,7,2,8,3,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,3,7,4,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,7,3,5,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,4,7,3,5,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,8,1,3,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,3,5,7,2,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,1,4,7,3,2,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,1,3,2,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,7,1,2,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,5,1,3,8,2,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,7,3,8,6,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,4,2,7,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,8,7,4,6,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,7,2,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,7,3,6,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,4,6,2,5,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,3,4,7,6,8,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,1,3,6,7,4,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,4,7,6,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,7,6,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,7,3,6,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,8,2,4,5,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,8,6,2,4,7,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,2,6,5,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,6,7,4,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,2,5,6,3,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,1,6,4,3,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,2,7,5,4,3,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,1,7,5,4,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,6,1,7,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,1,2,8,4,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,1,3,8,6,5,4,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,1,7,5,4,3,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,3,2,8,6,5,4,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,1,7,6,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,7,1,8,4,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,7,1,6,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,7,6,1,8,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,4,7,6,8,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,7,8,6,3,2,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,4,6,7,5,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,3,7,5,6,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,8,6,7,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,8,6,7,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,2,7,8,6,3,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,7,6,4,3,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,1,7,6,4,3,2,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,1,8,6,7,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,7,5,6,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,8,1,7,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,1,8,7,3,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,8,4,1,7,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,5,8,7,3,1,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,1,8,4,7,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,8,4,3,7,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,1,7,2,5,6,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,3,5,2,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,7,1,5,4,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,2,4,3,7,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,4,1,6,7,5,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,4,5,6,3,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,4,5,6,2,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,4,7,6,2,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,1,7,8,6,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,6,2,8,7,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,4,5,1,7,6,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,3,1,5,6,4,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,5,3,7,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,5,6,2,8,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,7,4,2,8,5,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,4,1,6,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,3,1,4,7,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,1,6,3,4,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,4,1,6,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,4,2,5,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,5,1,4,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,7,1,3,6,8,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,7,1,3,8,4,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,7,1,6,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,7,1,4,5,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,4,2,1,8,6,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,5,7,2,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,4,5,7,3,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,7,2,4,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,7,2,1,4,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,7,5,1,2,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,4,6,2,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,4,6,1,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,7,6,1,2,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,8,7,6,1,3,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,3,6,7,2,5,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,7,2,6,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,3,7,5,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,8,2,5,6,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,7,3,5,6,1,4,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,3,8,1,4,5,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,3,1,4,5,2,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,4,7,2,1,5,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,2,5,1,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,3,1,6,4,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,4,1,5,6,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,6,4,1,7,5,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,3,1,7,4,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,3,7,1,6,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,3,8,1,4,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,8,2,6,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,7,3,1,5,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,3,1,2,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,3,6,1,2,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,3,2,1,7,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,3,1,6,4,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,5,1,2,6,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,4,1,2,5,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,3,7,4,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,6,3,8,4,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,2,5,3,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,4,5,2,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,8,6,4,2,5,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,6,4,1,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,3,4,6,1,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,7,5,3,1,6,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,1,4,8,3,2,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,6,4,2,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,7,4,2,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,8,5,2,4,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,2,5,1,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,2,1,6,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,2,8,6,5,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,8,6,1,5,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,2,6,1,4,5,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,7,8,6,2,4,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,6,3,1,2,5,4,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,8,1,5,6,2,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,4,1,5,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,8,1,6,4,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,1,3,7,6,4,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,2,8,3,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,6,7,3,2,8,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,6,3,2,7,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,3,7,2,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,7,3,8,2,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,6,2,8,5,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,5,2,6,4,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,6,2,7,4,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,6,2,8,4,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,3,1,7,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,6,1,8,7,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,8,6,5,7,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,2,5,7,4,3,6,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,5,7,4,6,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,8,6,1,7,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,6,8,1,7,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,7,1,8,6,4,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,3,6,7,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,6,1,7,8,5,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,8,5,6,7,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,8,5,6,7,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,8,6,2,7,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,8,2,5,1,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,1,4,6,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,4,7,3,6,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,5,7,4,6,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,2,1,6,8,4,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,8,3,1,6,5,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,5,8,3,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,8,5,4,2,7,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,5,8,4,2,1,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,7,4,5,1,3,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,3,5,4,2,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,6,4,2,5,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,7,6,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,5,8,6,4,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,8,5,6,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,7,2,6,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,4,6,1,3,5,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,3,8,2,7,5,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,7,3,2,5,6,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,1,2,3,8,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,7,6,2,1,8,5,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,2,7,1,6,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,1,7,6,8,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,2,7,5,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,4,7,8,1,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,7,8,3,4,1,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,8,4,2,5,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,2,8,7,5,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,2,8,5,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,6,8,4,2,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,8,5,2,3,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,7,4,3,1,5,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,8,6,2,4,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,7,4,2,5,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,8,4,6,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,6,3,1,7,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,6,4,7,2,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,6,2,7,5,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,1,8,6,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,4,2,6,8,1,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,4,6,2,8,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,5,8,2,3,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,6,4,8,2,1,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,7,4,8,2,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,6,1,2,4,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,6,3,8,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,6,2,1,8,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,6,2,1,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,4,3,1,6,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,3,1,6,4,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,8,2,5,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,8,7,3,4,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,5,2,3,8,1,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,8,6,4,2,5,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,6,2,1,8,4,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,1,8,7,5,3,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,1,6,5,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,8,1,7,5,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,2,1,4,8,3,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,6,4,3,8,7,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,4,7,3,1,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,2,3,1,4,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,1,8,4,7,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,4,6,8,1,3,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,7,5,3,2,1,8,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,7,1,6,4,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,6,7,2,5,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,2,5,3,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,3,7,6,4,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,8,1,6,7,5,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,3,8,7,5,4,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,7,2,6,1,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,8,6,3,1,5,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,8,7,3,1,6,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,8,4,6,7,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,8,4,5,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,3,8,6,4,7,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,3,7,8,4,5,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,3,4,8,5,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,4,1,8,2,5,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,8,3,1,6,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,3,7,4,5,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,7,1,5,6,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,3,4,8,1,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,2,6,8,1,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,5,7,3,2,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,6,2,7,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,1,7,8,3,4,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,1,7,2,8,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,4,1,7,3,8,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,1,6,2,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,1,8,2,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,2,5,3,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,4,1,8,3,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,3,4,8,2,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,6,2,8,1,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,3,6,1,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,2,3,5,1,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,4,5,1,2,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,4,7,1,8,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,1,3,4,7,2,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,5,2,7,6,3,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,3,5,6,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,2,5,6,1,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,2,5,1,6,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,3,5,6,1,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,2,6,8,3,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,5,6,1,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,2,7,8,6,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,2,3,8,1,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,7,6,8,1,2,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,6,1,3,4,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,6,8,5,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,5,4,7,6,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,8,6,5,1,3,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,8,5,2,6,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,1,6,3,2,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,1,8,6,3,2,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,1,2,5,3,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,2,5,8,1,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,8,7,2,6,3,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,6,8,4,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,6,2,4,8,1,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,7,3,8,6,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,8,2,6,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,7,5,6,2,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,5,1,8,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,1,7,3,2,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,6,1,2,4,3,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,3,1,8,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,2,1,5,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,2,3,1,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,2,8,7,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,8,3,2,7,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,3,1,7,6,5,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,3,8,7,1,6,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,7,3,1,6,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,3,8,2,1,7,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,7,2,6,5,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,1,8,6,5,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,2,8,1,7,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,8,4,2,1,7,6,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,4,7,1,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,8,3,1,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,1,5,4,3,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,1,8,5,4,3,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,1,8,3,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,1,7,3,4,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,8,1,5,2,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,6,8,2,4,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,5,8,4,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,6,1,4,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,5,6,1,4,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,6,8,1,4,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,7,4,2,5,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,8,5,2,4,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,7,4,2,5,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,6,7,5,8,1,2,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,7,5,8,3,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,8,5,7,4,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,8,6,5,7,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,7,5,8,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,7,4,1,5,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,4,1,5,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,1,5,7,4,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,8,1,6,5,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,4,1,6,5,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,8,7,3,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,6,5,7,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,2,1,5,7,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,2,1,6,8,4,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,8,7,4,2,3,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,8,6,5,7,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,5,7,4,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,7,5,8,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,6,5,7,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,7,8,5,6,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,8,5,6,3,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,8,5,3,6,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,7,8,5,3,4,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,7,8,5,3,1,4,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,7,5,3,8,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,5,8,3,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,5,8,3,4,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,5,6,3,4,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,5,6,3,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,5,6,3,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,5,3,6,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,5,3,1,4,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,5,3,1,6,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,5,3,1,6,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,5,3,6,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,5,3,6,4,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,3,8,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,5,3,1,8,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,5,3,1,8,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,5,3,8,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,3,8,6,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,8,3,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,5,3,8,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,5,3,8,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,5,3,6,1,4,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,7,5,3,8,6,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,8,6,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,5,8,6,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,5,6,8,3,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,5,6,8,3,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,5,3,6,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,5,3,4,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,5,3,6,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,6,3,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,5,6,3,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,5,3,6,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,5,3,6,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,5,3,6,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,3,1,6,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,7,5,3,1,6,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,7,5,3,1,4,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,7,5,3,1,4,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,7,5,3,4,1,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,5,3,4,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,5,3,4,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,5,3,4,6,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,5,3,4,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,2,8,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,6,3,2,4,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,6,1,8,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,7,1,2,5,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,7,2,1,5,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,5,2,1,4,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,6,5,7,8,3,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,6,3,8,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,6,1,8,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,6,1,7,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,7,2,8,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,5,6,7,3,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,7,2,8,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,6,2,8,5,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,1,8,4,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,7,1,8,4,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,1,7,3,8,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,8,3,2,5,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,3,2,4,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,7,8,3,1,5,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,6,8,7,3,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,8,5,6,7,2,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,7,2,3,4,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,6,2,7,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,2,8,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,2,8,5,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,6,3,7,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,7,3,2,4,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,5,8,7,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,6,3,7,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,1,7,2,6,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,5,1,2,8,7,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,1,2,8,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,7,1,6,2,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,5,1,7,6,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,5,1,7,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,1,4,8,2,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,1,4,8,2,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,6,1,7,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,1,3,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,1,5,4,8,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,1,3,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,5,1,3,7,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,6,1,3,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,7,1,4,2,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,1,4,2,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,1,8,6,5,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,3,1,7,4,5,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,7,1,2,4,8,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,1,6,4,8,3,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,7,8,4,2,3,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,7,8,3,6,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,7,8,2,4,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,8,1,7,2,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,4,7,3,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,4,2,7,5,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,3,2,1,5,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,5,3,6,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,1,4,6,7,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,8,4,1,7,6,5,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,5,4,2,7,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,4,6,3,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,8,5,3,2,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,5,6,1,4,2,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,3,8,4,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,3,6,8,4,2,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,3,1,4,7,6,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,3,2,7,5,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,5,6,1,3,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,7,8,3,5,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,1,4,8,7,3,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,6,5,7,8,3,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,6,8,2,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,6,8,7,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,8,2,6,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,6,7,8,2,1,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,5,7,1,6,3,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,2,8,3,6,5,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,8,7,2,4,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,6,1,8,2,4,5,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,5,6,3,4,8,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,2,4,7,8,6,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,5,1,2,8,6,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,4,5,7,1,8,6,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,6,4,7,3,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,4,7,3,8,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,5,7,4,3,2,8,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,4,8,6,7,2,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,7,2,4,3,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,8,7,3,2,6,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,3,4,5,2,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,3,6,4,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,5,3,6,7,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,7,2,5,6,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,4,1,7,3,6,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,5,8,2,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,8,6,4,7,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,8,6,7,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,8,2,5,1,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,6,2,5,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,7,6,3,2,8,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,6,4,2,3,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,3,4,1,8,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,6,8,2,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,2,5,8,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,2,5,8,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,5,3,6,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,7,5,1,6,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,1,4,7,8,2,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,8,7,4,6,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,7,1,5,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,8,4,6,5,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,8,5,4,6,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,8,7,5,2,6,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,7,4,6,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,7,2,5,6,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,7,8,5,3,6,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,4,8,1,5,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,8,3,5,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,8,6,3,7,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,6,7,8,4,5,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,1,2,8,4,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,1,8,5,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,1,8,2,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,2,1,8,6,4,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,3,8,4,7,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,8,1,7,4,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,8,3,7,6,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,7,2,8,6,4,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,7,8,1,6,2,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,7,8,5,6,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,7,8,5,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,8,6,4,7,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,8,5,7,6,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,3,8,5,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,5,8,6,7,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,4,3,7,2,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,8,2,6,3,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,3,5,2,4,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,6,3,4,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,3,8,4,6,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,3,5,8,6,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,8,2,4,6,1,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,8,4,6,1,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,3,7,5,2,1,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,4,7,6,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,5,1,3,2,8,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,4,3,2,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,3,5,8,7,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,2,7,4,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,1,4,8,3,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,7,2,1,8,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,8,2,1,4,7,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,2,4,7,1,8,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,5,4,1,3,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,2,3,5,7,1,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,4,6,3,1,7,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,6,5,1,8,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,6,8,7,3,2,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,4,8,3,6,5,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,8,1,3,6,5,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,4,1,6,7,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,1,8,6,5,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,3,8,6,4,7,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,8,6,4,3,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,2,1,6,4,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,1,8,7,3,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,1,7,6,8,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,7,6,4,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,1,7,6,4,3,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,5,1,2,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,4,5,7,3,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,4,7,6,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,4,7,6,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,3,2,6,1,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,4,7,6,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,6,3,7,4,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,7,4,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,1,7,8,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,3,8,4,5,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,6,7,8,3,4,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,8,1,2,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,5,1,8,7,2,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,3,7,2,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,2,8,7,3,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,2,8,4,6,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,5,1,7,6,2,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,2,7,6,3,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,2,6,8,3,5,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,8,1,7,6,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,2,8,6,5,3,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,1,8,7,6,5,2,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,5,2,8,4,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,5,2,7,4,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,5,2,6,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,5,2,6,1,4,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,1,8,7,4,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,5,1,8,6,4,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,5,1,7,6,4,3,2]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,5,3,7,6,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,2,5,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,8,6,1,5,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,6,2,5,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,7,6,1,5,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,6,7,8,4,5,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,6,2,8,4,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,7,5,4,1,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,4,5,3,1,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,6,5,4,1,7,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,6,5,8,4,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,5,7,3,1,6,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[8,2,6,7,4,5,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,2,7,8,4,6,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,6,3,5,4,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,3,1,8,7,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,1,5,8,6,4,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,4,8,1,5,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,8,1,5,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,2,6,7,1,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,8,5,2,7,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,8,2,7,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,6,3,1,7,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,5,2,6,1,4,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,6,2,8,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,2,4,6,8,7,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,1,6,5,7,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,6,2,5,7,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,6,5,7,1,3,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,6,5,2,8,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,8,6,2,7,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,4,7,1,3,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,3,6,7,4,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,7,5,2,4,3,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,1,8,5,7,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,2,1,7,4,3,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,7,4,2,3,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,4,3,8,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,5,3,4,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,5,2,6,4,3,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,4,5,2,1,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,2,6,1,4,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,6,4,2,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,2,4,8,1,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,5,8,1,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,3,5,8,1,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,7,3,8,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,6,4,1,3,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,1,6,7,3,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,7,5,8,2,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,6,7,1,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,3,7,8,2,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,4,7,8,1,2,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,1,4,3,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,6,7,8,2,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,6,3,7,8,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,6,7,8,4,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,2,7,8,5,3,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,7,4,8,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,2,8,1,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,4,3,1,6,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,6,1,7,8,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,5,8,6,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,1,3,8,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,7,1,8,5,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,4,7,8,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,7,4,8,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,4,7,8,3,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,2,4,5,3,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,7,3,2,6,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,2,1,5,4,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,7,4,8,6,5,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[7,6,5,2,4,1,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,1,8,7,2,3,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,1,2,7,3,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,6,8,2,7,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,8,7,2,5,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,1,3,4,6,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,2,6,4,8,7,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,2,8,6,5,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,1,8,6,5,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,7,4,8,3,6,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,3,8,6,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,3,6,8,7,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,8,2,5,7,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,2,6,8,7,5,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,1,6,4,8,7,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,6,8,7,5,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,8,1,4,5,7,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,8,1,4,2,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,8,3,5,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,1,2,5,4,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,3,6,8,7,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,8,3,5,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,8,3,5,7,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,2,4,5,7,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,2,5,1,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,8,5,7,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,1,5,2,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,6,4,1,3,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,8,6,4,1,3,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,4,2,5,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,2,1,4,6,5,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,6,2,1,5,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,6,1,5,8,7,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,7,1,5,6,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,6,7,4,1,2,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,2,7,1,6,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,2,8,1,6,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,8,1,5,6,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,8,1,5,3,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,8,2,1,5,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,2,5,3,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,8,2,3,6,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,4,8,5,3,6,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,3,2,6,4,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,4,5,3,8,6,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,5,2,8,6,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,5,3,2,6,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,5,4,2,8,6,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,1,2,7,5,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,7,4,2,8,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,5,7,4,6,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,5,2,4,3,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,8,1,2,5,4,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,1,8,5,2,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,1,8,5,4,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,2,8,5,6,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,2,6,8,5,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,7,6,4,8,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,1,6,8,5,4,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,5,8,4,6,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,2,8,4,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,5,8,2,6,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,4,2,8,3,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,4,8,2,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,4,8,3,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,2,5,8,4,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,8,3,5,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,8,3,2,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,5,6,4,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,1,7,4,5,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,5,6,4,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,5,6,4,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,6,8,3,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,6,8,3,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,5,8,6,3,7,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,8,7,3,5,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,2,7,3,5,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,5,2,7,1,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,6,7,3,2,5,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,1,7,8,2,4,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,6,8,3,2,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,4,5,2,7,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,7,6,8,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,7,6,3,2,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,4,6,7,3,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,6,7,3,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,7,6,2,4,5,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,5,2,1,6,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,2,4,1,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,2,4,7,6,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,4,6,2,3,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,2,6,3,4,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,2,1,4,3,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,4,1,7,5,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,7,8,5,4,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,4,5,2,8,6,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,5,2,8,1,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,5,2,8,6,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,5,2,6,8,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,5,2,1,8,6,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,4,8,5,6,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,8,6,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,8,2,5,1,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,4,2,1,5,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,4,1,3,6,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,7,5,1,8,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,6,5,3,8,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,4,6,3,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,6,4,7,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,1,8,6,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,8,1,7,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,8,6,2,1,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,6,2,4,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,3,2,4,6,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,2,8,5,3,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,5,4,8,7,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,2,8,7,3,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,6,8,1,7,4,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,8,6,3,1,4,5,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,6,1,7,5,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,4,8,3,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,7,6,2,8,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,6,5,2,7,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,7,8,5,6,2,3,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,7,8,5,6,1,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,8,4,2,1,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,7,8,1,2,5,6,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,1,4,7,2,5,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,7,8,3,5,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,7,8,3,6,5,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,7,8,2,1,5,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,6,2,1,7,5,4,3]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[3,6,1,2,5,7,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,6,3,2,7,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,4,3,7,5,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,4,7,1,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,7,8,4,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,3,6,1,8,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,7,3,6,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,5,6,7,3,8,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[7,5,6,1,2,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,1,5,8,6,2,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,6,5,7,1,2,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,7,5,6,3,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,5,1,6,3,4,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,3,5,4,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,2,4,3,6,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,7,2,4,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,7,5,8,1,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,7,5,8,3,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,8,7,6,3,4,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,5,8,7,6,2,3,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,4,8,2,1,5,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,2,4,1,6,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,2,7,5,4,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,2,7,1,6,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,7,1,6,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,4,7,8,6,3,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,2,1,7,6,5,3,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,7,4,1,6,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,6,8,7,3,2,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,5,8,3,6,2,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,5,1,2,8,3,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,6,8,1,3,7,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,4,2,8,3,7,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,4,8,6,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,2,5,6,3,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,8,5,3,2,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,1,2,8,3,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,2,1,3,7,4,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,8,1,6,7,4,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,7,2,3,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,4,2,8,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,2,6,5,1,3,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,8,3,1,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,1,8,3,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,2,8,4,6,7,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,2,8,4,6,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,7,4,3,8,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,5,7,3,4,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,8,4,6,2,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,1,8,4,6,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,6,5,4,7,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,6,1,4,7,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,6,5,4,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,6,8,7,3,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,4,6,7,3,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,8,6,1,5,7,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,3,7,2,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,3,7,2,4,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,8,2,5,7,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,3,4,1,2,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,3,4,6,2,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,7,3,4,6,2,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,2,8,5,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,6,5,2,4,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,1,4,6,3,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,7,1,3,6,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,5,2,8,4,7,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,4,7,5,8,6,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,5,7,2,3,6,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,8,3,4,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,8,3,4,6,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,8,6,3,5,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,1,3,5,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,1,6,8,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,8,2,6,4,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,5,2,8,4,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,5,8,6,3,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,2,8,3,5,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,5,6,3,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,1,5,3,8,7,6]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,8,2,4,7,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,2,4,3,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,1,4,2,3,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,8,4,2,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,8,7,5,2,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,4,7,8,5,3,6,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,1,8,6,5,7,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,3,6,8,4,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,4,6,2,5,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,7,3,4,2,6,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,2,5,3,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,2,3,4,7,1,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,2,1,3,8,6,4,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,1,5,2,7,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,3,2,5,1,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,2,1,3,8,7,4,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,5,8,7,3,4,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,7,3,2,5,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,2,5,4,8,7,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,4,8,6,3,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,2,4,7,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,4,1,8,6,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,3,5,7,4,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,7,6,8,5,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,2,7,6,8,4,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,3,4,2,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,6,8,5,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,6,3,5,8,4,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,6,3,2,8,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,5,8,4,6,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,3,2,7,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,1,8,5,2,6,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,1,3,7,4,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,8,6,2,3,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,6,3,2,7,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,5,8,6,2,3,4,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,6,4,3,8,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,5,7,6,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,7,3,6,8,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,6,3,5,7,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,5,6,3,2,7,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,7,6,8,4,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,4,7,5,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,5,2,1,7,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,8,5,6,3,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,2,6,8,4,3,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,3,7,2,6,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,8,2,6,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,2,5,3,4,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,4,5,3,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,2,4,3,5,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,3,5,4,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,2,7,1,6,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,3,2,8,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,6,1,5,3,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,4,3,1,5,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,7,6,1,4,3,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,6,1,5,4,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,2,7,1,5,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,7,2,8,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,4,3,1,5,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,3,7,1,5,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,6,1,2,5,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,7,6,1,4,2,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,7,5,8,6,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,7,3,8,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,7,1,5,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,6,1,3,4,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,8,1,3,4,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,8,5,1,3,4,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,8,3,4,6,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,5,1,3,4,2,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,7,1,3,4,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,3,5,6,4,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,3,8,2,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,3,7,8,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,7,3,8,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,1,5,3,6,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,3,5,8,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,7,5,8,6,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,8,5,3,6,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,5,8,3,4,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,5,6,3,4,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,5,6,4,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,5,8,4,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,5,6,8,1,3,4,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,3,4,7,8,1,2,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,3,7,6,8,1,2,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,7,1,2,5,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,2,7,5,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,1,5,4,6,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,5,1,2,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,1,2,8,5,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,1,7,4,6,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,5,7,4,6,3,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,4,8,3,5,6,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,7,3,5,6,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,7,6,4,2,3,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,8,2,5,6,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,8,4,6,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,2,4,6,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,1,4,8,5,2,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,8,4,7,2,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,1,8,3,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,5,8,1,6,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,5,1,8,2,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,7,4,2,1,5,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,3,2,7,8,6,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,6,8,4,7,3,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,3,5,4,2,8,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,2,4,3,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,1,6,8,5,2,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,8,1,5,6,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,8,1,3,2,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,5,8,2,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,5,1,8,2,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,1,8,5,3,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,2,3,8,1,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,5,7,1,6,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,6,2,7,5,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,2,5,3,7,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,7,1,8,6,3,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,6,1,3,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,3,2,6,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,6,5,3,7,4,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[3,5,4,6,1,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,5,4,6,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,1,5,6,4,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,5,1,8,6,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,6,3,1,7,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,2,5,6,3,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,2,7,5,4,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,4,7,2,8,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,5,6,4,1,7,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,6,1,7,4,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,7,1,8,6,5,4,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,7,6,1,8,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,7,8,5,3,2,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,3,2,8,6,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,3,2,6,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,8,5,6,3,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,5,6,3,2,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,8,6,7,3,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,6,7,3,2,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,7,5,2,4,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,8,5,2,4,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,7,8,3,2,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,4,5,8,6,7,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,8,4,5,6,7,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,2,8,6,7,4,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,8,6,3,5,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,7,4,3,8,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,8,4,3,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,8,6,7,4,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,7,8,4,2,3,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,6,7,3,5,2,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,7,8,3,4,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,8,5,6,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,4,2,3,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,3,5,6,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,8,3,4,2,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,8,6,7,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,7,4,6,3,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,8,6,7,3,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,4,5,2,3,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,8,4,5,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,8,3,4,5,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,8,4,5,6,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,8,4,5,6,2,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,2,5,6,3,4,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,2,7,3,4,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,7,2,3,4,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,7,5,2,6,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,3,6,4,5,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,4,6,3,5,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,2,7,8,5,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,8,7,3,2,5,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,4,2,6,7,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,3,8,1,6,7,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,2,8,1,6,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,2,1,3,7,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,3,4,1,2,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,3,2,8,5,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,8,2,6,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,3,6,7,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,2,8,3,6,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,8,4,6,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,7,6,4,3,5,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,1,4,7,5,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,7,5,6,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,8,7,5,3,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,1,8,7,5,4,2,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,3,5,6,1,4,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,7,3,2,4,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,3,7,5,6,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,2,4,7,5,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,7,6,5,3,1,4]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[2,8,7,6,4,5,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,7,6,4,1,5,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,8,7,6,4,2,5,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,3,4,7,5,2,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,7,4,6,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,8,7,6,2,5,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,7,6,3,1,5,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,5,2,4,7,6,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,2,6,4,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,2,6,7,4,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,2,7,6,4,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,2,8,4,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,2,7,4,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,2,5,7,4,6,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,7,5,4,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,5,2,4,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,7,5,4,8,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,3,5,1,6,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,5,6,1,3,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,7,6,8,2,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,6,4,1,8,2,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,4,2,1,6,3,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,1,6,7,3,4,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,1,6,7,4,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,8,6,3,7,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,8,1,2,5,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,3,4,8,5,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,7,1,2,6,8,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,5,2,3,6,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,7,4,5,2,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,4,3,1,8,5,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,7,4,1,8,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,4,6,8,3,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,4,6,5,8,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,2,5,8,7,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,4,5,6,2,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,3,1,8,5,4,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,3,1,6,5,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,3,8,5,6,4,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,7,4,8,6,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,6,4,1,2,5,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,8,4,3,1,6,5,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,8,2,3,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,4,6,1,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,8,2,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,8,4,3,2,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,5,6,3,4,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,6,2,5,4,7,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,8,5,7,6,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,3,1,7,6,4,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,3,5,6,1,4,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,8,3,6,2,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,1,6,5,3,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,6,4,1,7,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,1,6,4,8,7,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,6,7,5,1,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,6,4,1,5,3,2,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,8,7,4,1,5,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,8,7,3,5,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,1,2,8,5,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,5,7,2,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,3,8,5,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,1,2,8,4,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,1,4,7,6,3,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,4,5,3,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,1,6,3,7,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,7,6,3,4,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,7,5,4,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,2,1,6,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,8,2,4,7,6,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,8,1,6,4,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,6,5,7,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,1,4,7,3,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,8,2,7,4,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,2,1,8,4,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,1,6,8,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,2,1,8,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,4,1,7,3,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,5,6,7,1,4,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,4,6,8,3,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,2,4,7,8,1,3,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,1,4,3,2,8,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,4,8,6,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,8,6,5,7,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,7,8,6,4,2,5,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,2,8,4,7,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,7,3,6,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,7,8,6,5,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,4,7,2,6,8,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,7,6,5,1,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,2,3,5,7,1,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,8,1,2,5,6,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,1,3,6,8,5,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,8,5,1,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,8,1,4,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,2,4,5,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,8,4,1,6,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,3,1,6,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,1,4,8,5,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,6,1,5,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,1,8,4,3,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,1,8,5,7,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,8,7,4,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,6,2,5,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,7,2,5,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,2,8,6,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,8,7,5,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,5,8,7,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,8,6,5,1,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,4,8,7,5,1,3,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,7,6,1,8,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,7,6,2,8,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,5,7,6,1,8,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,1,4,7,3,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,3,8,7,2,5,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,6,2,8,7,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,5,3,8,7,6,4,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,5,3,2,8,7,6,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,1,4,3,8,7,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,4,1,8,7,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,1,8,7,5,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,2,8,7,6,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[6,4,1,8,7,5,2,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,3,1,8,7,4,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,2,5,1,8,6,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,2,8,1,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,2,8,5,1,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,6,2,8,7,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,5,2,1,8,7,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,5,1,4,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,4,1,3,7,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,7,1,3,6,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,8,1,4,7,6,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,2,7,3,8,6,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,8,6,2,5,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,1,8,3,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,1,7,4,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,1,2,8,6,4,3,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,8,1,3,7,6,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,3,5,8,7,6,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,4,7,5,8,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,7,8,3,4,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,8,6,7,5,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[7,2,6,8,1,4,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,6,2,8,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,6,3,7,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,3,7,1,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,5,7,3,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,2,7,4,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,7,8,5,3,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,6,5,4,7,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,3,4,6,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,7,4,2,5,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,7,1,5,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,3,1,5,7,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,3,8,2,7,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,1,6,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,4,8,2,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,4,5,2,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,7,1,5,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,1,5,3,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,3,4,7,1,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,4,7,1,6,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,6,7,1,5,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,4,7,1,5,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,5,2,6,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,7,1,5,2,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,3,4,6,7,1,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,6,8,3,4,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,7,1,8,3,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,1,6,3,4,5,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,4,8,7,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,7,1,5,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,8,7,1,5,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,5,2,8,7,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,7,1,8,4,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,1,6,8,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,4,6,7,1,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,5,2,6,7,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,1,4,8,5,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,5,2,7,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,1,4,6,5,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,1,8,4,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,3,4,7,1,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,4,7,1,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,6,4,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,5,2,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,6,5,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,6,5,2,8,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,5,2,7,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,8,4,6,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,8,5,2,7,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,7,1,6,5,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,6,7,1,5,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,1,5,2,8,6,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,3,4,7,1,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,7,1,6,4,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,6,4,7,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,1,4,8,6,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,1,4,5,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,7,1,4,5,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,2,6,7,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,2,8,6,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,8,7,1,4,5,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,2,6,8,7,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,4,6,7,8,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,7,6,5,8,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,5,4,7,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,7,6,8,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,5,3,7,6,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,4,3,7,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,6,4,7,5,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,2,5,3,6,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,3,6,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,5,3,7,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,3,7,5,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,3,6,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,2,5,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,8,2,5,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,1,4,6,5,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,7,2,5,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,3,6,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,8,4,6,5,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,7,3,6,5,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,2,5,4,1,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,6,4,1,5,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,8,3,7,5,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,2,1,4,8,5,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,1,4,8,6,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,1,5,8,6,4,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,2,8,3,7,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,3,7,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,7,2,6,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,1,4,8,5,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,3,7,4,8,5,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,2,6,3,7,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,3,8,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,3,8,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,4,8,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,3,8,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,5,3,8,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,3,8,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,5,3,7,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,6,4,8,5,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,4,8,6,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,2,4,3,7,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,3,8,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,4,3,8,5,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,4,3,8,6,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,5,3,8,6,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,5,3,1,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,4,3,1,7,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,4,3,1,6,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,1,3,6,4,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,1,3,6,5,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,5,2,4,7,6,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,5,3,1,6,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,5,3,1,7,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,6,3,1,7,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,6,4,1,7,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,7,4,1,6,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,3,1,6,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,3,1,6,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,7,3,1,5,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,6,3,1,5,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,2,4,8,6,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,4,1,3,7,5,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,1,5,3,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,6,4,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,8,5,1,6,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,8,4,1,5,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,7,4,1,5,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,3,2,5,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,8,7,5,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,1,7,4,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,5,2,4,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,2,8,7,4,3,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,1,2,6,4,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,2,5,7,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,4,3,2,5,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,5,6,7,1,4,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,7,2,8,1,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,7,1,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,1,2,6,4,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,1,6,8,4,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,2,8,5,1,4,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,8,1,6,3,2,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,3,6,4,1,2,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,3,7,8,4,1,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,4,7,2,3,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,8,3,1,5,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,3,5,8,7,6,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[7,3,5,1,4,6,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,5,1,2,6,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,1,8,6,4,3,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,2,6,5,8,4,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,7,2,6,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,5,3,2,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,5,7,8,6,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,7,2,6,4,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,3,5,8,7,4,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,6,2,3,1,5,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,5,2,1,4,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,6,3,8,7,4,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,3,6,8,5,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,5,2,4,7,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,1,7,4,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,7,3,5,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,2,7,3,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,2,1,7,8,5,4,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,4,2,1,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,2,3,7,4,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,4,3,8,6,5,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,7,5,3,8,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,6,7,4,1,5,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,5,2,1,3,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,6,3,2,4,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,7,8,6,4,1,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,1,6,4,7,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,3,7,5,8,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,8,5,3,2,4,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,7,8,2,5,1,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,4,8,6,2,3,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,5,7,8,1,4,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,5,8,6,1,3,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,7,8,1,5,6,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,7,1,8,4,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,7,5,1,6,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,3,5,1,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,4,6,1,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,6,7,2,8,3,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,7,3,8,4,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,2,7,5,3,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,8,2,7,4,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,1,4,3,8,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,1,8,5,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,1,5,8,6,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,2,7,8,3,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,4,1,8,5,6,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,5,8,1,6,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,8,1,5,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,4,2,6,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,2,6,4,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,8,2,3,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,8,5,2,4,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,1,8,4,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,1,4,7,5,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,1,3,7,4,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,2,3,8,4,5,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,1,3,4,8,7,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,2,6,3,5,7,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,8,4,6,3,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,1,5,4,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,8,5,4,6,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,6,8,4,5,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,2,8,4,6,3,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,3,5,7,8,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,7,6,5,1,4,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,7,4,8,1,3,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,6,8,4,1,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,6,8,4,7,5,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,7,2,8,6,3,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,8,5,4,7,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,8,4,7,3,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,1,4,8,3,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,6,1,4,8,7,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,5,8,7,1,6,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,4,2,3,7,1,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,4,8,7,3,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,5,7,6,1,8,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,3,2,6,7,4,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,7,3,1,2,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,2,4,1,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,8,2,6,7,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,5,7,1,2,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,2,4,6,7,1,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,7,6,1,2,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,5,1,2,7,4,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,6,8,1,3,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,1,6,3,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,7,3,5,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,1,5,2,6,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,5,2,6,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,1,3,8,7,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,8,5,6,2,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,5,2,6,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,2,4,6,1,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,3,5,7,2,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,7,6,1,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,4,8,6,3,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,2,1,8,5,4,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,3,2,1,6,4,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,5,2,1,8,4,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,5,2,1,8,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,8,4,2,5,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,2,4,3,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,7,4,2,5,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,3,6,2,1,7,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,6,5,1,7,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,2,7,1,6,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,5,3,7,2,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,3,8,2,1,5,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,2,8,1,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,5,8,3,2,7,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,8,3,4,7,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,5,2,7,3,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,4,6,1,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,6,2,1,7,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,7,3,2,8,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,7,4,8,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,7,2,4,8,3,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,4,7,8,2,3,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,8,2,1,6,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,2,8,1,5,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,5,3,2,6,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,7,4,5,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,7,5,6,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,4,6,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,2,3,7,6,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,5,1,7,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,7,6,2,4,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,7,6,3,4,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,7,6,4,3,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,7,2,5,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,3,5,2,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,7,6,4,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,7,8,3,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,7,3,1,5,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,8,6,2,5,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,8,1,3,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,7,3,8,1,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,4,1,7,2,5,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,1,7,6,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,7,8,5,4,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,6,7,8,5,4,2,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,6,7,1,8,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,7,8,3,4,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,8,6,2,5,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,1,6,4,5,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,1,7,6,4,2,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,5,8,2,6,4,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,5,3,7,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,5,7,4,6,8,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,7,5,6,8,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,6,7,4,5,8,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,6,7,4,8,1,3,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,4,7,5,8,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,2,1,8,4,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,2,7,6,4,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,1,2,6,4,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,1,7,2,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,7,1,5,4,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,1,5,6,4,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,1,6,4,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,2,7,6,5,3,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,8,2,6,4,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,2,5,6,4,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,6,7,2,5,4,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,7,6,5,8,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,7,6,5,2,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,3,7,6,5,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,7,3,4,5,8,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,1,8,4,5,6,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,7,4,5,8,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,3,2,5,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,1,8,4,5,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,2,5,1,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,4,6,2,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,5,2,1,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,1,2,6,3,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,5,6,3,8,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,6,3,8,7,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,7,1,3,8,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,8,7,4,6,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,8,7,5,3,6,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,3,8,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,2,6,1,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,2,6,8,1,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,4,8,6,5,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,5,3,7,4,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,6,8,5,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,4,5,7,3,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,4,7,8,6,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,1,6,8,2,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,6,8,5,2,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,5,8,6,2,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,5,7,8,6,2,4,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,7,5,8,6,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,3,6,2,1,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,6,4,7,3,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,2,3,1,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,2,7,5,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[5,8,1,7,6,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,6,3,2,1,5,4,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,3,2,4,1,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,5,2,4,3,6,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,1,4,6,3,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,1,6,3,4,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,3,6,1,5,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,3,5,2,1,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,3,2,8,7,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,1,4,3,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,7,3,6,1,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,6,2,4,1,5,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,6,3,7,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,8,2,6,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,5,1,7,6,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,4,6,3,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,6,4,3,5,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,3,7,2,1,4,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,6,4,1,3,2,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,3,8,2,1,5,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,5,7,4,3,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,5,4,8,7,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,8,5,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,7,6,8,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,6,2,8,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,6,3,8,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,8,1,3,5,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,2,8,5,1,3,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,8,5,3,2,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,8,2,5,6,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,5,8,7,2,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,5,7,4,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,5,7,8,3,4,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,6,7,3,1,8,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,2,6,3,1,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,4,2,5,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,5,3,8,4,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,3,5,8,4,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,6,4,2,8,5,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,7,6,4,8,5,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,7,4,1,3,2,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,1,4,8,3,6,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,8,5,7,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,5,8,4,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,5,8,3,4,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,5,1,3,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,2,6,1,7,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,6,8,3,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,5,1,4,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,4,5,1,3,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,8,5,3,4,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,8,3,6,4,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,8,1,4,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,1,5,6,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,2,6,5,3,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,1,7,2,6,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,3,8,1,2,6,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,2,4,6,5,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,2,8,3,5,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,3,7,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,1,5,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,7,1,5,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,3,5,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,5,3,4,6,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,4,2,5,3,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,8,4,3,6,2,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,6,2,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,2,6,3,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,5,1,6,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,1,4,6,2,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,8,4,3,1,7,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,7,6,3,5,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,8,5,2,4,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,7,8,4,3,2,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,4,8,6,5,7,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,8,4,7,2,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,8,3,4,7,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,4,2,8,3,7,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,7,6,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,1,5,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,7,4,3,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,7,4,8,5,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,1,3,2,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,2,6,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,4,3,1,7,2,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,7,6,5,8,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,4,2,8,6,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,3,7,8,2,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,3,7,8,6,1,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,8,5,7,6,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,6,8,7,2,5,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,7,8,6,2,4,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,8,7,2,4,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,2,5,1,4,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,7,1,4,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,2,4,1,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,3,5,4,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,3,7,8,2,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,6,4,3,5,1,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,8,4,3,1,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,6,1,4,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,6,5,3,8,1,4,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,8,6,4,5,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,6,8,5,3,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,2,1,6,7,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,1,3,5,4,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,8,2,5,4,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,3,6,4,1,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,2,6,7,3,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,2,3,5,8,4,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,7,6,8,4,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,6,1,5,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,5,6,8,2,4,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,1,6,5,3,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,6,4,2,5,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,6,4,1,5,3,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,8,7,1,5,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,8,4,6,5,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,4,6,5,1,3,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,5,3,6,4,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,3,7,4,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,3,5,7,2,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,3,7,2,1,8,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,4,3,2,8,5,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,6,3,5,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,1,5,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,1,8,5,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,3,8,6,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,3,6,8,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,4,7,3,8,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,7,2,4,6,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,6,4,2,5,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,2,4,6,3,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,3,6,8,5,7,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,3,5,8,2,4,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,4,8,3,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,6,2,8,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,6,8,3,5,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,5,7,2,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,6,8,3,7,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,7,2,8,5,4,3,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,8,3,6,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,8,5,7,4,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,8,2,5,7,1,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,2,4,6,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,7,5,2,6,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,6,2,7,5,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,4,2,7,3,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,6,3,5,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,2,7,3,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,7,3,4,5,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,2,4,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,5,7,2,3,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,5,7,2,4,6,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,3,7,2,5,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,5,1,4,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,3,6,4,2,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,3,6,7,4,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,6,8,7,3,4,5,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,7,8,3,6,4,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,8,3,2,4,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,7,8,5,6,4,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,1,7,5,8,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,3,2,4,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,6,5,8,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,3,7,4,1,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,5,6,4,2,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,5,8,1,6,4,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,8,2,7,4,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,3,2,7,4,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,5,1,7,3,2,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,1,6,4,2,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,7,5,4,3,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,1,6,5,4,3,2,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,6,8,1,5,4,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,2,1,7,6,3,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,5,8,2,1,4,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,2,8,5,3,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,7,5,3,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,5,1,8,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,7,8,3,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,5,8,1,3,7,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,3,6,8,7,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,6,2,8,1,4,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,7,2,6,8,3,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,2,8,7,4,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,3,8,5,6,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,1,5,8,7,6,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,1,6,5,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,1,8,6,5,7,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,7,6,4,5,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,6,5,1,8,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,8,5,6,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,2,1,8,7,3,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,7,3,2,5,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,2,5,1,7,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,5,3,8,7,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,5,8,7,4,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,5,3,8,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,5,3,8,4,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,5,2,6,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,5,6,7,4,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,8,5,2,6,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,8,1,7,4,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,4,1,8,7,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,3,2,5,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,7,3,2,5,4,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,1,7,6,2,4,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,7,3,1,6,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,4,8,3,1,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,4,8,1,6,5,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,5,6,1,8,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,6,2,7,3,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,3,4,7,1,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,2,1,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,5,1,4,6,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,3,7,1,6,5,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,3,2,5,4,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,3,2,5,4,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,3,6,7,4,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,8,4,2,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,3,7,4,1,8,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,4,5,1,8,6,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,1,6,7,5,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,7,1,5,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,3,7,8,2,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,4,8,6,5,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,3,4,2,1,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,5,3,8,6,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,2,7,5,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,2,5,1,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,2,4,8,7,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,2,4,1,3,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,2,4,3,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,1,4,3,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,2,7,5,3,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,2,1,5,8,3,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,3,8,7,1,5,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,3,8,1,5,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,3,6,7,2,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,4,5,8,2,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,8,1,6,5,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,8,5,1,3,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,1,7,6,3,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,8,6,5,1,2,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,7,8,6,5,1,2,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,7,8,2,6,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,8,2,5,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,4,5,7,2,6,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,5,8,6,1,3,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,8,7,1,5,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,8,2,6,3,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,8,2,7,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,8,2,7,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,8,3,1,7,5,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,3,7,5,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,4,8,3,2,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,8,2,7,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,8,2,7,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,3,1,7,4,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,3,1,6,4,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,6,3,4,5,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,1,3,6,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,1,3,7,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,3,8,6,1,4,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,1,3,7,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,3,8,2,7,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,8,2,7,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,7,8,3,2,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,7,3,4,2,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,7,3,2,8,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,3,2,4,5,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,3,4,6,1,2,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,4,8,2,3,5,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,6,8,2,3,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,8,2,3,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,4,7,8,2,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,1,3,2,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,1,2,7,6,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,3,7,2,6,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,5,4,6,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,3,2,8,5,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,4,3,2,6,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,7,2,1,8,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,3,2,5,1,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,4,3,7,2,6,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,8,3,7,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,8,5,2,1,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,1,5,4,7,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,3,6,5,8,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,3,6,2,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,6,8,2,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,6,5,3,2,8,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,3,2,7,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,4,8,3,2,7,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,5,4,7,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,5,7,2,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,3,7,8,2,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,4,8,6,3,2,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,8,3,6,5,4,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,8,6,2,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,5,3,6,7,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,2,5,3,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,6,2,5,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,7,4,6,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,4,8,1,2,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,5,2,8,6,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,2,8,1,7,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,6,3,8,4,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,4,6,8,3,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,1,2,3,5,4,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,5,4,3,7,8,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,4,1,6,8,3,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,6,8,3,5,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,3,1,5,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,2,1,4,8,6,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,6,2,3,5,4,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,6,5,3,4,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,3,2,6,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,8,5,7,3,4,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,1,6,8,4,7,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,4,1,8,7,6,3,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,3,5,8,4,7,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,8,7,5,1,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,8,7,2,4,1,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,1,3,5,6,2,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,4,6,1,3,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,8,7,3,5,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,3,5,6,1,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,2,3,4,6,1,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,7,4,3,5,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,2,7,6,4,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,8,6,2,7,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,8,2,7,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,8,7,2,4,6,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,2,8,7,6,4,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,7,1,4,6,5,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,1,2,6,5,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,5,8,3,7,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,3,4,5,1,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,8,1,5,6,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,8,3,2,5,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,8,1,3,2,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,8,1,3,5,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,1,3,5,2,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,7,8,5,2,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,7,8,3,5,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,8,3,2,5,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,7,8,5,4,6,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,6,4,8,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,8,5,4,6,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,7,8,5,4,2,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,3,7,8,2,5,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,2,7,8,5,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,7,6,8,3,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,4,7,8,6,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,5,7,6,8,4,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,7,6,8,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,4,6,8,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,1,4,3,2,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,2,1,3,6,5,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,8,4,3,7,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,6,7,8,4,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,7,8,4,6,5,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,2,7,6,3,8,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,5,7,1,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,8,3,2,4,6,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,6,2,3,7,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,8,3,6,7,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,3,1,5,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,2,4,1,8,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,6,7,2,1,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,1,7,4,3,8,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,2,8,3,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,3,8,5,4,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,4,1,7,8,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,4,3,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,1,5,6,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,8,7,3,2,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,1,5,2,7,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,1,5,6,2,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,5,7,6,3,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,5,7,4,6,8,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,8,2,3,6,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,7,3,2,6,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,6,7,3,5,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,3,4,8,2,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,8,2,6,7,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,7,8,2,3,6,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,8,3,5,7,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,4,6,2,3,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,7,8,3,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,4,8,7,3,2,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,5,2,3,4,1,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,3,5,8,6,2,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,8,4,1,7,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,5,1,7,8,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,8,5,4,2,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,7,5,2,3,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,3,2,7,5,6,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,6,7,4,1,5,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,7,1,6,2,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,8,5,7,4,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,3,7,5,4,6,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,4,2,8,6,3,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,6,5,3,4,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,6,3,5,7,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,7,4,3,1,8,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,8,6,7,4,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,8,2,5,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,1,5,7,3,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,1,5,2,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,6,4,2,7,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,6,2,1,7,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,2,5,7,4,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,4,8,3,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,8,4,3,1,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,1,8,7,2,5,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,6,2,8,1,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,1,8,2,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,1,8,5,3,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,8,7,3,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,7,8,6,3,4,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,1,2,8,6,7,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,2,4,8,6,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,1,2,5,8,7,4,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,5,2,1,8,4,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,6,2,4,3,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,5,2,8,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,4,1,3,6,2,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,4,7,3,2,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,5,4,8,6,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,5,7,4,8,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,7,1,6,8,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,1,5,8,6,2,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,4,8,6,3,7,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,4,8,2,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,5,2,3,7,4,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,2,3,1,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,5,3,8,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,6,4,8,3,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,4,8,3,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,4,7,5,2,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,4,7,2,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,5,4,8,6,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,7,5,4,6,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,6,3,7,4,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,3,1,7,5,6,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,5,8,6,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,5,1,8,7,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,3,1,6,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,3,6,1,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,6,4,1,8,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,2,1,5,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,1,5,7,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,4,2,7,8,3,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,5,6,7,4,1,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,5,6,8,3,1,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,1,4,5,3,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,2,4,5,3,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,7,4,5,3,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,4,7,3,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,6,4,8,2,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,4,7,5,2,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,2,6,7,4,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,5,6,1,4,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,4,7,8,3,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,4,8,2,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,4,5,8,2,3,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,1,3,2,5,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,8,1,4,6,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,6,7,8,1,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,7,8,2,5,1,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,8,2,5,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,3,7,8,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,3,8,5,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,3,2,7,5,8,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,5,3,2,6,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,4,5,3,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,5,3,2,4,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,7,3,8,2,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,4,1,3,6,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,6,1,3,2,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,8,2,4,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,3,7,8,1,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,3,7,8,1,5,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,3,7,8,1,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,8,1,6,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,7,3,8,5,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,1,4,3,7,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,8,5,3,2,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[8,2,7,6,4,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,4,3,8,5,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,1,7,8,4,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,7,1,8,6,4,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,7,6,3,8,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,2,6,1,8,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,8,7,1,5,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,2,7,3,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,1,4,7,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,6,1,2,8,5,3,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,1,8,4,6,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,8,3,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,6,3,4,1,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,2,8,5,3,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,8,7,3,5,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,5,8,3,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,7,2,6,8,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,2,8,1,6,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,5,7,1,3,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,7,2,1,5,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,8,2,7,1,3,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,1,8,7,4,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,1,7,4,6,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,5,8,3,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,6,8,3,2,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,5,6,8,2,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,7,8,2,4,1,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,2,8,7,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,2,3,6,4,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,7,6,8,2,3,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,5,3,1,6,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,2,3,1,7,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,2,3,8,7,4,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,3,6,8,4,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,1,7,3,4,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,1,7,8,4,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,1,3,8,4,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,7,8,4,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,2,7,8,3,5,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,8,6,4,1,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,7,3,2,4,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,1,2,8,4,3,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,7,8,3,4,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,8,3,2,5,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,7,2,6,4,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,1,3,7,5,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,7,3,4,5,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,2,3,7,8,1,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,4,3,2,5,8,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,2,4,3,5,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,3,8,6,4,2,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,3,5,8,4,2,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,8,4,5,2,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,6,2,3,5,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,2,5,8,6,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,4,7,2,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,7,5,8,4,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,7,2,4,8,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,7,2,4,3,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,3,4,6,2,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,3,6,1,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,5,6,2,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,2,5,3,1,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,5,8,1,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,4,8,6,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,2,3,8,4,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,7,5,1,4,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,6,1,2,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,4,6,5,1,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,4,1,7,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,3,2,6,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,5,2,8,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,3,8,2,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,4,8,5,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,3,8,4,2,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,4,1,8,6,2,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,8,1,3,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,1,5,8,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,8,3,5,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,8,2,4,1,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,8,4,1,3,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,8,1,2,4,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,5,4,7,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,6,3,5,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,7,4,6,3,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,2,6,1,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,3,6,2,7,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,4,7,3,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,7,3,6,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,8,5,4,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,2,5,1,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,8,4,7,5,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,2,8,4,1,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,8,5,7,1,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,5,8,3,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,6,8,5,7,1,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,6,3,5,7,2,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,4,6,8,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,3,5,7,2,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,5,2,3,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,7,6,8,3,5,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,8,3,5,7,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,4,6,3,5,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,7,2,6,1,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,3,6,2,8,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,8,2,4,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,8,3,5,7,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,8,6,3,7,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,8,3,7,5,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,7,1,4,6,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,5,8,2,4,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,8,6,2,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,3,7,4,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,1,3,5,2,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,5,6,2,8,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,6,2,1,7,4,3,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,3,5,1,6,7,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,6,2,8,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,7,2,5,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,8,1,2,5,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,5,1,6,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,5,2,6,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,2,6,3,4,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,4,8,5,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,5,3,8,4,2,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,5,4,2,8,3,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[7,5,4,8,6,3,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,6,5,3,2,8,4,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[1,5,7,2,4,3,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,2,4,6,5,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,7,2,6,5,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,2,6,8,7,4,3,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,2,7,4,3,5,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,2,8,7,4,3,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,5,2,3,6,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,4,8,5,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,7,5,2,8,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,6,3,7,4,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,5,2,7,4,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,2,5,8,6,3,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,4,7,5,8,6,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,5,8,7,6,2,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,3,5,8,7,6,2,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,5,2,4,3,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,2,5,7,4,3,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,5,3,2,6,8,7,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,4,2,6,8,7,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,5,8,6,3,2,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,8,5,2,6,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,4,6,3,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,3,2,8,5,4,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,8,6,4,2,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,5,7,4,2,3,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,3,7,5,4,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,2,6,3,4,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,2,7,5,4,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,8,6,7,1,2,3]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,2,4,1,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,7,3,6,8,5,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,2,8,1,6,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,8,7,1,4,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,5,8,2,4,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,6,5,8,2,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,7,1,6,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,8,6,4,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,5,1,6,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,1,3,6,2,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,7,2,3,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,3,4,7,2,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,4,7,1,5,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,7,2,5,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,4,5,2,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,4,7,2,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,6,7,2,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,4,2,6,1,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,1,4,7,3,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,6,7,2,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,6,7,2,4,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,3,6,7,2,4,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,2,5,6,7,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,4,1,6,7,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,6,7,8,1,2,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,8,3,6,1,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,6,3,1,7,2,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,4,2,7,1,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,6,2,7,1,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,6,7,4,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,6,3,4,7,5,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,1,4,7,5,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,1,8,2,6,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,5,1,6,7,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,1,5,6,7,3,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,5,6,7,3,2,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,8,1,5,6,7,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,5,8,2,6,7,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,8,6,1,7,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,1,3,6,5,2,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,4,7,5,2,3,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,1,7,5,4,2,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,3,6,5,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,6,2,4,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,5,6,4,8,1,2]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,8,1,3,5,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,4,6,1,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,6,4,7,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,8,6,7,1,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,1,5,8,6,2,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,5,4,6,8,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,2,5,8,6,4,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,2,8,3,4,7,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,4,3,8,7,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,8,7,4,2,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,8,7,5,4,3,1,2]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[5,3,4,8,6,2,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,2,6,3,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,5,8,6,2,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,5,8,6,2,7,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,2,6,3,4,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,6,1,5,2,4,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,4,2,3,6,1,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,7,3,2,6,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,8,5,4,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,4,3,6,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,1,5,7,6,4,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,3,7,6,8,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,8,5,2,7,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,2,4,7,1,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,4,2,3,7,1,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,7,1,6,4,5,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,1,3,7,2,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,1,4,7,3,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,1,5,8,4,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,3,7,2,5,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,7,8,3,2,6,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,3,4,7,6,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,4,5,7,1,3,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,8,7,2,4,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,6,1,8,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,6,5,8,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,3,2,8,5,4,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,6,8,7,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,8,2,7,6,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,5,1,8,7,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,3,7,1,8,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,6,8,2,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,4,2,6,1,8,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,6,1,8,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,8,7,2,1,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,8,7,2,5,6,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,8,5,6,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,6,2,5,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,2,1,4,7,5,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,7,6,2,8,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,4,2,1,6,8,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,3,1,8,5,4,2,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,8,3,2,7,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,3,1,8,5,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,6,2,5,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,2,5,6,8,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,6,8,2,1,7,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,8,2,5,6,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,3,4,7,8,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,1,7,8,6,2,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,5,1,6,7,2,3,4]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,1,5,2,7,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,2,6,4,5,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,7,3,6,4,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,3,6,4,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,6,2,7,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,2,5,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,6,2,5,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,7,2,5,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,2,7,4,5,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,3,7,4,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,6,7,5,2,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,1,2,6,4,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,1,2,8,5,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,3,1,2,7,4,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,7,3,4,6,8,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,7,3,8,4,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,8,2,5,3,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,7,2,5,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,2,6,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,8,2,6,3,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,6,3,7,4,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,7,3,4,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,3,5,1,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,8,4,3,6,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,8,6,3,5,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,7,5,4,1,6,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,4,6,2,1,5,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,4,7,2,1,6,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,8,5,4,1,2,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,8,3,5,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,6,1,5,8,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,7,1,6,5,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,1,3,6,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,4,7,8,1,3,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,3,8,1,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,5,7,1,4,6,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,7,1,6,3,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,3,7,1,6,5,4,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,7,1,4,3,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,7,2,1,6,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,3,7,1,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,3,2,8,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,7,1,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,7,1,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,8,5,4,1,7,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,6,8,3,5,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,7,8,1,3,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,7,1,4,6,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,4,7,1,6,3,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,1,6,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,8,3,1,7,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,3,6,4,7,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,5,1,2,4,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,5,1,4,7,2,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,4,8,1,3,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,3,5,7,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,3,5,8,4,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,5,1,4,8,3,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,5,3,8,2,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,8,3,7,4,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,3,6,1,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,1,4,2,5,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,7,4,2,8,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,7,4,1,5,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,1,2,5,3,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,4,3,7,5,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,1,2,5,3,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,8,4,2,5,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,8,4,2,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,5,1,4,2,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,1,4,2,5,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,1,4,3,2,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,6,3,1,5,4,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[2,8,3,7,4,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,7,4,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,5,2,4,3,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,2,5,7,3,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,2,4,5,3,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,5,1,3,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,6,7,4,3,2,5,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,5,7,3,2,6,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,5,1,4,7,2,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,1,4,7,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,3,7,1,5,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,1,6,4,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,1,7,3,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,3,2,7,4,5,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,5,7,1,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,6,5,7,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,3,2,5,6,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,3,2,5,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,6,5,2,7,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,2,1,4,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,1,6,4,3,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,4,1,6,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,6,1,5,2,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,5,3,7,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,2,4,7,5,3,6,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,5,4,7,3,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,5,3,4,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,8,3,6,5,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,3,7,6,1,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,6,5,1,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,2,7,6,1,8,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,1,3,6,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,8,2,6,1,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,7,6,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,3,7,2,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,8,2,4,6,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,8,3,6,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,8,7,1,4,5,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,1,4,6,5,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,7,3,1,6,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,2,6,4,7,3,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,7,8,3,5,6,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,6,8,7,2,4,5,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,8,7,6,2,1,5,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,4,2,3,8,6,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,6,3,4,1,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,2,1,4,3,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,2,3,4,1,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,4,5,8,1,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,1,8,5,4,3,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,6,2,3,4,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,6,2,1,4,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,8,6,2,1,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,4,7,5,8,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,4,2,5,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,8,2,1,5,7,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,1,4,8,5,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,5,6,2,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,1,5,8,4,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,6,2,4,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,6,3,4,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,3,4,1,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,2,5,7,3,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,8,5,3,6,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,3,6,4,1,8,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,8,4,2,5,3,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,4,5,8,1,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,1,7,4,5,6,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,8,3,4,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,1,7,8,4,3,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,5,7,8,3,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,8,3,5,6,2,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,7,8,4,5,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,1,4,3,7,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,2,3,8,1,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,4,2,1,8,3,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[5,4,3,1,8,6,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,5,3,2,1,8,4,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[5,4,1,6,2,8,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,3,1,8,6,5,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,2,1,8,6,3,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,1,6,5,2,8,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,3,1,7,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,8,6,7,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,3,2,6,4,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,8,2,3,6,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,2,5,1,8,6,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,8,1,4,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,3,7,1,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,8,5,3,6,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,7,4,1,8,5,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,8,1,4,7,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,6,3,5,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,2,8,6,4,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,3,6,2,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,4,7,6,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,5,1,6,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,2,3,6,1,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,5,8,4,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,2,3,6,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,1,4,7,2,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,8,2,5,4,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,6,8,3,2,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,6,5,8,2,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,3,2,4,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,7,1,6,4,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,2,5,6,4,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,8,3,7,5,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,6,1,5,2,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,4,6,1,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,2,3,8,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,1,2,4,7,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,7,1,3,8,6,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,1,4,8,5,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,4,8,1,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,4,7,2,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,4,6,1,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,4,6,2,5,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,7,6,2,1,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,2,7,6,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,8,2,7,6,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,3,7,6,2,5,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,8,6,5,1,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,4,7,5,3,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,3,2,5,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,3,7,5,4,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,4,5,2,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,4,6,8,7,5,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,7,5,1,4,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,4,7,1,3,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,4,6,2,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,2,6,4,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,5,1,4,7,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,1,7,2,4,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,7,5,2,8,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,6,3,1,8,2,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,1,7,6,3,4,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,4,2,5,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,5,8,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,2,8,5,6,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,7,3,8,4,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,8,4,6,2,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,5,2,3,7,1,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,4,8,5,6,2,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,8,6,4,5,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,8,2,3,4,6,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,3,5,2,4,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,3,5,2,4,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,5,7,3,6,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,5,3,1,6,4,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,5,1,3,4,2,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,7,4,3,2,6,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,7,4,3,5,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,7,8,4,3,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,7,8,4,5,3,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,1,8,5,3,4,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,4,2,1,6,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,1,4,7,3,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,8,6,3,5,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,3,5,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,5,8,7,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,3,8,7,5,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,6,2,1,8,3,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,1,3,6,8,2,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,7,5,6,8,2,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,7,5,8,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,4,5,2,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,4,2,1,8,6,3]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[3,6,7,4,2,8,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,3,2,7,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,6,1,3,4,2,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,8,2,6,4,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,2,5,4,6,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,2,1,5,6,4,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,6,2,1,7,5,4,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,7,3,1,5,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,1,6,4,7,5,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,8,5,6,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,6,8,5,4,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,8,4,6,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,6,3,1,5,4,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,6,1,4,5,3,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,1,5,6,4,3,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,3,8,6,2,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,8,2,1,6,7,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,1,2,8,4,6,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,3,2,8,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,6,3,1,5,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,5,3,6,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,5,6,7,4,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,1,6,4,7,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,5,3,4,7,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,5,3,4,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,3,2,4,1,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,2,5,3,4,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,3,6,8,4,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,6,8,5,3,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,7,2,8,3,4,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,8,4,6,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,3,8,6,5,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,4,1,6,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,4,6,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,2,8,3,1,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,8,5,3,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,6,4,8,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,2,3,8,4,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,2,4,3,1,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,5,3,4,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,6,7,4,2,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,6,7,4,2,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,6,4,5,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,6,4,5,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,4,7,2,3,5,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,1,4,2,5,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,1,4,5,2,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,7,4,2,5,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,4,2,5,3,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,4,2,5,3,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,4,2,7,3,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,6,4,1,5,7,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,6,4,2,1,7,3,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,1,4,7,2,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,1,4,7,2,3,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,6,7,1,4,5,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,4,5,2,7,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,6,7,4,2,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,4,7,2,1,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,4,2,5,1,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,4,5,1,2,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,4,2,5,7,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,4,7,5,8,2,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,7,1,4,6,5,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,7,6,4,5,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,8,6,4,1,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,5,1,2,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,7,1,8,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,4,2,3,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,8,2,5,1,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,4,2,3,7,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,5,2,1,7,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,7,6,1,2,4,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,7,5,2,4,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,8,4,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,3,1,7,4,8,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,1,8,6,4,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,4,1,7,3,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,6,8,3,7,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,2,8,4,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,8,3,7,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,2,8,7,4,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,4,2,7,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,8,6,7,3,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,7,8,5,1,2,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,2,7,6,4,5,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,3,6,8,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,6,5,1,8,7,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,3,1,2,6,4,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,7,8,2,4,3,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,4,7,1,2,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,4,8,1,3,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,7,8,1,5,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,4,2,6,1,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,2,6,8,7,4,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,3,7,5,1,8,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,3,1,2,8,7,4,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,2,1,5,3,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,5,8,2,4,3,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,3,6,8,1,5,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,6,8,3,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,6,8,4,5,1,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,6,1,7,2,4,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,1,2,8,6,4,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,3,7,6,1,8,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,2,7,8,6,4,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,8,3,1,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,2,8,7,4,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,1,3,8,7,4,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,3,8,7,4,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,6,8,3,2,4,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,5,1,7,2,4,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,1,6,2,7,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,3,2,8,7,6,4,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,3,8,7,6,4,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,7,2,6,3,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,8,2,6,3,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,3,7,2,5,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,6,8,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,7,2,4,6,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,2,8,4,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,8,3,1,5,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,2,8,4,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,3,7,8,2,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,8,3,1,6,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,4,2,6,1,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,8,3,1,6,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,8,4,2,1,6,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,4,2,7,1,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,3,5,7,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,3,7,6,2,5,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,7,1,4,3,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,4,6,1,3,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,8,6,1,4,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,7,8,3,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,5,4,6,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,5,8,3,1,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,5,4,7,3,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,4,5,7,3,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,4,8,5,7,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,8,2,5,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,6,8,7,2,5,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,7,2,8,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,6,8,3,5,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,7,5,8,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,6,5,8,2,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,2,5,7,6,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,2,6,8,5,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,6,8,3,5,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,6,8,3,5,4,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,5,7,6,3,2,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,6,3,2,4,7,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,3,2,4,8,7,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,2,7,6,4,3,5,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,8,7,5,2,4,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,5,2,4,6,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,4,2,5,3,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,4,7,5,2,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,5,2,3,6,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,5,2,6,3,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,3,7,4,2,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,2,7,5,4,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,7,5,2,6,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,6,4,8,7,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,7,6,4,2,5,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,2,4,8,5,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,8,7,5,2,4,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,6,3,2,7,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,6,3,2,8,7,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,7,6,4,2,3,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,6,3,2,8,4,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,3,5,2,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,3,5,2,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,3,7,5,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,4,7,1,5,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,8,2,6,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,8,2,6,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,1,8,3,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,2,8,3,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,1,4,8,2,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,5,7,1,4,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,3,5,7,6,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,8,3,5,7,6,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,3,4,2,8,5,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,6,1,4,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,6,2,4,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,7,5,2,3,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,7,5,3,8,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,2,1,4,8,5,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,1,4,2,6,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,3,2,5,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,4,2,5,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,1,5,3,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,1,6,2,5,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,5,1,4,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,2,6,1,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,5,1,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,1,7,2,5,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,8,3,5,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,8,2,5,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,8,2,5,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,1,4,3,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,1,8,2,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,8,2,6,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,1,7,2,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,7,1,5,2,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,1,5,2,7,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,4,2,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,3,2,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,4,3,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,1,3,2,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,4,2,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,5,1,4,2,8,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,1,5,2,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,1,8,3,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,8,4,7,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,8,7,3,4,5,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,7,4,5,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,2,6,8,7,3,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,3,7,8,4,5,6,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,4,2,3,1,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,2,3,6,5,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,5,2,1,8,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,5,2,8,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,6,2,3,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,2,3,1,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,4,2,8,5,3,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,4,2,1,8,5,3,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,2,6,1,5,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,5,2,8,7,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,3,6,5,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,2,3,1,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,3,1,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,2,1,4,3,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,8,6,4,5,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,2,1,4,7,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,4,2,1,8,3,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,8,2,5,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,4,6,7,1,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,6,7,2,1,4,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,8,6,1,4,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,4,3,7,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,6,3,1,7,4,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,2,6,1,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,1,8,3,2,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,6,1,2,5,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,1,7,5,4,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,7,3,8,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,3,7,2,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,7,4,5,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,7,2,8,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,1,3,8,7,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,2,6,7,8,4,5,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,7,4,6,3,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,1,3,8,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,6,3,5,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,3,1,8,7,6,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,3,4,2,7,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,4,5,1,6,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,8,1,3,5,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,2,8,6,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,1,8,4,3,7,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,8,3,5,6,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,4,8,2,5,6,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[8,1,6,7,2,5,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,8,3,6,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,1,4,6,5,3,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,1,4,7,6,5,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,1,3,2,6,4,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,3,7,5,2,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,3,6,7,5,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,3,6,8,5,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,5,3,2,6,4,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,5,8,1,6,7,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,8,2,6,4,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,8,6,1,5,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,7,2,5,8,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,8,4,1,5,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,2,8,3,5,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,7,4,5,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,2,5,3,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,4,5,6,1,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,4,6,5,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,4,5,6,1,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,3,5,2,8,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,7,3,5,8,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,6,1,2,5,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,1,8,7,4,5,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,8,7,3,4,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,3,7,8,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,7,6,3,5,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,6,7,2,5,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,7,8,1,6,2,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,7,1,6,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,2,7,5,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,8,7,6,4,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,2,7,5,6,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,3,2,6,8,7,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,8,2,5,4,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,2,5,8,7,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,8,7,2,3,5,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,6,8,7,2,5,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,2,4,8,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,8,3,5,4,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,8,2,5,4,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,7,5,2,4,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,6,4,7,2,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,4,2,5,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,4,3,7,5,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,5,4,7,2,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,3,2,6,4,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,8,2,3,6,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,3,2,6,8,5,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,3,2,7,4,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,8,5,4,2,3,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,8,4,2,3,6,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,2,7,5,3,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,7,6,2,4,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,4,7,3,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,8,4,2,6,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,4,2,6,5,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,5,8,3,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,4,8,3,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,8,3,2,7,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,3,6,4,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,4,7,3,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,3,7,4,5,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,5,7,2,3,6,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,5,6,8,4,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,5,2,1,6,8,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,3,6,8,4,2,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[7,6,1,5,4,8,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,3,2,1,8,4,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[2,8,7,3,4,6,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,5,1,3,7,2,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,7,3,4,5,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,8,3,4,5,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,8,2,5,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,1,4,8,5,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,8,7,3,4,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,3,4,6,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,4,3,1,6,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,6,5,4,3,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,3,6,4,5,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,5,3,6,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,3,7,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,7,1,2,6,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,2,3,4,7,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,1,7,3,8,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,5,8,7,4,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,5,8,7,3,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,3,4,1,6,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,8,5,7,2,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,4,8,5,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,4,7,3,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,2,8,7,3,1,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,8,2,1,7,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,4,3,8,7,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,3,2,6,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,3,8,7,2,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,2,8,4,5,7,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,2,1,8,7,6,3,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,5,8,7,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,3,8,7,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,8,4,7,1,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,2,4,8,5,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,6,5,8,7,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,5,3,6,7,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,5,3,4,7,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,7,5,6,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,1,4,7,6,3,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,1,7,3,4,5,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,6,2,4,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,7,1,3,6,4,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,1,7,3,5,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,7,3,5,6,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,2,7,4,1,8,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,6,3,2,5,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,4,8,5,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,5,4,8,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,8,3,2,7,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,5,2,3,7,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,2,4,7,5,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,3,4,8,6,7,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,4,5,8,3,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,7,8,5,6,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,6,2,1,5,7,3,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,6,2,8,5,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,2,4,8,3,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,2,4,1,5,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,6,8,7,3,5,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,1,3,5,4,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,7,3,4,5,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,1,5,2,8,6,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,3,4,2,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,8,3,5,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,1,2,4,3,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,3,2,7,5,4,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,1,2,6,5,4,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,2,3,7,5,4,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,8,3,7,6,4,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,3,7,6,4,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,3,7,5,4,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,3,7,5,4,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,8,3,7,6,4,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,3,7,6,4,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,8,1,7,6,4,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,1,7,5,4,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,1,2,7,5,4,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,2,7,6,4,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,7,2,6,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,7,2,6,3,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,7,2,6,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,7,1,6,3,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,2,8,7,6,5,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,8,7,1,6,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,7,1,6,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,2,7,6,5,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,8,7,5,2,4,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,6,3,1,4,5,2,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,2,3,6,4,5,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,1,4,6,5,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,6,2,4,5,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,1,4,5,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,7,2,4,5,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,2,5,7,4,8,6,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,2,1,8,7,5,3,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,3,8,7,4,5,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,1,5,3,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,5,3,2,8,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,3,5,4,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,4,3,5,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,1,7,6,5,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,7,3,6,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,7,5,4,8,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,8,7,5,4,1,6,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,5,6,3,1,8,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,6,3,5,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,7,5,3,6,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,1,3,2,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,2,1,4,3,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,4,3,1,8,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,6,3,8,4,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,4,6,3,8,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,8,6,3,1,4,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,7,1,4,3,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,5,3,8,4,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,3,8,4,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,8,3,2,4,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,3,6,2,8,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,6,5,4,8,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,5,4,8,3,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,6,5,4,8,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,5,4,8,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,7,1,2,8,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,2,7,6,4,8,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,3,8,7,1,2,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,8,7,6,1,3,5,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,3,8,7,1,4,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,7,5,4,8,1,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,4,8,2,5,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,8,7,2,5,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,7,6,1,5,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,6,4,8,1,3,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,8,7,1,4,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,1,6,7,5,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,4,1,7,5,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,4,6,7,5,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,6,8,1,7,4,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,8,1,4,7,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,4,8,1,2,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,4,1,6,7,2,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,4,6,7,2,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,1,6,7,4,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,6,1,7,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,8,1,4,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,8,1,6,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,4,8,1,6,7,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,2,8,6,1,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,6,4,1,7,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,2,6,4,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,4,1,6,2,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,8,6,1,2,7,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,1,2,6,7,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,8,2,1,6,7,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,2,1,4,7,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,6,2,1,7,4,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,1,6,2,4,7,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,2,4,1,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,2,6,1,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,4,2,8,1,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,4,2,6,1,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,4,6,1,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,6,4,8,1,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,8,4,1,5,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,8,6,4,1,5,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,6,5,7,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,1,3,2,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,6,7,1,3,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,4,8,2,3,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,6,5,4,7,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,3,6,7,1,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,7,8,3,5,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,6,1,3,5,2,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,6,3,5,8,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,5,1,4,8,3,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,6,2,1,4,5,3,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,1,2,8,7,6,3,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,4,3,8,6,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,1,6,4,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,3,5,1,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,2,5,4,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,4,1,7,3,5,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,6,2,8,5,4,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,5,3,2,7,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,2,1,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,4,6,3,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,4,2,1,6,5,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,4,7,1,2,6,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,4,5,8,6,2,1,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,6,3,5,4,7,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,5,3,7,1,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,6,2,5,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,1,8,6,3,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,2,4,5,3,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,5,3,4,6,1,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,5,3,7,1,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,6,2,5,3,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,2,8,7,1,3,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,5,3,6,1,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,7,2,1,6,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,7,6,2,5,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,3,6,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,7,5,6,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,7,5,6,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,7,5,6,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,7,5,6,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,6,3,8,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,3,8,4,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,5,7,8,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,5,6,3,7,2,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,5,3,6,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,7,3,4,2,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,8,3,4,2,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,5,3,7,2,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,5,3,8,2,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,5,1,4,2,7,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,1,4,2,8,7,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,7,5,4,2,8,6,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,1,2,7,5,3,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,6,8,3,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,5,6,8,3,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,8,5,2,1,4,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,4,8,2,1,6,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,4,8,2,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,7,1,8,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,5,6,8,4,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,1,8,2,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,2,1,7,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,8,2,6,5,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,5,1,3,6,2,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,8,1,2,6,5,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,8,5,6,4,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,5,1,8,3,4,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,8,1,7,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,8,2,6,7,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,6,8,2,7,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,6,1,8,2,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,7,3,4,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,5,7,8,2,4,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,6,7,2,8,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,6,1,2,8,7,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,6,1,8,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,3,7,2,6,4,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,7,2,6,3,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,8,1,4,7,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,4,6,8,3,7,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,8,6,7,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,5,8,7,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,7,6,2,8,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,5,8,6,7,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,6,5,7,3,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,5,8,6,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,8,6,4,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,7,6,3,4,8,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,5,8,1,2,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,7,8,1,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,6,8,1,3,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,3,6,8,1,2,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,6,5,8,3,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,6,8,2,3,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,5,8,7,1,6,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,7,5,8,3,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,3,6,8,5,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,3,6,7,5,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,5,7,3,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,4,7,8,5,6,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,6,8,7,5,2,4,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,4,7,8,5,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,8,4,6,5,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,4,7,5,1,3,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,2,6,4,3,8,7,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,5,8,3,1,4,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,4,6,1,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,1,6,5,4,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,7,2,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,6,8,1,7,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,1,3,8,4,2,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,8,7,5,1,6,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[1]=>0
[5,8,7,2,3,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,8,1,4,7,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,5,3,7,4,6,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,7,5,2,6,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,6,3,1,8,7,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,6,7,1,5,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,7,5,1,2,6,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,1,3,5,6,2,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,8,3,7,1,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,7,4,2,6,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,3,2,4,7,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,4,5,3,7,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,8,2,4,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,8,3,2,6,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,3,7,2,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,7,1,2,8,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,8,2,1,4,6,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,1,5,8,3,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,8,3,6,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,1,7,8,3,5,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,7,8,1,3,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,7,8,3,1,5,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,2,7,1,8,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,8,5,2,3,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,2,7,8,1,5,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,1,3,8,5,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,7,8,4,1,3,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,6,7,8,4,3,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[7,1,2,6,3,8,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,2,6,5,3,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,4,6,7,2,3,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,3,5,6,1,2,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,5,1,7,2,6,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,4,6,1,2,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,8,1,2,5,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,1,8,2,5,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,7,2,8,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,4,1,2,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,2,1,8,3,6,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,4,5,1,3,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,5,6,3,2,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,2,5,7,6,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,4,8,3,1,2,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,5,3,1,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,3,1,6,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,6,8,4,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,5,1,6,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,7,3,4,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,8,3,2,7,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,1,6,4,8,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,3,1,8,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,1,7,4,8,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,4,2,5,7,6,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,6,8,5,2,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,4,5,7,2,8,6,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,7,4,3,6,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,5,8,2,4,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,1,6,3,4,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,3,4,6,2,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,8,4,5,7,2,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,4,7,5,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,2,8,6,3,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,7,6,3,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,1,8,5,3,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,5,6,8,4,7,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,4,1,8,6,7,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,8,4,5,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,2,1,8,7,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,3,8,2,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,3,1,8,6,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,1,3,7,4,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,4,7,8,2,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,5,8,1,3,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,6,7,2,4,5,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,8,7,5,2,1,6,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,8,5,6,2,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,5,8,4,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,3,2,5,7,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,1,5,6,8,7,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,5,1,3,7,6,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,4,8,6,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,2,4,5,8,7,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,1,3,7,4,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,2,8,7,4,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,3,4,8,5,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,7,5,3,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,2,8,6,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,8,7,4,2,5,6,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,6,3,5,1,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,5,3,6,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,1,3,7,8,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,6,4,8,3,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,2,3,8,1,4,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,4,1,5,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,5,1,4,6,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,6,5,2,4,3,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,5,2,4,3,1,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,2,3,5,1,4,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,6,4,5,2,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,1,8,3,6,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,5,6,3,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,5,6,3,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,6,4,5,2,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,5,4,7,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,1,4,6,8,7,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,6,5,3,4,1,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,5,2,8,3,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,5,4,1,8,2,3]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[3,6,4,1,5,7,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,5,4,7,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,1,4,6,7,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,6,5,2,8,4,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,4,3,7,5,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,6,5,2,8,7,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,7,4,3,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,2,4,3,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,3,4,5,1,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,1,7,4,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,7,4,3,5,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,2,4,5,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,5,3,6,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,3,1,4,7,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,3,1,8,7,2,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,7,3,8,6,4,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,6,3,2,7,4,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,4,2,3,8,6,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,3,1,8,4,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,3,1,8,2,5,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,1,8,4,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,8,7,3,6,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,8,4,5,3,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,8,3,5,6,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,7,4,8,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,8,3,1,5,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,8,1,3,5,4,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,2,8,6,4,3,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,8,5,2,1,3,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,1,5,2,8,7,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,3,5,7,4,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,8,5,4,7,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,4,8,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,3,4,2,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,5,1,8,7,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,2,7,1,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,7,3,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,6,3,1,5,7,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,8,3,1,4,7,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,2,5,4,7,8,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,8,3,2,6,4,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,1,2,5,3,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,4,1,3,7,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,2,6,1,7,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,6,4,1,8,3,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,4,1,6,7,3,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,1,6,5,8,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,7,3,2,8,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,1,2,7,5,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,3,5,2,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,3,6,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,1,2,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,4,6,2,1,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,1,7,2,3,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,2,6,4,8,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,1,6,4,7,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,3,4,8,5,2,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[8,2,4,6,1,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,3,5,8,6,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,8,2,3,6,7,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,5,7,2,3,6,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[8,4,1,7,2,5,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,7,1,5,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,1,4,2,5,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,5,7,8,4,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,4,7,8,2,5,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,2,5,3,7,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,5,1,6,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,2,6,1,5,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,1,7,4,6,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,1,7,6,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,5,1,7,4,3,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,8,3,1,7,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,4,8,3,2,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,8,1,7,6,5,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,3,8,7,2,6,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,7,2,6,4,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,5,7,4,3,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,7,4,6,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,6,3,5,4,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[2,8,4,7,6,1,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,4,8,3,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,8,2,1,3,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,7,2,6,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,4,7,6,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,3,7,6,5,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,3,8,7,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,5,4,6,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,1,5,2,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,1,3,6,2,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,6,1,8,4,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,6,4,1,5,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,4,3,1,7,6,2,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,1,6,5,7,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,3,7,5,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,1,7,4,2,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,7,8,5,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,8,6,4,5,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,6,1,7,4,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,8,3,1,7,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,4,8,1,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,2,4,8,3,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,2,8,4,3,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,8,1,2,5,7,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,8,2,6,3,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,6,4,7,5,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,2,6,5,8,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,3,1,4,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,5,3,4,8,7,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,2,3,6,7,4,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,6,2,7,4,5,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,7,1,6,4,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,7,8,5,1,6,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,6,2,4,7,8,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,2,3,6,4,8,7,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,7,5,4,2,6,3,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[3,7,6,2,5,4,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,6,4,8,7,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,4,8,6,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,2,7,6,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,1,2,6,4,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,8,1,2,7,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,1,8,6,5,3,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,3,1,2,7,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,6,2,5,3,8,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,3,4,6,5,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,5,2,4,7,3,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,5,7,4,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,3,7,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,5,7,2,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,6,1,3,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,6,1,5,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,2,4,5,1,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,5,1,3,8,6,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,3,6,5,2,7,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,5,6,2,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,8,3,6,4,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,8,4,6,2,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,5,6,2,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,3,6,5,8,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,4,6,8,3,2,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,7,3,8,5,4,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,6,7,4,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,8,5,1,2,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,5,7,2,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,5,6,4,7,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,8,1,3,6,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,6,8,4,5,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,6,8,5,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,8,1,6,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,2,4,8,3,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,8,3,1,6,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,8,4,3,1,5,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,3,8,1,6,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,5,8,2,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,2,8,1,4,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,7,8,2,1,6,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,8,1,6,3,5,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,8,2,5,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,7,8,3,1,5,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,8,1,6,2,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,8,3,7,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,6,8,3,4,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,7,1,6,5,4,2,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,7,6,2,5,3,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,1,6,5,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,2,8,4,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,2,8,5,4,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,6,3,5,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,8,2,5,3,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,8,2,3,6,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,6,8,1,5,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,7,4,1,3,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,8,1,2,3,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,6,1,8,2,4,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,7,1,3,6,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,8,1,2,7,6,5,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,6,1,2,8,5,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,2,1,8,5,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,2,1,8,6,5,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,4,7,3,2,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,3,5,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,2,7,5,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,6,2,8,1,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,8,2,1,6,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,8,4,2,1,3,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,4,8,3,1,2,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,8,3,5,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,6,5,7,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,1,6,3,5,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,4,5,2,7,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,5,2,7,3,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,1,6,5,7,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,6,7,4,3,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,4,3,5,1,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,1,4,3,5,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,6,7,4,2,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,7,2,4,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,3,7,4,5,2,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,7,2,6,3,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,2,1,4,5,3,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,1,5,7,3,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,4,8,3,5,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,4,5,3,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,5,8,2,6,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,1,3,7,2,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,8,3,6,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,7,3,6,5,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,4,5,8,3,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,3,6,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,8,4,3,1,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,8,5,1,6,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,1,5,2,6,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,6,5,2,4,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,7,4,2,8,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,8,4,3,6,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,8,1,4,3,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,3,7,8,2,4,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,7,8,4,3,2,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,4,7,2,3,6,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,7,1,4,3,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,5,7,3,4,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,1,6,4,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,5,1,3,2,7,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,6,3,8,7,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,3,4,7,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,1,5,7,6,2,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,3,1,4,2,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,4,3,7,6,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,7,6,5,2,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,7,6,8,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,2,1,5,6,3,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,1,8,6,2,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,1,5,2,8,7,6,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,2,8,4,3,7,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,6,1,8,7,4,3,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,1,8,3,2,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,7,6,3,1,8,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,4,2,8,6,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,2,8,5,3,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,4,8,3,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,2,4,8,5,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,7,8,1,4,2,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,3,8,1,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,1,8,6,3,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,6,4,1,7,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,4,2,7,5,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,1,7,2,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,8,1,7,5,3,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,7,8,6,3,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,5,7,8,4,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,8,7,6,3,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,2,6,3,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,5,7,1,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,8,5,3,6,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,5,8,2,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,8,5,4,6,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,8,4,5,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,2,7,1,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,5,7,1,6,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,1,8,5,3,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,8,4,5,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,8,5,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,1,8,5,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,3,8,4,5,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,8,7,2,3,4,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,8,4,5,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,1,6,8,5,3,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,6,8,5,4,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,8,5,2,6,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,8,5,2,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,5,8,7,4,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,5,8,7,2,4,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,8,4,5,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,8,4,5,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,2,7,3,5,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,6,2,4,8,5,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,3,5,2,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,5,4,3,8,6,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,5,1,8,4,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,1,8,5,4,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,2,3,8,6,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,4,8,3,7,6,5,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,6,8,2,5,7,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,1,7,8,4,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,7,4,8,3,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,8,5,4,3,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,6,8,2,5,4,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,8,3,2,5,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,2,8,3,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,1,8,5,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,6,8,4,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,3,8,7,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,2,4,8,6,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,8,2,7,4,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,7,8,5,1,4,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,6,8,5,7,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,4,8,7,6,3,5,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,5,3,1,7,4,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,4,1,7,2,5,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,1,6,3,2,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,7,6,3,4,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,6,3,1,2,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,5,4,2,6,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,2,1,7,5,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,8,5,7,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,4,8,6,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,2,1,7,5,3,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,4,7,1,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,7,4,2,8,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,1,6,7,3,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,2,8,1,7,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,8,7,5,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,7,6,4,5,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,8,7,6,3,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,5,1,8,7,6,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,2,7,8,1,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,3,5,6,1,2,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,3,5,6,8,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,7,8,3,5,6,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,7,8,3,5,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,8,5,2,6,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,5,1,4,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,5,6,8,4,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,4,6,5,2,3,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,5,2,6,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,6,4,8,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,5,7,3,8,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,3,1,6,8,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,3,6,7,1,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,2,7,6,8,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,4,6,8,3,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,5,7,6,3,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,4,3,2,7,1,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,3,7,8,6,5,2,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,6,5,7,3,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,2,6,8,1,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,6,7,1,3,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,4,3,7,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,7,6,1,8,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,3,7,1,2,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,2,5,6,3,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,2,7,6,4,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,5,8,3,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,2,7,5,3,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,2,4,7,5,3,8,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,1,5,8,4,3,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,1,6,8,3,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,4,3,7,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,3,7,2,4,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,4,1,8,3,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,2,1,7,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,5,6,3,4,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,7,8,5,1,6,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,2,8,5,7,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,7,6,2,3,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,2,6,7,4,3,5,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,6,7,4,5,1,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,8,6,3,4,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,2,3,1,8,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,2,6,4,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,2,3,7,5,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,2,8,6,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,8,2,5,6,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,5,6,3,7,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,3,6,7,4,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,7,8,3,4,6,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,1,3,6,5,4,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,3,2,5,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,7,8,5,1,4,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,8,2,7,5,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,3,2,5,8,4,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,6,7,2,8,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,1,7,6,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,7,1,3,5,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,3,6,4,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,4,6,1,3,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,8,5,2,7,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,8,2,4,3,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,4,5,7,2,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,7,4,5,2,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,8,5,7,1,3,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,1,5,8,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,1,4,7,5,3,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,7,1,6,4,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,5,1,7,4,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,5,1,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,7,4,1,5,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,5,8,4,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,8,1,3,4,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,5,1,8,7,4,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,8,7,5,2,3,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,7,1,2,5,3,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,6,1,2,5,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,1,3,8,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,1,2,3,7,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,7,4,8,6,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,3,1,8,4,6,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,3,7,6,8,1,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,1,8,4,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,2,6,7,4,3,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,5,1,2,6,3,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,7,8,3,2,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,7,6,2,8,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,6,7,4,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,5,1,8,7,6,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,8,7,3,1,5,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,2,8,6,7,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,1,4,2,8,7,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,4,6,8,5,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,7,2,6,8,4,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,6,5,2,7,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,4,6,2,7,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,1,8,6,4,2,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,1,8,2,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,8,3,1,5,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,1,8,5,7,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,6,3,8,5,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,7,2,3,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,6,2,3,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,8,1,3,4,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,7,6,8,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,7,8,1,3,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,7,2,8,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,2,7,8,4,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,7,8,2,4,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,4,7,1,8,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,8,2,7,6,5,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,7,3,1,5,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,3,1,7,5,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,4,3,1,2,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,1,4,7,5,3,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,7,3,6,5,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,6,3,1,5,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,4,7,3,8,5,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,7,3,1,8,5,4,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,3,1,7,4,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,4,3,1,7,5,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,3,8,6,5,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,3,1,7,4,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,5,2,1,4,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,6,2,1,5,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,6,3,2,5,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,6,3,8,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,4,2,6,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,4,8,5,3,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,6,3,5,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,2,5,7,8,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,7,8,2,5,4,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,6,8,3,4,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,6,2,5,3,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,2,6,7,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,6,8,4,7,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,6,8,3,2,4,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,7,3,5,4,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,2,7,3,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,3,2,7,4,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,2,8,5,3,4,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,7,4,8,6,5,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,6,8,7,2,4,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,3,7,2,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,6,5,4,8,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,3,5,7,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,2,3,7,4,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,2,3,8,4,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,4,7,2,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,5,6,2,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,7,1,5,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,8,4,7,5,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,5,2,6,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,5,2,6,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,4,8,5,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,1,5,2,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,1,2,6,5,3,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,4,2,5,6,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,2,7,5,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,1,3,4,2,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,7,1,3,4,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,2,8,6,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,8,6,1,4,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,1,5,2,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,4,2,5,7,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,1,6,8,3,4,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,2,6,3,5,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,4,8,1,2,6,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,8,4,7,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,4,2,5,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,8,4,2,5,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,8,4,2,5,6,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,1,5,2,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,3,4,8,5,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,1,3,4,2,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,2,8,5,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,6,8,5,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,1,3,4,2,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,8,2,7,5,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,4,3,7,6,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,8,7,1,2,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,8,4,5,7,6,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,3,8,5,7,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,4,8,7,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,8,4,7,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,8,7,1,4,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,8,7,1,6,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,8,3,1,6,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,7,8,5,1,4,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,8,7,4,1,6,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,4,6,8,3,5,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,8,1,3,6,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,8,1,5,4,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,7,8,1,4,5,6,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,6,7,8,2,4,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,7,8,6,3,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,4,6,8,7,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,5,8,6,7,1,3,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,6,8,2,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,6,8,2,4,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,7,8,6,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,5,7,8,2,6,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,6,8,7,3,1,2]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[8,1,7,5,4,3,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,1,3,4,8,5,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,7,3,4,2,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,6,5,3,7,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,6,4,5,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,3,8,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,6,7,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,2,8,3,6,7,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,3,6,1,2,5,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,7,1,2,5,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,1,7,3,2,5,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,7,2,8,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,1,8,2,3,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,3,4,8,6,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,2,7,4,8,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,8,6,2,5,4,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,4,1,6,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,1,6,4,3,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,2,8,3,4,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,4,1,7,5,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,7,4,8,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,5,2,8,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,8,5,1,4,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,5,2,1,7,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,6,4,8,7,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,8,2,5,7,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,4,2,7,6,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,2,3,7,6,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,8,2,7,5,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,3,4,5,6,1,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,3,6,4,7,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,5,7,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,6,2,7,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,6,5,8,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,6,5,8,7,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,5,8,7,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,6,4,8,7,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,7,6,8,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,7,5,8,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,5,8,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,5,8,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,7,2,8,5,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,6,2,8,5,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,7,6,8,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,6,8,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,7,2,8,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,6,4,8,7,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,3,8,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,6,8,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,6,8,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,6,8,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,5,8,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,1,7,3,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,4,8,2,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,8,2,5,4,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,5,8,3,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,1,3,2,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,6,4,1,5,3,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[3,8,5,2,6,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,5,3,4,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,8,3,5,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,4,6,8,7,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,4,7,8,5,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,5,3,7,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,6,2,4,1,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,8,6,2,3,5,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,2,6,3,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,2,3,7,5,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,6,2,3,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,7,5,6,4,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,4,3,7,5,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,5,7,6,4,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[7,8,6,3,5,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,7,6,3,8,5,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,4,2,5,6,3,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,2,7,5,3,8,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,8,3,7,5,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,3,7,5,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,2,5,8,3,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,3,8,2,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,2,5,6,3,7,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,4,1,3,5,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,5,3,6,1,4,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,3,7,4,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,2,6,7,4,1,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,2,7,4,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,5,6,4,1,3,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,8,5,1,4,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,2,8,4,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,3,2,8,4,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,8,3,1,5,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,8,1,3,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,8,1,6,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,8,1,2,6,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,5,4,7,2,8,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,7,3,5,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,7,5,4,8,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,7,1,3,8,6,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,6,7,4,3,8,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,6,4,5,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,6,5,4,8,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,2,8,3,4,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,2,8,5,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,5,8,4,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,5,6,8,4,3,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,1,5,8,6,4,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,7,2,8,5,3,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,8,6,4,5,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,8,6,4,7,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,1,7,8,3,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,2,8,7,4,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,6,1,8,7,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,2,8,4,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,3,8,6,7,4,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,7,4,6,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,3,8,5,7,4,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,2,8,7,4,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,6,8,7,3,4,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,8,6,7,5,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,3,8,7,6,4,5,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,5,6,3,1,4,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,1,3,4,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,6,3,4,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,5,3,6,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,5,6,4,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,3,5,1,6,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,8,5,6,2,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,8,5,6,1,4,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,5,6,4,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,8,3,4,6,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,8,6,4,1,2,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,5,1,8,6,4,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,3,5,8,6,2,4,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[7,5,3,8,6,4,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,5,3,8,6,4,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,3,8,6,4,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,8,1,6,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,3,1,6,4,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,1,3,6,4,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,8,3,6,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,8,3,6,4,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,5,8,3,6,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,8,6,3,4,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,8,2,5,6,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,1,8,3,6,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,8,3,6,4,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,1,3,8,6,4,2,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,7,5,8,2,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,7,8,4,2,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,7,8,1,4,6,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,7,8,4,6,1,2,3]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,3,7,8,4,2,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,1,2,4,6,3,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,1,2,5,4,3,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,4,6,7,3,2,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,4,6,5,7,2,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,3,5,4,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,6,7,3,5,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,4,1,6,5,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,5,1,3,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,3,2,6,8,4,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,6,5,7,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,7,3,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,2,5,6,3,4,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,5,4,1,6,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,4,3,5,1,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,3,5,2,6,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,5,6,1,2,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,7,5,4,2,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,2,6,4,7,3,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,4,3,7,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,4,5,7,1,6,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,7,8,3,2,6,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,8,3,2,4,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,8,5,2,3,7,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,4,3,7,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,4,3,8,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,5,1,3,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,5,1,3,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,6,4,3,7,1,5,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,6,5,7,3,1,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,6,7,1,3,4,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,1,6,7,4,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,6,8,1,3,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,5,7,3,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,8,2,6,5,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,7,5,4,2,3,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,3,1,8,6,5,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,1,3,2,4,6,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,3,5,1,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,2,1,4,8,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,7,3,1,4,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,4,6,3,7,8,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,1,6,5,7,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,6,5,8,4,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,6,8,1,3,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,2,5,1,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,6,7,3,2,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,7,2,5,6,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,2,1,5,8,4,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,7,6,8,3,1,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,6,5,8,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,3,5,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,4,7,3,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,4,8,6,1,7,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,1,8,5,6,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,6,4,5,7,1,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,4,7,1,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,2,4,5,7,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,3,2,4,1,8,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,3,6,4,5,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,5,1,3,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,3,8,4,5,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,5,1,3,6,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,6,4,5,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,1,8,7,3,6,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,6,3,1,2,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,2,7,1,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,5,7,6,3,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,4,2,1,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,1,7,6,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,4,1,7,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,4,7,8,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,6,1,4,5,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,4,5,2,8,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,2,1,8,7,3,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,8,6,3,1,5,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,1,5,4,3,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,1,4,8,3,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,4,5,3,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,2,6,8,4,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,2,6,7,8,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,4,2,5,6,8,7,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,4,6,5,7,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,3,6,7,8,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,4,2,7,8,3,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,1,6,8,7,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,8,6,2,4,3,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,3,1,4,2,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,2,5,3,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,8,3,1,7,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,3,4,7,5,8,6,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,6,2,4,8,5,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,2,4,7,3,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,1,3,2,7,4,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,2,8,7,4,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,8,5,4,2,1,6,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,5,2,8,6,4,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,8,3,2,6,5,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,5,2,8,1,4,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,2,6,4,1,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,1,8,6,4,3,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,6,1,3,2,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,6,3,8,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,6,3,7,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,6,7,3,4,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,6,8,3,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,3,7,8,4,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,8,7,4,1,3,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,7,2,5,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,2,7,8,4,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,2,7,5,4,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,6,8,2,7,5,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,6,3,2,8,1,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,7,3,1,2,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,1,7,4,3,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,1,4,8,2,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,3,7,2,4,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,7,8,6,4,2,3,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,4,2,6,5,3,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,5,3,7,4,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,6,4,3,2,8,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,4,3,6,2,5,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,7,6,3,4,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,2,7,4,3,8,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,7,6,3,5,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,7,3,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,6,3,5,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,2,7,4,3,6,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,4,2,3,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,6,4,5,2,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,3,7,6,2,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,2,7,5,3,6,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,7,6,3,5,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,6,3,5,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,1,3,2,6,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,2,8,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,7,5,6,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,1,3,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,4,1,8,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,5,1,6,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,1,4,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,7,6,8,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,6,4,8,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,8,3,6,5,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,3,5,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,8,5,7,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,8,5,7,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,4,1,6,2,8,7]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,7,6,8,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,6,1,8,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,6,1,8,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,8,1,6,3,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,4,1,2,6,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,7,1,2,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,1,7,4,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,4,8,2,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,3,4,5,1,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,5,6,4,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,8,5,4,3,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,8,2,6,4,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,5,7,4,8,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,3,7,5,8,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,1,5,3,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,5,8,4,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,3,6,8,4,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,6,7,4,5,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,5,3,1,4,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,3,4,7,5,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,4,7,3,5,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,8,6,2,7,3,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,5,8,3,2,7,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,7,1,2,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,4,2,3,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,3,5,4,8,1,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,2,4,7,8,3,5,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,7,2,6,5,3,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,6,7,1,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,7,1,6,3,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,5,6,8,1,2,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,1,2,5,3,7,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,6,5,2,4,1,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,1,6,4,2,5,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,6,5,3,4,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,1,6,4,5,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,5,1,3,4,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,8,5,3,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,5,7,4,3,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,5,8,1,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,7,5,2,4,3,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,8,6,7,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,5,2,4,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,6,5,2,4,3,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,8,5,2,4,3,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,5,8,4,3,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,7,2,5,6,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,1,6,5,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,8,6,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,6,2,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,4,1,6,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,5,2,4,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,4,2,7,6,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,2,4,3,1,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,7,5,2,4,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,1,6,2,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,4,1,6,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,2,5,1,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,2,5,1,7,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,1,8,5,2,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,7,2,5,1,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,2,5,1,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,2,7,6,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,2,8,1,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,2,7,8,1,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,2,5,1,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,3,4,7,2,5,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,5,2,4,7,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,2,7,1,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,2,8,7,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,3,4,6,5,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,6,8,1,4,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,3,4,1,7,5,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,6,7,2,1,8,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,7,1,8,6,4,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[5,1,8,6,7,2,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,8,5,2,4,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,4,2,5,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,5,1,2,4,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,3,1,4,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,1,2,5,4,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,4,3,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,3,4,6,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,2,3,8,6,4,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,2,3,8,7,4,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,5,8,2,1,4,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,3,7,2,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,6,3,2,4,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,2,7,8,1,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,7,8,2,1,3,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[8,6,3,2,1,7,5,4]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[5,3,4,1,7,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,3,5,8,4,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,8,2,3,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,1,4,8,2,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,8,1,4,3,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,3,4,2,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,3,6,2,4,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,8,4,2,3,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,6,3,4,2,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,5,7,6,8,2,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,1,8,5,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,1,3,8,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,1,4,3,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,2,4,3,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,5,7,6,4,1,2]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,5,7,6,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,1,7,6,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,6,3,8,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,3,7,6,1,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,7,6,3,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,6,3,7,8,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,7,6,3,8,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,3,5,6,1,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,6,1,5,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,3,7,8,5,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,7,8,6,3,5,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,6,1,7,5,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,5,6,1,8,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,5,1,8,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,1,8,5,4,3,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,7,3,4,6,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,6,2,8,4,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,8,2,3,7,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,1,7,6,8,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,1,8,6,4,3,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,5,7,1,2,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,8,1,7,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,1,5,7,4,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,1,3,4,7,5,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,4,5,8,6,7,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,7,6,3,4,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,5,4,6,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,4,7,6,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,4,6,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,5,4,6,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,3,5,4,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,7,6,3,4,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,1,2,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,6,1,3,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,4,1,2,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,3,1,2,5,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,5,1,3,2,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,5,6,1,3,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,5,1,3,6,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,3,1,5,4,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,4,1,7,6,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,1,4,7,6,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,8,5,1,4,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,1,3,8,6,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,1,3,8,2,5,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,5,8,6,1,3,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,6,8,3,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,5,4,2,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,5,4,7,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,6,1,3,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,6,3,8,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,1,5,7,4,2,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,7,5,4,8,6,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,3,7,6,2,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,6,8,2,3,5,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,8,1,4,7,6,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,3,4,5,2,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,7,5,4,2,3,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,7,8,5,1,3,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,1,8,7,5,3,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,2,5,1,7,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,2,4,8,1,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,5,7,4,1,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,7,5,1,6,3,4,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,1,3,6,5,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,5,3,2,7,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,7,2,6,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,2,7,1,3,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,5,3,6,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,6,5,1,8,7,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,6,5,1,7,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,1,5,3,2,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,5,1,4,8,6,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,1,4,7,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,1,8,7,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,4,7,3,2,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,4,8,7,3,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,5,3,1,4,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,4,8,5,3,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,8,2,6,7,1,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,2,6,7,1,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,2,5,3,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,1,3,4,5,2,8,7]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,1,3,4,2,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,2,3,1,4,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,1,3,4,8,2,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,4,2,7,3,5,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,5,3,8,4,2,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,2,6,3,8,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,2,7,3,4,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,1,8,3,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,5,3,7,8,2,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,6,4,2,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,7,4,2,6,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,1,4,2,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,8,2,3,5,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,5,2,7,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,1,3,2,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,7,3,2,5,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,5,2,7,3,1,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[6,4,5,2,1,3,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,7,6,2,8,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,8,1,7,4,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,6,8,4,2,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,1,8,7,4,2,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,5,6,2,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,5,7,2,3,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,6,7,3,4,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,6,8,3,2,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,4,5,6,2,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,6,7,2,5,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,2,8,3,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,2,3,7,4,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,4,7,3,5,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,8,5,3,6,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,6,3,1,8,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,1,2,7,8,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,6,7,5,1,2,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,8,1,4,5,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,4,7,3,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,6,3,4,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,4,6,3,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,2,6,3,5,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,7,4,1,5,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,4,1,7,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,5,1,3,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,6,2,4,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,1,3,6,2,5,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,6,3,8,4,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,1,3,7,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,1,8,2,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,1,2,8,4,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,8,6,4,1,2,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,7,8,3,6,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,7,8,1,6,4,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,8,1,6,4,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,8,6,3,4,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,5,8,6,4,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,7,3,8,6,4,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,1,8,6,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,8,1,5,6,4,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,3,5,6,4,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,1,8,5,6,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,5,8,6,4,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,1,8,5,6,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,1,5,6,4,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,3,5,6,4,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,3,5,6,4,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,3,8,5,6,4,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,8,6,4,2,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,5,7,8,6,4,2,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,8,2,6,5,3,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,1,2,3,7,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,1,5,4,2,3,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,2,3,1,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,2,5,3,4,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,5,6,4,2,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,7,3,5,8,4,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,6,2,5,8,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,2,7,3,4,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,4,7,3,5,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,7,2,3,5,8,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,5,8,3,6,4,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,4,2,1,5,3,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,6,8,2,3,5,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,7,1,5,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,8,7,1,6,5,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,2,1,6,5,7,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,5,8,2,6,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,2,1,4,7,3,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,7,4,5,6,1,2,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,4,6,5,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,7,4,5,1,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,3,1,2,8,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,7,5,2,1,4,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[7,8,2,6,3,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,6,3,5,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,6,4,1,5,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,6,5,3,4,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,6,4,5,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,7,2,6,4,3,1,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,2,8,6,4,5,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,8,7,6,3,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,4,6,8,5,3,2,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,4,7,8,5,6,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,2,5,8,6,4,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,8,6,7,2,3,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,8,5,6,3,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,4,8,5,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,3,2,6,8,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,3,6,4,2,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,8,5,2,7,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,8,5,4,2,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,7,4,5,8,6,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,8,6,5,3,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,3,6,7,2,8,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,8,5,2,6,7,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,3,4,8,5,2,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,8,5,2,4,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,8,7,6,2,4,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,1,5,4,6,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,6,4,2,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,8,2,4,6,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,8,1,6,4,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,3,2,1,8,6,4,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,2,4,1,3,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,6,3,5,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,7,8,6,2,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,1,8,3,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,1,6,5,3,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,5,7,6,3,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,5,1,7,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,5,8,2,3,4,7,6]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,2,7,8,4,5,6,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,3,8,7,6,2,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,8,2,7,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,3,6,4,1,7,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,6,1,7,5,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,5,2,1,7,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,6,1,7,5,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,5,7,6,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,6,5,1,7,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,4,5,2,1,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,6,4,2,8,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,5,3,1,7,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,5,8,2,3,1,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,4,8,1,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,6,8,1,4,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,5,1,8,6,4,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,2,8,3,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,3,8,4,6,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,8,1,5,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,2,1,6,5,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,1,5,6,8,7,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,5,6,8,4,7,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,6,8,1,2,4,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,8,1,4,5,7,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,3,5,1,8,6,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,8,2,3,4,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,8,7,2,1,3,6,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,1,7,2,8,6,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,5,3,4,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,1,6,3,5,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,2,1,7,8,6,4,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,7,1,2,5,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,6,4,2,8,7,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,5,1,4,8,2,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,2,8,1,7,5,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,3,1,7,5,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,1,7,8,4,2,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,4,3,1,8,5,2,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,1,6,3,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,1,7,3,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,3,8,2,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,6,3,8,1,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,7,6,4,5,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,2,5,8,4,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,4,5,3,8,6,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,8,4,7,6,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,4,2,6,7,5,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,3,5,2,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,6,3,5,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,7,5,2,4,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,8,2,4,5,7,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,2,4,5,7,3,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,8,2,4,6,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,8,1,5,6,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,1,7,4,5,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,7,5,1,4,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,5,7,4,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,3,7,5,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,5,4,7,3,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,3,8,2,4,6,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,1,7,3,4,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,3,6,7,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,3,7,8,6,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,8,5,4,7,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,5,3,7,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,2,6,5,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,7,2,5,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,7,8,1,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,8,7,6,3,5,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,4,7,6,5,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,7,1,5,6,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,5,6,2,8,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,1,8,6,2,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,1,4,6,8,2,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,1,5,7,3,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,5,8,4,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,8,5,4,3,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,6,8,2,5,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,6,5,7,8,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,5,7,4,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,5,7,4,2,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,4,7,5,2,1,8,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,6,7,5,8,4,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,7,2,5,6,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,5,3,7,8,6,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,2,8,4,5,6,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,3,8,5,4,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,4,7,8,6,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,7,8,6,4,1,3,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,8,7,3,2,4,5,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,1,4,8,6,7,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,7,4,1,3,8,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,1,4,8,5,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,1,6,5,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,5,8,6,4,1,3,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,5,6,4,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,5,1,4,6,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,6,3,8,5,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,3,7,8,5,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,1,7,8,4,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,1,8,4,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,7,6,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,8,4,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,3,6,8,5,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,2,3,1,8,4,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,3,5,1,8,6,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,7,2,6,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,7,3,6,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,5,1,7,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,5,2,7,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,5,3,7,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,5,4,1,7,3,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,3,8,6,5,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,4,8,6,3,2,1,5]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,5,8,1,6,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,5,8,2,6,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,2,8,5,4,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,4,2,1,8,7,3]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[6,5,4,2,8,1,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,3,2,8,1,7,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,6,8,7,1,3,5,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,3,8,7,6,2,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,7,6,1,4,5,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,1,6,2,7,5,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,3,1,2,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,5,3,1,8,6,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,6,2,3,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,1,3,7,5,2,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,6,3,2,7,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,4,8,5,6,3,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,4,1,3,2,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,8,4,5,3,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,2,3,7,4,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,5,1,6,3,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,5,1,6,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,2,4,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,4,2,1,8,6,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,6,5,7,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,2,6,7,4,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,5,7,2,4,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,3,6,4,7,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,5,3,6,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,8,3,4,7,6,5]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,8,5,2,7,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,7,2,6,8,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,6,4,5,2,1,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,4,7,6,3,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,3,8,5,4,2,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,3,4,7,2,8,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,7,3,6,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,8,5,3,4,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,4,3,1,5,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,4,1,8,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,5,8,3,2,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,2,4,7,8,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,2,7,4,3,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,3,4,8,5,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,6,8,3,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,4,5,3,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,7,3,1,2,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,2,3,7,4,5,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,3,2,7,5,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,5,2,6,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,2,7,1,5,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,5,3,6,4,7,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,5,2,4,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,7,2,4,6,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,7,2,5,4,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,4,2,7,3,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,2,8,7,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,8,3,5,2,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,8,3,6,5,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,8,6,5,2,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,7,3,2,8,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,8,6,5,2,4,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,6,8,4,3,2,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,7,5,3,2,6,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,2,6,5,3,8,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,3,2,8,4,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,5,2,8,4,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,3,7,2,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,2,8,7,6,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,3,2,1,6,5,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,3,2,6,1,5,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,8,5,2,7,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,2,5,1,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,5,2,8,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,1,2,6,7,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,8,5,7,2,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,8,2,7,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,5,7,3,1,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,4,6,5,3,2,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,2,1,7,5,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,6,3,1,5,2,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,6,4,8,5,3,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,1,6,5,4,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,5,6,2,8,7,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,2,7,5,1,3,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,8,6,1,3,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,3,8,6,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,1,7,6,4,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,6,7,8,1,3,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,1,8,3,6,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,7,2,6,4,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,5,2,6,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,1,8,7,6,4,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[4,2,5,7,6,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,7,6,2,5,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,7,6,5,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,7,5,6,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,1,7,6,4,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,7,2,1,6,5,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,6,4,1,5,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,4,3,6,7,8,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,4,1,7,2,8,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,8,5,2,7,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,5,2,8,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,7,6,8,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,2,4,1,8,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,2,6,1,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,1,7,6,2,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,2,1,3,8,4,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,1,2,8,5,4,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,1,6,3,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,6,8,2,4,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,1,7,3,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,1,8,3,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,5,2,6,3,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,8,6,7,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,1,7,2,6,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,1,6,3,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,1,4,3,5,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,1,2,7,4,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,5,4,3,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,2,1,3,5,4,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,2,8,6,5,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,2,6,8,7,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,2,7,8,6,3,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,6,2,3,5,1,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,2,4,3,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,2,4,6,3,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,2,6,5,3,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,4,8,7,2,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,8,5,7,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,6,7,5,8,3,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,7,5,8,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,7,8,2,3,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,1,2,3,7,5,4,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,6,8,7,5,3,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,1,7,4,8,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,7,8,5,1,2,4,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,8,5,6,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,8,6,7,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,8,1,5,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,6,1,5,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,8,3,7,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,8,1,7,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,2,7,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,3,1,5,4,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,4,8,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,8,5,7,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,4,7,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,3,4,8,7,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,7,4,5,1,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,5,7,6,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,5,7,1,3,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,6,7,5,1,2,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,2,1,6,5,7,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,7,1,8,5,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,8,6,1,5,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,2,3,5,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,8,2,1,3,5,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,1,6,4,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,8,6,2,1,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,4,8,5,6,1,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,8,2,5,6,1,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,3,8,4,2,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,5,3,1,4,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,8,4,6,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,7,2,4,6,3,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,3,2,1,6,4,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,8,3,4,6,5,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,7,3,6,5,2,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,1,2,8,6,5,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,2,7,5,4,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,1,4,5,3,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,7,4,6,3,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,7,4,6,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,1,3,2,5,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,8,4,6,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,6,4,7,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,2,6,5,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,8,5,7,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,7,5,2,4,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,1,2,7,5,6,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,7,3,4,6,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,5,4,8,1,3,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,5,6,4,7,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,5,6,2,4,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,1,3,4,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,4,5,1,3,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,8,7,5,3,2,1]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[6,7,1,4,3,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,2,5,1,4,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,1,3,4,2,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,6,3,2,8,7,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,7,6,8,4,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,7,3,2,8,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,2,7,6,8,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,3,8,5,2,7,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,4,1,5,2,8,7,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,5,3,1,8,2,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[2,5,1,4,7,3,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,6,5,7,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,1,5,7,4,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,7,1,6,3,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,1,5,7,4,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,5,1,4,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,1,7,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,4,3,6,1,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,5,2,7,6,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,4,1,6,3,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,6,3,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,5,7,1,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,5,1,4,7,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,6,5,7,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,6,5,3,7,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,5,7,6,1,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,5,7,6,3,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,6,5,2,7,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,5,7,2,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,7,6,2,4,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,4,2,6,3,7,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,5,2,7,3,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,6,5,2,1,7,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,8,2,4,6,7,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,8,2,1,4,3,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,2,4,1,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,2,4,6,3,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,2,4,3,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,4,6,2,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,8,4,6,7,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,8,4,6,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,2,4,6,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,4,6,7,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,8,4,6,7,2,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,3,6,7,2,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,3,6,7,2,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,6,2,4,5,3,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,8,6,4,5,7,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,6,2,4,5,3,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,8,6,2,4,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,3,6,2,4,5,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,6,7,2,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,8,6,7,2,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,2,6,4,5,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,4,6,7,5,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,4,6,2,3,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,4,7,2,1,3,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,3,1,7,2,4,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,7,1,6,3,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,4,2,6,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,2,1,5,3,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,2,1,4,7,3,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,3,1,5,7,2,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,4,2,1,5,7,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,6,2,5,8,4,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,2,1,6,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,4,2,6,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,1,8,4,6,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,1,8,5,6,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,2,1,7,4,5,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,2,1,7,5,3,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,2,7,6,1,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,8,6,1,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,7,2,1,5,6,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,6,8,5,1,7,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,2,6,8,1,4,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,5,8,7,3,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,1,6,7,3,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,1,6,7,4,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,1,7,8,5,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,1,5,2,6,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,5,1,7,4,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,3,1,4,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,8,2,4,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,8,5,1,4,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,8,6,4,1,7,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,4,3,6,8,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,8,5,3,6,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,2,8,6,4,7,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,2,3,6,7,1,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,2,7,8,3,5,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,8,7,2,5,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,8,3,7,1,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,7,1,5,3,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,7,6,1,2,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,2,8,3,5,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,7,3,5,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,4,5,6,3,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,5,6,4,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,4,2,7,6,5,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,1,6,4,3,7,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,8,7,3,6,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,3,2,6,4,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,8,3,7,1,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,3,2,7,5,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,4,8,7,5,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,8,1,5,3,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,5,6,8,1,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,8,1,6,4,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,3,6,5,4,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,3,6,2,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,2,4,8,6,3,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,2,1,5,3,4,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,7,2,3,1,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,4,2,7,3,5,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,8,6,4,7,5,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,5,8,7,3,1,2,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,8,5,1,7,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,6,4,7,5,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,4,6,3,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,8,6,4,7,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,1,8,6,3,7,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,4,8,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,1,7,4,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,5,4,2,8,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,4,3,8,1,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,4,3,7,1,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,7,2,8,6,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,2,8,6,4,3,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,1,7,8,3,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,3,1,5,2,7,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,4,2,7,3,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,4,2,7,1,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,3,1,6,2,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,5,4,1,7,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,2,1,5,7,3,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,1,5,8,7,2,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,2,5,7,8,4,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,3,7,4,2,6,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,7,4,2,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,4,3,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,4,3,6,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,7,4,1,6,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,5,7,8,4,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,1,5,7,8,4,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,2,7,4,1,3,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,3,7,4,8,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,3,7,4,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,7,4,5,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,3,7,4,5,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,8,6,4,3,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,1,3,7,4,5,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,8,1,2,4,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,5,8,7,2,1,4,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,8,6,3,5,4,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,8,2,1,4,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,1,8,5,3,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,7,2,8,5,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,7,8,1,6,3,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,5,7,8,4,6,3,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,8,6,7,5,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,2,7,5,3,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,5,4,1,8,6,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,4,5,8,2,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,1,5,8,6,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,4,2,1,8,6,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,7,5,8,1,6,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,8,3,4,2,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,5,3,8,6,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,5,1,8,6,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,3,4,8,2,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,2,8,3,6,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,5,2,1,8,6,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,5,1,4,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,4,6,1,7,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,7,1,4,2,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,1,7,8,2,4,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,4,6,1,7,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,8,4,1,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,3,2,4,8,1,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,3,2,4,8,6,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,2,4,7,1,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,3,5,1,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,2,8,4,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,7,8,6,3,2,5,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,4,5,3,7,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,1,7,2,4,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,5,3,7,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,2,8,4,7,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,7,1,5,3,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,1,7,3,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,2,4,8,7,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,1,2,8,4,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,1,7,4,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,6,3,1,4,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,4,5,6,8,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,7,1,4,2,5,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,8,3,7,1,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,3,5,8,1,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,3,5,7,1,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,7,6,4,2,5,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,1,5,2,7,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,2,6,5,7,8,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,6,4,2,8,3,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,2,4,3,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,2,4,3,7,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,1,4,3,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,1,4,3,2,7,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,1,4,3,6,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,1,4,3,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,4,1,3,6,2,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[1,2,6,4,8,3,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,5,4,3,1,7,2,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,5,2,4,3,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,7,2,5,1,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,5,7,1,4,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,1,7,8,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,2,4,6,8,7,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,1,2,4,7,6,5,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,4,1,8,6,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,8,5,1,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,3,2,8,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,3,2,4,7,1,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,7,4,2,5,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,5,4,2,6,3,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,5,2,1,6,4,3,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,4,6,5,1,3,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,8,4,7,5,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,2,6,1,4,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,5,7,6,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,8,6,4,7,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,7,4,6,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,8,6,3,7,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,3,1,7,6,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,6,4,8,1,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,2,1,6,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,8,5,1,6,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,6,3,1,7,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,6,7,4,1,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,5,1,4,2,8,7,6]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,1,4,2,6,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,8,4,6,2,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,7,5,6,2,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,3,6,4,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,2,3,7,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,2,3,8,6,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,5,3,7,4,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,2,7,6,4,3,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,8,3,2,7,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,7,6,5,2,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,5,3,8,4,2,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,2,4,7,5,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,5,2,4,3,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,6,5,2,4,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,5,4,2,7,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,3,2,6,4,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,2,8,6,7,5,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,8,5,7,4,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,6,3,2,5,1,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,2,7,8,3,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,3,7,5,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,2,5,7,8,6,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,2,5,7,3,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,2,4,5,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,7,8,3,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,8,3,1,6,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,3,8,6,2,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,7,8,1,3,6,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,7,3,8,6,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,3,5,1,4,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,1,3,8,5,4,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,2,3,1,7,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,3,1,4,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,2,5,1,4,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,3,4,1,2,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,5,4,1,2,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,4,3,1,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,1,3,2,7,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,2,8,4,1,3,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,5,2,8,7,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,6,2,8,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,3,5,2,4,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,6,5,1,7,4,2,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,7,4,5,1,2,6,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,3,1,2,7,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,6,2,7,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,3,5,1,2,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,8,5,1,4,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,8,2,1,7,6,5]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,3,4,1,7,2,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,2,1,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,4,2,1,7,6,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,4,5,2,7,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,1,7,5,6,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,1,7,5,2,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,2,7,5,3,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,5,7,6,4,3,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,4,7,6,5,2,1,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,3,1,4,7,6,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,5,7,6,2,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,4,6,8,2,5,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,2,6,8,1,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,6,2,4,8,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,3,8,2,4,6,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,5,8,3,6,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,1,6,8,3,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,2,6,8,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,3,1,8,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,8,1,4,6,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,7,8,3,6,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,8,3,5,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,7,3,8,4,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,8,3,1,4,5,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,1,7,3,2,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,1,7,3,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,1,8,2,4,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,2,5,1,8,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,2,8,3,5,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,8,2,1,4,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,7,8,2,1,5,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,7,2,8,5,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,8,5,2,1,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,7,8,2,1,5,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,1,7,8,2,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,2,7,8,4,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,1,8,4,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,1,5,6,3,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,3,4,1,8,6,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,6,3,5,8,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,7,6,5,2,4,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,4,7,8,6,2,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,6,7,8,3,2,5,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,2,7,8,4,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,4,8,5,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,1,5,3,4,8,7,6]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,2,3,5,7,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,2,4,3,8,7,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,1,3,8,7,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,1,4,6,2,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,5,1,4,7,6,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,6,4,2,7,1,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,7,1,6,2,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,4,5,2,8,6,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,4,1,5,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,7,1,5,4,6,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,5,7,1,8,6,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,7,3,8,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,8,6,5,2,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,3,8,6,5,1,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,4,1,6,5,7,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,1,8,6,5,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,4,7,5,6,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,3,6,8,4,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,3,6,5,8,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,7,3,1,8,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,4,1,6,5,2,7,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,2,1,5,4,3,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,5,2,6,7,4,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,7,2,6,1,3,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,7,1,8,5,4,3,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,2,8,5,4,3,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,1,2,7,6,4,3,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,1,2,6,5,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,2,6,1,4,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,5,6,2,4,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,4,6,5,2,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,1,2,5,7,4,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,2,5,6,8,4,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,2,6,1,5,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,1,8,5,4,3,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,6,8,2,5,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,8,6,2,4,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,1,5,7,2,4,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,7,5,6,2,4,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,1,5,6,2,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,1,5,6,8,3,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,2,5,8,6,3,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,2,6,7,3,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,6,7,4,5,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,2,4,3,8,6,5,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,4,2,8,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,4,2,7,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,5,3,7,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,4,8,1,2,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,1,4,8,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,6,1,2,8,3,4,5]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,2,1,3,8,4,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,4,3,5,6,8,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,3,2,4,8,5,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,1,7,4,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,6,2,8,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,1,3,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,7,1,2,5,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,6,1,2,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,4,6,1,8,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,5,6,7,2,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,6,7,2,4,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,6,7,1,2,4,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,3,7,6,2,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,3,5,7,4,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,3,6,5,4,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,6,3,8,4,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,5,1,7,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,8,1,5,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,3,1,5,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,6,2,5,1,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,5,4,1,2,7,3,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,8,4,2,3,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,6,2,8,3,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,6,3,1,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,5,6,3,2,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,4,1,7,6,5,3,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,3,8,5,2,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,8,5,4,7,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,5,6,4,3,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,4,3,8,6,5,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,4,5,8,6,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,3,2,5,4,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,1,7,3,2,8,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,8,1,3,2,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,2,4,1,6,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,1,6,7,3,5,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,7,3,6,2,4,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,7,4,8,3,6,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,6,1,3,5,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,5,8,4,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,7,5,3,4,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,2,6,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,3,4,2,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,6,2,3,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,3,5,8,7,1,4,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,4,5,8,1,7,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,8,4,5,3,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,4,2,7,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,4,2,7,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,3,7,8,2,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,3,4,7,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,6,3,4,7,2,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,8,6,7,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,6,2,7,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,5,6,2,7,1,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,6,2,1,7,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,6,2,1,7,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,8,6,2,1,7,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,3,4,1,7,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,3,1,7,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,6,7,2,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,8,7,2,3,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,6,7,4,1,3,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,3,6,7,1,4,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,1,6,7,3,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,1,8,7,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,7,3,1,2,5,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,4,8,1,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,1,8,3,7,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,8,6,5,7,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,3,8,4,1,5,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,3,4,1,7,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,7,2,5,8,3,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,2,1,3,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,7,5,4,1,6,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,8,5,4,1,6,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,6,1,3,2,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,6,4,7,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,5,4,2,6,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,1,8,3,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,5,6,3,7,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,3,6,7,1,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,4,5,6,8,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,5,8,1,6,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,7,5,6,8,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,3,4,6,2,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,6,5,2,8,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,5,4,8,6,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,4,1,6,8,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,2,1,7,6,3,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,3,6,2,1,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,7,3,2,1,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,7,3,6,4,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,7,5,3,1,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,7,3,6,5,4,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,8,4,1,7,3,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,4,6,8,7,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,2,1,8,5,6,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,6,5,1,4,8,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,2,1,5,4,8,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,5,4,8,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,5,2,3,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,4,6,2,3,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,7,6,3,4,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,1,5,7,3,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,2,8,5,1,7,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,8,4,6,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,1,4,6,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,5,6,4,2,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,6,4,3,1,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,3,5,6,7,1,2,4]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,1,4,7,3,6,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,3,7,6,4,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,4,2,8,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,1,4,3,7,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,7,5,1,6,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,5,3,7,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,1,4,7,6,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,4,1,6,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,4,2,6,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,6,8,1,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,5,8,4,1,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,5,3,8,7,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,4,8,7,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,5,4,1,7,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,6,5,4,7,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,5,1,3,6,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,6,5,3,1,7,2,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[8,6,4,3,7,2,1,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,1,4,3,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,1,4,3,2,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,5,3,8,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,3,8,2,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,4,3,8,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,1,6,7,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,5,4,3,2,8,6,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,4,1,3,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,1,4,3,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,1,8,4,5,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,1,8,6,5,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,2,7,5,1,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,2,3,7,4,1,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,7,4,3,6,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,2,5,4,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,3,8,1,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,5,3,4,1,7,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,3,4,1,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,2,3,1,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,1,5,2,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,6,4,5,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,7,8,6,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,4,8,7,2,3,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,4,5,3,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,5,1,4,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,2,1,7,4,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,7,2,1,8,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,4,7,3,8,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,1,3,8,5,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,6,8,4,1,7,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,1,8,4,7,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,5,6,8,4,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,2,4,7,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,5,6,3,8,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,2,7,4,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,2,6,1,5,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,1,6,2,5,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,4,5,1,6,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,3,7,5,4,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,6,2,4,3,5,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,3,1,7,5,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,5,8,7,1,6,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,4,2,7,6,1,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,1,2,6,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,7,6,2,3,5,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,3,4,8,1,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,8,4,6,1,2,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,6,7,5,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,7,2,8,1,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,4,7,1,6,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,7,6,1,2,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,7,4,6,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,6,2,1,5,3,4]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[5,7,8,1,6,2,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,8,4,7,5,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,2,7,1,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,7,4,2,5,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,4,5,2,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,4,5,7,2,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,4,2,5,7,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,4,2,5,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,1,4,6,2,3,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,6,2,3,7,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,3,7,6,4,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,5,7,6,4,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,1,6,5,4,7,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,6,8,3,4,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,1,3,6,5,2,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,6,2,4,5,7,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,6,2,5,4,7,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,1,7,6,4,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,1,4,5,7,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,1,2,6,5,3,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,6,1,3,5,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,4,2,5,7,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,6,3,5,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,4,7,6,5,1,2,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,6,1,2,5,3,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,4,7,3,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,4,8,6,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,4,3,7,5,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,5,1,4,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,5,1,7,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,4,7,1,3,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,4,7,1,3,5,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,1,3,5,7,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,8,3,2,7,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,3,1,5,4,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,1,2,5,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,7,1,6,4,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,5,8,6,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,3,6,7,4,2,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,8,3,6,7,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,7,8,5,6,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,7,1,8,5,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,8,6,7,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,2,4,7,3,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,3,1,6,4,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,3,4,7,5,8,6,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,5,2,3,7,8,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,2,8,1,6,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,1,4,8,3,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,6,4,1,7,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,6,3,7,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,4,1,3,7,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,6,1,5,7,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,1,6,4,7,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,6,3,7,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,6,8,2,3,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,4,8,1,2,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,7,5,8,1,4,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,5,6,8,2,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,1,6,8,4,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,4,7,2,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,5,8,3,1,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,4,7,5,8,3,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,8,7,3,5,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,8,6,2,5,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,7,3,5,6,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,7,6,3,5,4,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,8,1,6,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,3,6,2,5,8,7,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,8,7,1,4,6,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,6,5,1,2,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,4,1,2,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,5,6,2,4,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,5,1,2,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,6,1,3,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,1,4,3,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,4,1,3,7,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,5,4,3,8,6,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,8,2,3,7,1,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,4,3,1,8,6,5]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,8,5,3,2,1,6,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,5,8,3,4,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,1,6,5,2,4,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,1,3,8,2,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,4,8,2,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,4,8,1,2,5,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,8,1,5,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,5,7,1,6,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,2,3,7,1,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,4,8,2,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,2,3,1,8,4,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,4,1,6,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,6,7,4,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,3,1,4,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,4,1,7,3,2,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,4,5,1,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,5,6,7,4,8,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,7,1,8,4,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,1,5,4,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,4,7,2,6,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,7,5,1,6,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,2,5,7,4,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,5,2,7,6,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,2,1,7,6,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,1,3,6,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,5,6,1,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,4,5,3,8,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,1,5,7,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,7,2,8,3,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,7,8,3,1,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,6,1,7,8,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,2,5,1,7,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,6,3,7,8,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,3,7,8,2,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,3,4,8,2,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,7,3,4,8,2,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,4,1,5,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,7,1,8,4,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,8,4,6,5,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,7,3,2,8,6,5,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[3,7,1,2,8,6,5,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,7,3,1,8,6,5,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,7,8,1,6,5,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,1,3,4,7,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,2,8,7,1,5,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,8,1,7,6,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,8,7,3,4,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,1,5,7,3,4,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,8,2,7,6,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,4,7,6,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,2,4,7,6,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,4,7,6,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,1,6,8,7,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,5,8,7,1,6,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,2,6,1,8,7,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,1,4,8,7,5,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,3,5,8,6,7,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,8,2,4,6,7,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,4,7,3,8,5,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,7,8,2,5,6,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,7,8,1,5,6,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,5,1,8,4,7,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,7,4,8,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,3,8,4,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,7,1,8,6,5,4]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,4,2,8,1,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,5,8,1,7,6,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,8,5,1,7,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,8,3,5,2,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,8,2,6,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,7,2,8,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,8,1,4,3,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,8,2,6,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,5,2,8,7,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,1,5,8,7,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,1,7,3,5,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,3,2,7,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,6,5,3,2,7,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,7,6,3,2,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,4,8,6,2,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,6,8,1,2,5,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,5,8,1,6,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,1,4,3,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,5,3,2,8,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,4,5,3,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,5,3,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,2,5,3,4,1,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,6,1,8,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,6,5,1,2,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,5,4,8,3,1,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,7,5,3,2,8,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,2,5,3,8,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,3,7,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,1,3,5,2,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,1,4,5,2,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,8,1,4,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,5,1,8,7,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,5,3,2,7,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,3,4,7,2,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,8,2,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,5,4,8,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,4,5,3,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,7,4,3,1,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,6,4,3,2,7,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,1,5,4,7,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,5,4,7,1,3,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,7,4,3,2,6,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,1,2,6,3,5,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,5,4,7,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,5,4,6,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,5,4,2,7,6,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,6,1,4,7,5,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,8,4,7,5,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,6,1,4,8,7,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,2,4,8,1,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,2,4,5,8,7,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,1,2,5,3,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,6,8,4,2,5,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,8,1,6,3,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,8,4,1,5,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,8,2,6,3,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,8,1,3,4,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,2,8,3,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,6,1,4,8,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,5,4,8,7,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,3,4,8,5,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,2,4,8,3,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,1,2,8,3,4,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,3,2,6,5,4,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,6,2,7,5,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,2,7,6,5,3,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,4,2,7,6,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,2,7,5,4,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,8,5,4,2,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,2,8,6,4,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,4,2,6,5,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,5,2,7,4,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,5,6,4,2,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,5,6,4,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,6,7,4,2,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,7,1,8,4,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,7,8,5,2,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,8,6,4,2,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,1,6,8,5,2,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,8,1,5,2,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,4,2,8,6,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,3,5,2,8,6,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,8,5,6,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,3,6,7,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,5,4,6,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,5,4,6,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,4,1,6,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,5,1,7,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,1,3,7,6,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,3,1,2,8,7,6]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,4,2,3,1,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,1,8,2,5,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,2,3,7,6,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,7,8,1,2,4,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,6,8,3,5,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,5,7,4,1,3,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,1,8,3,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,6,8,2,5,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,1,8,3,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,3,6,1,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,8,6,4,5,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,2,8,6,4,5,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,3,6,2,5,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,6,8,7,4,3,5,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,1,4,3,5,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,6,7,3,5,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,2,6,8,7,5,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,5,6,3,7,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,4,2,1,8,6,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[8,6,5,7,2,4,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,6,1,8,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,6,3,8,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,8,1,6,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,8,3,6,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,4,1,5,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,4,8,1,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,8,2,4,1,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,8,2,5,7,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,4,8,2,5,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,4,5,8,3,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,8,2,4,7,3,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,4,2,3,5,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,8,2,3,1,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,8,2,5,1,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,8,2,5,7,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,8,4,2,3,7,1,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,8,2,3,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,6,2,7,1,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,4,2,7,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,2,6,7,5,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,4,6,7,5,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,2,6,7,4,1,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,2,6,7,1,4,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,2,4,1,7,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,2,4,1,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,2,6,1,5,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,1,6,2,4,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,2,5,7,1,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,6,5,7,2,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,5,8,1,3,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,2,1,8,4,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,1,5,6,4,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,6,8,4,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,8,6,5,3,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,4,8,2,6,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,8,5,6,7,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,7,4,8,6,3,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,2,3,8,7,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,1,5,4,6,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,4,7,6,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,2,3,7,6,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,3,7,6,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,7,3,5,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,2,3,8,4,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,2,3,1,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,2,3,4,1,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,2,7,3,5,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,6,3,5,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,2,3,1,7,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,2,3,8,4,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,2,3,1,6,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,2,3,1,5,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,6,3,1,7,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,3,4,2,7,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,5,2,7,3,4,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,8,3,2,5,6,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,8,1,4,6,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,8,1,5,6,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,8,2,3,1,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,2,3,1,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,2,3,8,1,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,1,5,3,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,3,8,4,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,1,3,4,2,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,3,4,2,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,3,7,4,6,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,3,7,4,6,1,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,7,3,4,5,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,2,7,3,4,5,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,4,5,2,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,6,3,4,5,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,7,2,8,3,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,5,2,6,1,8,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,5,3,7,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,4,3,1,7,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,6,5,7,2,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,5,3,7,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,2,6,1,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,1,5,2,7,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,5,7,2,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,6,8,1,2,4,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,5,6,2,8,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,3,5,8,7,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,5,4,6,2,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,4,6,2,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,6,4,8,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,5,6,8,2,4,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,5,6,2,8,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,1,5,8,4,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,6,8,4,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,7,5,1,4,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,5,7,3,6,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,2,6,4,5,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,5,6,2,7,1,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,7,2,6,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,3,2,6,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,2,3,6,4,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,5,3,7,8,1,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,2,8,1,6,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,3,4,1,5,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,7,5,1,6,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,1,4,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,5,2,8,6,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,7,4,2,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,1,5,7,4,6,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,2,5,8,6,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,7,1,3,5,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[5,6,1,3,4,7,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,5,3,7,8,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,1,3,8,4,5,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,8,3,4,6,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,2,7,5,8,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,7,4,3,1,5,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,1,6,7,8,4,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,4,5,6,2,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,2,5,6,7,3,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,4,5,2,7,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,5,6,2,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,6,3,8,4,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,8,4,2,3,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,3,1,4,5,2,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,1,3,5,2,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,4,1,7,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,2,6,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,1,5,3,4,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,5,6,1,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,8,3,4,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,8,3,4,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,3,6,1,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,8,2,3,7,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,3,4,8,2,5,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,5,1,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,1,5,4,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,4,7,3,1,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,7,2,5,1,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,4,5,8,2,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,7,3,1,8,2,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,3,8,5,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,3,8,4,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,5,1,3,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,2,8,4,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,7,4,6,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,6,2,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,6,5,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,7,2,1,5,3,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,8,5,3,7,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,2,8,1,5,6,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,6,1,4,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,4,2,1,8,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,1,3,2,7,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,3,6,4,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,2,4,3,8,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,4,3,5,8,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,2,6,7,4,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,5,1,6,4,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,5,7,3,4,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,5,3,8,1,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,2,7,4,8,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,5,8,1,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,7,4,1,3,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,5,6,1,4,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,6,1,4,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,5,8,2,7,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,1,2,4,3,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,6,7,4,1,3,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,6,8,4,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,6,5,3,8,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,5,7,1,3,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,4,3,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,2,4,3,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,4,5,8,2,3,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,6,1,3,7,8,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,4,1,5,2,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,2,4,3,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,5,6,3,8,7,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,8,4,7,1,3,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,2,6,8,7,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,5,2,7,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,5,2,6,7,1,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,7,2,4,1,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,8,7,1,4,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,5,3,1,8,7,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,6,1,5,4,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,2,6,1,5,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,6,4,7,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,8,7,5,4,3,2,6]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[8,6,4,7,1,3,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,1,4,7,6,2,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,4,7,1,6,3,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,4,1,6,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,7,1,4,6,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,1,5,2,4,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,4,5,2,7,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,5,8,2,7,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,2,3,6,4,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,3,1,8,5,4,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,1,8,7,5,4,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,3,7,5,4,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,3,8,7,4,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,1,3,7,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,3,8,5,4,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,5,6,1,3,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,8,4,6,5,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,1,3,6,5,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,4,7,1,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,8,1,6,4,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,1,7,6,3,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,8,7,2,1,3,5,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,2,8,1,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,6,8,3,1,5,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,4,8,2,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,1,2,6,3,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,8,4,6,1,2,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,1,4,8,7,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,4,7,5,1,8,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,5,1,4,7,3,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,4,5,1,7,3,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,8,4,1,3,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,6,5,7,8,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,6,7,5,8,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,6,3,7,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,4,5,6,3,8,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,8,6,3,4,7,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,6,5,1,4,2,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,6,3,5,8,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,8,3,4,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,7,3,8,6,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,1,8,5,4,3,2,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,2,1,6,4,5,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,6,4,1,8,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,1,2,5,3,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,2,7,6,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,1,5,6,2,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,2,8,1,3,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,5,2,1,6,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,1,5,4,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,5,4,1,6,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,6,8,7,1,3,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,6,8,3,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,8,6,3,5,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,2,7,6,5,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,2,8,6,5,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,5,2,7,1,4,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,5,8,2,7,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,8,2,1,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,1,6,5,8,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,4,8,5,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,8,5,2,1,7,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,8,7,1,3,2,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,7,4,6,1,3,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,1,8,7,6,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,7,5,4,1,6,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,1,5,7,4,2,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,7,3,4,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,1,3,2,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,5,8,3,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,8,2,4,5,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,2,8,4,5,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,8,2,4,5,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,3,6,4,2,7,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,8,4,7,6,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,4,7,8,5,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,4,3,7,6,1,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,3,7,1,4,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,1,2,8,7,6,4,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,3,2,1,6,4,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,3,8,4,1,7,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,1,3,2,7,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,2,5,8,4,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,7,8,2,5,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,6,7,1,5,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,8,7,4,3,5,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,7,5,1,4,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,2,8,1,3,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,3,6,5,1,4,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,4,5,8,1,3,7,6]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,3,5,8,7,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,3,1,7,4,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,3,8,1,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,7,4,6,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,3,6,7,8,1,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,5,6,2,7,8,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,1,8,4,3,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,4,1,6,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,1,8,6,7,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,7,8,2,6,3,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,6,2,5,3,4,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,8,1,3,5,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,4,6,5,7,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,1,5,8,4,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,8,3,5,6,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,6,4,2,7,5,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,7,5,8,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,8,5,6,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,5,8,1,4,6,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,7,5,8,1,2,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,7,5,2,8,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,5,8,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,4,7,3,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,7,8,4,2,1,6,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,3,5,6,8,1,2,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,8,2,7,6,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,4,7,6,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,1,3,4,8,7,5,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,8,1,4,5,2,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,1,8,5,7,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,8,7,6,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,4,5,8,1,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,4,7,8,2,5,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,8,4,2,7,6,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,8,4,2,7,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,7,5,1,6,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,3,7,6,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,4,7,6,3,8,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,3,7,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,5,1,7,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,4,1,6,2,8,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,2,8,5,1,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,3,6,8,2,4,7,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,8,3,7,4,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,7,4,3,8,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,3,1,6,5,2,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,1,8,5,4,2,7,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,4,2,7,1,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,6,1,8,5,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,5,1,6,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,4,1,6,2,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,7,3,1,6,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,8,2,6,3,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,6,3,1,7,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,2,8,5,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,1,7,2,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,3,8,7,5,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,4,1,8,6,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,7,3,1,4,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,5,8,2,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,7,5,1,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,5,8,6,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,8,1,3,4,7,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,3,5,8,6,2,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,8,6,2,1,5,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,8,6,2,1,4,5,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,1,3,7,5,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,4,8,6,5,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,6,2,7,3,5,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,8,6,1,3,7,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,7,5,2,4,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,6,8,4,2,5,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,7,2,3,5,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,6,2,4,5,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,1,3,8,7,5,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,7,3,6,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,4,7,3,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,8,1,6,3,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,5,6,3,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,8,6,4,5,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,7,2,1,4,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,4,8,5,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,4,2,5,8,7,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,4,1,6,3,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,7,8,6,4,5,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,6,2,4,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,2,7,3,6,5,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,8,6,1,4,5,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,7,3,4,8,6,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,3,2,4,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,4,6,3,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,4,3,5,6,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,8,3,6,4,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,4,8,5,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,1,4,6,5,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,5,4,1,8,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,1,8,5,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,5,2,1,6,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,1,4,8,2,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,8,1,3,7,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,6,7,1,4,3,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,7,8,6,3,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[8,5,2,6,3,4,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,6,1,2,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,6,2,1,8,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,3,7,6,1,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,3,2,7,1,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,8,1,5,4,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,5,4,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,2,4,8,5,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,6,8,7,3,1,2,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[8,7,5,2,1,4,3,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[5,7,2,1,6,3,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,3,6,8,7,4,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,8,4,6,2,3,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,2,6,8,3,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,8,1,7,3,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,3,4,5,2,1,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,4,5,2,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,5,2,6,3,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,6,2,8,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,8,5,2,6,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,1,8,6,7,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,7,2,5,6,4,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,7,4,6,8,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,5,6,8,4,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,1,2,5,6,4,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,8,5,1,6,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,2,4,3,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,8,2,4,3,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,1,5,3,4,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,1,3,5,4,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,2,4,1,3,6,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,2,3,1,5,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,6,8,2,5,3,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,5,2,7,3,6,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,6,4,1,8,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,7,6,2,4,5,1,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,5,2,7,3,6,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,3,8,1,7,4,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,7,4,6,3,1,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,5,6,1,3,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,8,7,1,2,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,8,7,5,4,2,6,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[8,1,2,6,5,4,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,6,4,3,8,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,5,6,4,8,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,1,8,5,2,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,3,5,1,4,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,6,3,1,8,2,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,5,2,1,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,3,5,2,6,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,3,5,2,4,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,2,7,6,5,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,2,1,7,4,8,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,6,3,4,8,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,3,4,2,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,3,8,5,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,7,6,2,3,5,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,4,3,1,5,6,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,1,3,8,5,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,8,4,5,6,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,8,4,5,6,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,2,4,7,1,6,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,1,5,8,7,4,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,8,3,1,6,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,3,4,2,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,8,3,4,2,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,8,6,3,2,5,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,7,2,4,5,6,1,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,7,1,4,5,6,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,2,8,1,5,7,4,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,7,4,5,6,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,6,7,2,1,5,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,3,1,7,4,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,2,6,5,7,3,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,8,6,5,1,3,4,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,2,5,4,6,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,5,1,6,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,1,7,8,3,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,6,7,1,4,3,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,6,2,1,8,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,7,4,5,1,2,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,3,8,6,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,7,4,8,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,8,5,4,2,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,6,1,3,5,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,3,8,7,4,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,3,8,7,4,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,3,8,7,4,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,3,5,1,2,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,2,7,4,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,2,8,3,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,5,1,6,4,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,7,5,1,6,4,3,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[4,5,8,3,1,2,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,8,3,2,1,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,8,3,5,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,8,3,1,6,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,3,5,2,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,4,2,6,1,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,6,3,4,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,5,2,4,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,1,3,4,8,7,6]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,4,6,3,7,5,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,5,8,3,4,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,2,6,8,7,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,7,6,3,1,5,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,6,3,8,5,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,8,1,4,5,6,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,8,7,4,2,5,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,8,4,2,7,5,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,1,3,7,5,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,3,8,7,4,5,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,3,1,8,4,5,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,8,7,4,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,4,3,7,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,4,3,7,5,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,2,5,1,7,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,2,1,5,7,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,3,2,5,7,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,3,2,8,7,4,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,2,1,7,4,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,5,2,8,3,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,7,3,2,5,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,4,7,3,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,2,7,3,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,7,2,1,3,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,6,3,7,8,1,2,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,2,7,1,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,5,4,1,6,8,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,8,5,4,7,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,3,5,4,7,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,5,4,8,7,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,5,4,1,7,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,1,6,4,3,2,7,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,1,8,4,3,2,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,1,5,6,3,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,7,4,3,2,5,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,7,8,4,3,2,5,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[8,1,5,4,6,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,5,6,3,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,8,5,1,3,7,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,4,5,8,3,7,6,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,3,5,4,1,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,3,4,1,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,4,6,3,2,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,4,1,8,2,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,5,1,3,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,3,5,4,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,3,8,7,2,5,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,4,1,8,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,4,8,3,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,8,3,2,7,6,5,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,8,7,3,4,6,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,1,2,8,7,5,4,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,1,3,2,8,4,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,8,3,5,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,3,8,5,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,3,4,7,5,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,1,5,2,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,7,6,4,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,1,3,6,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,3,4,8,6,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,8,2,4,7,3,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,7,3,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,4,3,5,8,6,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,1,5,8,3,4,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,8,5,1,2,7,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,1,6,5,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,3,8,1,5,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,3,5,7,4,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,4,7,5,3,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,7,4,8,3,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,5,6,2,4,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,3,1,5,8,2,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,6,1,7,3,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,5,6,7,1,3,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,2,6,8,7,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,2,8,7,5,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,7,2,6,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,1,5,7,3,6,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,5,1,8,2,4,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,7,1,2,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,7,3,8,4,5,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,7,6,4,3,8,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,1,7,4,6,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,7,5,3,6,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,6,2,7,5,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,8,1,6,2,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,2,7,5,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,4,2,5,7,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,8,5,2,3,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,5,8,1,4,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,2,6,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,5,8,6,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,4,6,1,2,7,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,7,1,2,6,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,8,7,2,4,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,4,2,8,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,2,8,7,3,5,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,1,3,2,5,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,1,2,6,8,4,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,7,4,2,8,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,1,6,8,7,2,3,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,1,6,8,2,7,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,3,7,4,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,2,5,7,6,8,3,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,7,5,6,2,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,5,2,8,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,4,3,2,7,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,7,6,3,5,4,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,1,5,7,6,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,7,3,5,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,4,1,8,3,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,1,2,8,4,6,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,1,7,5,3,4,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,6,3,5,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,3,7,6,4,8,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,6,5,7,2,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,7,6,4,1,5,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,6,4,8,7,3,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,1,8,7,3,5,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,2,8,7,6,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,1,8,5,7,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,4,2,7,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,3,7,2,4,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,7,3,5,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,6,7,3,5,8,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,3,1,6,4,8,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,5,6,7,1,4,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,7,3,5,8,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,5,3,2,8,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,2,3,6,8,4,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,7,5,2,8,6,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,6,4,8,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,2,5,7,1,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,3,6,8,2,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,1,3,6,8,2,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,7,6,1,5,4,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,6,7,2,5,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,1,2,7,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,3,7,8,1,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,1,8,4,5,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,3,6,8,1,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,2,4,8,7,5,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,3,2,7,5,8,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,1,3,5,8,4,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,4,7,5,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,6,8,5,2,1,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,2,6,4,8,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,2,4,8,3,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,8,1,4,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,2,7,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,4,2,7,5,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,7,5,8,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,7,5,8,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,4,1,6,2,7,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,3,5,2,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,8,3,1,2,5,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,6,4,7,1,2,3]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,1,8,7,3,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,2,4,3,8,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,8,4,3,5,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,2,6,7,1,5,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,7,5,6,8,4,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,8,1,7,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,7,6,8,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,6,1,4,5,2,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,4,6,7,2,5,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,4,7,3,6,8,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,1,4,6,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,4,7,3,6,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,3,7,2,6,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,1,5,2,8,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,6,7,4,5,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,5,7,6,1,3,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,5,6,1,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,6,7,4,5,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[6,5,2,8,7,1,4,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,6,5,7,2,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,7,2,5,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,1,4,6,8,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,2,3,6,8,1,4,5]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,3,1,7,5,2,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,1,3,8,5,4,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,1,4,2,7,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,1,4,2,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,4,8,3,5,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,8,6,1,5,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,3,2,1,8,4,6,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,3,2,1,6,7,4,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,8,7,4,2,3,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,3,2,1,6,8,4,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,3,1,6,8,7,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,4,8,2,1,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,3,1,8,7,5,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,4,3,2,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,4,3,2,6,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,8,2,3,6,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,6,7,2,4,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,8,3,7,1,2,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,2,1,4,7,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,3,5,1,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,8,1,6,5,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,3,4,7,2,1,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,7,5,2,4,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,2,4,1,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,6,4,1,5,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,7,3,6,2,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,6,1,8,2,4,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,4,5,1,3,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,3,2,6,8,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,5,3,8,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,8,3,2,5,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,3,2,5,4,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,1,5,7,4,3,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,6,1,2,4,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,7,4,5,1,3,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,4,7,8,6,3,2,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,7,1,2,8,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,1,5,7,4,2,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,1,2,7,4,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,1,8,7,2,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,3,8,4,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,3,7,4,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,1,6,4,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,5,1,3,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,1,6,8,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,2,4,7,6,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,8,1,6,7,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,2,4,6,1,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,8,3,6,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,4,3,8,5,1,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,4,3,6,2,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,4,8,5,3,6,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,4,8,7,1,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,1,4,7,6,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,8,5,2,1,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,3,7,6,8,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,6,7,2,1,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,5,7,2,8,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,4,7,5,8,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,8,1,7,4,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,8,4,7,3,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,6,7,5,4,8,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,2,6,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,5,4,2,8,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,5,6,8,3,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,5,6,4,1,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,3,6,8,5,7,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[4,6,8,5,7,2,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,4,5,6,2,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,5,7,4,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,4,6,8,2,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,3,5,6,4,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,4,7,5,3,6,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,7,1,3,6,2,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,2,4,7,3,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,1,7,2,4,6,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,8,1,4,7,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,7,1,2,5,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,3,6,8,5,7,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,4,7,8,3,5,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,6,2,5,8,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,2,5,8,4,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,8,3,6,4,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,8,1,3,6,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,3,6,8,2,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,5,2,4,7,8,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,3,5,2,4,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,8,1,2,6,3,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,1,2,6,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,2,3,7,5,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,2,6,5,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,4,2,7,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,5,2,3,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,1,4,7,3,5,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,3,6,1,7,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,1,8,3,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,2,1,3,7,5,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,5,1,7,6,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,1,8,2,4,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,2,6,3,7,5,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,1,8,3,2,4,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,8,5,7,3,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,8,7,3,1,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,4,2,1,3,8,5,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,2,1,3,8,5,4,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,1,7,3,8,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,7,5,3,2,4,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,4,2,7,6,5,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,1,6,5,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,7,3,4,1,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,2,3,8,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,7,6,2,8,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,1,8,7,5,2,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,6,8,7,2,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,8,3,1,5,4,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,2,1,5,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,2,1,4,3,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,3,1,4,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,1,5,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,5,1,4,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,1,5,8,3,2,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,7,8,3,2,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,1,7,8,3,2,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,8,6,2,4,3,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,7,2,4,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,6,2,5,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,1,6,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,3,1,6,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,2,1,6,3,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,2,1,6,4,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,3,1,6,4,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,3,1,7,4,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,2,1,7,3,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,3,6,8,2,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,2,6,8,3,1,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,8,3,1,7,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,5,1,7,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,6,1,5,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,8,6,3,7,2,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,7,1,5,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,6,7,2,5,4,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,5,1,3,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,4,3,1,2,7,6,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,1,5,2,3,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,1,6,3,7,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,1,2,8,3,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,3,6,7,2,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,6,7,4,3,1,5,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,3,1,7,4,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,5,3,7,2,4,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,3,6,7,1,5,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,7,5,8,1,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,6,7,3,2,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,1,4,7,2,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,5,8,6,4,3,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,8,2,3,5,7,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,2,6,7,4,5,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,2,6,8,5,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,7,8,4,6,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,8,5,6,3,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,3,6,4,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,2,6,7,1,4,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,6,5,2,1,7,4,3]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[5,7,3,2,1,8,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,1,6,4,7,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,8,6,7,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,1,8,6,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,5,6,8,1,3,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,3,2,4,7,1,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,2,8,6,1,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,8,2,6,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,8,7,6,3,2,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,6,8,7,3,5,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,8,2,7,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,2,5,4,1,3,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,1,4,6,3,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,4,1,2,6,5,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,7,4,6,1,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,7,1,6,5,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,8,4,7,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,1,4,7,3,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,6,8,4,2,5,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,5,1,4,6,2,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,4,8,6,3,2,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,2,5,6,8,4,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,4,6,7,3,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,6,8,3,4,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,8,5,1,2,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,1,8,4,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,4,6,3,5,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,3,1,7,6,4,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,2,4,1,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,5,6,1,2,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,3,4,1,8,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,3,1,8,4,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,2,8,4,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,3,8,7,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,3,6,8,5,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,2,5,7,4,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,5,7,1,2,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,4,6,1,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,3,6,1,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,8,4,2,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,2,1,7,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,6,7,3,4,2,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,8,3,4,2,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,8,7,5,3,4,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,8,5,3,4,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,7,6,8,4,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,8,5,7,1,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,7,1,5,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,8,6,4,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,1,7,8,4,2,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,4,2,7,6,5,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,2,1,6,7,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,8,3,1,7,5,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,3,1,6,5,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,2,5,4,1,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,6,4,3,2,7,5,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,7,1,2,6,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,5,6,2,1,4,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,3,2,5,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,2,4,5,6,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,4,1,5,3,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,7,4,1,5,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,1,6,4,7,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,8,3,4,2,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,5,3,8,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,3,2,7,1,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,4,7,8,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,8,3,5,2,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,8,4,5,7,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,8,4,5,6,1,3,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,8,4,5,7,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,1,3,8,4,5,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,1,8,4,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,2,5,8,4,6,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,3,4,8,2,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,2,8,4,6,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,3,8,4,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,1,8,3,6,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,8,1,4,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,8,3,4,2,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,3,5,8,4,6,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,1,5,8,4,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,5,8,4,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,5,8,2,1,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[8,2,7,6,3,4,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,8,2,7,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,2,6,1,4,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,1,2,4,6,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,2,8,3,4,5,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,8,3,4,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,1,2,4,3,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,8,1,4,2,3,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,5,2,4,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,6,2,5,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,5,3,7,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,7,3,4,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,6,8,3,4,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,7,8,3,4,5,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,4,3,7,8,5,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,8,7,2,4,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,1,2,7,4,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,8,6,3,4,5,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,3,5,2,1,8,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,5,3,8,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,3,6,8,5,1,7,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,2,4,8,6,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,3,8,4,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,1,2,8,6,7,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,4,5,2,3,8,7,6]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,2,1,5,3,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,1,6,3,8,7,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,2,8,5,4,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,3,7,8,4,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,1,3,8,4,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,1,2,8,4,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,8,7,5,4,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,7,2,3,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,1,4,8,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,6,5,7,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,2,7,5,6,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,5,6,8,7,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,5,8,6,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,7,5,8,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,1,4,8,6,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,1,8,4,3,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,1,8,7,3,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,1,8,6,3,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,1,8,7,4,6,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,1,8,3,5,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,7,1,8,3,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,7,8,3,5,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,1,8,7,4,5,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,7,5,2,6,4,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,7,4,6,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,8,4,7,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,4,6,8,5,7,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,3,5,7,6,4,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,8,5,1,6,4,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,7,1,8,3,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,8,3,7,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,3,5,4,7,6,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,1,7,5,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,2,3,4,1,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,6,8,4,3,5,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,5,7,1,4,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,5,4,2,6,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,4,1,6,5,3,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,1,2,7,6,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,8,2,5,6,3,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,4,3,5,6,1,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,5,4,2,3,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,5,1,2,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,6,3,5,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,2,5,3,8,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,5,2,1,8,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,4,3,6,7,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,2,1,5,3,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,3,8,6,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,6,5,1,8,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,8,1,6,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,8,1,6,7,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,1,8,4,6,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,1,7,2,3,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,6,5,8,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,3,8,1,7,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,7,1,6,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,2,8,6,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,4,6,5,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,7,5,6,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,1,5,3,7,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,8,1,5,2,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,6,7,4,2,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,7,2,5,6,3,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,7,2,8,3,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,3,6,8,1,5,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,6,3,7,8,1,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,3,8,7,2,1,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,5,6,3,4,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,2,8,6,3,1,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,2,4,5,8,6,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,3,8,4,7,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,3,6,8,5,4,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,4,5,2,8,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,5,4,2,8,1,6,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,6,3,2,8,4,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,2,3,6,8,4,5,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,5,4,8,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,8,3,6,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,5,2,8,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,6,7,4,5,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,5,4,7,6,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,6,8,2,4,5,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,4,2,5,1,7,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,2,5,7,3,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,7,8,4,2,3,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[6,4,5,2,8,3,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,2,4,3,8,7,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,3,4,1,8,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,5,3,8,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,4,8,3,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,3,4,7,5,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,2,6,3,4,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,2,6,4,8,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,7,2,6,5,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,2,4,6,3,8,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,3,7,6,2,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,8,3,7,6,1,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,7,3,1,6,5,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[3,7,2,5,8,6,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,2,3,5,8,6,4,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,6,5,3,8,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,3,4,8,1,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,3,8,4,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,4,8,7,6,1,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,2,8,7,4,6,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,2,8,3,7,6,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,1,7,4,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,2,5,6,1,4,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,6,5,1,4,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,2,5,1,4,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,5,2,7,6,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,8,6,2,7,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,2,8,5,6,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,2,7,4,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,6,5,7,1,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,7,8,6,2,5,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,4,8,6,2,5,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,8,4,7,2,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,7,2,4,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,4,8,6,2,5,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,3,8,6,2,5,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,8,1,6,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,8,1,6,4,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,5,1,7,6,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,8,1,7,6,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,1,8,5,6,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,8,6,4,5,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,8,6,5,2,3,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,6,2,8,5,4,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[3,4,6,2,5,7,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,5,2,6,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,5,7,1,6,2,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,8,6,1,2,4,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,6,1,3,8,7,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,7,8,6,5,1,4]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,7,4,8,2,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,1,7,2,4,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,5,6,2,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,2,1,4,8,5,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,2,1,7,6,4,3,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,4,8,3,6,5,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,8,5,1,7,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,2,7,4,5,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,3,8,5,6,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,8,7,4,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,2,1,8,7,3,5,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,2,6,8,5,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,4,3,2,7,5,1]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[5,1,8,6,2,4,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,5,4,3,8,7,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,2,5,8,4,3,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,8,2,6,4,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,6,2,4,7,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,5,6,7,2,4,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,5,7,6,8,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,7,2,6,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,5,2,7,6,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,7,4,2,6,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,4,7,2,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,5,7,2,6,8,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,4,5,7,2,8,6,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,5,4,7,8,2,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,4,7,2,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,5,7,4,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,7,4,2,8,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,7,8,4,2,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,5,2,7,8,6,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,5,7,8,2,6,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,5,7,8,6,2,4,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,2,5,6,7,3,8,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,6,1,4,3,5,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,8,4,3,5,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,6,4,8,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,4,2,5,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,8,4,1,5,3,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,1,3,5,2,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,1,8,3,5,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,1,2,5,4,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,1,8,2,5,4,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,5,1,8,7,6,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,4,8,1,7,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,4,8,6,7,2,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,5,7,3,8,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,6,8,1,2,5,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,5,6,8,2,1,4,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[8,2,5,4,1,3,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,4,5,8,6,3,1,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,4,8,2,3,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,7,5,8,2,3,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,7,5,1,8,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,7,3,6,5,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,3,4,2,6,7,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,3,8,6,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,3,1,8,2,6,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,7,5,2,8,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,8,7,2,4,3,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,2,8,6,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,7,8,6,1,4,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,2,6,8,4,5,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,7,6,8,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,7,1,6,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,1,6,5,2,8,7]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,7,2,1,5,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,7,1,5,4,3,2,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,7,6,2,4,3,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,6,2,4,5,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,7,2,1,5,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,3,6,7,1,5,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,6,7,4,5,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,4,8,5,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,4,1,5,3,6,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,2,5,6,3,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,5,8,3,4,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,8,7,1,3,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,3,8,6,5,1,4,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[6,4,1,3,5,2,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,3,4,8,2,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,3,6,5,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,6,5,7,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,8,6,5,7,4,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,2,7,4,3,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,5,2,8,4,3,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,5,8,3,4,2,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,8,5,2,4,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,3,7,2,4,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,1,2,8,6,3,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,5,7,2,4,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,8,2,6,5,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,4,7,8,5,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,1,5,7,8,4,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,6,8,3,7,4,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,6,1,5,7,2,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,8,4,6,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,3,6,7,5,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,1,6,5,2,7,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,1,5,2,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,6,2,8,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,8,2,3,7,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,6,2,1,3,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,1,4,8,2,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,7,2,5,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,5,3,6,7,2,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,5,8,6,7,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,6,8,3,7,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,6,2,3,1,4,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,8,2,3,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,4,7,5,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,8,6,7,1,4,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,2,7,4,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,3,2,4,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,3,1,8,2,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,8,1,3,2,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,5,3,8,6,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,3,8,1,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,2,5,8,1,3,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,2,4,3,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,4,3,8,1,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,7,4,8,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,5,3,2,8,7,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,3,8,5,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,8,2,6,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,2,8,1,4,5,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,3,8,4,1,5,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,4,2,3,1,5,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,3,4,1,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,6,2,4,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,8,1,4,3,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,5,8,1,3,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,8,1,5,2,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,6,3,1,5,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,2,8,4,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,6,3,8,1,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,4,5,6,8,1,3,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,6,8,1,4,5,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,1,8,4,6,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,2,5,3,6,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,5,1,8,6,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,8,6,1,5,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,4,1,8,6,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,5,8,1,6,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,7,8,5,6,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,7,1,3,5,8,4,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,8,6,4,5,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,8,1,7,4,5,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,8,6,5,1,4,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,2,5,8,6,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,4,6,8,1,3,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,4,5,8,6,1,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,3,6,2,5,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,2,6,4,8,5,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,1,8,5,6,4,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,1,5,7,4,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,7,8,1,6,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,6,2,3,5,8,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,1,2,4,8,5,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,8,5,6,4,3,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,8,4,5,1,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,5,7,8,1,3,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,8,6,4,7,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,6,5,1,4,2,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,1,7,2,3,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,3,6,4,2,1,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,4,5,7,1,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,4,5,8,2,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,5,7,4,1,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,1,7,4,5,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,3,2,1,7,8,4,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,1,5,7,8,3,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,3,6,7,1,4,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,8,3,5,2,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,6,5,7,1,3,4,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,8,6,4,2,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,3,8,5,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,6,5,3,8,4,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,2,3,5,1,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,5,3,4,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,5,3,4,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,5,3,4,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,4,8,1,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,3,4,8,7,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,5,3,4,8,7,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,3,8,4,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,8,1,4,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,5,8,1,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,6,5,4,8,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,5,4,8,2,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,2,4,8,7,6,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,4,6,1,5,7,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,5,3,6,8,4,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,3,6,4,1,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,2,5,1,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,5,3,1,7,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,6,3,1,7,5,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,3,6,5,8,4,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,5,1,7,6,4,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,3,1,7,4,8,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,3,1,8,6,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,5,1,3,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,3,7,4,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,3,7,6,4,1,5,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,6,3,7,4,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,8,7,4,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,6,3,8,4,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,8,3,1,6,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,4,8,2,5,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,3,1,6,5,4,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,2,3,1,6,4,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,3,5,2,7,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,3,5,4,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,1,6,4,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,3,6,4,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,7,4,8,5,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,3,1,7,5,4,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,3,8,4,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,2,3,1,4,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,2,3,1,4,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,1,4,2,6,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,1,6,3,5,4,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,1,7,3,6,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,7,3,2,5,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,6,2,5,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,8,5,2,6,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,1,3,6,4,2,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,2,5,7,4,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,7,4,6,3,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,3,6,2,5,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,7,1,4,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,7,3,6,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,1,3,7,2,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,1,3,8,2,5,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,1,3,8,2,5,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,2,5,3,6,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,5,3,6,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,3,1,6,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,3,4,1,2,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,8,3,6,5,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,2,4,8,3,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,8,4,7,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,1,5,7,8,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,6,7,8,3,2,5,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,2,1,7,6,5,3,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,7,5,1,4,6,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,7,5,6,2,4,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,8,5,2,3,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,7,4,1,5,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,2,7,3,1,4,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,4,1,3,6,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,2,5,3,7,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,4,7,5,1,3,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,4,6,5,7,1,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,7,5,2,3,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,7,4,5,3,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,4,7,5,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,6,2,7,5,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,4,2,5,3,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,2,6,7,8,5,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,2,7,4,5,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,4,7,8,5,3,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[6,7,4,5,2,8,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,3,6,4,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,2,1,7,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,4,1,8,7,5,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,7,8,6,5,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,2,7,8,6,4,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,8,1,2,6,5,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,5,1,2,4,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,1,6,2,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,7,1,3,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,6,3,2,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,1,5,3,4,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,7,1,2,3,8,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,1,7,5,2,3,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,4,1,6,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,1,8,3,2,6,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,2,4,8,3,7,5,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,3,4,2,5,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,5,1,6,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,1,4,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,6,8,4,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,8,5,7,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,3,8,5,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,1,4,6,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,3,7,4,8,6,5,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[5,6,7,3,1,4,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,6,1,3,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,7,5,1,3,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,5,8,1,4,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,8,7,2,3,1,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,8,1,5,3,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,3,1,7,6,5,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,6,5,2,7,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,1,6,5,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,4,3,6,8,2,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,8,5,4,7,6,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,6,8,7,3,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,6,5,1,3,8,7,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,4,6,2,1,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,5,4,1,2,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,8,1,4,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,8,1,4,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,7,5,8,6,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,5,7,6,3,4,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,2,6,1,4,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,4,5,1,8,3,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,8,5,3,4,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,5,3,1,7,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,5,6,4,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,3,5,2,6,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,1,8,5,6,7,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,7,6,1,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,6,2,8,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,7,6,4,1,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,5,7,8,4,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,5,2,4,7,3,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,3,1,8,5,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,4,3,5,8,1,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,5,3,1,6,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,7,6,1,5,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,2,7,6,4,3,8,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,4,7,6,8,1,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,6,8,1,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,1,7,6,4,5,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,7,6,8,5,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,5,6,3,4,1,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,2,1,5,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,7,2,3,8,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,6,8,7,1,5,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,7,8,4,5,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,5,8,7,4,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,3,5,8,7,4,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,7,8,6,4,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,6,4,1,8,3,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,4,1,8,6,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,3,7,8,1,2,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,5,8,1,7,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,4,2,7,8,3,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,3,5,8,1,6,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,8,7,3,6,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,2,5,4,7,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,1,5,7,4,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,8,4,5,7,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,4,5,8,7,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,4,5,8,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,1,5,4,2,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,6,1,8,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,5,6,3,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,6,8,7,4,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[2,5,8,1,3,6,7,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,8,2,6,1,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,3,1,4,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,7,8,3,4,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,3,7,4,1,5,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,3,7,8,1,5,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,5,8,1,3,7,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,2,6,7,8,3,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,8,5,6,3,4,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,2,7,8,3,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,4,2,8,3,5,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,7,8,5,3,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,8,6,3,5,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,6,1,4,5,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,7,3,8,1,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,8,4,1,2,5,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,8,4,3,1,5,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[8,4,5,1,6,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,7,8,4,1,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,7,5,8,4,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,3,1,6,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,7,2,8,1,4,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,8,5,1,4,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,6,7,1,8,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,5,3,6,4,2,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,3,7,4,8,5,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,7,8,5,4,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,3,8,5,4,2,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,7,8,1,2,5,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,6,1,2,5,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,8,6,1,5,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,8,7,4,6,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,1,4,8,7,3,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,1,8,7,5,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,3,7,6,2,4,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,8,2,7,4,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,2,7,1,6,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,3,2,8,1,7,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,4,1,6,3,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,6,5,3,2,4,8,7]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,7,3,5,2,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,7,2,5,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,4,3,2,6,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,1,3,5,4,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,3,7,5,4,2,6,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,5,4,6,2,7,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,1,4,5,2,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,1,7,6,4,8,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,6,8,7,5,2,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,2,4,8,5,6,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,3,4,8,7,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,5,4,8,2,3,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,6,3,7,8,4,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,6,1,8,5,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,3,5,6,8,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,3,6,2,5,4,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,8,7,3,6,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,8,6,2,5,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,7,6,3,1,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,7,5,1,3,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,7,3,1,5,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,4,1,8,7,3,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,5,8,1,6,7,4,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,3,2,5,4,6,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,4,7,5,3,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,5,1,8,7,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,6,1,5,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,1,8,4,5,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,8,7,6,4,2,3]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,1,4,5,3,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,4,2,3,8,1,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,1,4,8,3,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,3,8,6,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,6,4,2,8,5,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,5,3,1,8,4,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,3,6,7,5,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,2,3,5,7,4,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,4,6,3,5,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,3,8,6,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,2,4,7,5,3,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,8,2,4,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,3,8,4,7,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,1,8,3,5,2,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,1,5,2,4,7,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,5,7,1,4,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,5,8,1,4,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,3,8,6,2,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,4,8,5,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,3,8,4,7,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,4,7,5,1,3,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,3,4,8,5,6,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,2,3,5,1,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,1,5,8,7,4,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,2,1,4,8,7,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,8,3,5,4,7,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,3,6,1,5,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,4,8,1,6,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,4,6,7,2,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,5,6,1,7,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,2,4,7,5,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,2,7,1,8,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,1,4,6,5,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,2,7,4,5,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,2,3,8,5,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,8,5,6,7,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,4,5,6,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,4,6,7,5,2,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,1,4,7,5,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,1,5,7,6,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,4,2,5,7,8,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,3,2,7,6,1,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,2,6,5,3,1,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,8,7,1,5,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,3,1,8,7,6,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,1,7,3,5,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,7,6,4,3,5,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,7,2,5,3,4,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,5,3,7,6,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,7,2,3,8,1,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,2,5,3,7,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,4,8,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,8,5,6,4,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,5,8,7,4,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,8,1,7,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,5,3,8,6,4,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,5,6,2,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,3,4,6,2,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,3,5,6,2,8,7,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,5,4,7,3,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,6,8,3,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,2,1,5,4,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,5,6,3,4,2,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,4,3,5,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,1,5,3,6,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,6,4,8,1,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,1,6,3,7,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,1,4,7,2,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,1,3,2,6,4,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,4,7,3,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,5,6,3,4,1,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,4,6,2,1,7,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,2,4,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,7,3,4,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,5,6,8,3,1,4,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[8,5,6,2,7,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,5,1,2,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,3,5,2,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,3,4,7,8,5,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,8,1,4,2,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,8,4,6,5,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,3,8,5,1,4,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,7,4,1,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,4,8,6,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,1,4,3,8,6,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,1,2,7,6,3,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,3,2,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,5,4,3,1,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,3,5,1,8,7,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,4,5,6,1,7,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,2,6,5,7,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,6,3,5,1,2,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,3,7,1,6,8,4,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,2,4,5,3,7,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,4,3,5,6,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,1,5,6,2,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,6,3,8,7,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,8,1,4,5,3,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,2,8,7,3,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,5,6,3,8,7,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,1,2,4,3,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,7,8,1,2,4,6,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[8,4,3,1,2,6,5,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,8,2,7,4,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,6,2,3,5,4,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,2,6,1,3,5,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,3,7,2,5,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,1,7,4,5,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,4,5,1,7,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,2,4,5,1,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,8,1,7,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,3,7,1,5,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,4,7,2,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,3,7,6,4,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,7,3,6,1,2,5,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,7,6,2,4,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,2,3,6,1,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,8,4,2,3,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,4,7,3,1,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,8,1,4,7,3,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,5,7,2,6,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,2,7,3,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,2,6,7,5,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,4,1,7,5,6,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,4,7,6,5,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,7,6,4,5,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,2,3,6,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,4,7,3,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,7,6,4,5,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,2,7,6,4,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,4,7,3,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,5,1,8,7,3,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,1,5,3,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,2,1,8,7,3,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,4,8,5,2,7,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,8,2,4,7,5,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,8,4,7,5,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,1,7,5,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,4,7,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,1,7,3,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,2,3,5,6,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,7,2,3,5,6,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,6,2,3,5,7,4,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,5,2,3,7,6,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,6,2,3,5,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,6,2,3,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,2,3,7,6,4,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,2,3,5,4,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,3,8,6,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,3,8,6,2,1,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,3,6,8,5,4,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,6,8,1,4,2,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,8,2,7,3,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,1,3,8,4,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,2,3,7,4,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,2,8,3,7,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,2,4,7,6,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,3,6,2,8,5,4,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,6,4,8,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,3,6,7,5,2,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,3,6,1,8,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,7,4,6,2,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,1,8,7,4,6,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,8,3,7,2,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,1,3,4,7,2,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[8,4,2,6,3,5,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,3,1,4,6,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,7,1,2,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,3,7,2,1,8,6]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,2,7,5,1,3,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,1,6,7,3,5,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,2,8,7,4,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,7,8,5,2,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,3,1,6,7,2,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,5,3,8,6,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,5,2,4,3,8,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,2,4,3,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,2,8,5,1,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,2,3,8,6,5,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,8,4,3,7,5,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,6,8,4,3,2,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[6,4,2,3,7,1,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,5,8,7,1,3,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,4,7,8,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,1,3,6,5,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,1,8,2,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,4,8,1,5,6,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,4,1,6,7,3,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,5,2,8,4,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,6,3,5,2,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,8,6,3,7,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,5,8,1,3,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,3,5,1,8,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,3,1,5,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,4,8,6,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,4,8,6,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,2,5,4,8,6,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,4,5,8,2,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,4,3,5,2,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,5,4,8,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,4,8,2,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,4,5,1,2,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,5,1,8,6,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,5,4,8,1,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,8,5,6,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,8,5,6,2,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,4,8,1,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,3,1,5,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,6,2,5,4,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,1,7,4,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,3,1,5,7,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,8,1,7,2,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,4,1,2,7,5,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,1,5,6,4,2,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,7,1,5,2,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,8,2,1,6,5,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,4,1,5,7,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,5,1,3,6,4,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,1,5,4,6,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,3,4,1,6,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,3,7,8,2,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,2,1,5,4,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,6,4,3,5,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,3,7,8,2,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,7,8,2,6,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,5,6,2,8,3,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,1,6,5,3,8,7,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,1,7,4,6,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,4,1,5,7,6,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,3,1,6,2,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,1,3,7,6,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,1,4,2,8,7,5,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,3,2,8,7,5,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,7,8,6,2,4,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,3,8,5,4,7,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,4,2,7,6,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,7,8,1,3,5,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,7,5,1,4,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,6,8,2,1,4,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,7,5,6,4,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,1,3,7,4,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,2,5,3,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,1,3,2,7,4,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,6,1,3,5,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,5,8,3,6,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,4,5,2,6,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,4,3,7,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,6,7,5,8,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,1,3,6,5,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,1,4,7,5,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,3,4,6,5,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,8,6,4,5,2,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,8,6,2,3,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,8,5,3,7,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,5,7,2,8,6,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,7,4,5,1,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,6,8,1,2,5,7,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,6,8,5,1,3,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,7,4,5,2,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,8,4,6,1,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,7,2,1,6,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,1,6,8,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,5,4,6,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,7,4,5,2,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,2,6,5,3,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,5,8,4,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,2,6,3,4,1,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,5,8,2,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,8,3,5,6,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,8,7,4,2,3,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,3,1,8,5,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,2,4,8,1,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,7,2,4,5,8,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,2,7,4,6,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,2,4,6,1,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,4,6,2,1,3,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,7,2,4,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,1,8,4,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,8,7,6,2,3,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,2,5,4,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,3,8,7,1,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,2,4,1,3,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,6,8,5,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,2,3,4,1,6,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,8,7,5,4,2,1,6]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[3,6,4,8,5,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,6,2,1,4,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,6,5,8,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,4,8,6,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,3,1,6,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,3,8,1,6,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,1,4,2,7,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,1,2,7,6,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,7,4,1,5,3,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,1,7,5,8,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,1,2,8,5,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,5,1,4,3,8,7,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,1,2,7,5,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,8,1,4,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,1,6,5,8,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,4,5,3,8,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,7,8,6,3,1,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[6,2,4,3,5,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,5,8,1,7,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,2,3,8,4,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,3,5,8,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,5,4,8,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,8,7,4,6,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,7,6,3,1,8,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,7,6,2,5,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,3,2,5,7,1,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,6,3,1,5,8,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,4,1,6,8,3,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,6,2,4,5,8,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,6,4,5,8,3,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,4,8,6,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,7,1,3,6,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,3,5,2,8,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,5,8,7,4,2,3,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,7,2,4,5,8,6,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,4,6,8,7,2,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,6,2,7,5,3,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,7,2,6,4,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,3,2,8,5,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,5,2,4,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,7,3,8,4,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,2,4,7,5,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,2,7,4,3,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,8,2,3,6,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,5,3,6,7,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,4,1,5,7,2,3,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,6,2,1,4,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,1,5,7,3,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,5,3,6,7,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,5,7,3,4,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,2,7,3,8,5,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,1,6,3,2,7,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,1,6,3,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,5,6,2,4,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,5,1,4,2,3,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,6,1,4,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,5,7,4,3,8,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,7,8,4,2,1,5,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,4,1,3,6,2,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,5,2,1,4,7,3,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,6,2,3,7,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,2,3,7,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,2,3,7,5,4,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,6,2,3,1,5,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,5,8,3,2,7,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,4,3,1,7,6,5,2]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[1,2,7,6,5,3,4,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,7,6,4,5,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,8,7,6,4,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,2,8,7,5,3,4,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,6,5,3,4,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,2,7,4,5,3,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,2,6,7,5,3,4,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,2,7,5,4,3,6,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,2,6,8,7,4,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,2,8,6,7,4,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,5,2,1,6,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,1,3,5,8,4,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,2,4,8,1,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,1,3,7,5,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,6,8,1,3,4,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,5,6,7,3,4,2,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,6,7,1,4,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,8,1,4,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,6,8,5,2,1,7,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,6,7,8,2,4,5,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[5,7,8,3,2,4,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,5,4,1,8,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,5,4,1,8,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,1,8,4,2,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,8,2,3,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,8,2,3,5,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,8,2,5,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,8,2,5,3,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,8,2,6,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,6,7,8,2,5,4,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,7,8,2,5,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,2,7,8,6,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,5,3,4,7,1,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,4,7,3,6,5,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,4,7,3,6,5,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,1,3,6,5,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,5,3,4,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,3,5,8,7,2,6,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,5,7,4,6,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,4,1,8,5,7,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,3,8,7,5,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,8,1,4,7,5,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,5,8,2,1,4,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,1,6,7,2,4,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,8,5,7,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,6,7,2,1,5,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,8,4,3,5,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,1,7,6,2,5,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,5,6,1,3,8,7,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,8,1,3,5,7,6,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,1,5,4,6,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,3,2,6,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,1,4,5,2,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,2,5,6,1,3,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,2,6,3,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,3,5,7,1,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,3,5,2,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,6,5,2,4,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,6,4,5,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,3,5,7,1,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,5,4,7,1,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,6,8,1,7,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,5,8,2,7,3,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,5,7,2,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,7,4,2,5,8,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,7,2,6,5,3,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,8,4,1,5,7,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,5,1,7,2,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,1,6,2,3,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,1,2,6,5,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,1,3,5,6,4,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,3,6,4,5,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,2,5,3,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,4,2,8,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,8,5,3,6,4,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,4,5,8,3,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,6,5,8,4,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,1,6,5,4,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,5,7,3,2,1,8,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,5,8,1,6,4,3,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,1,2,5,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,6,7,3,1,4,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[7,2,5,6,1,4,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,5,1,3,2,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,8,6,7,2,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,8,3,6,4,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,5,7,1,3,4,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,8,7,3,2,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,3,4,8,2,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,8,7,3,6,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,5,6,2,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,5,6,2,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,6,3,7,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,7,1,2,5,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,7,6,8,3,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,5,2,7,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,7,4,5,2,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,4,2,8,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,5,8,2,7,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,7,4,5,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,8,4,5,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,8,2,7,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,8,4,7,5,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,3,6,2,7,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,7,8,2,6,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,2,6,8,4,5,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,6,5,8,4,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,5,6,8,2,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,6,5,8,7,4,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,4,6,8,5,2,1,7]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[1,7,8,4,3,6,5,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,7,8,3,6,5,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,4,5,8,7,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,8,1,7,2,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,7,8,3,1,2,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,3,4,6,8,1,2,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,6,4,5,8,1,2,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,4,1,3,7,5,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,7,1,6,4,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,8,5,4,2,3,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,1,6,4,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,4,8,7,2,5,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,1,7,2,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,6,8,4,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,5,8,3,2,4,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,7,3,8,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,4,1,3,2,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,5,6,2,3,8,7,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,3,5,2,1,6,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,8,3,4,7,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,5,1,6,3,8,7,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,2,7,6,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,2,7,5,8,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,5,4,7,2,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,6,4,7,1,8,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,3,7,1,8,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,1,7,3,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,4,7,1,8,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,5,1,7,6,8,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,5,7,4,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,7,1,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,6,4,7,3,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,6,5,7,3,8,2,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,8,2,4,5,6,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,5,3,7,6,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,7,6,4,2,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,3,7,4,2,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,4,2,7,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,5,1,3,7,4,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,6,1,8,3,4,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,4,2,7,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,3,2,7,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,8,2,4,7,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,6,7,1,4,8,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,7,4,2,3,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,7,3,2,4,6,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,1,3,2,5,8,6,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,3,2,6,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,1,4,6,8,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,1,4,8,3,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,2,3,6,4,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,4,3,2,8,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,4,1,7,5,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,5,1,3,2,7,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,1,3,5,2,8,7,6]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,5,8,6,3,7,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,2,7,4,1,8,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,4,6,8,1,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,1,7,8,3,4,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,7,8,5,1,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,3,2,5,8,4,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,3,5,8,4,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,4,3,7,6,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,2,7,6,3,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,5,4,2,7,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,5,1,7,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,6,2,5,7,3,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,7,8,2,6,3,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,2,7,6,8,5,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,6,1,7,8,5,3]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,3,8,2,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,7,3,6,4,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,7,2,4,8,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,2,8,4,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,1,4,6,3,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,3,6,2,8,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,3,5,8,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,1,6,8,4,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,6,4,1,8,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,1,5,8,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,4,1,7,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,7,6,5,8,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,4,7,8,6,2,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[2,3,8,4,5,6,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,8,4,5,7,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,3,5,7,2,1,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,3,5,7,2,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,3,8,4,7,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,1,7,6,5,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,8,3,2,6,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,5,1,6,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,7,4,3,5,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,2,8,3,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,7,5,6,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,2,6,8,4,3,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[7,2,6,3,1,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,1,3,7,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,4,6,5,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,8,4,1,7,3,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,3,5,8,4,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,4,2,1,6,8,5,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,2,8,4,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,3,5,6,4,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,4,7,1,5,6,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,8,2,6,5,3,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,7,2,5,6,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,6,4,7,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,5,2,3,1,6,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,8,6,3,5,1,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,2,6,4,1,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,1,5,3,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,6,2,5,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,6,5,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,7,4,2,5,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,2,5,1,4,7,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,5,3,2,6,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,6,4,1,3,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,1,3,5,2,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,6,4,7,1,3,5,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,3,5,7,2,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,8,6,2,1,4,7,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,5,3,1,4,6,2,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[6,8,4,3,2,1,7,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,1,8,5,4,3,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,6,4,8,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,8,5,3,2,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,1,8,5,4,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,8,5,3,2,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,8,5,4,2,6,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,4,2,6,3,8,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,8,5,6,2,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,8,6,2,7,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,5,6,3,2,8,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,6,5,7,3,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,2,8,6,7,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,6,3,8,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,5,4,6,2,7,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,7,5,6,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,8,5,7,3,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,5,4,7,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,7,1,8,5,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,4,8,1,2,6,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,2,5,6,7,1,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,5,7,3,4,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,3,5,6,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,2,4,7,8,1,3,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,8,5,6,1,2,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,6,8,7,1,4,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,7,8,5,4,6,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,8,1,5,2,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,2,5,3,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,3,4,8,7,2,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,8,7,1,5,2,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,3,7,6,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,6,4,2,7,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,1,3,6,7,2,4,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,1,4,7,5,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,1,7,4,6,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,2,3,6,4,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,3,7,5,8,6,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,7,5,2,8,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,6,4,8,2,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,2,7,8,3,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,1,5,3,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,6,2,8,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,7,3,5,8,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,5,8,6,4,7,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,2,8,1,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,8,4,5,1,3,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,8,1,6,2,5,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,5,3,7,4,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,7,3,4,1,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,7,6,3,4,1,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,1,3,7,4,2,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,2,7,3,4,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,5,3,1,8,4,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,6,5,2,4,3,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,2,5,3,7,4,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,4,2,6,3,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,3,2,6,4,7,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,4,6,5,8,2,3,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,6,5,8,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,6,4,8,2,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,5,4,8,2,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,6,8,4,5,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,6,5,7,4,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,5,7,4,2,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,3,5,7,1,8,6,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,4,5,1,8,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,2,7,4,8,5,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,5,6,3,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,6,7,4,8,5,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,6,7,4,8,5,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,8,5,1,3,6,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,8,2,5,3,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,3,6,2,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,1,3,7,2,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,3,4,8,5,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,3,4,8,5,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,3,4,8,5,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,4,8,2,5,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,5,4,6,8,1,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,8,6,4,3,7,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,4,2,5,7,1,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,7,5,4,6,8,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,4,7,3,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,4,5,7,3,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,8,4,5,3,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,4,6,2,8,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,4,6,3,2,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,4,5,3,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,5,4,2,8,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,7,6,4,8,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,3,4,2,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,5,8,2,3,6,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,2,4,6,5,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,6,1,5,3,7,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,3,5,4,7,8,1,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,7,4,6,8,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,8,1,5,3,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,5,7,1,2,4,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,6,4,1,3,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,1,3,5,7,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,6,2,5,1,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,2,7,5,8,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,8,5,2,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,5,3,2,1,8,6,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,5,8,1,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,1,6,8,5,2,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,5,2,8,6,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,2,8,6,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,8,6,2,4,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,1,6,4,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,4,5,8,6,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,5,2,1,3,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,3,6,8,5,1,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,5,1,3,2,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,5,8,6,1,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,4,5,8,6,1,2,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[6,8,5,2,4,7,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,7,8,1,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,7,6,1,5,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,3,1,2,5,4,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,1,2,5,4,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,2,6,4,1,3,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,5,8,2,4,3,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,8,2,5,3,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,2,5,3,1,4,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,6,3,1,4,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,6,4,1,5,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,7,4,1,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,7,3,1,5,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,2,7,3,1,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,3,7,4,1,2,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,7,8,2,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,4,7,8,3,6,5,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,4,7,8,3,6,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,1,3,2,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,8,5,7,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,6,2,7,3,4,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,2,7,3,4,5,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,3,2,8,7,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,6,7,8,3,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,5,6,3,7,2,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,6,7,4,2,3,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,1,6,7,3,4,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,1,7,3,4,5,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,8,5,1,7,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,5,2,3,1,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,7,3,2,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,5,1,7,3,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,2,7,3,8,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,2,6,7,1,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,7,8,3,6,5,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,5,1,8,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,2,6,8,7,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,3,6,8,4,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,4,2,3,7,5,8,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,7,5,1,2,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,5,4,8,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,3,8,7,4,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,2,8,4,6,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,5,8,1,2,7,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,4,3,6,8,5,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,6,2,8,5,3,4,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,8,3,5,4,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,7,5,1,6,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,7,1,4,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,2,5,6,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,1,5,6,3,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,7,1,6,3,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,7,1,5,6,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,3,1,8,7,4,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,7,3,6,1,2,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,7,2,6,1,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,5,8,1,6,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,6,5,7,2,3,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,7,2,5,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[5,3,6,7,4,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,2,7,8,3,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,2,7,8,5,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,4,3,7,8,1,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,5,7,8,4,2,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,6,7,3,2,8,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,5,3,7,8,1,2]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,2,4,7,8,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,6,3,2,8,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,2,8,3,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,4,8,1,6,5,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,2,4,8,6,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,6,4,8,7,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,7,8,6,5,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[3,4,2,5,8,1,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,2,6,7,8,1,4,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,2,4,7,8,1,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,4,7,1,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,3,1,7,8,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,1,6,5,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,7,6,2,3,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,2,7,5,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,7,6,5,1,8,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,2,4,6,5,8,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,8,7,1,6,4,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,7,8,6,4,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,8,5,6,3,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,4,2,3,1,7,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,5,1,7,6,3,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,3,5,1,4,8,7,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,5,1,8,7,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,5,8,1,7,4,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,7,1,2,4,8,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,7,8,1,2,3,6,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,5,1,4,3,8,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,7,8,3,5,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,7,8,4,2,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,7,8,3,6,1,2,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,3,2,6,5,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,1,4,3,7,6,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,8,6,1,7,2,3,4]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,1,4,8,2,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,3,7,2,6,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,2,6,3,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,4,3,8,2,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,7,5,6,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,6,7,5,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,5,4,7,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,8,7,3,6,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,8,6,1,4,5,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,7,8,2,1,5,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,7,6,3,8,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,7,4,3,6,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,2,6,4,3,7,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,7,1,4,8,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,8,1,4,6,2,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,8,4,6,3,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,8,3,4,6,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,5,3,8,7,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,3,5,2,6,8,7,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,7,5,6,2,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,5,8,4,7,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,7,4,8,5,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,7,5,1,6,3,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,6,2,3,5,1,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,4,6,7,3,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,6,7,8,2,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,6,3,4,1,2,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,5,8,4,6,1,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,7,8,6,5,1,3,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,5,7,3,6,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,6,7,3,5,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,4,6,3,5,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,4,6,7,3,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,8,4,7,3,5,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,5,8,3,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,4,7,3,5,6,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,8,7,3,2,6,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,6,4,2,8,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,2,6,5,3,7,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,7,3,5,8,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,1,3,6,8,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,7,2,3,5,4,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,8,3,5,4,1,2]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,8,7,3,6,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,7,3,6,4,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,1,7,6,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,3,4,7,6,5,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,4,7,6,1,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,2,4,1,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,8,7,4,2,3,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,4,8,6,2,1,7,5]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,4,6,2,1,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,3,1,6,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,7,3,1,6,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,2,4,3,1,8,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,1,2,7,5,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,4,6,2,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,8,6,2,1,7,4,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,8,2,4,6,5,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,7,6,2,5,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,5,4,3,7,6,1,2]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,8,1,3,6,7,5,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,5,8,6,1,7,4,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[8,1,4,7,5,2,6,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,4,8,6,7,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,6,7,8,5,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,7,8,6,4,1,5,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,6,7,1,3,4,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,6,1,5,7,2,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,5,1,2,7,3,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,2,7,6,3,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,3,7,6,1,2,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,8,7,3,5,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,8,3,7,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,1,6,5,2,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,2,4,5,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,1,3,4,2,6,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,2,1,5,3,7,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,8,5,3,2,7,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,8,1,3,7,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,5,3,1,7,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,5,3,1,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,8,7,2,4,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[5,7,8,6,4,2,3,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,8,7,5,1,3,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,2,6,7,5,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,6,3,8,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,4,1,8,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,6,8,3,2,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,6,4,2,8,1,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,3,4,8,6,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,3,4,8,7,1,2,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,7,5,3,6,8,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,4,8,7,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,4,8,1,6,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,7,4,6,8,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,5,7,8,1,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,5,7,8,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,4,7,8,6,1,2,5]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,1,4,7,8,6,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,1,5,7,6,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,7,6,8,1,2,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,5,8,1,6,3,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,4,6,8,2,5,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,8,7,5,2,6,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,3,5,8,1,6,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,8,4,6,3,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,5,6,4,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,1,8,2,4,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,5,3,8,1,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,8,3,7,5,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,5,8,1,6,7,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,8,7,6,2,4,5,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,4,2,5,8,1,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,4,8,5,7,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,2,4,7,1,5,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,4,7,2,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,5,1,8,6,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,1,3,2,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,1,3,4,2,7,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,3,4,5,1,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,1,6,5,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,1,4,5,3,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,1,5,3,6,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,1,5,6,3,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,6,1,7,4,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,5,6,4,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,8,3,5,1,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,4,8,5,7,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,3,6,7,1,2,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,3,1,4,6,2,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,2,5,3,1,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,3,6,1,2,7,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,3,1,7,2,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,3,5,4,7,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,3,5,2,7,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,3,6,7,4,8,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,2,6,4,5,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,1,4,7,6,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,2,7,6,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,6,5,4,8,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,2,3,7,8,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,4,2,5,7,8,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,2,5,4,6,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,2,7,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,3,4,6,1,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,8,5,1,2,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,7,4,8,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,1,6,8,7,2,5,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,7,1,8,2,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,5,8,4,1,7,6]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[7,2,4,1,3,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,3,5,2,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,7,1,5,3,8,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,6,5,2,3,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,5,7,2,8,4,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,3,8,5,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,8,2,3,1,6,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,3,4,1,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,2,7,3,5,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,6,1,8,4,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,7,2,4,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,7,6,8,2,5,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,7,1,4,5,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,3,7,1,8,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,4,6,2,5,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,1,6,8,3,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,7,3,5,8,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,7,1,6,3,5,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,2,3,6,5,1,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,8,1,5,7,6,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,1,2,5,7,6,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,7,2,6,1,3,5,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,2,6,1,5,3,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,2,5,8,6,4,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[7,1,3,8,2,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,8,3,6,7,1,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,8,5,4,7,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,6,1,3,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[5,2,6,7,1,4,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,4,1,5,7,6,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,5,3,4,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,4,8,3,1,5,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,3,4,1,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,1,6,2,5,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,8,4,3,5,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,5,8,1,6,7,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,7,2,5,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,2,6,5,3,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,1,7,4,3,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,6,8,3,5,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,8,3,4,5,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,2,6,4,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,4,6,5,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,5,8,2,4,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,1,8,2,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,1,8,5,3,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,4,6,8,2,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,1,3,7,2,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,4,6,1,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,8,4,6,1,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,7,3,2,5,1,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,2,7,1,4,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,1,4,2,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,5,4,1,6,2,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,7,2,8,3,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,5,1,7,6,2,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,6,7,3,1,8,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,3,6,2,7,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,2,6,5,3,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,2,7,1,8,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,6,5,3,2,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,3,6,7,1,8,5,4]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[3,6,1,2,7,8,5,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,5,1,8,7,6,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,4,5,2,7,6,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,1,3,6,7,5,2,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,1,4,5,7,6,2,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,5,1,3,6,8,7,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,5,1,2,4,3,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,5,8,1,4,2,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,8,5,7,1,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,2,4,6,3,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,6,1,4,2,3,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,1,2,7,8,4,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,8,1,2,5,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,8,4,7,5,2,3,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,4,7,2,1,6,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,8,2,1,6,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,4,2,5,3,6,1,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,1,6,7,5,2,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,2,5,3,6,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,8,1,5,3,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,7,5,2,6,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,4,6,3,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,5,3,6,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,3,6,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,5,4,6,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,8,2,5,6,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,8,5,4,6,7,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,8,7,3,1,6,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,5,2,6,1,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,2,4,7,1,6,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,5,6,8,3,4,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,8,6,7,3,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,5,2,6,7,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,6,5,7,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,5,3,7,4,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,2,4,1,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,2,4,1,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,3,2,1,7,4,6]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[6,8,3,2,4,1,5,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,2,4,1,5,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,3,5,6,4,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,5,2,4,1,7,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,6,1,7,5,4,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,5,1,3,2,8,4,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,4,8,3,2,6,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,3,4,2,5,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,8,4,2,7,5,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,1,7,4,3,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,3,2,7,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,4,6,3,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,1,7,2,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,1,8,2,5,4,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,1,7,2,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,4,1,6,7,3,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,8,2,3,7,1,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,4,3,1,5,8,2,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,8,4,2,1,6,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,7,1,2,5,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,7,4,1,2,8,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,6,7,8,2,5,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,6,4,1,2,5,3,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,4,2,8,1,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,7,2,1,6,5,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,3,8,2,5,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,7,1,3,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,7,2,6,4,5,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,6,1,7,4,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,3,1,7,4,5,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,7,8,6,4,5,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,2,8,4,3,6,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,8,6,4,5,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,3,5,8,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,5,4,8,6,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,3,4,7,6,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,2,8,5,6,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,5,1,8,6,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,3,2,8,5,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,7,3,2,5,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[7,3,8,6,4,2,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,4,2,8,5,7,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,6,2,1,7,3,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,4,2,8,6,7,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,6,3,2,7,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,5,3,6,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,6,3,5,2,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,6,3,2,7,1,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,7,6,3,2,4,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,3,2,8,6,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,4,3,7,1,8,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,5,8,2,7,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,1,8,3,7,6,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,1,6,8,4,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,1,6,8,2,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,1,7,8,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,1,3,8,4,7,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,6,3,7,2,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,8,4,6,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,3,8,1,5,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,2,1,6,3,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,6,1,5,7,2,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,3,7,1,6,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,1,6,7,2,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,3,1,5,7,2,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,1,5,8,4,2,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,5,1,4,8,6,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,4,1,3,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,4,1,3,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,1,4,8,6,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,2,1,8,4,6,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,2,1,3,7,4,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[8,4,1,2,6,5,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,5,2,1,3,7,6,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,8,1,5,2,3,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,2,8,1,6,4,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,3,1,4,7,6,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,2,3,1,7,6,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,2,1,3,7,6,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,3,1,5,8,4,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,2,7,4,1,5,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,4,6,1,3,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,2,7,4,1,6,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,1,5,4,8,6,3,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,1,2,8,6,3,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,8,4,3,6,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,8,4,1,6,5,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,5,4,6,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,6,4,1,5,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,6,4,8,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,2,7,6,3,4,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,2,8,3,5,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,5,2,4,1,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,2,4,8,6,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,1,8,5,4,6,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,6,5,4,2,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,1,4,8,2,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,2,6,5,1,4,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,8,4,2,3,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,1,5,4,7,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,3,1,5,4,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,7,6,4,5,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,5,6,4,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,5,2,8,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,4,6,2,5,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,2,3,6,4,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,8,1,7,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,8,2,7,4,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,4,5,7,2,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,8,3,7,1,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,8,1,5,7,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,8,2,6,4,1,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,8,1,5,7,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,3,7,1,4,5,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,7,1,4,5,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,7,2,6,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,8,3,1,6,7,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,5,6,8,2,1,7,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,5,6,8,1,3,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,5,8,3,2,1,7,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,7,3,2,1,6,5,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,8,3,5,1,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,1,3,5,6,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,8,3,2,1,6,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,6,3,7,8,1,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,1,4,3,6,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,3,7,1,5,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,8,1,5,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,3,4,5,2,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,4,2,5,3,7,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,5,1,3,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,5,1,3,8,6,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,6,2,1,8,7,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,5,3,6,4,2,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[1,3,6,7,5,2,4,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,5,2,6,8,7,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,4,1,3,2,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,5,2,4,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,7,2,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,5,8,1,4,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,6,5,3,4,1,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,3,6,5,4,1,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,7,3,5,4,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,7,8,6,1,2,3]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,2,4,5,3,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,2,4,5,8,1,3,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,7,3,1,2,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,2,5,8,1,3,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,2,5,1,7,8,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,4,3,1,2,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,2,3,7,6,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,2,3,4,1,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,6,2,3,8,4,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,2,3,1,4,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,2,8,7,3,5,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,8,5,2,6,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,4,1,6,3,2,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,6,3,2,5,8,7,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,1,6,4,3,2,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,3,2,7,5,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,4,3,2,6,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,3,6,5,2,4,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,3,2,7,1,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,7,4,8,6,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,1,5,7,3,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,5,4,7,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,1,8,3,2,5,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,6,2,3,1,8,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,3,5,1,7,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,7,3,4,1,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,2,7,8,6,4,3,5]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,7,8,6,2,1,3,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[8,6,7,1,5,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,5,1,7,8,6,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,2,4,1,7,6,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,1,8,6,7,4,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,6,2,4,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,6,8,5,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,5,6,4,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,1,5,6,3,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,7,1,3,4,8,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,5,6,1,3,7,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,3,4,8,7,6,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,4,3,8,1,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,4,6,5,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,7,6,2,1,8,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,5,7,6,1,8,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,8,7,2,3,1,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,6,8,1,2,4,3,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,1,2,4,3,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,4,7,6,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,8,5,3,7,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,2,8,3,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,5,4,7,1,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,6,5,8,1,2,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,6,7,5,1,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,4,6,7,5,1,2,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,5,6,7,3,4,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,3,5,7,6,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,3,5,7,1,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,2,5,8,7,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[2,5,4,3,8,7,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,6,4,1,8,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,4,7,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,3,2,7,1,8,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,6,2,5,7,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,6,7,3,1,8,4]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,5,7,1,3,6,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,7,8,3,6,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,3,1,6,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,8,6,2,1,3,4]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[4,1,8,2,5,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,2,3,1,5,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,8,1,6,2,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,4,3,8,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,4,3,7,2,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,5,3,8,7,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,4,2,7,3,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,4,2,5,8,6,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,2,7,5,4,3,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,8,7,1,5,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,2,1,5,7,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,7,1,6,3,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,2,5,1,6,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,1,2,4,6,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,1,7,3,6,4,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,7,5,6,1,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,1,6,4,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,1,7,5,4,2,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,2,8,7,3,4,5,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,4,8,5,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,6,8,4,5,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,6,2,8,3,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,3,4,8,5,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,3,1,6,8,2,7,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,4,7,5,6,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,7,8,2,3,6,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,4,7,2,6,8,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,6,5,2,8,4,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,1,2,8,4,5,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,7,2,8,5,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,5,7,1,2,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,6,2,5,4,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,6,8,4,2,7,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[1,6,5,8,2,7,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,4,8,3,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,2,8,3,6,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,2,3,8,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,2,8,4,7,3,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,7,2,5,3,8,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,5,6,8,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,4,7,5,1,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,4,8,3,7,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,6,8,3,5,4,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,1,4,8,6,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,3,4,1,5,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,3,5,8,4,6,2,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,2,4,8,3,1,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,7,3,5,4,1,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,7,5,3,1,6,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,8,4,1,7,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,5,1,8,6,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,5,6,2,8,7,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,3,1,2,7,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,8,3,6,4,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,8,4,7,6,2,1,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,3,7,6,2,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,1,5,7,6,3,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,8,6,7,5,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,8,6,1,7,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,6,1,2,7,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,5,3,1,7,6,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,3,2,6,1,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,7,1,3,8,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,4,8,3,1,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,8,4,2,7,6,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,8,4,2,7,6,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,8,1,5,2,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,8,2,3,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,1,5,8,3,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,3,7,8,2,4,6,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,7,8,1,3,4,6,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[8,1,6,3,5,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,1,2,5,3,6,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,5,3,6,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,7,4,6,3,1,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,1,5,3,7,6,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,8,1,3,4,7,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,3,5,7,6,1,4,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,6,8,2,5,4,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,2,3,6,4,7,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,4,8,7,3,5,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,6,1,3,8,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,6,1,2,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,2,7,8,3,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,4,5,3,7,1,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,2,4,5,7,1,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,5,1,8,3,7,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,1,4,3,8,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,6,3,8,2,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,5,7,2,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,8,2,6,7,4,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,4,8,7,6,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,4,1,8,5,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,4,3,5,8,6,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,2,8,5,6,1,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,3,5,7,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,2,6,1,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,7,3,5,2,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,8,5,3,2,1,7,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[6,2,4,1,7,8,3,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,7,3,2,1,5,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,6,7,3,2,1,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,8,3,2,6,7,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,1,6,4,8,5,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,1,3,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,7,5,3,6,2,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,1,5,4,7,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,8,1,3,4,2,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,1,3,5,2,4,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,3,5,8,7,2,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,2,5,7,8,1,3,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,3,6,2,5,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,8,4,6,3,5,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,1,3,6,2,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,8,1,4,7,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,1,4,7,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,5,3,6,8,1,4,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,5,7,1,3,6,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,8,3,5,7,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,7,2,5,3,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,5,1,3,8,2,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,1,5,3,2,7,6,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,5,1,4,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,2,1,7,4,3,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,4,3,6,7,1,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,3,5,2,1,6,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,6,1,4,3,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,1,5,3,7,2,4,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,5,4,1,7,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,7,5,4,2,1,3]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1]=>0
[1,6,8,7,3,2,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[8,7,5,4,6,1,3,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,7,8,2,4,6,3,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,5,4,8,1,3,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,1,8,4,3,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,2,6,7,5,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,7,5,1,6,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,3,6,2,8,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,5,4,2,7,3,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,4,3,7,6,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,1,8,3,4,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,8,3,5,7,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,4,7,6,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,2,6,7,5,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,6,1,4,8,3,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,4,3,6,2,8,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,2,7,4,3,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,5,3,6,4,2,7,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,2,8,5,3,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,2,1,6,5,4,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,2,6,1,4,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,8,1,6,5,3,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,3,2,1,8,7,4,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,8,5,3,2,7,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,8,7,2,5,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,8,1,6,2,5,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,1,4,2,7,6,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,2,8,1,7,5,4,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,8,2,7,3,4,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,5,8,2,6,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,2,1,4,7,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[8,2,5,7,6,3,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,8,7,3,4,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,1,5,7,6,3,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,8,6,5,7,3,4,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,6,3,7,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,6,5,7,3,2,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,6,4,1,2,8,3,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,6,4,5,2,8,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,3,6,5,7,2,4,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,6,5,7,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,3,7,1,8,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,3,5,6,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,8,3,5,6,2,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,6,7,2,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,8,1,4,3,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,7,8,1,5,2,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,8,6,2,4,5,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,6,8,5,1,3,4,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,6,7,1,4,5,8,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,6,8,1,4,5,7,2]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[1,8,5,6,3,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,4,6,3,7,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,4,7,8,3,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,4,7,8,3,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,8,5,7,3,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,2,4,7,8,3,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,4,7,8,3,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,8,6,1,2,7,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,1,5,6,2,3,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,6,1,5,8,7,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,8,5,3,7,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,4,3,7,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,4,1,7,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,7,8,2,5,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,4,6,2,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,1,4,5,8,6,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[1,7,4,5,6,8,3,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,7,4,5,6,8,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,7,4,3,1,6,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,4,1,6,3,8,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,4,7,8,3,1,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,4,3,6,8,1,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,4,6,2,5,8,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,7,4,5,8,1,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,3,5,6,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,6,5,8,2,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,6,1,7,3,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,3,6,4,2,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,3,5,1,2,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,3,5,2,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,8,4,7,5,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,7,3,1,5,2,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,7,1,5,6,4,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,7,3,6,1,4,5,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,1,4,6,3,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,3,7,1,5,6,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,6,7,1,5,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,2,1,3,7,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,2,3,6,7,5,4,1]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[8,7,3,6,2,4,5,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,8,7,1,3,5,4,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,1,6,8,2,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,5,8,2,3,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,8,2,4,5,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,8,2,3,4,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,2,3,8,7,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,1,2,8,7,3,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,5,7,2,3,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,5,4,6,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,7,5,3,6,8,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,1,7,5,2,6,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,1,6,2,4,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,1,8,2,7,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,5,1,7,6,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,1,3,2,6,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,5,7,6,2,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,7,3,6,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,6,4,8,3,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,3,7,5,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,6,2,1,3,7,4,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,8,3,5,6,1,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,2,5,3,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,1,2,4,7,3,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,2,3,6,8,5,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,7,3,2,6,5,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,7,8,2,1,6,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,8,7,2,1,5,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,3,8,2,5,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,3,8,6,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,3,5,8,4,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,8,4,5,1,2,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,7,5,1,2,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,8,4,6,1,3,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,7,5,1,3,6,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,5,3,6,8,1,2,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,8,6,2,1,4,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,6,3,1,2,5,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,6,4,1,5,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,8,3,1,4,7,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,1,8,5,2,6,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,4,1,5,8,2,3]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,1,2,5,8,7,6,4]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,2,8,4,7,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,6,4,8,3,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,6,8,5,2,3,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,4,5,7,2,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,7,1,3,2,6,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,1,3,6,5,7,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,5,7,2,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,8,2,4,6,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,2,1,4,5,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,2,7,3,6,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,5,8,6,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,4,8,7,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,2,4,6,7,3,1,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,7,1,3,5,8,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,3,1,2,6,5,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,5,1,7,3,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,5,1,4,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,4,1,5,8,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,4,8,3,5,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,2,4,3,6,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,4,5,8,3,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,5,8,1,2,4,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,2,4,3,6,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,8,1,4,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,3,4,6,8,7,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,7,1,6,3,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,5,2,1,6,7,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,1,5,2,8,7,4,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,1,5,8,7,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,4,1,2,6,3,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,2,5,1,4,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,1,4,7,5,3,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,5,2,1,7,3,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,1,2,8,4,7,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,6,7,1,3,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,1,3,8,5,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,1,4,3,8,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,1,2,4,3,7,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,5,1,8,6,3,2,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,6,3,1,2,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,8,6,4,1,5,7,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,7,1,4,5,2,3,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[3,8,6,4,5,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,7,6,4,5,1,2,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,4,6,3,1,2,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,6,2,5,7,8,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,6,3,5,7,1,2,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,3,5,8,6,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,8,3,5,7,1,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,3,5,6,1,2,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,2,5,6,8,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,8,2,5,6,7,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,7,2,6,5,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,7,2,6,4,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,4,6,1,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,6,2,1,8,3,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,2,7,8,3,5,4,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,1,4,5,8,2,3,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,7,6,2,8,5,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,2,7,8,3,4,6,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,7,6,8,3,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,2,5,8,4,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,1,4,5,8,3,2,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,4,1,7,8,6,5,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,4,8,6,5,7,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,1,3,4,8,2,7,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,7,3,6,1,4,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,5,1,8,3,4,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,2,1,5,6,4,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,7,2,4,6,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,1,5,6,3,8,7,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,7,5,8,6,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,5,3,8,1,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,5,4,3,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,3,7,1,6,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,7,3,1,2,6,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,8,7,3,5,2,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,1,6,2,5,7,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,8,3,6,5,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,2,1,8,6,5,7,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,7,8,5,2,1,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,1,8,2,6,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,3,6,1,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,4,7,3,5,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,8,3,5,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,3,8,4,6,5,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,1,8,6,5,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,2,8,6,5,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,8,2,6,5,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,3,8,4,6,5,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,8,5,1,6,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,8,5,2,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[4,7,2,1,8,6,5,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,6,2,8,4,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,2,4,8,6,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,2,4,8,5,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,3,2,8,5,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,3,1,8,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,8,3,5,6,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,2,3,8,4,6,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,3,4,8,5,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,7,3,8,5,4,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,8,4,5,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,8,6,4,3,1,7,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,7,3,4,8,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,5,8,3,4,6,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,8,4,2,5,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,7,6,2,3,8,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,8,4,6,7,2,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,7,4,5,1,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,2,3,7,8,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[6,7,1,2,4,8,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,5,6,2,1,8,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,2,4,8,5,6,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,4,6,2,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,1,7,4,5,2,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,3,4,8,1,2,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,1,6,4,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,8,6,7,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,3,4,8,6,2,5,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,7,8,4,5,6,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,6,3,5,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,6,3,7,5,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,4,5,8,1,3,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,7,8,6,4,2,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,2,5,8,4,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,6,8,7,5,1,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,1,5,7,4,8,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,4,6,1,5,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,7,1,6,4,2,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,6,3,5,1,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,3,6,2,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,6,3,2,5,8,7]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,3,6,5,8,2,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,6,3,2,8,5,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,4,1,5,7,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,6,7,4,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,5,6,4,1,7,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,3,1,6,4,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,2,6,3,1,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,8,1,6,3,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,1,4,6,2,5,7,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,5,8,1,6,2,7,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,2,6,8,1,4,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,3,8,2,1,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,7,4,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,3,6,4,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,7,3,1,5,8,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,3,5,4,1,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,7,4,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,1,4,8,5,3,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,7,3,8,4,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,1,5,4,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,3,1,5,4,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,5,8,3,4,7,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,3,8,1,4,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,8,1,3,6,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,4,6,5,2,8,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,3,8,5,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,3,7,2,8,6,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,6,3,1,7,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,6,3,1,8,5,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,7,2,5,3,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,6,3,2,8,7,4,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,1,7,5,4,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,3,1,5,7,2,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,6,1,3,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,7,4,2,6,5,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,3,6,1,8,5,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,4,8,7,1,3,6,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,8,6,2,5,7,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,1,3,6,4,2,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,8,2,5,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,5,7,1,6,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,3,1,5,2,8,7,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,6,4,2,5,3,8,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,7,6,8,5,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,7,6,8,5,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,5,1,2,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,7,5,8,2,6,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,1,8,7,6,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,4,6,1,8,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,7,1,5,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,6,4,2,8,1,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,3,7,8,1,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,4,6,7,1,5,3,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,4,3,1,8,6,7,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,4,3,6,1,7,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,7,5,8,1,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,2,7,8,5,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,8,3,2,1,7,5,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,1,2,6,4,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,8,4,5,6,3,2,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,4,3,6,1,8,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,7,6,1,5,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,4,7,6,3,5,8,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,6,7,3,4,5,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[4,7,6,5,1,8,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,4,6,5,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,4,7,8,3,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,6,5,4,8,7,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,6,5,8,7,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,5,1,7,4,6,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,4,8,1,6,7,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,7,8,4,1,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,3,7,8,4,6,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,3,7,8,4,6,2,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,1,7,8,4,6,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,8,1,6,7,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,8,7,3,6,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,4,3,7,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,1,8,3,7,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,4,8,3,6,7,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,6,5,8,7,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,6,4,8,7,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,6,8,3,5,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,8,6,5,3,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,8,3,7,6,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,4,7,1,3,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,3,4,5,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,1,4,5,6,2,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,6,1,4,5,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,8,2,4,5,1,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,2,1,5,6,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,8,1,5,4,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,4,6,3,5,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,3,6,5,7,2,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,7,4,6,2,5,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,2,5,6,4,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,8,5,4,3,7,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,5,7,8,4,3,1,6]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[6,8,5,3,2,4,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,8,5,3,2,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,6,1,8,7,5,3,2]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[1,4,7,8,3,2,6,5]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,8,5,1,2,7,6,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,3,7,6,8,5,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,8,1,7,2,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,7,8,3,1,2,5,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,1,2,7,5,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,1,7,6,8,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,7,6,8,5,3,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,1,7,8,6,5,2,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,3,7,6,5,8,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,4,8,3,5,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,7,8,5,2,3,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,3,1,7,8,6,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,1,7,8,6,5,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,5,2,6,7,8,1,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,6,2,1,7,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,3,1,8,5,2,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,7,1,8,3,2,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,3,2,7,8,4,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,7,6,2,3,8,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,5,2,8,7,3,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,1,3,7,6,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,3,8,6,4,5,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,5,4,3,8,6,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,4,5,8,2,3,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,3,7,5,8,4,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,2,5,4,3,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,4,5,6,2,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,7,5,6,4,2,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,7,6,4,2,3,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,5,6,2,4,3,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,2,5,7,4,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,1,5,3,4,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,5,4,1,6,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,5,7,1,6,4,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,5,6,1,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,5,6,3,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,1,3,7,8,2,6,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,6,2,7,8,5,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,8,1,2,7,6,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,6,7,4,5,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,7,5,6,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,2,6,3,5,4,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,5,6,2,4,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,7,3,5,4,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,2,6,7,5,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,4,5,3,2,8,6,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,2,4,6,5,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,2,1,5,4,8,6,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,3,5,4,2,8,6,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,2,7,6,4,3,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,3,7,4,5,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,5,7,3,2,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,7,1,5,3,4,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,1,5,2,4,3,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,6,4,3,1,5,2,7]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[7,2,1,6,4,3,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,7,2,6,4,3,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,2,3,1,7,6,4]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,2,5,4,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,2,1,3,7,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,6,1,3,4,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,7,1,8,2,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,7,8,2,3,5,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,8,7,2,3,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[8,5,6,3,1,4,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,1,6,2,4,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,6,2,3,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,4,6,2,3,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,3,2,6,5,7,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,2,6,5,7,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,8,1,2,6,4,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,2,7,8,1,5,3,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,6,5,8,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,7,1,5,8,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,6,8,7,1,3,4]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,8,1,3,4,6,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,8,4,5,7,6,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,8,3,4,6,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,5,3,4,1,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,5,6,4,7,8,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,8,4,5,7,6,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,2,4,8,7,5,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[2,5,4,8,6,1,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,4,7,1,8,6,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,8,6,5,2,7,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[1,8,6,2,7,4,3,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,3,4,8,6,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,2,6,4,1,8,5,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,8,6,5,3,7,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,7,2,8,6,5,4,3]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,4,2,7,5,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,7,4,2,1,6,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[7,2,4,5,1,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,4,1,8,5,3,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,7,4,3,5,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,3,4,8,2,6,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,7,3,4,6,5,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,2,7,1,4,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,8,2,4,5,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,7,2,3,8,6,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,4,1,8,3,7,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,5,8,7,3,6,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,5,4,1,7,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,5,6,1,7,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,7,2,1,5,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,7,3,5,4,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,1,7,3,8,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,2,7,5,4,3,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,8,6,2,5,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,1,8,3,7,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,8,3,7,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,1,6,3,7,5,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,6,5,3,7,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,4,6,5,3,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,8,6,3,7,5,4,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,7,5,8,6,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[8,3,6,5,4,2,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,4,5,1,7,6,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,2,3,5,7,1,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,3,4,2,7,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,3,5,7,2,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,3,6,7,2,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,3,6,7,4,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,2,4,6,7,1,8,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,8,1,5,6,4,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,6,8,3,4,7,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,1,5,7,4,3,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,8,3,4,7,5,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,3,7,4,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,2,4,7,5,6,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,6,7,5,8,4,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,7,5,8,4,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,3,1,6,5,2,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,4,1,6,5,2,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,8,3,1,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,2,8,1,5,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,4,2,8,6,5,3,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[6,8,4,7,3,2,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,7,3,2,1,6,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,7,2,6,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[6,8,7,3,5,1,4,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,2,5,8,6,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,6,4,8,7,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,5,6,8,3,4,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,2,5,7,8,3,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,6,5,7,8,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,3,6,8,2,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,7,2,3,5,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,8,6,7,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,2,7,3,1,6,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,6,4,2,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,5,2,7,3,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,3,1,8,5,2,7]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,4,8,6,5,3,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,8,5,2,6,7,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,3,2,1,8,5,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,5,7,2,4,3,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,2,7,5,8,4,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,3,8,2,7,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,1,3,2,8,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,1,6,3,2,8,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,7,2,3,6,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,1,2,6,4,3,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,4,7,8,3,2,5,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[8,7,1,3,2,4,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,1,6,3,2,4,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,8,2,7,6,3,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,6,3,2,7,4,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,8,4,3,5,1,2,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,3,8,5,7,2,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,7,4,6,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,7,2,3,5,1,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,6,3,4,1,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,5,2,8,1,4,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,3,1,7,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,2,3,1,4,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,8,3,6,5,1,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,7,4,2,6,5,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,7,6,5,2,3,1,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,6,1,2,5,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,1,3,8,7,6,4]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,7,3,4,8,1,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,6,1,3,8,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,7,6,2,3,1,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,4,2,6,8,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,1,6,4,8,7,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,6,4,3,8,1,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,1,5,3,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,7,6,1,3,2,8,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,1,3,5,6,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,6,3,4,7,8,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,6,3,1,8,5,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,6,3,8,1,5,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,6,4,7,8,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,2,5,8,6,1,3,4]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,6,4,2,7,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,7,3,8,1,4,2,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,1,3,6,2,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,4,6,3,2,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,5,6,4,7,8,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,3,5,2,1,7,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,1,5,3,2,7,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,5,2,8,7,4,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,1,8,6,3,2,5]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,7,4,1,5,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,3,5,1,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,5,8,6,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,4,7,8,3,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,6,1,3,4,8,7,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,6,1,3,8,2,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,1,6,4,7,8,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,7,8,1,3,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,7,2,3,8,4,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,4,7,5,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,3,4,8,2,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,3,4,8,5,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,7,8,1,5,4,3,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,5,6,2,8,7,3]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[7,3,4,8,1,5,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,2,6,8,7,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[1,8,3,7,5,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,3,6,5,2,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,3,8,5,2,6,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,7,1,5,2,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,1,5,2,6,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,1,6,7,5,2,8,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,6,2,4,5,1,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,7,5,2,1,4,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,4,5,2,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,1,6,2,3,8,7,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,7,4,2,8,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,4,2,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,1,8,2,3,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,2,1,7,6,3,8,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,3,1,8,7,6,2,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[4,3,1,6,2,8,7,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,3,1,8,7,2,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[4,1,7,5,2,8,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,6,5,2,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,7,6,5,2,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,2,1,7,3,8,6]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,4,1,6,2,8,7,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,5,6,4,2,8,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,4,6,3,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,3,5,4,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,2,4,5,1,7,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,6,1,5,7,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,6,2,3,4,8,7,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,5,6,2,3,8,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,5,4,6,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,1,5,6,2,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,1,4,7,3,2,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,4,5,3,6,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,3,1,6,7,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,8,4,7,3,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,4,8,3,2,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,5,7,6,3,8,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,6,3,1,7,8,4,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,1,7,8,3,5,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,8,6,7,4,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,7,1,3,5,2,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,7,8,2,5,4,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,6,5,8,1,3,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,8,6,2,1,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,8,6,3,2,1,7,5]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,1,4,7,6,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,6,4,7,1,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,7,4,6,1,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,5,7,8,6,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,6,7,1,5,4,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,6,4,7,5,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,4,5,3,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,7,4,1,8,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,5,3,7,8,1,4,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,5,6,7,3,8,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[6,5,7,3,1,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,1,5,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,7,4,2,1,8,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,3,4,7,8,2,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,6,1,8,2,5,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,8,3,7,4,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[3,2,6,1,8,5,4,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,3,1,4,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,3,8,4,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,2,8,4,5,1,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,1,3,5,2,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,6,8,2,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,4,8,2,5,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,7,4,5,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,4,3,5,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,4,8,5,2,3,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,1,8,4,5,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,8,5,4,3,1,6]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[5,3,7,1,4,6,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,1,5,4,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,3,7,4,8,1,5,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,4,6,8,2,5,1,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[3,7,2,5,4,6,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,6,5,7,4,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,6,5,2,8,7,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,1,7,2,5,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,7,5,2,8,6,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,2,5,8,6,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,5,1,7,2,8,6,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,3,1,8,7,5,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[2,8,5,3,6,7,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,3,5,2,6,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,8,6,3,4,7,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,6,4,7,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,2,3,8,7,1,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,6,4,1,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,7,2,5,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,4,3,6,8,2,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,6,1,7,5,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,8,6,3,5,4,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,1,8,6,3,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,3,5,4,1,8,7,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,6,3,5,1,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,1,2,4,3,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,1,5,4,8,7,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,5,8,4,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,2,1,8,5,4,6,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,6,3,7,5,4,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,3,8,5,4,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,8,2,7,3,4,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,1,6,3,5,4,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,8,7,3,5,1,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,8,7,1,6,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,2,4,7,3,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,6,7,2,5,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,1,7,8,2,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,1,7,4,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,5,7,1,3,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,2,7,6,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,4,1,6,2,8,7,5]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,2,6,1,8,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,6,7,4,3,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,5,1,6,4,3,2,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,6,3,5,2,7,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,4,6,2,1,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,2,1,6,4,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,7,2,8,5,4,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,7,1,4,8,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,1,7,3,2,8,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,5,2,4,7,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,3,7,8,6,1,5,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,2,6,3,7,8,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[6,1,3,7,8,5,4,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,3,5,7,8,2,1,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[8,2,7,6,3,5,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,7,3,5,8,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,4,1,7,5,8,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,5,1,4,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,6,5,2,3,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,7,1,3,2,8,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,5,8,3,4,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,4,7,6,1,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,8,4,7,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,5,1,4,3,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,4,7,5,3,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,2,5,7,3,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,3,4,2,8,7,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,3,7,2,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,5,1,8,6,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,6,1,8,7,2,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,6,2,8,7,1,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,2,6,7,8,5,1,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,3,8,6,7,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,5,1,6,8,7,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[2,8,3,4,5,6,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,8,6,1,5,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,2,8,1,5,6,4,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,4,7,6,8,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,8,1,3,7,5,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,7,2,5,6,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,3,6,4,7,8,1,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,3,7,4,5,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,7,1,5,8,2,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,2,7,1,5,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,6,3,5,1,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,1,6,2,5,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,2,5,7,3,4,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,4,6,3,8,5,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,5,6,3,1,7,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,4,6,2,5,1,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,6,5,8,2,3,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,4,8,3,7,6,2,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,5,3,7,2,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,5,7,2,1,8,4,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,7,3,8,6,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,4,7,8,3,6,1,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,5,7,6,8,3,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,5,7,6,8,3,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,3,4,8,5,2,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,3,5,4,8,1,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,3,6,5,4,7,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,8,3,5,4,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,7,1,3,5,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,6,8,2,7,1,3,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,7,1,5,4,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,5,4,7,1,8,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,3,1,6,5,4,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,1,6,7,2,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[1,6,8,5,3,4,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,3,6,8,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,6,4,7,1,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,1,3,8,4,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,3,6,8,4,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,8,4,6,5,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,4,8,5,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,3,1,6,8,4,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,8,4,5,1,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[8,4,5,1,6,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,7,5,6,8,2,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,4,7,8,5,2,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,5,8,6,1,7,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,8,6,3,7,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,7,2,8,6,5,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[2,8,1,5,7,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,3,8,4,7,5,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,4,1,2,5,3,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[4,1,3,5,2,8,6,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,3,1,6,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,7,3,5,4,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,4,2,1,6,5,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,7,5,4,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[2,7,3,1,4,6,5,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,1,8,7,2,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,5,3,1,7,6,4,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,3,1,2,7,6,4,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,5,1,3,6,2,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,4,1,3,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,4,2,3,6,5,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,3,1,4,8,5,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,5,4,8,7,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,4,3,1,7,5,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,1,7,5,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,7,2,8,4,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,8,7,2,3,6,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,8,7,5,2,6,3,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,7,4,5,6,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,8,7,3,6,4,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,4,7,5,8,2,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,4,7,2,3,6,5,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,7,2,5,6,3,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,6,5,8,3,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[1,5,8,2,6,3,4,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[6,3,5,1,4,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,3,2,7,5,1,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,6,7,3,5,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,6,8,1,2,5,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,3,5,6,8,2,4,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,2,6,4,8,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,5,7,2,6,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,2,1,3,6,4,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,1,8,7,2,5,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,6,3,5,1,4,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,1,5,3,7,6,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,4,1,7,6,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,6,8,3,2,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,6,8,7,3,5,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,7,8,6,5,3,4,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,5,6,7,2,4,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,4,7,5,2,3,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,6,4,8,3,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,1,5,6,4,8,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,1,4,7,8,6,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,6,7,2,8,5,4,3]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,4,3,8,6,1,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,3,7,1,5,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,2,4,5,3,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,4,3,2,7,5,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,7,2,6,1,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,8,2,1,7,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,4,1,7,3,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,1,8,2,7,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,8,5,2,1,7,6,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,4,8,7,5,1,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[4,1,7,8,3,2,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,4,7,1,3,6,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,8,2,4,5,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,8,2,4,5,3,7,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,8,6,2,1,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[6,5,7,2,3,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,6,8,2,7,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,6,2,8,4,5,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,8,2,1,3,6,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,2,1,7,4,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,6,2,8,4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,8,6,2,3,1,5,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,6,1,7,5,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,2,4,3,7,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,8,5,7,3,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[8,2,3,7,1,6,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,1,7,3,4,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,2,4,7,3,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,2,5,4,1,7,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,8,7,4,1,5,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,6,1,5,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,2,6,5,7,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,6,5,4,1,7,3,2]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[5,7,6,3,4,1,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,1,6,4,7,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,5,6,2,7,4,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,5,6,4,1,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,1,5,7,3,6,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,4,5,8,2,1,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,3,8,2,1,5,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,6,2,8,5,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,8,6,1,7,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,3,6,8,1,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,1,5,6,4,8,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,8,3,6,2,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,1,8,6,2,5,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,2,3,1,7,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[1,8,3,5,2,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,4,6,1,8,5,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,8,7,4,5,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,8,3,5,7,4,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,8,4,6,7,1,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,1,2,6,4,3,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,1,2,6,5,3,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,4,6,2,7,1,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,6,8,3,7,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,4,6,3,5,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,4,6,3,5,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,6,7,2,5,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,3,6,8,2,5,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,8,6,2,3,5,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,4,8,7,1,5,6,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,2,8,6,4,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,7,3,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,1,4,8,7,5,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,1,5,8,2,6,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,2,4,8,6,5,3]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[3,5,4,1,8,7,6,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,2,4,1,8,7,6,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,4,1,8,7,6,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,1,3,2,8,6,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,5,3,1,8,7,6,4]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,3,5,1,8,7,6,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,6,1,8,7,2,3,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,5,6,4,8,1,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,7,3,5,6,1,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,2,5,6,1,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,4,7,1,5,6,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,6,7,1,5,8,4,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,8,3,6,5,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,7,1,8,6,2,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,1,6,2,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,8,4,1,6,7,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,4,3,1,6,5,2,8]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[3,5,1,2,6,8,7,4]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,1,2,4,8,7,5,6]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[1,6,8,4,7,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,8,5,4,7,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,8,5,4,7,3,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,5,1,4,7,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,6,8,3,1,4,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,5,6,8,3,4,7,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[1,3,6,8,5,4,7,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,6,7,1,4,8,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,6,7,2,5,8,3,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,8,5,6,2,4,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,8,6,2,4,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,4,6,3,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,7,8,6,2,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,7,4,8,3,1,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,2,1,3,7,4,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,8,2,3,6,4,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,2,7,5,3,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,2,8,1,3,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,4,1,3,7,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,6,2,3,7,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,1,8,2,3,6,4,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,6,7,5,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,7,2,5,3,8,1,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,7,4,2,8,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,7,6,3,8,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,5,7,1,3,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,7,6,1,8,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,8,6,1,4,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,7,2,4,1,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,3,4,7,6,1,2]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,5,3,4,1,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,3,4,7,1,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,2,3,6,4,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,6,2,1,8,7,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,6,5,8,3,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,6,1,3,2,7,5,4]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,5,2,4,6,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,7,5,4,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,6,1,2,7,3,5,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,1,6,4,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,6,1,8,7,4,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,8,5,7,1,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,5,1,2,6,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,2,5,7,3,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,7,2,4,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,5,8,4,6,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,7,4,5,3,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,2,6,7,4,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,6,5,8,3,7,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,2,7,8,5,3,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,6,5,7,8,1,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,7,1,8,6,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,6,8,3,1,4,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,5,1,7,3,6,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,6,4,7,5,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,5,8,1,7,3,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,3,1,4,6,5,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,4,8,1,5,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,4,7,3,8,6,5,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,2,4,1,6,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,1,5,3,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,8,7,5,4,2,6,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,7,8,2,3,6,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,8,6,7,5,4,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[7,8,5,1,4,6,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,2,7,5,4,6,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,7,1,3,2,8,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,4,7,5,3,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,4,6,3,1,5,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,1,2,4,5,3,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,5,7,3,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,5,8,3,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,3,2,4,1,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,2,4,1,8,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,4,3,6,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,2,4,7,1,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,7,3,4,2,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,4,8,3,1,5,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,2,3,5,1,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,1,6,5,2,4,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,8,7,6,3,4,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,8,7,4,5,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,8,7,4,5,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,3,5,7,1,4,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,5,2,8,6,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,4,2,6,3,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,3,8,6,4,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,2,8,5,3,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,8,3,2,6,4,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,3,2,7,4,1,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,8,3,6,4,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,3,8,2,6,4,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,2,3,8,6,4,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,2,5,8,6,3,1,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,8,3,4,6,2,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,7,4,1,8,3,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,7,1,5,8,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,1,7,3,4,5,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,3,1,6,4,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,1,5,4,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,4,1,3,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,4,1,3,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,4,3,1,7,2,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,3,6,5,1,7,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,4,3,1,7,8,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,4,1,6,3,8,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,4,1,3,6,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,8,1,5,3,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,8,1,3,4,2,5,6]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,1,4,3,5,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,6,3,1,8,5,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,3,4,7,6,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,5,3,6,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,2,6,5,3,7,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,3,5,1,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,8,4,6,1,2,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,4,6,2,7,1,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,4,6,3,5,2,8,7]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,3,8,6,2,1,7]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,7,2,1,4,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,4,8,3,1,6,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,2,1,6,3,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,2,1,6,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,8,6,2,4,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,5,1,6,4,3,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,2,8,5,7,1,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,6,8,1,5,7,2,3]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,2,5,7,6,3,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,6,5,8,1,7,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,1,3,6,4,8,7,5]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,8,1,2,7,5,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,5,2,7,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,4,3,8,7,5,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,1,2,3,7,4,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,4,2,6,5,3,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,1,3,6,5,7,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,3,2,6,5,8,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,4,7,3,5,8,1,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,5,1,6,8,7,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,4,7,2,5,8,6,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,2,7,4,5,1,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,3,5,2,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,1,6,5,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,2,7,3,5,6,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,7,6,1,5,2,4]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,5,8,2,4,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,8,6,4,5,7,2]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[2,5,1,8,6,4,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,2,8,5,4,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,5,8,7,3,1,4,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,2,5,3,8,1,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,1,6,4,8,7,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,4,2,5,1,7,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,7,4,8,5,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,7,2,6,1,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,5,1,6,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,4,7,3,1,5,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,1,8,3,6,4,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,8,1,6,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,2,8,7,1,3,6,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,5,8,2,3,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,8,1,2,6,3,5,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,2,5,4,3,6,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,5,1,4,6,8,3,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,6,1,8,3,4,5,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,4,7,3,2,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,4,2,7,3,1,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[5,6,8,4,2,7,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,6,5,7,1,3,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,8,1,3,4,7,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,7,1,8,6,3,2,5]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,3,7,6,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,3,5,6,1,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,3,4,2,7,6,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,7,5,6,4,1,3,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,2,4,5,3,1,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,3,4,1,7,2,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,2,6,3,5,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,4,3,6,8,1,5]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,6,2,8,5,3,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,5,8,2,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,5,3,2,1,7,4,8]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[1]=>0
[1,6,7,3,4,8,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,3,8,5,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,7,4,6,2,1,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,8,1,2,5,4,6]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[5,1,3,6,4,7,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,4,1,7,8,6,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,4,7,8,1,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,3,7,6,5,1,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,4,1,7,3,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,6,1,5,3,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,1,4,8,2,3,7,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,7,8,4,5,1,3,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,8,5,6,7,1,4,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,6,1,4,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,4,2,3,8,5,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,5,7,2,6,8,3,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,2,8,3,4,6,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,1,2,7,3,5,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,1,2,6,3,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,2,7,5,6,3,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[4,8,1,2,3,6,5,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,2,3,8,7,1,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,2,3,6,4,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,2,3,6,4,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,2,1,6,4,7,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,1,6,2,7,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,1,4,2,5,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,4,5,7,6,1,3,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[6,3,5,7,4,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,5,2,3,8,1,4,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,1,3,5,4,2,8,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,5,2,1,8,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,2,3,8,1,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,6,8,2,4,5,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,5,4,7,1,2,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,4,8,3,6,2,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,3,2,4,8,7,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,3,2,6,5,8,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,6,2,5,7,4,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,7,1,5,8,6,4,3]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,2,4,1,6,8,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,7,2,3,8,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,1,8,5,7,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,4,3,6,5,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,5,6,3,4,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[6,1,8,5,4,7,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,6,1,5,4,2,8,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,1,6,8,7,2,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,7,5,3,1,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,4,6,2,8,7,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,5,8,6,7,2,3,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,7,6,1,2,8,3]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,6,5,7,2,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,3,4,2,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,8,6,3,4,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,4,6,7,1,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,4,8,6,3,5,1,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,3,4,6,1,5,7,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,4,5,6,1,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,1,5,4,2,3,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,4,3,6,1,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,4,8,5,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,2,4,7,3,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,1,8,4,2,5,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,4,8,1,5,2,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,4,8,7,5,1,2,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[3,7,6,8,4,1,2,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,8,6,4,2,7,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,3,2,6,7,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,3,7,1,4,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,2,6,8,4,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[8,5,3,1,6,7,2,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[3,7,5,1,8,4,2,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,4,6,7,3,1,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[4,8,1,6,7,2,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,2,1,5,8,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,8,1,4,5,7,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[5,6,2,3,1,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,3,1,5,8,2,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,6,3,5,1,8,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,3,4,6,1,2,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,7,2,5,3,6,4,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,5,7,6,2,3,4,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,5,2,6,1,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,1,4,8,7,6,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[7,4,1,8,3,6,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,5,3,7,4,8,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,5,1,6,2,4,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,7,4,6,8,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,2,4,6,5,1,7,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,8,4,6,5,2,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,6,7,3,8,1,4]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,5,4,6,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,2,3,7,8,6,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,6,4,8,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,3,4,7,1,6,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,2,8,5,7,6,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,8,2,3,7,4,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,7,1,4,3,6,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,4,6,2,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,4,6,2,3,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,6,8,3,4,2,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,5,8,4,2,3,7,6]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,1,7,6,2,8,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,8,2,7,5,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,2,8,5,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,6,3,7,4,8,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,5,3,8,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,6,5,3,7,4,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,6,3,5,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,3,2,8,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,6,1,7,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,1,5,2,7,4,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,1,4,2,8,5,3,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,6,8,1,7,5,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,6,5,3,8,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,5,8,7,1,3,6]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,1,8,7,5,6,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,8,7,6,3,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,2,7,5,3,6,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,2,3,1,5,6,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,8,5,7,6,1,3,4]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,8,7,2,6,4,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,7,2,1,6,4,5,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,8,4,7,6,2,5,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,1,6,4,3,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,4,1,7,3,6,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,3,5,8,4,2,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[4,3,8,1,7,5,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,7,8,2,1,5,6,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,7,1,4,6,2,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,2,5,7,1,6,4,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,6,2,1,5,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,8,2,7,4,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,2,3,6,8,5,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,5,2,3,7,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,3,8,6,1,7,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,1,7,3,5,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,1,7,3,5,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,8,5,2,7,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,6,7,3,5,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,3,6,8,2,5,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,3,7,6,2,5,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,4,5,8,7,2,6,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,5,1,8,7,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,4,6,2,7,5,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,8,5,2,6,7,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,4,1,6,7,3,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,6,5,8,3,4,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,8,5,2,6,1,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,5,4,1,8,2,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,6,4,7,5,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,4,7,3,1,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[2,8,4,5,3,1,7,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,2,5,3,4,1,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,5,4,1,8,7,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[2,6,5,4,1,7,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,4,1,2,8,7,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,7,4,1,5,2,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,6,7,5,3,1,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,4,5,2,6,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,6,3,4,5,1,7,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,3,5,4,1,7,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,4,5,1,3,6,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,3,5,1,6,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,8,3,2,6,1,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,3,7,6,1,5,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,4,3,6,1,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,6,8,5,3,1,2,7]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[5,6,8,4,3,7,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,5,8,4,2,1,6,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,8,7,6,2,5,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,2,4,1,5,3,8,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,3,4,1,7,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,8,5,4,3,6,1,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,6,5,3,2,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,7,2,3,8,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[8,4,2,6,5,7,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[1,7,4,2,8,5,6,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,1,7,4,6,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,2,5,7,1,4,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,5,2,4,6,1,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,5,3,4,7,2,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[8,4,6,1,5,7,3,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,7,2,1,3,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,8,7,6,2,5,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,3,8,6,7,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,2,3,6,1,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,6,4,7,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,2,5,7,8,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,7,4,6,8,3,5,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,6,8,1,5,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,7,6,8,4,2,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[2,7,4,6,8,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,6,8,5,1,4,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,1,3,8,6,2,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,1,8,6,5,3,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,2,3,4,1,5,8,7]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,1,6,5,4,3,7,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,5,2,6,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,7,2,5,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,3,4,1,8,6,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,7,3,6,2,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,3,8,5,2,1,7,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,3,4,7,6,2,1,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,4,7,5,1,2,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,4,6,1,7,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,4,8,2,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,4,6,3,1,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,2,5,6,8,1,4,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,1,5,8,4,7,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,7,5,2,6,4,1,3]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[8,2,1,4,3,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,1,8,5,7,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,1,8,2,7,5,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,8,2,4,3,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,5,3,8,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,6,1,4,2,8,5]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,4,2,3,8,7,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,3,8,6,5,7,2,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,1,7,2,4,8,6,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,3,8,2,4,6,5,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,1,3,7,8,4,6,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,5,8,4,1,3,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,8,2,3,6,5,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,2,5,8,1,6,3,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,7,2,6,4,5,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,4,8,2,3,1,6,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,6,4,8,3,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,4,8,5,3,2,7,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,5,8,4,6,7,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,2,4,8,5,7,3,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,3,4,1,8,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,6,3,1,8,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,6,5,1,8,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,2,1,4,8,6,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[7,6,3,5,2,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,6,5,2,7,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,7,4,1,8,6,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,5,7,2,1,3,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,1,2,7,6,4,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,2,6,7,5,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,3,2,6,8,7,1,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,2,7,8,5,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,6,4,1,8,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,5,4,3,8,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,1,2,8,4,6,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,4,3,8,6,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,8,1,7,4,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,8,5,7,4,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,4,8,3,1,2,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,7,4,1,8,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,7,4,6,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,6,2,8,1,3,5,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,3,2,5,1,6,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,6,2,1,8,4,7,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,5,1,7,6,4,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,7,4,2,1,6,5,3]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[1,1]=>0
[5,4,7,6,2,1,8,3]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,5,2,8,7,1,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,6,5,4,1,8,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,6,5,3,1,8,7,2]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,5,2,6,7,3,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,6,4,5,1,3,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,7,4,3,1,5,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[4,7,1,8,5,3,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,1,8,4,3,6,2,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,6,7,1,4,3,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,7,2,1,3,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,4,5,7,1,3,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,5,1,8,3,2,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,3,2,6,5,4,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[8,7,2,3,1,4,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,5,1,6,4,7,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,3,4,1,2,7,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,6,1,7,4,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,6,8,2,7,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,1,5,4,2,7,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,4,2,3,1,7,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,4,6,1,8,2,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,3,1,4,7,6,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,4,5,2,7,1,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,4,3,5,1,6,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,4,3,7,1,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,1,2,7,6,4,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,2,7,6,3,4,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,1,7,2,4,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,5,6,8,1,2,7,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,3,7,1,5,6,4,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,6,5,3,4,1,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,6,1,3,5,4,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,6,1,5,2,8,7,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,1,5,4,2,7,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,6,1,5,2,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,8,6,5,1,3,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,1,8,6,2,7,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,6,8,2,7,5,1,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,4,1,7,2,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,4,5,3,8,7,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,5,3,6,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,4,1,6,8,5,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,6,1,5,7,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,6,7,1,3,5,4,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,4,1,6,7,5,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,5,8,2,1,6,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,1,3,8,5,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,6,3,4,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,4,1,5,8,7,6,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,4,1,5,7,8,6,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,4,1,5,8,6,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,8,3,6,1,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,1,6,2,4,7,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,4,7,2,5,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,7,3,6,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,4,2,3,1,6,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,7,4,5,1,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,2,5,4,3,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,5,6,4,1,2,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,1,5,3,4,2,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,4,2,3,7,1,6,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,4,3,7,1,8,5,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,3,6,2,5,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,7,2,8,5,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,4,5,7,3,2,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,6,4,5,7,2,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,7,5,6,4,8,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,5,6,7,3,2,4,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[3,1,5,4,2,7,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,3,5,7,8,1,2,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[6,3,5,4,1,7,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,7,2,6,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,4,1,6,8,3,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,1,3,7,6,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,4,7,6,1,3,2,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,6,5,8,3,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,7,6,1,5,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,6,5,8,3,2,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,3,1,6,8,5,2,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,1,5,7,6,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,2,4,3,8,7,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,2,8,4,1,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,4,3,1,7,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,1,4,3,7,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,8,2,1,5,3,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,4,6,7,2,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,7,2,5,4,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,1,8,4,7,5,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,2,5,1,3,7,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,2,4,1,6,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,5,8,6,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,1,6,8,3,2,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,8,3,6,1,2,5,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,8,6,1,3,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,2,6,4,1,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,7,6,2,3,5,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,4,3,1,6,8,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,5,6,1,3,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,3,5,7,4,2,8,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,6,4,8,5,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[8,2,1,6,4,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,3,8,6,5,2,7,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,7,3,8,5,6,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,2,8,5,7,4,6,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,6,8,5,4,7,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,8,4,5,6,7,1,2]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[2,1,3,7,4,6,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,7,1,8,3,2,6,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,2,4,1,8,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,3,5,1,6,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,3,8,6,4,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,8,1,3,2,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,7,6,1,3,2,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,2,5,4,3,7,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,4,3,7,6,2,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[8,1,5,3,4,7,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,1,8,7,4,5,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,8,6,4,3,7,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,8,6,4,2,1,7,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[2,6,1,8,4,7,5,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,3,8,6,1,2,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,8,1,4,6,2,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,6,2,1,4,8,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,6,2,3,7,1,8,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,7,5,1,3,4,2]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,7,6,1,5,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,8,6,4,2,5,3,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,4,5,8,7,1,3,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,4,1,7,8,3,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,6,3,2,1,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,5,6,2,3,1,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,4,6,2,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,5,2,3,6,1,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,3,6,2,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[6,5,7,1,4,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,8,2,5,7,6,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,8,1,2,7,5,6,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,5,2,6,1,3,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,2,1,6,3,8,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,3,2,8,4,7,5,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,4,3,8,7,2,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,4,7,2,1,3,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,6,4,5,7,1,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,7,4,6,1,5,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,6,5,2,8,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,7,5,8,2,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,6,3,1,4,7,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,7,8,3,5,6,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[2,3,5,8,4,7,6,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,2,6,5,1,4,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,3,1,8,4,2,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,2,8,4,5,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,4,1,8,3,6,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,6,4,3,8,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,7,2,1,4,8,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,7,6,4,1,8,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[5,1,4,6,2,7,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,2,5,3,7,8,6,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[4,8,3,5,1,2,7,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,3,7,2,8,4,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,8,5,4,1,7,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,5,8,2,6,7,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,8,5,3,1,7,4,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,5,2,3,7,1,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,2,1,6,4,8,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,1,3,7,5,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,4,5,7,1,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,3,8,7,1,4,6,5]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,2,7,5,6,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,4,7,6,5,2,3,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[2,7,8,3,5,1,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,2,7,4,5,1,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,4,1,3,7,6,5,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,5,4,7,3,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[7,2,8,3,5,6,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,2,5,4,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,6,8,1,4,7,3,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,1,3,8,6,5,2,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,3,4,1,8,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,8,7,3,6,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,6,3,8,4,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,8,2,3,1,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,2,3,5,1,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,2,1,3,7,5,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,3,2,7,6,1,8,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,6,4,2,8,7,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,7,4,2,6,1,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,4,7,1,6,2,8,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,1,8,2,4,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,7,1,2,5,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,1,4,6,5,2,3,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,8,6,3,7,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,3,7,6,2,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,3,8,2,5,6,4,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[1,3,2,7,4,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,3,8,4,6,2,7,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,4,3,5,1,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,3,1,5,4,7,2,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,3,5,8,4,1,6,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[2,5,8,4,3,6,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[4,5,3,8,2,6,7,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,8,4,6,7,2,3,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,2,5,8,6,7,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,2,3,6,7,4,5,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,8,4,6,2,7,3,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,8,3,7,2,4,5,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,3,8,5,4,2,7]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,6,2,1,5,4,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,6,1,2,5,4,7,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,6,4,2,1,7,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,2,7,6,5,3,8,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,7,6,5,1,8,4]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[2,3,7,6,4,8,5,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,5,7,6,3,8,4,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,5,7,8,6,2,3,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,4,7,1,2,5,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,6,7,5,4,1,8,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,4,3,6,5,7,1,2]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,4,6,5,7,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,2,6,4,3,1,8,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[6,8,5,2,1,4,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,2,8,5,7,4,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,3,6,4,7,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,6,5,2,7,1,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,1,5,7,4,3,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,1,7,2,3,8,6,5]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,5,2,7,8,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[1,2,7,5,8,6,3,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,2,5,7,8,4,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,4,5,1,6,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,4,5,2,7,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,7,8,4,2,6,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,3,2,5,7,4,1,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,3,2,6,8,1,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,2,8,4,6,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,8,5,2,7,3,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,2,6,3,1,8,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,3,1,8,4,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,4,2,7,1,3,8,6]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,7,1,5,2,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,1,7,4,6,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,2,1,5,3,7,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,8,1,6,2,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,5,8,2,7,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,2,7,3,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,4,7,6,2,8,5,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,5,8,3,2,6,4,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,2,5,1,3,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,2,8,5,1,3,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,7,8,3,6,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,7,1,4,8,2,3,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,1,2,3,5,4,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,3,5,7,1,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,5,7,1,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,3,6,2,4,1,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,2,4,3,1,8,5,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,5,8,4,3,6,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,7,8,5,1,6,3,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,7,8,3,5,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,7,8,5,6,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,3,7,5,8,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,3,7,5,8,6,4,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[4,3,1,7,8,2,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[2,5,7,8,1,3,6,4]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[2,5,7,8,3,6,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[5,8,1,6,4,7,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,7,5,1,8,6,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[2,3,7,1,8,5,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,5,1,2,7,4,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[3,6,5,7,8,2,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,6,5,1,8,7,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[7,4,5,8,1,3,2,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,2,1,6,4,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,2,1,6,4,3,5]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,8,1,2,5,4,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,1,2,6,4,3,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[8,1,7,2,6,5,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,1,2,7,6,5,4,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[2,7,8,1,6,4,3,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,7,1,6,5,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,7,6,1,5,2,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,1,6,8,4,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,7,6,8,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[3,4,7,6,5,8,1,2]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,4,3,5,1,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,4,2,6,5,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,2,5,8,6,4,7,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,5,3,6,8,7,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,8,4,1,6,5,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,5,2,6,4,7,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,5,1,6,4,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,5,1,6,3,7,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,1,5,8,6,3,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,1,5,3,6,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,8,5,4,6,2,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,4,7,6,8,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,5,7,4,8,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,1,7,6,8,2,5,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,2,6,4,1,5,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,2,6,5,8,3,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,3,5,6,1,4,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,8,3,1,6,7,4,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,5,8,1,7,3,6,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,7,1,6,8,5,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,8,7,1,6,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,1,8,3,2,5,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,3,8,2,5,4,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,4,2,1,6,3,7,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,2,6,1,5,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,1,8,4,3,6,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,3,5,6,2,7,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,6,1,3,7,5,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,5,1,7,6,3,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,8,2,4,6,1,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,4,7,8,5,2,6,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[3,8,5,2,6,4,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,5,7,6,1,4,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,3,1,8,6,7,4,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,7,1,6,4,2,8,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,3,2,1,4,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,6,3,2,4,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,2,7,1,4,3,5,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,6,2,8,5,3,1,4]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[6,1,5,7,3,4,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,1,2,3,8,4,6,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,5,8,1,6,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,1,3,5,2,7,6,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,5,7,2,8,6,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,5,7,6,2,8,3,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,5,6,2,8,7,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,2,8,5,4,3,7,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[3,7,4,8,6,5,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[3,8,6,5,4,2,7,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[5,8,4,7,6,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,3,2,7,5,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,8,5,7,3,2,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,7,4,8,1,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,4,2,1,6,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,8,4,3,1,2,7,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,3,2,6,5,1,7,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,3,6,5,1,2,7,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,5,4,6,8,3,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,6,5,8,7,1,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,8,4,7,1,3,5]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,8,3,7,5,4,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,8,4,1,5,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,3,4,2,1,5,7,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,8,6,3,2,5,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,1,3,8,4,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,2,8,1,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,3,1,8,7,4,6,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,1,7,8,6,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[4,2,5,6,8,3,7,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,4,8,1,2,6,5,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[1,6,8,3,7,5,4,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,3,6,5,1,8,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,2,4,1,8,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,8,2,7,3,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,8,7,2,1,3,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,1,3,7,4,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,4,8,1,7,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[2,8,5,6,4,1,7,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,7,3,5,8,6,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,7,8,2,5,1,6,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,6,1,4,3,2,7,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[7,3,8,2,4,1,5,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,3,7,8,1,2,5,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,6,1,5,2,3,8,4]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,1,8,6,7,2,3,4]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,7,1,6,8,2,3,4]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,8,4,2,1,7,3,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[6,3,2,8,1,7,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[1,8,5,6,3,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[6,7,8,2,4,1,5,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,2,1,7,6,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[2,3,1,7,4,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,7,5,4,6,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,8,5,4,3,7,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,8,3,2,7,4,5,6]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,5,1,7,3,2,8,6]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,8,6,7,4,3,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,7,8,2,3,4,6,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,7,2,1,6,5,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,6,3,4,2,8,5,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,2,3,8,1,6,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,4,7,6,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,8,4,3,1,5,6]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,4,2,1,6,3,8,5]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,5,8,4,2,7,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,6,7,4,1,2,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[5,1,3,6,8,4,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,6,4,8,7,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,5,4,2,8,7,3,1]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[1,1,1]=>0
[1,8,5,2,7,6,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,2,4,6,3,1,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,6,4,8,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,6,5,2,1,7,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,4,8,3,1,2,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,5,8,3,6,2,1,7]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,3,7,1,2,6,4,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,1,2,6,4,7,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,1,2,4,8,3,7,5]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,7,2,8,1,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,4,5,6,3,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,7,1,3,5,2,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,1,4,5,6,2,3,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[2,5,6,8,1,4,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,1,6,5,2,3,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,5,1,7,8,6,2,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,5,7,3,4,6,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,7,4,3,5,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[6,8,7,5,3,4,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,8,6,2,4,7,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,8,6,2,5,7,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[1,6,4,7,5,3,2,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[1,6,5,3,2,7,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,6,8,7,4,5,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,4,7,5,3,2,6,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,7,5,4,3,2,8,6]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[1,4,7,5,3,2,8,6]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,7,4,6,8,5,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[6,8,7,2,3,5,4,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,7,6,1,8,2,4,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,6,5,7,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,7,8,5,1,4,3,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,5,6,4,7,1,3,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,7,2,1,6,4,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,3,7,6,2,8,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,5,6,1,4,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,4,1,7,6,8,3,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,4,3,7,6,8,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,1,6,4,3,7,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,7,1,6,4,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,4,6,1,3,7,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,5,6,2,4,7,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,5,8,4,2,6,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,1,3,6,4,5,2,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,5,4,7,8,2,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,6,5,1,7,4,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[4,3,1,6,2,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,5,2,1,8,4,3,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[7,1,2,4,8,3,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[3,6,8,5,1,4,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,2,4,1,6,8,3,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,5,3,4,6,8,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,7,1,2,5,6,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[6,7,3,1,8,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,3,1,4,6,2,8,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,7,4,8,1,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,7,3,4,6,2,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,3,5,6,2,4,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,7,2,5,6,1,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,1,2,7,5,8,6,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,7,2,5,1,6,4,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,5,8,2,7,6,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[1,5,7,2,6,4,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,3,5,1,4,7,2,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,3,4,6,1,5,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,6,8,1,7,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,5,7,4,6,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,4,7,2,3,5,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,3,7,8,1,6,4,5]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[2,7,3,8,5,4,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[6,5,3,8,2,4,7,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,7,6,5,4,1,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,3,6,5,7,4,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,6,5,7,4,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,4,7,1,5,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,6,3,7,5,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,2,5,3,7,6,4,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,5,7,1,4,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,6,7,5,1,8,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[2,6,7,1,4,3,5,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,6,2,1,4,5,3,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,1,2,6,4,3,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,2,7,4,3,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,1,2,7,6,4,3,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[5,3,8,1,7,4,2,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,8,7,2,4,6,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,5,3,1,2,6,4,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[5,6,3,1,2,8,4,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,3,8,4,6,1,2,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,8,3,1,6,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,6,8,3,1,4,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,3,6,8,4,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,1,2,6,4,8,7]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,3,4,8,6,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[4,3,6,5,1,2,8,7]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,4,1,6,8,7,2,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,5,4,7,8,1,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,3,6,8,7,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,1,6,7,2,8,5,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,1,6,5,8,7,3,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,5,7,1,8,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,8,2,5,7,3,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,5,2,7,8,3,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[3,7,8,1,6,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,4,6,1,7,5,8,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[6,1,5,4,7,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,2,5,6,7,1,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,6,5,2,7,4,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,4,5,1,7,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,3,7,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,1,5,3,7,4,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,2,5,4,7,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,5,7,6,1,3,4,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,6,5,1,7,3,4,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,8,5,7,1,3,4,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,4,7,6,1,5,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,2,7,6,3,5,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,7,2,1,6,3,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[3,1,8,4,2,7,6,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,7,4,1,3,6,5]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[8,2,3,1,7,6,4,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,7,2,3,1,6,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,5,8,3,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,8,2,3,1,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,2,5,7,3,1,4,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[3,1,6,2,7,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,3,1,7,8,2,6,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,7,4,3,8,5,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,3,7,1,8,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,2,8,7,1,6,4]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,7,4,1,3,5,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,1,3,6,5,2,8,7]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,6,3,2,5,1,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,3,2,6,5,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,8,3,6,5,2,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[8,1,6,2,5,4,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,4,3,8,6,1,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,6,3,8,5,4,7,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,3,2,5,8,7,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,8,4,2,5,3,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[6,8,4,3,5,2,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,1,4,6,5,3,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,4,6,1,2,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,3,5,6,1,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,7,6,3,4,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,6,7,2,3,5,8,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[6,5,4,8,7,2,3,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,8,4,1,7,5,6,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,5,2,4,1,7,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,7,1,2,6,3,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,7,4,3,6,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,5,3,8,1,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,7,1,2,6,8,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,8,5,6,2,3,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,4,6,8,1,5,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[6,2,5,4,7,8,1,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,2,6,1,7,4,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[4,3,7,8,5,2,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,6,1,8,4,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[7,4,2,6,1,3,8,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[6,1,7,4,2,3,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,5,6,1,3,2,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,3,7,5,2,8,6,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,1,8,7,4,6,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[5,1,7,6,2,4,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,4,8,1,5,3,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,6,5,1,8,2,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,1,6,8,3,5,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,3,4,1,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,7,8,2,6,1,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,7,6,3,5,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,1,6,4,3,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,8,5,3,7,4,1,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,4,3,8,7,2,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,8,1,6,4,5,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,8,3,6,1,7,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,4,6,1,2,8,7,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,7,5,3,2,6,8,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,4,6,8,1,2,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,8,4,5,7,2,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,8,7,2,3,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,6,1,3,7,8,2,4]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[3,8,4,6,5,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,6,4,5,8,7,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,6,4,3,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,3,1,8,7,4,5,2]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,6,3,2,7,4,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,3,6,8,7,4,5,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[5,7,1,3,6,2,4,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,7,1,3,2,5,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,1,3,2,6,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,7,1,3,6,2,8,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,8,2,5,7,3,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,8,5,2,3,6,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,8,6,3,4,7,2,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[3,7,5,4,2,8,1,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,6,5,1,7,8,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,7,1,3,2,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,6,5,1,8,2,4,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[5,8,7,3,4,2,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,8,6,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,8,5,6,4,1,7,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,2,8,1,6,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,7,8,4,2,1,6,3]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,4,6,8,7,5,2,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[6,4,3,8,7,5,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,5,2,3,7,4,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,5,2,3,6,4,7,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,7,2,3,5,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,8,2,7,4,5,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,7,2,6,8,5,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,7,2,4,5,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,8,2,5,6,7,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,5,8,3,2,6,7,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[3,8,5,2,7,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,2,8,6,3,5,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,5,8,4,3,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[4,2,7,6,8,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[3,7,4,6,8,5,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,8,4,5,6,2,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,1,5,4,8,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,7,6,3,5,2,8,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,5,3,4,8,6,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[5,8,2,3,4,7,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[8,7,3,2,6,4,5,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,3,1,4,7,5,2,6]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,1,6,4,8,7,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,4,8,5,7,2,6,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[8,3,4,1,7,6,5,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,3,8,6,1,7,5,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[6,5,8,3,1,4,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,6,7,1,2,4,8,3]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[7,1,6,8,3,2,5,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,1,5,4,6,2,3,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[8,2,6,3,1,5,4,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,7,1,6,4,3,8,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,7,3,6,8,2,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[2,3,8,4,5,1,7,6]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[4,5,7,8,1,2,6,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[7,2,6,4,5,8,3,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,3,5,4,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[4,3,7,5,2,8,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,7,8,5,6,2,4,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,8,2,1,7,6,4]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,5,7,3,8,1,2,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,4,3,6,2,5,8,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,3,8,7,1,6,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,3,8,4,7,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,2,3,1,6,5,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,2,7,1,3,6,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,4,2,3,1,6,7,5]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[4,7,2,3,6,5,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,2,6,4,7,1,5]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,7,5,8,6,2,4,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,5,1,7,4,8,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,3,6,1,8,4,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,2,1,8,5,7,6,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[5,2,1,7,8,4,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,2,8,6,3,7,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,3,2,8,6,4,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,8,2,6,7,3,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,8,2,1,5,6,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,2,6,4,8,5,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,5,7,1,6,4,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[5,1,4,6,3,8,7,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,2,6,4,3,7,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,4,8,7,5,6,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,2,3,7,6,8,1,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,1,7,4,2,6,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,7,1,3,5,2,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,1,4,8,5,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,2,7,5,3,4,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,4,8,1,7,5,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,6,3,5,1,4,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,3,6,1,7,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,2,6,4,8,3,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,1,8,6,2,4,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,4,6,2,1,8,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,1,3,7,8,2,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,4,7,3,8,6,2,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,7,5,6,1,3,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,4,5,1,6,8,3]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,2,5,8,7,6,1,3]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,7,2,5,8,6,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[1,8,7,5,4,6,2,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,8,1,4,7,5,6,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,4,1,5,3,8,7,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,6,7,4,5,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,6,7,2,3,5,1,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[8,1,6,4,7,5,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[6,4,8,1,5,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,6,3,8,1,5,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,1,3,8,6,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,8,5,2,3,7,1,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,8,6,1,3,7,5,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,2,4,7,5,1,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,2,4,5,7,1,3,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[5,1,8,6,3,7,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,1,3,7,4,6,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,1,5,7,4,3,6,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[8,3,6,2,7,1,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,4,7,5,2,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,6,4,3,5,8,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,1,4,3,7,8,6,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[6,4,1,5,8,2,3,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,7,6,2,1,8,4,3]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,7,1,8,6,3,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,1,6,3,2,7,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,6,8,2,5,1,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,7,6,3,5,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,4,3,1,6,7,2,5]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[2,8,7,5,3,4,6,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,6,3,4,2,1,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,7,3,4,2,6,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,5,7,6,3,4,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,6,5,1,7,8,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,1,6,4,3,7,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[2,6,7,3,5,1,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[8,4,7,6,1,3,2,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,6,2,4,7,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,7,8,1,3,6,2,4]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,1,3,7,6,5,2,8]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[3,4,1,7,2,6,5,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,5,1,6,7,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,6,2,7,5,1,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,7,6,2,5,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,4,1,8,7,2,5,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,7,4,3,6,1,5,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,7,2,5,3,1,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,6,5,3,2,8,7]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,3,6,1,8,2,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,8,5,3,2,4,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[2,5,7,4,6,1,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,8,3,4,6,2,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,6,1,5,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,6,1,5,2,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,6,3,4,1,5,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,8,3,6,7,2,4,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,1,6,2,5,7,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,7,1,5,3,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,7,3,4,2,5,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,6,2,4,7,5,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[4,1,6,3,2,8,7,5]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[2,4,1,8,7,5,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,7,5,1,4,6,3]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,7,3,6,4,2,1,8]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,3,6,4,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,7,5,6,4,1,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,1,4,5,3,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[6,2,5,3,8,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,4,5,7,3,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,4,6,5,3,2,1,8]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[7,5,1,3,4,2,8,6]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,8,5,7,3,4,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[8,5,1,3,4,2,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[6,1,5,3,4,2,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,3,6,4,7,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,4,5,3,2,1,7]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,8,7,4,3,6,5,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,8,1,3,5,2,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,3,8,5,4,6,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,3,6,8,2,4,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,7,8,6,3,2,4,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,1,2,5,3,8,4,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,7,4,2,5,1,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,8,3,4,5,7,2,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,7,5,8,2,3,6,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,6,7,5,3,8,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,5,2,6,8,7,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,5,2,6,8,3,1,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,6,5,7,2,1,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,7,5,2,1,4,3,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,2,5,8,6,7,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,6,2,5,4,3,8,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[8,2,6,7,3,5,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,5,7,6,2,1,3,8]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[7,8,2,6,5,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[5,3,7,8,4,2,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,3,6,8,1,5,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,4,6,7,2,5,1,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[7,5,8,2,4,3,6,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,5,8,2,3,4,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[8,1,5,3,4,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,8,7,2,4,3,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,2,4,8,5,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,8,2,3,7,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[7,8,2,3,5,4,6,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,1,3,2,6,5,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,7,2,3,5,4,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,7,6,8,4,5,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[2,7,3,1,8,5,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,5,2,1,6,7,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,4,5,2,1,8,7,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,4,1,3,8,6,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[4,3,8,6,1,5,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,6,3,4,8,5,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,8,2,1,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,5,3,4,2,8,6,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,4,1,2,8,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,8,6,1,5,7,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,3,5,1,7,6,4,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,3,5,4,7,1,6,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[4,8,7,1,2,5,3,6]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,7,2,6,1,4,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,7,3,8,2,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,5,6,4,3,8,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,1,3,5,8,2,6,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,6,2,4,5,3,8,7]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,2,4,6,5,7,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,8,2,6,4,3,7,5]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,6,4,3,8,7,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,6,1,5,7,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,8,2,4,6,5,7,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,4,2,1,6,5,7,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[6,8,7,1,4,2,3,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,8,7,4,5,2,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,8,5,7,4,6,3,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,4,7,6,8,3,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,2,8,6,5,3,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,7,1,6,4,2,3,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,8,2,7,5,1,6,3]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,8,4,6,7,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,8,5,1,4,2,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,6,2,5,3,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,5,2,4,3,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,8,5,1,4,3,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,1,2,4,5,3,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,3,5,2,4,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,5,7,1,3,6,8,4]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[3,6,5,2,8,4,7,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,8,7,1,4,6,2,5]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,8,6,1,7,2,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,7,1,6,2,5,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,1,8,2,6,7,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,7,6,1,5,3,4,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,2,4,5,3,8,6,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[2,7,1,4,6,5,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,3,5,7,8,4,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,6,3,5,4,8,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[4,2,6,8,3,7,5,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,4,8,1,3,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,2,4,8,3,6,7,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,4,2,5,7,1,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[3,2,4,6,1,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,7,6,2,1,5,4,8]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[2,6,8,3,4,1,5,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,1,6,5,8,4,2,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,1,4,8,5,3,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,3,8,6,4,7,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,5,6,7,4,2,8,3]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[6,1,7,8,3,5,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,5,7,8,6,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[7,2,1,3,6,4,5,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,4,3,6,1,5,8,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[7,2,4,1,5,6,3,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,2,5,7,6,8,4]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,1,7,3,2,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,7,2,3,5,1,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,8,2,3,7,5,1,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,2,4,3,5,6,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,6,2,4,3,5,1,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,1,2,4,7,3,5,6]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,6,2,8,4,5,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,5,7,3,1,6,4,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,2,6,4,3,7,1,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,7,3,4,2,1,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[4,5,6,8,2,1,3,7]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[8,7,1,3,6,4,5,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,1,5,7,4,6,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,1,5,7,3,2,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,2,3,5,7,6,1,4]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,4,8,6,1,3,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,4,5,6,7,1,3,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,8,4,6,5,2,1,3]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[7,2,6,4,1,5,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,7,1,6,3,8,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[1,7,2,5,3,6,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,6,3,2,5,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,2,5,7,1,8,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,3,5,7,2,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,1,8,2,7,6,5,3]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[1,5,8,4,3,6,2,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,5,2,6,7,4,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,7,3,2,5,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,5,3,8,7,4,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[4,1,7,5,6,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,8,2,3,1,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,3,8,1,4,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[5,2,7,6,1,4,8,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[4,2,1,6,7,5,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,7,6,4,3,8,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,5,8,3,7,2,4,6]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[5,8,2,6,7,3,1,4]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,2,3,6,1,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,1,3,7,6,8,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[1,6,8,7,2,5,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,4,1,6,5,2,8,7]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,3,6,1,7,5,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,3,1,6,7,2,8,4]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,8,5,3,7,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[3,8,4,5,2,6,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[3,8,2,4,5,6,1,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,4,8,7,6,3,5,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,1,6,3,7,5,2,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,5,8,6,2,3,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,4,7,1,8,2,3,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,1,3,6,2,8,4,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,3,2,7,6,8,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,8,3,2,1,6,5,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[1,4,3,2,7,5,6,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,3,2,8,6,7,1,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,5,3,6,1,4,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[3,4,2,1,5,8,6,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[2,5,3,7,1,4,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,5,3,6,1,7,8,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,4,3,1,7,6,8,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,5,2,7,1,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,5,2,8,7,4,1,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[3,1,8,4,5,2,7,6]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,3,7,6,1,8,4,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[4,8,5,2,1,3,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,8,4,2,1,3,7,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[4,6,7,5,2,3,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,2,5,3,1,8,7,4]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,2,5,3,8,7,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,4,5,3,8,7,1,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,6,4,5,8,7,3,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,4,7,5,2,3,1,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[8,2,7,4,5,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,4,7,5,3,1,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,2,6,7,5,3,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[8,4,6,7,5,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,4,5,8,7,3,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[6,2,8,7,5,3,1,4]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[4,6,5,3,8,7,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,7,2,4,5,3,1,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,8,7,4,5,3,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,4,7,5,3,1,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[5,8,7,4,6,3,1,2]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,5,8,4,7,2,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,8,6,2,5,7,1,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,1,6,2,5,7,3,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,8,1,2,4,7,3,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[8,1,5,3,2,7,4,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,2,8,6,1,4,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,7,8,1,2,6,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[8,6,1,3,7,4,2,5]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[6,1,2,8,3,7,5,4]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,8,1,2,6,4,3,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[8,7,2,5,3,4,1,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,6,2,3,8,7,1,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,7,4,2,8,5,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,2,8,5,7,1,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,7,6,2,5,4,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,6,1,2,5,4,7,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,6,1,3,5,8,2,7]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[4,5,1,3,8,7,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,2,7,1,8,3,4,5]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,4,5,8,1,7,2,3]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,2,8,5,1,4,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,4,7,6,1,8,3,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,6,2,3,8,5,7,4]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,3,2,5,4,8,7]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,3,4,5,2,6,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[7,3,1,6,5,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[6,1,2,7,4,3,5,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[2,7,3,6,5,8,4,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,6,7,5,3,2,8,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,3,4,6,1,8,2,5]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,7,4,1,2,8,6,5]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,8,1,2,7,3,4,5]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[1,6,2,8,7,3,4,5]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,8,5,7,4,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[3,8,1,2,4,7,6,5]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[1,4,5,7,3,6,8,2]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,6,8,7,1,5,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,3,8,7,5,2,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[3,2,1,6,4,5,8,7]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[3,2,4,5,7,1,8,6]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[3,2,4,6,1,7,8,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,4,6,1,8,5,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,3,8,1,4,6,5,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[3,6,2,4,7,5,8,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,8,4,6,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[4,2,7,3,5,8,1,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,1,8,4,5,6,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[4,2,7,8,6,3,1,5]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,1,4,2,8,6,3,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,3,7,4,8,1,6,5]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,1,3,6,8,4,5,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[1,6,3,5,8,7,4,2]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[8,4,6,3,5,1,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,2,6,8,4,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[2,4,5,7,1,6,8,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,4,2,6,7,3,5,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[1,4,2,7,5,6,3,8]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,1,7,6,3,5,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,3,2,8,7,5,6,1]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[5,2,4,8,7,3,6,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,3,8,7,4,5,2,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,1,4,2,6,3,7,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[7,1,2,4,6,3,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[1,6,5,2,4,3,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,6,5,3,4,7,2,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[7,8,2,3,5,6,4,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,1,3,4,6,5,2,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,1,3,5,4,7,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,1,5,7,8,6,2,3]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[6,1,4,8,2,3,7,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[2,8,5,7,6,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,7,8,6,4,1,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[7,4,1,6,2,5,8,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[8,7,4,6,2,5,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,1,7,4,6,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,4,1,7,6,2,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,7,5,4,6,2,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,1,7,4,8,5,2,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,4,6,3,1,7,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,4,1,8,6,2,5,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[1,8,6,2,7,5,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,8,5,1,7,6,3,4]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[4,8,7,1,6,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,2,8,6,4,3,1,7]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1]=>0
[1,8,3,7,5,4,2,6]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[3,8,7,1,6,2,4,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[2,8,4,3,1,7,5,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,2,4,8,7,3,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[3,6,5,8,4,1,2,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[8,5,6,2,3,7,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,8,1,4,5,6,2,3]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[5,4,7,8,6,2,3,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,7,5,6,4,8,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,4,8,3,5,6,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[3,1,8,6,4,5,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[2,6,1,4,7,5,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[3,1,5,7,2,6,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,1,7,5,2,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,2,7,5,1,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,2,7,3,1,6,8,4]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[5,3,4,6,8,1,7,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,5,6,8,2,7,1,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[1,7,2,5,8,4,6,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,7,1,3,8,5,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[2,5,3,8,7,1,4,6]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,1,3,7,6,8,4,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,7,2,4,6,8,3,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,4,5,8,3,6,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[3,1,6,4,2,7,5,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,5,7,8,3,6,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[8,4,6,2,5,3,1,7]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,1,7,5,3,6,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,8,5,1,6,2,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,6,5,3,4,2,7,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[1,7,5,4,2,3,8,6]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[5,1,7,6,4,8,2,3]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,7,3,6,2,4,8,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[2,3,7,1,4,6,8,5]=>[3,4,1]=>[[6,6,3],[5,2]]=>[5,2]=>3
[2,6,5,1,7,4,8,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,6,2,4,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,1,2,4,7,5,8,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[4,6,1,7,5,3,8,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,1,7,5,3,4,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,7,4,6,5,3,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,2,8,3,6,1,7,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,1,4,3,6,2,5,7]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[5,2,3,6,8,1,4,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,7,8,2,3,1,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[6,7,1,2,4,3,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[5,3,7,2,1,6,4,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,1,2,8,6,3,4,5]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,1,4,6,7,5,3,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[4,6,8,1,7,5,3,2]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[6,1,5,7,4,2,3,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,4,7,8,3,6,5,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[1,4,6,7,5,2,3,8]=>[4,1,3]=>[[6,4,4],[3,3]]=>[3,3]=>0
[1,3,5,8,2,6,4,7]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,7,1,3,5,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,6,3,7,8,4,2,5]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,3,8,4,6,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,3,5,8,6,7,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,2,7,8,5,6,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,7,3,8,5,6,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,1,4,8,5,6,3,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[4,3,8,7,2,5,6,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,7,3,8,6,4,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,4,2,8,5,6,3,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[3,4,8,2,6,7,5,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,6,3,8,7,4,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[1,4,5,8,7,6,2,3]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[3,3,3]=>0
[5,2,1,3,8,4,6,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,4,3,5,8,2,6,7]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,1,3,8,6,4,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,3,6,4,5,8,2,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,1,4,3,5,8,2,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[6,5,1,3,8,2,4,7]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[1,4,3,8,6,2,5,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[4,1,3,8,6,2,5,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,3,5,6,2,1,7,4]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,5,8,7,6,1,4,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[7,1,5,4,6,3,8,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,3,6,5,4,8,2,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[6,4,7,8,3,5,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,5,6,7,1,8,4,2]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[2,7,8,3,6,1,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,7,8,3,6,2,5,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,4,3,5,8,1,6,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,3,6,4,1,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,8,4,3,6,1,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,1,6,4,3,8,5,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,7,3,4,1,5,2,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,2,6,4,3,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,4,3,8,2,6]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,4,5,1,8,2,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[6,3,1,2,8,5,4,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[1,6,4,8,5,2,3,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,6,3,8,4,5,1,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,3,6,4,2,5,8,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,8,5,3,6,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,6,4,2,7,1,3]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[7,1,5,3,8,2,4,6]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[1,3,8,7,6,4,5,2]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,6,4,5,2,8,3,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[2,8,3,4,6,7,1,5]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[7,2,3,4,6,1,5,8]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,5,1,6,3,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,7,5,2,8,1,6,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,2,1,6,3,8,4,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[4,5,8,1,7,3,2,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,6,7,1,3,8,2,5]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[2,7,3,4,1,8,5,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[8,5,3,2,7,4,6,1]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[4,8,7,1,5,6,2,3]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[8,6,3,7,4,5,2,1]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,2,6,8,5,3,4,1]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,8,2,7,5,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[7,8,2,6,5,3,4,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[2,5,3,4,7,8,6,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[2,6,7,8,3,5,4,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[4,4,3]=>1
[8,4,6,5,1,3,7,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,8,2,4,3,1,6]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[4,7,8,6,1,5,3,2]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[1,4,3,5,7,2,6,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[2,3,7,8,1,4,6,5]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[8,2,3,5,4,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,1,3,8,2,4,6,5]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,2,3,6,4,1,8,5]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[6,5,2,4,1,8,3,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,7,2,4,1,3,8,6]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,2,5,4,1,8,3,7]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,2,6,3,5,8,1,7]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,7,8,6,3,5,1,4]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[8,4,1,5,3,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[8,3,1,4,2,7,6,5]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,5,8,7,3,1,6,4]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[8,1,2,5,4,3,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[1,6,2,5,7,4,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,3,6,4,2,7,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,1,8,3,6,4,5,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,2,6,3,5,8,4]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[7,2,1,8,4,3,6,5]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[2,1,1]=>1
[3,7,5,2,8,4,6,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,7,2,5,6,4,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,5,2,4,6,3,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,4,1,2,8,5,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,4,1,6,3,5,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,3,4,1,6,8,5,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[8,6,2,5,7,3,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,3,4,8,5,1,2,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[8,5,1,2,7,4,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,2,6,8,3,4,5,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,6,7,5,4,8,2,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[3,5,8,4,6,2,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[3,5,8,4,2,7,6,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[7,4,6,2,5,3,8,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,4,3,8,6,5,1,2]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[7,2,6,5,8,3,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,8,5,4,2,6,3,7]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[5,4,2,6,8,3,1,7]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[3,5,6,7,4,8,1,2]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,7,3,6,2,1,4,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[2,3,8,5,4,6,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[6,8,7,1,4,5,3,2]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[8,1,3,6,4,7,5,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[6,8,7,1,2,5,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,7,3,1,8,4,6,5]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,7,2,5,6,1,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[7,1,3,5,4,2,6,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,5,1,6,2,4,3,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,8,6,1,2,4,3,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,1,5,7,3,6,8,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,4,5,7,6,8,2,3]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,7,2,1,6,8,4,3]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[2,6,3,1,7,8,5,4]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,2,5,7,4,1,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,6,1,8,7,4,5,2]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,2,7,5,1,6,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,1,3,5,7,6,8,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[5,7,6,1,4,2,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[4,8,7,5,2,1,6,3]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,7,1,2,6,4,5,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,1,7,6,3,5,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,6,2,1,4,3,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,5,1,4,7,2,8,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[6,5,1,3,7,4,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,3,5,7,8,2,6,1]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[7,1,6,2,5,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,1,6,7,3,5,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,5,1,4,7,6,3,8]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[4,7,5,1,6,2,3,8]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[3,8,1,4,6,2,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,3,2,7,6,4,1,8]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[5,3,7,4,6,2,1,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,7,3,2,1,8,6,4]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[5,7,6,3,2,1,8,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,2,7,5,4,1,8,6]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[1,7,3,5,4,2,6,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[5,3,7,4,1,8,6,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[7,3,5,4,1,6,8,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,5,1,6,8,3,2,4]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[5,3,1,7,6,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,1,5,3,2,4,8,6]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[1,3,6,2,5,4,7,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[3,1,4,8,5,7,6,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,4,1,8,2,6,5,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[7,1,8,3,5,2,6,4]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[7,1,2,8,4,3,5,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,6,2,1,4,7,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,6,2,5,4,8,7,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,1,5,8,4,2,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[7,3,6,2,1,4,8,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,3,1,4,2,8,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,1,4,2,7,5,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,2,1,3,7,4,5,6]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[5,1,3,4,8,6,2,7]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[2,7,4,1,8,5,3,6]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,7,3,8,1,4,6,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,1,5,2,4,3,6,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[6,8,7,3,2,1,5,4]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[3,6,8,7,2,4,1,5]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[5,7,3,6,2,1,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,5,2,4,8,1,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[5,2,6,1,7,4,3,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[6,3,4,5,1,7,2,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[2,1,5,4,7,8,3,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[2,6,1,7,5,3,8,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[6,3,8,2,5,7,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,5,8,2,3,6,1,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,5,4,8,3,6,7,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,6,5,2,3,7,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[1,4,5,8,2,6,7,3]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[7,3,5,2,8,6,1,4]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[1,8,3,6,2,4,7,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,8,7,5,6,4,2,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[6,8,2,1,5,4,3,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,3,6,5,8,7,2,4]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,8,7,6,2,3,5]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[2,2,2]=>0
[1,4,5,2,7,6,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,4,7,6,2,5,3,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[1,3,7,2,6,5,4,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[1,6,7,2,5,4,3,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[7,5,6,3,2,8,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[7,5,1,4,6,3,2,8]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[2,2]=>0
[7,5,1,2,6,3,4,8]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[2]=>0
[7,5,1,4,6,3,8,2]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[7,5,4,1,2,6,3,8]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,5,1,4,2,8,3,6]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,4,7,5,3,8,1,6]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[7,5,2,1,4,8,3,6]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[7,1,2,6,8,4,3,5]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[5,4,1,8,6,7,3,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[6,3,2,1,5,8,4,7]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[2]=>0
[4,3,5,6,2,8,1,7]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,3,5,2,7,8,4,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[4,5,3,1,6,8,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[3,4,6,7,5,1,8,2]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[4,3,3]=>1
[4,8,2,6,7,1,5,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,5,8,3,7,1,4,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[5,6,7,1,2,4,3,8]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[4,8,6,5,3,7,1,2]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[4,8,6,5,3,7,2,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[2,2,1,1,1]=>1
[4,1,5,7,6,2,8,3]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[3,2,4,7,1,5,8,6]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[4,7,5,8,6,2,3,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,2,6,8,7,5,1,4]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[7,2,4,5,8,1,6,3]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[4,3]=>1
[2,7,5,6,1,8,3,4]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[5,6,1,3,8,4,7,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[5,4,7,1,6,2,3,8]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[2,1]=>1
[3,1,7,4,6,5,2,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,4,3,5,1,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[3,6,8,5,2,4,1,7]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,8,6,7,1,4,5,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,8,2,5,7,6,1,3]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[5,1,4,7,2,6,3,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,1,5,6,2,3,8]=>[2,3,3]=>[[6,4,2],[3,1]]=>[3,1]=>2
[4,2,5,6,3,7,1,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[4,7,3,1,6,5,2,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[7,2,6,4,3,5,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[3,6,8,5,7,1,2,4]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[2,6,1,8,7,3,5,4]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[3,6,8,7,4,2,5,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[1,5,2,4,6,7,3,8]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,6,2,8,5,7,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,8,4,7,2,5,6,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[6,8,4,5,7,3,1,2]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[7,5,6,1,3,8,2,4]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[5,4,8,3,6,7,2,1]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,8,4,6,3,7,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[7,3,2,8,5,4,1,6]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[1,1,1]=>0
[2,6,8,3,5,7,4,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[7,3,4,8,5,1,2,6]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[7,4,8,1,3,5,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,2,4,1,8,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,3,6,4,1,2,7,5]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[8,2,5,4,6,1,7,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,5,6,1,7,3,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[6,8,4,1,7,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[7,6,8,5,1,2,4,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[7,2,5,1,8,4,6,3]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[2,8,5,3,6,4,1,7]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[8,4,5,1,6,3,7,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[8,2,1,5,7,4,6,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[8,6,5,3,7,1,4,2]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[1,5,2,4,7,6,8,3]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[1,5,4,3,8,2,7,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,7,1,6,3,2,8]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,7,8,3,6,2,1,5]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[3,4,2,6,8,1,7,5]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,8,6,2,7,5,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[1,7,5,3,2,6,8,4]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[6,2,1,8,4,7,3,5]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[7,6,2,8,3,4,5,1]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[2,5,4,7,1,8,3,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[6,2,7,4,3,8,5,1]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[1,5,4,7,3,8,2,6]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[1,2,6,7,3,5,4,8]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[5,6,8,7,4,2,3,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[3,2,2,2]=>1
[2,3,8,5,7,4,1,6]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[4,2,5,6,3,1,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[5,2,3,7,6,8,4,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,1,2,4,6,3,5,7]=>[1,4,3]=>[[6,4,1],[3]]=>[3]=>0
[4,2,5,6,3,7,8,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,7,8,4,5,6,1,2]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[6,3,5,7,4,8,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[5,6,3,8,1,7,4,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,3,7,1,2,6,4]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[4,5,2,1,8,3,6,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[7,4,2,1,6,5,8,3]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[8,5,2,1,7,3,6,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[5,4,3,6,1,8,2,7]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[3,5,4,1,7,2,8,6]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[1,3,8,6,7,4,5,2]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[2,6,5,3,7,1,8,4]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[5,7,1,3,6,4,8,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[8,2,5,4,1,7,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[6,1,7,2,5,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[2,6,8,4,5,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[1,8,6,3,7,4,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[4,5,7,1,6,2,8,3]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[5,7,3,4,2,8,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,3,4,2,7,6,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[3,5,6,8,2,4,7,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[5,3]=>2
[4,8,7,3,2,5,6,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[3,1,1,1]=>2
[3,7,4,2,6,8,5,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[3,3,1,1]=>2
[6,4,8,7,3,2,5,1]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[5,6,2,8,7,4,3,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[2,2,2,2,1]=>1
[2,5,7,6,4,8,1,3]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,5,6,4,8,7,1,3]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[3,3,2]=>1
[6,2,8,3,7,4,5,1]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[3,2,1]=>2
[3,7,5,6,4,2,8,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[5,2,3,8,6,1,4,7]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[1,4,3,8,5,6,2,7]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,8,2,6,4,3,5,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[3,2,2,1]=>2
[4,5,8,7,2,3,6,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[7,8,6,1,4,2,5,3]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[8,3,6,4,7,2,1,5]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,1,4,6,8,5,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[7,2,5,1,6,8,4,3]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[7,6,2,5,8,3,4,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[5,1,8,7,2,4,3,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,1,3,6,7,4,2]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[3,6,8,1,5,2,7,4]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,3,6,8,1,5,2,4]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[8,3,6,5,2,7,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,1,3,6,4,2,7,8]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[2,2]=>0
[6,1,2,4,7,5,3,8]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[3,3]=>0
[3,8,5,1,4,6,2,7]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,2,8,5,7,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[2,7,8,5,6,4,3,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[8,4,6,7,1,3,5,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,1,5,8,7,4,2,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[1,3,8,4,5,2,6,7]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,8,5,1,2,6,3,4]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[6,4,5,1,8,7,3,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[8,6,2,1,7,3,5,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[2,1]=>1
[7,2,8,4,6,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[4,8,6,3,1,7,2,5]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[2,1,1,1]=>1
[3,1,8,4,5,7,2,6]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[3,7,8,4,6,5,2,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[3,3,3,2]=>1
[7,8,6,1,4,3,5,2]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[3,2,1,1]=>2
[2,5,8,3,4,6,1,7]=>[3,3,2]=>[[6,5,3],[4,2]]=>[4,2]=>2
[7,8,4,3,6,1,2,5]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[8,4,3,5,1,6,7,2]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[3,1]=>2
[5,6,1,2,4,8,7,3]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[4,4,1]=>3
[4,3,6,2,5,7,1,8]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[1,6,5,7,3,4,8,2]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[5,2,8,6,7,4,1,3]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[8,2,6,5,1,7,4,3]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[2,2,1,1]=>1
[8,3,2,1,7,5,4,6]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[1,1]=>0
[1,8,4,5,7,3,2,6]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
[6,1,3,2,8,7,5,4]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[2,4,8,5,6,3,7,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[4,3,2]=>2
[7,2,1,3,8,4,6,5]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,1,8,6,2,7,3,5]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[1,7,3,8,6,5,2,4]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[2,2,2,1]=>1
[2,6,5,4,8,7,1,3]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[5,6,7,1,3,2,4,8]=>[3,2,3]=>[[6,4,3],[3,2]]=>[3,2]=>1
[7,1,8,4,3,2,6,5]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[2,1,1,1]=>1
[8,1,5,4,2,6,7,3]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[6,5,3,7,2,8,1,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[8,6,3,7,5,4,2,1]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1]=>0
[8,3,5,7,4,6,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[8,3,2,4,7,5,6,1]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[3,2]=>1
[4,8,6,2,5,1,3,7]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[2,1,1]=>1
[6,2,8,7,3,5,1,4]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,8,7,3,5,2,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[3,8,2,5,7,6,4,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[3,3,3,1]=>2
[5,8,3,4,2,1,6,7]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[6,5,8,3,2,4,7,1]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[3,1,1]=>2
[3,1,7,8,4,5,6,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[3,2,7,8,4,5,6,1]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[4,2]=>2
[1,3,8,2,6,7,5,4]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[3,1,7,2,6,8,5,4]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[3,3,1]=>2
[5,4,1,8,3,7,6,2]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[2,2,1]=>1
[2,8,3,4,5,7,1,6]=>[2,4,2]=>[[6,5,2],[4,1]]=>[4,1]=>3
[1,8,5,2,7,6,4,3]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[1,7,6,8,2,5,4,3]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[1,7,8,6,2,5,4,3]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[3,3,2,2]=>1
[4,6,5,7,1,8,2,3]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[3,2,1]=>2
[7,2,5,6,4,8,3,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[7,4,6,2,8,5,3,1]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[2,2,2,1]=>1
[5,3,4,7,6,8,2,1]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[5,3,4,8,2,1,7,6]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[3,2,2]=>1
[5,2,3,6,1,7,4,8]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[7,8,4,6,5,1,2,3]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,6,3,4,2,5,8,7]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[1,5,7,6,2,3,8,4]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[4,2,2]=>2
[1,4,3,7,6,2,5,8]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[2,2,1]=>1
[1,3,7,4,6,8,5,2]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[4,4,2]=>2
[1,5,3,4,7,2,8,6]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[6,1,5,4,7,8,2,3]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[3,1]=>2
[7,6,3,5,1,8,2,4]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[2,7,3,6,1,4,8,5]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,4,2,3,1,6,5,8]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[2,1]=>1
[5,6,2,1,7,4,3,8]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[3,7,4,6,8,1,5,2]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[4,3,1]=>3
[4,1,5,6,2,8,7,3]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[3,3,2]=>1
[3,4,7,8,1,5,2,6]=>[4,2,2]=>[[6,5,4],[4,3]]=>[4,3]=>1
[4,8,3,1,7,6,2,5]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[2,2,1,1]=>1
[2,6,7,5,3,4,1,8]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[3,2,2]=>1
[2,4,1,7,5,6,8,3]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[4,2,1]=>3
[7,2,4,8,3,5,1,6]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[3,2]=>1
[3,2,6,1,7,5,4,8]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[2,2,1]=>1
[5,6,1,4,3,8,7,2]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[3,3,2,1]=>2
[5,8,6,4,3,1,7,2]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[2,1,1,1,1]=>1
[4,1,3,7,8,6,5,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[3,3,3]=>0
[5,1,2,8,7,4,3,6]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[2,2,2]=>0
[4,1,7,5,3,8,2,6]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[4,6,5,1,8,7,3,2]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[2,2,2,1,1]=>1
[5,7,6,1,2,4,3,8]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[3,1,1]=>2
[4,3,7,6,2,5,1,8]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[2,1,1]=>1
[5,8,1,2,6,4,3,7]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[3,3,1]=>2
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Description
Difference between largest and smallest parts in a partition.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition (a1,…,an), this is the ribbon shape whose ith row from the bottom has ai cells.
For an integer composition (a1,…,an), this is the ribbon shape whose ith row from the bottom has ai cells.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
Map
inner shape
Description
The inner shape of a skew partition.
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